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<article xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:oasis="http://docs.oasis-open.org/ns/oasis-exchange/table" xml:lang="en" dtd-version="3.0" article-type="research-article"><?xmltex \bartext{Research article}?>
  <front>
    <journal-meta><journal-id journal-id-type="publisher">ACP</journal-id><journal-title-group>
    <journal-title>Atmospheric Chemistry and Physics</journal-title>
    <abbrev-journal-title abbrev-type="publisher">ACP</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">Atmos. Chem. Phys.</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">1680-7324</issn><publisher>
    <publisher-name>Copernicus Publications</publisher-name>
    <publisher-loc>Göttingen, Germany</publisher-loc>
  </publisher></journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.5194/acp-22-7461-2022</article-id><title-group><article-title>Satellite soil moisture data assimilation impacts on modeling weather
variables and ozone in the southeastern US – Part 2: Sensitivity to dry-deposition parameterizations</article-title><alt-title>Soil moisture, weather, and ozone in the southeastern US – Part 2</alt-title>
      </title-group><?xmltex \runningtitle{Soil moisture, weather, and ozone in the southeastern US -- Part~2}?><?xmltex \runningauthor{M.~Huang et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1 aff7">
          <name><surname>Huang</surname><given-names>Min</given-names></name>
          <email>mhuang10@gmu.edu</email>
        <ext-link>https://orcid.org/0000-0001-9361-0198</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Crawford</surname><given-names>James H.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Carmichael</surname><given-names>Gregory R.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4">
          <name><surname>Bowman</surname><given-names>Kevin W.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-8659-1117</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff5">
          <name><surname>Kumar</surname><given-names>Sujay V.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff6">
          <name><surname>Sweeney</surname><given-names>Colm</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-4517-0797</ext-link></contrib>
        <aff id="aff1"><label>1</label><institution>College of Science, George Mason University, Fairfax, VA, USA</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>NASA Langley Research Center, Hampton, VA, USA</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>College of Engineering, The University of Iowa, Iowa City, IA, USA</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>Jet Propulsion Laboratory, California Institute of Technology,
Pasadena, CA, USA</institution>
        </aff>
        <aff id="aff5"><label>5</label><institution>NASA Goddard Space Flight Center, Greenbelt, MD, USA</institution>
        </aff>
        <aff id="aff6"><label>6</label><institution>NOAA Earth System Research Laboratory Global Monitoring Division,
Boulder, CO, USA</institution>
        </aff>
        <aff id="aff7"><label>7</label><institution>National Centers for Environmental Prediction, College Park, MD, USA</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Min Huang (mhuang10@gmu.edu)</corresp></author-notes><pub-date><day>10</day><month>June</month><year>2022</year></pub-date>
      
      <volume>22</volume>
      <issue>11</issue>
      <fpage>7461</fpage><lpage>7487</lpage>
      <history>
        <date date-type="received"><day>21</day><month>December</month><year>2021</year></date>
           <date date-type="rev-request"><day>20</day><month>January</month><year>2022</year></date>
           <date date-type="rev-recd"><day>19</day><month>April</month><year>2022</year></date>
           <date date-type="accepted"><day>13</day><month>May</month><year>2022</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2022 </copyright-statement>
        <copyright-year>2022</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://acp.copernicus.org/articles/.html">This article is available from https://acp.copernicus.org/articles/.html</self-uri><self-uri xlink:href="https://acp.copernicus.org/articles/.pdf">The full text article is available as a PDF file from https://acp.copernicus.org/articles/.pdf</self-uri>
      <abstract><title>Abstract</title>

      <p id="d1e169">Ozone (O<inline-formula><mml:math id="M1" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>) dry deposition is a major O<inline-formula><mml:math id="M2" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> sink.
As a follow-up study of Huang et al. (2021), we quantify the impact of
satellite soil moisture (SM) on model representations of this process when
different dry-deposition parameterizations are implemented, based on which
the implications for interpreting O<inline-formula><mml:math id="M3" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> air pollution levels and assessing
the O<inline-formula><mml:math id="M4" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> impacts on human and ecosystem health are provided. The SM data
from NASA's Soil Moisture Active Passive mission are assimilated into the
Noah-Multiparameterization (Noah-MP) land surface model within the NASA Land
Information System framework, semicoupled with Weather Research and
Forecasting model with online Chemistry (WRF-Chem) regional-scale simulations covering
the southeastern US. Major changes in the modeling system used include
enabling the dynamic vegetation option, adding the irrigation process, and
updating the scheme for the surface exchange coefficient. Two dry-deposition
schemes are implemented, i.e., the Wesely scheme and a “dynamic” scheme,
in the latter of which dry-deposition parameterization is coupled with
photosynthesis and vegetation dynamics. It is demonstrated that, when the
dynamic scheme is applied, the simulated O<inline-formula><mml:math id="M5" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> dry-deposition
velocities <inline-formula><mml:math id="M6" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and their stomatal and cuticular portions, as well as the
total O<inline-formula><mml:math id="M7" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> fluxes <inline-formula><mml:math id="M8" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, are larger overall; <inline-formula><mml:math id="M9" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M10" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are
2–3 times more sensitive to the SM changes due to the data assimilation
(DA). Further, through case studies at two forested sites with different
soil types and hydrological regimes, we highlight that, applying the
Community Land Model type of SM factor controlling stomatal resistance
(i.e., <inline-formula><mml:math id="M11" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> factor) scheme in replacement of the Noah-type <inline-formula><mml:math id="M12" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula>
factor scheme reduced the <inline-formula><mml:math id="M13" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> sensitivity to SM changes by
<inline-formula><mml:math id="M14" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">75</mml:mn></mml:mrow></mml:math></inline-formula> % at one site, while it doubled this sensitivity at the
other site. Referring to multiple evaluation datasets, which may be
associated with variable extents of uncertainty, the model performance of
vegetation, surface fluxes, weather, and surface O<inline-formula><mml:math id="M15" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> concentrations
shows mixed responses to the DA, some of which display land cover
dependency. Finally, using model-derived concentration- and flux-based
policy-relevant O<inline-formula><mml:math id="M16" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> metrics as well as their matching exposure–response
functions, the relative biomass/crop yield losses for several types of
vegetation/crops are estimated to be within a wide range of 1 %–17 %. Their
sensitivities to the model's dry-deposition scheme and the implementation of
SM DA are discussed.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d1e334">Ground-level ozone (O<inline-formula><mml:math id="M17" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>) is a regulated secondary air pollutant harmful
to human and ecosystem health (Fleming et al., 2018; Mills et al., 2018a, b).
It is closely connected with O<inline-formula><mml:math id="M18" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> at higher altitudes where O<inline-formula><mml:math id="M19" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> plays
a more important role in the Earth's climate system by trapping infrared
radiation and absorbing ultraviolet radiation (e.g., Lacis et al., 1990). To
better protect human health and public welfare, in 2015, the US primary and
secondary National Ambient Air Quality Standards were lowered from 75
to 70 ppbv, in the format of daily maximum 8 h average (MDA8). Several other
O<inline-formula><mml:math id="M20" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>-exposure-based metrics have also been applied and/or proposed to
assess O<inline-formula><mml:math id="M21" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> impacts on vegetation, such as the accumulated O<inline-formula><mml:math id="M22" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
exposure over given thresholds (e.g., SUM40, SUM60, and AOT40), the averaged
O<inline-formula><mml:math id="M23" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> exposure during daylight hours (e.g., M7 and M12), and the
sigmoidal-weighted W126 cumulative exposure (e.g., Fredericksen et al.,
1996; van Dingenen et al., 2009; Hemispheric Transport of Air Pollution,
2010, and references therein; Avnery et al., 2011; Hollaway et al., 2012;
Huang et al., 2013; Lapina et al., 2014; Mills et al., 2007, 2018a, b). To
help comply with the tighter air quality standards, an improved
understanding of the individual processes affecting the (near-)surface
O<inline-formula><mml:math id="M24" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> concentrations and exceedances is demanded. Many O<inline-formula><mml:math id="M25" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>-related
processes are highly sensitive to environmental and/or biophysical
conditions (e.g., Steinkamp and Lawrence, 2011; Strode et al., 2015; Jiang
et al., 2018; Huang et al., 2021, and references therein). These
O<inline-formula><mml:math id="M26" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>-related processes include dry deposition of O<inline-formula><mml:math id="M27" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> and its
precursors, which is a major sink for near-surface O<inline-formula><mml:math id="M28" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> and depends on
dry-deposition velocities (<inline-formula><mml:math id="M29" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) and the deposited chemicals'
concentrations (Baublitz et al., 2020; Huang et al., 2021). As recognized in
numerous studies, accurately estimating dry-deposition fluxes is critical to
understanding O<inline-formula><mml:math id="M30" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> budgets and exceedances in the past, present, and
future (e.g., Stevenson et al., 2006; Griffiths et al., 2021); moreover, it
could contribute to a more reasonable assessment of the O<inline-formula><mml:math id="M31" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> impacts on
vegetation (e.g., Mills et al., 2011; Lombardozzi et al., 2015; Mills et
al., 2018a; Ducker et al., 2018; Ronan et al., 2020; Fu et al., 2022), which
is also relevant to the budgets of other greenhouse gases, weather, and
climate.</p>
      <p id="d1e476">Ozone uptake by plants is generally higher in warm/growing seasons and
during the daytime when O<inline-formula><mml:math id="M32" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> concentrations and <inline-formula><mml:math id="M33" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values peak. As
introduced in Huang et al. (2021) and references therein, over the land,
surface resistance <inline-formula><mml:math id="M34" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, which is composed of stomatal–mesophyll
(<inline-formula><mml:math id="M35" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>–<inline-formula><mml:math id="M36" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), cuticular (<inline-formula><mml:math id="M37" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">lu</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), in-canopy, and ground resistance
terms, often exerts the strongest effects on the magnitude and variability
of <inline-formula><mml:math id="M38" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. <inline-formula><mml:math id="M39" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> also includes the aerodynamic resistance (<inline-formula><mml:math id="M40" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) and
quasi-laminar sublayer resistance (<inline-formula><mml:math id="M41" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) terms.</p>
      <p id="d1e588">Soil moisture (SM) and its variability impact <inline-formula><mml:math id="M42" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in the following ways:
(1) SM can play a key role in controlling the opening and closing of plants'
stomata as well as the mesophyll functioning (Egea et al., 2011; Baillie and
Fleming, 2019), and thus it can directly affect the <inline-formula><mml:math id="M43" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M44" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
terms of <inline-formula><mml:math id="M45" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. (2) SM is closely linked with vegetation attributes, such
as the growing-season above-ground biomass, which is often expressed as leaf
area index (LAI) or vegetation optical depth (VOD) and controls the stomatal
and cuticular uptake of O<inline-formula><mml:math id="M46" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>-related species. (3) SM as well as
vegetation conditions can affect multiple <inline-formula><mml:math id="M47" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> terms through its
interactions with other environmental conditions (e.g., temperatures,
radiation, precipitation, and humidity fields) that modulate these <inline-formula><mml:math id="M48" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
terms, and such effects are generally stronger over transitional climate
zones located between dry and wet climates. The SM impacts on <inline-formula><mml:math id="M49" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and
atmospheric states through the above-mentioned pathways are likely to
continue to grow in future. This is because, according to Intergovernmental
Panel on Climate Change (2021), the occurrence and severity of droughts,
some of which are characterized by surface and/or column-averaged SM
deficits, are projected to increase over many US regions under warmer future
environments. Better understanding the potentially enhanced SM dependency of
dry deposition and weather conditions under the changing climate is
important because O<inline-formula><mml:math id="M50" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> stress, together with heat, water, and
other stresses, can pose more complex threats to plant health than single
stress alone (Otu-Larbi et al., 2020).</p>
      <p id="d1e687">Single-point models and three-dimensional chemical transport models have
long been used to estimate <inline-formula><mml:math id="M51" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values and their responses to climate
change. In the widely used, empirical Wesely scheme (Wesely, 1989), <inline-formula><mml:math id="M52" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
is sensitive to only a few meteorological variables, with SM and plants'
physiological effects ignored. In previous studies, Wesely-scheme-based
<inline-formula><mml:math id="M53" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> fluxes as well as their various terms from different global,
regional, and point-scale modeling systems were intercompared and/or
evaluated with <inline-formula><mml:math id="M54" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M55" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> observations from sparsely distributed
sites (e.g., Val Martin et al., 2014; Hardacre et al., 2015; Clifton et al.,
2017; Silva and Heald, 2018; Wu et al., 2018; Lin et al., 2019) in terms of
their magnitude and variability. Studies such as Hardacre et al. (2015) show
that, even when similar (Wesely and Wesely-like) <inline-formula><mml:math id="M56" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> schemes were
applied, various models behaved differently in calculating <inline-formula><mml:math id="M57" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>,
reflecting the impacts of land use and land cover (LULC) and meteorological
fields which depend on the individual models' configurations (e.g., scales,
inputs). In almost all above-cited studies, large model–model and
model–observation discrepancies (i.e., by a factor of 2 or more) have been
found in places, suggesting the strong need of diagnosing and addressing
issues in the models' configurations and dry-deposition parameterizations.</p>
      <p id="d1e769">Revised or alternative dry-deposition schemes have been applied in an
increasing number of global- and regional-scale modeling studies. In some of
these works, stomatal conductance is calculated based on one-big-leaf
multiplicative algorithms that are more complicated than the Wesely (1989)
approach, in the way that the empirical maximum stomatal conductance is
adjusted by more factors, including water availability and vegetation
attributes (e.g., Anav et al., 2018; Falk and Søvde Haslerud, 2019; Emmerichs et al., 2021). In
others, <inline-formula><mml:math id="M58" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> calculations are coupled with photosynthesis and vegetation
phenology (e.g., Val Martin et al., 2014; Wu et al., 2018; Lin et al., 2019;
Wong et al., 2019; Clifton et al., 2020), which in this paper are frequently
referred to as “dynamic” schemes. Such types of modifications have been the
recommended directions for improving the estimates of <inline-formula><mml:math id="M59" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> as well as the
<inline-formula><mml:math id="M60" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and O<inline-formula><mml:math id="M61" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> responses to climate change, in that they have been
demonstrated to be capable of enhancing the dynamics and reducing the systematic biases of the modeled <inline-formula><mml:math id="M62" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. However, results based on such updated
<inline-formula><mml:math id="M63" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> schemes are still associated with variable extents of uncertainty
due to limitations in model parameterizations (related to structures,
empirical parameters, and stress functions) and/or configurations. In some
existing works that applied the dynamic schemes, such uncertainty was
quantified and addressed by simply scaling the fluxes resulting from the
dynamic schemes towards flux measurements available at very limited
locations during non-recent time periods (e.g., Val Martin et al., 2014).
These types of modified dry-deposition schemes still require further
investigations and optimizations, which can be approached by (1) quantifying
the sensitivities of process-based model variables to SM and other
environmental and/or biophysical variables for various LULC and soil types;
(2) improving model representations of processes central to SM states and
land–atmosphere interactions, such as including irrigation and other human
activities, tuning physics schemes (e.g., those related to the surface
exchange coefficient, <inline-formula><mml:math id="M64" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">H</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) in land surface models (LSMs), and using
available observations to constrain (some of) the key land variables in
models; and (3) including a wide range of observations and/or
observation-derived carbon, water, and energy fluxes as well as vegetation
states in model evaluation for broad geographical regions. Furthermore, it
is important to explicitly connect the progress in dry-deposition modeling
with the impact assessments of O<inline-formula><mml:math id="M65" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> and other air pollutants on ecosystem
health, productivity, and diversity.</p>
      <p id="d1e857">A regional-scale land modeling and SM data assimilation (DA) framework
coupled with weather and atmospheric chemistry modeling by the Weather
Research and Forecasting model with online Chemistry (WRF-Chem) is
implemented in this work. Using this tool, we quantify and discuss the
responses of <inline-formula><mml:math id="M66" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and its key components as well as O<inline-formula><mml:math id="M67" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
concentrations and plant uptake to SM changes due to the DA, for different
soil texture, LULC, and crop types. The central parts of this work rely on
the Noah-Multiparameterization (Noah-MP; Niu et al., 2011) LSM with dynamic
vegetation that enables the implementation of a modified dynamic dry-deposition scheme. This implemented dynamic scheme couples the <inline-formula><mml:math id="M68" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
calculation with photosynthesis for sunlit and shaded leaves and the
<inline-formula><mml:math id="M69" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">lu</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> calculation with vegetation phenology. With this modified scheme,
both the indirect (i.e., via changing weather and vegetation fields) and
direct effects of SM on dry deposition are considered in this modeling
system. Results based on this modified scheme and the WRF-Chem default Wesely
scheme are compared and evaluated with independent datasets. As an extended
work of Huang et al. (2021), here we continue to focus on the southeastern
US during summer 2016 for which period prior Noah- and Wesely-based model
calculations were conducted and aircraft observations are available. This
paper introduces the applied two dry-deposition schemes in Sect. 2.
It then presents SM and vegetation states (Sect. 3.1), surface fluxes, and
weather fields (Sect. 3.2) from this Noah-MP-based modeling system, in
comparison with those from Huang et al. (2021). Discussions on O<inline-formula><mml:math id="M70" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
concentrations and fluxes based on all related WRF-Chem simulations are also
connected with the assessment of O<inline-formula><mml:math id="M71" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> impacts on societies, ecosystem
health, and crop yield (Sect. 3.3). Summary and suggestions on future
directions are provided in Sect. 4.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Methods</title>
<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>Modeling and DA experiment design</title>
      <p id="d1e936">The modeling tools and DA experiment design of this study were largely
consistent with the Huang et al. (2021) study: we conducted model
simulations over the southeastern US in a semicoupled Land Information
System (LIS)–WRF-Chem system without and with the assimilation of the
enhanced SM retrievals from NASA's Soil Moisture Active Passive (SMAP;
Entekhabi et al., 2010) mission. Two dry-deposition schemes (details in
Sect. 2.3) were applied in cases without and with the SM DA. The 12 km/63
vertical layer Lambert conformal grid, atmospheric/land initialization, and
SM DA methods were adapted from our previous study based on the Noah LSM.
Major model input datasets and physics and chemistry schemes were kept similar
to before except a few aspects relevant to the upgrade of LSM from Noah to
Noah-MP (version 3.6) and the implementation of an irrigation scheme to be
introduced in Sect. 2.2.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1" specific-use="star"><?xmltex \currentcnt{1}?><?xmltex \def\figurename{Figure}?><label>Figure 1</label><caption><p id="d1e941"><bold>(a)</bold> Grid-dominant land use/land cover types grouped from
the original 20-category model input (Fig. 1c in Huang et al., 2021) based
on the method in Table S1, <bold>(b)</bold> grid-dominant crop type over
cropland-dominant regions, <bold>(c)</bold> gridded population density in 2015, and <bold>(d)</bold> highlighted grid-dominant soil types of sand/loamy sand, loam, and clay
which are most relevant to discussions in this paper. The original soil type
input from the State Soil Geographic database is shown in Fig. S1 in Huang
et al. (2021). Locations of the two CASTNET sites for the case studies are
denoted in green.</p></caption>
          <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://acp.copernicus.org/articles/22/7461/2022/acp-22-7461-2022-f01.png"/>

        </fig>

      <p id="d1e961">As in Huang et al. (2021), the LULC and soil texture type inputs of our
coupled modeling system were based on the International Geosphere-Biosphere
Programme-modified Moderate Resolution Imaging Spectroradiometer dataset (Table S1)
and the State Soil Geographic dataset, respectively. Crop type data from
Monfreda et al. (2008) were used in the irrigation scheme and the assessment
of the O<inline-formula><mml:math id="M72" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> impacts on vegetation (Fig. 1b), which are roughly consistent
with the 2016 records from the US Department of Agriculture National
Agricultural Statistics Service for several major crops such as maize,
soybean, and wheat (<uri>https://nassgeodata.gmu.edu/CropScape</uri>, last access: 8 November 2021). In Sect. 3 of this paper, model results are summarized
and/or discussed by groups of grid-dominant LULC and soil type that are
shown in Fig. 1a and d. The original 20 LULC types were grouped into urban
and non-urban areas and for vegetation-dominant areas, into forests,
croplands, and shrub/grasslands, following the criteria introduced in Table S1. The grid-dominant LULC groups for vegetated regions used in our analysis
are vastly similar to independently developed data products, e.g., a dataset
derived from the European Space Agency–Climate Change Initiative Land Cover
project (<uri>https://gwis.jrc.ec.europa.eu/apps/country.profile/overview/USA</uri>,
last access: 8 November 2021) and the 2016 National Land Cover Database
(Wickham et al., 2021). Urban-dominant grid cells are well aligned with
dense population areas (Fig. 1c) based on the Gridded Population of the
World version 4.11 (NASA Socioeconomic Data and Applications Center, 2018).
Grid-scale discrepancies exist between the LULC input used and independent
LULC products, which, however, are not anticipated to considerably impact
the results averaged by LULC groups. Three groups of soil are highlighted,
namely sand/loamy sand, loam, and clay. The original sand and loamy sand
categories are combined because of their high sand fractions
(<uri>http://www.soilinfo.psu.edu/index.cgi?soil_data&amp;conus&amp;data_cov&amp;fract&amp;methods</uri>, last access:
10 December 2021).</p>
</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>Physics and configurations of the Noah-MP LSM</title>
      <p id="d1e990">The Noah-MP LSM includes a number of improvements from Noah, and one of the
enhanced features in Noah-MP is that it contains a separate canopy layer
that explicitly computes photosynthetically active radiation, canopy
temperature, and related energy, water, and carbon fluxes so that it
facilities a dynamic vegetation model. A modified two-stream radiation
transfer scheme was used to compute fractions of sunlit and shaded leaves
and their absorbed solar radiation. The Ball–Berry type of <inline-formula><mml:math id="M73" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> scheme
(e.g., Ball et al., 1987) was applied as required by the dynamic vegetation
option. When this option is used, the green vegetation fraction (GVF) does not
come from an input dataset as in Huang et al. (2021) but is related to the LAI
based on Eq. (1):
            <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M74" display="block"><mml:mrow><mml:mi mathvariant="normal">GVF</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.52</mml:mn><mml:mi mathvariant="normal">LAI</mml:mi></mml:mrow></mml:msup><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          Niyogi and Raman (1997) concluded that Ball–Berry, along with two other
physiological schemes, performed better on <inline-formula><mml:math id="M75" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> than the multiplicative
Jarvis type, which has been frequently used with the prescribed vegetation
option. Specifically, it helps better capture the variance in <inline-formula><mml:math id="M76" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and is
more responsive to environmental changes. As described in Appendix B of Niu
et al. (2011), this scheme relates stomatal resistance <inline-formula><mml:math id="M77" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi mathvariant="normal">s</mml:mi><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> of sunlit
and shaded leaves <inline-formula><mml:math id="M78" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula> to the photosynthesis rates (<inline-formula><mml:math id="M79" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) per unit LAI of
sunlit and shaded leaves <inline-formula><mml:math id="M80" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula> separately:
            <disp-formula id="Ch1.E2" content-type="numbered"><label>2</label><mml:math id="M81" display="block"><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi mathvariant="normal">s</mml:mi><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:mi>m</mml:mi><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">air</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mi mathvariant="normal">air</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mi mathvariant="normal">sat</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mtext>TV</mml:mtext><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">air</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>g</mml:mi><mml:mi mathvariant="normal">min</mml:mi></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M82" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">air</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is CO<inline-formula><mml:math id="M83" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> concentration at the leaf surface. For our study
period, this was set at 400 ppmv according to the median value of Atmospheric
Carbon and Transport (ACT)-America B-200 aircraft near-surface (i.e.,
<inline-formula><mml:math id="M84" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">900</mml:mn></mml:mrow></mml:math></inline-formula> hPa) CO<inline-formula><mml:math id="M85" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> observations, which is close to the global
monthly-mean CO<inline-formula><mml:math id="M86" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> concentrations in August 2016
(<uri>https://gml.noaa.gov/webdata/ccgg/trends/co2/co2_mm_gl.txt</uri>, last access: 8 November 2021); TV, <inline-formula><mml:math id="M87" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">air</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>,
<inline-formula><mml:math id="M88" display="inline"><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mi mathvariant="normal">air</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M89" display="inline"><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mi mathvariant="normal">sat</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>(TV) are canopy temperature, surface air pressure, vapor
pressure at the leaf surface, and saturation vapor pressure inside leaf,
respectively; <inline-formula><mml:math id="M90" display="inline"><mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mi mathvariant="normal">min</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M91" display="inline"><mml:mi>m</mml:mi></mml:math></inline-formula> are land-cover-dependent empirical parameters.
<inline-formula><mml:math id="M92" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is determined by Eqs. (3)–(6):

                <disp-formula specific-use="gather" content-type="numbered"><mml:math id="M93" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E3"><mml:mtd><mml:mtext>3</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:msub><mml:mi>A</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi mathvariant="normal">gs</mml:mi></mml:msub><mml:mi mathvariant="normal">min</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">C</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi mathvariant="normal">L</mml:mi><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">S</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E4"><mml:mtd><mml:mtext>4</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">C</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>c</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>c</mml:mi><mml:mi mathvariant="normal">cp</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">max</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:msub><mml:mi>o</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">o</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E5"><mml:mtd><mml:mtext>5</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi mathvariant="normal">L</mml:mi><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>c</mml:mi><mml:mi mathvariant="normal">cp</mml:mi></mml:msub></mml:mrow></mml:mfenced><mml:mn mathvariant="normal">4.6</mml:mn><mml:mi mathvariant="italic">α</mml:mi><mml:msub><mml:mtext>PAR</mml:mtext><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:msub><mml:mi>c</mml:mi><mml:mi mathvariant="normal">cp</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E6"><mml:mtd><mml:mtext>6</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">S</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.5</mml:mn><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">max</mml:mi></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

            where <inline-formula><mml:math id="M94" display="inline"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi mathvariant="normal">gs</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is a TV-dependent growing season index, and <inline-formula><mml:math id="M95" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">C</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M96" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi mathvariant="normal">L</mml:mi><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, and
<inline-formula><mml:math id="M97" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">S</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are carboxylase-limited, light-limited, and export-limited
photosynthesis rates per unit LAI, respectively; <inline-formula><mml:math id="M98" display="inline"><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M99" display="inline"><mml:mrow><mml:msub><mml:mi>o</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are
CO<inline-formula><mml:math id="M100" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> concentrations inside leaf cavity, which is about 0.7 times of the
atmospheric CO<inline-formula><mml:math id="M101" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> concentration and atmospheric O<inline-formula><mml:math id="M102" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> concentration,
respectively. PAR represents the photosynthetically active radiation per unit
LAI. <inline-formula><mml:math id="M103" display="inline"><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi mathvariant="normal">cp</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the CO<inline-formula><mml:math id="M104" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> compensation point, and it is equal to
<inline-formula><mml:math id="M105" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.5</mml:mn><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">o</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mn mathvariant="normal">0.21</mml:mn><mml:msub><mml:mi>o</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, where <inline-formula><mml:math id="M106" display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M107" display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">o</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are the
Michaelis–Menten constants for CO<inline-formula><mml:math id="M108" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> and O<inline-formula><mml:math id="M109" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>, respectively, varying
with TV; and <inline-formula><mml:math id="M110" display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula> is the quantum efficiency.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T1" specific-use="star"><?xmltex \currentcnt{1}?><label>Table 1</label><caption><p id="d1e1694">Model cases and their configurations relevant to the
discussions of this study.</p></caption><oasis:table frame="topbot"><?xmltex \begin{scaleboxenv}{.95}[.95]?><oasis:tgroup cols="8">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:colspec colnum="4" colname="col4" align="left"/>
     <oasis:colspec colnum="5" colname="col5" align="left"/>
     <oasis:colspec colnum="6" colname="col6" align="left"/>
     <oasis:colspec colnum="7" colname="col7" align="left"/>
     <oasis:colspec colnum="8" colname="col8" align="left"/>
     <oasis:thead>
       <oasis:row>

         <oasis:entry colname="col1">Case</oasis:entry>

         <oasis:entry colname="col2">Land surface</oasis:entry>

         <oasis:entry colname="col3">Stomatal</oasis:entry>

         <oasis:entry colname="col4">Soil moisture factor</oasis:entry>

         <oasis:entry colname="col5">Surface exchange</oasis:entry>

         <oasis:entry colname="col6">Irrigation</oasis:entry>

         <oasis:entry colname="col7">Dry-deposition</oasis:entry>

         <oasis:entry colname="col8">Note</oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col1">name</oasis:entry>

         <oasis:entry colname="col2">model</oasis:entry>

         <oasis:entry colname="col3">resistance</oasis:entry>

         <oasis:entry colname="col4">controlling <inline-formula><mml:math id="M111" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col5">coefficient for heat</oasis:entry>

         <oasis:entry colname="col6">scheme</oasis:entry>

         <oasis:entry colname="col7">scheme</oasis:entry>

         <oasis:entry colname="col8"/>

       </oasis:row>
       <oasis:row rowsep="1">

         <oasis:entry colname="col1"/>

         <oasis:entry colname="col2"/>

         <oasis:entry colname="col3">scheme</oasis:entry>

         <oasis:entry colname="col4">(<inline-formula><mml:math id="M112" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula>)</oasis:entry>

         <oasis:entry colname="col5">(<inline-formula><mml:math id="M113" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">H</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) scheme</oasis:entry>

         <oasis:entry colname="col6"/>

         <oasis:entry colname="col7"/>

         <oasis:entry colname="col8"/>

       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>

         <oasis:entry colname="col1">Noah_D</oasis:entry>

         <oasis:entry colname="col2">Noah-MP</oasis:entry>

         <oasis:entry colname="col3">Ball–Berry</oasis:entry>

         <oasis:entry colname="col4">Noah-type</oasis:entry>

         <oasis:entry colname="col5">Monin–Obukhov</oasis:entry>

         <oasis:entry colname="col6">Sprinkler</oasis:entry>

         <oasis:entry colname="col7">Dynamic</oasis:entry>

         <oasis:entry rowsep="1" colname="col8" morerows="2">new in this study</oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col1">CLM_D</oasis:entry>

         <oasis:entry colname="col2">Noah-MP</oasis:entry>

         <oasis:entry colname="col3">Ball–Berry</oasis:entry>

         <oasis:entry colname="col4">CLM (version 4.5)-type</oasis:entry>

         <oasis:entry colname="col5">Monin–Obukhov</oasis:entry>

         <oasis:entry colname="col6">Sprinkler</oasis:entry>

         <oasis:entry colname="col7">Dynamic</oasis:entry>

       </oasis:row>
       <oasis:row rowsep="1">

         <oasis:entry colname="col1">Noah_W</oasis:entry>

         <oasis:entry colname="col2">Noah-MP</oasis:entry>

         <oasis:entry colname="col3">Ball–Berry</oasis:entry>

         <oasis:entry colname="col4">Noah-type</oasis:entry>

         <oasis:entry colname="col5">Monin–Obukhov</oasis:entry>

         <oasis:entry colname="col6">Sprinkler</oasis:entry>

         <oasis:entry colname="col7">Wesely</oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col1">P1_W</oasis:entry>

         <oasis:entry colname="col2">Noah</oasis:entry>

         <oasis:entry colname="col3">Jarvis</oasis:entry>

         <oasis:entry colname="col4">Noah</oasis:entry>

         <oasis:entry colname="col5">Chen97</oasis:entry>

         <oasis:entry colname="col6">not included</oasis:entry>

         <oasis:entry colname="col7">Wesely</oasis:entry>

         <oasis:entry colname="col8">from Part 1</oasis:entry>

       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup><?xmltex \end{scaleboxenv}?></oasis:table></table-wrap>

      <p id="d1e1937"><inline-formula><mml:math id="M114" display="inline"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">max</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> represents the maximum rate of carboxylation, expressed as
            <disp-formula id="Ch1.E7" content-type="numbered"><label>7</label><mml:math id="M115" display="block"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">max</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi mathvariant="normal">max</mml:mi><mml:mn mathvariant="normal">25</mml:mn></mml:mrow></mml:msub><mml:msubsup><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">vmax</mml:mi><mml:mstyle scriptlevel="+1"><mml:mfrac><mml:mrow><mml:mtext>TV</mml:mtext><mml:mo>-</mml:mo><mml:mn mathvariant="normal">25</mml:mn></mml:mrow><mml:mn mathvariant="normal">10</mml:mn></mml:mfrac></mml:mstyle></mml:msubsup><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mo>)</mml:mo><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mtext>TV</mml:mtext><mml:mo>)</mml:mo><mml:mi mathvariant="italic">β</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M116" display="inline"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi mathvariant="normal">max</mml:mi><mml:mn mathvariant="normal">25</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is the maximum carboxylation rate at 25 <inline-formula><mml:math id="M117" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C; <inline-formula><mml:math id="M118" display="inline"><mml:mi>f</mml:mi></mml:math></inline-formula>(TV) is a
function that mimics thermal breakdown of metabolic processes; <inline-formula><mml:math id="M119" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is a foliage
nitrogen factor; and <inline-formula><mml:math id="M120" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> is the SM factor controlling <inline-formula><mml:math id="M121" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, which
presents strong dependencies on soil type and hydrological regime. In this
study model results based on the Noah and the Community Land Model (CLM;
versions 4.5 and earlier) types of <inline-formula><mml:math id="M122" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> schemes are compared (Table 1),
the latter of which is known to often result in sharper and narrower ranges
of variation with SM than the former does. The Noah and CLM types of <inline-formula><mml:math id="M123" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> parameterizations are based on Eqs. (8) and (9), respectively:

                <disp-formula specific-use="gather" content-type="numbered"><mml:math id="M124" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E8"><mml:mtd><mml:mtext>8</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mi mathvariant="italic">β</mml:mi><mml:mo>=</mml:mo><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">root</mml:mi></mml:msub></mml:mrow></mml:munderover><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>z</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">root</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mi mathvariant="normal">min</mml:mi><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1.0</mml:mn><mml:mo>,</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mrow><mml:mi mathvariant="normal">liq</mml:mi><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mi mathvariant="normal">wilt</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mi mathvariant="normal">ref</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mi mathvariant="normal">wilt</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E9"><mml:mtd><mml:mtext>9</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mi mathvariant="italic">β</mml:mi><mml:mo>=</mml:mo><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">root</mml:mi></mml:msub></mml:mrow></mml:munderover><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>z</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">root</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo movablelimits="false">min⁡</mml:mo><mml:mfenced open="(" close=")"><mml:mrow><mml:mn mathvariant="normal">1.0</mml:mn><mml:mo>,</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ψ</mml:mi><mml:mi mathvariant="normal">wilt</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">ψ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">ψ</mml:mi><mml:mi mathvariant="normal">wilt</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">ψ</mml:mi><mml:mi mathvariant="normal">sat</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

            where
            <disp-formula id="Ch1.Ex1"><mml:math id="M125" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ψ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">ψ</mml:mi><mml:mi mathvariant="normal">sat</mml:mi></mml:msub><mml:msup><mml:mfenced close=")" open="("><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mrow><mml:mi mathvariant="normal">liq</mml:mi><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mi mathvariant="normal">sat</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:mrow><mml:mo>-</mml:mo><mml:mi>b</mml:mi></mml:mrow></mml:msup><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          <inline-formula><mml:math id="M126" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mrow><mml:mi mathvariant="normal">liq</mml:mi><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>,
<inline-formula><mml:math id="M127" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mi mathvariant="normal">wilt</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>,
<inline-formula><mml:math id="M128" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mi mathvariant="normal">ref</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M129" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mi mathvariant="normal">sat</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are SM at soil layer <inline-formula><mml:math id="M130" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula>, wilting point, and
reference and saturated SM, respectively. <inline-formula><mml:math id="M131" display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">root</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M132" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi mathvariant="normal">root</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are the
numbers of soil layers containing roots and total depth of the root zone,
respectively. <inline-formula><mml:math id="M133" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ψ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M134" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ψ</mml:mi><mml:mi mathvariant="normal">wilt</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M135" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ψ</mml:mi><mml:mi mathvariant="normal">sat</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are matric
potential at soil layer <inline-formula><mml:math id="M136" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula>, and wilting and saturated matric potential,
respectively, and <inline-formula><mml:math id="M137" display="inline"><mml:mi>b</mml:mi></mml:math></inline-formula> is the Clapp–Hornberger parameter. Major parameters for the
calculations of <inline-formula><mml:math id="M138" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> in both schemes are soil-type-dependent.</p>
      <p id="d1e2442">Other Noah-MP configurations which can affect the modeled land state and
flux variables include the three-layer snowpack physics and the CLASS snow
surface albedo; the Jordan scheme for partitioning precipitation into
rainfall and snowfall; the Niu-Yang-2006 frozen soil permeability and
supercooled liquid water option; the SIMple Groundwater Model runoff scheme;
and the Monin–Obukhov <inline-formula><mml:math id="M139" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">H</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> scheme, which is based on more general
Monin–Obukhov similarity theory and, unlike Noah's default Chen97 (Chen et al., 1997) scheme
(Niu et al., 2011; and Sect. S1 of Huang et al., 2021), accounts for the
zero-displacement height. Being affected by stability correction and
additional effects of planetary boundary layer height on friction velocity,
it is likely that the Monin–Obukhov scheme can result in either weaker or
greater <inline-formula><mml:math id="M140" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">H</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (i.e., less or more efficient ventilation of the land
surface) than the Chen97 scheme during the daytime in summer (Niu et al.,
2011; Yang et al., 2011).</p>
      <p id="d1e2467">The irrigation process was included in all Noah-MP-based simulations in this
study. The benefit of including irrigation relies on the choice and
parameterization of the irrigation scheme, as well as the LSM's inputs
(Lawston et al., 2015). The sprinkler scheme was chosen as it was reported
as the prevalent irrigation method in 2015 across the US and many of the
states within our model domain (Dieter et al., 2018). Irrigation was
triggered over irrigated land in growing season within local morning times
(06:00–10:00) when root zone SM drops below 50 % of the soil field capacity.
The irrigated land was determined by the model's LULC input and irrigation
intensity information in Salmon et al. (2015), and the root zone area was
derived from the maximum root depth, which varies by crop type and GVF.</p>
</sec>
<sec id="Ch1.S2.SS3">
  <label>2.3</label><?xmltex \opttitle{Wesely and dynamic O${}_{{3}}$ dry-deposition schemes}?><title>Wesely and dynamic O<inline-formula><mml:math id="M141" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> dry-deposition schemes</title>
      <p id="d1e2488">Dry-deposition velocity <inline-formula><mml:math id="M142" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is estimated based on the resistance analogy
approach:
            <disp-formula id="Ch1.E10" content-type="numbered"><label>10</label><mml:math id="M143" display="block"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          <inline-formula><mml:math id="M144" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M145" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are aerodynamic resistance and quasi-laminar sublayer
resistance, respectively, sensitive to surface properties such as surface
roughness, and follow the Monin–Obukhov similarity theory. Over the land,
surface resistance <inline-formula><mml:math id="M146" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, the major component of <inline-formula><mml:math id="M147" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, is classified
into stomatal–mesophyll resistance (<inline-formula><mml:math id="M148" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>–<inline-formula><mml:math id="M149" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), cuticular resistance
(<inline-formula><mml:math id="M150" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">lu</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), in-canopy resistance (<inline-formula><mml:math id="M151" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">dc</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M152" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">cl</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), and ground
resistance (<inline-formula><mml:math id="M153" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">ac</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M154" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">gs</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>):
            <disp-formula id="Ch1.E11" content-type="numbered"><label>11</label><mml:math id="M155" display="block"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">lu</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">dc</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">cl</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">ac</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">gs</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M156" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">dc</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is resistance for gas-phase transfer affected by buoyant
convection in the canopy when sunlight heats the (near-)surface, <inline-formula><mml:math id="M157" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">cl</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
is resistance for leaves, twigs, bark, and others in the lower canopy,
<inline-formula><mml:math id="M158" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">ac</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is resistance for transfer that depends mostly on canopy
structure, and <inline-formula><mml:math id="M159" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">gs</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is resistance for soil, leaf litter, snow, and
others at the ground surface.</p>
      <p id="d1e2796">Two deposition schemes, namely the Wesely and a dynamic scheme, were applied
in this study, in which <inline-formula><mml:math id="M160" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M161" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">lu</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are treated differently. In the
Wesely scheme, <inline-formula><mml:math id="M162" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M163" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">lu</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are calculated based on Eqs. (12) and (13):

                <disp-formula specific-use="gather" content-type="numbered"><mml:math id="M164" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E12"><mml:mtd><mml:mtext>12</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfenced close="" open="{"><mml:mtable class="array" rowspacing="0.2ex 5.690551pt 0.2ex 0.2ex" columnalign="left"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mfenced open="{" close="}"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:msup><mml:mfenced close="]" open="["><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mn mathvariant="normal">200</mml:mn><mml:mrow><mml:mi>G</mml:mi><mml:mo>+</mml:mo><mml:mn mathvariant="normal">0.1</mml:mn></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:mfenced><mml:mfenced open="{" close="}"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mn mathvariant="normal">400</mml:mn><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mn mathvariant="normal">40</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow><mml:mo>≤</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>≤</mml:mo><mml:mn mathvariant="normal">40</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">9999</mml:mn><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><?xmltex \hack{\hbox\bgroup\fontsize{9.5}{9.5}\selectfont$\displaystyle}?><mml:mtext mathvariant="normal"> assuming mass transfer through stomata stops</mml:mtext><mml:mo>,</mml:mo><?xmltex \hack{$\egroup}?></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">40</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mtext> or</mml:mtext><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mfenced></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E13"><mml:mtd><mml:mtext>13</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><?xmltex \hack{\hbox\bgroup\fontsize{8.5}{8.5}\selectfont$\displaystyle}?><mml:mtable class="split" rowspacing="0.2ex" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">lu</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi mathvariant="normal">lu</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">min</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:msup><mml:mi>H</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:mn mathvariant="normal">1000</mml:mn><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>for dry
surfaces according to humidity and precipitation fields</mml:mtext><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable><?xmltex \hack{$\egroup}?></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

            where the LULC- and season-dependent constants <inline-formula><mml:math id="M165" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M166" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi mathvariant="normal">lu</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">min</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>
represent the minimum stomatal and cuticular resistances, respectively,
which are subject to uncertainty; <inline-formula><mml:math id="M167" display="inline"><mml:mi>G</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M168" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are radiation and surface
temperature, respectively, whose definitions are different than those of
PAR and TV in Eqs. (2)–(7); <inline-formula><mml:math id="M169" display="inline"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M170" display="inline"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are molecular diffusivities
for water vapor and trace gas <inline-formula><mml:math id="M171" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> (e.g., O<inline-formula><mml:math id="M172" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>), respectively; <inline-formula><mml:math id="M173" display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula>, which is
sensitive to surface temperature, represents the Henry's law constant for
the focused trace gas; and <inline-formula><mml:math id="M174" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> is a reactivity factor for oxidation. The
Wesely-scheme-related results that are new from this study and those from
Huang et al. (2021) are compared (Table 1).</p>
      <p id="d1e3215">As expressed in Eq. (14), in the dynamic scheme, <inline-formula><mml:math id="M175" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> used in dry-deposition modeling was taken from what's calculated from Noah-MP's dynamic
vegetation model and thus considers the physiological process of leaf
responses to photosynthesis rate, humidity, and CO<inline-formula><mml:math id="M176" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> concentrations. The
direct effects of SM, as reflected in the <inline-formula><mml:math id="M177" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> formula, as well as other
environmental variables, are included in this method, and this work
quantifies the impact of the <inline-formula><mml:math id="M178" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> factor configurations in Noah-MP
(Table 1) on the dynamic-scheme-related results.
            <disp-formula id="Ch1.E14" content-type="numbered"><label>14</label><mml:math id="M179" display="block"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfenced open="(" close=")"><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi mathvariant="normal">s</mml:mi><mml:mo>,</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">sunlit</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>L</mml:mi><mml:mi mathvariant="normal">sunlit</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi mathvariant="normal">s</mml:mi><mml:mo>,</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">shaded</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>L</mml:mi><mml:mi mathvariant="normal">shaded</mml:mi></mml:msub></mml:mrow><mml:mtext>LAI</mml:mtext></mml:mfrac></mml:mstyle></mml:mfenced><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M180" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi mathvariant="normal">s</mml:mi><mml:mo>,</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">sunlit</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M181" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi mathvariant="normal">s</mml:mi><mml:mo>,</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">shaded</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> are computed based on Eqs. (2)–(7), and <inline-formula><mml:math id="M182" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mi mathvariant="normal">sunlit</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M183" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mi mathvariant="normal">shaded</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are proportional to the sunlit and
shaded fractions of canopy, respectively, calculated based on the modified
two-stream radiation transfer scheme.</p>
      <p id="d1e3385">In the dynamic scheme, <inline-formula><mml:math id="M184" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">lu</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> for dry surfaces is modified from the Wesely
formula by considering its LAI dependency:
            <disp-formula id="Ch1.E15" content-type="numbered"><label>15</label><mml:math id="M185" display="block"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">lu</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi mathvariant="normal">lu</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">min</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mtext>LAI</mml:mtext><mml:mo>×</mml:mo><mml:mo>(</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:msup><mml:mi>H</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:mn mathvariant="normal">1000</mml:mn><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          In both the Wesely and the dynamic schemes, <inline-formula><mml:math id="M186" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">dc</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is sensitive to surface
radiation, and <inline-formula><mml:math id="M187" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is expressed as
            <disp-formula id="Ch1.E16" content-type="numbered"><label>16</label><mml:math id="M188" display="block"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi>H</mml:mi><mml:mn mathvariant="normal">3000</mml:mn></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:mn mathvariant="normal">100</mml:mn><mml:msub><mml:mi>f</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          Similar to the <inline-formula><mml:math id="M189" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">lu</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> calculations in Eqs. (13) and (15), to approximate an
effect that coldness sometimes reduces the uptake, <inline-formula><mml:math id="M190" display="inline"><mml:mrow><mml:mn mathvariant="normal">1000</mml:mn><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> is
added to LULC- and season-dependent constants to derive <inline-formula><mml:math id="M191" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">gs</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and
<inline-formula><mml:math id="M192" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">cl</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. It is worth mentioning that the direct effects of water stress on
mesophyll resistance have been recognized (e.g., Egea et al., 2011). Yet, in
neither scheme we applied have such effects been incorporated into the
<inline-formula><mml:math id="M193" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> formula as part of the <inline-formula><mml:math id="M194" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> calculation.</p>
</sec>
<sec id="Ch1.S2.SS4">
  <label>2.4</label><?xmltex \opttitle{Model evaluation, analysis, and O${}_{{3}}$ impact assessments}?><title>Model evaluation, analysis, and O<inline-formula><mml:math id="M195" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> impact assessments</title>
      <p id="d1e3626">For the cases listed in Table 1, we quantify the impacts of SM DA on the
modeled SM, vegetation dynamics, surface fluxes, and meteorological and surface
O<inline-formula><mml:math id="M196" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> fields during the 16–28 August 2016 period. The focused surface
fluxes are gross primary productivity (GPP), which is integrated by LAI
from <inline-formula><mml:math id="M197" display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula> in Eqs. (2)–(3), energy fluxes and their partitioning in the format
of evaporative fraction (EF <inline-formula><mml:math id="M198" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> daily latent heat <inline-formula><mml:math id="M199" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> (daily latent heat <inline-formula><mml:math id="M200" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> daily sensible heat)), dry-deposition flux and individual <inline-formula><mml:math id="M201" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> terms for
O<inline-formula><mml:math id="M202" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>, particularly the <inline-formula><mml:math id="M203" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>- and <inline-formula><mml:math id="M204" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">lu</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>-related terms. The SM DA impacts on
most of these model fields are expressed as daily and/or daytime (around
13:00–24:00 UTC) averaged absolute or relative changes referring to the
results from the no-DA cases. For O<inline-formula><mml:math id="M205" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> dry-deposition fluxes, we also
conducted linear regression analyses to determine the relationships between
the relative flux changes and the relative changes in column-averaged
initial SM due to the DA. Results of O<inline-formula><mml:math id="M206" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> dry-deposition fluxes and the
regression analyses (i.e., slopes and their standard errors, correlation
coefficient <inline-formula><mml:math id="M207" display="inline"><mml:mi>r</mml:mi></mml:math></inline-formula> values, and <inline-formula><mml:math id="M208" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> values) are summarized by grouped LULC types
defined in Fig. 1a. Case studies were also conducted at two low-elevation
forested sites where we investigated in detail the diurnal and daily
variability of O<inline-formula><mml:math id="M209" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> dry-deposition fluxes from various model cases and an
independent dataset.</p>

<?xmltex \floatpos{p}?><table-wrap id="Ch1.T2" specific-use="star"><?xmltex \currentcnt{2}?><label>Table 2</label><caption><p id="d1e3754">Evaluation datasets relevant to this study, along with
their key attributes. References of these products can be found in the “Data
availability” section of this work and Huang et al. (2021).</p></caption><oasis:table frame="topbot"><?xmltex \begin{scaleboxenv}{.85}[.85]?><oasis:tgroup cols="6">
     <oasis:colspec colnum="1" colname="col1" align="justify" colwidth="3cm"/>
     <oasis:colspec colnum="2" colname="col2" align="justify" colwidth="3cm"/>
     <oasis:colspec colnum="3" colname="col3" align="justify" colwidth="3cm"/>
     <oasis:colspec colnum="4" colname="col4" align="justify" colwidth="3cm"/>
     <oasis:colspec colnum="5" colname="col5" align="justify" colwidth="3cm"/>
     <oasis:colspec colnum="6" colname="col6" align="justify" colwidth="3cm"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Measurement platform, network, or name of dataset</oasis:entry>
         <oasis:entry colname="col2">Measured or derived variable</oasis:entry>
         <oasis:entry colname="col3">Type of dataset</oasis:entry>
         <oasis:entry colname="col4">Spatial resolution</oasis:entry>
         <oasis:entry colname="col5">Temporal resolution; coverage of the dataset used</oasis:entry>
         <oasis:entry colname="col6">Note</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">SMAP</oasis:entry>
         <oasis:entry colname="col2">VOD</oasis:entry>
         <oasis:entry colname="col3">satellite retrieval</oasis:entry>
         <oasis:entry colname="col4">9 km</oasis:entry>
         <oasis:entry colname="col5">twice-daily; <?xmltex \hack{\hfill\break}?>morning time data during August 2015–2019</oasis:entry>
         <oasis:entry colname="col6">new in this study but available in the SMAP enhanced product introduced in Part 1</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry rowsep="1" colname="col1">SMAP L4C</oasis:entry>
         <oasis:entry rowsep="1" colname="col2">GPP</oasis:entry>
         <oasis:entry rowsep="1" colname="col3">observation-derived</oasis:entry>
         <oasis:entry rowsep="1" colname="col4">9 km</oasis:entry>
         <oasis:entry rowsep="1" colname="col5">daily; <?xmltex \hack{\hfill\break}?>April–September 2016</oasis:entry>
         <oasis:entry colname="col6">new in this study</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry rowsep="1" colname="col1">OCO-2</oasis:entry>
         <oasis:entry rowsep="1" colname="col2">SIF</oasis:entry>
         <oasis:entry rowsep="1" colname="col3">observation-derived</oasis:entry>
         <oasis:entry rowsep="1" colname="col4">0.05<inline-formula><mml:math id="M210" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> <inline-formula><mml:math id="M211" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 0.05<inline-formula><mml:math id="M212" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry rowsep="1" colname="col5">approximately biweekly; April–September 2016</oasis:entry>
         <oasis:entry colname="col6"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry rowsep="1" colname="col1">NASA B-200 and C-130 aircraft</oasis:entry>
         <oasis:entry rowsep="1" colname="col2">OCS</oasis:entry>
         <oasis:entry rowsep="1" colname="col3">flask observation</oasis:entry>
         <oasis:entry rowsep="1" colname="col4">variable</oasis:entry>
         <oasis:entry rowsep="1" colname="col5">variable; <?xmltex \hack{\hfill\break}?>16–28 August 2016</oasis:entry>
         <oasis:entry colname="col6"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">CASTNET</oasis:entry>
         <oasis:entry rowsep="1" colname="col2">O<inline-formula><mml:math id="M213" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> dry-deposition velocity <inline-formula><mml:math id="M214" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mo>[</mml:mo><mml:mi mathvariant="normal">ozone</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry rowsep="1" colname="col3">modeled</oasis:entry>
         <oasis:entry colname="col4">at the SUM156 and PED108 sites</oasis:entry>
         <oasis:entry colname="col5">hourly; <?xmltex \hack{\hfill\break}?>16–28 August 2016</oasis:entry>
         <oasis:entry colname="col6"/>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">O<inline-formula><mml:math id="M215" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> flux <inline-formula><mml:math id="M216" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi mathvariant="normal">t</mml:mi><mml:mo>[</mml:mo><mml:mi mathvariant="normal">ozone</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">modeled multiplied by observed</oasis:entry>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6"/>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">European Space Agency PROBA-V, via the Copernicus Global Land Service</oasis:entry>
         <oasis:entry colname="col2">GVF</oasis:entry>
         <oasis:entry colname="col3">satellite retrieval</oasis:entry>
         <oasis:entry colname="col4">1 km</oasis:entry>
         <oasis:entry colname="col5">10 d average; <?xmltex \hack{\hfill\break}?>August 2015–2019</oasis:entry>
         <oasis:entry colname="col6">used as a model input in Part 1</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry rowsep="1" colname="col1">Land and water surface reports operationally collected by the National Centers for Environmental Prediction; and NASA B-200 aircraft</oasis:entry>
         <oasis:entry rowsep="1" colname="col2">air temperature and humidity</oasis:entry>
         <oasis:entry rowsep="1" colname="col3">in situ observation</oasis:entry>
         <oasis:entry rowsep="1" colname="col4">variable</oasis:entry>
         <oasis:entry rowsep="1" colname="col5">variable; <?xmltex \hack{\hfill\break}?>16–28 August 2016</oasis:entry>
         <oasis:entry colname="col6">also used as evaluation datasets in Part 1</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry rowsep="1" colname="col1">AQS and CASTNET</oasis:entry>
         <oasis:entry rowsep="1" colname="col2">surface O<inline-formula><mml:math id="M217" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> concentration</oasis:entry>
         <oasis:entry rowsep="1" colname="col3">in situ observation</oasis:entry>
         <oasis:entry rowsep="1" colname="col4">variable</oasis:entry>
         <oasis:entry rowsep="1" colname="col5">hourly; <?xmltex \hack{\hfill\break}?>April–September 2016</oasis:entry>
         <oasis:entry colname="col6"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">FLUXCOM</oasis:entry>
         <oasis:entry colname="col2">latent and sensible heat</oasis:entry>
         <oasis:entry colname="col3">observation-derived</oasis:entry>
         <oasis:entry colname="col4">0.5<inline-formula><mml:math id="M218" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> <inline-formula><mml:math id="M219" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 0.5<inline-formula><mml:math id="M220" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">daily; <?xmltex \hack{\hfill\break}?>April–September 2016</oasis:entry>
         <oasis:entry colname="col6"/>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup><?xmltex \end{scaleboxenv}?></oasis:table><?xmltex \begin{scaleboxenv}{.85}[.85]?><table-wrap-foot><p id="d1e3757">Acronyms: AQS – Air Quality System, CASTNET – Clean Air Status and Trends
Network, GPP – gross primary productivity, GVF – green vegetation fraction,
L4C – level 4 carbon, OCO-2 – Orbiting Carbon Observatory-2, OCS – carbonyl
sulfide, PROBA-V – Project for On-Board Autonomy – Vegetation, SIF – solar-induced chlorophyll fluorescence, SMAP – Soil Moisture Active Passive, and
VOD – vegetation optical depth.</p></table-wrap-foot><?xmltex \end{scaleboxenv}?></table-wrap>

      <p id="d1e4143">A variety of data products were utilized in this study to assess the model
performance in no-DA and DA cases (Table 2). Many of these evaluation
datasets have been applied and introduced in detail in Huang et al. (2021),
which are (1) National Centers for Environmental Prediction Global Surface
Observational Weather Data as well as weather data collected on board the
NASA B-200 aircraft during the ACT-America campaign; (2) hourly surface
O<inline-formula><mml:math id="M221" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> measurements at the US Environmental Protection Agency Clean Air
Status and Trends Network (CASTNET) and Air Quality System (AQS) sites; and
(3) daily, 0.5<inline-formula><mml:math id="M222" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> <inline-formula><mml:math id="M223" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 0.5<inline-formula><mml:math id="M224" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> FLUXCOM latent and
sensible heat fluxes. New evaluation datasets used in this work include (1) VOD retrievals from the 9 km enhanced SMAP product, which indicates the
attenuation of microwave signals by vegetation, proportional to above-ground
canopy biomass, and was used together with a 10 d average Copernicus
Global Land Service GVF product to derive GVF for the focused 13 d period;
(2) daily GPP estimates from the 9 km SMAP level 4 carbon (L4C) product
version 6, developed based on the SMAP L4 surface (0–5 cm) and root zone
(0–100 cm) SM together with satellite LULC and vegetation datasets; (3) two
independent GPP proxies (Whelan et al., 2020) of satellite-derived
solar-induced chlorophyll fluorescence (SIF) data (Yu et al., 2019) and the
Portable Flask Package (Sweeney et al., 2015) carbonyl sulfide (OCS)
measurements collected on board the B-200 and C-130 aircraft during the
ACT-America campaign, with the OCS data being analyzed together with other
airborne trace gas (e.g., benzene) measurements during this campaign to help
distinguish the influences of combustion sources from plant CO<inline-formula><mml:math id="M225" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> uptake
on the observed OCS distributions; and (4) <inline-formula><mml:math id="M226" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> data from two selected
CASTNET sites, estimated using a multilayer model (MLM; not supported by
CASTNET as of 2017) version 3.0, which has known limitations and biases
against eddy covariance flux measurements as well as <inline-formula><mml:math id="M227" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> estimated using
other methods (e.g., Finkelstein et al., 2000; Saylor et al., 2014; Wu et
al., 2018). The known limitations of MLM and how they may affect our model
comparisons with the CASTNET <inline-formula><mml:math id="M228" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> data are discussed. Our O<inline-formula><mml:math id="M229" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> dry-deposition results are also compared with eddy covariance measurements
reported in independent works for similar climate and/or LULC types during
other time periods.</p>
      <p id="d1e4233">This study also evaluates how the SM DA affected the assessments of surface
O<inline-formula><mml:math id="M230" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> impacts on human and ecosystem health. Specifically, (1) MDA8 O<inline-formula><mml:math id="M231" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
fields over urban and nonurban terrestrial regions were investigated linked
to their respective population ranges, and (2) the LULC-specific phytotoxic
ozone dose above the critical level of <inline-formula><mml:math id="M232" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> nmol m<inline-formula><mml:math id="M233" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math id="M234" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>
(POD<inline-formula><mml:math id="M235" display="inline"><mml:msub><mml:mi/><mml:mi>y</mml:mi></mml:msub></mml:math></inline-formula>) and the crop-specific AOT40, which are defined in Eqs. (17) and (18), were evaluated.
            <disp-formula id="Ch1.E17" content-type="numbered"><label>17</label><mml:math id="M236" display="block"><mml:mrow><mml:msub><mml:mtext>POD</mml:mtext><mml:mi>y</mml:mi></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>(</mml:mo><mml:mi mathvariant="normal">mmol</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mo movablelimits="false">∑</mml:mo><mml:mfenced close="]" open="["><mml:mrow><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mi>y</mml:mi></mml:mrow></mml:mfenced><mml:mo>×</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">3600</mml:mn><mml:mrow><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mn mathvariant="normal">6</mml:mn></mml:msup></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          for hourly daytime stomatal uptake <inline-formula><mml:math id="M237" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>&gt;</mml:mo><mml:mi>y</mml:mi></mml:mrow></mml:math></inline-formula> nmol m<inline-formula><mml:math id="M238" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math id="M239" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, and
            <disp-formula id="Ch1.E18" content-type="numbered"><label>18</label><mml:math id="M240" display="block"><mml:mrow><mml:mi mathvariant="normal">AOT</mml:mi><mml:mn mathvariant="normal">40</mml:mn><mml:mfenced open="(" close=")"><mml:mi mathvariant="normal">ppmh</mml:mi></mml:mfenced><mml:mo>=</mml:mo><mml:mo movablelimits="false">∑</mml:mo><mml:mo>[</mml:mo><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.04</mml:mn><mml:mo>)</mml:mo><mml:mo>]</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          for hourly daytime O<inline-formula><mml:math id="M241" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> concentration <inline-formula><mml:math id="M242" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0.04</mml:mn></mml:mrow></mml:math></inline-formula> ppmv.</p>
      <p id="d1e4448">According to Convention on Long-Range Transboundary Air Pollution (CLRTAP,
2017), the stomatal O<inline-formula><mml:math id="M243" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> uptake <inline-formula><mml:math id="M244" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> needed in POD<inline-formula><mml:math id="M245" display="inline"><mml:msub><mml:mi/><mml:mi>y</mml:mi></mml:msub></mml:math></inline-formula> calculations
was derived based on Eq. (19):
            <disp-formula id="Ch1.E19" content-type="numbered"><label>19</label><mml:math id="M246" display="block"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>C</mml:mi><mml:mfenced open="(" close=")"><mml:mrow class="unit"><mml:mi mathvariant="normal">nmol</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:mfenced><mml:mo>×</mml:mo><mml:msub><mml:mi>g</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>×</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1.3</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">150</mml:mn><mml:mo>×</mml:mo><mml:msqrt><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi>L</mml:mi><mml:mi>u</mml:mi></mml:mfrac></mml:mstyle></mml:msqrt><mml:mo>+</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M247" display="inline"><mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M248" display="inline"><mml:mi>L</mml:mi></mml:math></inline-formula>, and <inline-formula><mml:math id="M249" display="inline"><mml:mi>u</mml:mi></mml:math></inline-formula> are stomatal conductance, leaf width (0.04 m
in this work), and surface wind speed, respectively.</p>
      <p id="d1e4577">The calculated POD<inline-formula><mml:math id="M250" display="inline"><mml:msub><mml:mi/><mml:mi>y</mml:mi></mml:msub></mml:math></inline-formula> and AOT40 were used to estimate the relative
biomass loss (RBL) or relative yield loss (RYL) for several types of
vegetation or crops based on dose–response functions reported in literature
(Table 3, CLRTAP, 2017; Mills et al., 2007, 2018b). Our 13 d WRF-Chem
model results were linearly extrapolated to approximately 3 months to
derive the POD<inline-formula><mml:math id="M251" display="inline"><mml:msub><mml:mi/><mml:mi>y</mml:mi></mml:msub></mml:math></inline-formula> and AOT40 fields. While we assess the uncertainty due
to such linear extrapolations by relating our 13 d/extrapolated surface
O<inline-formula><mml:math id="M252" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> and flux results to seasonal (e.g., averaged for 3 consecutive
months) conditions in 2016, we focus on qualitatively interpreting the
results and discussing their implications. The outcome from this analysis is
also compared with the findings from several independent O<inline-formula><mml:math id="M253" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> impact
assessment studies for different time periods.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T3" specific-use="star"><?xmltex \currentcnt{3}?><label>Table 3</label><caption><p id="d1e4619">Dose–response functions used to estimate the LULC- and
crop-specific relative yield losses (i.e., 1 – relative yield, RY) due to
O<inline-formula><mml:math id="M254" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> exposure and uptake, along with their references.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="4">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="justify" colwidth="4cm"/>
     <oasis:colspec colnum="4" colname="col4" align="justify" colwidth="4cm"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1">LULC type</oasis:entry>
         <oasis:entry colname="col2">Crop type</oasis:entry>
         <oasis:entry rowsep="1" namest="col3" nameend="col4" align="center">Dose–response function (references) </oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3">Based on phytotoxic ozone dose above the critical level <inline-formula><mml:math id="M255" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> nmol m<inline-formula><mml:math id="M256" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math id="M257" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> (POD<inline-formula><mml:math id="M258" display="inline"><mml:msub><mml:mi/><mml:mi>y</mml:mi></mml:msub></mml:math></inline-formula>, in mmol m<inline-formula><mml:math id="M259" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col4">Based on AOT40 in ppmh</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Deciduous forest</oasis:entry>
         <oasis:entry colname="col2">/</oasis:entry>
         <oasis:entry colname="col3">RY <inline-formula><mml:math id="M260" display="inline"><mml:mrow><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0154</mml:mn></mml:mrow></mml:math></inline-formula> POD<inline-formula><mml:math id="M261" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn mathvariant="normal">1.012</mml:mn></mml:mrow></mml:math></inline-formula> (CLRTAP, 2017)</oasis:entry>
         <oasis:entry colname="col4">/</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Grasslands</oasis:entry>
         <oasis:entry colname="col2">/</oasis:entry>
         <oasis:entry colname="col3">RY <inline-formula><mml:math id="M262" display="inline"><mml:mrow><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0074</mml:mn></mml:mrow></mml:math></inline-formula> POD<inline-formula><mml:math id="M263" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn mathvariant="normal">0.982</mml:mn></mml:mrow></mml:math></inline-formula> (CLRTAP, 2017)</oasis:entry>
         <oasis:entry colname="col4">/</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Croplands</oasis:entry>
         <oasis:entry colname="col2">Maize</oasis:entry>
         <oasis:entry colname="col3">/</oasis:entry>
         <oasis:entry colname="col4">RY <inline-formula><mml:math id="M264" display="inline"><mml:mrow><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0036</mml:mn></mml:mrow></mml:math></inline-formula> AOT40 <inline-formula><mml:math id="M265" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> 1.02 (Mills et al., 2007)</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">Soybean</oasis:entry>
         <oasis:entry colname="col3">/</oasis:entry>
         <oasis:entry colname="col4">RY <inline-formula><mml:math id="M266" display="inline"><mml:mrow><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0116</mml:mn></mml:mrow></mml:math></inline-formula> AOT40 <inline-formula><mml:math id="M267" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> 1.02 (Mills et al., 2007)</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">Wheat</oasis:entry>
         <oasis:entry colname="col3">RY <inline-formula><mml:math id="M268" display="inline"><mml:mrow><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0064</mml:mn></mml:mrow></mml:math></inline-formula> POD<inline-formula><mml:math id="M269" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn mathvariant="normal">0.9756</mml:mn></mml:mrow></mml:math></inline-formula> (Mills et al., 2018b; CLRTAP, 2017)</oasis:entry>
         <oasis:entry colname="col4">RY <inline-formula><mml:math id="M270" display="inline"><mml:mrow><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0161</mml:mn></mml:mrow></mml:math></inline-formula> AOT40 <inline-formula><mml:math id="M271" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> 0.99 (Mills et al., 2007)</oasis:entry>
       <?xmltex \interline{[-11.381102pt]}?></oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4">RY <inline-formula><mml:math id="M272" display="inline"><mml:mrow><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.009</mml:mn></mml:mrow></mml:math></inline-formula> AOT40 <inline-formula><mml:math id="M273" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> 0.969 (Mills et al., 2018b)</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <?xmltex \floatpos{p}?><fig id="Ch1.F2" specific-use="star"><?xmltex \currentcnt{2}?><?xmltex \def\figurename{Figure}?><label>Figure 2</label><caption><p id="d1e4970">Period-mean (16–28 August 2016) WRF-Chem <bold>(a, b)</bold>
column-averaged and <bold>(c, d)</bold> surface-layer soil moisture fields at initial
times and <bold>(e–h)</bold> their relative changes in percent due to the SMAP DA. Results
based on the Noah_D and CLM_D cases are shown
in <bold>(a)</bold>, <bold>(c)</bold>, <bold>(e)</bold>, and <bold>(g)</bold> and <bold>(b)</bold>, <bold>(d)</bold>, <bold>(f)</bold>, and <bold>(h)</bold>, respectively.</p></caption>
          <?xmltex \igopts{width=483.69685pt}?><graphic xlink:href="https://acp.copernicus.org/articles/22/7461/2022/acp-22-7461-2022-f02.png"/>

        </fig>

</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Results and discussions</title>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Modeled SM and vegetation fields</title>
      <p id="d1e5029">Figure 2 compares the horizontal and vertical gradients of the model's
initial SM conditions from the Noah_D and CLM_D cases defined in Table 1, in which the Noah and CLM types of <inline-formula><mml:math id="M274" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula>
factor schemes were applied. At the surface layer (0–10 cm belowground),
both cases produced SM horizontal gradients that resemble the Noah-based
results presented in Huang et al. (2021). They are moderately correlated
with the column-averaged SM fields (<inline-formula><mml:math id="M275" display="inline"><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.875</mml:mn></mml:mrow></mml:math></inline-formula> and 0.871, respectively), and
the mean differences in column-averaged and surface SM from the
Noah_D and CLM_D cases are 0.003 and <inline-formula><mml:math id="M276" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.006</mml:mn></mml:mrow></mml:math></inline-formula> m<inline-formula><mml:math id="M277" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> m<inline-formula><mml:math id="M278" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, respectively. Kumar et al. (2009) have found that,
compared to other LSMs such as the Catchment model (based on which the SMAP L4
datasets are produced), the 4-soil-layer Noah and 10-soil-layer CLM LSMs
display successively weaker surface–subsurface coupling strengths, and the
weakest coupling strength of CLM was primarily attributed to its
significantly larger number of soil layers. The slightly weaker
surface–subsurface correlations in the CLM_D case than in the
Noah_D from this work, both based on a 4-soil-layer
Noah-MP modeling system, indicate the minor role of the LSM physics, in
particular the <inline-formula><mml:math id="M279" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> factor scheme, in controlling the vertical coupling
strength of SM conditions.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3" specific-use="star"><?xmltex \currentcnt{3}?><?xmltex \def\figurename{Figure}?><label>Figure 3</label><caption><p id="d1e5092">Period-mean (16–28 August 2016) green vegetation fraction (GVF)
<bold>(a)</bold> derived from the Copernicus Global Land Service product and the SMAP
morning-time (AM) vegetation optical depth (VOD) using the method described
in Fig. S2 and <bold>(b, c, e, f)</bold> based on WRF-Chem calculations as well as their
responses to the SMAP DA. The GVF results from the Noah_D and
CLM_D cases are shown in <bold>(b)</bold> and <bold>(c)</bold> and <bold>(e)</bold> and <bold>(f)</bold>, respectively.
Period-mean SMAP AM VOD is shown in <bold>(d)</bold>. In <bold>(a)</bold> and <bold>(d)</bold>, grey indicates missing
data over terrestrial regions.</p></caption>
          <?xmltex \igopts{width=483.69685pt}?><graphic xlink:href="https://acp.copernicus.org/articles/22/7461/2022/acp-22-7461-2022-f03.png"/>

        </fig>

      <p id="d1e5129">The modeled SM fields from the Noah_D and CLM_D differ on grid scale, particularly in the subsurface zones (Fig. 2a and b).
For example, in sand-dominant regions that were experiencing drought
conditions during this period (e.g., Florida and the Texas–Oklahoma border
regions, where simulated SM is mostly under 0.2 m<inline-formula><mml:math id="M280" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> m<inline-formula><mml:math id="M281" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>),
column-averaged SM values from the CLM_D case are notably
smaller than those from the Noah_D case. These results
contrast with those reported by Niu et al. (2011), in which cases using Noah-MP
with the CLM-type <inline-formula><mml:math id="M282" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> factor led to less soil water consumption and thus
smaller SM variability during drought periods than using it with the Noah-type <inline-formula><mml:math id="M283" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> factor. In their cases focusing on loam and clay soil that have higher
wilting points when the CLM-type <inline-formula><mml:math id="M284" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> factor scheme was applied, plant
transpiration ceased to save soil water under drought conditions. Our
results can be explained by the steeper CLM-type <inline-formula><mml:math id="M285" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula>–SM curve than the
Noah-type <inline-formula><mml:math id="M286" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula>–SM curve for low SM, sand-dominant areas, as illustrated
in Fig. 3a of Niu et al. (2011). For such conditions, Noah-MP with the
CLM-type <inline-formula><mml:math id="M287" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> factor produces stronger evapotranspiration (ET) and
consumes more soil water, resulting in drier soil. For wet regions where SM
values exceed 0.4 m<inline-formula><mml:math id="M288" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> m<inline-formula><mml:math id="M289" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, such as Louisiana and Arkansas, the CLM-
and Noah-type <inline-formula><mml:math id="M290" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> values are close to 1.0 and insensitive to soil type
and SM variations; therefore, SM and ET produced from the
Noah_D and CLM_D cases do not diverge. These
findings corroborate the conclusions by Yang et al. (2011) that the degree
of the <inline-formula><mml:math id="M291" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> impacts on the SM–ET relationship should depend on the soil
type and hydrological regime, and they are important for understanding the
vegetation and surface flux results to be presented in the later parts of
this paper.</p>
      <p id="d1e5233">Referring to the SMAP SM data, in general, surface SM produced by the no-DA
modeling systems shows wet biases in non-forested regions and dry biases over
the forests for the study period. These SMAP–model discrepancies were
successfully reduced by the DA for all vegetated LULC groups (Fig. S1,
left), leading to overall slightly drier soil in DA-enabled simulations. For
both the Noah_D and CLM_D cases, the DA
adjusted the modeled SM fields across the entire soil columns, demonstrating
that observational information at the surface was propagated into deep soil
layers. The SM responses to the DA as a function of soil layer from the
Noah_D and CLM_D cases are roughly similar but
different at small spatial scales, which reflect the controls of the <inline-formula><mml:math id="M292" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> factor scheme on the surface–subsurface coupling strengths of the
modeling/DA system used. With the SMAP DA enabled, the <inline-formula><mml:math id="M293" display="inline"><mml:mi>r</mml:mi></mml:math></inline-formula> values between
column-averaged and surface SM from the Noah_D and
CLM_D cases increased to 0.902 and 0.897, respectively.</p>
      <p id="d1e5250">The satellite-derived GVF fields (methods introduced in Fig. S2 caption)
transition from low to moderate (<inline-formula><mml:math id="M294" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.6</mml:mn></mml:mrow></mml:math></inline-formula>) to high (<inline-formula><mml:math id="M295" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0.8</mml:mn></mml:mrow></mml:math></inline-formula>)
values from the western (mostly shrub/grasslands) to the central and eastern
parts (forests- and croplands-dominant) of the study region, and such spatial
gradients are highly correlated with the SMAP VOD retrievals (Fig. 3a and d).
The Noah_D and CLM_D cases both reproduced these spatial patterns moderately
well. Major differences between these
cases are found in dry sandy regions, where, as discussed in previous
paragraphs, more soil water was consumed for ET and plant growth in the
CLM_D case and therefore higher GVF values are given.
Overall, the DA adjustments to the modeled GVF and SM fields are positively
correlated (Fig. S1, right), and the relative changes in GVF are smaller.
While the SM changes in the Noah_D and CLM_D
cases are of close magnitude, GVF responded more strongly in the
CLM_D case except for sandy regions. Referring to the
satellite-derived GVF fields which are also subject to large uncertainty (as
discussed in Fig. S2 caption), the modeled vegetation fields are more
effectively improved by the DA over sparsely vegetated regions such as the
South Central Plains. The DA also remarkably reduced the model–satellite
mismatches over some of the dense vegetation regions such as
southwestern Ohio. The likely degraded model performance over certain dense
vegetation areas can be partially explained by weaknesses related to the
SM–vegetation growth feedbacks (more details in Fig. S1 caption) in the
dynamic vegetation model parameterizations which need to be identified and
addressed in future work. It is also suggested that joint assimilation of
satellite SM and vegetation phenology products such as the VOD retrievals
needs to be attempted, which may maximize the positive DA impacts on
multiple land variables and their atmospheric feedbacks.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T4" specific-use="star"><?xmltex \currentcnt{4}?><label>Table 4</label><caption><p id="d1e5276">Evaluation of daily-averaged WRF-Chem gross primary
productivity and evaporative fraction, referring to the SMAP L4C and FLUXCOM
datasets.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="9">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right" colsep="1"/>
     <oasis:colspec colnum="6" colname="col6" align="right"/>
     <oasis:colspec colnum="7" colname="col7" align="right" colsep="1"/>
     <oasis:colspec colnum="8" colname="col8" align="right"/>
     <oasis:colspec colnum="9" colname="col9" align="right"/>
     <oasis:thead>
       <oasis:row>

         <oasis:entry colname="col1">Flux variable</oasis:entry>

         <oasis:entry colname="col2">LULC type</oasis:entry>

         <oasis:entry colname="col3">Reference datasets</oasis:entry>

         <oasis:entry rowsep="1" namest="col4" nameend="col9" align="center">Model case </oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col1"/>

         <oasis:entry colname="col2"/>

         <oasis:entry colname="col3">(observation-derived)</oasis:entry>

         <oasis:entry rowsep="1" namest="col4" nameend="col5" align="center" colsep="1">Noah_D </oasis:entry>

         <oasis:entry rowsep="1" namest="col6" nameend="col7" align="center" colsep="1">CLM_D </oasis:entry>

         <oasis:entry rowsep="1" namest="col8" nameend="col9" align="center">P1_W </oasis:entry>

       </oasis:row>
       <oasis:row rowsep="1">

         <oasis:entry colname="col1"/>

         <oasis:entry colname="col2"/>

         <oasis:entry colname="col3"/>

         <oasis:entry colname="col4">No DA</oasis:entry>

         <oasis:entry colname="col5">DA</oasis:entry>

         <oasis:entry colname="col6">No DA</oasis:entry>

         <oasis:entry colname="col7">DA</oasis:entry>

         <oasis:entry colname="col8">No DA</oasis:entry>

         <oasis:entry colname="col9">DA</oasis:entry>

       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>

         <oasis:entry colname="col1">Gross primary productivity (g m<inline-formula><mml:math id="M298" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> d<inline-formula><mml:math id="M299" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>

         <oasis:entry rowsep="1" colname="col2">forests</oasis:entry>

         <oasis:entry rowsep="1" colname="col3">7.39</oasis:entry>

         <oasis:entry rowsep="1" colname="col4">7.88</oasis:entry>

         <oasis:entry rowsep="1" colname="col5">7.08</oasis:entry>

         <oasis:entry rowsep="1" colname="col6">9.06</oasis:entry>

         <oasis:entry rowsep="1" colname="col7">6.94</oasis:entry>

         <oasis:entry rowsep="1" namest="col8" nameend="col9" morerows="2" align="center">/ </oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col1"/>

         <oasis:entry rowsep="1" colname="col2">shrub/grass</oasis:entry>

         <oasis:entry rowsep="1" colname="col3">5.11</oasis:entry>

         <oasis:entry rowsep="1" colname="col4">3.28</oasis:entry>

         <oasis:entry rowsep="1" colname="col5">3.29</oasis:entry>

         <oasis:entry rowsep="1" colname="col6">4.74</oasis:entry>

         <oasis:entry rowsep="1" colname="col7">3.89</oasis:entry>

       </oasis:row>
       <oasis:row rowsep="1">

         <oasis:entry colname="col1"/>

         <oasis:entry colname="col2">croplands</oasis:entry>

         <oasis:entry colname="col3">8.94</oasis:entry>

         <oasis:entry colname="col4">7.64</oasis:entry>

         <oasis:entry colname="col5">7.40</oasis:entry>

         <oasis:entry colname="col6">9.77</oasis:entry>

         <oasis:entry colname="col7">8.13</oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col1">Evaporative fraction (unitless)</oasis:entry>

         <oasis:entry colname="col2">forests</oasis:entry>

         <oasis:entry colname="col3">0.75</oasis:entry>

         <oasis:entry colname="col4">0.65</oasis:entry>

         <oasis:entry colname="col5">0.60</oasis:entry>

         <oasis:entry colname="col6">0.67</oasis:entry>

         <oasis:entry colname="col7">0.60</oasis:entry>

         <oasis:entry colname="col8">0.66</oasis:entry>

         <oasis:entry colname="col9">0.63</oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col1"/>

         <oasis:entry colname="col2">shrub/grass</oasis:entry>

         <oasis:entry colname="col3">0.67</oasis:entry>

         <oasis:entry colname="col4">0.53</oasis:entry>

         <oasis:entry colname="col5">0.58</oasis:entry>

         <oasis:entry colname="col6">0.57</oasis:entry>

         <oasis:entry colname="col7">0.61</oasis:entry>

         <oasis:entry colname="col8">0.48</oasis:entry>

         <oasis:entry colname="col9">0.48<inline-formula><mml:math id="M300" display="inline"><mml:msup><mml:mi/><mml:mo>∗</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col1"/>

         <oasis:entry colname="col2">croplands</oasis:entry>

         <oasis:entry colname="col3">0.79</oasis:entry>

         <oasis:entry colname="col4">0.67</oasis:entry>

         <oasis:entry colname="col5">0.67<inline-formula><mml:math id="M301" display="inline"><mml:msup><mml:mi/><mml:mo>∗</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>

         <oasis:entry colname="col6">0.71</oasis:entry>

         <oasis:entry colname="col7">0.68</oasis:entry>

         <oasis:entry colname="col8">0.63</oasis:entry>

         <oasis:entry colname="col9">0.62</oasis:entry>

       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table><table-wrap-foot><p id="d1e5279"><inline-formula><mml:math id="M296" display="inline"><mml:msup><mml:mi/><mml:mo>∗</mml:mo></mml:msup></mml:math></inline-formula> The increases from no-DA cases, which led to improved model
performance, are <inline-formula><mml:math id="M297" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.005</mml:mn></mml:mrow></mml:math></inline-formula>.</p></table-wrap-foot></table-wrap>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4" specific-use="star"><?xmltex \currentcnt{4}?><?xmltex \def\figurename{Figure}?><label>Figure 4</label><caption><p id="d1e5604">Period-mean (16–28 August 2016) WRF-Chem calculated <bold>(b–e)</bold> gross primary productivity (GPP) and <bold>(g–j)</bold> evaporative fraction as
well as their responses to the SMAP DA. Results based on the
Noah_D and CLM_D cases are shown in <bold>(b)</bold>, <bold>(d)</bold>, <bold>(g)</bold>, and
<bold>(i)</bold> and <bold>(c)</bold>, <bold>(e)</bold>, <bold>(h)</bold>, and <bold>(j)</bold>, respectively. Period-mean SMAP L4C GPP and FLUXCOM
evaporative fractions are shown in <bold>(a)</bold> and <bold>(f)</bold>, respectively, which are also
used to evaluate the model results (Table 4).</p></caption>
          <?xmltex \igopts{width=483.69685pt}?><graphic xlink:href="https://acp.copernicus.org/articles/22/7461/2022/acp-22-7461-2022-f04.png"/>

        </fig>

</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Modeled fluxes and weather conditions</title>
<sec id="Ch1.S3.SS2.SSS1">
  <label>3.2.1</label><title>Carbon/energy fluxes and weather conditions</title>
      <p id="d1e5666">Figure 4 compares the spatial distributions of the period-mean WRF-Chem
carbon and energy fluxes with SMAP L4C and FLUXCOM products which contain
observation information, and Table 4 summarizes WRF-Chem and
observation-derived flux results by three LULC groups. The
observation-derived products indicate the highest GPP and EF over croplands.
Without the DA, the Noah-MP-related cases outperformed the Noah-related
P1_W case on simulating EF, especially over shrub/grassland
and cropland regions. This indicates that, from Noah to Noah-MP, the
multiple updates in LSM physics related to <inline-formula><mml:math id="M302" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, irrigation, and <inline-formula><mml:math id="M303" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">H</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
are beneficial. Larger GPP and EF values are found in CLM_D
than in Noah_D; most of these larger values match better with
the SMAP L4C and FLUXCOM data. The DA led to increased EF over
shrub/grasslands in all model cases as well as over croplands in the
Noah_D case, bringing the model results closer to the FLUXCOM
data. The EF values were unfavorably reduced by the DA in the
CLM_D and P1_W cases over croplands and in all
model cases over forests, reflecting the challenges of satellite SM DA over
regions with dense vegetation and/or affected by human activities, which
have also been reported and discussed in previous studies (e.g., Huang et
al., 2021). For the Noah_D and CLM_D cases,
this may also be due to the possibly degraded vegetation performance
discussed in Sect. 3.1. The modeled GPP in the CLM_D cases
was lowered by the DA overall, which helped reduce the model–SMAP L4C
discrepancies over forests and croplands. In the Noah_D case,
GPP was improved by the DA over forests and (slightly) over
shrub/grasslands. Based on the evaluation statistics, for this case, the
CLM-type <inline-formula><mml:math id="M304" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> factor scheme is shown to be slightly superior to the Noah type.
Note that the quality of the SMAP L4C and FLUXCOM products may also be
strongly LULC-dependent; e.g., it has been known that the uncertainty of
SMAP L4C data is generally larger for highly productive plant functional
types (Kimball et al., 2021). Such evaluation, therefore, has demonstrated
the critical role of LULC type in understanding the model performance of
carbon and energy fluxes and its responses to satellite SM DA.</p>
      <p id="d1e5698">Additional datasets were also utilized to help understand terrestrial carbon
uptake, including satellite SIF and ACT-America aircraft OCS, as well as its
vertical gradients (Fig. S3). Consistent with the SMAP L4C- and WRF-Chem-based results, the largest SIF values are shown over croplands, especially
maize and soybean fields in Illinois and Indiana, 2–3 times as high as
those over shrub/grasslands in the South Central Plains. All these datasets
suggest moderate to high terrestrial carbon uptake around the Lower
Mississippi croplands and the forests and croplands near the Texas–Oklahoma
border, which is supported by the large OCS drawdowns (i.e., the free
tropospheric-near surface gradients far exceeded 60 pptv) along with other
trace gas measurements taken on board the B-200 and C-130 aircraft.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5" specific-use="star"><?xmltex \currentcnt{5}?><?xmltex \def\figurename{Figure}?><label>Figure 5</label><caption><p id="d1e5703">Period-mean (16–28 August 2016) WRF-Chem calculated
daytime <bold>(a–c)</bold> surface air temperature and <bold>(g–i)</bold> surface radiation as well
as <bold>(d–f, j–l)</bold> their responses to the SMAP DA. Results based on the
Noah_D, CLM_D, and P1_W cases
are shown in <bold>(a)</bold>, <bold>(d)</bold>, <bold>(g)</bold>, and <bold>(j)</bold>, <bold>(b)</bold>, <bold>(e)</bold>, <bold>(h)</bold>, and <bold>(k)</bold>, and <bold>(c)</bold>, <bold>(f)</bold>, <bold>(i)</bold>, and <bold>(l)</bold>, respectively.
Overall, the weather fields from Noah_D and
Noah_W (not shown in figures) cases are nearly the same. Grey
lines in <bold>(a)</bold> indicate the B-200 flight paths over the southeastern US during
the 2016 ACT-America campaign.</p></caption>
            <?xmltex \igopts{width=483.69685pt}?><graphic xlink:href="https://acp.copernicus.org/articles/22/7461/2022/acp-22-7461-2022-f05.png"/>

          </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6"><?xmltex \currentcnt{6}?><?xmltex \def\figurename{Figure}?><label>Figure 6</label><caption><p id="d1e5765">Evaluation of <bold>(a)</bold> air temperature and <bold>(b)</bold> water vapor
mixing ratios from several WRF-Chem simulations with the B-200 aircraft
observations during the 2016 ACT-America campaign. The RMSEs are summarized
in barplots based on model comparisons against observations at all altitudes
and near the surface (i.e., <inline-formula><mml:math id="M305" display="inline"><mml:mrow><mml:mo>≥</mml:mo><mml:mn mathvariant="normal">800</mml:mn></mml:mrow></mml:math></inline-formula> hPa). Colored texts above the
barplots indicate the SMAP DA impacts on RMSEs. The B-200 flight paths are
indicated in Fig. 5a.</p></caption>
            <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://acp.copernicus.org/articles/22/7461/2022/acp-22-7461-2022-f06.png"/>

          </fig>

      <p id="d1e5790">In general, the modeled EF fields as well as their directions of changes due
to the DA resemble those of latent heat flux and relative humidity (RH),
which are opposite to those of sensible heat and surface temperatures (Figs. 5 and S4). The model reproduced the observed spatiotemporal
variability of 2 m air temperature (T2) and RH, as well as FLUXCOM latent
and sensible heat fluxes, well overall. The diagnostic 2 m weather fields and their
responses to the DA strongly correlate with the model's surface-level
results. The Noah-MP-related cases reacted more strongly to the DA than the
Noah-related cases, with the responses in the CLM_D case
larger than in the Noah_D case except for dry, sandy regions,
which can be attributed to combined effects of the <inline-formula><mml:math id="M306" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">H</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and stomatal
resistance schemes used. It is important to note that diagnostic temperature and
humidity variables are represented differently in Noah and Noah-MP and thus
are not directly comparable. Specifically, in Noah, T2 is an explicit
function of surface temperature, air density, specific heat of dry air at
constant pressure, and 2 m surface exchange coefficient for heat, and 2 m
specific humidity is a function of surface specific humidity, upward
moisture flux at the surface, air density, and 2 m surface exchange
coefficient for moisture, whereas in Noah-MP, they are expressed as
functions of temperatures and water vapor for vegetated land and bare soil
being weighted by their respective fractions. We therefore focus on
quantitatively evaluating and intercomparing prognostic model weather
variables (i.e., the model-level air temperature and humidity) against
ACT-America aircraft observations (Fig. 6). For air temperature, at all
altitudes and near the surface (i.e., <inline-formula><mml:math id="M307" display="inline"><mml:mrow><mml:mo>≥</mml:mo><mml:mn mathvariant="normal">800</mml:mn></mml:mrow></mml:math></inline-formula> hPa), the CLM_D case responded most strongly to the DA, and the DA-enabled
CLM_D case outperformed the Noah_D and
P1_W cases. This performance is qualitatively consistent with
the model's sensible heat performance referring to the FLUXCOM data. As for
humidity, despite the most significant DA improvements in CLM_D, the Noah-MP-related cases did not perform as well as the Noah-related
cases, which is also found in the model's latent heat performance in
comparison with the FLUXCOM data. However, note that the model's humidity
performance is more strongly related to that of <inline-formula><mml:math id="M308" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M309" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in the
Noah-MP-based cases via the direct impacts of humidity on <inline-formula><mml:math id="M310" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
calculations (Eq. 2). The solar radiation fields from all model cases, which
play vital roles in controlling the land–atmosphere exchanges of water and
trace gases, do not differ remarkably, and their responses to the DA are
negligible (e.g., Fig. 5g–l). This indicates that the DA impacts on the
modeled surface fluxes resulted primarily from the changes in the modeled
SM, humidity, and canopy and/or surface temperatures, as well as vegetation fields. In
many cases, these primary contributing factors to the DA impacts are
interdependent, and their relative contributions vary by location and time.</p>

<?xmltex \floatpos{p}?><table-wrap id="Ch1.T5" specific-use="star"><?xmltex \currentcnt{5}?><label>Table 5</label><caption><p id="d1e5850">The 24 h and daytime mean O<inline-formula><mml:math id="M311" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
deposition velocity (<inline-formula><mml:math id="M312" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mo>[</mml:mo><mml:mi mathvariant="normal">ozone</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) and flux
(<inline-formula><mml:math id="M313" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi mathvariant="normal">t</mml:mi><mml:mo>[</mml:mo><mml:mi mathvariant="normal">ozone</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) for three LULC groups, from various model cases.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="9">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <oasis:colspec colnum="3" colname="col3" align="right" colsep="1"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right" colsep="1"/>
     <oasis:colspec colnum="6" colname="col6" align="right"/>
     <oasis:colspec colnum="7" colname="col7" align="right" colsep="1"/>
     <oasis:colspec colnum="8" colname="col8" align="right"/>
     <oasis:colspec colnum="9" colname="col9" align="right"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1">LULC type</oasis:entry>
         <oasis:entry rowsep="1" namest="col2" nameend="col3" align="center" colsep="1">Noah_D </oasis:entry>
         <oasis:entry rowsep="1" namest="col4" nameend="col5" align="center" colsep="1">CLM_D </oasis:entry>
         <oasis:entry rowsep="1" namest="col6" nameend="col7" align="center" colsep="1">Noah_W </oasis:entry>
         <oasis:entry rowsep="1" namest="col8" nameend="col9" align="center">P1_W </oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">No DA</oasis:entry>
         <oasis:entry colname="col3">DA</oasis:entry>
         <oasis:entry colname="col4">No DA</oasis:entry>
         <oasis:entry colname="col5">DA</oasis:entry>
         <oasis:entry colname="col6">No DA</oasis:entry>
         <oasis:entry colname="col7">DA</oasis:entry>
         <oasis:entry colname="col8">No DA</oasis:entry>
         <oasis:entry colname="col9">DA</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row rowsep="1">
         <oasis:entry namest="col1" nameend="col9">24 h mean <inline-formula><mml:math id="M314" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mo>[</mml:mo><mml:mi mathvariant="normal">ozone</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> (cm s<inline-formula><mml:math id="M315" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) </oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Forests</oasis:entry>
         <oasis:entry colname="col2">0.64</oasis:entry>
         <oasis:entry colname="col3">0.56</oasis:entry>
         <oasis:entry colname="col4">0.68</oasis:entry>
         <oasis:entry colname="col5">0.51</oasis:entry>
         <oasis:entry colname="col6">0.54</oasis:entry>
         <oasis:entry colname="col7">0.53</oasis:entry>
         <oasis:entry colname="col8">0.49</oasis:entry>
         <oasis:entry colname="col9">0.48</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Shrub/grass</oasis:entry>
         <oasis:entry colname="col2">0.48</oasis:entry>
         <oasis:entry colname="col3">0.45</oasis:entry>
         <oasis:entry colname="col4">0.53</oasis:entry>
         <oasis:entry colname="col5">0.45</oasis:entry>
         <oasis:entry colname="col6">0.47</oasis:entry>
         <oasis:entry colname="col7">0.48</oasis:entry>
         <oasis:entry colname="col8">0.46</oasis:entry>
         <oasis:entry colname="col9">0.46</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Croplands</oasis:entry>
         <oasis:entry colname="col2">0.62</oasis:entry>
         <oasis:entry colname="col3">0.54</oasis:entry>
         <oasis:entry colname="col4">0.67</oasis:entry>
         <oasis:entry colname="col5">0.54</oasis:entry>
         <oasis:entry colname="col6">0.58</oasis:entry>
         <oasis:entry colname="col7">0.58</oasis:entry>
         <oasis:entry colname="col8">0.56</oasis:entry>
         <oasis:entry colname="col9">0.56</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry namest="col1" nameend="col9">24 h mean <inline-formula><mml:math id="M316" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi mathvariant="normal">t</mml:mi><mml:mo>[</mml:mo><mml:mi mathvariant="normal">ozone</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> (nmol m<inline-formula><mml:math id="M317" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math id="M318" display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Forests</oasis:entry>
         <oasis:entry colname="col2">7.11</oasis:entry>
         <oasis:entry colname="col3">6.38</oasis:entry>
         <oasis:entry colname="col4">7.47</oasis:entry>
         <oasis:entry colname="col5">6.35</oasis:entry>
         <oasis:entry colname="col6">6.31</oasis:entry>
         <oasis:entry colname="col7">6.24</oasis:entry>
         <oasis:entry colname="col8">5.75</oasis:entry>
         <oasis:entry colname="col9">5.68</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Shrub/grass</oasis:entry>
         <oasis:entry colname="col2">4.79</oasis:entry>
         <oasis:entry colname="col3">4.48</oasis:entry>
         <oasis:entry colname="col4">5.21</oasis:entry>
         <oasis:entry colname="col5">4.54</oasis:entry>
         <oasis:entry colname="col6">4.76</oasis:entry>
         <oasis:entry colname="col7">4.79</oasis:entry>
         <oasis:entry colname="col8">4.62</oasis:entry>
         <oasis:entry colname="col9">4.63</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Croplands</oasis:entry>
         <oasis:entry colname="col2">6.90</oasis:entry>
         <oasis:entry colname="col3">6.11</oasis:entry>
         <oasis:entry colname="col4">7.39</oasis:entry>
         <oasis:entry colname="col5">6.06</oasis:entry>
         <oasis:entry colname="col6">6.69</oasis:entry>
         <oasis:entry colname="col7">6.64</oasis:entry>
         <oasis:entry colname="col8">6.44</oasis:entry>
         <oasis:entry colname="col9">6.42</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry namest="col1" nameend="col9">Daytime-mean <inline-formula><mml:math id="M319" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mo>[</mml:mo><mml:mi mathvariant="normal">ozone</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> (cm s<inline-formula><mml:math id="M320" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) </oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Forests</oasis:entry>
         <oasis:entry colname="col2">0.94</oasis:entry>
         <oasis:entry colname="col3">0.80</oasis:entry>
         <oasis:entry colname="col4">1.02</oasis:entry>
         <oasis:entry colname="col5">0.71</oasis:entry>
         <oasis:entry colname="col6">0.79</oasis:entry>
         <oasis:entry colname="col7">0.77</oasis:entry>
         <oasis:entry colname="col8">0.70</oasis:entry>
         <oasis:entry colname="col9">0.69</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Shrub/grass</oasis:entry>
         <oasis:entry colname="col2">0.63</oasis:entry>
         <oasis:entry colname="col3">0.56</oasis:entry>
         <oasis:entry colname="col4">0.72</oasis:entry>
         <oasis:entry colname="col5">0.58</oasis:entry>
         <oasis:entry colname="col6">0.61</oasis:entry>
         <oasis:entry colname="col7">0.63</oasis:entry>
         <oasis:entry colname="col8">0.58</oasis:entry>
         <oasis:entry colname="col9">0.58</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Croplands</oasis:entry>
         <oasis:entry colname="col2">0.88</oasis:entry>
         <oasis:entry colname="col3">0.74</oasis:entry>
         <oasis:entry colname="col4">0.99</oasis:entry>
         <oasis:entry colname="col5">0.73</oasis:entry>
         <oasis:entry colname="col6">0.83</oasis:entry>
         <oasis:entry colname="col7">0.83</oasis:entry>
         <oasis:entry colname="col8">0.80</oasis:entry>
         <oasis:entry colname="col9">0.79</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry namest="col1" nameend="col9">Daytime-mean <inline-formula><mml:math id="M321" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi mathvariant="normal">t</mml:mi><mml:mo>[</mml:mo><mml:mi mathvariant="normal">ozone</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> (nmol m<inline-formula><mml:math id="M322" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math id="M323" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) </oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Forests</oasis:entry>
         <oasis:entry colname="col2">11.51</oasis:entry>
         <oasis:entry colname="col3">10.04</oasis:entry>
         <oasis:entry colname="col4">12.25</oasis:entry>
         <oasis:entry colname="col5">8.99</oasis:entry>
         <oasis:entry colname="col6">10.05</oasis:entry>
         <oasis:entry colname="col7">9.93</oasis:entry>
         <oasis:entry colname="col8">9.04</oasis:entry>
         <oasis:entry colname="col9">8.88</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Shrub/grass</oasis:entry>
         <oasis:entry colname="col2">6.91</oasis:entry>
         <oasis:entry colname="col3">6.32</oasis:entry>
         <oasis:entry colname="col4">7.77</oasis:entry>
         <oasis:entry colname="col5">6.43</oasis:entry>
         <oasis:entry colname="col6">6.83</oasis:entry>
         <oasis:entry colname="col7">6.99</oasis:entry>
         <oasis:entry colname="col8">6.52</oasis:entry>
         <oasis:entry colname="col9">6.49</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Croplands</oasis:entry>
         <oasis:entry colname="col2">10.99</oasis:entry>
         <oasis:entry colname="col3">9.42</oasis:entry>
         <oasis:entry colname="col4">12.04</oasis:entry>
         <oasis:entry colname="col5">9.31</oasis:entry>
         <oasis:entry colname="col6">10.61</oasis:entry>
         <oasis:entry colname="col7">10.57</oasis:entry>
         <oasis:entry colname="col8">10.17</oasis:entry>
         <oasis:entry colname="col9">10.07</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <?xmltex \floatpos{p}?><fig id="Ch1.F7" specific-use="star"><?xmltex \currentcnt{7}?><?xmltex \def\figurename{Figure}?><label>Figure 7</label><caption><p id="d1e6523">Period-mean (16–28 August 2016) WRF-Chem <bold>(a–d)</bold> O<inline-formula><mml:math id="M324" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> dry-deposition velocity and <bold>(i–l)</bold> O<inline-formula><mml:math id="M325" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> dry-deposition flux, as well as <bold>(e–h, m–p)</bold> the
impacts of SMAP DA on these model fields. Results are shown for <bold>(a, e, i, m)</bold> Noah_D, <bold>(b, f, j, n)</bold> CLM_D, <bold>(c, g, k, o)</bold> Noah_W, and <bold>(d, h, l, p)</bold> P1_W cases, averaged
throughout the day.</p></caption>
            <?xmltex \igopts{width=483.69685pt}?><graphic xlink:href="https://acp.copernicus.org/articles/22/7461/2022/acp-22-7461-2022-f07.png"/>

          </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F8" specific-use="star"><?xmltex \currentcnt{8}?><?xmltex \def\figurename{Figure}?><label>Figure 8</label><caption><p id="d1e6575">Period-mean (16–28 August 2016) WRF-Chem <bold>(a–h)</bold> stomatal–mesophyll and <bold>(i–p)</bold> cuticular conductances over terrestrial
regions that do not belong to the urban category in Fig. 1a. Results are
shown for <bold>(a, e, i, m)</bold> Noah_D, <bold>(b, f, j, n)</bold> CLM_D, <bold>(c, g, k, o)</bold> Noah_W, and <bold>(d, h, l, p)</bold> P1_W no-DA cases, averaged <bold>(a–d, i–l)</bold> throughout the day
and <bold>(e–h, m–p)</bold> during the daytime.</p></caption>
            <?xmltex \igopts{width=483.69685pt}?><graphic xlink:href="https://acp.copernicus.org/articles/22/7461/2022/acp-22-7461-2022-f08.png"/>

          </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F9" specific-use="star"><?xmltex \currentcnt{9}?><?xmltex \def\figurename{Figure}?><label>Figure 9</label><caption><p id="d1e6611"><bold>(a)</bold> Regression slopes of the relative changes of
O<inline-formula><mml:math id="M326" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> dry-deposition velocity <inline-formula><mml:math id="M327" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
versus the relative changes of column-averaged soil moisture initial
conditions (SM ICs) due to the SMAP DA, summarized by three LULC groups for
all model cases listed in Table 1. The <inline-formula><mml:math id="M328" display="inline"><mml:mi>r</mml:mi></mml:math></inline-formula> values
of these regression analyses and the standard errors of slopes (%, scaled
by 1000) are indicated in <bold>(b)</bold> and <bold>(c)</bold>, respectively. The
<inline-formula><mml:math id="M329" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> values for all regression analyses are
<inline-formula><mml:math id="M330" display="inline"><mml:mrow><mml:mo>≪</mml:mo><mml:mn mathvariant="normal">0.01</mml:mn></mml:mrow></mml:math></inline-formula>. Regression results for the relative changes of
O<inline-formula><mml:math id="M331" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> deposition flux versus the relative changes of SM
ICs are similar (not shown in figures).</p></caption>
            <?xmltex \igopts{width=483.69685pt}?><graphic xlink:href="https://acp.copernicus.org/articles/22/7461/2022/acp-22-7461-2022-f09.png"/>

          </fig>

</sec>
<sec id="Ch1.S3.SS2.SSS2">
  <label>3.2.2</label><title>Ozone dry-deposition velocities and fluxes</title>
      <p id="d1e6690">Figure 7 presents the period-mean, daily-averaged <inline-formula><mml:math id="M332" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and dry-deposition
flux <inline-formula><mml:math id="M333" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (i.e., <inline-formula><mml:math id="M334" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> multiplied by concentration at the surface
level, Wesely, 1989) for O<inline-formula><mml:math id="M335" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> from all model cases, along with their
responses to the SMAP DA. The daytime averages of these fields have similar
spatial gradients but of larger magnitudes (not shown in figures). Table 5
summarizes for three LULC groups the daily- and daytime-averaged results.
The modeled stomatal–mesophyll and cuticular conductances, as well as their
diurnal variability, are indicated in Fig. 8. All model cases produced lower
<inline-formula><mml:math id="M336" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M337" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values over shrub/grasslands than over forests and
croplands, qualitatively consistent with results from many existing model-
and measurement-based studies (e.g., Val Martin et al., 2014; Hardacre et
al., 2015; Silva and Heald, 2018; Lin et al., 2019). The results from
Noah_W and P1_W, both of which are based on
the same scheme (Wesely), are generally similar, with minor differences
largely attributed to different surface temperature fields (Figs. 5 and S4).
The WRF-Chem-modeled <inline-formula><mml:math id="M338" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M339" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> fluxes were more strongly affected
by the upgrade from the Wesely to the dynamic scheme; i.e., with the updated
scheme, they show enhanced magnitudes, stronger spatial variability, and more intensive responses to the DA, especially over forests and
croplands. These results can be mainly explained by the fact that the
stomatal–mesophyll and cuticular resistances in the dynamic scheme are
sensitive to more environmental and biophysical variables, accounting for
both the direct and indirect (i.e., via influencing the weather fields and
plants' physiology) effects of SM on <inline-formula><mml:math id="M340" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. <inline-formula><mml:math id="M341" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> from the
Noah_D and CLM_D cases, as well as its major
term stomatal–mesophyll conductance, shows strong correlations with the
modeled GPP, latent heat, and EF fields, which have been discussed in earlier
sections. Comparing the cases that implemented the CLM- and Noah-type <inline-formula><mml:math id="M342" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> schemes, O<inline-formula><mml:math id="M343" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>-related fluxes resulting from the former configuration
are of notably larger magnitude, spatial variability, and absolute changes
due to the DA. The SM impacts on the modeled <inline-formula><mml:math id="M344" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M345" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> were
further quantified using linear regression analyses between the relative
changes in the modeled O<inline-formula><mml:math id="M346" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> fluxes due to the DA versus those in
column-averaged SM initial conditions. All regression models yielded low <inline-formula><mml:math id="M347" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> values (i.e., <inline-formula><mml:math id="M348" display="inline"><mml:mrow><mml:mo>≪</mml:mo><mml:mn mathvariant="normal">0.01</mml:mn></mml:mrow></mml:math></inline-formula>), suggesting good <inline-formula><mml:math id="M349" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>–<inline-formula><mml:math id="M350" display="inline"><mml:mi mathvariant="normal">Δ</mml:mi></mml:math></inline-formula>SM and <inline-formula><mml:math id="M351" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>–<inline-formula><mml:math id="M352" display="inline"><mml:mi mathvariant="normal">Δ</mml:mi></mml:math></inline-formula>SM relationships. The regression slopes, all with standard errors
of <inline-formula><mml:math id="M353" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.01</mml:mn></mml:mrow></mml:math></inline-formula> %, are summarized in barplots (Fig. 9) by three LULC
groups for all model cases in Table 1. For all LULC groups, the slopes based
on the two cases that implemented the dynamic scheme are 2–3 times larger
than those from the two cases using the Wesely scheme, and the slopes differ
most strongly among the cases over forests and croplands. The low <inline-formula><mml:math id="M354" display="inline"><mml:mi>r</mml:mi></mml:math></inline-formula> values
(<inline-formula><mml:math id="M355" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.5</mml:mn></mml:mrow></mml:math></inline-formula>) associated with several regression models reflect the
stronger nonlinear relationships between the changes in the studied O<inline-formula><mml:math id="M356" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
fluxes and SM. These results emphasize the importance of better
understanding and representing in models the SM control on plants' stomatal
behaviors which regulate the land–atmosphere exchanges of water, energy, and
trace gases. The earlier evaluation of the period-mean GPP and EF across the
domain has demonstrated some advantages of using the CLM-type <inline-formula><mml:math id="M357" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula>
scheme and that the DA more effectively improved the model performance in
sparsely vegetated shrub/grassland regions. These conclusions are likely
also applicable to the modeled O<inline-formula><mml:math id="M358" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> dry-deposition process, particularly
its stomatal–mesophyll pathway.</p>
      <p id="d1e6961">In all no-DA and DA cases, the diurnal variability of O<inline-formula><mml:math id="M359" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>-related
surface fluxes shows clear LULC dependency. Over the shrub/grassland
and forests/croplands regions, the daytime-averaged <inline-formula><mml:math id="M360" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values
are 24 %–31 % and 35 %–50 % higher than the 24 h mean, respectively, while
the daytime-averaged <inline-formula><mml:math id="M361" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> results are 40 %–50 % and 42 %–63 % higher
than the 24 h mean, respectively (Table 5). Such <inline-formula><mml:math id="M362" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> diurnal cycles are
a result of the strongest diurnal variability in stomatal–mesophyll
conductance (i.e., its daytime mean values are approximately twice as high
as the 24 h mean for all LULC types) being balanced out by weak diurnal
variability associated with other <inline-formula><mml:math id="M363" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> terms. As the most diurnally
variable <inline-formula><mml:math id="M364" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> component, stomatal–mesophyll conductance, on average,
contributes less substantially to <inline-formula><mml:math id="M365" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> for shrub/grassland areas (24 h/daytime: up to <inline-formula><mml:math id="M366" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">30</mml:mn></mml:mrow></mml:math></inline-formula> %/40 %) than for forests/croplands
(24 h/daytime: up to <inline-formula><mml:math id="M367" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula> %/66 %), which helps explain the
weaker diurnal variability in the modeled <inline-formula><mml:math id="M368" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> over shrub/grasslands. The
stronger diurnal cycles in <inline-formula><mml:math id="M369" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> than in <inline-formula><mml:math id="M370" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> reflect the impacts of
higher daytime O<inline-formula><mml:math id="M371" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> surface concentrations used in the <inline-formula><mml:math id="M372" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
calculations. The DA did not dominantly intensify or dampen the diurnal
cycles of these fluxes for any given grouped LULC type. Whether the DA
improved the estimated diurnal cycles of fluxes for various LULC types
remains to be evaluated, which can benefit from independent
observation-constrained flux products of broad spatial coverage and subdaily
variability.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T6" specific-use="star"><?xmltex \currentcnt{6}?><label>Table 6</label><caption><p id="d1e7117">Period-mean (16–28 August 2016) soil moisture and surface
fluxes at two CASTNET sites shown in Fig. 1d. Standard deviations calculated
based on the hourly O<inline-formula><mml:math id="M373" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> dry-deposition velocity
<inline-formula><mml:math id="M374" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mo>[</mml:mo><mml:mi mathvariant="normal">ozone</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and flux <inline-formula><mml:math id="M375" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi mathvariant="normal">t</mml:mi><mml:mo>[</mml:mo><mml:mi mathvariant="normal">ozone</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>
results are also included. Daytime is defined as approximately
08:00–19:00 local standard time.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="5">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <oasis:colspec colnum="3" colname="col3" align="right" colsep="1"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1">CASTNET sites (soil type; LULC type; elevation/terrain)</oasis:entry>
         <oasis:entry namest="col2" nameend="col3" align="center" colsep="1">SUM156, Florida </oasis:entry>
         <oasis:entry namest="col4" nameend="col5" align="center">PED108, Virginia </oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry namest="col2" nameend="col3" align="center" colsep="1">(sand; forest; 16 m/flat) </oasis:entry>
         <oasis:entry namest="col4" nameend="col5" align="center">(loam; forest; 149 m/rolling) </oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Modeled soil moisture initial condition, column-averaged (m<inline-formula><mml:math id="M376" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> m<inline-formula><mml:math id="M377" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">No DA</oasis:entry>
         <oasis:entry colname="col3">DA</oasis:entry>
         <oasis:entry colname="col4">No DA</oasis:entry>
         <oasis:entry colname="col5">DA</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Noah_D</oasis:entry>
         <oasis:entry colname="col2">0.15</oasis:entry>
         <oasis:entry colname="col3">0.12</oasis:entry>
         <oasis:entry colname="col4">0.22</oasis:entry>
         <oasis:entry colname="col5">0.20</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">CLM_D</oasis:entry>
         <oasis:entry colname="col2">0.16</oasis:entry>
         <oasis:entry colname="col3">0.12</oasis:entry>
         <oasis:entry colname="col4">0.20</oasis:entry>
         <oasis:entry colname="col5">0.18</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">SMAP L4C daily gross primary productivity (g m<inline-formula><mml:math id="M378" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> d<inline-formula><mml:math id="M379" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry namest="col2" nameend="col3" align="center" colsep="1">7.30 </oasis:entry>
         <oasis:entry namest="col4" nameend="col5" align="center">8.10 </oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Modeled daily gross primary productivity (g m<inline-formula><mml:math id="M380" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> d<inline-formula><mml:math id="M381" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">No DA</oasis:entry>
         <oasis:entry colname="col3">DA</oasis:entry>
         <oasis:entry colname="col4">No DA</oasis:entry>
         <oasis:entry colname="col5">DA</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Noah_D</oasis:entry>
         <oasis:entry colname="col2">4.70</oasis:entry>
         <oasis:entry colname="col3">3.83</oasis:entry>
         <oasis:entry colname="col4">7.42</oasis:entry>
         <oasis:entry colname="col5">5.45</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">CLM_D</oasis:entry>
         <oasis:entry colname="col2">5.84</oasis:entry>
         <oasis:entry colname="col3">5.88</oasis:entry>
         <oasis:entry colname="col4">10.10</oasis:entry>
         <oasis:entry colname="col5">4.51</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">CASTNET (MLM-calculated) daytime <inline-formula><mml:math id="M382" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mo>[</mml:mo><mml:mi mathvariant="normal">ozone</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> (cm s<inline-formula><mml:math id="M383" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry namest="col2" nameend="col3" align="center" colsep="1"><inline-formula><mml:math id="M384" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.39</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.15</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry namest="col4" nameend="col5" align="center"><inline-formula><mml:math id="M385" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.39</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.18</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Modeled daytime <inline-formula><mml:math id="M386" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mo>[</mml:mo><mml:mi mathvariant="normal">ozone</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> (cm s<inline-formula><mml:math id="M387" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">No DA</oasis:entry>
         <oasis:entry colname="col3">DA</oasis:entry>
         <oasis:entry colname="col4">No DA</oasis:entry>
         <oasis:entry colname="col5">DA</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Noah_D</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M388" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.68</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.13</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M389" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.64</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.11</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M390" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.84</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.23</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M391" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.65</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.14</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">CLM_D</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M392" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.73</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.13</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M393" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.74</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.14</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M394" display="inline"><mml:mrow><mml:mn mathvariant="normal">1.01</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.29</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M395" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.50</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.09</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Noah_W</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M396" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.63</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.11</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M397" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.61</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.10</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M398" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.78</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.22</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M399" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.75</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.22</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">CASTNET daytime <inline-formula><mml:math id="M400" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi mathvariant="normal">t</mml:mi><mml:mo>[</mml:mo><mml:mi mathvariant="normal">ozone</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> (nmol m<inline-formula><mml:math id="M401" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math id="M402" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry namest="col2" nameend="col3" align="center" colsep="1"><inline-formula><mml:math id="M403" display="inline"><mml:mrow><mml:mn mathvariant="normal">3.81</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">2.02</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry namest="col4" nameend="col5" align="center"><inline-formula><mml:math id="M404" display="inline"><mml:mrow><mml:mn mathvariant="normal">5.02</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">2.83</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Modeled daytime <inline-formula><mml:math id="M405" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi mathvariant="normal">t</mml:mi><mml:mo>[</mml:mo><mml:mi mathvariant="normal">ozone</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> (nmol m<inline-formula><mml:math id="M406" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math id="M407" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">No DA</oasis:entry>
         <oasis:entry colname="col3">DA</oasis:entry>
         <oasis:entry colname="col4">No DA</oasis:entry>
         <oasis:entry colname="col5">DA</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Noah_D</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M408" display="inline"><mml:mrow><mml:mn mathvariant="normal">7.23</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1.71</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M409" display="inline"><mml:mrow><mml:mn mathvariant="normal">6.91</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1.56</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M410" display="inline"><mml:mrow><mml:mn mathvariant="normal">12.21</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">3.88</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M411" display="inline"><mml:mrow><mml:mn mathvariant="normal">9.67</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">2.45</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">CLM_D</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M412" display="inline"><mml:mrow><mml:mn mathvariant="normal">7.60</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1.74</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M413" display="inline"><mml:mrow><mml:mn mathvariant="normal">7.63</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1.84</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M414" display="inline"><mml:mrow><mml:mn mathvariant="normal">14.27</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">5.01</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M415" display="inline"><mml:mrow><mml:mn mathvariant="normal">7.67</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1.88</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Noah_W</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M416" display="inline"><mml:mrow><mml:mn mathvariant="normal">6.81</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1.56</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M417" display="inline"><mml:mrow><mml:mn mathvariant="normal">6.64</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1.45</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M418" display="inline"><mml:mrow><mml:mn mathvariant="normal">11.74</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">3.74</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M419" display="inline"><mml:mrow><mml:mn mathvariant="normal">11.18</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">3.56</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <?xmltex \floatpos{t}?><fig id="Ch1.F10" specific-use="star"><?xmltex \currentcnt{10}?><?xmltex \def\figurename{Figure}?><label>Figure 10</label><caption><p id="d1e7996">Period-mean (16–28 August 2016) diurnal cycles of <bold>(a, b)</bold> O<inline-formula><mml:math id="M420" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> dry-deposition velocity <inline-formula><mml:math id="M421" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
and <bold>(e, f)</bold> O<inline-formula><mml:math id="M422" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> dry-deposition flux
<inline-formula><mml:math id="M423" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> based on the CASTNET dataset (shown by solid black
lines) and their WRF-Chem counterparts (purple, blue, and brown lines) at
the <bold>(a, c, e, g)</bold> SUM156 and <bold>(b, d, f, h)</bold> PED108 sites, whose locations are
shown in Fig. 1d. Panels <bold>(c)</bold> and <bold>(d)</bold> and <bold>(g)</bold> and <bold>(h)</bold> indicate the diurnal variability of
WRF-Chem stomatal–mesophyll conductance <inline-formula><mml:math id="M424" display="inline"><mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mi mathvariant="normal">sm</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and
column-averaged soil moisture (normalized) at these two sites, respectively.
The grey vertical lines in <bold>(g)</bold> and <bold>(h)</bold> denote the initial times of WRF-Chem.
WRF-Chem results from the no-DA and DA cases are indicated by solid and
dashed lines, respectively. Additional time series plots indicating the
daily variability of these fluxes are shown in Fig. S5.</p></caption>
            <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://acp.copernicus.org/articles/22/7461/2022/acp-22-7461-2022-f10.png"/>

          </fig>

      <p id="d1e8088">A detailed analysis was then conducted at two forest CASTNET sites with
different soil types and hydrological regimes. The modeled <inline-formula><mml:math id="M425" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and
<inline-formula><mml:math id="M426" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> from various cases are compared with the operational MLM-based
calculations produced at a Florida site SUM156 and a Virginia site PED108
(Figs. 10a, b, e, f and S5; Table 6), where many, most, or all MLM assumptions
apply. The dominant soil types at these sites are sand and loam, and the
column-averaged SM values from various model cases are approximately 0.15
and 0.20 m<inline-formula><mml:math id="M427" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> m<inline-formula><mml:math id="M428" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, respectively. These various datasets show that
stomatal–mesophyll conductance, <inline-formula><mml:math id="M429" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M430" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> sharply increase soon
after sunrise, reaching their daily maxima in the late morning or early
afternoon. The slight declines in fluxes around midday based on some
simulations can result from the water and heat stresses which cause stomata
closures (Fig. 10c and d). The water stress starts to get relieved from the
mid-afternoon at the SUM156 site under the influences of convective
precipitation, whereas it persists throughout the afternoon at the PED108 site
(Fig. 10g and h). This helps shape the slightly different afternoon flux
dynamics at these two locations. Without the DA, at both sites, the highest
daytime fluxes were produced from the CLM_D case, followed by
the Noah_D and Noah_W cases, which are 2–3 times as high as the MLM-estimated cases. The fluxes from all WRF-Chem cases
during the nighttime are close, up to <inline-formula><mml:math id="M431" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">80</mml:mn></mml:mrow></mml:math></inline-formula> % lower than their
daytime maxima, contributed mostly by <inline-formula><mml:math id="M432" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M433" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, and non-stomatal
<inline-formula><mml:math id="M434" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> pathways as stomatal–mesophyll conductance is shown to be negligible
(Fig. 10c and d). Despite the uncertainty possibly introduced by the
limitations of the Monin–Obukhov similarity theory, our nighttime <inline-formula><mml:math id="M435" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
results are close to flux observations at European forest sites during both
dry and wet periods in the past decades (Lin et al., 2020). They are,
however, dramatically higher than the MLM-based results that are nearly
zero. Wu et al. (2018) compared <inline-formula><mml:math id="M436" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> observations with single-point model
calculations based on the operational MLM, Wesely, and Noah-Gas Exchange
Model photosynthesis-based scheme, at a Canadian mixed forest site dominated
by sand-like soil. Their diverse model results are qualitatively consistent
with our findings at the SUM156 and PED108 sites. The remarkably lower
<inline-formula><mml:math id="M437" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values from the operational MLM calculations can be partially
attributed to the MLM's simplified approaches of calculating <inline-formula><mml:math id="M438" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M439" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
using wind speed and direction, as well as the empirical approach of
calculating <inline-formula><mml:math id="M440" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> which is subject to errors in the season- and
LULC-dependent <inline-formula><mml:math id="M441" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. The possible uncertainty in MLM <inline-formula><mml:math id="M442" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> can also be
explained by the lack of continuous, accurate model input data.
Specifically, the factual data such as plant and canopy attributes used in
the MLM calculations are outdated, which, according to the CASTNET database,
represent the conditions in the 2000s; and based on the little day-by-day
variability found in the MLM <inline-formula><mml:math id="M443" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> data during the study period which
contrasts with our WRF-Chem results (Fig. S5), it is likely that many but
not all of these are filled historical average <inline-formula><mml:math id="M444" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values due to the
lack of meteorological measurements that are needed in the MLM calculation.
Additionally, based on the surface heterogeneity within the WRF-Chem grids
that these sites fall in, representation errors are estimated to be
pronounced when comparing the point-scale MLM fluxes with our 12 km WRF-Chem
results.</p>
      <p id="d1e8312">Within the respective ranges of the modeled SM at these two sites, <inline-formula><mml:math id="M445" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula>
factors based on the CLM-type scheme are both larger than those based on the
Noah-type <inline-formula><mml:math id="M446" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> scheme (referring to Niu et al., 2011, Fig. 3), which helps
explain the higher and more variable model fluxes from the
CLM_D case than the Noah_D case without the
DA. At SUM156, despite the strongest SM decrease (<inline-formula><mml:math id="M447" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">0.04</mml:mn></mml:mrow></mml:math></inline-formula> m<inline-formula><mml:math id="M448" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> m<inline-formula><mml:math id="M449" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) by the DA in case CLM_D, the modeled fluxes
responded least strongly to the DA, in part due to the flattened CLM-type
SM–<inline-formula><mml:math id="M450" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> curves in contrast to the linear Noah-type SM–<inline-formula><mml:math id="M451" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula>
function for sand within the 0.12–0.16 m<inline-formula><mml:math id="M452" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> m<inline-formula><mml:math id="M453" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> SM range. At
PED108, the modeled SM values from all model cases were lowered by the DA by
<inline-formula><mml:math id="M454" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">0.02</mml:mn></mml:mrow></mml:math></inline-formula> m<inline-formula><mml:math id="M455" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> m<inline-formula><mml:math id="M456" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. The stronger reactions of fluxes
(i.e., <inline-formula><mml:math id="M457" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M458" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, and their stomatal–mesophyll portions) to the DA
from the CLM_D case than those from the Noah_D
case can be partially explained by the steep CLM-type SM–<inline-formula><mml:math id="M459" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> curve
versus the linear Noah-type SM–<inline-formula><mml:math id="M460" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> relationship for loam within the
0.18–0.22 m<inline-formula><mml:math id="M461" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> m<inline-formula><mml:math id="M462" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> SM range. Our case studies at these two sites
with the same type of LULC emphasize the importance of soil type and
hydrological regimes for understanding SM controls on dry deposition, which
was often omitted or discussed little in previous dry-deposition studies. It
is noted that the effectiveness of SM DA in improving the accuracy of land
surface states and fluxes at point scale is dependent on the
representativeness of the assimilated satellite SM data for these sites,
which is expected to increase with the resolutions of the model and the
assimilated satellite land product.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F11" specific-use="star"><?xmltex \currentcnt{11}?><?xmltex \def\figurename{Figure}?><label>Figure 11</label><caption><p id="d1e8488">Period-mean (16–28 August 2016) WRF-Chem <bold>(a–d)</bold> surface
MDA8 O<inline-formula><mml:math id="M463" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> fields and <bold>(e–h)</bold> their responses to the SMAP
DA. Results based on the Noah_D, CLM_D,
Noah_W, and P1_W cases are shown in <bold>(a)</bold> and <bold>(e)</bold>,
<bold>(b)</bold> and <bold>(f)</bold>, <bold>(c)</bold> and <bold>(g)</bold>, and <bold>(d)</bold> and <bold>(h)</bold>, respectively, and the differences between the
Noah-MP-related cases and the P1_W case are shown in <bold>(i)</bold>–<bold>(k)</bold>.</p></caption>
            <?xmltex \igopts{width=483.69685pt}?><graphic xlink:href="https://acp.copernicus.org/articles/22/7461/2022/acp-22-7461-2022-f11.png"/>

          </fig>

</sec>
</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><?xmltex \opttitle{Policy-relevant O${}_{{3}}$ metrics and implications for O${}_{{3}}$ impact
assessments}?><title>Policy-relevant O<inline-formula><mml:math id="M464" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> metrics and implications for O<inline-formula><mml:math id="M465" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> impact
assessments</title>
<sec id="Ch1.S3.SS3.SSS1">
  <label>3.3.1</label><?xmltex \opttitle{MDA8 and implications for O${}_{{3}}$ health impacts}?><title>MDA8 and implications for O<inline-formula><mml:math id="M466" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> health impacts</title>
      <p id="d1e8589">Figure 11 illustrates the impacts of the choice of dry-deposition scheme and
SM DA on WRF-Chem-modeled surface MDA8 O<inline-formula><mml:math id="M467" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>. During the study period,
several warmer- and drier-than-normal Atlantic states experienced high MDA8
at times (i.e., <inline-formula><mml:math id="M468" display="inline"><mml:mrow><mml:mo>≥</mml:mo><mml:mn mathvariant="normal">60</mml:mn></mml:mrow></mml:math></inline-formula> ppbv, which can negatively affect lung function
and, at <inline-formula><mml:math id="M469" display="inline"><mml:mrow><mml:mo>≥</mml:mo><mml:mn mathvariant="normal">70</mml:mn></mml:mrow></mml:math></inline-formula> ppbv, cause respiratory symptoms and other adverse effects;
Fleming et al., 2018, and references therein). Numerous populated urban
centers reside in these areas. The levels of MDA8 are shown to be much lower
(i.e., <inline-formula><mml:math id="M470" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">40</mml:mn></mml:mrow></mml:math></inline-formula> ppbv) over the southern part of the domain, including
several major urban/suburban regions such as the Texas Triangle, which was
frequently influenced by passing cold fronts and tropical systems from the
Gulf of Mexico.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F12" specific-use="star"><?xmltex \currentcnt{12}?><?xmltex \def\figurename{Figure}?><label>Figure 12</label><caption><p id="d1e8633"><bold>(a)</bold> Period-mean (16–28 August 2016) observed surface
MDA8 O<inline-formula><mml:math id="M471" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> and <bold>(c)</bold> AOT40 in cropland-dominant model
grids derived from surface observations during 16–28 August 2016. The RMSEs
of modeled MDA8 and model-derived AOT40 from various WRF-Chem cases
referring to <bold>(a)</bold> and <bold>(c)</bold> are summarized in <bold>(b)</bold> and <bold>(d)</bold>, respectively.</p></caption>
            <?xmltex \igopts{width=483.69685pt}?><graphic xlink:href="https://acp.copernicus.org/articles/22/7461/2022/acp-22-7461-2022-f12.png"/>

          </fig>

      <p id="d1e8669">All model cases reproduced the observed MDA8 spatial patterns (Fig. 12a)
moderately well. Referring to observations at AQS and CASTNET sites, their
domain-wide mean root-mean-square errors (RMSEs) all fall within 6–8.5 ppbv (Fig. 12b). We first
intercompare the MDA8 levels from all no-DA cases. Positive and negative
differences between the results from Noah_W and
P1_W, both of which implemented the Wesely scheme, are almost
equally distributed across the domain, with the MDA8 from the former case
associated with negligibly lower RMSEs (i.e., <inline-formula><mml:math id="M472" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.02</mml:mn></mml:mrow></mml:math></inline-formula> ppbv on
average) referring to AQS and CASTNET observations (Figs. 11k and 12b). The
differences between these two cases are largely due to the impact of the
chosen LSM on the model's meteorological fields, particularly temperatures,
which affected the simulations of various O<inline-formula><mml:math id="M473" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>-related processes
including dry deposition. As Figs. 11i and j and 12b show, replacing Wesely
with the dynamic dry-deposition scheme considerably lowered the calculated
MDA8 levels in majority of the model grids, as well as their associated
RMSEs (i.e., by <inline-formula><mml:math id="M474" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0.5</mml:mn></mml:mrow></mml:math></inline-formula> ppbv on average) relative to surface
observations. These reductions in MDA8 are of comparable magnitude with
those due to updating anthropogenic emissions from the National Emission
Inventory 2014 to 2016 beta (Huang et al., 2021). Comparing the
implementations of the CLM- and Noah-type <inline-formula><mml:math id="M475" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> schemes, the former led
to stronger reductions in the modeled MDA8 fields and their associated
uncertainty. These results reflect the impacts of the faster O<inline-formula><mml:math id="M476" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> removal
via dry deposition in the dynamic-scheme-related cases, as well as the
different model meteorology. Our findings are qualitatively consistent with
the conclusions from several global-scale modeling experiments that compared
the Wesely and dynamic schemes (e.g., Val Martin et al., 2014; Lin et al.,
2019).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F13" specific-use="star"><?xmltex \currentcnt{13}?><?xmltex \def\figurename{Figure}?><label>Figure 13</label><caption><p id="d1e8720">Box-and-whisker plots of WRF-Chem <bold>(a)</bold> MDA8
O<inline-formula><mml:math id="M477" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>, <bold>(b)</bold> daytime stomatal O<inline-formula><mml:math id="M478" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
uptake <inline-formula><mml:math id="M479" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi mathvariant="normal">s</mml:mi><mml:mo>[</mml:mo><mml:mi mathvariant="normal">ozone</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, <bold>(c)</bold> derived
POD<inline-formula><mml:math id="M480" display="inline"><mml:msub><mml:mi/><mml:mi>y</mml:mi></mml:msub></mml:math></inline-formula>, and <bold>(d)</bold> derived AOT40, summarized by LULC and
crop types from all DA-enabled cases. The impacts of the SMAP DA on these
model fields are shown in <bold>(e)</bold>–<bold>(h)</bold>. Red filled circles indicate the mean
values. The mean relative biomass/crop yield losses estimated based on all
DA-enabled cases, as well as the SMAP DA impacts on these values, are
included in <bold>(c)</bold>, <bold>(d)</bold>, <bold>(g)</bold>, and <bold>(h)</bold> in blue text. The crop yield losses for wheat,
estimated based on the derived AOT40 and two dose–response functions (M07:
Mills et al., 2007; M18: Mills et al., 2018b), are included in <bold>(d)</bold> and <bold>(h)</bold>.</p></caption>
            <?xmltex \igopts{width=483.69685pt}?><graphic xlink:href="https://acp.copernicus.org/articles/22/7461/2022/acp-22-7461-2022-f13.png"/>

          </fig>

      <p id="d1e8812">In all model cases, the DA reduced surface and subsurface SM in many of the
grids, leading to enhanced MDA8 (Fig. 11e–h). The responses of the
period-mean MDA8 to the DA from the Noah_W and
P1_W cases are mostly within <inline-formula><mml:math id="M481" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:math></inline-formula> ppbv. When the dynamic
dry-deposition scheme was applied, the modeled MDA8 responded several times
more strongly to the DA (i.e., by up to 6 and 8 ppbv in the
Noah_D and CLM_D cases, respectively),
especially over nonurban regions, where surface MDA8 is on average several
parts per billion by volume (ppbv) lower than in urban grids. In urban grids where population densities
are <inline-formula><mml:math id="M482" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">25</mml:mn></mml:mrow></mml:math></inline-formula> times higher than in nonurban grids (Fig. 1c), the DA
impacts on MDA8 reach 3–4 ppbv in places, under the controls of the
local-to-regional circulation patterns (Fig. 13a and e). As the no-DA cases are
positively biased against surface observations in many places, corresponding
to the DA-induced surface O<inline-formula><mml:math id="M483" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> changes, the overall model performance of
MDA8 was not improved, or much degraded, by the DA. Over limited areas such
as the South Central Plains, the modeled MDA8 decreased due to the DA by up
to <inline-formula><mml:math id="M484" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> ppbv, corresponding to improved performance. The no-DA and
DA results based on different LSMs and dry-deposition schemes confirm that
drier soil conditions exacerbate O<inline-formula><mml:math id="M485" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> air pollution, which, together with
heat stress, threatens human health. Such O<inline-formula><mml:math id="M486" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>–SM relationships have
also been demonstrated by Falk and Søvde Haslerud (2019) and Anav et al. (2018) using other chemical transport models and multiplicative dry-deposition schemes. Our Noah_W- and P1_W-related results indicate the influences of SM on air quality via its
feedbacks to weather; and results from the Noah_D and
CLM_D cases provide valuable information regarding both the
indirect (i.e., via adjusting vegetation phenology and weather conditions)
and direct SM effects on O<inline-formula><mml:math id="M487" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>. The complex SM impacts on O<inline-formula><mml:math id="M488" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> dry-deposition as well as surface O<inline-formula><mml:math id="M489" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> concentrations based on the coupled
photosynthesis–<inline-formula><mml:math id="M490" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> calculations rely heavily on the application of
water stress function (<inline-formula><mml:math id="M491" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> scheme), soil properties, and hydrological
regime. The WRF-Chem results from this case indicate that, to more
accurately simulate MDA8, improving land DA must be combined with strong
efforts to identify other sources of uncertainty in O<inline-formula><mml:math id="M492" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> modeling (e.g.,
emissions, chemistry, and extra-regional pollution contributions) and reduce
their negative impacts on model performance.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F14" specific-use="star"><?xmltex \currentcnt{14}?><?xmltex \def\figurename{Figure}?><label>Figure 14</label><caption><p id="d1e8930">Period-mean (16–28 August 2016) WRF-Chem <bold>(a–d)</bold> daytime
stomatal O<inline-formula><mml:math id="M493" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> uptake <inline-formula><mml:math id="M494" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi mathvariant="normal">s</mml:mi><mml:mo>[</mml:mo><mml:mi mathvariant="normal">ozone</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> fields over terrestrial regions that do not belong to the urban
category in Fig. 1a and <bold>(e–h)</bold> their responses to the SMAP DA. Results based
on the <bold>(a, e)</bold> Noah_D, <bold>(b, f)</bold> CLM_D, <bold>(c, g)</bold> Noah_W, and <bold>(d, h)</bold> P1_W cases are shown.</p></caption>
            <?xmltex \igopts{width=483.69685pt}?><graphic xlink:href="https://acp.copernicus.org/articles/22/7461/2022/acp-22-7461-2022-f14.png"/>

          </fig>

</sec>
<sec id="Ch1.S3.SS3.SSS2">
  <label>3.3.2</label><?xmltex \opttitle{Implications for O${}_{{3}}$ vegetation impact assessments using
concentration- and flux-based metrics}?><title>Implications for O<inline-formula><mml:math id="M495" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> vegetation impact assessments using
concentration- and flux-based metrics</title>
      <p id="d1e9003">Both O<inline-formula><mml:math id="M496" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> flux- and concentration-based metrics have been applied to
assess O<inline-formula><mml:math id="M497" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> impacts on vegetation as well as the associated economic
loss. Estimating the plants' stomatal O<inline-formula><mml:math id="M498" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> uptake <inline-formula><mml:math id="M499" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the basis
for constructing flux-based O<inline-formula><mml:math id="M500" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> impact assessments. Figure 14
illustrates the period-mean daytime <inline-formula><mml:math id="M501" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> fields based on all WRF-Chem
no-DA cases as well as their responses to the SM DA. Box-and-whisker plots
in Fig. 13b and f summarize these results by three LULC groups. The averaged
<inline-formula><mml:math id="M502" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values for all three LULC groups exceed their respective critical
levels (i.e., 1 nmol m<inline-formula><mml:math id="M503" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math id="M504" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> for forest and grasslands and 3 nmol m<inline-formula><mml:math id="M505" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math id="M506" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> for crops). As a major contributor to O<inline-formula><mml:math id="M507" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> dry-deposition flux during the daytime, <inline-formula><mml:math id="M508" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> fields appear to be closely
correlated in space and time with the surface humidity and flux fields
(e.g., GPP, latent heat, and EF, as well as <inline-formula><mml:math id="M509" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), which differ distinctly
from the surface O<inline-formula><mml:math id="M510" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> concentration fields. For example, <inline-formula><mml:math id="M511" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> hotspots
are shown over some low O<inline-formula><mml:math id="M512" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> concentration areas including the humid,
Lower Mississippi River regions, and the lowest <inline-formula><mml:math id="M513" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values occur in
certain high O<inline-formula><mml:math id="M514" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> concentration regions strongly affected by urban
pollution (e.g., Georgia) and pollution transport from upwind US states
and/or the stratosphere (e.g., western Kansas and Oklahoma, as discussed in
Huang et al., 2021). The changes in <inline-formula><mml:math id="M515" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and surface O<inline-formula><mml:math id="M516" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
concentrations due to the DA show opposite directions; i.e., drier soil
enhances surface O<inline-formula><mml:math id="M517" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> concentrations, whereas it slows down the plants'
stomatal O<inline-formula><mml:math id="M518" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> uptake (Figs. 11e–h and 14e–h). This comparison
highlights how the choice of O<inline-formula><mml:math id="M519" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> metrics can affect the assessment of
O<inline-formula><mml:math id="M520" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> vegetation impacts under the changing climate. As emphasized by
Mills et al. (2018b) and Ronan et al. (2020), flux-based metrics have
evident advantages over concentration-based metrics. To conduct reliable
impact assessments using these flux-based metrics, accurate information on
stomatal and non-stomatal fluxes as well as the various environmental and
biophysical variables that they are sensitive to becomes increasingly
important.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F15" specific-use="star"><?xmltex \currentcnt{15}?><?xmltex \def\figurename{Figure}?><label>Figure 15</label><caption><p id="d1e9265">WRF-Chem-based AOT40, derived from the modeled surface
O<inline-formula><mml:math id="M521" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> fields during 16–28 August 2016, as well as their
responses to the SMAP DA. Panels <bold>(a)</bold> and <bold>(e)</bold>, <bold>(b)</bold> and <bold>(f)</bold>, <bold>(c)</bold> and <bold>(g)</bold>, and <bold>(d)</bold> and <bold>(h)</bold> show results
derived from the Noah_D, CLM_D,
Noah_W, and P1_W cases, respectively, in
cropland-dominant model grids.</p></caption>
            <?xmltex \igopts{width=483.69685pt}?><graphic xlink:href="https://acp.copernicus.org/articles/22/7461/2022/acp-22-7461-2022-f15.png"/>

          </fig>

      <p id="d1e9308">An assessment of O<inline-formula><mml:math id="M522" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> vegetation impacts was conducted based on the
results from various model cases and different metrics, namely POD<inline-formula><mml:math id="M523" display="inline"><mml:msub><mml:mi/><mml:mi>y</mml:mi></mml:msub></mml:math></inline-formula>
(where <inline-formula><mml:math id="M524" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> is the LULC-dependent critical level) and AOT40. For this
demonstration, the 13 d model results were linearly extrapolated to
approximately 3 months. This also assumed similar DA adjustments to SM
dynamics (driven by factors such as clouds/radiation, rainfall, and
irrigation for cropland-dominant regions) at the seasonal timescale. Based on
the seasonal variability of surface O<inline-formula><mml:math id="M525" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> and surface fluxes in the study
region in 2016 (Fig. S6), the linearly scaled POD<inline-formula><mml:math id="M526" display="inline"><mml:msub><mml:mi/><mml:mi>y</mml:mi></mml:msub></mml:math></inline-formula> and AOT40 values are
underestimated overall referring to the 2016 peak AOT40 and surface fluxes
occurring during April–May–June and June–July–August, respectively. These
overall underestimations may be invalid if the (sub)seasonal variability of
surface O<inline-formula><mml:math id="M527" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> and surface fluxes of other years was referred to. We
therefore focus on discussing the results qualitatively and highlighting
their implications for O<inline-formula><mml:math id="M528" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> impact assessments using long-term records.
Statistics of the derived POD<inline-formula><mml:math id="M529" display="inline"><mml:msub><mml:mi/><mml:mi>y</mml:mi></mml:msub></mml:math></inline-formula> and AOT40 fields are summarized by
O<inline-formula><mml:math id="M530" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>-sensitive LULC and crop types in Fig. 13c, d, g, and h. Figures 15 and
12c and d present the estimated AOT40 fields and the evaluation of them, as well
as their responses to the SM DA for cropland-dominant grids. The highs and
lows in AOT40-related results are found over maize- and wheat-dominant
fields, respectively. Among the three focused LULC types, the highest and
lowest POD<inline-formula><mml:math id="M531" display="inline"><mml:msub><mml:mi/><mml:mi>y</mml:mi></mml:msub></mml:math></inline-formula> values are estimated for forests and grasslands,
respectively. Largely driven by daytime peak O<inline-formula><mml:math id="M532" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> concentrations, the
spatial variability and biases (referring to AQS and CASTNET observations)
of the model-derived AOT40 fields, as well as their responses to the DA,
match those of the MDA8-based results (Fig. 11). In contrast, the spatial variability of
POD<inline-formula><mml:math id="M533" display="inline"><mml:msub><mml:mi/><mml:mi>y</mml:mi></mml:msub></mml:math></inline-formula> and <inline-formula><mml:math id="M534" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> aligns well, and so do their responses to the DA. Both
POD<inline-formula><mml:math id="M535" display="inline"><mml:msub><mml:mi/><mml:mi>y</mml:mi></mml:msub></mml:math></inline-formula> and AOT40 reacted several times more intensively in the cases that
implemented the dynamic dry-deposition scheme, especially the
CLM_D case.</p>
      <p id="d1e9440">For selected LULC and crop types, the WRF-Chem-derived POD<inline-formula><mml:math id="M536" display="inline"><mml:msub><mml:mi/><mml:mi>y</mml:mi></mml:msub></mml:math></inline-formula> and AOT40
fields were used together with dose–response functions in literature to
evaluate the RBL/RYL due to O<inline-formula><mml:math id="M537" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> exposure and uptake. As reported in Fig. 13c and g, with the SM DA enabled, the mean RBLs based on Noah_D- and CLM_D-derived POD<inline-formula><mml:math id="M538" display="inline"><mml:msub><mml:mi/><mml:mi>y</mml:mi></mml:msub></mml:math></inline-formula> are 0.05–0.08, 0.01–0.02, and
0.04 for deciduous forest, grasslands, and wheat, respectively, which are
<inline-formula><mml:math id="M539" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">33</mml:mn></mml:mrow></mml:math></inline-formula> % lower than the Noah_W- and
P1_W-based RBL estimates. It is shown that, in response to
the DA which lowered SM in many places, the Noah_W- and
P1_W-based RBL estimates did not drop as strongly as the
Noah_D- and CLM_D-based ones and even increased by
0.01 for grasslands and wheat. For wheat, one of the most O<inline-formula><mml:math id="M540" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>-sensitive
crops, the estimated RYL values based on the POD<inline-formula><mml:math id="M541" display="inline"><mml:msub><mml:mi/><mml:mi>y</mml:mi></mml:msub></mml:math></inline-formula> and AOT40 approaches
differ by up to a factor of 2–3, and the DA had contrasting effects on
these estimates (Fig. 13c, d, g, h). The POD<inline-formula><mml:math id="M542" display="inline"><mml:msub><mml:mi/><mml:mi>y</mml:mi></mml:msub></mml:math></inline-formula>- and AOT40-based RYL
values differ more significantly when the model-derived POD<inline-formula><mml:math id="M543" display="inline"><mml:msub><mml:mi/><mml:mi>y</mml:mi></mml:msub></mml:math></inline-formula> and AOT40
fields came from the Noah_D and CLM_D cases.
Using the model-derived AOT40 and different AOT40 dose–response functions
(Mills et al., 2007, 2018b, Table 3), the estimated RYLs and their changes
due to the DA are nonnegligible (Fig. 13d and h). Our estimated RBL/RYL results
for various LULC and crop types mostly fall within the ranges reported in
previous studies which applied model-derived O<inline-formula><mml:math id="M544" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> metrics and
dose–response functions (e.g., Avnery et al., 2011; Mills et al., 2007,
2018b). Our results emphasize that the selected O<inline-formula><mml:math id="M545" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> impact assessment
metrics for various LULC/crop types and their matching dose–response
functions, as well as the model results used to derive the chosen O<inline-formula><mml:math id="M546" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
metrics which are sensitive to dry-deposition schemes and SM, all introduce
uncertainty to the estimated O<inline-formula><mml:math id="M547" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> impacts on vegetation. The widely used
dose–response functions are considered appropriate for studying North
America and Europe, but they may not be applicable to other regions
(Emberson et al., 2009). Therefore, updating and developing dose–response
relationships for a larger number of vegetation types in different regions
of the world are needed, which may require new experiments to be conducted.
Yue and Unger (2014) and Lombardozzi et al. (2015), as well as follow-on
investigations, parameterized the O<inline-formula><mml:math id="M548" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> impacts on several types of
vegetation using the relationships between cumulative O<inline-formula><mml:math id="M549" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> uptake and
O<inline-formula><mml:math id="M550" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> damage factors for photosynthesis and conductance from empirical and
experimental studies. Based on multidecadal model simulations, they reported
<inline-formula><mml:math id="M551" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">20</mml:mn></mml:mrow></mml:math></inline-formula> % changes of biomass, GPP, and energy fluxes due to O<inline-formula><mml:math id="M552" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>,
which are roughly consistent with our RBL/RYL results in Fig. 13. Such
approaches that dynamically assess the impacts of O<inline-formula><mml:math id="M553" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> along with other
factors (e.g., non-O<inline-formula><mml:math id="M554" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> pollutants and environmental stresses), as
highlighted in Emberson et al. (2018), will be considered in future work.</p>
      <p id="d1e9619">We note that, revising the dry-deposition scheme and constraining the
modeled SM fields with observations would not only better be combined with
adding O<inline-formula><mml:math id="M555" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> impacts on vegetation but also multi-stress impacts on biogenic
emissions. Considering O<inline-formula><mml:math id="M556" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>-induced vegetation injuries would more
evidently affect longer-term climate simulations via feedbacks to biomass, surface
fluxes, weather, and weather-driven emissions. As for biogenic emissions,
Fig. S7 shows SM anomalies during the study period determined by our Noah-MP
modeling system as well as drought stress activity factor <inline-formula><mml:math id="M557" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">γ</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
estimated from <inline-formula><mml:math id="M558" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> of a multiyear, independent CLM (version 4.5)
simulation by Jiang et al. (2018). Based on this analysis, we estimate that,
depending on soil type, hydrological regime, and <inline-formula><mml:math id="M559" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula>
configurations, omitting the direct impacts of water stress on biogenic
emissions may have introduced larger uncertainty (i.e., <inline-formula><mml:math id="M560" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">30</mml:mn></mml:mrow></mml:math></inline-formula> %) to biogenic emission and O<inline-formula><mml:math id="M561" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> modeling over several states
experiencing drier-than-normal conditions, particularly South Carolina,
Georgia, and Alabama. Quantitatively understanding the interplay between
these processes and O<inline-formula><mml:math id="M562" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> pollution levels is recommended for more
accurate air quality modeling and O<inline-formula><mml:math id="M563" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> impact assessments.</p>
</sec>
</sec>
</sec>
<sec id="Ch1.S4" sec-type="conclusions">
  <label>4</label><title>Summary and suggestions on future directions</title>
      <p id="d1e9713">This paper described a follow-up study of Huang et al. (2021). It presented
how the choice of O<inline-formula><mml:math id="M564" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> dry-deposition scheme affected our evaluation of
SMAP SM DA impacts on coupled WRF-Chem modeling over the southeastern US in
August 2016. In new Noah-MP LSM-related simulations, two dry-deposition
schemes were implemented, namely the WRF-Chem default Wesely scheme and a
dynamic scheme, in the latter of which the calculation of <inline-formula><mml:math id="M565" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
(particularly its stomatal and cuticular terms) was modified to be coupled
with photosynthesis and vegetation phenology. We showed that dry-deposition
parameterizations significantly affected the modeled O<inline-formula><mml:math id="M566" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> dry-deposition
process, as well as its response to the DA. Comparing the no-DA cases, it
was found that, when the dynamic scheme was applied, overall, the modeled
O<inline-formula><mml:math id="M567" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> dry-deposition velocities and fluxes were larger and surface O<inline-formula><mml:math id="M568" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
concentrations were lower. The modeled O<inline-formula><mml:math id="M569" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> fluxes responded 2–3 times
more strongly to the SM changes due to the DA, which can be mainly explained
by the fact that both the direct and indirect (i.e., via influencing weather
and vegetation fields) effects of SM on O<inline-formula><mml:math id="M570" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> dry-deposition modeling are
considered in the dynamic scheme. Depending on soil type and hydrological
regime, the selection of SM factor controlling <inline-formula><mml:math id="M571" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (i.e., <inline-formula><mml:math id="M572" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula>
factor, a key variable representing the direct effects of SM on the modeled
surface fluxes) scheme can strongly affect the quantitative results. The
Wesely-scheme-derived dry-deposition results driven by meteorological fields
from Noah-MP-based and (from Huang et al., 2021) Noah-LSM-based WRF-Chem
simulations displayed much smaller differences than those due to updating
the dry-deposition parameterizations. While we note that accounting for
physiological effects in dry-deposition modeling can be beneficial, the
Ball–Berry <inline-formula><mml:math id="M573" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> scheme applied in land surface and dry-deposition
modeling in this work needs to be compared with other semi-empirical <inline-formula><mml:math id="M574" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
schemes, for a better understanding of their respective strengths and
weaknesses. Alternative schemes include the Medlyn scheme, which has been
integrated into the CLM version 5. Model intercomparison efforts such as the
ongoing Air Quality Model Evaluation International Initiative Phase 4
activity (Galmarini et al., 2021) can also help determine areas for
improvement in commonly used dry-deposition modeling approaches for studying
2016 and other years, over North America and other regions of the world.</p>
      <p id="d1e9822">By analyzing the model responses to the SM DA from these various cases, we
conclude that, in coupled modeling systems that consider the direct and
indirect influences of SM on O<inline-formula><mml:math id="M575" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> dry deposition, the accuracy of SM is
particularly critical to dry deposition and O<inline-formula><mml:math id="M576" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> modeling, as well as the
scientific analyses and impact assessments based on model simulations. The
usefulness of SM DA for improving the modeled state and flux variables was
evaluated by multiple observation(-derived) data products. Referring to in
situ measurements, key meteorological variables relevant to <inline-formula><mml:math id="M577" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
calculations such as surface temperature and humidity are shown to be
improved by the DA by up to <inline-formula><mml:math id="M578" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">9</mml:mn></mml:mrow></mml:math></inline-formula> %. Referring to
satellite(-derived) datasets which may be associated with high uncertainty,
the model performance of vegetation phenology, GPP, as well as energy fluxes
and their partitioning, showed mixed, LULC-dependent reactions to the DA.
According to the evaluation statistics, for this case, the CLM-type <inline-formula><mml:math id="M579" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula>
factor scheme was slightly superior to the Noah-type one. The modeled carbon
and energy fields, as well as their DA-related changes, correlated strongly
with the modeled <inline-formula><mml:math id="M580" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> fields, implying that the DA impacts on the
accuracy of <inline-formula><mml:math id="M581" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> were also possibly complicated, which is difficult to
verify due to the lack of high-accuracy, independent <inline-formula><mml:math id="M582" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> evaluation
datasets, a point that has also been brought up in previous dry-deposition
modeling works (e.g., Baublitz et al., 2020; Clifton et al., 2020).
Observation(-derived) <inline-formula><mml:math id="M583" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> datasets covering diverse LULC types nested in
broad geographical regions and through more recent periods are in strong
need. In places, the likely ineffectiveness of SM DA on vegetation and
surface fluxes can not only be attributed to the quality of satellite SM
retrievals and the DA approach used as discussed in previous Noah-LSM-based
DA experiments, but also shortcomings in the Noah-MP LSM and its dynamic
vegetation scheme regarding its surface–subsurface coupling and
representation of SM-vegetation growth feedbacks. Continued efforts on
advancing land measurement/retrieval skills and identifying and addressing
deficits in LSMs, as well as practicing multivariate land DA, are recommended
in future work.</p>
      <p id="d1e9916">This study also demonstrated that model-driven assessments of O<inline-formula><mml:math id="M584" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
impacts on human health and various types of vegetation can be significantly
affected by the applied O<inline-formula><mml:math id="M585" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> dry-deposition scheme, the implementation of
land DA, the chosen O<inline-formula><mml:math id="M586" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> metrics, and their matching exposure–response
functions. Various model cases showed that the DA impacts on MDA8 were more
evident in nonurban areas where the mean MDA8 was <inline-formula><mml:math id="M587" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:math></inline-formula> ppbv
lower and the average population density is <inline-formula><mml:math id="M588" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">25</mml:mn></mml:mrow></mml:math></inline-formula> of that in
urban areas. Using concentration- and flux-based metrics AOT40 and
POD<inline-formula><mml:math id="M589" display="inline"><mml:msub><mml:mi/><mml:mi>y</mml:mi></mml:msub></mml:math></inline-formula>, the mean RYLs of maize, soybean, and wheat fell within ranges of
0.01–0.04, 0.10–0.17, and 0.04–0.14, respectively. The multiple no-DA and
DA cases helped us better understand the indirect and/or direct effects of
SM on O<inline-formula><mml:math id="M590" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> dry-deposition process, which have important implications for
O<inline-formula><mml:math id="M591" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> impact assessments. It is also recognized that the DA often
exacerbated the positive surface O<inline-formula><mml:math id="M592" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> biases in free-running systems,
which has been a common issue shared by numerous regional and global models
for this study region/season. It is necessary to combine land DA with
efforts to identify, quantify, and reduce other sources of uncertainty in
O<inline-formula><mml:math id="M593" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> modeling. These should include reasonably representing the impacts
of O<inline-formula><mml:math id="M594" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> along with other factors on vegetation, the direct impacts of
water stress on biogenic emissions of volatile organic compounds and
nitrogen species, and the reduction of photolysis reaction rates and
the modification of vertical transport due to the presence of foliage (Li et
al., 2016; Jiang et al., 2018; Makar et al., 2017).</p>
</sec>

      
      </body>
    <back><notes notes-type="codedataavailability"><title>Code and data availability</title>

      <p id="d1e10030">Dry-deposition-related updates to LIS/WRF-Chem since Huang et al. (2021) are
undergoing reporting processes via NASA's New Technology Reporting System
(<uri>https://invention.nasa.gov</uri>, last access: 4 June 2022). Model results as well as observations and observation-derived
evaluation datasets emphasized in this work but not in Huang et al. (2021)
can be found at the following locations: <ext-link xlink:href="https://doi.org/10.5281/zenodo.6615022" ext-link-type="DOI">10.5281/zenodo.6615022</ext-link> (Huang, 2022),
<uri>https://land.copernicus.eu/global/products/fcover</uri> (last access: 10 April 2022; Copernicus Global Land
Service, 2020),
<ext-link xlink:href="https://doi.org/10.5067/L6C9EY1O8VIC" ext-link-type="DOI">10.5067/L6C9EY1O8VIC</ext-link> (Kimball et al., 2021),
<ext-link xlink:href="https://doi.org/10.7927/H49C6VHW" ext-link-type="DOI">10.7927/H49C6VHW</ext-link> (NASA Socioeconomic Data and Applications
Center, 2018), <uri>https://www-air.larc.nasa.gov/cgi-bin/ArcView/actamerica.2016</uri>
(last access: 8 November 2021; NASA, 2020),
<uri>https://java.epa.gov/castnet/clearsession.do</uri> (last access: 8 November 2021; US Environmental Protection
Agency, 2021), and
<ext-link xlink:href="https://doi.org/10.3334/ORNLDAAC/1696" ext-link-type="DOI">10.3334/ORNLDAAC/1696</ext-link> (Yu et al., 2019).</p>
  </notes><app-group>
        <supplementary-material position="anchor"><p id="d1e10058">The supplement related to this article is available online at: <inline-supplementary-material xlink:href="https://doi.org/10.5194/acp-22-7461-2022-supplement" xlink:title="pdf">https://doi.org/10.5194/acp-22-7461-2022-supplement</inline-supplementary-material>.</p></supplementary-material>
        </app-group><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e10067">MH led the design and execution of the study as well as the paper writing,
benefitting from discussions with JHC, GRC, KWB, and SVK, with the feedback
from the <italic>Atmospheric Chemistry and Physics</italic> Editorial Board and reviewers for Huang et al. (2021) also accounted for. CS contributed to data collection during the
ACT-America campaign. All authors helped finalize the paper.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e10076">The contact author has declared that neither they nor their co-authors have any competing interests.</p>
  </notes><notes notes-type="disclaimer"><title>Disclaimer</title>

      <p id="d1e10082">Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e10088">We acknowledge NASA SMAP and ACT-America Science Teams and NASA's high-end computing systems and services at Ames and Goddard. We
thank Jiang et al. (2018) for developing the <inline-formula><mml:math id="M595" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">γ</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> dataset shown
in Fig. S7. We also greatly appreciate active and relevant discussions with
multiple colleagues from the Air Quality Model Evaluation International
Initiative 4 and the Tropospheric Ozone Assessment Report II communities
during and after recent conferences and workshops, particularly Christian Hogrefe, Jonathan Pleim, Paul Makar, Lisa Emberson, Bärbel Sinha, Danica Lombardozzi, Olivia Clifton, Louisa Emmons, Tamara Emmerichs, and Domenico Taraborrelli.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d1e10104">This research has been supported by NASA's Earth Science Division, through the Science Utilization of SMAP program (grant no. NNX16AN39G).</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e10110">This paper was edited by Farahnaz Khosrawi and reviewed by two anonymous referees.</p>
  </notes><ref-list>
    <title>References</title>

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