A mass-weighted isentropic coordinate for mapping chemical tracers and computing atmospheric inventories

oleh: Y. Jin, R. F. Keeling, E. J. Morgan, E. Ray, N. C. Parazoo, B. B. Stephens

Format: Article
Diterbitkan: Copernicus Publications 2021-01-01

Deskripsi

<p>We introduce a transformed isentropic coordinate <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>M</mi><mrow><msub><mi mathvariant="italic">θ</mi><mi mathvariant="normal">e</mi></msub></mrow></msub></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="20pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="3f74d33e342f737e9a1530e09f181206"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-21-217-2021-ie00001.svg" width="20pt" height="14pt" src="acp-21-217-2021-ie00001.png"/></svg:svg></span></span>, defined as the dry air mass under a given equivalent potential temperature surface (<span class="inline-formula"><i>θ</i><sub>e</sub></span>) within a hemisphere. Like <span class="inline-formula"><i>θ</i><sub>e</sub></span>, the coordinate <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M4" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>M</mi><mrow><msub><mi mathvariant="italic">θ</mi><mi mathvariant="normal">e</mi></msub></mrow></msub></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="20pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="b7591ca93bfb3746d6f5d8e2c3980896"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-21-217-2021-ie00002.svg" width="20pt" height="14pt" src="acp-21-217-2021-ie00002.png"/></svg:svg></span></span> follows the synoptic distortions of the atmosphere but, unlike <span class="inline-formula"><i>θ</i><sub>e</sub></span>, has a nearly fixed relationship with latitude and altitude over the seasonal cycle. Calculation of <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M6" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>M</mi><mrow><msub><mi mathvariant="italic">θ</mi><mi mathvariant="normal">e</mi></msub></mrow></msub></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="20pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="b60c5e515dc4e50d53cfbee65d15ac3a"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-21-217-2021-ie00003.svg" width="20pt" height="14pt" src="acp-21-217-2021-ie00003.png"/></svg:svg></span></span> is straightforward from meteorological fields. Using observations from the recent HIAPER Pole-to-Pole Observations (HIPPO) and Atmospheric Tomography Mission (ATom) airborne campaigns, we map the CO<span class="inline-formula"><sub>2</sub></span> seasonal cycle as a function of pressure and <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M8" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>M</mi><mrow><msub><mi mathvariant="italic">θ</mi><mi mathvariant="normal">e</mi></msub></mrow></msub></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="20pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="a52cd3826f4cd389e183a124cf4e951d"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-21-217-2021-ie00004.svg" width="20pt" height="14pt" src="acp-21-217-2021-ie00004.png"/></svg:svg></span></span>, where <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M9" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>M</mi><mrow><msub><mi mathvariant="italic">θ</mi><mi mathvariant="normal">e</mi></msub></mrow></msub></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="20pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="03c0f68a28e3a2e7187207741ebf4f3f"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-21-217-2021-ie00005.svg" width="20pt" height="14pt" src="acp-21-217-2021-ie00005.png"/></svg:svg></span></span> is thereby effectively used as an alternative to latitude. We show that the CO<span class="inline-formula"><sub>2</sub></span> seasonal cycles are more constant as a function of pressure using <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M11" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>M</mi><mrow><msub><mi mathvariant="italic">θ</mi><mi mathvariant="normal">e</mi></msub></mrow></msub></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="20pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="d1c0911d64f5c61a322c107212237992"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-21-217-2021-ie00006.svg" width="20pt" height="14pt" src="acp-21-217-2021-ie00006.png"/></svg:svg></span></span> as the horizontal coordinate compared to latitude. Furthermore, short-term variability in CO<span class="inline-formula"><sub>2</sub></span> relative to the mean seasonal cycle is also smaller when the data are organized by <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M13" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>M</mi><mrow><msub><mi mathvariant="italic">θ</mi><mi mathvariant="normal">e</mi></msub></mrow></msub></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="20pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="b718c983b98a29b56671d96fab685f96"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-21-217-2021-ie00007.svg" width="20pt" height="14pt" src="acp-21-217-2021-ie00007.png"/></svg:svg></span></span> and pressure than when organized by latitude and pressure. We also present a method using <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M14" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>M</mi><mrow><msub><mi mathvariant="italic">θ</mi><mi mathvariant="normal">e</mi></msub></mrow></msub></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="20pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="8994dfc2db233503cc970f115b0e7a0c"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-21-217-2021-ie00008.svg" width="20pt" height="14pt" src="acp-21-217-2021-ie00008.png"/></svg:svg></span></span> to compute mass-weighted averages of CO<span class="inline-formula"><sub>2</sub></span> on a hemispheric scale. Using this method with the same airborne data and applying corrections for limited coverage, we resolve the average CO<span class="inline-formula"><sub>2</sub></span> seasonal cycle in the Northern Hemisphere (mass-weighted tropospheric climatological average for 2009–2018), yielding an amplitude of 7.8 <span class="inline-formula">±</span> 0.14 ppm and a downward zero-crossing on Julian day 173 <span class="inline-formula">±</span> 6.1 (i.e., late June). <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M19" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>M</mi><mrow><msub><mi mathvariant="italic">θ</mi><mi mathvariant="normal">e</mi></msub></mrow></msub></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="20pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="fe3b020f3c0015607396838e828de15f"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-21-217-2021-ie00009.svg" width="20pt" height="14pt" src="acp-21-217-2021-ie00009.png"/></svg:svg></span></span> may be similarly useful for mapping the distribution and computing inventories of any long-lived chemical tracer.</p>