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href="https://cdn.copernicus.org/libraries/photoswipe/4.1/dark-icon-skin/dark-icon-skin.css"> <base href="/"> <link rel="stylesheet" type="text/css" href="https://cdn.copernicus.org/libraries/unsemantic/unsemantic.min.css"> <link rel="stylesheet" type="text/css" href="https://cdn.copernicus.org/libraries/jquery/1.11.1/ui/jquery-ui.min.css"> <link rel="stylesheet" type="text/css" href="https://cdn.copernicus.org/libraries/jquery/1.11.1/ui/jquery-ui-slider-pips.css"> <link rel="stylesheet" type="text/css" href="https://cdn.copernicus.org/libraries/photoswipe/4.1/photoswipe.css"> <link rel="stylesheet" type="text/css" href="https://cdn.copernicus.org/apps/htmlgenerator/css/htmlgenerator.css?v=1"> <meta name="citation_fulltext_world_readable" content=""> <meta name="citation_publisher" content="Copernicus GmbH"/> <meta name="citation_title" content="No increase is detected and modeled for the seasonal cycle amplitude of <i>δ</i><sup>13</sup>C of atmospheric carbon dioxide"/> <meta name="citation_abstract" content="<p><strong class="journal-contentHeaderColor">Abstract.</strong> Measurements of the seasonal cycle of <span class="inline-formula"><i>δ</i><sup>13</sup></span>C of atmospheric CO<span class="inline-formula"><sub>2</sub></span> (<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) provide information on the global carbon cycle and the regulation of carbon and water fluxes by leaf stomatal openings on ecosystem and decadal scales. Land biosphere carbon exchange is the primary driver of <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> seasonality in the Northern Hemisphere (NH). We use isotope-enabled simulations of the Bern3D-LPX (Land surface Processes and eXchanges) Earth system model of intermediate complexity and fossil fuel emission estimates with a model of atmospheric transport to simulate atmospheric <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> at globally distributed monitoring sites. Unlike the observed growth of the seasonal amplitude of CO<span class="inline-formula"><sub>2</sub></span> at northern sites, no significant temporal trend in the seasonal amplitude of <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> was detected at most sites, consistent with the insignificant model trends. Comparing the preindustrial (1700) and modern (1982–2012) periods, the modeled small-amplitude changes at northern sites are linked to the near-equal increase in background atmospheric CO<span class="inline-formula"><sub>2</sub></span> and the seasonal signal of the net atmosphere–land <span class="inline-formula"><i>δ</i><sup>13</sup></span>C flux in the northern extratropical region, with no long-term temporal changes in the isotopic fractionation in these ecosystems dominated by C<span class="inline-formula"><sub>3</sub></span> plants. The good data–model agreement in the seasonal amplitude of <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> and in its decadal trend provides implicit support for the regulation of stomatal conductance by C<span class="inline-formula"><sub>3</sub></span> plants towards intrinsic water use efficiency growing proportionally to atmospheric CO<span class="inline-formula"><sub>2</sub></span> over recent decades. Disequilibrium fluxes contribute little to the seasonal amplitude of the net land isotope flux north of 40° N but contribute near equally to the isotopic flux associated with growing season net carbon uptake in tropical and Southern Hemisphere (SH) ecosystems, pointing to the importance of monitoring <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> over these ecosystems. We propose applying seasonally resolved <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> observations as an additional constraint for land biosphere models and underlying processes for improved projections of the anthropogenic carbon sink.</p>"/> <meta name="citation_publication_date" content="2025/01/03"/> <meta name="citation_online_date" content="2025/01/03"/> <meta name="citation_journal_title" content="Biogeosciences"/> <meta name="citation_volume" content="22"/> <meta name="citation_issue" content="1"/> <meta name="citation_issn" content="1726-4170"/> <meta name="citation_doi" content="https://doi.org/10.5194/bg-22-19-2025"/> <meta name="citation_firstpage" content="19"/> <meta name="citation_lastpage" content="39"/> <meta name="citation_author" content="Joos, Fortunat"/> <meta name="citation_author_institution" content="Climate and Environmental Physics, University of Bern, Bern, Switzerland"/> <meta name="citation_author_institution" content="Oeschger Centre for Climate Change Research, University of Bern, Bern, Switzerland"/> <meta name="citation_author_orcid" content="0000-0002-9483-6030"> <meta name="citation_author_email" content="fortunat.joos@unibe.ch"> <meta name="citation_author" content="Lienert, Sebastian"/> <meta name="citation_author_institution" content="Climate and Environmental Physics, University of Bern, Bern, Switzerland"/> <meta name="citation_author_institution" content="Oeschger Centre for Climate Change Research, University of Bern, Bern, Switzerland"/> <meta name="citation_author" content="Zaehle, Sönke"/> <meta name="citation_author_institution" content="Max Planck Institute for Biogeochemistry, P.O. 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Change Biol., 14, 1745–1764, https://doi.org/10.1111/j.1365-2486.2008.01625.x, 2008. a"> <meta name="citation_funding_source" content="citation_funder=Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung;citation_funder_id=501100001711;citation_grant_number=200020_200511"> <meta name="citation_pdf_url" content="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025.pdf"/> <meta name="citation_xml_url" content="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025.xml"/> <meta name="fulltext_pdf" content="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025.pdf"/> <meta name="citation_language" content="English"/> <meta name="libraryUrl" content="https://bg.copernicus.org/articles/"/> <meta property="og:image" content="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-avatar-web.png"/> <meta property="og:title" content="No increase is detected and modeled for the seasonal cycle amplitude of δ13C of atmospheric carbon dioxide"> <meta property="og:description" content="Abstract. Measurements of the seasonal cycle of δ13C of atmospheric CO2 (δ13Ca) provide information on the global carbon cycle and the regulation of carbon and water fluxes by leaf stomatal openings on ecosystem and decadal scales. Land biosphere carbon exchange is the primary driver of δ13Ca seasonality in the Northern Hemisphere (NH). We use isotope-enabled simulations of the Bern3D-LPX (Land surface Processes and eXchanges) Earth system model of intermediate complexity and fossil fuel emission estimates with a model of atmospheric transport to simulate atmospheric δ13Ca at globally distributed monitoring sites. Unlike the observed growth of the seasonal amplitude of CO2 at northern sites, no significant temporal trend in the seasonal amplitude of δ13Ca was detected at most sites, consistent with the insignificant model trends. Comparing the preindustrial (1700) and modern (1982–2012) periods, the modeled small-amplitude changes at northern sites are linked to the near-equal increase in background atmospheric CO2 and the seasonal signal of the net atmosphere–land δ13C flux in the northern extratropical region, with no long-term temporal changes in the isotopic fractionation in these ecosystems dominated by C3 plants. The good data–model agreement in the seasonal amplitude of δ13Ca and in its decadal trend provides implicit support for the regulation of stomatal conductance by C3 plants towards intrinsic water use efficiency growing proportionally to atmospheric CO2 over recent decades. Disequilibrium fluxes contribute little to the seasonal amplitude of the net land isotope flux north of 40° N but contribute near equally to the isotopic flux associated with growing season net carbon uptake in tropical and Southern Hemisphere (SH) ecosystems, pointing to the importance of monitoring δ13Ca over these ecosystems. We propose applying seasonally resolved δ13Ca observations as an additional constraint for land biosphere models and underlying processes for improved projections of the anthropogenic carbon sink."> <meta property="og:url" content="https://bg.copernicus.org/articles/22/19/2025/"> <meta property="twitter:image" content="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-avatar-web.png"/> <meta name="twitter:card" content="summary_large_image"> <meta name="twitter:title" content="No increase is detected and modeled for the seasonal cycle amplitude of δ13C of atmospheric carbon dioxide"> <meta name="twitter:description" content="Abstract. Measurements of the seasonal cycle of δ13C of atmospheric CO2 (δ13Ca) provide information on the global carbon cycle and the regulation of carbon and water fluxes by leaf stomatal openings on ecosystem and decadal scales. Land biosphere carbon exchange is the primary driver of δ13Ca seasonality in the Northern Hemisphere (NH). We use isotope-enabled simulations of the Bern3D-LPX (Land surface Processes and eXchanges) Earth system model of intermediate complexity and fossil fuel emission estimates with a model of atmospheric transport to simulate atmospheric δ13Ca at globally distributed monitoring sites. Unlike the observed growth of the seasonal amplitude of CO2 at northern sites, no significant temporal trend in the seasonal amplitude of δ13Ca was detected at most sites, consistent with the insignificant model trends. Comparing the preindustrial (1700) and modern (1982–2012) periods, the modeled small-amplitude changes at northern sites are linked to the near-equal increase in background atmospheric CO2 and the seasonal signal of the net atmosphere–land δ13C flux in the northern extratropical region, with no long-term temporal changes in the isotopic fractionation in these ecosystems dominated by C3 plants. The good data–model agreement in the seasonal amplitude of δ13Ca and in its decadal trend provides implicit support for the regulation of stomatal conductance by C3 plants towards intrinsic water use efficiency growing proportionally to atmospheric CO2 over recent decades. Disequilibrium fluxes contribute little to the seasonal amplitude of the net land isotope flux north of 40° N but contribute near equally to the isotopic flux associated with growing season net carbon uptake in tropical and Southern Hemisphere (SH) ecosystems, pointing to the importance of monitoring δ13Ca over these ecosystems. We propose applying seasonally resolved δ13Ca observations as an additional constraint for land biosphere models and underlying processes for improved projections of the anthropogenic carbon sink."> <link rel="icon" href="https://www.biogeosciences.net/favicon.ico" type="image/x-icon"/> <script type="text/javascript" src="https://cdn.copernicus.org/libraries/jquery/1.11.1/ui/jquery-ui.min.js"></script> <script type="text/javascript" src="https://cdn.copernicus.org/libraries/jquery/1.11.1/ui/jquery-ui-slider-pips.js"></script> <script type="text/javascript" src="https://cdn.copernicus.org/libraries/jquery/1.11.1/ui/template_jquery-ui-touch.min.js"></script> <script type="text/javascript" src="https://cdn.copernicus.org/js/respond.js"></script> <script type="text/javascript" src="https://cdn.copernicus.org/libraries/highstock/2.0.4/highstock.js"></script> <script type="text/javascript" src="https://cdn.copernicus.org/apps/htmlgenerator/js/CoPublisher.js"></script> <script 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} #templateSearchResultTerm { font-weight: bold; } #resultsSearchHeader { display: block !important; } #scrolltopmodal { font-size: 3.0em; margin-top: 0 !important; margin-right: 15px; } @-webkit-keyframes animation_dots_breath { 50% { -webkit-transform: scale(1); transform: scale(1); opacity: 1; } 100% { opacity: 0; } } @keyframes animation_dots_breath { 50% { -webkit-transform: scale(1); transform: scale(1); opacity: 1; } 100% { opacity: 0; } } @media (min-width: 768px) and (max-width: 991px) { #templateSearchResultModal .modal-dialog { max-width: 90%; } } </style> <script> if(document.querySelector('meta[name="global_moBaseURL"]').content == "https://meetingorganizer.copernicus.org/") FINDER_URL = document.querySelector('meta[name="global_moBaseURL"]').content.replace('meetingorganizer', 'finder-app')+"search/library.php"; else FINDER_URL = document.querySelector('meta[name="global_moBaseURL"]').content.replace('meetingorganizer', 'finder')+"search/library.php"; SEARCH_INPUT = document.getElementById('search_query_solr'); SEARCH_INPUT_MODAL = document.getElementById('search_query_modal'); searchRunning = false; offset = 20; INITIAL_OFFSET = 20; var MutationObserver = window.MutationObserver || window.WebKitMutationObserver || window.MozMutationObserver; const targetNodeSearchModal = document.getElementById("templateSearchResultModal"); const configSearchModal = { attributes: true, childList: true, subtree: true }; // Callback function to execute when mutations are observed const callbackSearchModal = (mutationList, observer) => { for (const mutation of mutationList) { if (mutation.type === "childList") { // console.log("A child node has been added or removed."); picturesGallery(); } else if (mutation.type === "attributes") { // console.log(`The ${mutation.attributeName} attribute was modified.`); } } }; // Create an observer instance linked to the callback function const observer = new MutationObserver(callbackSearchModal); // Start observing the target node for configured mutations observer.observe(targetNodeSearchModal, configSearchModal); 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Distributed under the Creative Commons Attribution 4.0 License." data-web="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-avatar-web.png" data-width="600" data-height="419"> </a> <h1>No increase is detected and modeled for the seasonal cycle amplitude of <i>δ</i><sup>13</sup>C of atmospheric carbon dioxide</h1> <div class="auto-fixed-top-forced article-title"> <div class="grid-container show-on-fixed" style="display: none"> <div class="grid-85 mobile-grid-85 tablet-grid-85 grid-parent"> <span class="d-block hide-on-mobile hide-on-tablet journal-contentHeaderColor">No increase is detected and modeled for the seasonal cycle amplitude of <i>δ</i><sup>13</sup>C of atmospheric carbon dioxide</span> <span class="d-block hide-on-desktop journal-contentHeaderColor">No increase is detected and modeled for the seasonal cycle amplitude of <i>δ</i><sup>13</sup>C of atmospheric...</span> <span>Fortunat Joos et al.</span> </div> <div class="grid-1 mobile-grid-15 tablet-grid-15 grid-parent text-right"> <a id="scrolltop" class="scrollto" href="https://bg.copernicus.org/articles/22/19/2025/#top"><i class="co-home"></i> </a> </div> </div> </div> <div class="mb-3 authors-with-affiliations"> <nobr><span class="hover-cursor-pointer journal-contentLinkColor hover-underline" data-toggle="modal" data-target=".author917168">Fortunat Joos<a href="mailto:fortunat.joos@unibe.ch"><i class="fal fa-envelope ml-1"></i></a></span>,</nobr> <nobr><span class="hover-cursor-pointer journal-contentLinkColor hover-underline" data-toggle="modal" data-target=".author917169">Sebastian Lienert</span>,</nobr> <nobr>and <span class="hover-cursor-pointer journal-contentLinkColor hover-underline" data-toggle="modal" data-target=".author917170">Sönke Zaehle</span></nobr> </div> <div class="modal fade author917168" tabindex="-1" aria-hidden="true"> <div class="modal-dialog modal-dialog-centered modal-dialog-scrollable"> <div class="modal-content"> <div class="modal-header"> <div class="container-fluid p-0"> <h3 class="modal-title">Fortunat Joos</h3> <div class="row no-gutters"> <div class="col-12">CORRESPONDING AUTHOR</div> <div class="col-12"><a href="mailto:fortunat.joos@unibe.ch"><i class="fal fa-envelope mr-2"></i>fortunat.joos@unibe.ch</a></div> </div> <div class="row no-gutters"> <div class="col-12"> <a class="orcid-authors-logo" target="_blank" href="https://orcid.org/0000-0002-9483-6030" data-title="https://orcid.org/0000-0002-9483-6030"><svg class="mr-2" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><image xlink:href="https://www.biogeosciences.net/orcid_icon.svg" src="https://www.biogeosciences.net/orcid_icon_128x128.png" width="100%" height="100%"></image></svg>https://orcid.org/0000-0002-9483-6030</a> </div> </div> </div> <button type="button" class="close" data-dismiss="modal" aria-label="Close"> <span aria-hidden="true">×</span> </button> </div> <div class="modal-body"> <div class="container-fluid p-0"> <div class="row"> <div class="col-12 mb-3"> Climate and Environmental Physics, University of Bern, Bern, Switzerland </div> </div> <div class="row"> <div class="col-12 mb-3"> Oeschger Centre for Climate Change Research, University of Bern, Bern, Switzerland </div> </div> </div> </div> </div> </div> </div> <div class="modal fade author917169" tabindex="-1" aria-hidden="true"> <div class="modal-dialog modal-dialog-centered modal-dialog-scrollable"> <div class="modal-content"> <div class="modal-header"> <div class="container-fluid p-0"> <h3 class="modal-title">Sebastian Lienert</h3> </div> <button type="button" class="close" data-dismiss="modal" aria-label="Close"> <span aria-hidden="true">×</span> </button> </div> <div class="modal-body"> <div class="container-fluid p-0"> <div class="row"> <div class="col-12 mb-3"> Climate and Environmental Physics, University of Bern, Bern, Switzerland </div> </div> <div class="row"> <div class="col-12 mb-3"> Oeschger Centre for Climate Change Research, University of Bern, Bern, Switzerland </div> </div> </div> </div> </div> </div> </div> <div class="modal fade author917170" tabindex="-1" aria-hidden="true"> <div class="modal-dialog modal-dialog-centered modal-dialog-scrollable"> <div class="modal-content"> <div class="modal-header"> <div class="container-fluid p-0"> <h3 class="modal-title">Sönke Zaehle</h3> <div class="row no-gutters"> <div class="col-12"> <a class="orcid-authors-logo" target="_blank" href="https://orcid.org/0000-0001-5602-7956" data-title="https://orcid.org/0000-0001-5602-7956"><svg class="mr-2" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><image xlink:href="https://www.biogeosciences.net/orcid_icon.svg" src="https://www.biogeosciences.net/orcid_icon_128x128.png" width="100%" height="100%"></image></svg>https://orcid.org/0000-0001-5602-7956</a> </div> </div> </div> <button type="button" class="close" data-dismiss="modal" aria-label="Close"> <span aria-hidden="true">×</span> </button> </div> <div class="modal-body"> <div class="container-fluid p-0"> <div class="row"> <div class="col-12 mb-3"> Max Planck Institute for Biogeochemistry, P.O. Box 600164, Hans-Knöll-Str. 10, 07745 Jena, Germany </div> </div> </div> </div> </div> </div> </div> <div class="abstract sec" id="abstract"><div class="grid-container no-margin header-element"><span class="grid-100 mobile-grid-100 tablet-grid-100 grid-parent more-less-mobile" data-show="#abstract .co-arrow-open,.abstract-content" data-hide="#abstract .co-arrow-closed,.abstract-mobile-bottom-border"><div class="h1"><span class="section-number"> </span>Abstract<span class="hide-on-desktop hide-on-tablet triangleWrapper"> <i class="co-arrow-closed" style="display:none"></i><i class="co-arrow-open" style="display:inline-block"></i></span></div></span></div> <div class="abstract-content show-no-js"><p id="d2e135">Measurements of the seasonal cycle of <span class="inline-formula"><i>δ</i><sup>13</sup></span>C of atmospheric CO<span class="inline-formula"><sub>2</sub></span> (<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) provide information on the global carbon cycle and the regulation of carbon and water fluxes by leaf stomatal openings on ecosystem and decadal scales. Land biosphere carbon exchange is the primary driver of <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> seasonality in the Northern Hemisphere (NH). We use isotope-enabled simulations of the Bern3D-LPX (Land surface Processes and eXchanges) Earth system model of intermediate complexity and fossil fuel emission estimates with a model of atmospheric transport to simulate atmospheric <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> at globally distributed monitoring sites. Unlike the observed growth of the seasonal amplitude of CO<span class="inline-formula"><sub>2</sub></span> at northern sites, no significant temporal trend in the seasonal amplitude of <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> was detected at most sites, consistent with the insignificant model trends. Comparing the preindustrial (1700) and modern (1982–2012) periods, the modeled small-amplitude changes at northern sites are linked to the near-equal increase in background atmospheric CO<span class="inline-formula"><sub>2</sub></span> and the seasonal signal of the net atmosphere–land <span class="inline-formula"><i>δ</i><sup>13</sup></span>C flux in the northern extratropical region, with no long-term temporal changes in the isotopic fractionation in these ecosystems dominated by C<span class="inline-formula"><sub>3</sub></span> plants. The good data–model agreement in the seasonal amplitude of <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> and in its decadal trend provides implicit support for the regulation of stomatal conductance by C<span class="inline-formula"><sub>3</sub></span> plants towards intrinsic water use efficiency growing proportionally to atmospheric CO<span class="inline-formula"><sub>2</sub></span> over recent decades. Disequilibrium fluxes contribute little to the seasonal amplitude of the net land isotope flux north of 40° N but contribute near equally to the isotopic flux associated with growing season net carbon uptake in tropical and Southern Hemisphere (SH) ecosystems, pointing to the importance of monitoring <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> over these ecosystems. We propose applying seasonally resolved <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> observations as an additional constraint for land biosphere models and underlying processes for improved projections of the anthropogenic carbon sink.</p></div><span class="abstract-mobile-bottom-border mobile-bottom-border hide-on-desktop hide-on-tablet" style="display:none"></span></div> <div id="oldMobileDownloadBox" class="widget dark-border hide-on-desktop download-and-links"> <div class="legend journal-contentLinkColor">Download & links</div> <div class="content"> <ul class="additional_info no-bullets no-styling"> <li> <a class="triangle" data-toggle=".box-notice" data-duration="300" title="PDF Version (4290 KB)" href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025.pdf" > Article (PDF, 4290 KB) </a> </li> </ul> </div> <div class="content"> <ul class="additional_info no-bullets"> <li> <a class="triangle" 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href="https://twitter.com/intent/tweet?text=No+increase+is+detected+and+modeled+for+the+seasonal+cycle+amplitude+of+%3Ci%3E%CE%B4%3C%2Fi%3E%3Csup%3E13%3C%2Fsup%3EC+of+atmospheric+carbon+dioxide https%3A%2F%2Fbg.copernicus.org%2Farticles%2F22%2F19%2F2025%2F" title="Twitter" target="_blank"> <img src="https://www.biogeosciences.net/twitter.png" alt="Twitter"/> </a> </div> <div class="col-auto"> <a class="share-one-line" href="https://www.facebook.com/share.php?u=https%3A%2F%2Fbg.copernicus.org%2Farticles%2F22%2F19%2F2025%2F&t=No+increase+is+detected+and+modeled+for+the+seasonal+cycle+amplitude+of+%3Ci%3E%CE%B4%3C%2Fi%3E%3Csup%3E13%3C%2Fsup%3EC+of+atmospheric+carbon+dioxide" title="Facebook" target="_blank"> <img src="https://www.biogeosciences.net/facebook.png" alt="Facebook"/> </a> </div> <div class="col-auto pr-0"> <a class="share-one-line last" href="https://www.linkedin.com/shareArticle?mini=true&url=https%3A%2F%2Fbg.copernicus.org%2Farticles%2F22%2F19%2F2025%2F&title=No+increase+is+detected+and+modeled+for+the+seasonal+cycle+amplitude+of+%3Ci%3E%CE%B4%3C%2Fi%3E%3Csup%3E13%3C%2Fsup%3EC+of+atmospheric+carbon+dioxide" title="LinkedIn" target="_blank"> <img src="https://www.biogeosciences.net/linkedin.png" alt="LinkedIn"> </a> </div> <div class="col pr-0 mobile-native-share"> <a href="#" data-title="Biogeosciences" data-text="*No increase is detected and modeled for the seasonal cycle amplitude of δ13C of atmospheric carbon dioxide* Fortunat Joos et al." data-url="https://bg.copernicus.org/articles/22/19/2025/" class="mobile-native-share share-one-line last"><i class="co-mobile-share display-none"></i></a> </div> </div> </div> <div id="citation-footer" class="sec"> <div class="h1-special journal-contentHeaderColor">How to cite. </div> <div class="citation-footer-content show-no-js"> <p> <div class="citation-footer"> Joos, F., Lienert, S., and Zaehle, S.: No increase is detected and modeled for the seasonal cycle amplitude of <i>δ</i><sup>13</sup>C of atmospheric carbon dioxide, Biogeosciences, 22, 19–39, https://doi.org/10.5194/bg-22-19-2025, 2025. </div> </p> </div> </div> <div id="article-dates" class="sec"> <div class="article-dates dates-content my-3"> <nobr>Received: 01 Jul 2024</nobr> – <nobr>Discussion started: 26 Jul 2024</nobr> – <nobr>Revised: 04 Nov 2024</nobr> – <nobr>Accepted: 07 Nov 2024</nobr> – <nobr>Published: 03 Jan 2025</nobr> </div> </div> <div id="1_introduction" class="sec"><div class="section1-content hide-on-mobile-soft show-no-js"><span id="page23"></span><span id="page24"></span></div></div><div class="sec intro" id="section1"><div class="grid-container no-margin header-element"><span class="grid-100 mobile-grid-100 tablet-grid-100 grid-parent more-less-mobile" data-hide="#section1 .co-arrow-open,.section1-content" data-show="#section1 .co-arrow-closed,.section1-mobile-bottom-border"><div id="Ch1.S1" class="h1"><span class="label">1</span> Introduction<span class="hide-on-desktop hide-on-tablet triangleWrapper"> <i class="co-arrow-closed"></i><i class="co-arrow-open" style="display:none"></i></span></div></span></div> <div class="section1-content show-no-js hide-on-mobile-soft"><p id="d2e366">The seasonal variations in the carbon exchange fluxes between the atmosphere and the surface cause a seasonal cycle in atmospheric CO<span class="inline-formula"><sub>2</sub></span> (C<span class="inline-formula"><sub>a</sub></span>) <span class="cit" id="xref_paren.1">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx53" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Keeling et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx53" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1996</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx31" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Graven et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx31" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2013</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx68" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Masarie et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx68" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2014</a>)</span> and its stable isotopic signature (<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) <span class="cit" id="xref_paren.2">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx50" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Keeling</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx50" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1960</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx51" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Keeling et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx51" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1984</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx52" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1989</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx55" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2005</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx29" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">GLOBALVIEW-CO2C13</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx29" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2009</a>)</span>, with <span class="inline-formula"><i>δ</i><sup>13</sup></span>C defined as <span class="inline-formula"><i>δ</i><sup>13</sup></span>C <span class="inline-formula">=</span> <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M32" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>[</mo><msub><mi>R</mi><mi mathvariant="normal">sample</mi></msub><mo>/</mo><msub><mi>R</mi><mi mathvariant="normal">std</mi></msub><mo>-</mo><mn mathvariant="normal">1</mn><mo>]</mo><mo>×</mo><mn mathvariant="normal">1000</mn></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="120pt" height="16pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="f5b3fc2469dee8186b5d6f33808b3aa1"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00001.svg" width="100%" height="16pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00001.png"></image></svg></span></span>, where <span class="inline-formula"><i>R</i><sub>sample</sub></span> and <span class="inline-formula"><i>R</i><sub>std</sub></span> are the <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M35" display="inline" overflow="scroll" dspmath="mathml"><mrow class="chem"><msup><mi></mi><mn mathvariant="normal">13</mn></msup><mi mathvariant="normal">C</mi><msup><mo>/</mo><mn mathvariant="normal">12</mn></msup><mi mathvariant="normal">C</mi></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="43pt" height="15pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="26171d9cc86afda3668b5f02f6a626cf"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00002.svg" width="100%" height="15pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00002.png"></image></svg></span></span> abundance ratios of the sample and the carbonate standard Pee Dee Belemnite (PDB; 0.0112372), respectively <span class="cit" id="xref_paren.3">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx20" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Craig</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx20" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1957</a>)</span>. Observations of the atmospheric seasonal cycles in background tropospheric air provide large-scale information on the carbon fluxes between the atmosphere, ocean, and land <span class="cit" id="xref_paren.4">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx37" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Heimann et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx37" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1989</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx38" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1998</a>)</span> and constraints for models used to project C<span class="inline-formula"><sub>a</sub></span> and global warming.</p><p id="d2e530">The additional information of <span class="inline-formula"><i>δ</i><sup>13</sup></span>C data in comparison to carbon data stems from differences in fractionation for different carbon fluxes. Carbon isotopic fractionation describes the preferential transfer of light <span class="inline-formula"><sup>12</sup></span>C compared to heavier <span class="inline-formula"><sup>13</sup></span>C. The degree of fractionation is different for the different physical, chemical, and biological processes <span class="cit" id="xref_paren.5">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx70" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Mook</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx70" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1986</a>)</span>, causing differences in the isotopic composition of carbon reservoirs and fluxes. The seasonal <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> variations result from<span id="page20"></span> the combination of carbon and isotopic fluxes from fossil fuel burning, land use, and the exchange of the atmosphere with the ocean and land biosphere. Comparing results of carbon-isotope-enabled models with observations of <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> is useful to assess whether the mix of carbon and isotopic sink and source fluxes is represented consistently in comparison with the observations. <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> observations offer, therefore, a benchmark for evaluating and improving Earth system models.</p><p id="d2e626">Fractionation is particularly large during the assimilation of CO<span class="inline-formula"><sub>2</sub></span> from the atmosphere by plants following the C<span class="inline-formula"><sub>3</sub></span> photosynthesis pathway, which are responsible for most of the global productivity <span class="cit" id="xref_paren.6">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx84" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Still et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx84" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2003</a>)</span>. Importantly, changes in isotopic fractionation by C<span class="inline-formula"><sub>3</sub></span> plants are indicative of changes in stomatal conductance, regulating the leaf-internal CO<span class="inline-formula"><sub>2</sub></span> mole fraction and thus photosynthesis <span class="cit" id="xref_paren.7">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx22" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Farquhar</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx22" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1989</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx78" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Saurer and Voelker</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx78" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2022</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx17" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Cernusak and Ubierna</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx17" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2022</a>)</span>. Photosynthesis, the associated water loss, and evaporative cooling are key characteristics of ecosystem function that are central to the cycles of carbon, nitrogen, water, and energy <span class="cit" id="xref_paren.8">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx57" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Keenan et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx57" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2013</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx60" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Knauer et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx60" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2017</a>)</span> and to the land sink of anthropogenic carbon. Acquisition of CO<span class="inline-formula"><sub>2</sub></span> for photosynthesis is accompanied by the loss of water through the stomatal pores that govern, by their conductance, the diffusion of these two gases between the leaf interior and the atmosphere. A key question is how ecosystems adjust their overall conductance and, thereby, co-regulate carbon uptake and plant growth, regulating water loss and evaporative cooling under rising C<span class="inline-formula"><sub>a</sub></span>, growing nitrogen inputs to ecosystems, and increasing water vapor deficits under global warming. Many studies relying on multi-decadal- to century-scale tree-ring <span class="inline-formula"><i>δ</i><sup>13</sup></span>C records and free-air CO<span class="inline-formula"><sub>2</sub></span> enrichment (FACE) experiments suggest that small changes in isotopic fractionation and intrinsic water use efficiency, the ratio of assimilation to conductance, grow roughly proportionally with C<span class="inline-formula"><sub>a</sub></span> <span class="cit" id="xref_paren.9">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx92" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Voelker et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx92" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2016</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx79" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Saurer et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx79" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2014</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx49" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Kauwe et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx49" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2013</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx74" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Peñuelas et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx74" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2011</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx59" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Keller et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx59" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2017</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx27" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Frank et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx27" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2015</a>)</span>. In contrast, <span class="cit" id="xref_text.10"><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx11" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Battipaglia et al.</a> (<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx11" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2013</a>)</span> and <span class="cit" id="xref_text.11"><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx57" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Keenan et al.</a> (<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx57" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2013</a>)</span> suggest a scenario where conductance and the flows of carbon and water are downregulated under increasing C<span class="inline-formula"><sub>a</sub></span>. <span class="cit" id="xref_text.12"><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx56" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Keeling et al.</a> (<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx56" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2017</a>)</span>, analyzing decadal-scale change in seasonally detrended <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> and the annual atmospheric budgets of carbon and <span class="inline-formula"><sup>13</sup></span>C, find a decrease in isotopic fractionation of global mean net primary production; the change is attributed to changes in fractionation associated with mesophyll conductance and photorespiration of C<span class="inline-formula"><sub>3</sub></span> plants, and intrinsic water use efficiency is inferred to grow proportionally with C<span class="inline-formula"><sub>a</sub></span>. Conflicting results for 20th-century changes in fractionation and intrinsic water use efficiency are also found in global land biosphere models <span class="cit" id="xref_paren.13">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx59" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Keller et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx59" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2017</a>)</span>.</p><p id="d2e795">The observational records from globally distributed monitoring sites <span class="cit" id="xref_paren.14">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx53" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Keeling et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx53" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1996</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx31" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Graven et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx31" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2013</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx68" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Masarie et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx68" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2014</a>)</span> demonstrate a significant growth trend in the seasonal cycle amplitude (SA) of C<span class="inline-formula"><sub>a</sub></span> <span class="cit" id="xref_paren.15">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx5" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Bacastow et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx5" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1985</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx53" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Keeling et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx53" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1996</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx31" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Graven et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx31" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2013</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx8" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Barlow et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx8" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2015</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx75" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Piao et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx75" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2018</a>)</span> driven by changes in the seasonality of net land carbon uptake <span class="cit" id="xref_paren.16">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx31" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Graven et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx31" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2013</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx26" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Forkel et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx26" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2016</a>)</span>. The observed seasonal cycle and amplitude growth of C<span class="inline-formula"><sub>a</sub></span> are widely used to evaluate carbon cycle models and system understanding by transporting fluxes from terrestrial, oceanic, and fossil fuel sources with a model of atmospheric transport to obtain local C<span class="inline-formula"><sub>a</sub></span> anomalies <span class="cit" id="xref_paren.17">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx38" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Heimann et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx38" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1998</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx21" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Dargaville et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx21" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2002</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx81" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Scholze et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx81" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2008</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx71" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Peng et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx71" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2015</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx63" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Lienert and Joos</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx63" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2018</a>)</span>. Studies address the role of different climatic drivers and terrestrial carbon cycle processes such as drought, land use, warming, productivity, and soil respiration <span class="cit" id="xref_paren.18">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx37" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Heimann et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx37" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1989</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx38" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1998</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx31" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Graven et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx31" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2013</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx26" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Forkel et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx26" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2016</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx40" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Ito et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx40" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2016</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx9" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Bastos et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx9" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2019</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx94" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Wang et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx94" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2020</a>)</span> and surface-to-atmosphere C fluxes (e.g., <span class="cit" id="xref_altparen.19"><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx72" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Peylin et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx72" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2013</a></span>). SAs(C<span class="inline-formula"><sub>a</sub></span>) and their temporal trends at different monitoring sites are used for constraining an ensemble of land biosphere model simulations <span class="cit" id="xref_paren.20">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx63" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Lienert and Joos</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx63" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2018</a>)</span>.</p><p id="d2e857">Comparable studies analyzing the temporal trends in SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) and the seasonal cycle of <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> are scarce. While seasonally resolved atmospheric <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> measurements are available <span class="cit" id="xref_paren.21">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx29" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">GLOBALVIEW-CO2C13</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx29" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2009</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx54" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Keeling et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx54" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2001</a>)</span>, these seasonally resolved records are yet to be fully utilized in the context of process-based carbon cycle models. <span class="cit" id="xref_text.22"><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx37" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Heimann et al.</a> (<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx37" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1989</a>)</span> simulated the spatiotemporal distribution of <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> and C<span class="inline-formula"><sub>a</sub></span> with an atmospheric transport model using estimates of net primary production (NPP) and heterotrophic respiration based on satellite data and surface temperature and prescribed surface ocean CO<span class="inline-formula"><sub>2</sub></span>, demonstrating the dominant role of land biosphere fluxes for Northern Hemisphere (NH) seasonality and finding relevant signals from the ocean and land in the Southern Hemisphere (SH). Van der Velde et al. (2018) applied their CarbonTracker Data Assimilation System for CO<span class="inline-formula"><sub>2</sub></span> and <span class="inline-formula"><sup>13</sup></span>CO<span class="inline-formula"><sub>2</sub></span> by varying the net exchange fluxes of CO<span class="inline-formula"><sub>2</sub></span> and <span class="inline-formula"><sup>13</sup></span>CO<span class="inline-formula"><sub>2</sub></span> in ocean and terrestrial biosphere models and propagating the fluxes through an atmospheric transport model to solve for weekly adjustments to fluxes and isotopic terrestrial discrimination, minimizing differences between observed and estimated mole fractions. They identified a decrease in stomatal conductance on a continent-wide scale during a severe drought. <span class="cit" id="xref_text.23"><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx7" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Ballantyne et al.</a> (<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx7" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2011</a>)</span> applied an analytical regression approach to analyze the differences in isotopic signatures between Northern Hemisphere site data and free-troposphere background data from Niwot Ridge to infer seasonal variations in the source signature of the net atmosphere–land biosphere flux and to evaluate models of stomatal conductance. Observations of <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> seasonal cycles were used to investigate isotopic fractionation <span class="cit" id="xref_paren.24">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx6" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Ballantyne et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx6" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2010</a>)</span> and trends in the phenology of northern terrestrial ecosystems <span class="cit" id="xref_paren.25">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx30" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Gonsamo et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx30" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2017</a>)</span> but to our knowledge have not been used for analyzing trends in SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) globally.</p><p id="d2e1071">This study addresses the following main questions: </p><ol><li> <p id="d2e1076"><span id="page21"></span>Is the seasonal cycle of <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> observed at a network of globally distributed sites represented well in model simulations? How large are the contributions of ocean, land, and fossil fuel fluxes to <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> seasonality?</p></li><li> <p id="d2e1120">What are the temporal trends in SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) in the observational records, and are the modeled trends in SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) consistent with the observed trends?</p></li><li> <p id="d2e1164">What are the different drivers of SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) versus SA(C<span class="inline-formula"><sub>a</sub></span>) and of their temporal trends? Is a model scenario with intrinsic water use efficiency growing proportional with C<span class="inline-formula"><sub>a</sub></span> consistent with <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> seasonality data?</p></li></ol><p id="d2e1071-3"> We simulate atmospheric <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> and C<span class="inline-formula"><sub>a</sub></span> at 19 globally distributed sites using the matrix representation of an atmospheric transport model and net atmosphere-to-surface fluxes of CO<span class="inline-formula"><sub>2</sub></span> and <span class="inline-formula"><i>δ</i><sup>13</sup></span>(CO<span class="inline-formula"><sub>2</sub></span>) from an Earth system model of intermediate complexity (EMIC) alongside gridded fossil fuel emission estimates and changes in land use and the distribution of C<span class="inline-formula"><sub>3</sub></span> and C<span class="inline-formula"><sub>4</sub></span> crops. We compare model results to observations and analyze trends in SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) using the records of the Scripps CO<span class="inline-formula"><sub>2</sub></span> program <span class="cit" id="xref_paren.26">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx54" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Keeling et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx54" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2001</a>)</span> and the <span class="cit" id="xref_text.27"><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx19" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Cooperative Global Atmospheric Data Integration Project</a> (<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx19" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2013</a>)</span> product. We discuss the implications of our results for changes in the fractionation by C<span class="inline-formula"><sub>3</sub></span> plants, their stomatal controls, and associated carbon and water fluxes. We develop a theoretical framework to explain the trends in SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) and decompose net carbon and isotope land biosphere fluxes into underlying component fluxes and changes in carbon fluxes and fractionation. The framework could serve future studies, e.g., studies applying an ensemble of different models for multi-model evaluation, and provide more robust conclusions in comparison to using a single model chain.</p></div><span class="section1-mobile-bottom-border mobile-bottom-border hide-on-desktop hide-on-tablet"></span></div> <div class="sec" id="section2"><div class="grid-container no-margin header-element"><span class="grid-100 mobile-grid-100 tablet-grid-100 grid-parent more-less-mobile" data-hide="#section2 .co-arrow-open,.section2-content" data-show="#section2 .co-arrow-closed,.section2-mobile-bottom-border"><div id="Ch1.S2" class="h1"><span class="label">2</span> Methods<span class="hide-on-desktop hide-on-tablet triangleWrapper"> <i class="co-arrow-closed"></i><i class="co-arrow-open" style="display:none"></i></span></div></span></div> <div class="section2-content show-no-js hide-on-mobile-soft"><div class="sec"><h2 id="Ch1.S2.SS1"><span class="label">2.1</span> Bern3D-LPX Earth system model of intermediate complexity</h2> <p id="d2e1384">Spatially resolved surface-to-atmosphere CO<span class="inline-formula"><sub>2</sub></span> and <span class="inline-formula"><sup>13</sup></span>CO<span class="inline-formula"><sub>2</sub></span> fluxes are simulated with the Bern3D-LPX (Land surface Processes and eXchanges) Earth system model of intermediate complexity. Here, the ocean–atmosphere model Bern3D <span class="cit" id="xref_paren.28">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx41" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Jeltsch-Thömmes and Joos</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx41" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2020</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx10" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Battaglia and Joos</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx10" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2018</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx77" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Ritz et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx77" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2011</a>)</span> is coupled to the dynamic global vegetation model (DGVM) framework of the Land surface Processes and eXchanges (LPX) model, LPX-Bern v1.4 <span class="cit" id="xref_paren.29">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx63" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Lienert and Joos</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx63" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2018</a>)</span>. The Bern3D model features a 41 <span class="inline-formula">×</span> 40 horizontal ocean grid (about 9° <span class="inline-formula">×</span> 4.5°) with 32 depth layers coupled to a single-layer energy–moisture balance atmosphere <span class="cit" id="xref_paren.30">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx77" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Ritz et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx77" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2011</a>)</span>. In Bern3D, carbon and its isotopes are implemented as tracers with fractionation for air–sea and sea–air gas exchange, aquatic chemistry, and the production of organic material and CaCO<span class="inline-formula"><sub>3</sub></span> as a function of surface ocean temperature, aqueous CO<span class="inline-formula"><sub>2</sub></span>, and the speciation of dissolved inorganic carbon, as described by <span class="cit" id="xref_text.31"><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx42" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Jeltsch-Thömmes and Joos</a> (<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx42" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2023</a>)</span>. LPX-Bern simulates the coupled cycling of carbon, nitrogen, and water <span class="cit" id="xref_paren.32">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx98" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Xu-Ri and Prentice</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx98" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2008</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx95" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Wania et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx95" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2009</a><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx95" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">a</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx96" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">b</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx85" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Stocker et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx85" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2014</a>)</span> and vegetation dynamics using plant functional types <span class="cit" id="xref_paren.33">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx83" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Sitch et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx83" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2003</a>)</span>. It is run here at a 3.75° <span class="inline-formula">×</span> 2.5° resolution. Grid cells are subdivided into different land use classes (mineral soil, wetlands, crop, pasture, urban). Carbon isotopes were added <span class="cit" id="xref_paren.34">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx80" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Scholze et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx80" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2003</a>)</span> using a photosynthetic fractionation scheme <span class="cit" id="xref_paren.35">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx64" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Lloyd and Farquhar</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx64" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1994</a>)</span> and without further isotopic fractionation during the transfer through the vegetation, litter, soil, and product pools. The scheme neglects fractionation by boundary layer transport and ternary effects associated with the interaction of CO<span class="inline-formula"><sub>2</sub></span>, water, and air <span class="cit" id="xref_paren.36">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx23" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Farquhar and Cernusak</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx23" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2012</a>)</span>, and fractionation by dark-day respiration is set to zero, while fractionation by the following terms is explicitly considered: stomatal conductance (with a scaling factor of 4.4 ‰), dissolution and liquid transport (1.8 ‰), carboxylation (27.5 ‰), and photorespiration (8 ‰ and the CO<span class="inline-formula"><sub>2</sub></span> compensation point that would occur in the absence of dark respiration, <span class="inline-formula">Γ<sup>*</sup></span>, increases with temperature) <span class="cit" id="xref_paren.37">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx64" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Lloyd and Farquhar</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx64" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1994</a>)</span>. The signature of respired carbon reflects the signature of carbon assimilated at previous times; the lag times between assimilation and respiration are dictated by the turnover timescales of the various pools, depending on temperature and soil moisture. Land carbon and isotope fluxes respond to altered climate, which influences, for example, photosynthesis through temperature and water limitation, fire frequency, and autotrophic and heterotrophic respiration rates; respond to increasing C<span class="inline-formula"><sub>a</sub></span>, which stimulates photosynthesis and affects water use efficiency (“CO<span class="inline-formula"><sub>2</sub></span> fertilization”); respond to land use <span class="cit" id="xref_paren.38">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx86" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Strassmann et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx86" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2008</a>)</span>, which causes, for example, transfer of tree carbon to the atmosphere, litter, and product pools after deforestation and shifts from natural vegetation to C<span class="inline-formula"><sub>3</sub></span> and C<span class="inline-formula"><sub>4</sub></span> crops and pasture; and respond to altered nitrogen deposition and the addition of nitrogen fertilizer on managed land alleviating nitrogen limitation.</p> <p id="d2e1555"><span id="page22"></span>Bern3D and LPX-Bern were spun up individually, followed by a 500-year coupled spinup to preindustrial equilibrium (1700 CE; 276.3 ppm, <span class="inline-formula">−6.27</span> ‰). A transient simulation, <span class="inline-formula"><i>E</i><sub>standard</sub></span>, from 1700 to 2020 is driven by annual fossil fuel carbon emissions (including the contribution from cement production) <span class="cit" id="xref_paren.39">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx28" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Friedlingstein et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx28" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2020</a>)</span>, net land use area changes <span class="cit" id="xref_paren.40">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx39" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Hurtt et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx39" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2020</a>)</span>, and non-CO<span class="inline-formula"><sub>2</sub></span> radiative forcing. <span class="inline-formula"><i>δ</i><sup>13</sup></span>C of the fossil fuel emissions follows <span class="cit" id="xref_text.41"><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx4" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Andres et al.</a> (<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx4" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2017</a>)</span> for 1751–2014 and is set to the value for 1751 before. For 2014–2020, signatures of major source categories (coal, oil, gas, cement) are assumed to be constant and combined with the emission sources from <span class="cit" id="xref_text.42"><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx28" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Friedlingstein et al.</a> (<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx28" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2020</a>)</span>, following the approach of <span class="cit" id="xref_text.43"><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx1" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Andres et al.</a> (<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx1" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2000</a>)</span>. Here, we explicitly distinguish land use classes for C<span class="inline-formula"><sub>3</sub></span> and C<span class="inline-formula"><sub>4</sub></span> crops and prescribe their extent, and net land use area changes are based on the Land-Use Harmonization 2 dataset <span class="cit" id="xref_paren.44">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx39" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Hurtt et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx39" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2020</a>)</span>. Nitrogen deposition and nitrogen fertilization are taken from the Global N<span class="inline-formula"><sub>2</sub></span>O Model Intercomparison Project <span class="cit" id="xref_paren.45">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx89" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Tian et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx89" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2018</a>)</span>. Nitrogen (N) is a limiting nutrient in LPX, and plant growth is downregulated under N stress, which tends to reduce plant growth and plant growth responses to rising C<span class="inline-formula"><sub>a</sub></span> compared to a model with absent N cycling. The monthly wind stress climatology from the NCEP/NCAR Reanalysis produced by the National Centers for Environmental Prediction (NCEP) and the National Center for Atmospheric Research (NCAR) <span class="cit" id="xref_paren.46">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx47" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Kalnay et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx47" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1996</a>)</span> is prescribed to the ocean. Climatic Research Unit (CRU) Time Series (TS) version 4.05 high-resolution gridded data of month-by-month variation in climate (CRU TS v4.05) <span class="cit" id="xref_paren.47">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx34" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Harris et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx34" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2020</a>)</span> are used for the land model. For 1700–1900 and the spinup, the climate of 1901–1931 is recycled. A baseline is provided by a control simulation, termed <span class="inline-formula"><i>E</i><sub>control</sub></span>, without anthropogenic CO<span class="inline-formula"><sub>2</sub></span> emissions; absent radiative forcing from non-CO<span class="inline-formula"><sub>2</sub></span> species (e.g., from CH<span class="inline-formula"><sub>4</sub></span>, N<span class="inline-formula"><sub>2</sub></span>O, ozone); and with land use, nitrogen deposition, and nitrogen fertilization at the 1700 level, as well as recycling the 1901–1931 land climate. C<span class="inline-formula"><sub>a</sub></span> and <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> evolve freely in all simulations presented and remain at their preindustrial values in <span class="inline-formula"><i>E</i><sub>control</sub></span>.</p> </div><div class="sec"><h2 id="Ch1.S2.SS2"><span class="label">2.2</span> Atmospheric transport model TM3 and the seasonal cycles of C<span class="inline-formula"><sub>a</sub></span> and <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span></h2> <p id="d2e1790">We employ the transport matrices of the global atmospheric tracer model TM3, a three-dimensional transport model <span class="cit" id="xref_paren.48">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx36" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Heimann and Körner</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx36" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2003</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx48" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Kaminski et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx48" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1998</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx82" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Schürmann et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx82" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2016</a>)</span>, to translate surface–atmosphere fluxes from Bern3D-LPX and fossil fuel emissions into C<span class="inline-formula"><sub>a</sub></span> and <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> anomalies at 19 measurement sites across the globe. Before transport, the fluxes are remapped to the TM3 grid with 72 <span class="inline-formula">×</span> 48 grid cells (5° <span class="inline-formula">×</span> 3.75°). Here, the matrices span 1982 to 2012 and are only available if there is also a CO<span class="inline-formula"><sub>2</sub></span> measurement available at the corresponding site. Each matrix represents the sensitivity of the local atmospheric concentration for a given month to the local surface fluxes of the previous period, spanning up to 48 months. The transport model is initialized with equal C<span class="inline-formula"><sub>a</sub></span> and <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> at all sites.</p> <p id="d2e1878">For <span class="inline-formula"><sup>13</sup></span>C, the signature-weighted net atmosphere-to-surface flux is </p><div class="disp-formula" content-type="numbered" id="Ch1.E1"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M158" display="block" overflow="scroll" dspmath="mathml"><mtable><mlabeledtr><mtd><mtext>(1)</mtext></mtd><mtd><mrow> <msup> <mi mathvariant="italic">δ</mi> <mn mathvariant="normal">13</mn> </msup> <msub> <mi>f</mi> <mrow> <mi mathvariant="normal">as</mi> <mo>,</mo> <mi mathvariant="normal">net</mi> </mrow> </msub> <mo>(</mo> <mi mathvariant="bold-italic">x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> <mo>=</mo> <msub> <mi>f</mi> <mrow> <mi mathvariant="normal">as</mi> <mo>,</mo> <mi mathvariant="normal">net</mi> </mrow> </msub> <mo>(</mo> <mi mathvariant="bold-italic">x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> <mo>⋅</mo> <msup> <mi mathvariant="italic">δ</mi> <mn mathvariant="normal">13</mn> </msup> <msub> <mi mathvariant="normal">C</mi> <mrow> <mi mathvariant="normal">as</mi> <mo>,</mo> <mi mathvariant="normal">net</mi> </mrow> </msub> <mo>(</mo> <mi mathvariant="bold-italic">x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> <mo>.</mo> </mrow></mtd></mlabeledtr></mtable></math><div><svg xmlns:svg="http://www.w3.org/2000/svg" width="416pt" height="16pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="881694693428141fbd66113a2e0c8552"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-e_1.svg" width="100%" height="16pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-e_1.png"></image></svg></div></div><p id="d2e1878-3"> <span class="inline-formula"><i>δ</i><sup>13</sup><i>f</i><sub>as,net</sub></span> is in units of mol ‰ m<span class="inline-formula"><sup>−2</sup></span> yr<span class="inline-formula"><sup>−1</sup></span>. <span class="inline-formula"><strong><em>x</em></strong></span> indicates location and <span class="inline-formula"><i>t</i></span> time at the monthly and spatial (5° <span class="inline-formula">×</span> 3.75°) resolution of TM3. The net carbon fluxes (<span class="inline-formula"><i>f</i><sub>as,net</sub></span>; mol m<span class="inline-formula"><sup>−2</sup></span> yr<span class="inline-formula"><sup>−1</sup></span>); their signatures (<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>as,net</sub></span>); and, therefore, <span class="inline-formula"><i>δ</i><sup>13</sup><i>f</i><sub>as,net</sub></span>, are readily available for fossil fuel emissions, including cement production <span class="cit" id="xref_paren.49">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx2" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Andres et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx2" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2009</a><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx2" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">a</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx3" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">b</a>)</span>. Bern3D-LPX simulates two-way exchange of CO<span class="inline-formula"><sub>2</sub></span> and <span class="inline-formula"><sup>13</sup></span>CO<span class="inline-formula"><sub>2</sub></span> from and to the ocean and land surface. Net transfer rates are determined by the difference in these gross fluxes to yield the atmosphere-to-surface net fluxes, <span class="inline-formula"><i>f</i><sub>as,net</sub></span> and <span class="inline-formula"><i>δ</i><sup>13</sup><i>f</i><sub>as,net</sub></span>, of Bern3D-LPX.</p> <p id="d2e2196">The matrices are applied with <span class="inline-formula"><i>f</i><sub>as,net</sub></span> to compute anomalies in C<span class="inline-formula"><sub>a</sub></span> and with <span class="inline-formula"><i>δ</i><sup>13</sup><i>f</i><sub>as,net</sub></span> to compute anomalies in <span class="inline-formula"><sup>13</sup></span>CO<span class="inline-formula"><sub>2</sub></span>. We get <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> from <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M183" display="inline" overflow="scroll" dspmath="mathml"><mrow class="chem"><msup><mi></mi><mn mathvariant="normal">13</mn></msup><msub><mi mathvariant="normal">CO</mi><mn mathvariant="normal">2</mn></msub><mo>/</mo><msub><mi mathvariant="normal">C</mi><mi mathvariant="normal">a</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="51pt" height="16pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="fa9ec2597e70d38111226b7c105cb181"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00003.svg" width="100%" height="16pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00003.png"></image></svg></span></span>. This method of transporting signature-weighted net fluxes was chosen instead of separately transporting <span class="inline-formula"><sup>13</sup></span>CO<span class="inline-formula"><sub>2</sub></span> and <span class="inline-formula"><sup>12</sup></span>CO<span class="inline-formula"><sub>2</sub></span>. Both approaches were tested and showed very similar results, except for numerical issues in months having very small local <span class="inline-formula"><sup>12</sup></span>CO<span class="inline-formula"><sub>2</sub></span> anomalies for the second approach.</p> <p id="d2e2362">Ocean, land, and fossil fuel fluxes from the standard simulation are transported separately to quantify the contributions of these individual components to the seasonal variations in C<span class="inline-formula"><sub>a</sub></span> and <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>. For <span class="inline-formula"><i>E</i><sub>control</sub></span>, fossil fuel fluxes are not transported, consistent with the model setup. A limitation is that transport matrices are only available for the period of 1982 to 2012, limiting the analysis period and direct model–data comparison to 3 decades only.</p> </div><div class="sec"><h2 id="Ch1.S2.SS3"><span class="label">2.3</span> Site data</h2> <p id="d2e2413">Background CO<span class="inline-formula"><sub>2</sub></span> from 19 monitoring sites for which transport matrices are available is used for comparison with simulated C<span class="inline-formula"><sub>a</sub></span> and <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> and to determine observation-based trends in their SAs. The <span class="cit" id="xref_text.50"><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx19" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Cooperative Global Atmospheric Data Integration Project</a> (<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx19" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2013</a>)</span> product is used for C<span class="inline-formula"><sub>a</sub></span>. For <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>, the records of the Scripps CO<span class="inline-formula"><sub>2</sub></span> program <span class="cit" id="xref_paren.51">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx54" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Keeling et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx54" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2001</a>)</span> for Alert, Mauna Loa, and the South Pole from monthly averaged flask data are used. These records span a longer period than the available transport matrices. For the remaining 16 sites, the shorter (1994 to 2009) records of <span class="cit" id="xref_text.52"><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx29" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">GLOBALVIEW-CO2C13</a> (<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx29" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2009</a>)</span> are used. In the main paper, we focus on 3 out of the 19 available transport sites: Alert (82.5° N, Canada), Mauna Loa (19.5° N, Hawaii), and the South Pole (90° S, Antarctica). Results for the other sites are shown in the Supplement and Table <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.T1" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1</a>. The Scripps and GLOBALVIEW-CO2C13 data are on slightly different scales <span class="cit" id="xref_paren.53">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx66" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Lueker et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx66" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2020</a>)</span>; this does not affect our analysis of seasonal anomalies. The <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> records of GLOBALVIEW-CO2C13 (2009) span the order of a decade and are, therefore, not used for trend detection, although we evaluated trends from the simulations for the GLOBALVIEW sites (Table <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.T2" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2</a>, excluding Key Biscayne). We require at least 10 monthly values for a year to be included in the linear regression.</p> <p id="d2e2530">Additional <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> monthly flask data from the Scripps CO<span class="inline-formula"><sub>2</sub></span> program <span class="cit" id="xref_paren.54">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx54" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Keeling et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx54" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2001</a>)</span> are used for analyzing temporal trends in the SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>). We focus on eight sites with more than 20 years of data: Alert (ALT, 82° N), Nuvuk (formerly Point Barrow) (PTB, 71° N), La Jolla (LJO, 33° N), Mauna Loa Observatory (MLO, 20° N), Cape Kumukahi (KUM, 20° N), Christmas Island (CHR, 2° N), Samoa (SAM, 14° S), and the South Pole (SPO, 90° S). The data are provided as (i) monthly samples, (ii) a fit to these monthly samples, and (iii) the monthly samples but with missing values replaced by fitted values. We also used the original, non-gap-filled data and years with at least 9, 10, or 11 monthly values per year in the regression.</p> </div></div><span class="section2-mobile-bottom-border mobile-bottom-border hide-on-desktop hide-on-tablet"></span></div> <div class="sec" id="section3"><div class="grid-container no-margin header-element"><span class="grid-100 mobile-grid-100 tablet-grid-100 grid-parent more-less-mobile" data-hide="#section3 .co-arrow-open,.section3-content" data-show="#section3 .co-arrow-closed,.section3-mobile-bottom-border"><div id="Ch1.S3" class="h1"><span class="label">3</span> The influence of carbon and isotope fluxes on the seasonal cycles of C<span class="inline-formula"><sub>a</sub></span> and <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>: a conceptual framework<span class="hide-on-desktop hide-on-tablet triangleWrapper"> <i class="co-arrow-closed"></i><i class="co-arrow-open" style="display:none"></i></span></div></span></div> <div class="section3-content show-no-js hide-on-mobile-soft"><p id="d2e2626">We develop a simplified conceptual framework to qualitatively explore the influence of carbon and isotope fluxes on the seasonal cycles of C<span class="inline-formula"><sub>a</sub></span> and <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>. For illustration, the atmosphere is considered to be well-mixed in this section; the atmospheric transport operator is linear, and the findings may qualitatively also apply to spatially resolved fluxes. The budgets for the atmospheric inventories of carbon and <span class="inline-formula"><sup>13</sup></span>C are approximated <span class="cit" id="xref_paren.55">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx88" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Tans et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx88" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1993</a>)</span> as </p><span id="Ch1.E2" class="equationLink"></span><span id="Ch1.E3" class="equationLink"></span><div class="disp-formula" content-type="numbered" specific-use="gather"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M216" display="block" overflow="scroll" dspmath="mathml"><mtable displaystyle="true"><mlabeledtr><mtd><mtext>(2)</mtext></mtd><mtd><mrow><mstyle displaystyle="true"><mfrac style="display"><mi mathvariant="normal">d</mi><mrow><mi mathvariant="normal">d</mi><mi>t</mi></mrow></mfrac></mstyle><msub><mi>N</mi><mi mathvariant="normal">a</mi></msub><mo>=</mo><mo>-</mo><msub><mi>F</mi><mrow><mi mathvariant="normal">as</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow></msub></mrow></mtd></mlabeledtr><mlabeledtr><mtd><mtext>(3)</mtext></mtd><mtd><mrow><mstyle class="stylechange" displaystyle="true"></mstyle><mtable rowspacing="0.2ex" class="split" displaystyle="true" columnalign="right left"><mtr><mtd><mrow><mstyle displaystyle="true"><mfrac style="display"><mi mathvariant="normal">d</mi><mrow><mi mathvariant="normal">d</mi><mi>t</mi></mrow></mfrac></mstyle><mo>(</mo><msub><mi>N</mi><mi mathvariant="normal">a</mi></msub><mo>⋅</mo><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msub><mi mathvariant="normal">C</mi><mi mathvariant="normal">a</mi></msub><mo>)</mo></mrow></mtd><mtd><mrow><mo>=</mo><mfenced open="(" close=")"><mrow><mstyle displaystyle="true"><mfrac style="display"><mi mathvariant="normal">d</mi><mrow><mi mathvariant="normal">d</mi><mi>t</mi></mrow></mfrac></mstyle><msub><mi>N</mi><mi mathvariant="normal">a</mi></msub></mrow></mfenced><mo>⋅</mo><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msub><mi mathvariant="normal">C</mi><mi mathvariant="normal">a</mi></msub><mo>+</mo><msub><mi>N</mi><mi mathvariant="normal">a</mi></msub><mo>⋅</mo><mfenced open="(" close=")"><mrow><mstyle displaystyle="true"><mfrac style="display"><mi mathvariant="normal">d</mi><mrow><mi mathvariant="normal">d</mi><mi>t</mi></mrow></mfrac></mstyle><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msub><mi mathvariant="normal">C</mi><mi mathvariant="normal">a</mi></msub></mrow></mfenced></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mrow><mo>=</mo><mo>-</mo><msub><mi>F</mi><mrow><mi mathvariant="normal">as</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow></msub><mo>⋅</mo><mover accent="true"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msub><mi mathvariant="normal">C</mi><mrow><mi mathvariant="normal">as</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow></msub></mrow><mo mathvariant="normal">‾</mo></mover><mo>.</mo></mrow></mtd></mtr></mtable></mrow></mtd></mlabeledtr></mtable></math><div><svg xmlns:svg="http://www.w3.org/2000/svg" width="414pt" height="78pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="2810b1fb60e5753c0fea0bb00eac97e5"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-e_2_3.svg" width="100%" height="78pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-e_2_3.png"></image></svg></div></div><p id="d2e2854"><span class="inline-formula"><i>N</i><sub>a</sub></span> and <span class="inline-formula"><i>N</i><sub>a</sub>⋅<i>δ</i><sup>13</sup>C<sub>a</sub></span> are the atmospheric inventories of carbon and (approximately) of <span class="inline-formula"><sup>13</sup></span>C (in mol ‰). <span class="inline-formula"><i>F</i><sub>as,net</sub></span> and <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M221" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>F</mi><mrow><mi mathvariant="normal">as</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow></msub><mo>⋅</mo><mover accent="true"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msub><mi mathvariant="normal">C</mi><mrow><mi mathvariant="normal">as</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow></msub></mrow><mo mathvariant="normal">‾</mo></mover></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="83pt" height="18pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="603f049fe50670c18cb827b6f44123bf"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00004.svg" width="100%" height="18pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00004.png"></image></svg></span></span> are the globally integrated net atmosphere-to-surface carbon and <span class="inline-formula"><sup>13</sup></span>C flux; <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M223" display="inline" overflow="scroll" dspmath="mathml"><mover accent="true"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msub><mi mathvariant="normal">C</mi><mrow><mi mathvariant="normal">as</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow></msub></mrow><mo mathvariant="normal">‾</mo></mover></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="49pt" height="18pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="3e8146ef76fc93897f4a1f2fd9cab379"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00005.svg" width="100%" height="18pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00005.png"></image></svg></span></span> is the signature of the global net carbon flux. We set <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M224" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>N</mi><mi mathvariant="normal">a</mi></msub><mo>=</mo><mi>c</mi><mo>⋅</mo><msub><mi mathvariant="normal">C</mi><mi mathvariant="normal">a</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="52pt" height="13pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="ea86b1083ffd850b65c43a34624c2517"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00006.svg" width="100%" height="13pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00006.png"></image></svg></span></span>, where <span class="inline-formula"><i>c</i></span> is a unit conversion factor. Solving Eqs. (<a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.E2" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2</a>) and (<a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.E3" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">3</a>) for the changes in C<span class="inline-formula"><sub>a</sub></span> and <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> yields </p><span id="Ch1.E4" class="equationLink"></span><span id="Ch1.E5" class="equationLink"></span><div class="disp-formula" content-type="numbered" specific-use="gather"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M229" display="block" overflow="scroll" dspmath="mathml"><mtable displaystyle="true"><mlabeledtr><mtd><mtext>(4)</mtext></mtd><mtd><mrow><mstyle displaystyle="true"><mfrac style="display"><mi mathvariant="normal">d</mi><mrow><mi mathvariant="normal">d</mi><mi>t</mi></mrow></mfrac></mstyle><msub><mi mathvariant="normal">C</mi><mi mathvariant="normal">a</mi></msub><mo>=</mo><mstyle displaystyle="true"><mfrac style="display"><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow><mi>c</mi></mfrac></mstyle><mo>⋅</mo><msub><mi>F</mi><mrow><mi mathvariant="normal">as</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow></msub></mrow></mtd></mlabeledtr><mlabeledtr><mtd><mtext>(5)</mtext></mtd><mtd><mrow><mstyle displaystyle="true"><mfrac style="display"><mi mathvariant="normal">d</mi><mrow><mi mathvariant="normal">d</mi><mi>t</mi></mrow></mfrac></mstyle><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msub><mi mathvariant="normal">C</mi><mi mathvariant="normal">a</mi></msub><mo>=</mo><mstyle displaystyle="true"><mfrac style="display"><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow><mrow><mi>c</mi><mo>⋅</mo><msub><mi mathvariant="normal">C</mi><mi mathvariant="normal">a</mi></msub></mrow></mfrac></mstyle><mo>⋅</mo><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>F</mi><mrow><mi mathvariant="normal">as</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup><mo>,</mo></mrow></mtd></mlabeledtr></mtable></math><div><svg xmlns:svg="http://www.w3.org/2000/svg" width="414pt" height="56pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="680c2312c9af56fb9c6454c0064138ff"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-e_4_5.svg" width="100%" height="56pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-e_4_5.png"></image></svg></div></div><p id="d2e2854-3"> with <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M230" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>F</mi><mrow><mi mathvariant="normal">as</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="46pt" height="17pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="2fa1d590f91c5a34b44dfe30f8f4a643"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00007.svg" width="100%" height="17pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00007.png"></image></svg></span></span> being the global integral of </p><div class="disp-formula" content-type="numbered" id="Ch1.E6"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M231" display="block" overflow="scroll" dspmath="mathml"><mtable><mlabeledtr><mtd><mtext>(6)</mtext></mtd><mtd><mrow> <msup> <mi mathvariant="italic">δ</mi> <mn mathvariant="normal">13</mn> </msup> <msubsup> <mi>f</mi> <mrow> <mi mathvariant="normal">as</mi> <mo>,</mo> <mi mathvariant="normal">net</mi> </mrow> <mo>*</mo> </msubsup> <mo>=</mo> <msub> <mi>f</mi> <mrow> <mi mathvariant="normal">as</mi> <mo>,</mo> <mi mathvariant="normal">net</mi> </mrow> </msub> <mo>⋅</mo> <mfenced open="(" close=")"> <mrow> <msup> <mi mathvariant="italic">δ</mi> <mn mathvariant="normal">13</mn> </msup> <msub> <mi mathvariant="normal">C</mi> <mrow> <mi mathvariant="normal">as</mi> <mo>,</mo> <mi mathvariant="normal">net</mi> </mrow> </msub> <mo>-</mo> <msup> <mi mathvariant="italic">δ</mi> <mn mathvariant="normal">13</mn> </msup> <msub> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">a</mi> </msub> </mrow> </mfenced> <mo>.</mo> </mrow></mtd></mlabeledtr></mtable></math><div><svg xmlns:svg="http://www.w3.org/2000/svg" width="416pt" height="22pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="b108c3960c007f3e3c83500ec2dc07d5"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-e_6.svg" width="100%" height="22pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-e_6.png"></image></svg></div></div><p id="d2e2854-5"> The superscript <span class="inline-formula"><sup>*</sup></span> indicates that the <span class="inline-formula"><sup>13</sup></span>C fluxes (e.g., in units of mol ‰ yr<span class="inline-formula"><sup>−1</sup></span> m<span class="inline-formula"><sup>−2</sup></span> for <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M236" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">as</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="44pt" height="17pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="07363d9e9ff6b815a02213e059fa34f8"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00008.svg" width="100%" height="17pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00008.png"></image></svg></span></span>) are referenced to the atmospheric signature. Equation (<a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.E6" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">6</a>) corresponds to Eq. (<a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.E1" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1</a>) for the net atmosphere-to-surface isotopic flux but is now referenced to the atmospheric signature instead of the signature of 0 ‰ of the Vienna Pee Dee Belemnite standard as in Eq. (<a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.E1" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1</a>). In this way, a positive (negative) flux causes a negative (positive) change in <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>.</p><p id="d2e3347">Equations (<a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.E4" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">4</a>) and (<a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.E5" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">5</a>) are readily integrated over the growing season from the intra-annual maximum to the minimum (subscripts indicate max and min) in C<span class="inline-formula"><sub>a</sub></span> and the corresponding beginning, <span class="inline-formula"><i>t</i><sub>beg</sub></span>, and end, <span class="inline-formula"><i>t</i><sub>end</sub></span>, of the growing season to get the seasonal cycle amplitude (SA) for the two tracers and (cumulative) net fluxes (see Appendix <a href="https://bg.copernicus.org/articles/22/19/2025/#App1.Ch1.S1" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">A</a> for calculation of SA for a flux): </p><span id="Ch1.E7" class="equationLink"></span><span id="Ch1.E8" class="equationLink"></span><div class="disp-formula" content-type="numbered" specific-use="gather"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M242" display="block" overflow="scroll" dspmath="mathml"><mtable displaystyle="true"><mlabeledtr><mtd><mtext>(7)</mtext></mtd><mtd><mrow><mstyle class="stylechange" displaystyle="true"></mstyle><munder><munder class="underbrace"><mrow><msub><mi mathvariant="normal">C</mi><mrow><mi mathvariant="normal">a</mi><mo>,</mo><mi mathvariant="normal">max</mi></mrow></msub><mo>-</mo><msub><mi mathvariant="normal">C</mi><mrow><mi mathvariant="normal">a</mi><mo>,</mo><mi mathvariant="normal">min</mi></mrow></msub></mrow><mo mathvariant="normal">︸</mo></munder><mrow><mi mathvariant="normal">SA</mi><mo>(</mo><msub><mi mathvariant="normal">C</mi><mi mathvariant="normal">a</mi></msub><mo>)</mo></mrow></munder><mo>=</mo><mstyle displaystyle="true"><mfrac style="display"><mn mathvariant="normal">1</mn><mi>c</mi></mfrac></mstyle><munder><munder class="underbrace"><mrow><munderover><mo movablelimits="false">∫</mo><mrow><msub><mi>t</mi><mi mathvariant="normal">beg</mi></msub></mrow><mrow><msub><mi>t</mi><mi mathvariant="normal">end</mi></msub></mrow></munderover><msub><mi>F</mi><mrow><mi mathvariant="normal">as</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo><mspace width="0.125em" linebreak="nobreak"></mspace><mi mathvariant="normal">d</mi><mi>t</mi></mrow><mo mathvariant="normal">︸</mo></munder><mrow><mi mathvariant="normal">SA</mi><mo>(</mo><msub><mi>F</mi><mrow><mi mathvariant="normal">as</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow></msub><mo>)</mo></mrow></munder></mrow></mtd></mlabeledtr><mlabeledtr><mtd><mtext>(8)</mtext></mtd><mtd><mrow><mstyle class="stylechange" displaystyle="true"></mstyle><munder><munder class="underbrace"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msub><mi mathvariant="normal">C</mi><mrow><mi mathvariant="normal">a</mi><mo>,</mo><mi mathvariant="normal">max</mi></mrow></msub><mo>-</mo><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msub><mi mathvariant="normal">C</mi><mrow><mi mathvariant="normal">a</mi><mo>,</mo><mi mathvariant="normal">min</mi></mrow></msub></mrow><mo mathvariant="normal">︸</mo></munder><mrow><mi mathvariant="normal">SA</mi><mo>(</mo><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msub><mi mathvariant="normal">C</mi><mi mathvariant="normal">a</mi></msub><mo>)</mo></mrow></munder><mo>=</mo><mstyle displaystyle="true"><mfrac style="display"><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow><mrow><mi>c</mi><mo>⋅</mo><msub><mi mathvariant="normal">C</mi><mi mathvariant="normal">a</mi></msub></mrow></mfrac></mstyle><munder><munder class="underbrace"><mrow><munderover><mo movablelimits="false">∫</mo><mrow><msub><mi>t</mi><mi mathvariant="normal">beg</mi></msub></mrow><mrow><msub><mi>t</mi><mi mathvariant="normal">end</mi></msub></mrow></munderover><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>F</mi><mrow><mi mathvariant="normal">as</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup><mo>(</mo><mi>t</mi><mo>)</mo><mspace width="0.125em" linebreak="nobreak"></mspace><mi mathvariant="normal">d</mi><mi>t</mi></mrow><mo mathvariant="normal">︸</mo></munder><mrow><mi mathvariant="normal">SA</mi><mo>(</mo><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>F</mi><mrow><mi mathvariant="normal">as</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup><mo>)</mo></mrow></munder><mo>.</mo></mrow></mtd></mlabeledtr></mtable></math><div><svg xmlns:svg="http://www.w3.org/2000/svg" width="416pt" height="136pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="9936046b04543903da5f5063e77986f4"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-e_7_8.svg" width="100%" height="136pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-e_7_8.png"></image></svg></div></div><p id="d2e3660">Equations (<a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.E5" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">5</a>) and (<a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.E8" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">8</a>) provide important insights. First, changes in <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> and its seasonal cycle are driven by <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M245" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>F</mi><mrow><mi mathvariant="normal">as</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="46pt" height="17pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="7e1dd2d07ff8e25c4b44251f211bbe80"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00009.svg" width="100%" height="17pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00009.png"></image></svg></span></span>; seasonal changes in C<span class="inline-formula"><sub>a</sub></span>, the denominator in Eq. (<a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.E5" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">5</a>), are small compared to C<span class="inline-formula"><sub>a</sub></span>, and C<span class="inline-formula"><sub>a</sub></span> is considered constant within a given year (the error associated with this approximation is less than 3 %). Second, the background CO<span class="inline-formula"><sub>2</sub></span> mole fraction, C<span class="inline-formula"><sub>a</sub></span>, modulates the magnitude of the <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> seasonal cycle. SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) would be larger under low preindustrial C<span class="inline-formula"><sub>a</sub></span> than under modern C<span class="inline-formula"><sub>a</sub></span> for equal seasonal variations in <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M257" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>F</mi><mrow><mi mathvariant="normal">as</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="46pt" height="17pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="ed5d71817fd01dcda744afc5adf6f5fa"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00010.svg" width="100%" height="17pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00010.png"></image></svg></span></span>. Correspondingly, SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) does not change over time as long as the relative changes in SA(<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M260" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>F</mi><mrow><mi mathvariant="normal">as</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="46pt" height="17pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="a92695b0a9fe2d1f396e6730b0b082fd"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00011.svg" width="100%" height="17pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00011.png"></image></svg></span></span>) and in <span class="inline-formula"><i>C</i><sub>a</sub></span> are equal. Equations (<a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.E7" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">7</a>) and (<a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.E8" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">8</a>) were derived for a globally well-mixed atmosphere and global fluxes but analogously also apply for the tracer seasonality at individual sites, with the integral on the right-hand side of Eqs. (<a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.E7" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">7</a>) and (<a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.E8" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">8</a>) representing the integral of (transport-weighted) fluxes over the region influencing tracer seasonality at the site. We recall that the above equations and conclusions were derived by assuming a well-mixed atmosphere, while in reality spatial flux patterns and transport and their changes influence seasonal cycles at individual atmospheric sites. Further, the start and end of the growing season are assumed to coincide with the switch in the sign of the isotopic flux; this is the case in our model for zonally integrated fluxes. These seasonal fluxes will be presented in Sect. <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.S4.SS3" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">4.3</a>. Equations (<a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.E2" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2</a>) to (<a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.E8" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">8</a>) are for illustrating the influence of carbon and carbon isotope fluxes on the seasonal cycles of C<span class="inline-formula"><sub>a</sub></span> and <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>; they were not used for calculating numerical results.</p><p id="d2e3940">The notation and sign convention introduced above are applied in this paper. In brief, <span class="inline-formula"><i>f</i><sub><i>i</i>,<i>j</i></sub></span> defines a one-way flux from the source reservoir <span class="inline-formula"><i>i</i></span> to the receiving reservoir <span class="inline-formula"><i>j</i></span> and is positive. The isotopic signature of this flux is <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub><i>i</i>,<i>j</i></sub></span>. The net flux from reservoir <span class="inline-formula"><i>i</i></span> to reservoir <span class="inline-formula"><i>j</i></span> is <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M272" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>f</mi><mrow><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="28pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="368429bad7e2642b86e795b40d8e3918"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00012.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00012.png"></image></svg></span></span> and is the difference between the corresponding one-way fluxes; e.g., <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M273" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>f</mi><mrow><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow></msub><mo>=</mo><msub><mi>f</mi><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mo>-</mo><msub><mi>f</mi><mrow><mi>j</mi><mo>,</mo><mi>i</mi></mrow></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="76pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="236e94bd0c2268e12b62fbc848a63488"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00013.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00013.png"></image></svg></span></span>. <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M274" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>f</mi><mrow><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="28pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="23c75ff81b2b53d4911a76a1d1c19186"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00014.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00014.png"></image></svg></span></span> is positive if the net flux results in the transfer of mass from <span class="inline-formula"><i>i</i></span> to <span class="inline-formula"><i>j</i></span>.</p><span class="tableCitations"></span><div class="table-wrap" id="Ch1.T1"><div class="caption"><p id="d2e4115"><strong class="caption-number">Table 1</strong>The seasonal cycle amplitude of C<span class="inline-formula"><sub>a</sub></span> and <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> from the standard simulation (mod; <span class="inline-formula"><i>E</i><sub>standard</sub></span>) and observations (obs) for 19 monitoring sites and the period of 1982–2012. The increase over the industrial period is estimated from the difference between the standard simulation and the preindustrial control (<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M281" display="inline" overflow="scroll" dspmath="mathml"><mrow><mn mathvariant="normal">100</mn><mo>⋅</mo><mo>(</mo><msub><mi>E</mi><mi mathvariant="normal">standard</mi></msub><mo>-</mo><msub><mi>E</mi><mi mathvariant="normal">control</mi></msub><mo>)</mo><mo>/</mo><msub><mi>E</mi><mi mathvariant="normal">control</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="152pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="8d65c8cefdb74c5a3456aec861debd31"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00015.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00015.png"></image></svg></span></span>).</p></div><a class="table-link" href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-t01.png" target="_blank"><img src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-t01-thumb.png" target="_blank" data-webversion="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-t01-web.png" data-width="2067" data-height="893" data-printversion="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-t01.png" data-csvversion="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-t01.xlsx"></a><p class="downloads"><a class="triangle journal-contentLinkColor table-download" href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-t01.png" target="_blank">Download Print Version</a><span class="hide-on-mobile download-separator"> | </span><a class="triangle journal-contentLinkColor table-download" href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-t01.xlsx" target="_blank">Download XLSX</a></p></div></div><span class="section3-mobile-bottom-border mobile-bottom-border hide-on-desktop hide-on-tablet"></span></div> <div class="sec" id="section4"><div class="grid-container no-margin header-element"><span class="grid-100 mobile-grid-100 tablet-grid-100 grid-parent more-less-mobile" data-hide="#section4 .co-arrow-open,.section4-content" data-show="#section4 .co-arrow-closed,.section4-mobile-bottom-border"><div id="Ch1.S4" class="h1"><span class="label">4</span> Results<span class="hide-on-desktop hide-on-tablet triangleWrapper"> <i class="co-arrow-closed"></i><i class="co-arrow-open" style="display:none"></i></span></div></span></div> <div class="section4-content show-no-js hide-on-mobile-soft"><div class="sec"><h2 id="Ch1.S4.SS1"><span class="label">4.1</span> Seasonal cycles of atmosphere–surface fluxes, C<span class="inline-formula"><sub>a</sub></span>, and <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span></h2> <p id="d2e5642">The Bern3D-LPX model simulates (<span class="inline-formula"><i>E</i><sub>standard</sub></span>) large seasonal variations in the net land biosphere–atmosphere exchange of CO<span class="inline-formula"><sub>2</sub></span> and <span class="inline-formula"><sup>13</sup></span>CO<span class="inline-formula"><sub>2</sub></span>, whereas seasonal variations in ocean–atmosphere fluxes are much smaller (Fig. <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.F1" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1</a>). This seasonality is broadly consistent with estimates of regional air–land carbon flux seasonality from an atmospheric inversion <span class="cit" id="xref_paren.56">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx33" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Gurney et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx33" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2004</a>)</span> and air–sea flux seasonality from surface ocean pCO<span class="inline-formula"><sub>2</sub></span> observations <span class="cit" id="xref_paren.57">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx62" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Landschützer et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx62" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2014</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx87" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Takahashi et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx87" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2009</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx25" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Fay et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx25" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2021</a>)</span>, except in the Southern Ocean and in the northern subpolar gyres. The LPX land biosphere model shows the expected uptake of isotopically depleted carbon, resulting in positive <span class="inline-formula"><i>f</i><sub>as,net</sub></span> and negative <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M389" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">as</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="44pt" height="17pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="d5bc1295353e4d7fac0ea7de616d0331"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00016.svg" width="100%" height="17pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00016.png"></image></svg></span></span> during the summer and vice versa in winter.</p> <div class="fig" id="Ch1.F1"><a target="_blank" class="figure-link" href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-f01-web.png"><img alt="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-f01" data-webversion="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-f01-web.png" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-f01-thumb.png" data-width="2067" data-height="1757"></a><div class="caption"><p id="d2e5742"><strong class="caption-number">Figure 1</strong>Net seasonal atmosphere-to-surface fluxes. Fluxes are for <strong>(a, c, e)</strong> carbon and <strong>(b, d, f)</strong> the <span class="inline-formula"><i>δ</i><sup>13</sup></span>C-weighted carbon flux, <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M391" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">as</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="44pt" height="17pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="31e4765abb085dc6c57333fc8e2828ba"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00017.svg" width="100%" height="17pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00017.png"></image></svg></span></span> (see Sect. <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.S3" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">3</a>), from the standard simulation (<span class="inline-formula"><i>E</i><sub>standard</sub></span>) and are averaged over 1982–2012 for <strong>(a, b)</strong> June, July, and August (JJA); <strong>(c, d)</strong> December, January, and February (DJF); and <strong>(e, f)</strong> JJA minus DJF. Note the non-linear color bars with blue colors in panels <strong>(a)</strong> to <strong>(d)</strong> indicating a lowering in atmospheric CO<span class="inline-formula"><sub>2</sub></span> and <span class="inline-formula"><i>δ</i><sup>13</sup></span>C.</p></div><p class="downloads"></p></div> <p id="d2e5841">The Bern3D ocean model shows a negative <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M395" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">as</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="44pt" height="17pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="ca6347cef522a2651240e3b2265ee28e"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00018.svg" width="100%" height="17pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00018.png"></image></svg></span></span> in the low latitudes and midlatitudes, small modern fluxes in the northern subpolar gyres, and a positive flux in the Southern Ocean in both seasons (Fig. <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.F1" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1</a>). These modern Bern3D fluxes are driven by the atmosphere–ocean isotopic disequilibrium, here defined as the isotopic signature of the atmosphere-to-surface carbon flux minus the signature of the surface-to-atmosphere flux (<span class="inline-formula"><i>δ</i><sub>dis,as</sub></span>; Eq. <a href="https://bg.copernicus.org/articles/22/19/2025/#App1.Ch1.S1.E13" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">A2</a>), with a negative <span class="inline-formula"><i>δ</i><sub>dis,as</sub></span> in the low latitudes and midlatitudes, a small modern disequilibrium in northern high latitudes, and a positive <span class="inline-formula"><i>δ</i><sub>dis,as</sub></span> south of 50° S, consistent with observations <span class="cit" id="xref_paren.58">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx69" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Menviel et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx69" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2015</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx76" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Quay et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx76" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2017</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx12" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Becker et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx12" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2018</a>)</span>.</p> <p id="d2e5924">The preindustrial <span class="inline-formula"><i>δ</i><sub>dis,as</sub></span> and <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M400" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">as</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="44pt" height="17pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="666092d94c239b802af336f655fdc6e8"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00019.svg" width="100%" height="17pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00019.png"></image></svg></span></span> are negative in the low latitudes and midlatitudes and positive in high-latitude ocean regions (not shown), mainly driven by the temperature dependency of isotopic fractionation during air–sea exchange and the cycling of marine biological matter (see Fig. 1 of <span class="cit" id="xref_altparen.59"><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx69" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Menviel et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx69" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2015</a></span>, to compare Bern3D and LOVECLIM results for <span class="inline-formula"><i>δ</i><sub>dis,as</sub></span>). Fossil fuel emissions cause a negative flux perturbation worldwide, shifting the net isotopic fluxes to more negative values over the industrial period.</p> <div class="fig" id="Ch1.F2"><a target="_blank" class="figure-link" href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-f02-web.png"><img alt="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-f02" data-webversion="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-f02-web.png" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-f02-thumb.png" data-printversion="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-f02-high-res.pdf" data-width="2067" data-height="1445"></a><div class="caption"><p id="d2e5987"><strong class="caption-number">Figure 2</strong>The simulated (red) seasonal cycle of atmospheric C<span class="inline-formula"><sub>a</sub></span> (left, <strong>a, d, g</strong>) and its signature <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> (middle, <strong>b, e, h</strong>) compared to observations (black dots). In the rightmost panels <strong>(c, f, i)</strong> the seasonal anomalies (<span class="inline-formula">Δ</span>) of C<span class="inline-formula"><sub>a</sub></span> are plotted against those of <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>, with lines connecting the monthly values (dots) fading from January to December. Results are for Alert, northern Canada <strong>(a, b, c)</strong>; Mauna Loa, Hawaii <strong>(d, e, f)</strong>; and the South Pole <strong>(g, h, i)</strong>. Simulated values are from transporting net TM3 fluxes of the Bern3D-LPX <span class="inline-formula"><i>E</i><sub>standard</sub></span> simulation from all (red, <span class="inline-formula"><i>E</i><sub>standard</sub></span>), terrestrial (green, dashed), oceanic (blue, dashed), and fossil fuel sources (brown, dashed). The observational and model anomalies are computed from monthly values between 1982 and 2012 if both the measurements and transport matrices are available. Error bars and shading correspond to the standard deviation from the interannual variability in monthly values.</p></div><p class="downloads"><a class="triangle journal-contentLinkColor figure-download" href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-f02-high-res.pdf" target="_blank">Download</a></p></div> <p id="d2e6103">Figure <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.F2" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2</a> compares the mean seasonal cycles of C<span class="inline-formula"><sub>a</sub></span> and <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> from <span class="inline-formula"><i>E</i><sub>standard</sub></span> with measurements from 1982 (at Alert from 1985) to 2012 at three sites and with factorial simulations, where the fluxes of the land (dashed green line), ocean (dashed blue line), and fossil fuel emissions (dashed brown lines) were considered individually (see Table <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.T1" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1</a> and Figs. S1 and S2 in the Supplement for additional sites). For the Northern Hemisphere (NH) sites of Alert (top panels) and Mauna Loa (middle panels), the seasonal variations are dominated by the terrestrial biosphere fluxes, with minor contributions from ocean fluxes and fossil fuel emissions.</p> <p id="d2e6151"><span id="page25"></span>Both the timing and amplitude of the observed seasonal cycle of C<span class="inline-formula"><sub>a</sub></span> and <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> are captured reasonably well by <span class="inline-formula"><i>E</i><sub>standard</sub></span> (Fig. <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.F2" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2</a>). The simulated SA(C<span class="inline-formula"><sub>a</sub></span>) and its interannual variability (IAV) are overestimated compared to observations at Alert (17.3 <span class="inline-formula">±</span> 0.84 ppm versus 14.8 <span class="inline-formula">±</span> 0.75 ppm) and Mauna Loa (8.3 <span class="inline-formula">±</span> 0.30 ppm versus 6.5 <span class="inline-formula">±</span> 0.24 ppm). SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) matches the observations (ALT – 0.72 <span class="inline-formula">±</span> 0.035 ‰ versus 0.75 <span class="inline-formula">±</span> 0.042 ‰; MLO – 0.34 <span class="inline-formula">±</span> 0.013 ‰ versus 0.33 <span class="inline-formula">±</span> 0.028 ‰). Good model–data agreement in the phasing of the seasonal cycle of C<span class="inline-formula"><sub>a</sub></span> relative to <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> is demonstrated for Alert in panel (c), where monthly anomalies in <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> are plotted versus anomalies in C<span class="inline-formula"><sub>a</sub></span>. Both the observations and the model show hysteresis throughout the year, with the loop rotating clockwise. At Mauna Loa, the rotation direction of the hysteresis loop is clockwise in the simulation and counterclockwise in the observations (panel f). Still, the observed hysteresis is small, with offsets of less than 0.03 ‰. The hysteresis arises as the ratio between the rate of change in <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> versus the rate of change in C<span class="inline-formula"><sub>a</sub></span> varies over the year <span class="cit" id="xref_paren.60">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx52" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Keeling et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx52" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1989</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx37" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Heimann et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx37" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1989</a>)</span>. This non-linearity in the atmospheric tracer relationship originates from seasonally varying transport in combination with spatially and temporally varying relationships of atmosphere–surface <span class="inline-formula"><i>δ</i><sup>13</sup></span>C to CO<span class="inline-formula"><sub>2</sub></span> flux. For example, the isotopic signature of the growing season net atmosphere-to-land carbon flux <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>al,net</sub></span> is <span class="inline-formula">−13.4</span> ‰ for the northern high-latitude region (<span class="inline-formula">></span>40° N) but only <span class="inline-formula">−10.7</span> ‰ for the region 10–40° N, and the signal observed at any measurement site results from varying contributions from these and other latitudinal bounds given intra-annually varying winds and hence transport.</p> <p id="d2e6448">Results for the South Pole are different than for the NH sites (Fig. <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.F2" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2</a>g, h, i). Neither the timing nor the amplitude of C<span class="inline-formula"><sub>a</sub></span> (2.1 <span class="inline-formula">±</span> 0.16 ppm simulated versus 1.1 <span class="inline-formula">±</span> 0.11 ppm observed) and <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> (0.094 <span class="inline-formula">±</span> 0.004 ‰ versus 0.033 <span class="inline-formula">±</span> 0.015 ‰) agrees with observations. SA(C<span class="inline-formula"><sub>a</sub></span>) and SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) at the South Pole are observed to be 14 and 23 times smaller than at Alert, respectively. The absolute data–model mismatches are therefore not as drastic as the relative mismatches. The disagreement between simulation and observational estimates is also apparent when considering the scatter plot in panel (i). The model shows a complex hysteresis relationship, whereas the observations display a clockwise loop.</p> <p id="d2e6541"><span id="page26"></span>The remote Antarctic sites (the South Pole, Palmer, and Halley) show an expected relatively larger dependence on the ocean, but the terrestrial contribution still dominates in the model (Figs. <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.F2" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2</a>, S1, and S2). The C<span class="inline-formula"><sub>a</sub></span> seasonal cycle resulting from atmosphere–ocean flux is shifted by up to 6 months compared to observations at the South Pole and the other two Antarctic sites (Palmer, Halley; blue lines versus black dots in Fig. S1), pointing to biases in the Bern3D ocean flux. Observation-based analyses indicate stronger ocean CO<span class="inline-formula"><sub>2</sub></span> uptake in summer than in winter in the Southern Ocean <span class="cit" id="xref_paren.61">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx43" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Jin et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx43" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2024</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx65" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Long et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx65" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2021</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx25" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Fay et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx25" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2021</a>)</span> in contrast to results from Bern3D (Fig. <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.F1" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1</a>) and more complex ocean models <span class="cit" id="xref_paren.62">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx35" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Hauck and Völker</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx35" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2015</a>)</span> and several Earth system models from CMIP5 <span class="cit" id="xref_paren.63">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx67" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Majkut et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx67" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2014</a>)</span> and CMIP6 <span class="cit" id="xref_paren.64">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx45" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Joos et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx45" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2023</a>)</span>. The simulated amplitude and phasing of the <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> seasonal cycle resulting from the ocean are broadly in line with observations at the Antarctic sites (Fig. S2). The air–sea isotopic disequilibrium is large in the Southern Ocean, and the two-way air–sea and sea–air exchange fluxes yield a substantial net isotopic flux, even under low net carbon flux. Temperature-dependent fractionation is higher in winter than in summer, and the air–sea gas exchange piston velocity and, in turn, the isotope fluxes are larger under high winds in winter than in summer in the modeled Southern Ocean, consistent with the observed seasonal phasing of <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> at the Antarctic sites. Errors in modeled Southern Ocean fluxes are expected to have a minor impact on simulated SA(C<span class="inline-formula"><sub>a</sub></span>) and SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) at NH sites, where the influence of land fluxes dominates by far (Figs. <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.F2" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2</a>, S1, S2).</p> <p id="d2e6651">Considering all extratropical Northern Hemisphere sites, model–data mismatches are less than 30 % for SA(C<span class="inline-formula"><sub>a</sub></span>) and SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) and their root-mean-square errors (RMSEs) are 2.6 ppm and 0.14 ‰, respectively. For the tropical and SH sites, large relative data–model deviations of up to 140 % for SA(C<span class="inline-formula"><sub>a</sub></span>) and up to 290 % for SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) are evident, although absolute deviations are less than 1.8 ppm, and 0.18 ‰ and the corresponding RMSEs are 1.2 ppm and 0.05 ‰ (Table <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.T1" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1</a>).</p> <p id="d2e6715"><span id="page27"></span>Interannual variability in simulated SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) compares reasonably well with observations at sites in the NH subtropics and extratropics (average of the <span class="inline-formula">1<i>σ</i></span> standard deviation of 12 sites is 0.031 ‰ in <span class="inline-formula"><i>E</i><sub>standard</sub></span> versus 0.031 ‰ in observations) and in the tropics and SH (0.009 ‰ versus 0.013 ‰) (Table <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.T1" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1</a>). Similar agreement between simulated and observation-derived IAV holds for SA(C<span class="inline-formula"><sub>a</sub></span>) (NH extratropics –0.75 versus 0.96 ppm; tropics and SH – 0.29 versus 0.30). This suggests that the variability in the seasonal amplitude of the carbon and isotope fluxes is reasonably represented by LPX-Bern. The correct simulation of variability can be challenging and <span class="cit" id="xref_text.65"><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx90" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">van der Velde et al.</a> (<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx90" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2013</a>)</span> report too low an interannual variability in the annually integrated isotopic disequilibrium flux for their model.</p> </div><div class="sec"><h2 id="Ch1.S4.SS2"><span class="label">4.2</span> Temporal trends in the seasonal cycle amplitude of <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> and C<span class="inline-formula"><sub>a</sub></span></h2> <p id="d2e6811">Detection of trends in SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) may be hampered by interannual-to-decadal variability, short record lengths, and a small SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) in comparison to measurement uncertainty and variability, as is typical at Southern Hemisphere sites. For example, dividing SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) by 2 standard deviations of IAV yields a signal-to-noise ratio <span class="cit" id="xref_paren.66">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx58" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Keller et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx58" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2014</a>)</span> below 2.7 at SH sites and as low as 1.1 at the South Pole and on American Samoa (Table <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.T1" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1</a>). Thus, SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) would need to roughly double over the observational period for a trend in SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) to emerge from the noise of IAV at these two sites. The situation is more favorable for trend detection at NH extratropical sites (Table <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.T1" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1</a>), where the signal-to-noise ratio ranges between 9 and 16, and changes of 6 % to 11 % in SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) would emerge.</p> <div class="fig" id="Ch1.F3"><a target="_blank" class="figure-link" href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-f03-web.png"><img alt="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-f03" data-webversion="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-f03-web.png" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-f03-thumb.png" data-printversion="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-f03-high-res.pdf" data-width="1539" data-height="1095"></a><div class="caption"><p id="d2e6945"><strong class="caption-number">Figure 3</strong>Temporal evolution of <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> <strong>(a)</strong> and its seasonal amplitude <strong>(b)</strong> from data of the Scripps network <span class="cit" id="xref_paren.67">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx54" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Keeling et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx54" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2001</a>)</span>. Gap-filled data provided by Scripps are used for the eight sites. The slope and its standard error from a linear regression through the seasonal amplitude data (dotted) are given in ‰ per century. Trends are not different from zero based on a two-sided <span class="inline-formula"><i>t</i></span> test and a significance level of 5 %, except at Christmas Island (CHR) and the South Pole (SPO). Sites are ordered according to latitude (Alert (ALT, 82° N), Nuvuk (formerly Point Barrow) (PTB, 71° N), La Jolla (LJO, 33° N), Mauna Loa Observatory (MLO, 20° N), Cape Kumukahi (KUM, 20° N), Christmas Island (CHR, 2° N), Samoa (SAM, 14° S), and the South Pole (SPO, 90° S)).</p></div><p class="downloads"><a class="triangle journal-contentLinkColor figure-download" href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-f03-high-res.pdf" target="_blank">Download</a></p></div> <span class="tableCitations"></span><div class="table-wrap" id="Ch1.T2"><div class="caption"><p id="d2e6995"><strong class="caption-number">Table 2</strong>Temporal trends in the seasonal cycle amplitude of C<span class="inline-formula"><sub>a</sub></span> and <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> from the standard simulation (<span class="inline-formula"><i>E</i><sub>standard</sub></span>) and observations for 19 monitoring sites from 1982 to 2012. Observational data of C<span class="inline-formula"><sub>a</sub></span> are from the GLOBALVIEW-CO<span class="inline-formula"><sub>2</sub></span> product and are fitted for the period of 1982–2012, while the data for <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> are from Scripps and are fitted as shown in Fig. <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.F3" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">3</a>. The seasonal cycle amplitude of a given year is only computed if at least 10 monthly values are available. The number of years included in the trend calculation for SA(C<span class="inline-formula"><sub>a</sub></span>) and model-based SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) is given in parentheses. The observed trend for C<span class="inline-formula"><sub>a</sub></span> is affected by anomalous values at Key Biscayne, which is not included. Over the period of 1982–2012, significant trends (two-sided <span class="inline-formula"><i>t</i></span> test at 5 % significance) are only found for Alert, Nuvuk (formerly Point Barrow), Ocean Station M, and Mahe Island for observed C<span class="inline-formula"><sub>a</sub></span>; for Mariana Islands, Mahe Island, Palmer, Halley, and the South Pole for simulated C<span class="inline-formula"><sub>a</sub></span>; and for Ascension, Mahe Island, and the South Pole for simulated <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>. The decadal-scale trends are given per century for better readability.</p></div><a class="table-link" href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-t02.png" target="_blank"><img src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-t02-thumb.png" target="_blank" data-webversion="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-t02-web.png" data-width="2067" data-height="1244" data-printversion="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-t02.png" data-csvversion="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-t02.xlsx"></a><p class="downloads"><a class="triangle journal-contentLinkColor table-download" href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-t02.png" target="_blank">Download Print Version</a><span class="hide-on-mobile download-separator"> | </span><a class="triangle journal-contentLinkColor table-download" href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-t02.xlsx" target="_blank">Download XLSX</a></p></div> <p id="d2e8285">Temporal trends in SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) from the Scripps gap-filled data are not statistically different from zero, except at the tropical site Christmas Island and at the South Pole (Fig. <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.F3" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">3</a>). Averaging the trends across all eight sites yields <span class="inline-formula">−0.0038</span> <span class="inline-formula">±</span> 0.026 ‰ per century (mean <span class="inline-formula">±</span> 1 SD of the mean), and averaging the trends for the extratropical sites ALT, PTB, and LJO yields <span class="inline-formula">+0.09</span> <span class="inline-formula">±</span> 0.06 ‰ per century, with both averaged trends not statistically different from zero. The trend for the NH extratropical sites translates into a change in SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) of around 5 <span class="inline-formula">±</span> 3 % over the 40-year observational period. For the fitted data, trends are statistically different from zero only at two sites (La Jolla and Christmas Island). This is consistent with <span class="cit" id="xref_text.68"><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx30" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Gonsamo et al.</a> (<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx30" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2017</a>)</span>, who did not detect a temporal trend in SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) and seasonal phasing by fitting Scripps daily flask data from the four sites of Alert, Nuvuk (formerly Point Barrow), La Jolla, and Mauna Loa. In summary, observed temporal trends in SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) are small (<span class="inline-formula">≤</span> 0.15 ‰per century) and are not statistically different from zero (at <span class="inline-formula"><i>p</i><0.05</span>) at individual sites. A significant negative trend is found for the tropical site Christmas Island, and detection of trends is difficult at the Southern Hemisphere sites, where SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) is small.</p> <p id="d2e8463">Simulated trends in SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) are small (often less than 0.01 ‰ per decade) and statistically insignificant (5 % level) except at three SH sites (Ascension, Mahe, the South Pole) with a small seasonal cycle amplitude (Table <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.T2" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2</a>). Observed relative trends in SA(C<span class="inline-formula"><sub>a</sub></span>) are larger than in SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) in the northern high latitudes and are statistically significant at Alert, Nuvuk (formerly Point Barrow), Ocean Station, and Mahe Island but insignificant at all other sites over the 1982–2012 analysis period. Simulated trends in SA(C<span class="inline-formula"><sub>a</sub></span>) are insignificant, except at four SH sites and on the Mariana Islands.</p> <p id="d2e8527">We compare model (<span class="inline-formula"><i>m</i></span>) and observed (<span class="inline-formula"><i>o</i></span>) slopes (<span class="inline-formula"><i>β</i></span>) to probe model–observation agreement. Under the null hypothesis of no slope difference, the <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M633" display="inline" overflow="scroll" dspmath="mathml"><mrow><mi>T</mi><mo>=</mo><mo>(</mo><msub><mi mathvariant="italic">β</mi><mi>m</mi></msub><mo>-</mo><msub><mi mathvariant="italic">β</mi><mi>o</mi></msub><mo>)</mo><mo>/</mo><msqrt><mrow><msubsup><mi>s</mi><mrow><msub><mi mathvariant="italic">β</mi><mi>m</mi></msub></mrow><mn mathvariant="normal">2</mn></msubsup><mo>+</mo><msubsup><mi>s</mi><mrow><msub><mi mathvariant="italic">β</mi><mi>o</mi></msub></mrow><mn mathvariant="normal">2</mn></msubsup></mrow></msqrt></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="127pt" height="22pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="a3531a8309b4f60d2936f6acc4963407"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00020.svg" width="100%" height="22pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00020.png"></image></svg></span></span> statistic (where <span class="inline-formula"><i>s</i><sub><i>β</i></sub></span> is the standard error in the <span class="inline-formula"><i>β</i></span> slope estimate) is Student's <span class="inline-formula"><i>t</i></span> distributed <span class="cit" id="xref_paren.69">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx97" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Welch</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx97" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1947</a>)</span>. Trends are different when the <span class="inline-formula"><i>T</i></span> values are larger than the 0.975 quantile of a <span class="inline-formula"><i>t</i></span> distribution with <span class="inline-formula"><i>ν</i></span> degrees of freedom (<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M640" display="inline" overflow="scroll" dspmath="mathml"><mrow><mi>T</mi><mo>></mo><mo>∼</mo><mn mathvariant="normal">2</mn></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="35pt" height="10pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="48743dbfff4322dc32683d3c2fc436ea"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00021.svg" width="100%" height="10pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00021.png"></image></svg></span></span>). Modeled and observed trends are different at one site, the South Pole, for SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) and at one site (Nuvuk, formerly Point Barrow) for SA(C<span class="inline-formula"><sub>a</sub></span>). As will become clear in the next section, the largest surface–atmosphere isotope fluxes and temporal changes in these fluxes are simulated in the region north of 40° N. We are therefore interested in quantifying how well the model represents temporal changes in SA(C<span class="inline-formula"><sub>a</sub></span>) in this region and over a 40-year period, representative of the <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> observational record. For the five NH high-latitude sites with more than 20 years of data, uncertainties in the temporal changes in SA(C<span class="inline-formula"><sub>a</sub></span>) range between 5 % and 13 % at individual sites over a 40-year period. The average trend in SA(C<span class="inline-formula"><sub>a</sub></span>) for these five NH sites (Alert, Nuvuk (formerly Point Barrow), Ocean Station M, Cold Bay, Shemya Island) is 4.8 <span class="inline-formula">±</span> 1.6 ppm per century (31 <span class="inline-formula">±</span> 10 % per century) from observations and 3.8 <span class="inline-formula">±</span> 1.8 ppm per century (22 <span class="inline-formula">±</span> 11 % per century) from the model. These estimates translate into a relative change in SA(C<span class="inline-formula"><sub>a</sub></span>) of around 4 % to 5 % over a 40-year period. This suggests that our model chain accurately represents the observed temporal changes in SA(C<span class="inline-formula"><sub>a</sub></span>) in the NH extratropical atmosphere.</p> <p id="d2e8794">Given the mostly insignificant trends at individual sites over the model analysis period of 1982–2012, the question of whether larger trends are detected when considering longer timescales arises. Century-scale trends, or their absence, can be readily estimated in the simulations by comparing SA(C<span class="inline-formula"><sub>a</sub></span>) and SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) for the modern period (1982–2012) (<span class="inline-formula"><i>E</i><sub>standard</sub></span>) and the preindustrial control (<span class="inline-formula"><i>E</i><sub>control</sub></span>) (Table <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.T1" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1</a>; solid red versus dashed blue lines in Figs. S3 and S4). For C<span class="inline-formula"><sub>a</sub></span>, a growth in SA is clearly visible (12.2 to 17.25 ppm at Alert, 6 to 8.3 ppm at Mauna Loa, 1.7 to 2.1 ppm at the South Pole). Across all 19 sites, SA(C<span class="inline-formula"><sub>a</sub></span>) has grown by 44 % <span class="inline-formula">±</span> 35 % (mean <span class="inline-formula">±</span> standard deviation) from 1700 CE to 1982–2012. The growth in SA(C<span class="inline-formula"><sub>a</sub></span>) ranges between 33 % and 42 % across the 12 extratropical NH sites (Table <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.T1" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1</a>).</p> <p id="d2e8895"><span id="page28"></span>For <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>, <span class="inline-formula"><i>E</i><sub>control</sub></span> and <span class="inline-formula"><i>E</i><sub>standard</sub></span> exhibit an almost identical SA averaged across all 19 sites (2 % <span class="inline-formula">±</span> 16 % lower in <span class="inline-formula"><i>E</i><sub>control</sub></span> than in <span class="inline-formula"><i>E</i><sub>standard</sub></span>). The change in SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) from the preindustrial (<span class="inline-formula"><i>E</i><sub>control</sub></span>) to modern (<span class="inline-formula"><i>E</i><sub>standard</sub></span>) periods ranges between <span class="inline-formula">−6</span> % and 9 % across the 12 extratropical NH sites, whereas more diverse results (<span class="inline-formula">−28</span> % to <span class="inline-formula">+63</span> %) are simulated at the tropical and SH sites (Fig. S4, Table <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.T1" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1</a>). The change in SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>), <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M681" display="inline" overflow="scroll" dspmath="mathml"><mrow><mi>S</mi><mo>=</mo><msub><mi>E</mi><mi mathvariant="normal">standard</mi></msub><mo>-</mo><msub><mi>E</mi><mi mathvariant="normal">control</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="104pt" height="12pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="ba12a9802a4884079e1f28596c13ac2f"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00022.svg" width="100%" height="12pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00022.png"></image></svg></span></span>, does not emerge from the noise of variability (<span class="inline-formula"><i>N</i></span> <span class="inline-formula">=</span> 2 standard deviations from IAV of <span class="inline-formula"><i>E</i><sub>standard</sub></span>), except at one tropical (Christmas Island) and three SH sites (Ascension Island, Mahe Island, Palmer Station); we require <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M685" display="inline" overflow="scroll" dspmath="mathml"><mrow><mfenced open="|" close="|"><mi>S</mi></mfenced><mo>/</mo><mi>N</mi><mo>></mo><mn mathvariant="normal">1</mn></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="49pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="d6a88d04a795bcd0d45fac7dd0360d02"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00023.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00023.png"></image></svg></span></span> for the signal <span class="inline-formula"><i>S</i></span> to emerge <span class="cit" id="xref_paren.70">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx58" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Keller et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx58" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2014</a>)</span>. The fact that trends in SA(C<span class="inline-formula"><sub>a</sub></span>) and the near-zero trends in SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) are better identified by the difference between the modern and preindustrial periods than by regression over the modern period motivates us to focus on the comparison between <span class="inline-formula"><i>E</i><sub>standard</sub></span> versus <span class="inline-formula"><i>E</i><sub>control</sub></span> in the remaining result sections.</p> </div><div class="sec"><h2 id="Ch1.S4.SS3"><span class="label">4.3</span> Zonal decomposition of seasonal land–biosphere fluxes</h2> <div class="sec"><h3 id="Ch1.S4.SS3.SSS1"><span class="label">4.3.1</span> Changes in the seasonal amplitude of land–biosphere fluxes and <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> over the historical period</h3> <p id="d2e9228">Next, we address the near-absent temporal trends in SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) at NH sites by analyzing the zonally averaged cumulative growing season flux of <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M696" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>|</mo><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup><mo>|</mo></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="49pt" height="18pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="817c6033a3be328ebbc15ceade1ec9f3"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00024.svg" width="100%" height="18pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00024.png"></image></svg></span></span>, i.e., SA(<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M697" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="18pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="b3837b0f23961b5748b59e38ef96575f"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00025.svg" width="100%" height="18pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00025.png"></image></svg></span></span>) (Fig. <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.F4" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">4</a>). The northern midlatitude to high-latitude ecosystem fluxes exhibit the largest seasonal cycle, followed by tropical rain-green forests and savannahs in <span class="inline-formula"><i>E</i><sub>standard</sub></span>. This flux pattern contributes to the larger SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) in the NH extratropics versus tropical and SH sites. A similar latitudinal flux pattern holds for <span class="inline-formula"><i>E</i><sub>control</sub></span>.</p> <div class="fig" id="Ch1.F4"><a target="_blank" class="figure-link" href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-f04-web.png"><img alt="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-f04" data-webversion="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-f04-web.png" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-f04-thumb.png" data-printversion="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-f04-high-res.pdf" data-width="1832" data-height="3168"></a><div class="caption"><p id="d2e9348"><strong class="caption-number">Figure 4</strong>The seasonal amplitude per 2.5° latitude band of the signature-weighted, detrended net atmosphere–land flux, <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M702" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="18pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="b7e953de1d50e7618cd07ce6cfa0ebb0"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00026.svg" width="100%" height="18pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00026.png"></image></svg></span></span>, in the period of 1982–2012 is shown in <strong>(a)</strong> in red (see Eq. <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.E8" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">8</a>). This quantity is the sum of three constituent seasonal amplitudes (Eq. <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.E9" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">9</a> and Appendix <a href="https://bg.copernicus.org/articles/22/19/2025/#App1.Ch1.S1" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">A</a>): net land–atmosphere flux weighted with photosynthetic fractionation (<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M703" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow></msub><mo>⋅</mo><msub><mi mathvariant="italic">ε</mi><mi mathvariant="normal">NPP</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="54pt" height="13pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="291f3d951017bbac9c101cc7cda23f91"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00027.svg" width="100%" height="13pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00027.png"></image></svg></span></span>, green) plus release fluxes weighted with the disequilibrium signature (<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M704" display="inline" overflow="scroll" dspmath="mathml"><mrow><mi>R</mi><mo>⋅</mo><msub><mi mathvariant="italic">δ</mi><mrow><mi mathvariant="normal">dis</mi><mo>,</mo><mi mathvariant="normal">la</mi></mrow></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="41pt" height="13pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="3814c7d6cd10f56144f532b6fff19875"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00028.svg" width="100%" height="13pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00028.png"></image></svg></span></span>, blue) plus the contribution to the seasonal amplitude by the underlying trend of <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M705" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="18pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="d1b0a449de44bfcf0786e33a788bd131"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00029.svg" width="100%" height="18pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00029.png"></image></svg></span></span> (<span class="inline-formula">Δ<sub>trend</sub></span>, orange) (sign convention – green <span class="inline-formula">+</span> blue <span class="inline-formula">+</span> orange <span class="inline-formula">=</span> red). In <strong>(b)</strong>, the seasonal amplitudes of (non-detrended) net carbon fluxes are shown. The net atmosphere–land flux (<span class="inline-formula"><i>f</i><sub>al,net</sub></span>, red) is split into net primary productivity (NPP, olive) and release flux (<span class="inline-formula"><i>R</i></span>, blue). In <strong>(c)</strong> the corresponding fractionation of photosynthesis <span class="inline-formula"><i>ε</i><sub>NPP</sub></span> and the disequilibrium signature <span class="inline-formula"><i>δ</i><sub>dis,la</sub></span> are shown. All values are for the period with <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M714" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="18pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="eccfdc6b626c3913a91860ccbd25bfe2"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00030.svg" width="100%" height="18pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00030.png"></image></svg></span></span> smaller than zero (<span class="inline-formula">∼</span> growing season). The results from the standard simulation (<span class="inline-formula"><i>E</i><sub>standard</sub></span>, solid lines) are compared to the preindustrial control simulation (<span class="inline-formula"><i>E</i><sub>control</sub></span>, dashed lines).</p></div><p class="downloads"><a class="triangle journal-contentLinkColor figure-download" href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-f04-high-res.pdf" target="_blank">Download</a></p></div> <p id="d2e9598">Turning to the change over the historical period, SA(<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M718" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="18pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="1409b25f573fb2b410fc4a1cad60d4e5"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00031.svg" width="100%" height="18pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00031.png"></image></svg></span></span>) is 28 % larger for the region north of 15° N (30 % larger for <span class="inline-formula">></span> 40° N and 20 % larger for 15–40° N) for <span class="inline-formula"><i>E</i><sub>standard</sub></span> than for <span class="inline-formula"><i>E</i><sub>control</sub></span>. This growth is comparable to the observed increase in C<span class="inline-formula"><sub>a</sub></span> of 32 % from the preindustrial period to the reference period of 1982–2012. In contrast, <span class="inline-formula"><i>E</i><sub>control</sub></span> sometimes exhibits larger SA(<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M724" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="18pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="728bf3ab641cb058cb55ce17192e53a8"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00032.svg" width="100%" height="18pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00032.png"></image></svg></span></span>) than <span class="inline-formula"><i>E</i><sub>standard</sub></span> in the tropical and SH ecosystems (Fig. <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.F4" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">4</a>). Following Eq. (<a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.E8" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">8</a>), the near-proportional growth in the SA(<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M726" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="18pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="07378299933a8e4a2317c90dd0395703"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00033.svg" width="100%" height="18pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00033.png"></image></svg></span></span>) and in annual mean <span class="inline-formula"><i>C</i><sub>a</sub></span> in the NH extratropics is consistent with the absence of any major long-term change in SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) at extratropical NH sites (Table <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.T1" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1</a> and Fig. S4). SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) and its change at extratropical NH sites is dominated by the large SA(<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M732" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="18pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="49fc2db86027e7b5015d3826952dbb6f"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00034.svg" width="100%" height="18pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00034.png"></image></svg></span></span>) in the northern extratropics (Fig. <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.F4" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">4</a>), and transport from low-latitude regions is less important. On the other hand, the large extratropical SA(<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M733" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="18pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="5c94db5e5cb400b9ba385af212af504e"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00035.svg" width="100%" height="18pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00035.png"></image></svg></span></span>) influences SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) and its temporal changes at lower latitudes. Without this influence, we would, based on Eq. (<a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.E8" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">8</a>), expect a decrease in SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) outside the extratropics, given that the relative increase in annual mean C<span class="inline-formula"><sub>a</sub></span> is larger than the increase in SA(<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M739" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="18pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="c9451fb23e03dcf169539d1545925260"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00036.svg" width="100%" height="18pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00036.png"></image></svg></span></span>) in these regions.</p> <p id="d2e9914"><span id="page29"></span>Factorial simulations with an individual forcing kept at preindustrial levels show small individual contributions by climate change, fossil fuel emissions, and land use to the industrial period growth in SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) at northern extratropical sites (Figs. S3 and S4). This suggests that the statistically insignificant trend in SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) at northern extratropical sites is not caused by offsetting impacts of climate change versus increasing C<span class="inline-formula"><sub>a</sub></span>. Fossil fuel emissions cause an increase and land use change a reduction in SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) at low-latitude and southern sites (Figs. S3 and S4). We attribute the dampening influence of land use change to the replacement of C<span class="inline-formula"><sub>4</sub></span> plants by C<span class="inline-formula"><sub>3</sub></span> crops, causing a general shift in the fractionation during photosynthesis to less negative values south of <span class="inline-formula">∼</span> 45° N (Fig. <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.F4" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">4</a>c). This damping influence highlights the importance of considering spatiotemporal variations in C<span class="inline-formula"><sub>3</sub></span> and C<span class="inline-formula"><sub>4</sub></span> plant distributions when analyzing <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>. In summary, the results suggest that the near-proportional growth in SA(<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M754" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="18pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="b983ab8356509d2a48cbce4caf49b3fa"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00037.svg" width="100%" height="18pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00037.png"></image></svg></span></span>) and in C<span class="inline-formula"><sub>a</sub></span> is mainly responsible for the statistically insignificant trend in SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) at high-northern-latitude sites and contributes to the statistically insignificant trend in SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) at other NH sites via atmospheric transport.</p> <p id="d2e10126">For CO<span class="inline-formula"><sub>2</sub></span>, the amplitude of the modeled zonally averaged net atmosphere-to-land CO<span class="inline-formula"><sub>2</sub></span> flux, SA(<span class="inline-formula"><i>f</i><sub>al,net</sub></span>), shows the largest values in the NH extratropics and a large increase over the historical period of 33 % in the region 15–90° N (15–40° N – 26 %; 40–90° N – 37 %) driven by a larger increase in NPP than release fluxes (<span class="inline-formula"><i>R</i></span>), whereas SA(<span class="inline-formula"><i>f</i><sub>al,net</sub></span>) is smaller in the tropics and SH and shows hardly any changes from the preindustrial (<span class="inline-formula"><i>E</i><sub>control</sub></span>) to modern (<span class="inline-formula"><i>E</i><sub>standard</sub></span>) periods south of 20° N. These results are consistent with previous studies showing northern ecosystems progressively taking up more carbon during the growing season <span class="cit" id="xref_paren.71">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx31" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Graven et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx31" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2013</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx26" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Forkel et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx26" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2016</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx75" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Piao et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx75" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2018</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx9" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Bastos et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx9" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2019</a>)</span>. For example, using carbon fluxes from two atmospheric inversions and 11 land models, <span class="cit" id="xref_text.72"><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx9" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Bastos et al.</a> (<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx9" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2019</a>)</span> find a positive trend in SA(<span class="inline-formula"><i>f</i><sub>al,net</sub></span>) north of 40° N and small or no growth in SA(<span class="inline-formula"><i>f</i><sub>al,net</sub></span>) between 25 and 40° N.</p> </div> <div class="sec"><h3 id="Ch1.S4.SS3.SSS2"><span class="label">4.3.2</span> The coupling between the seasonal amplitude of C<span class="inline-formula"><sub>a</sub></span> and <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span></h3> <p id="d2e10284"><span id="page30"></span>SA(C<span class="inline-formula"><sub>a</sub></span>) and SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) are partly coupled by the underlying carbon fluxes. The question to which extent SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) holds information independent from SA(C<span class="inline-formula"><sub>a</sub></span>) arises. We decompose <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M778" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="18pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="2c82d26bd96b56e5853d3e1ac08adf8f"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00038.svg" width="100%" height="18pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00038.png"></image></svg></span></span> in a contribution linked to the net atmosphere-to-land carbon flux, <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M779" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow></msub><mo>=</mo><mi mathvariant="normal">NPP</mi><mo>-</mo><mi>R</mi></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="80pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="57ce1ebf5e66a10f6100faf7bf2dc1f2"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00039.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00039.png"></image></svg></span></span>, and an isotopic disequilibrium flux (see Appendix <a href="https://bg.copernicus.org/articles/22/19/2025/#App1.Ch1.S1" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">A</a> and Sect. <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.S3" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">3</a> for notation; <span class="inline-formula"><i>f</i><sub>al,net</sub></span> is positive for a flux into the land biosphere): </p><div class="disp-formula" content-type="numbered" id="Ch1.E9"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M781" display="block" overflow="scroll" dspmath="mathml"><mtable><mlabeledtr><mtd><mtext>(9)</mtext></mtd><mtd><mrow> <msup> <mi mathvariant="italic">δ</mi> <mn mathvariant="normal">13</mn> </msup> <msubsup> <mi>f</mi> <mrow> <mi mathvariant="normal">al</mi> <mo>,</mo> <mi mathvariant="normal">net</mi> </mrow> <mo>*</mo> </msubsup> <mo>=</mo> <munder> <munder class="underbrace"> <mrow> <mo>(</mo> <mtext>NPP</mtext> <mo>-</mo> <mi>R</mi> <mo>)</mo> </mrow> <mo mathvariant="normal">︸</mo> </munder> <mrow> <msub> <mi>f</mi> <mrow> <mi mathvariant="normal">al</mi> <mo>,</mo> <mi mathvariant="normal">net</mi> </mrow> </msub> </mrow> </munder> <mo>⋅</mo> <msub> <mi mathvariant="italic">ε</mi> <mi mathvariant="normal">NPP</mi> </msub> <mspace linebreak="nobreak" width="0.125em"></mspace> <mo>-</mo> <mspace width="0.125em" linebreak="nobreak"></mspace> <mi>R</mi> <mo>⋅</mo> <munder> <munder class="underbrace"> <mrow> <mfenced open="(" close=")"> <mrow> <msup> <mi mathvariant="italic">δ</mi> <mn mathvariant="normal">13</mn> </msup> <msub> <mi mathvariant="normal">C</mi> <mi>R</mi> </msub> <mo>-</mo> <msup> <mi mathvariant="italic">δ</mi> <mn mathvariant="normal">13</mn> </msup> <msub> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">NPP</mi> </msub> </mrow> </mfenced> </mrow> <mo mathvariant="normal">︸</mo> </munder> <mrow> <msub> <mi mathvariant="italic">δ</mi> <mrow> <mi mathvariant="normal">dis</mi> <mo>,</mo> <mi mathvariant="normal">la</mi> </mrow> </msub> </mrow> </munder> <mo>.</mo> </mrow></mtd></mlabeledtr></mtable></math><div><svg xmlns:svg="http://www.w3.org/2000/svg" width="416pt" height="40pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="864cbf64b6767ffa624277ef9290a46c"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-e_9.svg" width="100%" height="40pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-e_9.png"></image></svg></div></div><p id="d2e10284-3"> NPP is the net primary productivity of all plants within a grid cell. <span class="inline-formula"><i>R</i></span> is the sum of all land biosphere release fluxes to the atmosphere, such as those from heterotrophic respiration, fire, mortality, and product pools, except autotrophic respiration. <span class="inline-formula"><i>δ</i><sup>13</sup>C<sub><i>R</i></sub></span> is the signature of <span class="inline-formula"><i>R</i></span>, and <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>NPP</sub></span> is the signature of NPP, with <span class="inline-formula"><i>ε</i><sub>NPP</sub></span> (or <span class="inline-formula"><i>ε</i><sub>al</sub></span>) representing the (flux-weighted) fractionation by NPP. The difference in signatures of <span class="inline-formula"><i>R</i></span> and NPP is the isotopic disequilibrium, <span class="inline-formula"><i>δ</i><sub>dis,la</sub></span>. Here, as in LPX-Bern, we have assumed that the uptake difference between gross primary production (GPP) and NPP is released on short timescales and without further carbon isotope fractionation.</p> <p id="d2e10619">Equation (<a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.E9" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">9</a>), together with Eqs. (<a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.E7" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">7</a>) and (<a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.E8" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">8</a>), provides insights into the driving factors for the seasonal amplitudes. Putting the ocean aside <span class="cit" id="xref_paren.73">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx37" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Heimann et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx37" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1989</a>)</span>, SA(C<span class="inline-formula"><sub>a</sub></span>) is driven by the spatiotemporal pattern of NPP<span class="inline-formula">−<i>R</i></span> , whereas SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) is additionally influenced by seasonal variations in <span class="inline-formula"><i>ε</i><sub>NPP</sub></span>, and the disequilibrium flux (<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M796" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>-</mo><mi>R</mi><mo>⋅</mo><msub><mi mathvariant="italic">δ</mi><mrow><mi mathvariant="normal">dis</mi><mo>,</mo><mi mathvariant="normal">la</mi></mrow></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="49pt" height="13pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="e0fe9e0a8fbf000f389956362178a7fe"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00040.svg" width="100%" height="13pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00040.png"></image></svg></span></span>). The latter is indicative of the transit time of carbon through the land biosphere.</p> <p id="d2e10704">The decomposition of zonally averaged SA(<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M797" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="18pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="eda631e2111bcae68a9215222af4f93b"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00041.svg" width="100%" height="18pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00041.png"></image></svg></span></span>) into the amplitude of constituent fluxes and their isotopic signatures is displayed in Fig. <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.F4" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">4</a> and Table S1 in the Supplement. On the global average, SA(<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M798" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow></msub><mo>⋅</mo><msub><mi mathvariant="italic">ε</mi><mi mathvariant="normal">NPP</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="54pt" height="13pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="ea79e2c7a189c42cff8d95b75b41fd68"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00042.svg" width="100%" height="13pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00042.png"></image></svg></span></span>) contributes to SA(<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M799" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="18pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="c3207c09cdcefce1f0b057d8f12456a3"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00043.svg" width="100%" height="18pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00043.png"></image></svg></span></span>) with a fraction of 90 % for both <span class="inline-formula"><i>E</i><sub>standard</sub></span> and <span class="inline-formula"><i>E</i><sub>control</sub></span>. For the region north of 40° N, SA(<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M802" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>-</mo><mi>R</mi><mo>⋅</mo><msub><mi mathvariant="italic">δ</mi><mrow><mi mathvariant="normal">dis</mi><mo>,</mo><mi mathvariant="normal">la</mi></mrow></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="49pt" height="13pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="cb96a5ebf7097df1b6f16327d053cf59"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00044.svg" width="100%" height="13pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00044.png"></image></svg></span></span>) contributes only 7 % to SA(<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M803" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="18pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="5360af53ac2cbf6b7e60aa023799cb82"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00045.svg" width="100%" height="18pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00045.png"></image></svg></span></span>) in <span class="inline-formula"><i>E</i><sub>standard</sub></span> and is almost negligible in <span class="inline-formula"><i>E</i><sub>control</sub></span> (2 %). In <span class="inline-formula"><i>E</i><sub>control</sub></span>, SA(<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M807" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>-</mo><mi>R</mi><mo>⋅</mo><msub><mi mathvariant="italic">δ</mi><mrow><mi mathvariant="normal">dis</mi><mo>,</mo><mi mathvariant="normal">la</mi></mrow></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="49pt" height="13pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="2933e0c6d177c40957b561fb8c301915"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00046.svg" width="100%" height="13pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00046.png"></image></svg></span></span>) and <span class="inline-formula"><i>δ</i><sub>dis,la</sub></span>, albeit to a smaller extent than in <span class="inline-formula"><i>E</i><sub>standard</sub></span>, are not negligible due to the lagged response of the respiration signatures to natural changes in <span class="inline-formula"><i>ε</i><sub>NPP</sub></span>. A small contribution (<span class="inline-formula">Δ<sub>trend</sub></span>) to the isotopic flux seasonality in <span class="inline-formula"><i>E</i><sub>standard</sub></span> arises from the long-term increase in flux (Fig. <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.F4" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">4</a>; see Appendix <a href="https://bg.copernicus.org/articles/22/19/2025/#App1.Ch1.S1" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">A</a>). The small contribution of the disequilibrium flux (<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M813" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>-</mo><mi>R</mi><mo>⋅</mo><msub><mi mathvariant="italic">δ</mi><mrow><mi mathvariant="normal">dis</mi><mo>,</mo><mi mathvariant="normal">la</mi></mrow></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="49pt" height="13pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="8bf398b7109c3560d63f18bb54d6c0bd"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00047.svg" width="100%" height="13pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00047.png"></image></svg></span></span>) relative to the net flux (<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M814" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow></msub><mo>⋅</mo><msub><mi mathvariant="italic">ε</mi><mi mathvariant="normal">NPP</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="54pt" height="13pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="6fade0bacfff4f9181f0c6de95add0e5"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00048.svg" width="100%" height="13pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00048.png"></image></svg></span></span>; Eq. <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.E9" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">9</a>) arises as the seasonal amplitude of the carbon release flux <span class="inline-formula"><i>R</i></span> is similar in magnitude to that of the net land carbon uptake <span class="inline-formula"><i>f</i><sub>al,net</sub></span> in the northern extratropics (blue versus red lines in Fig. <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.F4" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">4</a>b), while the disequilibrium <span class="inline-formula"><i>δ</i><sub>dis,la</sub></span> is an order of magnitude smaller than <span class="inline-formula"><i>ε</i><sub>NPP</sub></span> (Fig. <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.F4" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">4</a>c). Thus in LPX, SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) is dominated by the growing season net carbon uptake flux in northern high latitudes, suggesting that SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) holds little information on the isotopic disequilibrium at high-latitude sites. Rather, the additional information of SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) compared to SA(C<span class="inline-formula"><sub>a</sub></span>) is on the magnitude of <span class="inline-formula"><i>ε</i><sub>NPP</sub></span> at northern high-latitude sites. In contrast, the contribution by the disequilibrium flux SA(<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M827" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>-</mo><mi>R</mi><mo>⋅</mo><msub><mi mathvariant="italic">δ</mi><mrow><mi mathvariant="normal">dis</mi><mo>,</mo><mi mathvariant="normal">la</mi></mrow></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="49pt" height="13pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="a3f0f88276d8e5653789470d1328eb44"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00049.svg" width="100%" height="13pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00049.png"></image></svg></span></span>) and the contribution by the net carbon flux SA(<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M828" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow></msub><mo>⋅</mo><msub><mi mathvariant="italic">ε</mi><mi mathvariant="normal">NPP</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="54pt" height="13pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="70d7fde6ebec2407d9dd08b0e28d79d6"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00050.svg" width="100%" height="13pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00050.png"></image></svg></span></span>) are nearly equal in the tropics (10° S–10° N) and the SH (Fig. <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.F4" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">4</a>, Table S1), suggesting that SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) potentially holds additional information on <span class="inline-formula"><i>R</i></span> and carbon turnover in these regions in comparison to SA(C<span class="inline-formula"><sub>a</sub></span>).</p> <p id="d2e11236">The zonal variation in (growing season) photosynthetic fractionation <span class="inline-formula"><i>ε</i><sub>NPP</sub></span> is mainly due to differences in vegetation composition, with C<span class="inline-formula"><sub>4</sub></span> plants having considerably lower photosynthetic fractionation than C<span class="inline-formula"><sub>3</sub></span> plants (Fig. <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.F4" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">4</a>c). Land use and the evolving distribution of C<span class="inline-formula"><sub>3</sub></span> and C<span class="inline-formula"><sub>4</sub></span> crops are prescribed in the model, and C<span class="inline-formula"><sub>4</sub></span> grasses are more prevalent than C<span class="inline-formula"><sub>3</sub></span> grasses in low-latitude dryland ecosystems. Accordingly, maxima in flux-weighted, zonal-mean <span class="inline-formula"><i>ε</i><sub>NPP</sub></span> are simulated at 35° N, 12° N, and broadly around 30° S. Minima are simulated for the C<span class="inline-formula"><sub>3</sub></span>-dominated high-latitude ecosystems and tropical rainforest zone. In <span class="inline-formula"><i>E</i><sub>standard</sub></span>, <span class="inline-formula"><i>ε</i><sub>NPP</sub></span> is generally less negative than in <span class="inline-formula"><i>E</i><sub>control</sub></span> and increased by 1.18 ‰ (9 % in relative units) on the global average (SA(NPP)-weighted), mainly due to the increase in the prevalence of C<span class="inline-formula"><sub>4</sub></span> plants, while <span class="inline-formula"><i>ε</i><sub>NPP</sub></span> remains time-invariant in the C<span class="inline-formula"><sub>3</sub></span>-dominated ecosystems north of 45° N (Fig. <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.F4" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">4</a>c). To estimate the influence of the increase in C<span class="inline-formula"><sub>4</sub></span> prevalence on global mean <span class="inline-formula"><i>ε</i><sub>NPP</sub></span> (but not on global GPP), we run a factorial simulation, <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M850" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>E</mi><mrow><msub><mi mathvariant="normal">C</mi><mn mathvariant="normal">3</mn></msub></mrow></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="19pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="6e461c58bb927ffb8afa4620e4e9d685"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00051.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00051.png"></image></svg></span></span>, with the fractionation formulation for all C<span class="inline-formula"><sub>4</sub></span><span id="page31"></span> plants replaced by that for C<span class="inline-formula"><sub>3</sub></span> plants. The difference between <span class="inline-formula"><i>E</i><sub>standard</sub></span> and <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M854" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>E</mi><mrow><msub><mi mathvariant="normal">C</mi><mn mathvariant="normal">3</mn></msub></mrow></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="19pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="0cc645703a8472132d16cb3a060450fb"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00052.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00052.png"></image></svg></span></span>, i.e., the change in fractionation attributable to C<span class="inline-formula"><sub>4</sub></span> plants, amounts to about 1.5 ‰ on a global average (1982–2012 versus 1720–1750) (Fig. S5), pointing again to the importance of C<span class="inline-formula"><sub>3</sub></span> and C<span class="inline-formula"><sub>4</sub></span> plant distribution changes for <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>.</p> <p id="d2e11520"><span class="cit" id="xref_text.74"><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx56" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Keeling et al.</a> (<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx56" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2017</a>)</span> analyzed the atmospheric budgets of carbon and <span class="inline-formula"><sup>13</sup></span>C using seasonally detrended data, using a three-box land model with time-invariant overturning timescales, using globally uniform isotopic fractionation, and neglecting changes in C<span class="inline-formula"><sub>3</sub></span> and C<span class="inline-formula"><sub>4</sub></span> distribution in their standard setup. They found that global mean <span class="inline-formula"><i>ε</i><sub>NPP</sub></span> decreased by 0.66 <span class="inline-formula">±</span> 0.34 ‰ from 1975 to 2005 and attributed this change to changes in fractionation associated with mesophyll conductance and photorespiration of C<span class="inline-formula"><sub>3</sub></span> plants. It appears challenging to detect and attribute changes in the fractionation of global mean NPP with a box model, given uncertainties in NPP <span class="cit" id="xref_paren.75">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx32" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Graven et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx32" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2024</a>)</span> and changes in C<span class="inline-formula"><sub>3</sub></span> versus C<span class="inline-formula"><sub>4</sub></span> plant distribution.</p> <p id="d2e11601">While the influence of the gross exchange flux and the isotopic disequilibrium on <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> seasonality is modeled to be small at northern sites of today, it remains to be explored how global warming will change these parameters, e.g., due to changes in fire frequency and tree mortality, and affect <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> and the information provided by continued <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> observations. We may also expect different disequilibrium fluxes and, in turn, <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> seasonality if the global carbon sink is driven by a stimulation of NPP, e.g., by CO<span class="inline-formula"><sub>2</sub></span> fertilization <span class="cit" id="xref_paren.76">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx93" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Walker et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx93" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2021</a>)</span> as in LPX-Bern, versus a change in tree longevity <span class="cit" id="xref_paren.77">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx14" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Bugmann and Christof</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx14" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2011</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx61" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Körner</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx61" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2017</a>)</span>. It remains to be investigated, e.g., by applying perturbed-parameter ensembles and sensitivity simulations, whether such differences indeed significantly affect <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> seasonality.</p> <p id="d2e11721">Monitoring C<span class="inline-formula"><sub>a</sub></span> and <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> over tropical and SH land regions could potentially provide valid information to disentangle NPP, respiration, and net carbon fluxes, given the substantial contribution of the disequilibrium flux to SA(<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M882" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="18pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="34248b413455dcc99330a242d7a8f780"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00053.svg" width="100%" height="18pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00053.png"></image></svg></span></span>). However, the seasonality of <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> and C<span class="inline-formula"><sub>a</sub></span> at the tropical background monitoring sites analyzed in this study is strongly influenced by long-range transport, adding uncertainty to the interpretation of seasonal signals at background sites. Ideally, seasonally resolved observations are taken in air masses influenced primarily by regional land biosphere fluxes – thereby minimizing uncertainties from long-range transport – and interpreted with the help of atmospheric transport and land biosphere models <span class="cit" id="xref_paren.78">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx13" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Botía et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx13" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2022</a>)</span>. For example, the data may be assimilated into atmospheric transport models applied in inverse mode to infer surface carbon and isotope fluxes or assimilated into isotope-enabled land biosphere models combined with atmospheric transport to optimize parameters governing modeled carbon and isotope fluxes <span class="cit" id="xref_paren.79">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx73" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Peylin et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx73" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2016</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx91" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">van der Velde et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx91" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2018</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx16" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Castro-Morales et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx16" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2019</a>)</span>.</p> </div> </div><div class="sec"><h2 id="Ch1.S4.SS4"><span class="label">4.4</span> Implications for stomatal conductance and water use</h2> <p id="d2e11821">Our result of a time-invariant <span class="inline-formula"><i>ε</i><sub>NPP</sub></span> in northern extratropical regions holds implications for carbon and water fluxes and evaporative cooling. The good agreement between observations and model results for SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) and its temporal trend at northern sites provides implicit support for regulation of stomatal conductance by C<span class="inline-formula"><sub>3</sub></span> plants towards a constant ratio of the CO<span class="inline-formula"><sub>2</sub></span> mole fraction in the leaf intercellular space (<span class="inline-formula"><i>c</i><sub>i</sub></span>) and ambient atmospheric air (<span class="inline-formula"><i>c</i><sub>a</sub></span>) on the continental scale. Following <span class="cit" id="xref_text.80"><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx22" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Farquhar</a> (<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx22" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1989</a>)</span> and <span class="cit" id="xref_text.81"><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx18" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Cernusak et al.</a> (<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx18" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2013</a>)</span>, <span class="inline-formula"><i>ε</i><sub>NPP</sub></span> is approximately proportional to <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M894" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>c</mi><mi mathvariant="normal">i</mi></msub><mo>/</mo><msub><mi>c</mi><mi mathvariant="normal">a</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="28pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="8a4cfd269b71038800c1c7bcde7b18f4"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00054.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00054.png"></image></svg></span></span>: </p><div class="disp-formula" content-type="numbered" id="Ch1.E10"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M895" display="block" overflow="scroll" dspmath="mathml"><mtable><mlabeledtr><mtd><mtext>(10)</mtext></mtd><mtd><mrow> <msub> <mi mathvariant="italic">ε</mi> <mi mathvariant="normal">NPP</mi> </msub> <mo>=</mo> <mo>-</mo> <mfenced close=")" open="("> <mrow> <mi>a</mi> <mo>+</mo> <mo>(</mo> <mi>b</mi> <mo>-</mo> <mi>a</mi> <mo>)</mo> <mo>⋅</mo> <mstyle displaystyle="true"> <mfrac style="display"> <mrow> <msub> <mi>c</mi> <mi mathvariant="normal">i</mi> </msub> </mrow> <mrow> <msub> <mi>c</mi> <mi mathvariant="normal">a</mi> </msub> </mrow> </mfrac> </mstyle> </mrow> </mfenced> <mo>,</mo> </mrow></mtd></mlabeledtr></mtable></math><div><svg xmlns:svg="http://www.w3.org/2000/svg" width="416pt" height="29pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="9f027fded6f0a5501cca85dad92a069a"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-e_10.svg" width="100%" height="29pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-e_10.png"></image></svg></div></div><p id="d2e11821-3"> with <span class="inline-formula"><i>a</i></span> (4.4) and <span class="inline-formula"><i>b</i></span> (27) being constants. Two contrasting scenarios are published for the regulation of leaf stomatal conductance for C<span class="inline-formula"><sub>3</sub></span> plants. First, many site studies (Voelker et al., 2016; Saurer et al., 2014; Kauwe et al., 2013; Peñuelas et al., 2011; Frank et al., 2015; Keller et al., 2017) suggest a regulation of stomatal conductance towards a constant <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M899" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>c</mi><mi mathvariant="normal">i</mi></msub><mo>/</mo><msub><mi>c</mi><mi mathvariant="normal">a</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="28pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="252f360090b486ecfec96bbe0080b890"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00055.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00055.png"></image></svg></span></span> and, hence, suggest that <span class="inline-formula"><i>c</i><sub>i</sub></span> grows proportionally to <span class="inline-formula"><i>c</i><sub>a</sub></span>. An absent temporal trend in <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M902" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>c</mi><mi mathvariant="normal">i</mi></msub><mo>/</mo><msub><mi>c</mi><mi mathvariant="normal">a</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="28pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="4f440a7f1cad8d434f65d6eef7b9098b"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00056.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00056.png"></image></svg></span></span> translates into an absent trend in <span class="inline-formula"><i>ε</i><sub>NPP</sub></span> and vice versa (Eq. <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.E10" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">10</a>). Focusing on regions north of <span class="inline-formula">></span> 40° N, where carbon fluxes are largest and C<span class="inline-formula"><sub>3</sub></span> plants dominate, LPX-Bern simulates a small role of isotopic disequilibrium fluxes and a dominant influence of net atmosphere–surface fluxes on SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) (Fig. <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.F4" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">4</a>, green versus blue lines). Importantly, LPX-Bern simulates small temporal changes in the (flux-weighted) fractionation of the zonally and seasonally integrated NPP at northern sites (Fig. <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.F4" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">4</a>c, green lines) and a stomatal regulation towards constant <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M908" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>c</mi><mi mathvariant="normal">i</mi></msub><mo>/</mo><msub><mi>c</mi><mi mathvariant="normal">a</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="28pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="2995c83445c0f20008c45c6fd26c9c33"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00057.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00057.png"></image></svg></span></span>. In turn, the good model–data agreement in the temporal trends of SA(C<span class="inline-formula"><sub>a</sub></span>) and SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) implies consistency with the observational evidence for this scenario towards constant <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M912" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>c</mi><mi mathvariant="normal">i</mi></msub><mo>/</mo><msub><mi>c</mi><mi mathvariant="normal">a</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="28pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="afc04d16212a81d5e9a1c984bc863f37"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00058.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00058.png"></image></svg></span></span>.</p> <p id="d2e12183"><span id="page32"></span>In contrast, <span class="cit" id="xref_text.82"><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx11" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Battipaglia et al.</a> (<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx11" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2013</a>)</span> and <span class="cit" id="xref_text.83"><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx57" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Keenan et al.</a> (<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx57" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2013</a>)</span> suggest a regulation of stomatal conductance towards a constant <span class="inline-formula"><i>c</i><sub>i</sub></span> and a decreasing ratio of <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M914" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>c</mi><mi mathvariant="normal">i</mi></msub><mo>/</mo><msub><mi>c</mi><mi mathvariant="normal">a</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="28pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="d5ba70cb464428820a0dcbe30128dbca"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00059.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00059.png"></image></svg></span></span> under rising C<span class="inline-formula"><sub>a</sub></span>. Evaluating Eq. (<a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.E10" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">10</a>) for 1980–2022, the period with <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> measurements, yields a decrease in <span class="inline-formula"><i>ε</i><sub>NPP</sub></span> of 15 % (<span class="inline-formula">−3.0</span> ‰ to <span class="inline-formula">−3.8</span> ‰) for an initial <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M921" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>c</mi><mi mathvariant="normal">i</mi></msub><mo>/</mo><msub><mi>c</mi><mi mathvariant="normal">a</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="28pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="1174ffc3fb85bb242c4566e130f4756b"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00060.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00060.png"></image></svg></span></span> ratio in the range of 0.7 to 0.9 and constant <span class="inline-formula"><i>c</i><sub>i</sub></span>. We argue that the good observation–model agreement in the simulated trends in SA(C<span class="inline-formula"><sub>a</sub></span>) implies that the influence of the simulated net atmosphere–land carbon flux is realistic, and SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) would decrease if <span class="inline-formula"><i>ε</i><sub>NPP</sub></span> decreases. A decrease in SA(<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) of 15 % would emerge from the noise of variability at individual northern sites. Taken together, we suggest that the scenario towards constant <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M929" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>c</mi><mi mathvariant="normal">i</mi></msub><mo>/</mo><msub><mi>c</mi><mi mathvariant="normal">a</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="28pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="422d6817c05d0341162f85c34979a89a"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00061.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00061.png"></image></svg></span></span> is consistent with the observations, whereas the scenario towards constant <span class="inline-formula"><i>c</i><sub>i</sub></span> appears less likely. However, uncertainties remain, and our conclusions for the two scenarios of stomatal regulation await confirmation by other modeling studies.</p> <p id="d2e12404">The two scenarios imply large differences in water fluxes <span class="cit" id="xref_paren.84">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx60" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Knauer et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx60" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2017</a>)</span>. The intrinsic water use efficiency (iWUE), the ratio between assimilation of CO<span class="inline-formula"><sub>2</sub></span> by photosynthesis (<span class="inline-formula"><i>A</i></span>) and conductance of CO<span class="inline-formula"><sub>2</sub></span> (<span class="inline-formula"><i>g</i></span>), is, as <span class="inline-formula"><i>ε</i><sub>NPP</sub></span>, a function of <span class="inline-formula"><i>c</i><sub>i</sub></span> and <span class="inline-formula"><i>c</i><sub>a</sub></span>: </p><div class="disp-formula" content-type="numbered" id="Ch1.E11"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M938" display="block" overflow="scroll" dspmath="mathml"><mtable><mlabeledtr><mtd><mtext>(11)</mtext></mtd><mtd><mrow> <mi mathvariant="normal">iWUE</mi> <mo>=</mo> <mstyle displaystyle="true"> <mfrac style="display"> <mi>A</mi> <mi>g</mi> </mfrac> </mstyle> <mo>=</mo> <msub> <mi>c</mi> <mi mathvariant="normal">a</mi> </msub> <mo>⋅</mo> <mfenced close=")" open="("> <mrow> <mn mathvariant="normal">1</mn> <mo>-</mo> <mstyle displaystyle="true"> <mfrac style="display"> <mrow> <msub> <mi>c</mi> <mi mathvariant="normal">i</mi> </msub> </mrow> <mrow> <msub> <mi>c</mi> <mi mathvariant="normal">a</mi> </msub> </mrow> </mfrac> </mstyle> </mrow> </mfenced> <mo>.</mo> </mrow></mtd></mlabeledtr></mtable></math><div><svg xmlns:svg="http://www.w3.org/2000/svg" width="416pt" height="29pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="b3ab9cb140e32ee566f4fc396ec3f20d"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-e_11.svg" width="100%" height="29pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-e_11.png"></image></svg></div></div><p id="d2e12404-3"> iWUE would have increased from 1980 to 2022 by 23 % for constant <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M939" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>c</mi><mi mathvariant="normal">i</mi></msub><mo>/</mo><msub><mi>c</mi><mi mathvariant="normal">a</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="28pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="00995d95f4f67f3f665d93d27610dea1"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00062.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00062.png"></image></svg></span></span> but by 77 % to 231 % for constant <span class="inline-formula"><i>c</i><sub>i</sub></span>, assuming an initial <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M941" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>c</mi><mi mathvariant="normal">i</mi></msub><mo>/</mo><msub><mi>c</mi><mi mathvariant="normal">a</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="28pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="e46f5c7237ebda73c35002cd492733ba"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00063.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00063.png"></image></svg></span></span> of 0.7 to 0.9. In the latter scenario, stomatal conductance and correspondingly water loss per stomatal pore would have decreased strongly over the last decades.</p> <p id="d2e12571">Equation (<a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.E10" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">10</a>) is an approximation <span class="cit" id="xref_paren.85">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx24" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Farquhar et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx24" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1982</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx64" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Lloyd and Farquhar</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx64" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1994</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx23" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Farquhar and Cernusak</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx23" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2012</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx18" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Cernusak et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx18" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2013</a>)</span> considered to be sufficient for many applications by <span class="cit" id="xref_text.86"><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx18" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Cernusak et al.</a> (<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx18" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2013</a>)</span> and applied in the publications cited in the previous two paragraphs. However, there are four contributions only implicitly considered by choosing parameter <span class="inline-formula"><i>b</i></span> in Eq. (<a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.E10" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">10</a>), and these may contribute small temporal trends to <span class="inline-formula"><i>ε</i><sub>NPP</sub></span>. In turn, inferred <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M944" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>c</mi><mi mathvariant="normal">i</mi></msub><mo>/</mo><msub><mi>c</mi><mi mathvariant="normal">a</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="28pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="5d9e724b26d7e2a08ac01ade4afd1c57"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00064.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00064.png"></image></svg></span></span> would also have a temporal trend for a constant <span class="inline-formula"><i>ε</i><sub>NPP</sub></span>. We estimate the trend contribution of these additional terms to be of small magnitude (<span class="inline-formula"><1</span> ‰) in comparison to the 3 ‰ to 3.8 ‰ difference estimated for our two scenarios (see Appendix <a href="https://bg.copernicus.org/articles/22/19/2025/#App1.Ch1.S2" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">B</a> for details).</p> </div></div><span class="section4-mobile-bottom-border mobile-bottom-border hide-on-desktop hide-on-tablet"></span></div> <div class="sec conclusions" id="section5"><div class="grid-container no-margin header-element"><span class="grid-100 mobile-grid-100 tablet-grid-100 grid-parent more-less-mobile" data-hide="#section5 .co-arrow-open,.section5-content" data-show="#section5 .co-arrow-closed,.section5-mobile-bottom-border"><div id="Ch1.S5" class="h1"><span class="label">5</span> Conclusions<span class="hide-on-desktop hide-on-tablet triangleWrapper"> <i class="co-arrow-closed"></i><i class="co-arrow-open" style="display:none"></i></span></div></span></div> <div class="section5-content show-no-js hide-on-mobile-soft"><p id="d2e12653">We explored the global-scale mechanisms driving the observed seasonal cycles of <span class="inline-formula"><i>δ</i><sup>13</sup></span>C of atmospheric CO<span class="inline-formula"><sub>2</sub></span> (<span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>) and of atmospheric CO<span class="inline-formula"><sub>2</sub></span> at 19 monitoring sites using atmosphere–surface fluxes from the Bern3D-LPX Earth system model of intermediate complexity and fossil fuel emissions in combination with transport matrices from the TM3 atmospheric transport model. We find good data–model agreement at northern and tropical sites. No significant trends are detected or modeled in the seasonal cycle amplitude of <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> at most monitoring sites, in contrast to the positive trends in the seasonal amplitude of CO<span class="inline-formula"><sub>2</sub></span>. We attribute the statistically insignificant trend in the seasonal amplitude of <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> to a near-equal percentage increase in the growing season net carbon uptake and isotope flux and in the background atmospheric CO<span class="inline-formula"><sub>2</sub></span> in the northern extratropical land regions. Over the industrial period and at low-latitude and SH sites, land use change has a dampening influence on <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> seasonality through the replacement of C<span class="inline-formula"><sub>3</sub></span> plants by C<span class="inline-formula"><sub>4</sub></span> crops. Modeled isotopic disequilibrium fluxes have a small influence on the seasonal signal of <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> at NH sites but play an important role in tropical and SH ecosystems, suggesting that monitoring the <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> seasonality over tropical and SH land would provide valuable information on gross carbon exchange fluxes and the timescales of carbon turnover in the land biosphere. Our results, based on a single model chain, provide implicit support for a regulation of the stomatal conductance of C<span class="inline-formula"><sub>3</sub></span> plants towards a constant <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M967" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>c</mi><mi mathvariant="normal">i</mi></msub><mo>/</mo><msub><mi>c</mi><mi mathvariant="normal">a</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="28pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="50e43be77d1868256947b7dffdd70598"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00065.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00065.png"></image></svg></span></span> ratio on biome scales and for intrinsic water use efficiency to grow proportionally to atmospheric CO<span class="inline-formula"><sub>2</sub></span> over recent decades, with implications for carbon and water fluxes. More generally, the results suggest that observations of the <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> seasonal cycle offer highly useful information on carbon and water cycle processes. We recommend seasonally resolved <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> observations as a constraint for land biosphere models used to simulate the terrestrial sink of anthropogenic carbon and land use emissions, for example, using perturbed parameter ensembles in Bayesian approaches <span class="cit" id="xref_paren.87">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx63" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Lienert and Joos</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx63" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2018</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx91" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">van der Velde et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx91" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2018</a>)</span>. Future studies may employ an ensemble of isotope-enabled models and perturbed parameter ensembles to elucidate whether our findings are robust and to show which models or process assumptions are compatible or incompatible with <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> data for improved projections of atmospheric CO<span class="inline-formula"><sub>2</sub></span> and global warming.</p></div><span class="section5-mobile-bottom-border mobile-bottom-border hide-on-desktop hide-on-tablet"></span></div> <div class="app sec" id="section6"> <div class="grid-container no-margin header-element"><span class="grid-100 mobile-grid-100 tablet-grid-100 grid-parent more-less-mobile" data-hide="#section6 .co-arrow-open,.section6-content" data-show="#section6 .co-arrow-closed,.section6-mobile-bottom-border"><div id="App1.Ch1.S1" class="h1"><span>Appendix A:</span> Decomposition of <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M976" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">as</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="44pt" height="17pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="4f8c1e5d9da4e0220a7da897010cd33a"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00066.svg" width="100%" height="17pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00066.png"></image></svg></span></span> and the calculation of seasonal amplitudes<span class="hide-on-desktop hide-on-tablet triangleWrapper"> <i class="co-arrow-closed"></i><i class="co-arrow-open" style="display:none"></i></span></div></span></div> <div class="section6-content show-no-js hide-on-mobile-soft"><p id="d2e12989">We reformulate the net isotope flux in terms of net and gross carbon fluxes, isotopic fractionation, and isotopic disequilibrium (e.g., <span class="cit" id="xref_altparen.88"><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx70" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Mook</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx70" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1986</a>; <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx44" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Joos and Bruno</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx44" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">1998</a></span>) to diagnose their influence on the seasonal cycles.</p><p id="d2e12995"><span id="page33"></span>The fractionation for a gross flux, e.g., from the atmosphere to the surface, is </p><div class="disp-formula" content-type="numbered" id="App1.Ch1.S1.E12"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M977" display="block" overflow="scroll" dspmath="mathml"><mtable><mlabeledtr><mtd><mtext>(A1)</mtext></mtd><mtd><mrow> <msub> <mi mathvariant="italic">ε</mi> <mi mathvariant="normal">as</mi> </msub> <mo>≅</mo> <mo>(</mo> <msup> <mi mathvariant="italic">δ</mi> <mn mathvariant="normal">13</mn> </msup> <msub> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">as</mi> </msub> <mo>-</mo> <msup> <mi mathvariant="italic">δ</mi> <mn mathvariant="normal">13</mn> </msup> <msub> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">a</mi> </msub> <mo>)</mo> <mo>,</mo> </mrow></mtd></mlabeledtr></mtable></math><div><svg xmlns:svg="http://www.w3.org/2000/svg" width="416pt" height="15pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="ec53b8ece87125dd167d8b8b9bb8f39a"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-e_A1.svg" width="100%" height="15pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-e_A1.png"></image></svg></div></div><p id="d2e12995-3"> with <span class="inline-formula"><i>δ</i><sup>13</sup>C<sub>as</sub></span> the signature of the gross flux from <span class="inline-formula"><i>a</i></span> to <span class="inline-formula"><i>s</i></span> (<span class="inline-formula"><i>f</i><sub>as</sub></span>) and <span class="inline-formula"><i>δ</i><sup>13</sup>C<sub>a</sub></span> the signature of the source. The isotopic disequilibrium (or difference) between atmosphere–surface gross fluxes is </p><div class="disp-formula" content-type="numbered" id="App1.Ch1.S1.E13"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M983" display="block" overflow="scroll" dspmath="mathml"><mtable><mlabeledtr><mtd><mtext>(A2)</mtext></mtd><mtd><mrow> <msub> <mi mathvariant="italic">δ</mi> <mrow> <mi mathvariant="normal">dis</mi> <mo>,</mo> <mi mathvariant="normal">sa</mi> </mrow> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi mathvariant="italic">δ</mi> <mrow> <mi mathvariant="normal">dis</mi> <mo>,</mo> <mi mathvariant="normal">as</mi> </mrow> </msub> <mo>=</mo> <mfenced close=")" open="("> <mrow> <msup> <mi mathvariant="italic">δ</mi> <mn mathvariant="normal">13</mn> </msup> <msub> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">sa</mi> </msub> <mo>-</mo> <msup> <mi mathvariant="italic">δ</mi> <mn mathvariant="normal">13</mn> </msup> <msub> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">as</mi> </msub> </mrow> </mfenced> <mo>.</mo> </mrow></mtd></mlabeledtr></mtable></math><div><svg xmlns:svg="http://www.w3.org/2000/svg" width="416pt" height="22pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="899d56c0995e8184eb5eb483f062a8bb"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-e_A2.svg" width="100%" height="22pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-e_A2.png"></image></svg></div></div><p id="d2e12995-5"> The net carbon and isotope fluxes are the differences between the gross fluxes: </p><span id="App1.Ch1.S1.E14" class="equationLink"></span><span id="App1.Ch1.S1.E15" class="equationLink"></span><div class="disp-formula" content-type="numbered" specific-use="gather"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M984" display="block" overflow="scroll" dspmath="mathml"><mtable displaystyle="true"><mlabeledtr><mtd><mtext>(A3)</mtext></mtd><mtd><mrow><mstyle class="stylechange" displaystyle="true"></mstyle><msub><mi>f</mi><mrow><mi mathvariant="normal">as</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow></msub><mo>=</mo><msub><mi>f</mi><mi mathvariant="normal">as</mi></msub><mo>-</mo><msub><mi>f</mi><mi mathvariant="normal">sa</mi></msub></mrow></mtd></mlabeledtr><mlabeledtr><mtd><mtext>(A4)</mtext></mtd><mtd><mrow><mstyle displaystyle="true" class="stylechange"></mstyle><mtable rowspacing="0.2ex" class="split" displaystyle="true" columnalign="right left"><mtr><mtd><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">as</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></mtd><mtd><mrow><mo>=</mo><msub><mi>f</mi><mi mathvariant="normal">as</mi></msub><mo>⋅</mo><mfenced close=")" open="("><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msub><mi mathvariant="normal">C</mi><mi mathvariant="normal">as</mi></msub><mo>-</mo><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msub><mi mathvariant="normal">C</mi><mi mathvariant="normal">a</mi></msub></mrow></mfenced></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mrow><mo>-</mo><msub><mi>f</mi><mi mathvariant="normal">sa</mi></msub><mo>⋅</mo><mfenced open="(" close=")"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msub><mi mathvariant="normal">C</mi><mi mathvariant="normal">sa</mi></msub><mo>-</mo><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msub><mi mathvariant="normal">C</mi><mi mathvariant="normal">a</mi></msub></mrow></mfenced><mo>.</mo></mrow></mtd></mtr></mtable></mrow></mtd></mlabeledtr></mtable></math><div><svg xmlns:svg="http://www.w3.org/2000/svg" width="416pt" height="63pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="8f1ff3772b830e2cd1ec711ee5e3ed32"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-e_A3_A4.svg" width="100%" height="63pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-e_A3_A4.png"></image></svg></div></div><p id="d2e12995-7"> Rearranging yields </p><div class="disp-formula" content-type="numbered" id="App1.Ch1.S1.E16"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M985" display="block" overflow="scroll" dspmath="mathml"><mtable><mlabeledtr><mtd><mtext>(A5)</mtext></mtd><mtd><mtable class="split" rowspacing="0.2ex" displaystyle="true" columnalign="right left"> <mtr> <mtd> <mrow> <msup> <mi mathvariant="italic">δ</mi> <mn mathvariant="normal">13</mn> </msup> <msubsup> <mi>f</mi> <mrow> <mi mathvariant="normal">as</mi> <mo>,</mo> <mi mathvariant="normal">net</mi> </mrow> <mo>*</mo> </msubsup> </mrow> </mtd> <mtd> <mrow> <mo>=</mo> <msub> <mi>f</mi> <mrow> <mi mathvariant="normal">as</mi> <mo>,</mo> <mi mathvariant="normal">net</mi> </mrow> </msub> <mo>⋅</mo> <munder> <munder class="underbrace"> <mrow> <mfenced close=")" open="("> <mrow> <msup> <mi mathvariant="italic">δ</mi> <mn mathvariant="normal">13</mn> </msup> <msub> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">as</mi> </msub> <mo>-</mo> <msup> <mi mathvariant="italic">δ</mi> <mn mathvariant="normal">13</mn> </msup> <msub> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">a</mi> </msub> </mrow> </mfenced> </mrow> <mo mathvariant="normal">︸</mo> </munder> <mrow> <msub> <mi mathvariant="italic">ε</mi> <mi mathvariant="normal">as</mi> </msub> </mrow> </munder> </mrow> </mtd> </mtr> <mtr> <mtd></mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>f</mi> <mi mathvariant="normal">sa</mi> </msub> <mo>⋅</mo> <munder> <munder class="underbrace"> <mrow> <mfenced open="(" close=")"> <mrow> <msup> <mi mathvariant="italic">δ</mi> <mn mathvariant="normal">13</mn> </msup> <msub> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">sa</mi> </msub> <mo>-</mo> <msup> <mi mathvariant="italic">δ</mi> <mn mathvariant="normal">13</mn> </msup> <msub> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">as</mi> </msub> </mrow> </mfenced> </mrow> <mo mathvariant="normal">︸</mo> </munder> <mrow> <msub> <mi mathvariant="italic">δ</mi> <mrow> <mi mathvariant="normal">dis</mi> <mo>,</mo> <mi mathvariant="normal">sa</mi> </mrow> </msub> </mrow> </munder> <mo>.</mo> </mrow> </mtd> </mtr> </mtable></mtd></mlabeledtr></mtable></math><div><svg xmlns:svg="http://www.w3.org/2000/svg" width="416pt" height="82pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="e4dbbb6ad4421f36eb31ba9a2af3d9ba"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-e_A5.svg" width="100%" height="82pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-e_A5.png"></image></svg></div></div><p id="d2e12995-9"> For the land biosphere (l), it follows from Eqs. (<a href="https://bg.copernicus.org/articles/22/19/2025/#App1.Ch1.S1.E14" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">A3</a>) and (<a href="https://bg.copernicus.org/articles/22/19/2025/#App1.Ch1.S1.E16" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">A5</a>) that </p><span id="App1.Ch1.S1.E17" class="equationLink"></span><span id="App1.Ch1.S1.E18" class="equationLink"></span><div class="disp-formula" content-type="numbered" specific-use="gather"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M986" display="block" overflow="scroll" dspmath="mathml"><mtable displaystyle="true"><mlabeledtr><mtd><mtext>(A6)</mtext></mtd><mtd><mrow><mstyle class="stylechange" displaystyle="true"></mstyle><msub><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow></msub><mo>=</mo><mi mathvariant="normal">NPP</mi><mo>-</mo><mi>R</mi></mrow></mtd></mlabeledtr><mlabeledtr><mtd><mtext>(A7)</mtext></mtd><mtd><mrow><mstyle class="stylechange" displaystyle="true"></mstyle><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup><mo>=</mo><msub><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow></msub><mo>⋅</mo><msub><mi mathvariant="italic">ε</mi><mi mathvariant="normal">NPP</mi></msub><mspace width="0.125em" linebreak="nobreak"></mspace><mo>-</mo><mspace linebreak="nobreak" width="0.125em"></mspace><mi>R</mi><mo>⋅</mo><msub><mi mathvariant="italic">δ</mi><mrow><mi mathvariant="normal">dis</mi><mo>,</mo><mi mathvariant="normal">la</mi></mrow></msub><mo>,</mo></mrow></mtd></mlabeledtr></mtable></math><div><svg xmlns:svg="http://www.w3.org/2000/svg" width="416pt" height="34pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="a796caccdfb1d164ef33d90925400ab2"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-e_A6_A7.svg" width="100%" height="34pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-e_A6_A7.png"></image></svg></div></div><p id="d2e12995-11"> with </p><div class="disp-formula" content-type="numbered" id="App1.Ch1.S1.E19"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M987" display="block" overflow="scroll" dspmath="mathml"><mtable><mlabeledtr><mtd><mtext>(A8)</mtext></mtd><mtd><mrow> <msub> <mi mathvariant="italic">δ</mi> <mrow> <mi mathvariant="normal">dis</mi> <mo>,</mo> <mi mathvariant="normal">la</mi> </mrow> </msub> <mo>=</mo> <msup> <mi mathvariant="italic">δ</mi> <mn mathvariant="normal">13</mn> </msup> <msub> <mi mathvariant="normal">C</mi> <mi>R</mi> </msub> <mo>-</mo> <msup> <mi mathvariant="italic">δ</mi> <mn mathvariant="normal">13</mn> </msup> <msub> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">NPP</mi> </msub> <mo>.</mo> </mrow></mtd></mlabeledtr></mtable></math><div><svg xmlns:svg="http://www.w3.org/2000/svg" width="416pt" height="16pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="e9471952cc69bf92a0aafab2a3cf2884"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-e_A8.svg" width="100%" height="16pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-e_A8.png"></image></svg></div></div><p id="d2e12995-13"> NPP is the net primary productivity of all plants within a grid cell. <span class="inline-formula"><i>R</i></span> is the sum of all release fluxes to the atmosphere, such as those from heterotrophic respiration, fire, mortality, and product pools, except autotrophic respiration. <span class="inline-formula"><i>δ</i><sup>13</sup>C<sub><i>R</i></sub></span> is the signature of <span class="inline-formula"><i>R</i></span>, and <span class="inline-formula"><i>δ</i><sup>13</sup>C<sub>NPP</sub></span> is the signature of NPP, with <span class="inline-formula"><i>ε</i><sub>NPP</sub></span> (or <span class="inline-formula"><i>ε</i><sub>al</sub></span>) representing the (flux-weighted) fractionation by NPP.</p><p id="d2e13637">The seasonal amplitudes of <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M994" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="18pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="04b98c627a2b94828fcc2b346eee213d"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00067.svg" width="100%" height="18pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00067.png"></image></svg></span></span> and its components are calculated as follows. The time series of <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M995" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="18pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="7684e9b8b8c23d95c32d55272651ea96"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00068.svg" width="100%" height="18pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00068.png"></image></svg></span></span> is detrended and normalized to zero. The trend is computed by a rolling 12-month mean of <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M996" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="18pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="7433a9b83c382c1da202410be711babf"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00069.svg" width="100%" height="18pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00069.png"></image></svg></span></span>. Then, the resulting trend curve is subtracted from <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M997" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="18pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="ee3fa3e9db6b293be3573f416b6c4e62"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00070.svg" width="100%" height="18pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00070.png"></image></svg></span></span> (disregarding the first and last 6 months of the original series) to get a detrended curve. Finally, the detrended curve is normalized by subtracting its period mean. <span class="inline-formula">Δ<sub>trend</sub></span> (e.g., in units of mol ‰ yr<span class="inline-formula"><sup>−1</sup></span> m<span class="inline-formula"><sup>−2</sup></span>) is the difference between <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1001" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="18pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="9ad6fc8f58b7d1b1c16da2741c6a5029"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00071.svg" width="100%" height="18pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00071.png"></image></svg></span></span> after and before this detrending and normalizing procedure. We define a seasonal mask to compute seasonal amplitudes of fluxes and their signatures. For each model year, we identify months in which detrended <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1002" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="18pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="bc6b8feb7af1c41302c117228b5443d7"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00072.svg" width="100%" height="18pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00072.png"></image></svg></span></span> is negative or equal to zero (roughly corresponding to the growing season). The sum of fluxes of these months is then termed the seasonal amplitude in a given year. For <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1003" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="18pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="13390bee2234affb6f1afc0687bf2504"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00073.svg" width="100%" height="18pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00073.png"></image></svg></span></span>, this procedure is consistent with considering the difference between maximum and minimum values of the detrended cumulative sum of <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1004" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="18pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="40412709a99f53c0032afa931c3f87d1"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00074.svg" width="100%" height="18pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00074.png"></image></svg></span></span>. Accordingly, the seasonal amplitudes of the component fluxes contributing to <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1005" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="18pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="c2853b81dd8fa277061d1707ce7db296"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00075.svg" width="100%" height="18pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00075.png"></image></svg></span></span> are computed by summation over months where <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1006" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="18pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="7c001e64e68165bed29920a19181d210"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00076.svg" width="100%" height="18pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00076.png"></image></svg></span></span> is less than or equal to zero within a given year. Component fluxes are [<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1007" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>(</mo><mi mathvariant="normal">NPP</mi><mo>-</mo><mi>R</mi><mo>)</mo><mo>⋅</mo><msub><mi mathvariant="italic">ε</mi><mi mathvariant="normal">NPP</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="80pt" height="13pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="f2645d0da44b38897a941913d45bc124"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00077.svg" width="100%" height="13pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00077.png"></image></svg></span></span>], [<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1008" display="inline" overflow="scroll" dspmath="mathml"><mrow><mi>R</mi><mo>⋅</mo><msub><mi mathvariant="italic">δ</mi><mrow><mi mathvariant="normal">dis</mi><mo>,</mo><mi mathvariant="normal">la</mi></mrow></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="41pt" height="13pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="6846a576a2a61fa2bf2ebcf07729fafe"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00078.svg" width="100%" height="13pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00078.png"></image></svg></span></span>], [<span class="inline-formula">Δ<sub>trend</sub></span>] and, further, [NPP], [<span class="inline-formula"><i>R</i></span>], and [<span class="inline-formula">NPP−<i>R</i></span>] (Fig. <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.F4" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">4</a>). These component fluxes are not detrended to readily calculate the signatures <span class="inline-formula"><i>δ</i><sub>dis,la</sub></span> and <span class="inline-formula"><i>ε</i><sub>NPP</sub></span> by division of the seasonal amplitude isotopic flux with the corresponding seasonal amplitude carbon flux.</p><p id="d2e14011">We note that the annual climatological mean values of the isotopic disequilibrium (<span class="inline-formula"><i>δ</i><sub>dis,la</sub></span>), the net carbon flux (<span class="inline-formula"><i>f</i><sub>al,net</sub></span>), and the net isotopic flux (<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1016" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="18pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="bca00747c1d4e467505e0000805399c2"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00079.svg" width="100%" height="18pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00079.png"></image></svg></span></span>) vanish by definition for the preindustrial equilibrium. However, this does not hold for their seasonal amplitudes. Further, detrending <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1017" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">al</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="42pt" height="18pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="c2bdc296a64c0deeb6da27be41f18d27"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00080.svg" width="100%" height="18pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00080.png"></image></svg></span></span> before the computation of its seasonal amplitude is consistent with the calculation of the C<span class="inline-formula"><sub>a</sub></span> and <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> seasonal amplitude from the detrended atmospheric time series.</p><p id="d2e14122">The seasonal cycles of C<span class="inline-formula"><sub>a</sub></span> or <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span> are computed from observations and the TM3 results using the following procedure for either C<span class="inline-formula"><sub>a</sub></span> or <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>. Months with missing values in either the observations or the TM3 simulation are masked in the TM3 and observational time series. Then the time series are detrended using a 12-month rolling mean, and the overall mean of the series is set to zero to get (for year, <span class="inline-formula"><i>y</i></span>, and month, <span class="inline-formula"><i>m</i></span>) seasonal anomalies <span class="inline-formula">Δ</span>C<span class="inline-formula"><sub>a</sub></span>(<span class="inline-formula"><i>y</i>,<i>m</i></span>) and <span class="inline-formula">Δ<i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>(<span class="inline-formula"><i>y</i>,<i>m</i></span>). Finally, the period means for each calendar month, <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1035" display="inline" overflow="scroll" dspmath="mathml"><mover accent="true"><mrow><mi mathvariant="normal">Δ</mi><msub><mi mathvariant="normal">C</mi><mi mathvariant="normal">a</mi></msub><mo>(</mo><mi>m</mi><mo>)</mo></mrow><mo mathvariant="normal">‾</mo></mover></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="40pt" height="16pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="8d8c47c08f8210bfda8fb2c15e7ab1ae"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00081.svg" width="100%" height="16pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00081.png"></image></svg></span></span> and <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1036" display="inline" overflow="scroll" dspmath="mathml"><mover accent="true"><mrow><mi mathvariant="normal">Δ</mi><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msub><mtext>C</mtext><mi mathvariant="normal">a</mi></msub><mo>(</mo><mi>m</mi><mo>)</mo></mrow><mo mathvariant="normal">‾</mo></mover></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="56pt" height="17pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="4483569f4cdabf5bbe03821509e050ac"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00082.svg" width="100%" height="17pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00082.png"></image></svg></span></span>, are computed by averaging over all corresponding monthly values. Additionally, the standard deviation is computed for each calendar month to inform about the interannual variability in the seasonality. The period-mean SA is computed as the difference between the month with the highest (<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1037" display="inline" overflow="scroll" dspmath="mathml"><mover accent="true"><mrow><msub><mi>m</mi><mo>max</mo></msub></mrow><mo mathvariant="normal">‾</mo></mover></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="27pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="a41e2f60ee63af0b3fd4010be2b7498d"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00083.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00083.png"></image></svg></span></span>) and lowest (<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1038" display="inline" overflow="scroll" dspmath="mathml"><mover accent="true"><mrow><msub><mi>m</mi><mo>min</mo></msub></mrow><mo mathvariant="normal">‾</mo></mover></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="25pt" height="13pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="d674d26c3c76ebbfe16679733d9e099a"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00084.svg" width="100%" height="13pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00084.png"></image></svg></span></span>) value in <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1039" display="inline" overflow="scroll" dspmath="mathml"><mover accent="true"><mrow><mi mathvariant="normal">Δ</mi><msub><mtext>C</mtext><mi mathvariant="normal">a</mi></msub><mo>(</mo><mi>m</mi><mo>)</mo></mrow><mo mathvariant="normal">‾</mo></mover></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="40pt" height="16pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="1d9d037847961f8bd0b0162f43f2b9c7"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00085.svg" width="100%" height="16pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00085.png"></image></svg></span></span> and <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1040" display="inline" overflow="scroll" dspmath="mathml"><mover accent="true"><mrow><mi mathvariant="normal">Δ</mi><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msub><mtext>C</mtext><mi mathvariant="normal">a</mi></msub><mo>(</mo><mi>m</mi><mo>)</mo></mrow><mo mathvariant="normal">‾</mo></mover></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="56pt" height="17pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="2e39ec9629a0cdd7fe92b1fd6180fbae"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00086.svg" width="100%" height="17pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00086.png"></image></svg></span></span>, respectively. For individual years, we computed SA by the difference from the extreme monthly values of each year.</p></div><span class="section6-mobile-bottom-border mobile-bottom-border hide-on-desktop hide-on-tablet"></span></div> <div class="app sec" id="section7"> <div class="grid-container no-margin header-element"><span class="grid-100 mobile-grid-100 tablet-grid-100 grid-parent more-less-mobile" data-hide="#section7 .co-arrow-open,.section7-content" data-show="#section7 .co-arrow-closed,.section7-mobile-bottom-border"><div id="App1.Ch1.S2" class="h1"><span>Appendix B:</span> Uncertainties in the relationship between <span class="inline-formula"><i>ε</i><sub>NPP</sub></span> and <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1042" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>c</mi><mi mathvariant="normal">i</mi></msub><mo>/</mo><msub><mi>c</mi><mi mathvariant="normal">a</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="28pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="23579f774e5a7f8aab47136a0ec1d106"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00087.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00087.png"></image></svg></span></span><span class="hide-on-desktop hide-on-tablet triangleWrapper"> <i class="co-arrow-closed"></i><i class="co-arrow-open" style="display:none"></i></span></div></span></div> <div class="section7-content show-no-js hide-on-mobile-soft"><p id="d2e14425">In Sect. <a href="https://bg.copernicus.org/articles/22/19/2025/#Ch1.S4.SS4" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">4.4</a>, we applied a simplified expression for fractionation of C<span class="inline-formula"><sub>3</sub></span> plants during photosynthesis (<span class="inline-formula"><i>ε</i><sub>NPP</sub></span>) and used this expression to translate trends in <span class="inline-formula"><i>ε</i><sub>NPP</sub></span> to trends in <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1046" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>c</mi><mi mathvariant="normal">i</mi></msub><mo>/</mo><msub><mi>c</mi><mi mathvariant="normal">a</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="28pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="4613cb72b8745c801912b309750cab99"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00088.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00088.png"></image></svg></span></span> and in iWUE. The potential contributions to trends in <span class="inline-formula"><i>ε</i><sub>NPP</sub></span> from neglected ternary effects, dark-day respiration, and transport through the mesophyll and photorespiration are discussed in this appendix.</p><p id="d2e14491"><span id="page34"></span>The isotopic fraction for C<span class="inline-formula"><sub>3</sub></span> photosynthesis is framed as a multi-step process considering the transport of CO<span class="inline-formula"><sub>2</sub></span> and the underlying gradients in CO<span class="inline-formula"><sub>2</sub></span> mole fractions from the ambient air (mole fraction – <span class="inline-formula"><i>c</i><sub>a</sub></span>) to the leaf surface (<span class="inline-formula"><i>c</i><sub>s</sub></span>) in the intercellular air spaces (<span class="inline-formula"><i>c</i><sub>i</sub></span>) and the sites of carboxylation (<span class="inline-formula"><i>c</i><sub>c</sub></span>), as well as the fractionation during carboxylation, dark-day respiration, <span class="inline-formula"><i>R</i><sub>d</sub></span>, and photorespiration (Cernusak, 2013). The transport of CO<span class="inline-formula"><sub>2</sub></span> equals the consumption of CO<span class="inline-formula"><sub>2</sub></span> by assimilation, <span class="inline-formula"><i>A</i></span>: <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1059" display="inline" overflow="scroll" dspmath="mathml"><mrow><mi>A</mi><mo>=</mo><mi>g</mi><mo>(</mo><msub><mi>c</mi><mi mathvariant="normal">a</mi></msub><mo>-</mo><msub><mi>c</mi><mi mathvariant="normal">i</mi></msub><mo>)</mo><mo>=</mo><msub><mi>g</mi><mi mathvariant="normal">m</mi></msub><mo>(</mo><msub><mi>c</mi><mi mathvariant="normal">i</mi></msub><mo>-</mo><msub><mi>c</mi><mi mathvariant="normal">c</mi></msub><mo>)</mo></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="132pt" height="13pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="f2764015676ea097d6daa6c106b39c89"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00089.svg" width="100%" height="13pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00089.png"></image></svg></span></span>, with <span class="inline-formula"><i>g</i></span> being the conductance of the stomatal pores and the boundary layer and <span class="inline-formula"><i>g</i><sub>m</sub></span> the mesophyll conductance. The relationship can be rewritten as <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1062" display="inline" overflow="scroll" dspmath="mathml"><mrow><mi>A</mi><mo>/</mo><mo>(</mo><mi>g</mi><mspace width="0.125em" linebreak="nobreak"></mspace><msub><mi>c</mi><mi mathvariant="normal">a</mi></msub><mo>)</mo><mo>=</mo><mo>(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mi>c</mi><mi mathvariant="normal">i</mi></msub><mo>/</mo><msub><mi>c</mi><mi mathvariant="normal">a</mi></msub><mo>)</mo><mo>=</mo><msub><mi>g</mi><mi mathvariant="normal">m</mi></msub><mo>/</mo><mi>g</mi><mspace linebreak="nobreak" width="0.125em"></mspace><mo>(</mo><msub><mi>c</mi><mi mathvariant="normal">i</mi></msub><mo>/</mo><msub><mi>c</mi><mi mathvariant="normal">a</mi></msub><mo>-</mo><msub><mi>c</mi><mi mathvariant="normal">c</mi></msub><mo>/</mo><msub><mi>c</mi><mi mathvariant="normal">a</mi></msub><mo>)</mo></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="220pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="aaade61fe9f6ed418aead373b019236c"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00090.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00090.png"></image></svg></span></span>. If <span class="inline-formula"><i>A</i></span> increases in proportion to <span class="inline-formula"><i>c</i><sub>a</sub></span> and <span class="inline-formula"><i>g</i></span> and <span class="inline-formula"><i>g</i><sub>m</sub></span> is assumed to be constant, then it follows that <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1067" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>c</mi><mi mathvariant="normal">i</mi></msub><mo>/</mo><msub><mi>c</mi><mi mathvariant="normal">a</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="28pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="1258f14e82776f108e2ebfb0f594d796"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00091.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00091.png"></image></svg></span></span> and <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1068" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>c</mi><mi mathvariant="normal">c</mi></msub><mo>/</mo><msub><mi>c</mi><mi mathvariant="normal">a</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="30pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="0ddafcb19434f74852be28e87b783a4b"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00092.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00092.png"></image></svg></span></span> are also constant. In turn, the fractionation associated with the boundary layer and stomatal conductance (<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1069" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>-</mo><mi>a</mi><mo>(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mi>c</mi><mi mathvariant="normal">i</mi></msub><mo>/</mo><msub><mi>c</mi><mi mathvariant="normal">a</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="63pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="9dd19c3276361817c6ea2d2e9da702ba"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00093.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00093.png"></image></svg></span></span>); <span class="inline-formula"><i>a</i>=4.4</span> ‰), mesophyll conductance (<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1071" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>-</mo><msub><mi>a</mi><mi mathvariant="normal">m</mi></msub><mo>(</mo><msub><mi>c</mi><mi mathvariant="normal">i</mi></msub><mo>/</mo><msub><mi>c</mi><mi mathvariant="normal">a</mi></msub><mo>-</mo><msub><mi>c</mi><mi mathvariant="normal">c</mi></msub><mo>/</mo><msub><mi>c</mi><mi mathvariant="normal">a</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="93pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="a823f550ca7ab99b35e82535b026785e"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00094.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00094.png"></image></svg></span></span>); <span class="inline-formula"><i>a</i><sub>m</sub>=1.8</span> ‰), and carboxylation (<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1073" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>-</mo><mi>b</mi><mo>×</mo><msub><mi>c</mi><mi mathvariant="normal">c</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="39pt" height="12pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="3bd9753944e70fe0427c9416dd466ec0"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00095.svg" width="100%" height="12pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00095.png"></image></svg></span></span>) remain constant. The overall influence of mesophyll transport on <span class="inline-formula"><i>ε</i><sub>NPP</sub></span> can also be written as <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1075" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>(</mo><mi>b</mi><mo>-</mo><msub><mi>a</mi><mi mathvariant="normal">m</mi></msub><mo>)</mo><mo>/</mo><msub><mi>g</mi><mi mathvariant="normal">m</mi></msub><mo>×</mo><mi>A</mi><mo>/</mo><msub><mi>c</mi><mi mathvariant="normal">a</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="96pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="a8be32d763894d949a7f4d7022dc2ac1"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00096.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00096.png"></image></svg></span></span> <span class="cit" id="xref_paren.89">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx56" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Keeling et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx56" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2017</a>)</span>.</p><p id="d2e14999"><span class="cit" id="xref_text.90"><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx56" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Keeling et al.</a> (<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx56" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2017</a>)</span> assumed that <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1076" display="inline" overflow="scroll" dspmath="mathml"><mrow><mi>A</mi><mo>/</mo><msub><mi>c</mi><mi mathvariant="normal">a</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="26pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="0e66a071cd264aba8509133894d22048"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00097.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00097.png"></image></svg></span></span> decreases over time, with <span class="inline-formula"><i>A</i></span> increasing by 45 % for a doubling of CO<span class="inline-formula"><sub>2</sub></span>, and that therefore fractionation by the mesophyll contribution would change by <span class="inline-formula">−0.006</span> ‰ ppm<span class="inline-formula"><sup>−1</sup></span>, i.e., a change in <span class="inline-formula"><i>ε</i><sub>NPP</sub></span> of 0.47 ‰ for the CO<span class="inline-formula"><sub>2</sub></span> increase of 78 ppm from 1980 to 2022. On the other hand, <span class="cit" id="xref_text.91"><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx15" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Campbell et al.</a> (<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx15" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2017</a>)</span> observationally constrained the growth in gross primary production over the 20th century to be 31 <span class="inline-formula">±</span> 5 %, larger than the increase in <span class="inline-formula"><i>c</i><sub>a</sub></span> of 25 %. Accordingly, <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1085" display="inline" overflow="scroll" dspmath="mathml"><mrow><mi>A</mi><mo>/</mo><msub><mi>c</mi><mi mathvariant="normal">a</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="26pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="2cef33127c8965d6854d5d71fdd2f40f"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00098.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00098.png"></image></svg></span></span> increases, and the mesophyll trend contribution is positive. With the central parameter values of <span class="cit" id="xref_text.92"><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx56" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Keeling et al.</a> (<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx56" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2017</a>)</span> (<span class="inline-formula"><i>A</i>=9</span> <span class="inline-formula">µ</span>mol m<span class="inline-formula"><sup>−2</sup></span> s<span class="inline-formula"><sup>−1</sup></span>, <span class="inline-formula"><i>g</i><sub>m</sub>=0.2</span> mol m<span class="inline-formula"><sup>−2</sup></span> s<span class="inline-formula"><sup>−1</sup></span>, CO<span class="inline-formula"><sub>2</sub></span> <span class="inline-formula">=</span> 355 ppm), the contribution is <span class="inline-formula">+0.002</span> ‰ ppm<span class="inline-formula"><sup>−1</sup></span>. <span class="cit" id="xref_text.93"><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx56" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Keeling et al.</a> (<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx56" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2017</a>)</span> also estimated changes in fractionation associated with photorespiration (<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1097" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>-</mo><mi>f</mi><mo>×</mo><msup><mi mathvariant="normal">Γ</mi><mo>*</mo></msup><mo>/</mo><msub><mi>c</mi><mi mathvariant="normal">a</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="54pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="619055fc4b1a1e47ba27bc47b08cd26a"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00099.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00099.png"></image></svg></span></span>; <span class="inline-formula"><i>f</i>=12</span> ‰) to be <span class="inline-formula">−0.004</span> ‰ ppm<span class="inline-formula"><sup>−1</sup></span> assuming a constant CO<span class="inline-formula"><sub>2</sub></span> compensation point, <span class="inline-formula">Γ<sup>*</sup></span>. The real sensitivity must be smaller, as <span class="inline-formula">Γ<sup>*</sup></span> increases with temperature and because <span class="cit" id="xref_text.94"><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx56" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Keeling et al.</a> (<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx56" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2017</a>)</span> applied an estimate for the CO<span class="inline-formula"><sub>2</sub></span> compensation point in the presence of <span class="inline-formula"><i>R</i><sub><i>d</i></sub></span> (43 ppm) instead of the absence of <span class="inline-formula"><i>R</i><sub><i>d</i></sub></span> (<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1107" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mi mathvariant="normal">Γ</mi><mo>*</mo></msup><mo>=</mo><mn mathvariant="normal">31</mn></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="38pt" height="11pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="602d178707a070bc235bf5d9b87a8282"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00100.svg" width="100%" height="11pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00100.png"></image></svg></span></span> ppm). Further, fractionation during day respiration is <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1108" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>-</mo><mi>e</mi><mo>×</mo><msub><mi>c</mi><mi mathvariant="normal">c</mi></msub><mo>/</mo><msub><mi>c</mi><mi mathvariant="normal">a</mi></msub><mo>×</mo><msub><mi>R</mi><mi>d</mi></msub><mo>/</mo><msub><mi>V</mi><mi mathvariant="normal">c</mi></msub></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="97pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="3fe11eb7a2fda8c50137ca655a2ebebf"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00101.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00101.png"></image></svg></span></span> <span class="cit" id="xref_paren.95">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx18" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Cernusak et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx18" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2013</a>)</span>, roughly about 0 to <span class="inline-formula">−0.3</span> ‰ for <span class="inline-formula"><i>e</i></span> in the range of 0 ‰ to 5 ‰; we apply RuBisCO carboxylation rates, <span class="inline-formula"><i>V</i><sub>c</sub></span>, of 11 <span class="inline-formula">µ</span>mol m<span class="inline-formula"><sup>−2</sup></span> s<span class="inline-formula"><sup>−1</sup></span> derived from the value of <span class="inline-formula"><i>A</i>=9</span> <span class="inline-formula">µ</span>mol m<span class="inline-formula"><sup>−2</sup></span> s<span class="inline-formula"><sup>−1</sup></span> by <span class="cit" id="xref_text.96"><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx56" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Keeling et al.</a> (<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx56" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2017</a>)</span>, (<span class="inline-formula"><i>R</i><sub><i>d</i></sub>=1</span> <span class="inline-formula">µ</span>mol m<span class="inline-formula"><sup>−2</sup></span> s<span class="inline-formula"><sup>−1</sup></span> and <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1123" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>c</mi><mi mathvariant="normal">c</mi></msub><mo>/</mo><msub><mi>c</mi><mi mathvariant="normal">a</mi></msub><mo>=</mo><mn mathvariant="normal">0.6</mn></mrow></math><span><svg xmlns:svg="http://www.w3.org/2000/svg" width="58pt" height="14pt" class="hide-js svg-formula" dspmath="mathimg" md5hash="8d295464800e6c4dbdf1e622ddb6dc9d"><image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00102.svg" width="100%" height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00102.png"></image></svg></span></span>). Finally, ternary effects of about <span class="inline-formula">−0.7</span> ‰ (0.024 <span class="inline-formula">×</span> <span class="inline-formula"><i>b</i></span>) increase with water vapor deficit <span class="cit" id="xref_paren.97">(<a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx23" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Farquhar and Cernusak</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx23" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2012</a>)</span>. Given the small amplitudes of these two contributions, their temporal trends have also been small over recent decades.</p></div><span class="section7-mobile-bottom-border mobile-bottom-border hide-on-desktop hide-on-tablet"></span></div> <div id="section8" class="sec"><div class="grid-container no-margin header-element"><span class="grid-100 mobile-grid-100 tablet-grid-100 grid-parent more-less-mobile" data-hide="#section8 .co-arrow-open,.section8-content" data-show="#section8 .co-arrow-closed,.section8-mobile-bottom-border"><div class="h1"><span class="section-number"> </span>Code and data availability<span class="hide-on-desktop hide-on-tablet triangleWrapper"> <i class="co-arrow-closed"></i><i class="co-arrow-open" style="display:none"></i></span></div></span></div> <div class="section8-content show-no-js hide-on-mobile-soft"><p id="d2e15635">The data from the Scripps CO<span class="inline-formula"><sub>2</sub></span> program are available here: <span class="uri"><a href="https://scrippsco2.ucsd.edu/data/atmospheric_co2/" target="_blank">https://scrippsco2.ucsd.edu/data/atmospheric_co2/</a></span> (last access: 17 April 2023, Keeling et al., 2001). The GLOBALVIEW data from the NOAA Global Monitoring Laboratory were downloaded here: <span class="uri"><a href="https://gml.noaa.gov/ccgg/globalview/" target="_blank">https://gml.noaa.gov/ccgg/globalview/</a></span> (last access: 27 April 2022, Cooperative Global Atmospheric Data Integration Project, 2013). The model data displayed in the figures and plotting scripts are available here: <span class="uri"><a href="https://zenodo.org/records/14051464" target="_blank">https://zenodo.org/records/14051464</a></span> (last access: 7 November 2024, <span class="uri"><a href="https://doi.org/10.5281/zenodo.14051464" target="_blank">https://doi.org/10.5281/zenodo.14051464</a></span>, <span class="cit" id="xref_altparen.98"><a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx46" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Joos et al.</a>, <a href="https://bg.copernicus.org/articles/22/19/2025/#bib1.bibx46" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">2024</a></span>).</p></div><span class="section8-mobile-bottom-border mobile-bottom-border hide-on-desktop hide-on-tablet"></span></div> <div id="section9" class="sec"> <div class="grid-container no-margin header-element"><span class="grid-100 mobile-grid-100 tablet-grid-100 grid-parent more-less-mobile" data-hide="#section9 .co-arrow-open,.section9-content" data-show="#section9 .co-arrow-closed,.section9-mobile-bottom-border"><div class="h1"><span class="section-number"> </span>Supplement<span class="hide-on-desktop hide-on-tablet triangleWrapper"> <i class="co-arrow-closed"></i><i class="co-arrow-open" style="display:none"></i></span></div></span></div> <div class="section9-content show-no-js hide-on-mobile-soft"><p id="d2e15663">The supplement related to this article is available online at: <a href="https://doi.org/10.5194/bg-22-19-2025-supplement">https://doi.org/10.5194/bg-22-19-2025-supplement</a>.</p></div><span class="section9-mobile-bottom-border mobile-bottom-border hide-on-desktop hide-on-tablet"></span></div> <div id="section10" class="sec"><div class="grid-container no-margin header-element"><span class="grid-100 mobile-grid-100 tablet-grid-100 grid-parent more-less-mobile" data-hide="#section10 .co-arrow-open,.section10-content" data-show="#section10 .co-arrow-closed,.section10-mobile-bottom-border"><div class="h1"><span class="section-number"> </span>Author contributions<span class="hide-on-desktop hide-on-tablet triangleWrapper"> <i class="co-arrow-closed"></i><i class="co-arrow-open" style="display:none"></i></span></div></span></div> <div class="section10-content show-no-js hide-on-mobile-soft"><p id="d2e15672">FJ and SL wrote the paper with inputs from SZ. SL performed all model runs, and FJ did the statistical analyses. SL and FJ produced the figures and tables.</p></div><span class="section10-mobile-bottom-border mobile-bottom-border hide-on-desktop hide-on-tablet"></span></div> <div id="section11" class="sec"><div class="grid-container no-margin header-element"><span class="grid-100 mobile-grid-100 tablet-grid-100 grid-parent more-less-mobile" data-hide="#section11 .co-arrow-open,.section11-content" data-show="#section11 .co-arrow-closed,.section11-mobile-bottom-border"><div class="h1"><span class="section-number"> </span>Competing interests<span class="hide-on-desktop hide-on-tablet triangleWrapper"> <i class="co-arrow-closed"></i><i class="co-arrow-open" style="display:none"></i></span></div></span></div> <div class="section11-content show-no-js hide-on-mobile-soft"><p id="d2e15678">The contact author has declared that none of the authors has any competing interests.</p></div><span class="section11-mobile-bottom-border mobile-bottom-border hide-on-desktop hide-on-tablet"></span></div> <div id="section12" class="sec"><div class="grid-container no-margin header-element"><span class="grid-100 mobile-grid-100 tablet-grid-100 grid-parent more-less-mobile" data-hide="#section12 .co-arrow-open,.section12-content" data-show="#section12 .co-arrow-closed,.section12-mobile-bottom-border"><div class="h1"><span class="section-number"> </span>Disclaimer<span class="hide-on-desktop hide-on-tablet triangleWrapper"> <i class="co-arrow-closed"></i><i class="co-arrow-open" style="display:none"></i></span></div></span></div> <div class="section12-content show-no-js hide-on-mobile-soft"><p id="d2e15684">The work reflects only the authors' view; the European Commission and their executive agency are not responsible for any use that may be made of the information the work contains. <br><br>Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.</p></div><span class="section12-mobile-bottom-border mobile-bottom-border hide-on-desktop hide-on-tablet"></span></div> <div class="ack sec" id="section13"> <div class="grid-container no-margin header-element"><span class="grid-100 mobile-grid-100 tablet-grid-100 grid-parent more-less-mobile" data-hide="#section13 .co-arrow-open,.section13-content" data-show="#section13 .co-arrow-closed,.section13-mobile-bottom-border"><div class="h1"><span class="section-number"> </span>Acknowledgements<span class="hide-on-desktop hide-on-tablet triangleWrapper"> <i class="co-arrow-closed"></i><i class="co-arrow-open" style="display:none"></i></span></div></span></div> <div class="section13-content show-no-js hide-on-mobile-soft"><p id="d2e15693">We thank the researchers of the Cooperative Atmospheric Data Integration Project, NOAA Earth System Research Laboratories (ESRL), Boulder, Colorado, and of the Scripps CO<span class="inline-formula"><sub>2</sub></span> program for making their CO<span class="inline-formula"><sub>2</sub></span> and <span class="inline-formula"><i>δ</i><sup>13</sup></span>C data freely available. We also thank Martin Heimann for suggesting that we plot seasonal anomalies of CO<span class="inline-formula"><sub>2</sub></span> versus those of <span class="inline-formula"><i>δ</i><sup>13</sup></span>C. A special thanks goes to Christoph Köstler for providing the TM3 transport matrices and to Aurich Jeltsch-Thömmes for help with Bern3D. We thank Gerbrand Koren and an anonymous reviewer for their careful reviews and Ji-Hyung Park for editing the paper.</p></div><span class="section13-mobile-bottom-border mobile-bottom-border hide-on-desktop hide-on-tablet"></span></div> <div id="section14" class="sec"><div class="grid-container no-margin header-element"><span class="grid-100 mobile-grid-100 tablet-grid-100 grid-parent more-less-mobile" data-hide="#section14 .co-arrow-open,.section14-content" data-show="#section14 .co-arrow-closed,.section14-mobile-bottom-border"><div class="h1"><span class="section-number"> </span>Financial support<span class="hide-on-desktop hide-on-tablet triangleWrapper"> <i class="co-arrow-closed"></i><i class="co-arrow-open" style="display:none"></i></span></div></span></div> <div class="section14-content show-no-js hide-on-mobile-soft"><p id="d2e15748">This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement no. 821003 (project 4C, Climate–Carbon Interactions in the Current Century) and from the Swiss National Science Foundation (project no. 200020_200511).</p></div><span class="section14-mobile-bottom-border mobile-bottom-border hide-on-desktop hide-on-tablet"></span></div> <div id="section15" class="sec"><div class="grid-container no-margin header-element"><span class="grid-100 mobile-grid-100 tablet-grid-100 grid-parent more-less-mobile" data-hide="#section15 .co-arrow-open,.section15-content" data-show="#section15 .co-arrow-closed,.section15-mobile-bottom-border"><div class="h1"><span class="section-number"> </span>Review statement<span class="hide-on-desktop hide-on-tablet triangleWrapper"> <i class="co-arrow-closed"></i><i class="co-arrow-open" style="display:none"></i></span></div></span></div> <div class="section15-content show-no-js hide-on-mobile-soft"><p id="d2e15754">This paper was edited by Ji-Hyung Park and reviewed by Gerbrand Koren and one anonymous referee.</p></div><span class="section15-mobile-bottom-border mobile-bottom-border hide-on-desktop hide-on-tablet"></span></div> <div class="ref-list sec" id="section16"> <div class="grid-container no-margin header-element"><span class="grid-100 mobile-grid-100 tablet-grid-100 grid-parent more-less-mobile" data-hide="#section16 .co-arrow-open,.section16-content" data-show="#section16 .co-arrow-closed,.section16-mobile-bottom-border"><div class="h1"><span class="section-number"> </span>References<span class="hide-on-desktop hide-on-tablet triangleWrapper"> <i class="co-arrow-closed"></i><i class="co-arrow-open" style="display:none"></i></span></div></span></div> <div class="section16-content show-no-js hide-on-mobile-soft"><p class="ref" id="bib1.bibx1"><span class="mixed-citation"> Andres, R., Marland, G., Boden, T., and Bischof, S.: Carbon dioxide emissions from fossil fuel consumption and cement manufacture, 1751–1991, and an estimate of their isotopic composition and latitudinal distribution, in: The Carbon Cycle, edited by: Wigley, T. 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L. and Schimmel, D., Cambridge University Press, New York, USA, 53–62, ISBN 0 521 58337 3, 2000. <a href="https://bg.copernicus.org/articles/22/19/2025/#xref_text.43" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">a</a></span></p><p class="ref" id="bib1.bibx2"><span class="mixed-citation">Andres, R., Boden, T., and Marland, G.: Monthly Fossil-Fuel CO<span class="inline-formula"><sub>2</sub></span> Emissions: Mass of Emissions Gridded by One Degree Latitude by One Degree Longitude – 2016, ESS-DIVE [data set], <a href="https://doi.org/10.3334/CDIAC/FFE.MONTHLYMASS.2016">https://doi.org/10.3334/CDIAC/FFE.MONTHLYMASS.2016</a>, 2009a. <a href="https://bg.copernicus.org/articles/22/19/2025/#xref_paren.49" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">a</a></span></p><p class="ref" id="bib1.bibx3"><span class="mixed-citation">Andres, R., Boden, T., and Marland, G.: Monthly Fossil-Fuel CO<span class="inline-formula"><sub>2</sub></span> Emissions: Isomass of Emissions Gridded by One Degree Latitude by One Degree Longitude, ESS-DIVE [data set], <span class="uri"><a href="https://data.ess-dive.lbl.gov/view/doi:10.3334/CDIAC/FFE.MONTHLYISOMASS.2016" target="_blank">https://data.ess-dive.lbl.gov/view/doi:10.3334/CDIAC/FFE.MONTHLYISOMASS.2016</a></span> (last access: 23 December 2024), 2009b. <a href="https://bg.copernicus.org/articles/22/19/2025/#xref_paren.49" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">a</a></span></p><p class="ref" id="bib1.bibx4"><span class="mixed-citation">Andres, R., Boden, T., and Marland, G.: Annual Fossil-Fuel CO<span class="inline-formula"><sub>2</sub></span> Emissions: Global Stable Carbon Isotopic Signature, ESS-DIVE [data set], <a href="https://doi.org/10.3334/CDIAC/FFE.DB1013.2017">https://doi.org/10.3334/CDIAC/FFE.DB1013.2017</a>, 2017. <a href="https://bg.copernicus.org/articles/22/19/2025/#xref_text.41" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">a</a></span></p><p class="ref" id="bib1.bibx5"><span class="mixed-citation">Bacastow, R. 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Change Biol., 14, 1745–1764, <a href="https://doi.org/10.1111/j.1365-2486.2008.01625.x">https://doi.org/10.1111/j.1365-2486.2008.01625.x</a>, 2008. <a href="https://bg.copernicus.org/articles/22/19/2025/#xref_paren.32" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">a</a></span></p></div><span class="section16-mobile-bottom-border mobile-bottom-border hide-on-desktop hide-on-tablet"></span></div> </div>  <div class="pswp" tabindex="-1" role="dialog" aria-hidden="true" >  <div class="pswp__bg"></div>  <div class="pswp__scroll-wrap">  <div class="pswp__container"> <div class="pswp__item"></div> <div class="pswp__item"></div> <div class="pswp__item"></div> </div>  <div class="pswp__ui pswp__ui--hidden"> <div class="pswp__top-bar">  <div class="pswp__counter"></div> <button class="pswp__button pswp__button--close" title="Close (Esc)"></button> <button class="pswp__button pswp__button--fs" title="Toggle fullscreen"></button>   <div class="pswp__preloader"> <div 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menu_level1"> <li class="menuitem_level1 co_function_get_navigation_is_parent co_function_get_navigation_is_closed" id="co_getnavigation_page_about"> <a href="https://bg.copernicus.org/articles/22/19/2025/#abstract" class="link_level1 scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Abstract</a></li> <li class="menuitem_level1 co_function_get_navigation_is_parent co_function_get_navigation_is_closed" id="co_getnavigation_page_about"> <a href="https://bg.copernicus.org/articles/22/19/2025/#section1" class="link_level1 scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Introduction</a></li> <li class="menuitem_level1 co_function_get_navigation_is_parent co_function_get_navigation_is_closed" id="co_getnavigation_page_about"> <a href="https://bg.copernicus.org/articles/22/19/2025/#section2" class="link_level1 scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Methods</a></li> <li class="menuitem_level1 co_function_get_navigation_is_parent co_function_get_navigation_is_closed" id="co_getnavigation_page_about"> <a href="https://bg.copernicus.org/articles/22/19/2025/#section3" class="link_level1 scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">The influence of carbon and isotope fluxes on the seasonal cycles of C<span class="inline-formula"><sub>a</sub></span> and <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>: a conceptual framework</a></li> <li class="menuitem_level1 co_function_get_navigation_is_parent co_function_get_navigation_is_closed" id="co_getnavigation_page_about"> <a href="https://bg.copernicus.org/articles/22/19/2025/#section4" class="link_level1 scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Results</a></li> <li class="menuitem_level1 co_function_get_navigation_is_parent co_function_get_navigation_is_closed" id="co_getnavigation_page_about"> <a href="https://bg.copernicus.org/articles/22/19/2025/#section5" class="link_level1 scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Conclusions</a></li> <li class="menuitem_level1 co_function_get_navigation_is_parent co_function_get_navigation_is_closed" id="co_getnavigation_page_about"> <a href="https://bg.copernicus.org/articles/22/19/2025/#section6" class="link_level1 scrollto" data-fixed-element=".auto-fixed-top-forced.article-title"><span>Appendix A:</span> Decomposition of <span class="inline-formula"><math display="inline" dspmath="mathml" id="M976" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">as</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg class="hide-js svg-formula" dspmath="mathimg" height="17pt" md5hash="4f8c1e5d9da4e0220a7da897010cd33a" width="44pt" xmlns:svg="http://www.w3.org/2000/svg"><image height="17pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00066.png" width="100%" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00066.svg" xmlns:xlink="http://www.w3.org/1999/xlink"></image></svg></span></span> and the calculation of seasonal amplitudes</a></li> <li class="menuitem_level1 co_function_get_navigation_is_parent co_function_get_navigation_is_closed" id="co_getnavigation_page_about"> <a href="https://bg.copernicus.org/articles/22/19/2025/#section7" class="link_level1 scrollto" data-fixed-element=".auto-fixed-top-forced.article-title"><span>Appendix B:</span> Uncertainties in the relationship between <span class="inline-formula"><i>ε</i><sub>NPP</sub></span> and <span class="inline-formula"><math display="inline" dspmath="mathml" id="M1042" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>c</mi><mi mathvariant="normal">i</mi></msub><mo>/</mo><msub><mi>c</mi><mi mathvariant="normal">a</mi></msub></mrow></math><span><svg class="hide-js svg-formula" dspmath="mathimg" height="14pt" md5hash="23579f774e5a7f8aab47136a0ec1d106" width="28pt" xmlns:svg="http://www.w3.org/2000/svg"><image height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00087.png" width="100%" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00087.svg" xmlns:xlink="http://www.w3.org/1999/xlink"></image></svg></span></span></a></li> <li class="menuitem_level1 co_function_get_navigation_is_parent co_function_get_navigation_is_closed" id="co_getnavigation_page_about"> <a href="https://bg.copernicus.org/articles/22/19/2025/#section8" class="link_level1 scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Code and data availability</a></li> <li class="menuitem_level1 co_function_get_navigation_is_parent co_function_get_navigation_is_closed" id="co_getnavigation_page_about"> <a href="https://bg.copernicus.org/articles/22/19/2025/#section10" class="link_level1 scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Author contributions</a></li> <li class="menuitem_level1 co_function_get_navigation_is_parent co_function_get_navigation_is_closed" id="co_getnavigation_page_about"> <a href="https://bg.copernicus.org/articles/22/19/2025/#section11" class="link_level1 scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Competing interests</a></li> <li class="menuitem_level1 co_function_get_navigation_is_parent co_function_get_navigation_is_closed" id="co_getnavigation_page_about"> <a href="https://bg.copernicus.org/articles/22/19/2025/#section12" class="link_level1 scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Disclaimer</a></li> <li class="menuitem_level1 co_function_get_navigation_is_parent co_function_get_navigation_is_closed" id="co_getnavigation_page_about"> <a href="https://bg.copernicus.org/articles/22/19/2025/#section13" class="link_level1 scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Acknowledgements</a></li> <li class="menuitem_level1 co_function_get_navigation_is_parent co_function_get_navigation_is_closed" id="co_getnavigation_page_about"> <a href="https://bg.copernicus.org/articles/22/19/2025/#section14" class="link_level1 scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Financial support</a></li> <li class="menuitem_level1 co_function_get_navigation_is_parent co_function_get_navigation_is_closed" id="co_getnavigation_page_about"> <a href="https://bg.copernicus.org/articles/22/19/2025/#section15" class="link_level1 scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Review statement</a></li> <li class="menuitem_level1 co_function_get_navigation_is_parent co_function_get_navigation_is_closed" id="co_getnavigation_page_about"> <a href="https://bg.copernicus.org/articles/22/19/2025/#section16" class="link_level1 scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">References</a></li> <li class="menuitem_level1 co_function_get_navigation_is_parent co_function_get_navigation_is_closed" id="co_getnavigation_page_about"> <a href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-supplement.pdf" class="link_level1 scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Supplement</a></li> </ul> </div> </div> <div id="leftColumnExtras" class="CMSCONTAINER w-sidebar col-auto d-none d-lg-block pt-2"> <div class="widget dark-border"> <div class="legend journal-contentLinkColor">Download</div> <div class="content"> <ul class="additional_info no-bullets no-styling"> <li><a class="triangle" title="PDF Version (4290 KB)" href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025.pdf">Article</a> <nobr>(4290 KB)</nobr> </li> <li> <a class="triangle" title="XML Version" href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025.xml">Full-text XML</a> </li> </ul> </div> <div class="content"> <ul class="additional_info no-bullets no-styling"> <li> <a class="triangle" href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-supplement.pdf">Supplement</a> <nobr>(692 KB)</nobr> </li> <li><a class="triangle" href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025.bib">BibTeX</a></li> <li><a class="triangle" href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025.ris">EndNote</a></li> </ul> </div> </div> <div class="widget dark-border"> <div class="legend journal-contentLinkColor">Short summary</div> <div class="content hide-js shortSummaryFull">How plants regulate their exchange of CO<sub>2</sub> and water with the atmosphere under global warming is critical for their carbon uptake and their cooling influence. We analyze the isotope ratio of atmospheric CO<sub>2</sub> and detect no significant decadal trends in the seasonal cycle amplitude. The data are consistent with the regulation towards leaf CO<sub>2</sub> and intrinsic water use efficiency growing proportionally to atmospheric CO<sub>2</sub>, in contrast to recent suggestions of downregulation of CO<sub>2</sub> and water fluxes.</div> <div style="display: none" class="content show-js shortSummaryShorten">How plants regulate their exchange of CO<sub>2</sub> and water with the atmosphere under global warming is...</div> <div class="content"> <a href="#" class="more-less show-js triangle" data-hide=".shortSummaryFull" data-show=".shortSummaryShorten" data-toggleCaption='Hide'>Read more</a> </div> </div> <div class="widget dark-border hide-on-mobile hide-on-tablet p-0" id="share"> <div class="legend journal-contentLinkColor">Share</div> <div class="row p-0"> <div class="col-auto pl-0"> <a class="share-one-line" href="https://www.mendeley.com/import/?url=https%3A%2F%2Fbg.copernicus.org%2Farticles%2F22%2F19%2F2025%2F" title="Mendeley" target="_blank"> <img 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href="https://www.facebook.com/share.php?u=https%3A%2F%2Fbg.copernicus.org%2Farticles%2F22%2F19%2F2025%2F&t=No+increase+is+detected+and+modeled+for+the+seasonal+cycle+amplitude+of+%3Ci%3E%CE%B4%3C%2Fi%3E%3Csup%3E13%3C%2Fsup%3EC+of+atmospheric+carbon+dioxide" title="Facebook" target="_blank"> <img src="https://www.biogeosciences.net/facebook.png" alt="Facebook"/> </a> </div> <div class="col-auto pr-0"> <a class="share-one-line last" href="https://www.linkedin.com/shareArticle?mini=true&url=https%3A%2F%2Fbg.copernicus.org%2Farticles%2F22%2F19%2F2025%2F&title=No+increase+is+detected+and+modeled+for+the+seasonal+cycle+amplitude+of+%3Ci%3E%CE%B4%3C%2Fi%3E%3Csup%3E13%3C%2Fsup%3EC+of+atmospheric+carbon+dioxide" title="LinkedIn" target="_blank"> <img src="https://www.biogeosciences.net/linkedin.png" alt="LinkedIn"> </a> </div> <div class="col pr-0 mobile-native-share"> <a href="#" data-title="Biogeosciences" data-text="*No increase is detected and modeled for the seasonal cycle amplitude of δ13C of atmospheric carbon dioxide* Fortunat Joos et al." data-url="https://bg.copernicus.org/articles/22/19/2025/" class="mobile-native-share share-one-line last"><i class="co-mobile-share display-none"></i></a> </div> </div> </div> <div class="widget dark-border"> <div class="legend journal-contentLinkColor">Altmetrics</div> <div class="wrapper"> <div class="content text-center"> Final-revised paper </div> <div class="content text-center"> <div class="altmetric-embed" data-link-target="_blank" data-hide-less-than="1" data-no-score data-badge-type="medium-donut" data-doi="10.5194/bg-22-19-2025"></div> </div> </div> <div class="wrapper"> <div class="content text-center"> Preprint </div> <div class="content text-center"> <div class="altmetric-embed" data-link-target="_blank" data-hide-less-than="1" data-no-score data-badge-type="medium-donut" data-doi="10.5194/egusphere-2024-1972"></div> </div> </div> </div> <script type="text/javascript"> !function (e, t, n) { var d = "createElement", 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articleNavigation" data-fixet-top-target="#section1"> <button class="btn btn-success mb-3 btn-block" id="mathjax-turn"><i class="fal fa-function"></i> Turn MathJax on</button> <div class="widget dark-border m-0"> <div class="legend journal-contentLinkColor">Sections</div> <div class="content"> <ul class="toc-styling p-0"> <li> <a href="https://bg.copernicus.org/articles/22/19/2025/#abstract" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Abstract</a> </li> <li> <a href="https://bg.copernicus.org/articles/22/19/2025/#section1" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Introduction</a> </li> <li> <a href="https://bg.copernicus.org/articles/22/19/2025/#section2" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Methods</a> </li> <li> <a href="https://bg.copernicus.org/articles/22/19/2025/#section3" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">The influence of carbon and isotope fluxes on the seasonal cycles of C<span class="inline-formula"><sub>a</sub></span> and <span class="inline-formula"><i>δ</i><sup>13</sup></span>C<span class="inline-formula"><sub>a</sub></span>: a conceptual framework</a> </li> <li> <a href="https://bg.copernicus.org/articles/22/19/2025/#section4" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Results</a> </li> <li> <a href="https://bg.copernicus.org/articles/22/19/2025/#section5" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Conclusions</a> </li> <li> <a href="https://bg.copernicus.org/articles/22/19/2025/#section6" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title"><span>Appendix A:</span> Decomposition of <span class="inline-formula"><math display="inline" dspmath="mathml" id="M976" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi mathvariant="italic">δ</mi><mn mathvariant="normal">13</mn></msup><msubsup><mi>f</mi><mrow><mi mathvariant="normal">as</mi><mo>,</mo><mi mathvariant="normal">net</mi></mrow><mo>*</mo></msubsup></mrow></math><span><svg class="hide-js svg-formula" dspmath="mathimg" height="17pt" md5hash="4f8c1e5d9da4e0220a7da897010cd33a" width="44pt" xmlns:svg="http://www.w3.org/2000/svg"><image height="17pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00066.png" width="100%" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00066.svg" xmlns:xlink="http://www.w3.org/1999/xlink"></image></svg></span></span> and the calculation of seasonal amplitudes</a> </li> <li> <a href="https://bg.copernicus.org/articles/22/19/2025/#section7" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title"><span>Appendix B:</span> Uncertainties in the relationship between <span class="inline-formula"><i>ε</i><sub>NPP</sub></span> and <span class="inline-formula"><math display="inline" dspmath="mathml" id="M1042" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>c</mi><mi mathvariant="normal">i</mi></msub><mo>/</mo><msub><mi>c</mi><mi mathvariant="normal">a</mi></msub></mrow></math><span><svg class="hide-js svg-formula" dspmath="mathimg" height="14pt" md5hash="23579f774e5a7f8aab47136a0ec1d106" width="28pt" xmlns:svg="http://www.w3.org/2000/svg"><image height="14pt" src="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00087.png" width="100%" xlink:href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-ie00087.svg" xmlns:xlink="http://www.w3.org/1999/xlink"></image></svg></span></span></a> </li> <li> <a href="https://bg.copernicus.org/articles/22/19/2025/#section8" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Code and data availability</a> </li> <li> <a href="https://bg.copernicus.org/articles/22/19/2025/#section10" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Author contributions</a> </li> <li> <a href="https://bg.copernicus.org/articles/22/19/2025/#section11" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Competing interests</a> </li> <li> <a href="https://bg.copernicus.org/articles/22/19/2025/#section12" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Disclaimer</a> </li> <li> <a href="https://bg.copernicus.org/articles/22/19/2025/#section13" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Acknowledgements</a> </li> <li> <a href="https://bg.copernicus.org/articles/22/19/2025/#section14" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Financial support</a> </li> <li> <a href="https://bg.copernicus.org/articles/22/19/2025/#section15" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Review statement</a> </li> <li> <a href="https://bg.copernicus.org/articles/22/19/2025/#section16" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">References</a> </li> <li> <a href="https://bg.copernicus.org/articles/22/19/2025/bg-22-19-2025-supplement.pdf" class="scrollto" data-fixed-element=".auto-fixed-top-forced.article-title">Supplement</a> </li> </ul> </div> </div> </div> </div> </div> </div> </main>  <footer class="d-print-none version-2023"> <div class="footer"> <div class="container"> <div class="row align-items-center mb-3"> <div class="col-12 col-lg-auto text-center text-md-left title-wrapper"> <div id="j-header-footer" class="text-center text-md-left"> <div class="h1 text-center text-md-left"> Biogeosciences </div> <p>An interactive open-access journal of the European Geosciences Union</p> </div> </div> <div class="col-12 col-lg-auto text-center text-md-left pt-lg-2"> <div class="row align-items-center"> <div class="col-12 col-sm col-md-auto text-center text-md-left mb-3 mb-sm-0"> 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