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<front>
<journal-meta>
<journal-id journal-id-type="publisher">GMDD</journal-id>
<journal-title-group>
<journal-title>Geoscientific Model Development Discussions</journal-title>
<abbrev-journal-title abbrev-type="publisher">GMDD</abbrev-journal-title>
<abbrev-journal-title abbrev-type="nlm-ta">Geosci. Model Dev. Discuss.</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">1991-962X</issn>
<publisher><publisher-name></publisher-name>
<publisher-loc>Göttingen, Germany</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.5194/gmd-2023-15</article-id>
<title-group>
<article-title>Assimilating the dynamic spatial gradient of a bottom-up carbon flux estimation as a unique observation in COLA (v2.0)</article-title>
</title-group>
<contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Liu</surname>
<given-names>Zhiqiang</given-names>
<ext-link>https://orcid.org/0000-0003-2982-8381</ext-link>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Zeng</surname>
<given-names>Ning</given-names>
<ext-link>https://orcid.org/0000-0002-7489-7629</ext-link>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Liu</surname>
<given-names>Yun</given-names>
</name>
<xref ref-type="aff" rid="aff5">
<sup>5</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Kalnay</surname>
<given-names>Eugenia</given-names>
<ext-link>https://orcid.org/0000-0002-9984-9906</ext-link>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Asrar</surname>
<given-names>Ghassem</given-names>
</name>
<xref ref-type="aff" rid="aff6">
<sup>6</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Cai</surname>
<given-names>Qixiang</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Han</surname>
<given-names>Pengfei</given-names>
<ext-link>https://orcid.org/0000-0002-2546-8190</ext-link>
</name>
<xref ref-type="aff" rid="aff7">
<sup>7</sup>
</xref>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
</contrib-group><aff id="aff1">
<label>1</label>
<addr-line>Laboratory of Numerical Modeling for Atmospheric Sciences &amp; Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China</addr-line>
</aff>
<aff id="aff2">
<label>2</label>
<addr-line>University of Chinese Academy of Sciences, Beijing, China</addr-line>
</aff>
<aff id="aff3">
<label>3</label>
<addr-line>Dept. of Atmospheric and Oceanic Science, University of Maryland, College Park, Maryland, USA</addr-line>
</aff>
<aff id="aff4">
<label>4</label>
<addr-line>Earth System Science Interdisciplinary Center, College Park, Maryland, USA</addr-line>
</aff>
<aff id="aff5">
<label>5</label>
<addr-line>Dept. of Oceanography, Texas A &amp; M University, College Station, TX, USA</addr-line>
</aff>
<aff id="aff6">
<label>6</label>
<addr-line>Universities Space Research Association, Columbia, Maryland, USA</addr-line>
</aff>
<aff id="aff7">
<label>7</label>
<addr-line>Carbon Neutrality Research Center, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China</addr-line>
</aff>
<pub-date pub-type="epub">
<day>21</day>
<month>02</month>
<year>2023</year>
</pub-date>
<volume>2023</volume>
<fpage>1</fpage>
<lpage>18</lpage>
<permissions>
<copyright-statement>Copyright: &#x000a9; 2023 Zhiqiang Liu et al.</copyright-statement>
<copyright-year>2023</copyright-year>
<license license-type="open-access">
<license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri"  xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p>
</license>
</permissions>
<self-uri xlink:href="https://gmd.copernicus.org/preprints/gmd-2023-15/">This article is available from https://gmd.copernicus.org/preprints/gmd-2023-15/</self-uri>
<self-uri xlink:href="https://gmd.copernicus.org/preprints/gmd-2023-15/gmd-2023-15.pdf">The full text article is available as a PDF file from https://gmd.copernicus.org/preprints/gmd-2023-15/gmd-2023-15.pdf</self-uri>
<abstract>
<p>&lt;p&gt;Atmospheric inversion of high spatiotemporal surface CO&lt;sub&gt;2&lt;/sub&gt; flux without dynamic constraints and sufficient observations is an ill-posed problem, and a priori flux from a &quot;bottom-up&quot; estimation is commonly used in &quot;top-down&quot; inversion systems for regularization purposes. Ensemble Kalman filter-based inversion algorithms usually weigh a priori flux to the background or directly replace the background with the a priori flux. However, the &quot;bottom-up&quot; flux estimations, especially the simulated terrestrial-atmosphere CO&lt;sub&gt;2&lt;/sub&gt; exchange, are usually systematically biased at different spatiotemporal scales because of the deficiencies in understanding of some underlying processes. Here, we introduced a novel regularization algorithm into the Carbon in Ocean‒Land‒Atmosphere (COLA) data assimilation system, which assimilates a priori information as a unique observation (AAPO). The a priori information is not limited to &quot;bottom-up&quot; flux estimation. With the comprehensive assimilation regularization approach, COLA can apply the spatial gradient of the &quot;bottom-up&quot; flux estimation as a priori information to reduce the bias impact and enhance the dynamic information concerning the a priori &quot;bottom-up&quot; flux estimation. Benefiting from the enhanced signal-to-noise ratio in the spatial gradient, the global, regional, and grided flux estimations using the AAPO algorithm are significantly better than those obtained by the traditional regularization approach, especially over highly uncertain tropical regions in the context of observing simulation system experiments (OSSEs). We suggest that the AAPO algorithm can be applied to other greenhouse gas (e.g., CH&lt;sub&gt;4&lt;/sub&gt;, NO&lt;sub&gt;2&lt;/sub&gt;) and pollutant data assimilation studies.&lt;/p&gt;</p>
</abstract>
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