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NowCast (air quality index) - Wikipedia
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lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">American environmental index</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For other uses, see <a href="/wiki/Nowcasting_(disambiguation)" class="mw-redirect mw-disambig" title="Nowcasting (disambiguation)">Nowcasting</a>.</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:PM2.5_dot_map.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c0/PM2.5_dot_map.gif/220px-PM2.5_dot_map.gif" decoding="async" width="220" height="168" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c0/PM2.5_dot_map.gif/330px-PM2.5_dot_map.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c0/PM2.5_dot_map.gif/440px-PM2.5_dot_map.gif 2x" data-file-width="525" data-file-height="400" /></a><figcaption>PM<sub>2.5</sub> AQI of US monitors, calculated utilizing NowCast, courtesy US EPA</figcaption></figure><figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:PM25_AQI_Map_8-27-14.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3c/PM25_AQI_Map_8-27-14.gif/220px-PM25_AQI_Map_8-27-14.gif" decoding="async" width="220" height="168" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3c/PM25_AQI_Map_8-27-14.gif/330px-PM25_AQI_Map_8-27-14.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3c/PM25_AQI_Map_8-27-14.gif/440px-PM25_AQI_Map_8-27-14.gif 2x" data-file-width="525" data-file-height="400" /></a><figcaption>PM2.5 AQI map, calculated utilizing NowCast, courtesy US EPA</figcaption></figure> <p>The PM (particulate matter) <b>NowCast</b> is a <a href="/wiki/Weighted_average" class="mw-redirect" title="Weighted average">weighted average</a> of hourly <a href="/wiki/Air_monitoring" class="mw-redirect" title="Air monitoring">air monitoring</a> data used by the <a href="/wiki/United_States_Environmental_Protection_Agency" title="United States Environmental Protection Agency">United States Environmental Protection Agency</a> (USEPA) for real-time reporting of the Air Quality Index (AQI) for PM (PM<sub>10</sub> - particles less than 10 micrometers, or PM<sub>2.5</sub> - particles less than 2.5 micrometers). </p><p>The PM NowCast is computed from the most recent 12 hours of PM monitoring data, but the NowCast weights the most recent hours of data more heavily than an ordinary 12-hour average when pollutant levels are changing. The PM NowCast is used in lieu of a 24-hour average PM concentration in the calculation of the AQI until an entire calendar day of hourly concentrations has been monitored. </p><p>The Ozone <b>NowCast</b> is an algorithm<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> developed by the USEPA to predict the 8-hour <a href="/wiki/Ozone" title="Ozone">ozone</a> average centered on the current hour from the current 1-hr average ozone data. At each ozone monitoring site, partial least squares regression is used to develop a predictive relationship between the 1-hr and 8-hr averages using the previous 2 weeks of ozone data. USEPA uses the Ozone Nowcast for real time public reporting of the ozone AQI.<a rel="nofollow" class="external autonumber" href="https://www.airnow.gov">[1]</a> </p> <div class="mw-heading mw-heading2"><h2 id="Calculation_of_the_PM_NowCast">Calculation of the PM NowCast</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=NowCast_(air_quality_index)&action=edit&section=1" title="Edit section: Calculation of the PM NowCast"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Let <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_{1},c_{2},...c_{12}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{1},c_{2},...c_{12}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f828c74110a8965f1ab4e628e56c38451fd16e1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.175ex; height:2.009ex;" alt="{\displaystyle c_{1},c_{2},...c_{12}}"></span> represent the hourly PM concentrations for the most recent 12-hour period, with <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_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77b7dc6d279091d354e0b90889b463bfa7eb7247" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.061ex; height:2.009ex;" alt="{\displaystyle c_{1}}"></span> the most recent hourly value, and let <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_{min}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{min}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b99f55b4a6d7b6a57e399d5cb997333270208510" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.236ex; height:2.009ex;" alt="{\displaystyle c_{min}}"></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 c_{max}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{max}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb97b08b6fc038ea6046d70024bd0085662da097" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.492ex; height:2.009ex;" alt="{\displaystyle c_{max}}"></span> represent the minimum and maximum hourly concentration for the 12-hour period. </p><p>Define: </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 w^{*}=1-{\frac {c_{max}-c_{min}}{c_{max}}}={\frac {c_{min}}{c_{max}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> <mo>=</mo> <mn>1</mn> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>−<!-- − --></mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </mrow> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w^{*}=1-{\frac {c_{max}-c_{min}}{c_{max}}}={\frac {c_{min}}{c_{max}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1cf564d110489854be4f8a50e47bacd329b3c0c9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:30.65ex; height:5.343ex;" alt="{\displaystyle w^{*}=1-{\frac {c_{max}-c_{min}}{c_{max}}}={\frac {c_{min}}{c_{max}}}}"></span></dd></dl> <p>and let </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 w={\begin{cases}w^{*}&{\mbox{if }}w^{*}>{\frac {1}{2}}\\{\frac {1}{2}}&{\mbox{if }}w^{*}\leq {\frac {1}{2}}\\\end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>w</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <msup> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>if </mtext> </mstyle> </mrow> <msup> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> <mo>></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>if </mtext> </mstyle> </mrow> <msup> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> <mo>≤<!-- ≤ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w={\begin{cases}w^{*}&{\mbox{if }}w^{*}>{\frac {1}{2}}\\{\frac {1}{2}}&{\mbox{if }}w^{*}\leq {\frac {1}{2}}\\\end{cases}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/beda5ddf0c6fb263d1c7eced7c3b9152a14827fa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:21.843ex; height:7.509ex;" alt="{\displaystyle w={\begin{cases}w^{*}&{\mbox{if }}w^{*}>{\frac {1}{2}}\\{\frac {1}{2}}&{\mbox{if }}w^{*}\leq {\frac {1}{2}}\\\end{cases}}}"></span></dd></dl> <p>With these definitions the PM NowCast<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> is given by: </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 NowCast={\frac {\sum _{i=1}^{12}w^{i-1}c_{i}}{\sum _{i=1}^{12}w^{i-1}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mi>o</mi> <mi>w</mi> <mi>C</mi> <mi>a</mi> <mi>s</mi> <mi>t</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <munderover> <mo>∑<!-- ∑ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </munderover> <msup> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msup> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <mrow> <munderover> <mo>∑<!-- ∑ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </munderover> <msup> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle NowCast={\frac {\sum _{i=1}^{12}w^{i-1}c_{i}}{\sum _{i=1}^{12}w^{i-1}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e67b1e57fce7e42b1af7fffe66920e46d4a4c0ec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:26.475ex; height:7.509ex;" alt="{\displaystyle NowCast={\frac {\sum _{i=1}^{12}w^{i-1}c_{i}}{\sum _{i=1}^{12}w^{i-1}}}.}"></span></dd></dl> <p>For the special case where there is no variability in the hourly values, <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_{min}=c_{max},w=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>,</mo> <mi>w</mi> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{min}=c_{max},w=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3dddb9f3300da51fcc1a6b8c68218858cf1c29ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:18.785ex; height:2.509ex;" alt="{\displaystyle c_{min}=c_{max},w=1}"></span>, and the NowCast reduces to the twelve-hour average: </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 NowCast={\frac {\sum _{i=1}^{12}c_{i}}{12}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mi>o</mi> <mi>w</mi> <mi>C</mi> <mi>a</mi> <mi>s</mi> <mi>t</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <munderover> <mo>∑<!-- ∑ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </munderover> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <mn>12</mn> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle NowCast={\frac {\sum _{i=1}^{12}c_{i}}{12}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ee51fe5eed52ac16192c124be2500bac8c1a2eaf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:21.911ex; height:6.176ex;" alt="{\displaystyle NowCast={\frac {\sum _{i=1}^{12}c_{i}}{12}}.}"></span></dd></dl> <p>For the special case where w=1/2: </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 NowCast={\frac {c_{1}+({\frac {1}{2}})c_{2}+...+{({\frac {1}{2}}})^{11}{c_{12}}}{1+{\frac {1}{2}}+({\frac {1}{2}})^{2}+...+{({\frac {1}{2}}})^{11}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mi>o</mi> <mi>w</mi> <mi>C</mi> <mi>a</mi> <mi>s</mi> <mi>t</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo stretchy="false">)</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>11</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </msub> </mrow> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo>+</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>11</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle NowCast={\frac {c_{1}+({\frac {1}{2}})c_{2}+...+{({\frac {1}{2}}})^{11}{c_{12}}}{1+{\frac {1}{2}}+({\frac {1}{2}})^{2}+...+{({\frac {1}{2}}})^{11}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7cb48fb1ef8ce78bffc56b9d15c54d17a751d8b0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:39.091ex; height:7.843ex;" alt="{\displaystyle NowCast={\frac {c_{1}+({\frac {1}{2}})c_{2}+...+{({\frac {1}{2}}})^{11}{c_{12}}}{1+{\frac {1}{2}}+({\frac {1}{2}})^{2}+...+{({\frac {1}{2}}})^{11}}}}"></span></dd></dl> <p>But 1/(1-x)=1 + x + x<sup>2</sup>+ ... , x < 1, so to a good approximation, when w = 1/2: </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 NowCast={\frac {1}{2}}c_{1}+({\frac {1}{2}})^{2}c_{2}+...+{({\frac {1}{2}}})^{12}{c_{12}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mi>o</mi> <mi>w</mi> <mi>C</mi> <mi>a</mi> <mi>s</mi> <mi>t</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </msub> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle NowCast={\frac {1}{2}}c_{1}+({\frac {1}{2}})^{2}c_{2}+...+{({\frac {1}{2}}})^{12}{c_{12}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0144bdb05455079d5be94bb875d6214525240d1e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:41.989ex; height:5.176ex;" alt="{\displaystyle NowCast={\frac {1}{2}}c_{1}+({\frac {1}{2}})^{2}c_{2}+...+{({\frac {1}{2}}})^{12}{c_{12}}}"></span></dd></dl> <p>Because the most recent hours of data are weighted so heavily in the NowCast when PM levels are changing, EPA does not report the NowCast when data is missing for c<sub>1</sub> or c<sub>2</sub>. </p><p>Consider a day when the hourly average PM<sub>2.5</sub> concentration is zero for all hours of the day, except for a single hour from noon to 1 pm, where a monitor records a concentration pulse of 144.0 micrograms per cubic meter (μg/m<sup>3</sup>). According to the equation above, the Nowcast is 144/2 μg/m<sup>3</sup>=72.0 μg/m<sup>3</sup> the hour after the pulse, two hours later it is 144/4 μg/m<sup>3</sup>=36.0 μg/m<sup>3</sup>, three hours later it is 144/8 μg/m<sup>3</sup>= 18.0 μg/m<sup>3</sup>, and four hours later it is 144/16 μg/m<sup>3</sup>= 9.0 μg/m<sup>3</sup>.To calculate the corresponding AQI values, each NowCast concentration is substituted into the AQI equation in place of the 24-hour average PM<sub>2.5</sub> concentration: </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 I={\frac {C-C_{low}}{C_{high}-C_{low}}}(I_{high}-I_{low})+I_{low}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>C</mi> <mo>−<!-- − --></mo> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>o</mi> <mi>w</mi> </mrow> </msub> </mrow> <mrow> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>i</mi> <mi>g</mi> <mi>h</mi> </mrow> </msub> <mo>−<!-- − --></mo> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>o</mi> <mi>w</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo stretchy="false">(</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>i</mi> <mi>g</mi> <mi>h</mi> </mrow> </msub> <mo>−<!-- − --></mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>o</mi> <mi>w</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>+</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>o</mi> <mi>w</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I={\frac {C-C_{low}}{C_{high}-C_{low}}}(I_{high}-I_{low})+I_{low}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6780d79cd5c530c5b3203f33ed839ad931e748fb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:36.884ex; height:6.176ex;" alt="{\displaystyle I={\frac {C-C_{low}}{C_{high}-C_{low}}}(I_{high}-I_{low})+I_{low}}"></span></dd></dl> <p>where: </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 I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\displaystyle I}"></span> = the AQI,</dd> <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 C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4fc55753007cd3c18576f7933f6f089196732029" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}"></span> = the 24-hour average PM<sub>2.5</sub> <a href="/wiki/Measures_of_pollutant_concentration" title="Measures of pollutant concentration">pollutant concentration</a>,</dd> <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 C_{low}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>o</mi> <mi>w</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{low}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/90e44bba740a008af76e65f0a6f40d631da2081b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.358ex; height:2.509ex;" alt="{\displaystyle C_{low}}"></span>= the concentration breakpoint that is ≤ <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4fc55753007cd3c18576f7933f6f089196732029" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}"></span>,</dd> <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 C_{high}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>i</mi> <mi>g</mi> <mi>h</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{high}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b6defe53ef79559aa23246bf50dcef27d5def487" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:5.144ex; height:2.843ex;" alt="{\displaystyle C_{high}}"></span>= the concentration breakpoint that is ≥ <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4fc55753007cd3c18576f7933f6f089196732029" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}"></span>,</dd> <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 I_{low}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>o</mi> <mi>w</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{low}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1e603c14ebdb2489fb8cc77d286055773a817900" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.72ex; height:2.509ex;" alt="{\displaystyle I_{low}}"></span>= the index breakpoint corresponding to <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_{low}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>o</mi> <mi>w</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{low}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/90e44bba740a008af76e65f0a6f40d631da2081b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.358ex; height:2.509ex;" alt="{\displaystyle C_{low}}"></span>,</dd> <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 I_{high}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>i</mi> <mi>g</mi> <mi>h</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{high}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51e25dc5f9c9ba3640ce3b4b33807b8eba64afbe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.506ex; height:2.843ex;" alt="{\displaystyle I_{high}}"></span>= the index breakpoint corresponding to <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_{high}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>i</mi> <mi>g</mi> <mi>h</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{high}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b6defe53ef79559aa23246bf50dcef27d5def487" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:5.144ex; height:2.843ex;" alt="{\displaystyle C_{high}}"></span>.</dd></dl> <p>and<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>:<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> </p> <table class="wikitable" style="text-align:center;"> <tbody><tr> <td><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_{low}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>o</mi> <mi>w</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{low}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/90e44bba740a008af76e65f0a6f40d631da2081b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.358ex; height:2.509ex;" alt="{\displaystyle C_{low}}"></span></td> <td><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_{high}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>i</mi> <mi>g</mi> <mi>h</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{high}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b6defe53ef79559aa23246bf50dcef27d5def487" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:5.144ex; height:2.843ex;" alt="{\displaystyle C_{high}}"></span></td> <td><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 I_{low}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>o</mi> <mi>w</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{low}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1e603c14ebdb2489fb8cc77d286055773a817900" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.72ex; height:2.509ex;" alt="{\displaystyle I_{low}}"></span></td> <td><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 I_{high}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>i</mi> <mi>g</mi> <mi>h</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{high}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51e25dc5f9c9ba3640ce3b4b33807b8eba64afbe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.506ex; height:2.843ex;" alt="{\displaystyle I_{high}}"></span></td> <td>Category </td></tr> <tr> <td>0</td> <td>9.0</td> <td>0</td> <td>50</td> <td style="background:#00e400;">Good </td></tr> <tr> <td>9.1</td> <td>35.4</td> <td>51</td> <td>100</td> <td style="background:#ff0;">Moderate </td></tr> <tr> <td>35.5</td> <td>55.4</td> <td>101</td> <td>150</td> <td style="background:#ff7e00;">Unhealthy for Sensitive Groups </td></tr> <tr> <td>55.5</td> <td>125.4</td> <td>151</td> <td>200</td> <td style="background:#f00; color:#fff;">Unhealthy </td></tr> <tr> <td>125.5</td> <td>225.4</td> <td>201</td> <td>300</td> <td style="background:#99004c; color:#fff;">Very Unhealthy </td></tr> <tr> <td>225.5</td> <td>325.4</td> <td>301</td> <td>500</td> <td style="background:#7e0023; color:#fff;">Hazardous </td></tr></tbody></table> <p>Thus, the four NowCast concentrations correspond to air quality indices<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> of </p><p>163, (AQI Color Code Red, Air Quality: Unhealthy), 102, (AQI Color Code Orange, Air Quality: Unhealthy for Sensitive Groups), 68 (AQI Color Code Yellow, Air Quality: Moderate ), and 50, (AQI Color Code Green, Air Quality: Good) respectively. After the day is over and all of the hourly data is available, the AQI for the day is calculated from the 24-hr average; 144/24 μg/m<sup>3</sup>= 6.0 μg/m<sup>3</sup>, an AQI of 33 (Color Code Green, Air Quality: Good). EPA has developed a calculator to compute the PM NowCast, AQI, and AQI category and color from the most recent 12 hours of monitoring data.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <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=NowCast_(air_quality_index)&action=edit&section=2" title="Edit section: References"><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"> <div class="mw-references-wrap"><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 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