CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-sticky-header-enabled vector-toc-available" lang="en" dir="ltr"> <head> <meta charset="UTF-8"> <title>Lapse rate - Wikipedia</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-sticky-header-enabled vector-toc-available";var cookie=document.cookie.match(/(?:^|; )enwikimwclientpreferences=([^;]+)/);if(cookie){cookie[1].split('%2C').forEach(function(pref){className=className.replace(new RegExp('(^| )'+pref.replace(/-clientpref-\w+$|[^\w-]+/g,'')+'-clientpref-\\w+( |$)'),'$1'+pref+'$2');});}document.documentElement.className=className;}());RLCONF={"wgBreakFrames":false,"wgSeparatorTransformTable":["",""],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"dmy", "wgMonthNames":["","January","February","March","April","May","June","July","August","September","October","November","December"],"wgRequestId":"65c13575-3db5-4f27-8a8e-02ee5e10d684","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Lapse_rate","wgTitle":"Lapse rate","wgCurRevisionId":1271834359,"wgRevisionId":1271834359,"wgArticleId":224312,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["Articles with short description","Short description matches Wikidata","Articles needing additional references from March 2022","All articles needing additional references","Atmospheric thermodynamics","Climate change feedbacks","Fluid mechanics","Meteorological quantities","Spatial gradient","Atmospheric temperature","Vertical position"],"wgPageViewLanguage":"en","wgPageContentLanguage":"en","wgPageContentModel":"wikitext","wgRelevantPageName":"Lapse_rate","wgRelevantArticleId":224312, "wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":false,"wgFlaggedRevsParams":{"tags":{"status":{"levels":1}}},"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"en","pageLanguageDir":"ltr","pageVariantFallbacks":"en"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":false,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":30000,"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q66900467","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled": false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false};RLSTATE={"ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","ext.cite.styles":"ready","ext.math.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","jquery.makeCollapsible.styles":"ready","ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready","ext.wikimediaBadges":"ready"};RLPAGEMODULES=["ext.cite.ux-enhancements","mediawiki.page.media","site","mediawiki.page.ready","jquery.makeCollapsible","mediawiki.toc","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.gadget.ReferenceTooltips","ext.gadget.switcher","ext.urlShortener.toolbar","ext.centralauth.centralautologin","mmv.bootstrap","ext.popups", "ext.visualEditor.desktopArticleTarget.init","ext.visualEditor.targetLoader","ext.echo.centralauth","ext.eventLogging","ext.wikimediaEvents","ext.navigationTiming","ext.uls.interface","ext.cx.eventlogging.campaigns","ext.cx.uls.quick.actions","wikibase.client.vector-2022","ext.checkUser.clientHints","ext.growthExperiments.SuggestedEditSession"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=en&modules=ext.cite.styles%7Cext.math.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cjquery.makeCollapsible.styles%7Cskins.vector.icons%2Cstyles%7Cskins.vector.search.codex.styles%7Cwikibase.client.init&only=styles&skin=vector-2022"> <script async="" src="/w/load.php?lang=en&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=en&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.15"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Tatra_Rysy_5.jpg/1200px-Tatra_Rysy_5.jpg"> <meta property="og:image:width" content="1200"> <meta property="og:image:height" content="877"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Tatra_Rysy_5.jpg/800px-Tatra_Rysy_5.jpg"> <meta property="og:image:width" content="800"> <meta property="og:image:height" content="585"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Tatra_Rysy_5.jpg/640px-Tatra_Rysy_5.jpg"> <meta property="og:image:width" content="640"> <meta property="og:image:height" content="468"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Lapse rate - Wikipedia"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//en.m.wikipedia.org/wiki/Lapse_rate"> <link rel="alternate" type="application/x-wiki" title="Edit this page" href="/w/index.php?title=Lapse_rate&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"> <link rel="icon" href="/static/favicon/wikipedia.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="Wikipedia (en)"> <link rel="EditURI" type="application/rsd+xml" href="//en.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://en.wikipedia.org/wiki/Lapse_rate"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en"> <link rel="alternate" type="application/atom+xml" title="Wikipedia Atom feed" href="/w/index.php?title=Special:RecentChanges&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="login.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-Lapse_rate rootpage-Lapse_rate skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Jump to content</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" title="Main menu" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="Main menu" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">Main menu</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Main menu</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">hide</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navigation </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Main_Page" title="Visit the main page [z]" accesskey="z"><span>Main page</span></a></li><li id="n-contents" class="mw-list-item"><a href="/wiki/Wikipedia:Contents" title="Guides to browsing Wikipedia"><span>Contents</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Portal:Current_events" title="Articles related to current events"><span>Current events</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Special:Random" title="Visit a randomly selected article [x]" accesskey="x"><span>Random article</span></a></li><li id="n-aboutsite" class="mw-list-item"><a href="/wiki/Wikipedia:About" title="Learn about Wikipedia and how it works"><span>About Wikipedia</span></a></li><li id="n-contactpage" class="mw-list-item"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us" title="How to contact Wikipedia"><span>Contact us</span></a></li> </ul> </div> </div> <div id="p-interaction" class="vector-menu mw-portlet mw-portlet-interaction" > <div class="vector-menu-heading"> Contribute </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-help" class="mw-list-item"><a href="/wiki/Help:Contents" title="Guidance on how to use and edit Wikipedia"><span>Help</span></a></li><li id="n-introduction" class="mw-list-item"><a href="/wiki/Help:Introduction" title="Learn how to edit Wikipedia"><span>Learn to edit</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedia:Community_portal" title="The hub for editors"><span>Community portal</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Special:RecentChanges" title="A list of recent changes to Wikipedia [r]" accesskey="r"><span>Recent changes</span></a></li><li id="n-upload" class="mw-list-item"><a href="/wiki/Wikipedia:File_upload_wizard" title="Add images or other media for use on Wikipedia"><span>Upload file</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Main_Page" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="The Free Encyclopedia" src="/static/images/mobile/copyright/wikipedia-tagline-en.svg" width="117" height="13" style="width: 7.3125em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Special:Search" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Search Wikipedia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Search</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Search Wikipedia" aria-label="Search Wikipedia" autocapitalize="sentences" title="Search Wikipedia [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Special:Search"> </div> <button class="cdx-button cdx-search-input__end-button">Search</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Personal tools"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Appearance" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Appearance</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=en.wikipedia.org&uselang=en" class=""><span>Donate</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:CreateAccount&returnto=Lapse+rate" title="You are encouraged to create an account and log in; however, it is not mandatory" class=""><span>Create account</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:UserLogin&returnto=Lapse+rate" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o" class=""><span>Log in</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Log in and more options" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Personal tools" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Personal tools</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="User menu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=en.wikipedia.org&uselang=en"><span>Donate</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:CreateAccount&returnto=Lapse+rate" title="You are encouraged to create an account and log in; however, it is not mandatory"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Create account</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:UserLogin&returnto=Lapse+rate" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Log in</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Pages for logged out editors <a href="/wiki/Help:Introduction" aria-label="Learn more about editing"><span>learn more</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Special:MyContributions" title="A list of edits made from this IP address [y]" accesskey="y"><span>Contributions</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:MyTalk" title="Discussion about edits from this IP address [n]" accesskey="n"><span>Talk</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Contents" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Contents</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Top)</div> </a> </li> <li id="toc-Definition" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Definition"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Definition</span> </div> </a> <ul id="toc-Definition-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Environmental_lapse_rate" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Environmental_lapse_rate"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Environmental lapse rate</span> </div> </a> <ul id="toc-Environmental_lapse_rate-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cause" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Cause"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Cause</span> </div> </a> <ul id="toc-Cause-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Convection_and_adiabatic_expansion" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Convection_and_adiabatic_expansion"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Convection and adiabatic expansion</span> </div> </a> <ul id="toc-Convection_and_adiabatic_expansion-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mathematics_of_the_adiabatic_lapse_rate" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Mathematics_of_the_adiabatic_lapse_rate"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Mathematics of the adiabatic lapse rate</span> </div> </a> <button aria-controls="toc-Mathematics_of_the_adiabatic_lapse_rate-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Mathematics of the adiabatic lapse rate subsection</span> </button> <ul id="toc-Mathematics_of_the_adiabatic_lapse_rate-sublist" class="vector-toc-list"> <li id="toc-Dry_adiabatic_lapse_rate" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Dry_adiabatic_lapse_rate"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Dry adiabatic lapse rate</span> </div> </a> <ul id="toc-Dry_adiabatic_lapse_rate-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Moist_adiabatic_lapse_rate" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Moist_adiabatic_lapse_rate"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Moist adiabatic lapse rate</span> </div> </a> <ul id="toc-Moist_adiabatic_lapse_rate-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Effect_on_weather" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Effect_on_weather"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Effect on weather</span> </div> </a> <ul id="toc-Effect_on_weather-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Impact_on_the_greenhouse_effect" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Impact_on_the_greenhouse_effect"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Impact on the greenhouse effect</span> </div> </a> <ul id="toc-Impact_on_the_greenhouse_effect-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lapse_rate_in_an_isolated_column_of_gas" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Lapse_rate_in_an_isolated_column_of_gas"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Lapse rate in an isolated column of gas</span> </div> </a> <ul id="toc-Lapse_rate_in_an_isolated_column_of_gas-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">13</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Lapse rate</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 15 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-15" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">15 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%B9%D8%AF%D9%84_%D8%A7%D9%84%D8%B3%D9%82%D9%88%D8%B7" title="معدل السقوط – Arabic" lang="ar" hreflang="ar" data-title="معدل السقوط" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Atmosph%C3%A4rischer_Temperaturgradient" title="Atmosphärischer Temperaturgradient – German" lang="de" hreflang="de" data-title="Atmosphärischer Temperaturgradient" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Tasa_de_ca%C3%ADda" title="Tasa de caída – Spanish" lang="es" hreflang="es" data-title="Tasa de caída" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A2%D9%87%D9%86%DA%AF_%DA%A9%D8%A7%D9%87%D8%B4" title="آهنگ کاهش – Persian" lang="fa" hreflang="fa" data-title="آهنگ کاهش" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B8%B0%EC%98%A8_%EA%B0%90%EB%A5%A0" title="기온 감률 – Korean" lang="ko" hreflang="ko" data-title="기온 감률" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Stopa_opadanja_temperature_u_troposferi" title="Stopa opadanja temperature u troposferi – Croatian" lang="hr" hreflang="hr" data-title="Stopa opadanja temperature u troposferi" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Gradiente_termico_verticale" title="Gradiente termico verticale – Italian" lang="it" hreflang="it" data-title="Gradiente termico verticale" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Verticale_temperatuurgradi%C3%ABnt" title="Verticale temperatuurgradiënt – Dutch" lang="nl" hreflang="nl" data-title="Verticale temperatuurgradiënt" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%B0%97%E6%B8%A9%E6%B8%9B%E7%8E%87" title="気温減率 – Japanese" lang="ja" hreflang="ja" data-title="気温減率" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Kj%C3%B8lingsraten_i_atmosf%C3%A6ren" title="Kjølingsraten i atmosfæren – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Kjølingsraten i atmosfæren" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Stopa_opadanja_temperature_u_troposferi" title="Stopa opadanja temperature u troposferi – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Stopa opadanja temperature u troposferi" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%AD%E0%B8%B1%E0%B8%95%E0%B8%A3%E0%B8%B2%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%A5%E0%B8%94%E0%B8%A5%E0%B8%87%E0%B8%82%E0%B8%AD%E0%B8%87%E0%B8%AD%E0%B8%B8%E0%B8%93%E0%B8%AB%E0%B8%A0%E0%B8%B9%E0%B8%A1%E0%B8%B4" title="อัตราการลดลงของอุณหภูมิ – Thai" lang="th" hreflang="th" data-title="อัตราการลดลงของอุณหภูมิ" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A2%D0%B5%D1%80%D0%BC%D1%96%D1%87%D0%BD%D0%B8%D0%B9_%D0%B3%D1%80%D0%B0%D0%B4%D1%96%D1%94%D0%BD%D1%82_%D0%B2_%D0%B0%D1%82%D0%BC%D0%BE%D1%81%D1%84%D0%B5%D1%80%D1%96" title="Термічний градієнт в атмосфері – Ukrainian" lang="uk" hreflang="uk" data-title="Термічний градієнт в атмосфері" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%B0%A3%E6%BA%AB%E5%9E%82%E7%9B%B4%E9%81%9E%E6%B8%9B%E7%8E%87" title="氣溫垂直遞減率 – Cantonese" lang="yue" hreflang="yue" data-title="氣溫垂直遞減率" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%B0%A3%E6%BA%AB%E5%9E%82%E7%9B%B4%E9%81%9E%E6%B8%9B%E7%8E%87" title="氣溫垂直遞減率 – Chinese" lang="zh" hreflang="zh" data-title="氣溫垂直遞減率" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q66900467#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Lapse_rate" title="View the content page [c]" accesskey="c"><span>Article</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talk:Lapse_rate" rel="discussion" title="Discuss improvements to the content page [t]" accesskey="t"><span>Talk</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Change language variant" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">English</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Views"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Lapse_rate"><span>Read</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Lapse_rate&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Lapse_rate&action=history" title="Past revisions of this page [h]" accesskey="h"><span>View history</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Tools" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Tools</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Tools</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">hide</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="More options" > <div class="vector-menu-heading"> Actions </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Lapse_rate"><span>Read</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Lapse_rate&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Lapse_rate&action=history"><span>View history</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> General </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Special:WhatLinksHere/Lapse_rate" title="List of all English Wikipedia pages containing links to this page [j]" accesskey="j"><span>What links here</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:RecentChangesLinked/Lapse_rate" rel="nofollow" title="Recent changes in pages linked from this page [k]" accesskey="k"><span>Related changes</span></a></li><li id="t-upload" class="mw-list-item"><a href="//en.wikipedia.org/wiki/Wikipedia:File_Upload_Wizard" title="Upload files [u]" accesskey="u"><span>Upload file</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Special:SpecialPages" title="A list of all special pages [q]" accesskey="q"><span>Special pages</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Lapse_rate&oldid=1271834359" title="Permanent link to this revision of this page"><span>Permanent link</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Lapse_rate&action=info" title="More information about this page"><span>Page information</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Special:CiteThisPage&page=Lapse_rate&id=1271834359&wpFormIdentifier=titleform" title="Information on how to cite this page"><span>Cite this page</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Special:UrlShortener&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FLapse_rate"><span>Get shortened URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Special:QrCode&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FLapse_rate"><span>Download QR code</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Print/export </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&page=Lapse_rate&action=show-download-screen" title="Download this page as a PDF file"><span>Download as PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Lapse_rate&printable=yes" title="Printable version of this page [p]" accesskey="p"><span>Printable version</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> In other projects </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q66900467" title="Structured data on this page hosted by Wikidata [g]" accesskey="g"><span>Wikidata item</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Vertical rate of change of temperature in atmosphere</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Tatra_Rysy_5.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Tatra_Rysy_5.jpg/220px-Tatra_Rysy_5.jpg" decoding="async" width="220" height="161" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Tatra_Rysy_5.jpg/330px-Tatra_Rysy_5.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Tatra_Rysy_5.jpg/440px-Tatra_Rysy_5.jpg 2x" data-file-width="5000" data-file-height="3655" /></a><figcaption>Higher <a href="/wiki/Czarny_Staw_pod_Rysami" title="Czarny Staw pod Rysami">Czarny Staw pod Rysami</a> lake (elevation 1,583 metres (5,194 ft)) is still frozen as the lower <a href="/wiki/Morskie_Oko" title="Morskie Oko">Morskie Oko</a> lake has already almost melted (elevation 1,395 metres (4,577 ft)). Photo from <a href="/wiki/Poland" title="Poland">Polish</a> side of the <a href="/wiki/Tatra_mountains" class="mw-redirect" title="Tatra mountains">Tatra mountains</a>, May 2019.</figcaption></figure> <p>The <b>lapse rate</b> is the rate at which an atmospheric variable, normally <a href="/wiki/Temperature" title="Temperature">temperature</a> in <a href="/wiki/Earth%27s_atmosphere" class="mw-redirect" title="Earth's atmosphere">Earth's atmosphere</a>, falls with <a href="/wiki/Altitude" title="Altitude">altitude</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> <i>Lapse rate</i> arises from the word <i>lapse</i> (in its "becoming less" sense, not its "interruption" sense). In dry air, the <b>adiabatic lapse rate</b> (i.e., decrease in temperature of a parcel of air that rises in the atmosphere without exchanging energy with surrounding air) is 9.8 °C/km (5.4 °F per 1,000 ft). The saturated adiabatic lapse rate (SALR), or moist adiabatic lapse rate (MALR), is the decrease in temperature of a parcel of water-saturated air that rises in the atmosphere. It varies with the temperature and pressure of the parcel and is often in the range 3.6 to <span class="nowrap">9.2 °C/km</span> (2 to <span class="nowrap">5 °F/1000 ft</span>), as obtained from the <a href="/wiki/International_Civil_Aviation_Organization" title="International Civil Aviation Organization">International Civil Aviation Organization</a> (ICAO). The <b>environmental lapse rate</b> is the decrease in temperature of air with altitude for a specific time and place (see below). It can be highly variable between circumstances. </p><p>Lapse rate corresponds to the vertical component of the <a href="/wiki/Spatial_gradient" title="Spatial gradient">spatial gradient</a> of <a href="/wiki/Temperature_gradient" title="Temperature gradient">temperature</a>. Although this concept is most often applied to the Earth's <a href="/wiki/Troposphere" title="Troposphere">troposphere</a>, it can be extended to any gravitationally supported <a href="/wiki/Fluid_parcel" title="Fluid parcel">parcel of gas</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definition">Definition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lapse_rate&action=edit&section=1" title="Edit section: Definition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A formal definition from the <i>Glossary of Meteorology</i><sup id="cite_ref-Glossary_of_Meteorology_3-0" class="reference"><a href="#cite_note-Glossary_of_Meteorology-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> is: </p> <dl><dd>The decrease of an atmospheric variable with height, the variable being temperature unless otherwise specified.</dd></dl> <p>Typically, the lapse rate is the negative of the rate of temperature change with altitude change: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Gamma =-{\frac {\mathrm {d} T}{\mathrm {d} z}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Γ</mi> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>T</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>z</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Gamma =-{\frac {\mathrm {d} T}{\mathrm {d} z}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e20101c5d6ceea6bb614a9d083ab54ad2f2c4088" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:10.124ex; height:5.509ex;" alt="{\displaystyle \Gamma =-{\frac {\mathrm {d} T}{\mathrm {d} z}}}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Gamma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Γ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Gamma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4cfde86a3f7ec967af9955d0988592f0693d2b19" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.453ex; height:2.176ex;" alt="{\displaystyle \Gamma }"></span> (sometimes <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103168b86f781fe6e9a4a87b8ea1cebe0ad4ede8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\displaystyle L}"></span>) is the lapse rate given in <a href="/wiki/Physical_unit" class="mw-redirect" title="Physical unit">units</a> of temperature divided by units of altitude, <i>T</i> is temperature, and <i>z</i> is altitude.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Environmental_lapse_rate">Environmental lapse rate</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lapse_rate&action=edit&section=2" title="Edit section: Environmental lapse rate"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <i>environmental lapse rate</i> (ELR), is the actual rate of decrease of temperature with altitude in the atmosphere at a given time and location.<sup id="cite_ref-Daidzic19_7-0" class="reference"><a href="#cite_note-Daidzic19-7"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>The ELR is the observed lapse rate, and is to be distinguished from the <i>adiabatic lapse rate</i> which is a theoretical construct. The ELR is forced towards the adiabatic lapse rate whenever air is moving vertically. </p><p>As an average, the <a href="/wiki/International_Civil_Aviation_Organization" title="International Civil Aviation Organization">International Civil Aviation Organization</a> (ICAO) defines an <a href="/wiki/International_standard_atmosphere" class="mw-redirect" title="International standard atmosphere">international standard atmosphere</a> (ISA) with a temperature lapse rate of <span class="nowrap">6.50 °C/km</span><sup id="cite_ref-ICAO_1993_8-0" class="reference"><a href="#cite_note-ICAO_1993-8"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> <span class="nowrap">(3.56 °F</span> or <span class="nowrap">1.98 °C/1,000 ft)</span> from sea level to 11 km <span class="nowrap">(36,090 ft</span> or <span class="nowrap">6.8 mi)</span>. From 11 km up to 20 km <span class="nowrap">(65,620 ft</span> or <span class="nowrap">12.4 mi)</span>, the constant temperature is <span class="nowrap">−56.5 °C</span> <span class="nowrap">(−69.7 °F)</span>, which is the lowest assumed temperature in the ISA. The <a href="/wiki/ICAO_Standard_Atmosphere" class="mw-redirect" title="ICAO Standard Atmosphere">standard atmosphere</a> contains no moisture. </p><p>Unlike the idealized ISA, the temperature of the actual atmosphere does not always fall at a uniform rate with height. For example, there can be an <a href="/wiki/Temperature_inversion" class="mw-redirect" title="Temperature inversion">inversion</a> layer in which the temperature increases with altitude. </p> <div class="mw-heading mw-heading2"><h2 id="Cause">Cause</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lapse_rate&action=edit&section=3" title="Edit section: Cause"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The temperature profile of the atmosphere is a result of the interaction between radiative heating from <a href="/wiki/Sunlight" title="Sunlight">sunlight</a>, cooling to space via <a href="/wiki/Thermal_radiation" title="Thermal radiation">thermal radiation</a>, and upward heat transport via <a href="/wiki/Convection" title="Convection">natural convection</a> (which carries hot air and <a href="/wiki/Latent_heat" title="Latent heat">latent heat</a> upward). Above the <a href="/wiki/Tropopause" title="Tropopause">tropopause</a>, convection does not occur and all cooling is radiative. </p><p>Within the <a href="/wiki/Troposphere" title="Troposphere">troposphere</a>, the lapse rate is a essentially the consequence of a balance between (a) radiative cooling of the air, which by itself would lead to a high lapse rate; and (b) convection, which is activated when the lapse rate exceeds a critical value; convection stabilizes the environmental lapse rate and prevents it from substantially exceeding the adiabatic lapse rate.<sup id="cite_ref-Manabe64_9-0" class="reference"><a href="#cite_note-Manabe64-9"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>Sunlight hits the surface of the earth (land and sea) and heats them. The warm surface heats the air above it. In addition, nearly a third of absorbed sunlight is absorbed within the atmosphere, heating the atmosphere directly.<sup id="cite_ref-nasa-eeb17_10-0" class="reference"><a href="#cite_note-nasa-eeb17-10"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Thermal_conduction" title="Thermal conduction">Thermal conduction</a> helps transfer heat from the surface to the air; this conduction occurs within the few millimeters of air closest to the surface. However, above that thin interface layer, thermal conduction plays a negligible role in transferring heat within the atmosphere; this is because the thermal conductivity of air is very low.<sup id="cite_ref-ucar-cond_11-0" class="reference"><a href="#cite_note-ucar-cond-11"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-WallaceHobbs_12-0" class="reference"><a href="#cite_note-WallaceHobbs-12"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 387">: 387 </span></sup> </p><p>The air is radiatively cooled by <a href="/wiki/Greenhouse_gases" class="mw-redirect" title="Greenhouse gases">greenhouse gases</a> (water vapor, carbon dioxide, etc.) and clouds emitting <a href="/wiki/Outgoing_longwave_radiation" title="Outgoing longwave radiation">longwave thermal radiation</a> to space.<sup id="cite_ref-Hartmann22_13-0" class="reference"><a href="#cite_note-Hartmann22-13"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p>If <a href="/wiki/Radiation" title="Radiation">radiation</a> were the only way to transfer energy within the atmosphere, then the lapse rate near the surface would be roughly 40 °C/km and the <a href="/wiki/Greenhouse_effect" title="Greenhouse effect">greenhouse effect</a> of gases in the atmosphere would keep the ground at roughly 333 K (60 °C; 140 °F).<sup id="cite_ref-Goody_14-0" class="reference"><a href="#cite_note-Goody-14"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 59–60">: 59–60 </span></sup> </p><p>However, when air gets hot or humid, its density decreases.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> Thus, air which has been heated by the surface tends to rise and carry internal energy upward, especially if the air has been moistened by evaporation from water surfaces. This is the process of <a href="/wiki/Convection" title="Convection">convection</a>. Vertical convective motion stops when a parcel of air at a given altitude has the same density as the other air at the same elevation. </p><p>Convection carries hot, moist air upward and cold, dry air downward, with a net effect of transferring heat upward. This makes the air below cooler than it would otherwise be and the air above warmer. </p><p>When convection happens, this shifts the <i>environmental lapse rate</i> towards the <i>adiabatic lapse rate</i>, which is a thermal gradient characteristic of vertically moving air packets. </p><p>Because convection is available to transfer heat within the atmosphere, the lapse rate in the troposphere is reduced to around 6.5 °C/km<sup id="cite_ref-Manabe64_9-1" class="reference"><a href="#cite_note-Manabe64-9"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> and the greenhouse effect is reduced to a point where Earth has its observed surface temperature of around 288 K (15 °C; 59 °F). </p> <div class="mw-heading mw-heading2"><h2 id="Convection_and_adiabatic_expansion">Convection and adiabatic expansion</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lapse_rate&action=edit&section=4" title="Edit section: Convection and adiabatic expansion"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Emagram.GIF" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/Emagram.GIF/350px-Emagram.GIF" decoding="async" width="350" height="264" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/Emagram.GIF/525px-Emagram.GIF 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/13/Emagram.GIF/700px-Emagram.GIF 2x" data-file-width="2540" data-file-height="1916" /></a><figcaption><a href="/wiki/Emagram" title="Emagram">Emagram</a> diagram showing variation of dry adiabats (bold lines) and moist adiabats (dash lines) according to pressure and temperature</figcaption></figure> <p>As convection causes parcels of air to rise or fall, there is little heat transfer between those parcels and the surrounding air. Air has low <a href="/wiki/Thermal_conductivity" class="mw-redirect" title="Thermal conductivity">thermal conductivity</a>, and the bodies of air involved are very large; so transfer of heat by <a href="/wiki/Heat_conduction" class="mw-redirect" title="Heat conduction">conduction</a> is negligibly small. Also, intra-atmospheric radiative heat transfer is relatively slow and so is negligible for moving air. Thus, when air ascends or descends, there is little exchange of heat with the surrounding air. A process in which no heat is exchanged with the environment is referred to as an <a href="/wiki/Adiabatic_process" title="Adiabatic process">adiabatic process</a>. </p><p>Air expands as it moves upward, and contracts as it moves downward. The expansion of rising air parcels, and the contraction of descending air parcels, are adiabatic processes, to a good approximation. </p><p>When a parcel of air expands, it pushes on the air around it, doing <a href="/wiki/Work_(thermodynamics)" title="Work (thermodynamics)">thermodynamic work</a>. Since the upward-moving and expanding parcel does work but gains no heat, it loses <a href="/wiki/Internal_energy" title="Internal energy">internal energy</a> so that its temperature decreases. Downward-moving and contracting air has work done on it, so it gains internal energy and its temperature increases. </p><p>Adiabatic processes for air have a characteristic temperature-pressure curve. As air circulates vertically, the air takes on that characteristic gradient. When the air contains little water, this lapse rate is known as the dry adiabatic lapse rate: the rate of temperature decrease is <span class="nowrap">9.8 °C/km</span> (<span class="nowrap">5.4 °F</span> per 1,000 ft) (3.0 °C/1,000 ft). The reverse occurs for a sinking parcel of air.<sup id="cite_ref-DLA_17-0" class="reference"><a href="#cite_note-DLA-17"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p><p>When the environmental lapse rate is less than the adiabatic lapse rate the atmosphere is stable and convection will not occur.<sup id="cite_ref-Goody_14-1" class="reference"><a href="#cite_note-Goody-14"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 63">: 63 </span></sup> </p><p>Only the <a href="/wiki/Troposphere" title="Troposphere">troposphere</a> (up to approximately 12 kilometres (39,000 ft) of altitude) in the Earth's atmosphere undergoes <a href="/wiki/Convection" title="Convection">convection</a>: the <a href="/wiki/Stratosphere" title="Stratosphere">stratosphere</a> does not generally convect.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> However, some exceptionally energetic convection processes, such as volcanic <a href="/wiki/Eruption_column" title="Eruption column">eruption columns</a> and <a href="/wiki/Overshooting_top" title="Overshooting top">overshooting tops</a> associated with severe <a href="/wiki/Supercell_thunderstorms" class="mw-redirect" title="Supercell thunderstorms">supercell thunderstorms</a>, may locally and temporarily inject convection through the <a href="/wiki/Tropopause" title="Tropopause">tropopause</a> and into the stratosphere. </p><p>Energy transport in the atmosphere is more complex than the interaction between radiation and dry convection. The <a href="/wiki/Water_cycle" title="Water cycle">water cycle</a> (including <a href="/wiki/Evaporation" title="Evaporation">evaporation</a>, <a href="/wiki/Condensation" title="Condensation">condensation</a>, <a href="/wiki/Deposition_(aerosol_physics)" title="Deposition (aerosol physics)">precipitation</a>) transports <a href="/wiki/Latent_heat" title="Latent heat">latent heat</a> and affects atmospheric humidity levels, significantly influencing the temperature profile, as described below. </p> <div class="mw-heading mw-heading2"><h2 id="Mathematics_of_the_adiabatic_lapse_rate">Mathematics of the adiabatic lapse rate</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lapse_rate&action=edit&section=5" title="Edit section: Mathematics of the adiabatic lapse rate"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Adiabatic_lapse_rate.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Adiabatic_lapse_rate.svg/220px-Adiabatic_lapse_rate.svg.png" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Adiabatic_lapse_rate.svg/330px-Adiabatic_lapse_rate.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Adiabatic_lapse_rate.svg/440px-Adiabatic_lapse_rate.svg.png 2x" data-file-width="512" data-file-height="384" /></a><figcaption>Simplified graph of atmospheric lapse rate near sea level</figcaption></figure> <p>The following calculations derive the temperature as a function of altitude for a packet of air which is ascending or descending without exchanging heat with its environment. </p> <div class="mw-heading mw-heading3"><h3 id="Dry_adiabatic_lapse_rate">Dry adiabatic lapse rate</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lapse_rate&action=edit&section=6" title="Edit section: Dry adiabatic lapse rate"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Thermodynamics defines an adiabatic process as: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P\,\mathrm {d} V=-{\frac {V\,\mathrm {d} P}{\gamma }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>V</mi> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>V</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>P</mi> </mrow> <mi>γ</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P\,\mathrm {d} V=-{\frac {V\,\mathrm {d} P}{\gamma }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/10050b1dd9247daf43d9f46d662b943542051178" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:16.167ex; height:5.843ex;" alt="{\displaystyle P\,\mathrm {d} V=-{\frac {V\,\mathrm {d} P}{\gamma }}}"></span></dd></dl> <p>the <a href="/wiki/First_law_of_thermodynamics" title="First law of thermodynamics">first law of thermodynamics</a> can be written as </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle mc_{\text{v}}\,\mathrm {d} T-{\frac {V\,\mathrm {d} P}{\gamma }}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>v</mtext> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>T</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>V</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>P</mi> </mrow> <mi>γ</mi> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle mc_{\text{v}}\,\mathrm {d} T-{\frac {V\,\mathrm {d} P}{\gamma }}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/072030196639e3a39de464b5f345642a3aeb9201" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:20.613ex; height:5.843ex;" alt="{\displaystyle mc_{\text{v}}\,\mathrm {d} T-{\frac {V\,\mathrm {d} P}{\gamma }}=0}"></span></dd></dl> <p>Also, since the density <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho =m/V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mo>=</mo> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho =m/V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0fc1491740a8e3cd017deeb787fe8ccd36697394" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.29ex; height:2.843ex;" alt="{\displaystyle \rho =m/V}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \gamma =c_{\text{p}}/c_{\text{v}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>γ</mi> <mo>=</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>p</mtext> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>v</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gamma =c_{\text{p}}/c_{\text{v}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f8693e645cb2d1dc60c5a1374983ac963848108" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:9.783ex; height:3.009ex;" alt="{\displaystyle \gamma =c_{\text{p}}/c_{\text{v}}}"></span>, we can show that: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho c_{\text{p}}\,\mathrm {d} T-\mathrm {d} P=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>p</mtext> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>T</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>P</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho c_{\text{p}}\,\mathrm {d} T-\mathrm {d} P=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1111a822eb5706f07d1295b3cd82416ac3c7870" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:16.81ex; height:2.843ex;" alt="{\displaystyle \rho c_{\text{p}}\,\mathrm {d} T-\mathrm {d} P=0}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{\text{p}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>p</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{\text{p}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/693d4dcf70a6906cc00d78a5257138b181a3ec1a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.153ex; height:2.343ex;" alt="{\displaystyle c_{\text{p}}}"></span> is the <a href="/wiki/Specific_heat" class="mw-redirect" title="Specific heat">specific heat</a> at constant pressure. </p><p>Assuming an atmosphere in <a href="/wiki/Hydrostatic_equilibrium" title="Hydrostatic equilibrium">hydrostatic equilibrium</a>:<sup id="cite_ref-LL_19-0" class="reference"><a href="#cite_note-LL-19"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} P=-\rho g\,\mathrm {d} z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>P</mi> <mo>=</mo> <mo>−</mo> <mi>ρ</mi> <mi>g</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} P=-\rho g\,\mathrm {d} z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/246026e1b83a8f19e16e2914d13279b20e55c1c1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.03ex; height:2.676ex;" alt="{\displaystyle \mathrm {d} P=-\rho g\,\mathrm {d} z}"></span></dd></dl> <p>where <i>g</i> is the <a href="/wiki/Standard_gravity" title="Standard gravity">standard gravity</a>. Combining these two equations to eliminate the pressure, one arrives at the result for the <i>dry adiabatic lapse rate</i> (DALR),<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Gamma _{\text{d}}=-{\frac {\mathrm {d} T}{\mathrm {d} z}}={\frac {g}{c_{\text{p}}}}=9.8\ ^{\circ }{\text{C}}/{\text{km}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>d</mtext> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>T</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>z</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>g</mi> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>p</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mn>9.8</mn> <msup> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>C</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>km</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Gamma _{\text{d}}=-{\frac {\mathrm {d} T}{\mathrm {d} z}}={\frac {g}{c_{\text{p}}}}=9.8\ ^{\circ }{\text{C}}/{\text{km}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a52f55ee835449963af6df459b1fdfd6f8b647c7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:31.067ex; height:6.009ex;" alt="{\displaystyle \Gamma _{\text{d}}=-{\frac {\mathrm {d} T}{\mathrm {d} z}}={\frac {g}{c_{\text{p}}}}=9.8\ ^{\circ }{\text{C}}/{\text{km}}}"></span></dd></dl> <p>The DALR (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Gamma _{\text{d}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>d</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Gamma _{\text{d}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ea35550d79ddeeffcce4658efc8044e95e67858" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.599ex; height:2.509ex;" alt="{\displaystyle \Gamma _{\text{d}}}"></span>) is the temperature gradient experienced in an ascending or descending packet of air that is not saturated with water vapor, i.e., with less than 100% relative humidity. </p> <div class="mw-heading mw-heading3"><h3 id="Moist_adiabatic_lapse_rate">Moist adiabatic lapse rate</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lapse_rate&action=edit&section=7" title="Edit section: Moist adiabatic lapse rate"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The presence of water within the atmosphere (usually the troposphere) complicates the process of convection. Water vapor contains latent <a href="/wiki/Heat_of_vaporization" class="mw-redirect" title="Heat of vaporization">heat of vaporization</a>. As a parcel of air rises and cools, it eventually becomes <a href="/wiki/Dew_point" title="Dew point">saturated</a>; that is, the vapor pressure of water in equilibrium with liquid water has decreased (as temperature has decreased) to the point where it is equal to the actual vapor pressure of water. With further decrease in temperature the water vapor in excess of the equilibrium amount condenses, forming <a href="/wiki/Cloud" title="Cloud">cloud</a>, and releasing heat (latent heat of condensation). Before saturation, the rising air follows the dry adiabatic lapse rate. After saturation, the rising air follows the moist (or <i>wet</i>) adiabatic lapse rate.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> The release of latent heat is an important source of energy in the development of thunderstorms. </p><p>While the dry adiabatic lapse rate is a constant <span class="nowrap">9.8 °C/km</span> (<span class="nowrap">5.4 °F</span> per 1,000 ft, <span class="nowrap">3 °C/1,000 ft</span>), the moist adiabatic lapse rate varies strongly with temperature. A typical value is around <span class="nowrap">5 °C/km</span>, (<span class="nowrap">9 °F/km</span>, <span class="nowrap">2.7 °F/1,000 ft</span>, <span class="nowrap">1.5 °C/1,000 ft</span>).<sup id="cite_ref-MLM_22-0" class="reference"><a href="#cite_note-MLM-22"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> The formula for the <i>saturated adiabatic lapse rate</i> (SALR) or <i>moist adiabatic lapse rate</i> (MALR) is given by:<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Gamma _{\text{w}}=g\,{\frac {\left(1+{\dfrac {H_{\text{v}}\,r}{R_{\text{sd}}\,T}}\right)}{\left(c_{\text{pd}}+{\dfrac {H_{\text{v}}^{2}\,r}{R_{\text{sw}}\,T^{2}}}\right)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>w</mtext> </mrow> </msub> <mo>=</mo> <mi>g</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mrow> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>v</mtext> </mrow> </msub> <mspace width="thinmathspace" /> <mi>r</mi> </mrow> <mrow> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sd</mtext> </mrow> </msub> <mspace width="thinmathspace" /> <mi>T</mi> </mrow> </mfrac> </mstyle> </mrow> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>pd</mtext> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mrow> <msubsup> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>v</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mspace width="thinmathspace" /> <mi>r</mi> </mrow> <mrow> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sw</mtext> </mrow> </msub> <mspace width="thinmathspace" /> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mstyle> </mrow> </mrow> <mo>)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Gamma _{\text{w}}=g\,{\frac {\left(1+{\dfrac {H_{\text{v}}\,r}{R_{\text{sd}}\,T}}\right)}{\left(c_{\text{pd}}+{\dfrac {H_{\text{v}}^{2}\,r}{R_{\text{sw}}\,T^{2}}}\right)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e87ea10af9a84d0e16a7a981c7883aa31c666f63" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.005ex; width:25.466ex; height:13.009ex;" alt="{\displaystyle \Gamma _{\text{w}}=g\,{\frac {\left(1+{\dfrac {H_{\text{v}}\,r}{R_{\text{sd}}\,T}}\right)}{\left(c_{\text{pd}}+{\dfrac {H_{\text{v}}^{2}\,r}{R_{\text{sw}}\,T^{2}}}\right)}}}"></span></dd></dl> <p>where: </p> <dl><dd><table border="0" cellpadding="2"> <tbody><tr> <td style="text-align:right;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Gamma _{\text{w}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>w</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Gamma _{\text{w}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f87cc3569211524c09c3603e37ce8ffa36039b6a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.872ex; height:2.509ex;" alt="{\displaystyle \Gamma _{\text{w}}}"></span>, </td> <td>wet adiabatic lapse rate, K/m </td></tr> <tr> <td style="text-align:right;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>g</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3556280e66fe2c0d0140df20935a6f057381d77" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.116ex; height:2.009ex;" alt="{\displaystyle g}"></span>, </td> <td>Earth's <a href="/wiki/Standard_gravity" title="Standard gravity">gravitational acceleration</a> = 9.8076 m/s<sup>2</sup> </td></tr> <tr> <td style="text-align:right;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H_{v}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{v}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d28ba17998d9411b7ddf3586f00fca2135c20ec8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.961ex; height:2.509ex;" alt="{\displaystyle H_{v}}"></span>, </td> <td><a href="/wiki/Heat_of_vaporization" class="mw-redirect" title="Heat of vaporization">heat of vaporization</a> of water = <span class="nowrap"><span data-sort-value="7006250100000000000♠"></span>2<span style="margin-left:.25em;">501</span><span style="margin-left:.25em;">000</span> J/kg</span> </td></tr> <tr> <td style="text-align:right;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{\text{sd}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sd</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{\text{sd}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d35b48e5061919019226fde6b7458818ef998c3c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.558ex; height:2.509ex;" alt="{\displaystyle R_{\text{sd}}}"></span>, </td> <td><a href="/wiki/Specific_gas_constant" class="mw-redirect" title="Specific gas constant">specific gas constant</a> of dry air = 287 J/kg·K </td></tr> <tr> <td style="text-align:right;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{\text{sw}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sw</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{\text{sw}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4db283b45fe1df00577d47fae8048448d27931c9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.831ex; height:2.509ex;" alt="{\displaystyle R_{\text{sw}}}"></span>, </td> <td>specific gas constant of water vapour = 461.5 J/kg·K </td></tr> <tr> <td style="text-align:right;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \epsilon ={\frac {R_{\text{sd}}}{R_{\text{sw}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϵ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sd</mtext> </mrow> </msub> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sw</mtext> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \epsilon ={\frac {R_{\text{sd}}}{R_{\text{sw}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6b911786c5b836552b5a1abbe86c450548a11246" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:8.709ex; height:5.676ex;" alt="{\displaystyle \epsilon ={\frac {R_{\text{sd}}}{R_{\text{sw}}}}}"></span>, </td> <td>the dimensionless ratio of the specific gas constant of dry air to the specific gas constant for water vapour = 0.622 </td></tr> <tr> <td style="text-align:right;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd253103f0876afc68ebead27a5aa9867d927467" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.083ex; height:1.676ex;" alt="{\displaystyle e}"></span>, </td> <td>the water <a href="/wiki/Vapour_pressure" class="mw-redirect" title="Vapour pressure">vapour pressure</a> of the saturated air </td></tr> <tr> <td style="text-align:right;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r={\frac {\epsilon e}{p-e}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>ϵ</mi> <mi>e</mi> </mrow> <mrow> <mi>p</mi> <mo>−</mo> <mi>e</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r={\frac {\epsilon e}{p-e}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e6e4175910e710ac34e1e0388b087647326851fa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:10.077ex; height:5.176ex;" alt="{\displaystyle r={\frac {\epsilon e}{p-e}}}"></span>, </td> <td>the <a href="/wiki/Mixing_ratio" title="Mixing ratio">mixing ratio</a> of the mass of water vapour to the mass of dry air<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td style="text-align:right;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span>, </td> <td>the pressure of the saturated air </td></tr> <tr> <td style="text-align:right;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span>, </td> <td>temperature of the saturated air, K </td></tr> <tr> <td style="text-align:right;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{\text{pd}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>pd</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{\text{pd}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/12e8c61ce248afd33bd09ba97e700ddbd510fe54" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.067ex; height:2.343ex;" alt="{\displaystyle c_{\text{pd}}}"></span>, </td> <td>the <a href="/wiki/Specific_heat" class="mw-redirect" title="Specific heat">specific heat</a> of dry air at constant pressure, = 1003.5<span class="nowrap"> </span>J/kg·K </td></tr></tbody></table></dd></dl> <p>The SALR or MALR (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Gamma _{\text{w}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>w</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Gamma _{\text{w}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f87cc3569211524c09c3603e37ce8ffa36039b6a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.872ex; height:2.509ex;" alt="{\displaystyle \Gamma _{\text{w}}}"></span>) is the temperature gradient experienced in an ascending or descending packet of air that is saturated with water vapor, i.e., with 100% relative humidity. </p> <div class="mw-heading mw-heading2"><h2 id="Effect_on_weather">Effect on weather</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lapse_rate&action=edit&section=8" title="Edit section: Effect on weather"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-One_source plainlinks metadata ambox ambox-content ambox-one_source" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>relies largely or entirely on a <a href="/wiki/Wikipedia:Articles_with_a_single_source" title="Wikipedia:Articles with a single source">single source</a></b>.<span class="hide-when-compact"> Relevant discussion may be found on the <a href="/wiki/Talk:Lapse_rate" title="Talk:Lapse rate">talk page</a>. Please help <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Lapse_rate&action=edit">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">introducing citations to additional sources</a>.<br /><small><span class="plainlinks"><i>Find sources:</i> <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&q=%22Lapse+rate%22">"Lapse rate"</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22Lapse+rate%22+-wikipedia&tbs=ar:1">news</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22Lapse+rate%22&tbs=bkt:s&tbm=bks">newspapers</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?tbs=bks:1&q=%22Lapse+rate%22+-wikipedia">books</a> <b>·</b> <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22Lapse+rate%22">scholar</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Lapse+rate%22&acc=on&wc=on">JSTOR</a></span></small></span> <span class="date-container"><i>(<span class="date">March 2022</span>)</i></span></div></td></tr></tbody></table> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Anvil_shaped_cumulus_panorama_edit_crop.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/Anvil_shaped_cumulus_panorama_edit_crop.jpg/365px-Anvil_shaped_cumulus_panorama_edit_crop.jpg" decoding="async" width="365" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/Anvil_shaped_cumulus_panorama_edit_crop.jpg/548px-Anvil_shaped_cumulus_panorama_edit_crop.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/98/Anvil_shaped_cumulus_panorama_edit_crop.jpg/730px-Anvil_shaped_cumulus_panorama_edit_crop.jpg 2x" data-file-width="2348" data-file-height="965" /></a><figcaption>The latent heat of vaporization adds energy to clouds and storms.</figcaption></figure> <p>The varying environmental lapse rates throughout the Earth's atmosphere are of critical importance in <a href="/wiki/Meteorology" title="Meteorology">meteorology</a>, particularly within the <a href="/wiki/Troposphere" title="Troposphere">troposphere</a>. They are used to determine if the <a href="/wiki/Air_parcel" class="mw-redirect" title="Air parcel">parcel</a> of rising air will rise high enough for its water to condense to form <a href="/wiki/Cloud" title="Cloud">clouds</a>, and, having formed clouds, whether the air will continue to rise and form bigger shower clouds, and whether these clouds will get even bigger and form <a href="/wiki/Cumulonimbus_cloud" title="Cumulonimbus cloud">cumulonimbus clouds</a> (thunder clouds). </p><p>As unsaturated air rises, its temperature drops at the dry adiabatic rate. The <a href="/wiki/Dew_point" title="Dew point">dew point</a> also drops (as a result of decreasing air pressure) but much more slowly, typically about <span class="nowrap">2 °C</span> per 1,000 m. If unsaturated air rises far enough, eventually its temperature will reach its <a href="/wiki/Dew_point" title="Dew point">dew point</a>, and condensation will begin to form. This altitude is known as the <a href="/wiki/Lifting_condensation_level" title="Lifting condensation level">lifting condensation level</a> (LCL) when mechanical lift is present and the <a href="/wiki/Convective_condensation_level" title="Convective condensation level">convective condensation level</a> (CCL) when mechanical lift is absent, in which case, the parcel must be heated from below to its <a href="/wiki/Convective_temperature" title="Convective temperature">convective temperature</a>. The <a href="/wiki/Cloud_base" title="Cloud base">cloud base</a> will be somewhere within the layer bounded by these parameters. </p><p>The difference between the dry adiabatic lapse rate and the rate at which the <a href="/wiki/Dew_point" title="Dew point">dew point</a> drops is around <span class="nowrap">4.5 °C</span> per 1,000 m. Given a difference in temperature and <a href="/wiki/Dew_point" title="Dew point">dew point</a> readings on the ground, one can easily find the LCL by multiplying the difference by 125 m/°C. </p><p>If the environmental lapse rate is less than the moist adiabatic lapse rate, the air is absolutely stable — rising air will cool faster than the surrounding air and lose <a href="/wiki/Buoyancy" title="Buoyancy">buoyancy</a>. This often happens in the early morning, when the air near the ground has cooled overnight. Cloud formation in stable air is unlikely. </p><p>If the environmental lapse rate is between the moist and dry adiabatic lapse rates, the air is conditionally unstable — an unsaturated parcel of air does not have sufficient buoyancy to rise to the LCL or CCL, and it is stable to weak vertical displacements in either direction. If the parcel is saturated it is unstable and will rise to the LCL or CCL, and either be halted due to an <a href="/wiki/Inversion_(meteorology)" title="Inversion (meteorology)">inversion layer</a> of <a href="/wiki/Convective_inhibition" title="Convective inhibition">convective inhibition</a>, or if lifting continues, deep, moist convection (DMC) may ensue, as a parcel rises to the <a href="/wiki/Level_of_free_convection" title="Level of free convection">level of free convection</a> (LFC), after which it enters the <a href="/wiki/Free_convective_layer" title="Free convective layer">free convective layer</a> (FCL) and usually rises to the <a href="/wiki/Equilibrium_level" title="Equilibrium level">equilibrium level</a> (EL). </p><p>If the environmental lapse rate is larger than the dry adiabatic lapse rate, it has a superadiabatic lapse rate, the air is absolutely unstable — a parcel of air will gain buoyancy as it rises both below and above the lifting condensation level or convective condensation level. This often happens in the afternoon mainly over land masses. In these conditions, the likelihood of <a href="/wiki/Cumulus_cloud" title="Cumulus cloud">cumulus clouds</a>, showers or even <a href="/wiki/Thunderstorm" title="Thunderstorm">thunderstorms</a> is increased. </p><p>Meteorologists use <a href="/wiki/Radiosonde" title="Radiosonde">radiosondes</a> to measure the environmental lapse rate and compare it to the predicted adiabatic lapse rate to forecast the likelihood that air will rise. Charts of the environmental lapse rate are known as <a href="/wiki/Thermodynamic_diagrams" title="Thermodynamic diagrams">thermodynamic diagrams</a>, examples of which include <a href="/wiki/Skew-T_log-P_diagram" title="Skew-T log-P diagram">Skew-T log-P diagrams</a> and <a href="/wiki/Tephigram" title="Tephigram">tephigrams</a>. (See also <a href="/wiki/Thermals" class="mw-redirect" title="Thermals">Thermals</a>). </p><p>The difference in moist adiabatic lapse rate and the dry rate is the cause of <a href="/wiki/Foehn_wind" title="Foehn wind">foehn wind</a> phenomenon (also known as "<a href="/wiki/Chinook_wind" title="Chinook wind">Chinook winds</a>" in parts of North America). The phenomenon exists because warm moist air rises through <a href="/wiki/Orographic_lifting" class="mw-redirect" title="Orographic lifting">orographic lifting</a> up and over the top of a mountain range or large mountain. The temperature decreases with the dry adiabatic lapse rate, until it hits the dew point, where water vapor in the air begins to condense. Above that altitude, the adiabatic lapse rate decreases to the moist adiabatic lapse rate as the air continues to rise. Condensation is also commonly followed by <a href="/wiki/Precipitation_(meteorology)" class="mw-redirect" title="Precipitation (meteorology)">precipitation</a> on the top and <a href="/wiki/Windward" class="mw-redirect" title="Windward">windward</a> sides of the mountain. As the air descends on the leeward side, it is warmed by <a href="/wiki/Adiabatic_compression" class="mw-redirect" title="Adiabatic compression">adiabatic compression</a> at the dry adiabatic lapse rate. Thus, the foehn wind at a certain altitude is warmer than the corresponding altitude on the windward side of the mountain range. In addition, because the air has lost much of its original water vapor content, the descending air creates an <a href="/wiki/Arid" class="mw-redirect" title="Arid">arid</a> region on the leeward side of the mountain.<sup id="cite_ref-Whiteman_25-0" class="reference"><a href="#cite_note-Whiteman-25"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Impact_on_the_greenhouse_effect">Impact on the greenhouse effect</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lapse_rate&action=edit&section=9" title="Edit section: Impact on the greenhouse effect"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>If the environmental lapse rate was zero, so that the atmosphere was the same temperature at all elevations, then there would be no <a href="/wiki/Greenhouse_effect" title="Greenhouse effect">greenhouse effect</a>. This doesn't mean the lapse rate and the greenhouse effect are the same thing, just that the lapse rate is a prerequisite for the greenhouse effect.<sup id="cite_ref-ThomasStamnes1999_26-0" class="reference"><a href="#cite_note-ThomasStamnes1999-26"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </p><p>The presence of greenhouse gases on a planet causes radiative cooling of the air, which leads to the formation of a non-zero lapse rate. So, the presence of greenhouse gases leads to there being a greenhouse effect at a global level. However, this need not be the case at a localized level. </p><p>The localized greenhouse effect is stronger in locations where the lapse rate is stronger. In Antarctica, thermal inversions in the atmosphere (so that air at higher altitudes is warmer) sometimes cause the localized greenhouse effect to become negative (signifying enhanced radiative cooling to space instead of inhibited radiative cooling as is the case for a positive greenhouse effect).<sup id="cite_ref-hsch_27-0" class="reference"><a href="#cite_note-hsch-27"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-sejas_28-0" class="reference"><a href="#cite_note-sejas-28"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Lapse_rate_in_an_isolated_column_of_gas">Lapse rate in an isolated column of gas</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lapse_rate&action=edit&section=10" title="Edit section: Lapse rate in an isolated column of gas"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A question has sometimes arisen as to whether a temperature gradient will arise in a column of still air in a gravitational field without external energy flows. This issue was addressed by <a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">James Clerk Maxwell</a> in 1902, who established that if any temperature gradient forms, then that temperature gradient must be universal (i.e., the gradient must be same for all materials) or the <a href="/wiki/Second_law_of_thermodynamics" title="Second law of thermodynamics">second law of thermodynamics</a> would be violated. Maxwell also concluded that the universal result must be one in which the temperature is uniform, i.e., the lapse rate is zero.<sup id="cite_ref-MaxwellToH_29-0" class="reference"><a href="#cite_note-MaxwellToH-29"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> </p><p>Santiago and Visser (2019) confirm the correctness of Maxwell's conclusion (zero lapse rate) provided relativistic effects are neglected. When <a href="/wiki/General_relativity" title="General relativity">relativity</a> is taken into account, gravity gives rise to an extremely small lapse rate, the Tolman gradient (derived by R. C. Tolman in 1930). At Earth's surface, the Tolman gradient would be about <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Gamma _{t}=T_{s}\times (10^{-16}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>×</mo> <mo stretchy="false">(</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>16</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Gamma _{t}=T_{s}\times (10^{-16}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa35110513845c5dbfb830f3bc0207447a32b3c9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.963ex; height:3.176ex;" alt="{\displaystyle \Gamma _{t}=T_{s}\times (10^{-16}}"></span>m<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ^{-1})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ^{-1})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/632fa976e6555059158ab55d3f77279a52507303" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.237ex; height:3.176ex;" alt="{\displaystyle ^{-1})}"></span>, where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{s}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{s}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/942b5ac7697c72b9e3bc1e3b340daf7189fdf61f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.361ex; height:2.509ex;" alt="{\displaystyle T_{s}}"></span> is the temperature of the gas at the elevation of Earth's surface. Santiago and Visser remark that "gravity is the only force capable of creating temperature gradients in thermal equilibrium states without violating the laws of thermodynamics" and "the existence of Tolman's temperature gradient is not at all controversial (at least not within the general relativity community)."<sup id="cite_ref-SantiagoVisser19_30-0" class="reference"><a href="#cite_note-SantiagoVisser19-30"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Tolman1930_31-0" class="reference"><a href="#cite_note-Tolman1930-31"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lapse_rate&action=edit&section=11" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Adiabatic_process" title="Adiabatic process">Adiabatic process</a></li> <li><a href="/wiki/Atmospheric_thermodynamics" title="Atmospheric thermodynamics">Atmospheric thermodynamics</a></li> <li><a href="/wiki/Fluid_dynamics" title="Fluid dynamics">Fluid dynamics</a></li> <li><a href="/wiki/Foehn_wind" title="Foehn wind">Foehn wind</a></li> <li><a href="/wiki/Climate_change_feedback#Lapse_rate" class="mw-redirect" title="Climate change feedback">Lapse rate climate feedback</a></li> <li><a href="/wiki/Scale_height" title="Scale height">Scale height</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lapse_rate&action=edit&section=12" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-lower-alpha"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text">Note: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Gamma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Γ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Gamma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4cfde86a3f7ec967af9955d0988592f0693d2b19" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.453ex; height:2.176ex;" alt="{\displaystyle \Gamma }"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \gamma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>γ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gamma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a223c880b0ce3da8f64ee33c4f0010beee400b1a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.262ex; height:2.176ex;" alt="{\displaystyle \gamma }"></span> are both used in this article but with very distinct meanings.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lapse_rate&action=edit&section=13" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist reflist-columns references-column-width reflist-columns-2"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFJacobson2005" class="citation book cs1">Jacobson, Mark Zachary (2005). <i>Fundamentals of Atmospheric Modeling</i> (2nd ed.). <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-83970-9" title="Special:BookSources/978-0-521-83970-9"><bdi>978-0-521-83970-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fundamentals+of+Atmospheric+Modeling&rft.edition=2nd&rft.pub=Cambridge+University+Press&rft.date=2005&rft.isbn=978-0-521-83970-9&rft.aulast=Jacobson&rft.aufirst=Mark+Zachary&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALapse+rate" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAhrens2006" class="citation book cs1">Ahrens, C. Donald (2006). <i>Meteorology Today</i> (8th ed.). Brooks/Cole Publishing. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-495-01162-0" title="Special:BookSources/978-0-495-01162-0"><bdi>978-0-495-01162-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Meteorology+Today&rft.edition=8th&rft.pub=Brooks%2FCole+Publishing&rft.date=2006&rft.isbn=978-0-495-01162-0&rft.aulast=Ahrens&rft.aufirst=C.+Donald&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALapse+rate" class="Z3988"></span></span> </li> <li id="cite_note-Glossary_of_Meteorology-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-Glossary_of_Meteorology_3-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTodd_S._Glickman2000" class="citation book cs1">Todd S. Glickman (June 2000). <i>Glossary of Meteorology</i> (2nd ed.). <a href="/wiki/American_Meteorological_Society" title="American Meteorological Society">American Meteorological Society</a>, <a href="/wiki/Boston" title="Boston">Boston</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-878220-34-9" title="Special:BookSources/978-1-878220-34-9"><bdi>978-1-878220-34-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Glossary+of+Meteorology&rft.edition=2nd&rft.pub=American+Meteorological+Society%2C+Boston&rft.date=2000-06&rft.isbn=978-1-878220-34-9&rft.au=Todd+S.+Glickman&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALapse+rate" class="Z3988"></span> <a rel="nofollow" class="external text" href="http://www.ametsoc.org/pubs/glossary_index.html">(Glossary of Meteorology)</a></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSalomons,_Erik_M.2001" class="citation book cs1">Salomons, Erik M. (2001). <i>Computational Atmospheric Acoustics</i> (1st ed.). Kluwer Academic Publishers. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4020-0390-5" title="Special:BookSources/978-1-4020-0390-5"><bdi>978-1-4020-0390-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Computational+Atmospheric+Acoustics&rft.edition=1st&rft.pub=Kluwer+Academic+Publishers&rft.date=2001&rft.isbn=978-1-4020-0390-5&rft.au=Salomons%2C+Erik+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALapse+rate" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStull,_Roland_B.2001" class="citation book cs1">Stull, Roland B. (2001). <i>An Introduction to Boundary Layer Meteorology</i> (1st ed.). Kluwer Academic Publishers. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-90-277-2769-5" title="Special:BookSources/978-90-277-2769-5"><bdi>978-90-277-2769-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=An+Introduction+to+Boundary+Layer+Meteorology&rft.edition=1st&rft.pub=Kluwer+Academic+Publishers&rft.date=2001&rft.isbn=978-90-277-2769-5&rft.au=Stull%2C+Roland+B.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALapse+rate" class="Z3988"></span></span> </li> <li id="cite_note-Daidzic19-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-Daidzic19_7-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDaidzic2019" class="citation journal cs1">Daidzic, Nihad E. (2019). <a rel="nofollow" class="external text" href="https://commons.erau.edu/cgi/viewcontent.cgi?article=1374&context=ijaaa">"On Atmospheric Lapse Rates"</a>. <i>International Journal of Aviation, Aeronautics, and Aerospace</i>. <b>6</b> (4). <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.15394%2Fijaaa.2019.1374">10.15394/ijaaa.2019.1374</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=International+Journal+of+Aviation%2C+Aeronautics%2C+and+Aerospace&rft.atitle=On+Atmospheric+Lapse+Rates&rft.volume=6&rft.issue=4&rft.date=2019&rft_id=info%3Adoi%2F10.15394%2Fijaaa.2019.1374&rft.aulast=Daidzic&rft.aufirst=Nihad+E.&rft_id=https%3A%2F%2Fcommons.erau.edu%2Fcgi%2Fviewcontent.cgi%3Farticle%3D1374%26context%3Dijaaa&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALapse+rate" class="Z3988"></span></span> </li> <li id="cite_note-ICAO_1993-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-ICAO_1993_8-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><i>Manual of the ICAO Standard Atmosphere (extended to 80 kilometres (262 500 feet))</i> (Third ed.). <a href="/wiki/International_Civil_Aviation_Organization" title="International Civil Aviation Organization">International Civil Aviation Organization</a>. 1993. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-92-9194-004-2" title="Special:BookSources/978-92-9194-004-2"><bdi>978-92-9194-004-2</bdi></a>. Doc 7488-CD.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Manual+of+the+ICAO+Standard+Atmosphere+%28extended+to+80+kilometres+%28262+500+feet%29%29&rft.edition=Third&rft.pub=International+Civil+Aviation+Organization&rft.date=1993&rft.isbn=978-92-9194-004-2&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALapse+rate" class="Z3988"></span></span> </li> <li id="cite_note-Manabe64-9"><span class="mw-cite-backlink">^ <a href="#cite_ref-Manabe64_9-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Manabe64_9-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFManabeStrickler1964" class="citation journal cs1">Manabe, Syukuro; Strickler, Robert F. (1964). <a rel="nofollow" class="external text" href="https://journals.ametsoc.org/view/journals/atsc/21/4/1520-0469_1964_021_0361_teotaw_2_0_co_2.xml">"Thermal Equilibrium of the Atmosphere with a Convective Adjustment"</a>. <i>Journal of the Atmospheric Sciences</i>. <b>21</b> (4): <span class="nowrap">361–</span>385. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1964JAtS...21..361M">1964JAtS...21..361M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1175%2F1520-0469%281964%29021%3C0361%3ATEOTAW%3E2.0.CO%3B2">10.1175/1520-0469(1964)021<0361:TEOTAW>2.0.CO;2</a><span class="reference-accessdate">. Retrieved <span class="nowrap">1 September</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+Atmospheric+Sciences&rft.atitle=Thermal+Equilibrium+of+the+Atmosphere+with+a+Convective+Adjustment&rft.volume=21&rft.issue=4&rft.pages=%3Cspan+class%3D%22nowrap%22%3E361-%3C%2Fspan%3E385&rft.date=1964&rft_id=info%3Adoi%2F10.1175%2F1520-0469%281964%29021%3C0361%3ATEOTAW%3E2.0.CO%3B2&rft_id=info%3Abibcode%2F1964JAtS...21..361M&rft.aulast=Manabe&rft.aufirst=Syukuro&rft.au=Strickler%2C+Robert+F.&rft_id=https%3A%2F%2Fjournals.ametsoc.org%2Fview%2Fjournals%2Fatsc%2F21%2F4%2F1520-0469_1964_021_0361_teotaw_2_0_co_2.xml&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALapse+rate" class="Z3988"></span></span> </li> <li id="cite_note-nasa-eeb17-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-nasa-eeb17_10-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.nasa.gov/centers-and-facilities/langley/what-is-earths-energy-budget-five-questions-with-a-guy-who-knows/">"What is Earth's Energy Budget? Five Questions with a Guy Who Knows"</a>. NASA. 10 April 2017<span class="reference-accessdate">. Retrieved <span class="nowrap">1 September</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=What+is+Earth%27s+Energy+Budget%3F+Five+Questions+with+a+Guy+Who+Knows&rft.pub=NASA&rft.date=2017-04-10&rft_id=https%3A%2F%2Fwww.nasa.gov%2Fcenters-and-facilities%2Flangley%2Fwhat-is-earths-energy-budget-five-questions-with-a-guy-who-knows%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALapse+rate" class="Z3988"></span></span> </li> <li id="cite_note-ucar-cond-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-ucar-cond_11-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://scied.ucar.edu/learning-zone/earth-system/conduction">"Conduction"</a>. Center for Science Education<span class="reference-accessdate">. Retrieved <span class="nowrap">1 September</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Conduction&rft.pub=Center+for+Science+Education&rft_id=https%3A%2F%2Fscied.ucar.edu%2Flearning-zone%2Fearth-system%2Fconduction&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALapse+rate" class="Z3988"></span></span> </li> <li id="cite_note-WallaceHobbs-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-WallaceHobbs_12-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWallaceHobbs2006" class="citation book cs1">Wallace, John M.; Hobbs, Peter V. (2006). <i>Atmospheric Science</i> (2 ed.). Elsevier. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780080499536" title="Special:BookSources/9780080499536"><bdi>9780080499536</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Atmospheric+Science&rft.edition=2&rft.pub=Elsevier&rft.date=2006&rft.isbn=9780080499536&rft.aulast=Wallace&rft.aufirst=John+M.&rft.au=Hobbs%2C+Peter+V.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALapse+rate" class="Z3988"></span></span> </li> <li id="cite_note-Hartmann22-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-Hartmann22_13-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHartmannDygertBlosseyFu2022" class="citation journal cs1">Hartmann, Dennis L.; Dygert, Brittany D.; Blossey, Peter N.; Fu, Qiang; Sokol, Adam B. (2022). <a rel="nofollow" class="external text" href="https://journals.ametsoc.org/view/journals/clim/35/19/JCLI-D-21-0861.1.xml">"The Vertical Profile of Radiative Cooling and Lapse Rate in a Warming Climate"</a>. <i>Journal of Climate</i>. <b>35</b> (19): <span class="nowrap">6253–</span>6265. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2022JCli...35.2653H">2022JCli...35.2653H</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1175%2FJCLI-D-21-0861.1">10.1175/JCLI-D-21-0861.1</a><span class="reference-accessdate">. Retrieved <span class="nowrap">1 September</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Climate&rft.atitle=The+Vertical+Profile+of+Radiative+Cooling+and+Lapse+Rate+in+a+Warming+Climate&rft.volume=35&rft.issue=19&rft.pages=%3Cspan+class%3D%22nowrap%22%3E6253-%3C%2Fspan%3E6265&rft.date=2022&rft_id=info%3Adoi%2F10.1175%2FJCLI-D-21-0861.1&rft_id=info%3Abibcode%2F2022JCli...35.2653H&rft.aulast=Hartmann&rft.aufirst=Dennis+L.&rft.au=Dygert%2C+Brittany+D.&rft.au=Blossey%2C+Peter+N.&rft.au=Fu%2C+Qiang&rft.au=Sokol%2C+Adam+B.&rft_id=https%3A%2F%2Fjournals.ametsoc.org%2Fview%2Fjournals%2Fclim%2F35%2F19%2FJCLI-D-21-0861.1.xml&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALapse+rate" class="Z3988"></span></span> </li> <li id="cite_note-Goody-14"><span class="mw-cite-backlink">^ <a href="#cite_ref-Goody_14-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Goody_14-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRichard_M._GoodyJames_C.G._Walker1972" class="citation book cs1">Richard M. Goody; James C.G. Walker (1972). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160603212954/http://lasp.colorado.edu/~bagenal/3720/GoodyWalker/AtmosCh3sm.pdf">"Atmospheric Temperatures"</a> <span class="cs1-format">(PDF)</span>. <i>Atmospheres</i>. Prentice-Hall. Archived from <a rel="nofollow" class="external text" href="http://lasp.colorado.edu/~bagenal/3720/GoodyWalker/AtmosCh3sm.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2016-06-03.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Atmospheric+Temperatures&rft.btitle=Atmospheres&rft.pub=Prentice-Hall&rft.date=1972&rft.au=Richard+M.+Goody&rft.au=James+C.G.+Walker&rft_id=http%3A%2F%2Flasp.colorado.edu%2F~bagenal%2F3720%2FGoodyWalker%2FAtmosCh3sm.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALapse+rate" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWilliams" class="citation web cs1">Williams, Jack. <a rel="nofollow" class="external text" href="https://iflycoast.com/understanding-air-density-and-its-effects/">"Understanding Air Density and its Effects"</a>. USAToday.com<span class="reference-accessdate">. Retrieved <span class="nowrap">1 September</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Understanding+Air+Density+and+its+Effects&rft.pub=USAToday.com&rft.aulast=Williams&rft.aufirst=Jack&rft_id=https%3A%2F%2Fiflycoast.com%2Funderstanding-air-density-and-its-effects%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALapse+rate" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://science.howstuffworks.com/nature/climate-weather/atmospheric/is-humid-air-heavier-than-dry-air.htm">"Is humid air heavier than dry air?"</a>. <i>howstuffworks</i><span class="reference-accessdate">. Retrieved <span class="nowrap">1 September</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=howstuffworks&rft.atitle=Is+humid+air+heavier+than+dry+air%3F&rft_id=https%3A%2F%2Fscience.howstuffworks.com%2Fnature%2Fclimate-weather%2Fatmospheric%2Fis-humid-air-heavier-than-dry-air.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALapse+rate" class="Z3988"></span></span> </li> <li id="cite_note-DLA-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-DLA_17-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDanielsonLevinAbrams2002" class="citation book cs1">Danielson, EW; Levin, J; Abrams, E (2002). <i>Meteorology</i>. McGraw Hill Higher Education. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780072420722" title="Special:BookSources/9780072420722"><bdi>9780072420722</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Meteorology&rft.pub=McGraw+Hill+Higher+Education&rft.date=2002&rft.isbn=9780072420722&rft.aulast=Danielson&rft.aufirst=EW&rft.au=Levin%2C+J&rft.au=Abrams%2C+E&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALapse+rate" class="Z3988"></span></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://scied.ucar.edu/shortcontent/stratosphere-overview">"The stratosphere: overview"</a>. UCAR<span class="reference-accessdate">. Retrieved <span class="nowrap">2016-05-02</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+stratosphere%3A+overview&rft.pub=UCAR&rft_id=http%3A%2F%2Fscied.ucar.edu%2Fshortcontent%2Fstratosphere-overview&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALapse+rate" class="Z3988"></span></span> </li> <li id="cite_note-LL-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-LL_19-0">^</a></b></span> <span class="reference-text">Landau and Lifshitz, <i>Fluid Mechanics</i>, Pergamon, 1979</span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKittelKroemer1980" class="citation book cs1">Kittel; Kroemer (1980). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=c0R79nyOoNMC&pg=PA179">"6"</a>. <i>Thermal Physics</i>. W. H. Freeman. p. 179. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7167-1088-2" title="Special:BookSources/978-0-7167-1088-2"><bdi>978-0-7167-1088-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=6&rft.btitle=Thermal+Physics&rft.pages=179&rft.pub=W.+H.+Freeman&rft.date=1980&rft.isbn=978-0-7167-1088-2&rft.au=Kittel&rft.au=Kroemer&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dc0R79nyOoNMC%26pg%3DPA179&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALapse+rate" class="Z3988"></span> problem 11</span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20160603041448/http://meteorologytraining.tpub.com/14312/css/14312_47.htm">"Dry Adiabatic Lapse Rate"</a>. tpub.com. Archived from <a rel="nofollow" class="external text" href="http://meteorologytraining.tpub.com/14312/css/14312_47.htm">the original</a> on 2016-06-03<span class="reference-accessdate">. Retrieved <span class="nowrap">2016-05-02</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Dry+Adiabatic+Lapse+Rate&rft.pub=tpub.com&rft_id=http%3A%2F%2Fmeteorologytraining.tpub.com%2F14312%2Fcss%2F14312_47.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALapse+rate" class="Z3988"></span></span> </li> <li id="cite_note-MLM-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-MLM_22-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMinderMoteLundquist2010" class="citation journal cs1">Minder, JR; Mote, PW; Lundquist, JD (2010). <a rel="nofollow" class="external text" href="https://doi.org/10.1029%2F2009JD013493">"Surface temperature lapse rates over complex terrain: Lessons from the Cascade Mountains"</a>. <i>J. Geophys. Res</i>. <b>115</b> (D14): D14122. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2010JGRD..11514122M">2010JGRD..11514122M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1029%2F2009JD013493">10.1029/2009JD013493</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=J.+Geophys.+Res.&rft.atitle=Surface+temperature+lapse+rates+over+complex+terrain%3A+Lessons+from+the+Cascade+Mountains&rft.volume=115&rft.issue=D14&rft.pages=D14122&rft.date=2010&rft_id=info%3Adoi%2F10.1029%2F2009JD013493&rft_id=info%3Abibcode%2F2010JGRD..11514122M&rft.aulast=Minder&rft.aufirst=JR&rft.au=Mote%2C+PW&rft.au=Lundquist%2C+JD&rft_id=https%3A%2F%2Fdoi.org%2F10.1029%252F2009JD013493&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALapse+rate" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://glossary.ametsoc.org/wiki/Saturation-adiabatic_lapse_rate">"Saturation adiabatic lapse rate"</a>. <i>Glossary</i>. American Meteorological Society.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Glossary&rft.atitle=Saturation+adiabatic+lapse+rate&rft_id=http%3A%2F%2Fglossary.ametsoc.org%2Fwiki%2FSaturation-adiabatic_lapse_rate&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALapse+rate" class="Z3988"></span></span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://glossary.ametsoc.org/wiki/Mixing_ratio">"Mixing ratio"</a>. <i>Glossary</i>. American Meteorological Society.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Glossary&rft.atitle=Mixing+ratio&rft_id=http%3A%2F%2Fglossary.ametsoc.org%2Fwiki%2FMixing_ratio&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALapse+rate" class="Z3988"></span></span> </li> <li id="cite_note-Whiteman-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-Whiteman_25-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWhiteman2000" class="citation book cs1">Whiteman, C. David (2000). <i>Mountain Meteorology: Fundamentals and Applications</i>. Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-513271-7" title="Special:BookSources/978-0-19-513271-7"><bdi>978-0-19-513271-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mountain+Meteorology%3A+Fundamentals+and+Applications&rft.pub=Oxford+University+Press&rft.date=2000&rft.isbn=978-0-19-513271-7&rft.aulast=Whiteman&rft.aufirst=C.+David&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALapse+rate" class="Z3988"></span></span> </li> <li id="cite_note-ThomasStamnes1999-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-ThomasStamnes1999_26-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFThomasStamnes1999" class="citation book cs1">Thomas, Gary E.; Stamnes, Knut (1999). <i>Radiative Transfer in the Atmosphere and Ocean</i>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-40124-0" title="Special:BookSources/0-521-40124-0"><bdi>0-521-40124-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Radiative+Transfer+in+the+Atmosphere+and+Ocean&rft.pub=Cambridge+University+Press&rft.date=1999&rft.isbn=0-521-40124-0&rft.aulast=Thomas&rft.aufirst=Gary+E.&rft.au=Stamnes%2C+Knut&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALapse+rate" class="Z3988"></span></span> </li> <li id="cite_note-hsch-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-hsch_27-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchmithüsenNotholtKönig-LangloLemke2015" class="citation journal cs1">Schmithüsen, Holger; Notholt, Justus; König-Langlo, Gert; Lemke, Peter; Jung, Thomas (16 December 2015). <a rel="nofollow" class="external text" href="https://doi.org/10.1002%2F2015GL066749">"How increasing CO<sub style="font-size: 80%;vertical-align: -0.35em">2</sub> leads to an increased negative greenhouse effect in Antarctica"</a>. <i>Geophysical Research Letters</i>. <b>42</b> (23). <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1002%2F2015GL066749">10.1002/2015GL066749</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0094-8276">0094-8276</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:131351000">131351000</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Geophysical+Research+Letters&rft.atitle=How+increasing+CO%3Csub+style%3D%22font-size%3A+80%25%3Bvertical-align%3A+-0.35em%22%3E2%3C%2Fsub%3E+leads+to+an+increased+negative+greenhouse+effect+in+Antarctica&rft.volume=42&rft.issue=23&rft.date=2015-12-16&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A131351000%23id-name%3DS2CID&rft.issn=0094-8276&rft_id=info%3Adoi%2F10.1002%2F2015GL066749&rft.aulast=Schmith%C3%BCsen&rft.aufirst=Holger&rft.au=Notholt%2C+Justus&rft.au=K%C3%B6nig-Langlo%2C+Gert&rft.au=Lemke%2C+Peter&rft.au=Jung%2C+Thomas&rft_id=https%3A%2F%2Fdoi.org%2F10.1002%252F2015GL066749&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALapse+rate" class="Z3988"></span></span> </li> <li id="cite_note-sejas-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-sejas_28-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSejasTaylorCai2018" class="citation journal cs1">Sejas, S.A.; Taylor, P. C.; Cai, M. (2018). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7580794">"Unmasking the negative greenhouse effect over the Antarctic Plateau"</a>. <i>npj Clim Atmos Sci</i>. <b>1</b> (17): 17. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2018npCAS...1...17S">2018npCAS...1...17S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fs41612-018-0031-y">10.1038/s41612-018-0031-y</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7580794">7580794</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/33102742">33102742</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=npj+Clim+Atmos+Sci&rft.atitle=Unmasking+the+negative+greenhouse+effect+over+the+Antarctic+Plateau&rft.volume=1&rft.issue=17&rft.pages=17&rft.date=2018&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC7580794%23id-name%3DPMC&rft_id=info%3Apmid%2F33102742&rft_id=info%3Adoi%2F10.1038%2Fs41612-018-0031-y&rft_id=info%3Abibcode%2F2018npCAS...1...17S&rft.aulast=Sejas&rft.aufirst=S.A.&rft.au=Taylor%2C+P.+C.&rft.au=Cai%2C+M.&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC7580794&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALapse+rate" class="Z3988"></span></span> </li> <li id="cite_note-MaxwellToH-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-MaxwellToH_29-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMaxwell1902" class="citation book cs1">Maxwell, J. Clerk (1902). <a rel="nofollow" class="external text" href="http://strangebeautiful.com/other-texts/maxwell-theory-of-heat.pdf"><i>Theory of Heat</i></a> <span class="cs1-format">(PDF)</span>. London: Longmans, Green and Company.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Theory+of+Heat&rft.place=London&rft.pub=Longmans%2C+Green+and+Company&rft.date=1902&rft.aulast=Maxwell&rft.aufirst=J.+Clerk&rft_id=http%3A%2F%2Fstrangebeautiful.com%2Fother-texts%2Fmaxwell-theory-of-heat.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALapse+rate" class="Z3988"></span></span> </li> <li id="cite_note-SantiagoVisser19-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-SantiagoVisser19_30-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSantiagoVisser2019" class="citation journal cs1">Santiago, Jessica; Visser, Matt (2019). "Tolman temperature gradients in a gravitational field". <i>European Journal of Physics</i>. <b>40</b> (25604): 025604. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1803.04106">1803.04106</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2019EJPh...40b5604S">2019EJPh...40b5604S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F1361-6404%2Faaff1c">10.1088/1361-6404/aaff1c</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=European+Journal+of+Physics&rft.atitle=Tolman+temperature+gradients+in+a+gravitational+field&rft.volume=40&rft.issue=25604&rft.pages=025604&rft.date=2019&rft_id=info%3Aarxiv%2F1803.04106&rft_id=info%3Adoi%2F10.1088%2F1361-6404%2Faaff1c&rft_id=info%3Abibcode%2F2019EJPh...40b5604S&rft.aulast=Santiago&rft.aufirst=Jessica&rft.au=Visser%2C+Matt&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALapse+rate" class="Z3988"></span></span> </li> <li id="cite_note-Tolman1930-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-Tolman1930_31-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTolman1930" class="citation journal cs1">Tolman, R. C. (1930). "On the weight of heat and thermal equilibrium in general relativity". <i>Phys. Rev</i>. <b>35</b> (8): 904. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1930PhRv...35..904T">1930PhRv...35..904T</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRev.35.904">10.1103/PhysRev.35.904</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Phys.+Rev.&rft.atitle=On+the+weight+of+heat+and+thermal+equilibrium+in+general+relativity&rft.volume=35&rft.issue=8&rft.pages=904&rft.date=1930&rft_id=info%3Adoi%2F10.1103%2FPhysRev.35.904&rft_id=info%3Abibcode%2F1930PhRv...35..904T&rft.aulast=Tolman&rft.aufirst=R.+C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALapse+rate" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lapse_rate&action=edit&section=14" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBeychok,_Milton_R.2005" class="citation book cs1">Beychok, Milton R. (2005). <a href="/wiki/Fundamentals_Of_Stack_Gas_Dispersion" class="mw-redirect" title="Fundamentals Of Stack Gas Dispersion"><i>Fundamentals Of Stack Gas Dispersion</i></a> (4th ed.). author-published. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-9644588-0-2" title="Special:BookSources/978-0-9644588-0-2"><bdi>978-0-9644588-0-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fundamentals+Of+Stack+Gas+Dispersion&rft.edition=4th&rft.pub=author-published&rft.date=2005&rft.isbn=978-0-9644588-0-2&rft.au=Beychok%2C+Milton+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALapse+rate" class="Z3988"></span> <a rel="nofollow" class="external text" href="http://www.air-dispersion.com">www.air-dispersion.com</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFR._R._Rogers_and_M._K._Yau1989" class="citation book cs1">R. R. Rogers and M. K. Yau (1989). <i>Short Course in Cloud Physics</i> (3rd ed.). Butterworth-Heinemann. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7506-3215-7" title="Special:BookSources/978-0-7506-3215-7"><bdi>978-0-7506-3215-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Short+Course+in+Cloud+Physics&rft.edition=3rd&rft.pub=Butterworth-Heinemann&rft.date=1989&rft.isbn=978-0-7506-3215-7&rft.au=R.+R.+Rogers+and+M.+K.+Yau&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALapse+rate" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lapse_rate&action=edit&section=15" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://pds-atmospheres.nmsu.edu/education_and_outreach/encyclopedia/adiabatic_lapse_rate.htm">Definition, equations and tables of lapse rate</a> from the Planetary Data system.</li> <li>National Science Digital Library glossary: <ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20050420085336/http://www.nsdl.arm.gov/Library/glossary.shtml#lapse_rate">Lapse Rate</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20050420085336/http://www.nsdl.arm.gov/Library/glossary.shtml#environmental_lapse_rate">Environmental lapse rate</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20050420085336/http://www.nsdl.arm.gov/Library/glossary.shtml#absolute_stable_air">Absolute stable air</a></li></ul></li> <li>An introduction to <a rel="nofollow" class="external text" href="http://farside.ph.utexas.edu/teaching/sm1/lectures/node56.html">lapse rate calculation from first principles</a> from U. Texas</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Meteorological_data_and_variables132" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2" style="background-color: skyblue"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Meteorological_variables" title="Template:Meteorological variables"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Meteorological_variables" title="Template talk:Meteorological variables"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Meteorological_variables" title="Special:EditPage/Template:Meteorological variables"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Meteorological_data_and_variables132" style="font-size:114%;margin:0 4em">Meteorological data and variables</div></th></tr><tr><th scope="row" class="navbox-group" style="background-color: skyblue;width:1%">General</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Adiabatic_process" title="Adiabatic process">Adiabatic processes</a></li> <li><a href="/wiki/Advection" title="Advection">Advection</a></li> <li><a href="/wiki/Buoyancy" title="Buoyancy">Buoyancy</a></li> <li><a class="mw-selflink selflink">Lapse rate</a></li> <li><a href="/wiki/Lightning" title="Lightning">Lightning</a></li> <li><a href="/wiki/Solar_radiation" class="mw-redirect" title="Solar radiation">Surface solar radiation</a></li> <li><a href="/wiki/Surface_weather_analysis" title="Surface weather analysis">Surface weather analysis</a></li> <li><a href="/wiki/Visibility" title="Visibility">Visibility</a></li> <li><a href="/wiki/Vorticity" title="Vorticity">Vorticity</a></li> <li><a href="/wiki/Wind" title="Wind">Wind</a></li> <li><a href="/wiki/Wind_shear" title="Wind shear">Wind shear</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="background-color: skyblue;width:1%"><a href="/wiki/Condensation" title="Condensation">Condensation</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cloud" title="Cloud">Cloud</a></li> <li><a href="/wiki/Cloud_condensation_nuclei" title="Cloud condensation nuclei">Cloud condensation nuclei (CCN)</a></li> <li><a href="/wiki/Fog" title="Fog">Fog</a></li> <li><a href="/wiki/Convective_condensation_level" title="Convective condensation level">Convective condensation level (CCL)</a></li> <li><a href="/wiki/Lifting_condensation_level" title="Lifting condensation level">Lifting condensation level (LCL)</a></li> <li><a href="/wiki/Precipitable_water" title="Precipitable water">Precipitable water</a></li> <li><a href="/wiki/Precipitation" title="Precipitation">Precipitation</a></li> <li><a href="/wiki/Water_vapor" title="Water vapor">Water vapor</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="background-color: skyblue;width:1%"><a href="/wiki/Atmospheric_convection" title="Atmospheric convection">Convection</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Convective_available_potential_energy" title="Convective available potential energy">Convective available potential energy (CAPE)</a></li> <li><a href="/wiki/Convective_inhibition" title="Convective inhibition">Convective inhibition (CIN)</a></li> <li><a href="/wiki/Convective_instability" title="Convective instability">Convective instability</a></li> <li><a href="/wiki/Convective_momentum_transport" title="Convective momentum transport">Convective momentum transport</a></li> <li><a href="/wiki/Conditional_symmetric_instability" title="Conditional symmetric instability">Conditional symmetric instability</a></li> <li><a href="/wiki/Convective_temperature" title="Convective temperature">Convective temperature (<i>T</i><sub>c</sub>)</a></li> <li><a href="/wiki/Equilibrium_level" title="Equilibrium level">Equilibrium level (EL)</a></li> <li><a href="/wiki/Free_convective_layer" title="Free convective layer">Free convective layer (FCL)</a></li> <li><a href="/wiki/Hydrodynamical_helicity#Meteorology" title="Hydrodynamical helicity">Helicity</a></li> <li><a href="/wiki/K-index_(meteorology)" title="K-index (meteorology)">K Index</a></li> <li><a href="/wiki/Level_of_free_convection" title="Level of free convection">Level of free convection (LFC)</a></li> <li><a href="/wiki/Lifted_index" title="Lifted index">Lifted index (LI)</a></li> <li><a href="/wiki/Maximum_parcel_level" title="Maximum parcel level">Maximum parcel level (MPL)</a></li> <li><a href="/wiki/Bulk_Richardson_number" title="Bulk Richardson number">Bulk Richardson number (BRN)</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="background-color: skyblue;width:1%"><a href="/wiki/Temperature" title="Temperature">Temperature</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Dew_point" title="Dew point">Dew point (<i>T</i><sub>d</sub>)</a></li> <li><a href="/wiki/Dew_point_depression" title="Dew point depression">Dew point depression</a></li> <li><a href="/wiki/Dry-bulb_temperature" title="Dry-bulb temperature">Dry-bulb temperature</a></li> <li><a href="/wiki/Equivalent_temperature" title="Equivalent temperature">Equivalent temperature (<i>T</i><sub>e</sub>)</a></li> <li><a href="/wiki/Forest_fire_weather_index" title="Forest fire weather index">Forest fire weather index</a></li> <li><a href="/wiki/Haines_Index" title="Haines Index">Haines Index</a></li> <li><a href="/wiki/Heat_index" title="Heat index">Heat index</a></li> <li><a href="/wiki/Humidex" title="Humidex">Humidex</a></li> <li><a href="/wiki/Humidity" title="Humidity">Humidity</a></li> <li><a href="/wiki/Relative_humidity" class="mw-redirect" title="Relative humidity">Relative humidity (RH)</a></li> <li><a href="/wiki/Mixing_ratio" title="Mixing ratio">Mixing ratio</a></li> <li><a href="/wiki/Potential_temperature" title="Potential temperature">Potential temperature (<i>θ</i>)</a></li> <li><a href="/wiki/Equivalent_potential_temperature" title="Equivalent potential temperature">Equivalent potential temperature (<i>θ</i><sub>e</sub>)</a></li> <li><a href="/wiki/Sea_surface_temperature" title="Sea surface temperature">Sea surface temperature (SST)</a></li> <li><a href="/wiki/Temperature_anomaly" title="Temperature anomaly">Temperature anomaly</a></li> <li><a href="/wiki/Thermodynamic_temperature" title="Thermodynamic temperature">Thermodynamic temperature</a></li> <li><a href="/wiki/Vapor_pressure" title="Vapor pressure">Vapor pressure</a></li> <li><a href="/wiki/Virtual_temperature" title="Virtual temperature">Virtual temperature</a></li> <li><a href="/wiki/Wet-bulb_temperature" title="Wet-bulb temperature">Wet-bulb temperature</a></li> <li><a href="/wiki/Wet-bulb_globe_temperature" title="Wet-bulb globe temperature">Wet-bulb globe temperature</a></li> <li><a href="/wiki/Wet-bulb_potential_temperature" title="Wet-bulb potential temperature">Wet-bulb potential temperature</a></li> <li><a href="/wiki/Wind_chill" title="Wind chill">Wind chill</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="background-color: skyblue;width:1%"><a href="/wiki/Pressure" title="Pressure">Pressure</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Atmospheric_pressure" title="Atmospheric pressure">Atmospheric pressure</a></li> <li><a href="/wiki/Baroclinity" title="Baroclinity">Baroclinity</a></li> <li><a href="/wiki/Barotropic" class="mw-redirect" title="Barotropic">Barotropicity</a></li> <li><a href="/wiki/Pressure_gradient" title="Pressure gradient">Pressure gradient</a></li> <li><a href="/wiki/Pressure-gradient_force" title="Pressure-gradient force">Pressure-gradient force (PGF)</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="background-color: skyblue;width:1%"><a href="/wiki/Velocity" title="Velocity">Velocity</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Maximum_potential_intensity" title="Maximum potential intensity">Maximum potential intensity</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox authority-control" aria-label="Navbox507" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control databases</a>: National <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q66900467#identifiers" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh87006388">United States</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.nli.org.il/en/authorities/987007534476905171">Israel</a></span></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Lapse_rate&oldid=1271834359">https://en.wikipedia.org/w/index.php?title=Lapse_rate&oldid=1271834359</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Atmospheric_thermodynamics" title="Category:Atmospheric thermodynamics">Atmospheric thermodynamics</a></li><li><a href="/wiki/Category:Climate_change_feedbacks" title="Category:Climate change feedbacks">Climate change feedbacks</a></li><li><a href="/wiki/Category:Fluid_mechanics" title="Category:Fluid mechanics">Fluid mechanics</a></li><li><a href="/wiki/Category:Meteorological_quantities" title="Category:Meteorological quantities">Meteorological quantities</a></li><li><a href="/wiki/Category:Spatial_gradient" title="Category:Spatial gradient">Spatial gradient</a></li><li><a href="/wiki/Category:Atmospheric_temperature" title="Category:Atmospheric temperature">Atmospheric temperature</a></li><li><a href="/wiki/Category:Vertical_position" title="Category:Vertical position">Vertical position</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_matches_Wikidata" title="Category:Short description matches Wikidata">Short description matches Wikidata</a></li><li><a href="/wiki/Category:Articles_needing_additional_references_from_March_2022" title="Category:Articles needing additional references from March 2022">Articles needing additional references from March 2022</a></li><li><a href="/wiki/Category:All_articles_needing_additional_references" title="Category:All articles needing additional references">All articles needing additional references</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 25 January 2025, at 23:38<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. By using this site, you agree to the <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use" class="extiw" title="foundation:Special:MyLanguage/Policy:Terms of Use">Terms of Use</a> and <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy" class="extiw" title="foundation:Special:MyLanguage/Policy:Privacy policy">Privacy Policy</a>. Wikipedia® is a registered trademark of the <a rel="nofollow" class="external text" href="https://wikimediafoundation.org/">Wikimedia Foundation, Inc.</a>, a non-profit organization.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Privacy policy</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedia:About">About Wikipedia</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedia:General_disclaimer">Disclaimers</a></li> <li id="footer-places-contact"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us">Contact Wikipedia</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Code of Conduct</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Developers</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/en.wikipedia.org">Statistics</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Cookie statement</a></li> <li id="footer-places-mobileview"><a href="//en.m.wikipedia.org/w/index.php?title=Lapse_rate&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Mobile view</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" lang="en" loading="lazy"></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/w/resources/assets/poweredby_mediawiki.svg" alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> </div> </div> </div> <div class="vector-header-container vector-sticky-header-container"> <div id="vector-sticky-header" class="vector-sticky-header"> <div class="vector-sticky-header-start"> <div class="vector-sticky-header-icon-start vector-button-flush-left vector-button-flush-right" aria-hidden="true"> <button class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-sticky-header-search-toggle" tabindex="-1" data-event-name="ui.vector-sticky-search-form.icon"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Search</span> </button> </div> <div role="search" class="vector-search-box-vue vector-search-box-show-thumbnail vector-search-box"> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail"> <form action="/w/index.php" id="vector-sticky-search-form" class="cdx-search-input cdx-search-input--has-end-button"> <div class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Search Wikipedia"> <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Special:Search"> </div> <button class="cdx-button cdx-search-input__end-button">Search</button> </form> </div> </div> </div> <div class="vector-sticky-header-context-bar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-sticky-header-toc" class="vector-dropdown mw-portlet mw-portlet-sticky-header-toc vector-sticky-header-toc vector-button-flush-left" > <input type="checkbox" id="vector-sticky-header-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-sticky-header-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-sticky-header-toc-label" for="vector-sticky-header-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-sticky-header-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div class="vector-sticky-header-context-bar-primary" aria-hidden="true" ><span class="mw-page-title-main">Lapse rate</span></div> </div> </div> <div class="vector-sticky-header-end" aria-hidden="true"> <div class="vector-sticky-header-icons"> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-talk-sticky-header" tabindex="-1" data-event-name="talk-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbles mw-ui-icon-wikimedia-speechBubbles"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-subject-sticky-header" tabindex="-1" data-event-name="subject-sticky-header"><span class="vector-icon mw-ui-icon-article mw-ui-icon-wikimedia-article"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-history-sticky-header" tabindex="-1" data-event-name="history-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-history mw-ui-icon-wikimedia-wikimedia-history"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only mw-watchlink" id="ca-watchstar-sticky-header" tabindex="-1" data-event-name="watch-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-star mw-ui-icon-wikimedia-wikimedia-star"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-edit-sticky-header" tabindex="-1" data-event-name="wikitext-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-wikiText mw-ui-icon-wikimedia-wikimedia-wikiText"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-ve-edit-sticky-header" tabindex="-1" data-event-name="ve-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-edit mw-ui-icon-wikimedia-wikimedia-edit"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-viewsource-sticky-header" tabindex="-1" data-event-name="ve-edit-protected-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-editLock mw-ui-icon-wikimedia-wikimedia-editLock"></span> <span></span> </a> </div> <div class="vector-sticky-header-buttons"> <button class="cdx-button cdx-button--weight-quiet mw-interlanguage-selector" id="p-lang-btn-sticky-header" tabindex="-1" data-event-name="ui.dropdown-p-lang-btn-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-language mw-ui-icon-wikimedia-wikimedia-language"></span> <span>15 languages</span> </button> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive" id="ca-addsection-sticky-header" tabindex="-1" data-event-name="addsection-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbleAdd-progressive mw-ui-icon-wikimedia-speechBubbleAdd-progressive"></span> <span>Add topic</span> </a> </div> <div class="vector-sticky-header-icon-end"> <div class="vector-user-links"> </div> </div> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-567b97b4dc-2qwkx","wgBackendResponseTime":111,"wgPageParseReport":{"limitreport":{"cputime":"0.589","walltime":"0.864","ppvisitednodes":{"value":3136,"limit":1000000},"postexpandincludesize":{"value":82415,"limit":2097152},"templateargumentsize":{"value":1588,"limit":2097152},"expansiondepth":{"value":16,"limit":100},"expensivefunctioncount":{"value":3,"limit":500},"unstrip-depth":{"value":1,"limit":20},"unstrip-size":{"value":124498,"limit":5000000},"entityaccesscount":{"value":1,"limit":400},"timingprofile":["100.00% 574.677 1 -total"," 41.47% 238.316 2 Template:Reflist"," 23.99% 137.837 15 Template:Cite_book"," 12.89% 74.077 1 Template:Meteorological_variables"," 12.55% 72.138 1 Template:Navbox"," 11.14% 63.997 1 Template:Short_description"," 10.94% 62.843 1 Template:Singlesource"," 9.68% 55.639 1 Template:Ambox"," 8.63% 49.604 8 Template:Cite_journal"," 7.18% 41.288 2 Template:Pagetype"]},"scribunto":{"limitreport-timeusage":{"value":"0.354","limit":"10.000"},"limitreport-memusage":{"value":9246956,"limit":52428800}},"cachereport":{"origin":"mw-web.codfw.main-7878cd4448-n8rgb","timestamp":"20250211200340","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Lapse rate","url":"https:\/\/en.wikipedia.org\/wiki\/Lapse_rate","sameAs":"http:\/\/www.wikidata.org\/entity\/Q66900467","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q66900467","author":{"@type":"Organization","name":"Contributors to Wikimedia projects"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2003-05-10T03:43:38Z","dateModified":"2025-01-25T23:38:44Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/b\/b6\/Tatra_Rysy_5.jpg","headline":"Vertical rate of change of temperature in atmosphere"}</script> </body> </html>