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  <front>
    <journal-meta><journal-id journal-id-type="publisher">HESS</journal-id><journal-title-group>
    <journal-title>Hydrology and Earth System Sciences</journal-title>
    <abbrev-journal-title abbrev-type="publisher">HESS</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">Hydrol. Earth Syst. Sci.</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">1607-7938</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/hess-24-2399-2020</article-id><title-group><article-title>A novel regional irrigation water productivity model coupling
irrigation- and drainage-driven soil hydrology and salinity dynamics and shallow groundwater movement in arid regions in China</article-title><alt-title>A novel regional irrigation water productivity model</alt-title>
      </title-group><?xmltex \runningtitle{A novel regional irrigation water productivity model}?><?xmltex \runningauthor{J.~Xue et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Xue</surname><given-names>Jingyuan</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Huo</surname><given-names>Zailin</given-names></name>
          <email>huozl@cau.edu.cn</email>
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Wang</surname><given-names>Shuai</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Wang</surname><given-names>Chaozi</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>White</surname><given-names>Ian</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Kisekka</surname><given-names>Isaya</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4">
          <name><surname>Sheng</surname><given-names>Zhuping</given-names></name>
          
        <ext-link>https://orcid.org/0000-0001-8533-527X</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Huang</surname><given-names>Guanhua</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Xu</surname><given-names>Xu</given-names></name>
          
        </contrib>
        <aff id="aff1"><label>1</label><institution>Center for Agricultural Water Research in China, China Agricultural
University, Beijing 100083, China</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Fenner School of Environment &amp; Society, Australian National
University, <?xmltex \hack{\break}?> Fenner Building 141, Canberra, ACT 0200, Australia</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>University of California Davis, Department of Land, Air and Water
Resources <?xmltex \hack{\break}?> and Department of Biological and Agricultural Engineering, Davis, California 95616-5270, USA</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>Texas A &amp; M AgriLife Research Center, El Paso, Texas 79927-5020, USA</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Zailin Huo (huozl@cau.edu.cn)</corresp></author-notes><pub-date><day>12</day><month>May</month><year>2020</year></pub-date>
      
      <volume>24</volume>
      <issue>5</issue>
      <fpage>2399</fpage><lpage>2418</lpage>
      <history>
        <date date-type="received"><day>10</day><month>July</month><year>2019</year></date>
           <date date-type="rev-request"><day>12</day><month>August</month><year>2019</year></date>
           <date date-type="rev-recd"><day>17</day><month>March</month><year>2020</year></date>
           <date date-type="accepted"><day>5</day><month>April</month><year>2020</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2020 Jingyuan Xue et al.</copyright-statement>
        <copyright-year>2020</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://hess.copernicus.org/articles/24/2399/2020/hess-24-2399-2020.html">This article is available from https://hess.copernicus.org/articles/24/2399/2020/hess-24-2399-2020.html</self-uri><self-uri xlink:href="https://hess.copernicus.org/articles/24/2399/2020/hess-24-2399-2020.pdf">The full text article is available as a PDF file from https://hess.copernicus.org/articles/24/2399/2020/hess-24-2399-2020.pdf</self-uri>
      <abstract><title>Abstract</title>
    <p id="d1e178">The temporal and spatial distributions of regional irrigation water
productivity (RIWP) are crucial for making decisions related to agriculture,
especially in arid irrigated areas with complex cropping patterns. Thus, in this study, we
developed a new RIWP model for an irrigated agricultural area with complex
cropping patterns. The model couples the irrigation- and drainage-driven soil water and salinity dynamics and shallow groundwater movement in order to quantify the temporal and spatial distributions of the target hydrological and biophysical variables. We divided the study area into 1 km <inline-formula><mml:math id="M1" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 1 km hydrological response units (HRUs). In each HRU, we considered four land use types: sunflower fields, wheat fields, maize fields, and uncultivated lands (bare soil). We coupled the regional soil hydrological processes and groundwater flow by taking a weighted average of the water exchange between unsaturated soil and groundwater under different land use types. The RIWP model was calibrated and validated using 8 years of hydrological variables obtained from regional observation sites in a typical arid irrigation area in North China, the Hetao Irrigation District. The model simulated soil moisture and salinity reasonably well as well as groundwater table depths and salinity. However, overestimations of groundwater discharge were detected in both the calibration and validation due to the assumption of well-operated drainage ditch conditions; regional evapotranspiration (ET) was reasonably estimated, whereas ET in the uncultivated area was slightly underestimated in the RIWP model. A sensitivity analysis indicated that the soil evaporation coefficient and the specific yield were the key parameters for the RIWP simulation. The results showed that the RIWP decreased from maize to sunflower to wheat from 2006 to 2013. It was also found that the maximum RIWP was reached when the groundwater table depth was between 2 and 4 m, regardless of the irrigation water depth applied. This implies the importance of groundwater table control on the RIWP. Overall, our distributed RIWP model can effectively simulate the temporal and spatial distribution of the RIWP and provide critical water allocation suggestions for decision-makers.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d1e197">An increasing food demand currently exists due to global population growth, and water
resources are limiting food production in many areas (Kijne et al., 2003;
Fraiture and Wichelns, 2010). Especially in arid and semiarid regions of
the world, where irrigated agriculture accounts for about 70 % to 90 % of
the total water use (Jiang et al., 2015; Gao et al., 2017; Dubois, 2011),
this water deficit and the related land salinity are the two major limitations on
agricultural<?pagebreak page2400?> production (Williams, 1999; Xue et al., 2018). To maximize
agricultural production, the improvement of irrigation water productivity (IWP) is vital (Bessembinder et al., 2005; Surendran et al., 2016). IWP is defined as the crop yield per cubic meter of irrigation water supplied, and it is expressed in kilograms per cubic meter (Singh et al., 2004).</p>
      <p id="d1e200">Furthermore, by changing hydrological processes, irrigation and drainage
affect water and salt dynamics in the crop root zone, the groundwater, and,
eventually, crop production (Morison et al., 2008; Bouman, 2007). Specifically, in arid regions, irrigation-induced deep seepage is the main groundwater recharge mechanism. Shallow groundwater can also move upward and
contribute to crop water use by capillary action, which means that the abovementioned irrigation
seepage can be reused by the crop to improve the IWP. Thus, the RIWP analysis
requires the quantification of complex agro-hydrological processes,
including soil water and salt dynamics, groundwater movement, crop water use,
and crop production.</p>
      <p id="d1e203">Various methods have been used to evaluate the IWP, such as field measurements
(Talebnejad and Sepaskhah, 2015; Gowing et al., 2009), remote sensing (Zwart and Bastiaanssen, 2007), and distributed hydrological models (Singh, 2005; Jiang et al., 2015; Steduto et al., 2009). Field experiments have also been widely used to evaluate the effect of water management on the IWP (Talebnejad and Sepaskhah, 2015; Gowing et al., 2009); however, field experiments are expensive and time-consuming, making them unsuitable for the regional evaluation of IWP. Therefore, remote sensing is commonly used to quantify regional IWP, as it can reveal temporal and spatial distributions of ET and crop yields (Biradar et al., 2008). Nevertheless, this method only reports the past IWP distribution and cannot readily predict the impacts of water management practices on the IWP.</p>
      <p id="d1e206">Recently, distributed integrated crop and hydrological models have been widely
used to simulate the complex agro-hydrological processes coupled with salt
dynamics and crop production (Aghdam et al., 2013; Noory et al., 2011; Van Dam et al., 2008; Vanuytrecht et al., 2014). Taking advantage of geographic information systems (GIS), distributed integrated crop and hydrological models provide precise simulations of regional hydrological processes and crop growth by incorporating the heterogeneity of soil moisture, salinity, and texture, the groundwater table depth and salinity, and cropping patterns (Amor et al., 2002; Bastiaanssen et al., 2003a; Jiang et al., 2015; Nazarifar et al., 2012; Xue et al., 2017).</p>
      <p id="d1e210">There are two types of distributed hydrological models that are used to
monitor complex regional hydrological processes: numerical distributed
models, such as SWAT and MODFLOW, and simplified distributed models, such as
FARME (Kumar and Singh, 2003) and HEC-HMS (USACE, 1999), the latter of which are based on water
balance equations. Numerical, process-based models consider the entire
complexity and heterogeneity of regional hydrological systems. MODFLOW is
commonly used for the simulation of groundwater dynamics (Kim et al., 2008), but it
is limited in well-monitored large irrigation areas due to the large number
of parameters and input data required. SWAT is used to simulate land surface
hydrological and crop growth processes. It relies on a digital elevation
model (DEM) to delineate surface water flow pathways. However, many
irrigation areas are quite flat, and surface water flow pathways are
controlled by irrigation and drainage systems instead of terrain elevation
differences.</p>
      <p id="d1e213">Simplified distributed models often employ mass balance equations to
describe the soil water and salt dynamics (Sharma, 1999; Sivapalan et al.,
1996), which means fewer input parameters as well as larger spatial grids and
temporal steps. However, the large spatial grids poorly reflect the regional
complex cropping pattern heterogeneity, and the large temporal steps cannot
capture daily soil water and salt dynamics, which are essential for crop
growth simulation. SWAT alone does not describe the complex interactions
between groundwater and soil water, which are fundamental in arid and
semiarid areas with shallow groundwater.</p>
      <p id="d1e216">Therefore, there are still two big challenges with respect to developing distributed
integrated irrigation water productivity models in irrigated areas. First,
the networks of irrigation canals and drainage ditches cause spatial
heterogeneity in irrigation, drainage, deep percolation, canal seepage, and
groundwater table depth within the irrigation area; however, previous studies
have overlooked the important role of the networks of irrigation canals and
drainage ditches in RIWP evaluations. Second, the multi-scale matching
problem arises when coupling the unsaturated and saturated zones in irrigation
areas with complex cropping patterns, as the spatial heterogeneity of
cropping patterns is much stronger than that of the groundwater table depth.
However, most of the existing distributed hydrological models simulated the
hydrological processes within the same hydrological response unit (HRU)
between the unsaturated and saturated zones independently but overlooked the
lateral exchange of groundwater between adjacent HRUs.</p>
      <p id="d1e219">Therefore, the main objectives of our study are (1) to develop a RIWP model
framework coupling the irrigation and drainage processes, soil water and
salt dynamics, crop water and salt response processes, and lateral movement
of groundwater and salt; and (2) to analyze the distributed RIWP of the study
area and establish the effects of crop type, irrigation water depth applied, and
groundwater table depth on the RIWP.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Methods</title>
      <p id="d1e230">We will present a four-module integrated RIWP model, the coupling between
the modules, and one case study evaluating the model performance.</p><?xmltex \hack{\newpage}?>
<?pagebreak page2401?><sec id="Ch1.S2.SS1">
  <label>2.1</label><title>Regional irrigation water productivity model</title>
      <p id="d1e241">General descriptions will be given for the four modules and their integration, the division and connections of HRUs, and the boundary
conditions of the model. Detailed descriptions will then be given for each
of the four modules: the irrigation system module, the drainage system module,
the groundwater module, and the field-scale IWP module.</p>
<sec id="Ch1.S2.SS1.SSS1">
  <label>2.1.1</label><title>General descriptions</title>
      <p id="d1e251">A four-module integrated RIWP model was developed in order to simulate the complex
system, including water supply from irrigation open canals, field crop water
consumption, groundwater drainage into open ditches, and groundwater lateral
flow.</p>
</sec>
<sec id="Ch1.S2.SS1.SSSx1" specific-use="unnumbered">
  <title>The four modules and their integration</title>
      <p id="d1e260">The RIWP model developed in this study couples an irrigation system module, a drainage
system module, a groundwater module, and a field-scale IWP evaluation module
(Fig. 1). The irrigation system module simulates the water flow along canals
and the canal seepage to groundwater (the recharge of the groundwater module), and it provides the amount of water available for field-scale
irrigation. The drainage system module simulates the drainage to the main
drainage ditches from groundwater, and this is the discharge of the
groundwater module. The groundwater module is used to simulate the
groundwater lateral movement, the groundwater boundary for the field-scale
water–salt balance processes, and the groundwater level dynamics for the
drainage module. In the field-scale IWP module, the vertical movement of water
and salt in the soil profile is simulated in order to obtain the soil moisture and
salinity of the crop root zone and to calculate the field-scale irrigation
water productivity. This module provides deep percolation to the groundwater
module and obtains capillary rise to soil from the groundwater module. The four abovementioned modules will be described comprehensively in Sect. 2.1.2–2.1.5.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1" specific-use="star"><?xmltex \currentcnt{1}?><label>Figure 1</label><caption><p id="d1e265">Schematic diagram of the conceptual RIWP model and the coupling between its sub-modules.</p></caption>
            <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/articles/24/2399/2020/hess-24-2399-2020-f01.png"/>

          </fig>

</sec>
<sec id="Ch1.S2.SS1.SSSx2" specific-use="unnumbered">
  <title>Hydrological response units</title>
      <p id="d1e280">The irrigation area is spatially heterogeneous in terms of soil, land use,
meteorology, and groundwater. To include the spatial heterogeneities in the
simulation of regional water and salt dynamics and its impact on crop
growth, the irrigation district was divided into hydrological response units (HRUs; Kalcic et al., 2015). The HRU is an abstract artifact created by a hydrological developer and is like the smallest spatial unit of the model,
which provides an efficient way to discretize large watersheds where
simulation at the field scale may not be computationally feasible. In each
HRU, soil texture and groundwater conditions are assumed to be homogeneous,
but different cropping patterns can exist, e.g., sunflower fields,
wheat fields, maize fields, and uncultivated lands. As the irrigation quota
is different for different cropping patterns, the model first runs the field IWP
model for each cropping pattern independently in each HRU in order to obtain the
soil water and salt dynamics, the IWP, and groundwater recharge. The
groundwater levels and salinity of each HRU can then be updated according to the
area proportions of different cropping patterns in each HRU. The groundwater
flow is determined by the pressure head gradient between adjacent HRUs.</p>
</sec>
<sec id="Ch1.S2.SS1.SSSx3" specific-use="unnumbered">
  <title>Boundary conditions</title>
      <p id="d1e290">The upper boundary of the model is the atmospheric boundary layer above the
plant canopy, which determines reference ET and precipitation. The main
irrigation canals and drainage ditches directly connect with groundwater and
can be considered as the side boundaries in the model. With the canal
conveyance water loss deducted from the gross water supplied, the amount of
water diverted into the field can be calculated as the actual amount of
irrigation. The local irrigation schedules of different crops and the actual
time of canal water supply are both considered to determine the actual
irrigation time and irrigation amounts. The lower boundary is the confining
bed at the bottom of phreatic layer. The phreatic layer is vitally important
due to its vertical exchange with the unsaturated soil zone in each HRU and
its lateral exchange with adjacent HRUs to bond the whole region together.</p>
</sec>
<sec id="Ch1.S2.SS1.SSS2">
  <label>2.1.2</label><title>Irrigation system module</title>
      <p id="d1e301">When irrigation water passes through canals, regardless of if they are lined or unlined,
seepage loss occurs and recharges groundwater. In a large irrigation area,
there are many main, submain, lateral, and field canals, which are
categorized as the first-, second-, third-, and fourth-order canals,
respectively. During the water allocation period, canal seepage loss from
different levels of canals can be divided into two parts: the
seepage loss from the main and submain canals, which are permanently filled
with water and recharge directly into groundwater along the route; and the seepage loss from lateral and field canals, which are
intermittently filled with water and only recharge the groundwater units
within their control area. Each HRU has its corresponding groundwater unit,
which is used when calculating lateral exchange of groundwater between
adjacent HRUs.</p>
      <?pagebreak page2402?><p id="d1e304">We calculated the decreasing water flow along the canal and water losses in the main and submain canals as follows (Men, 2000):

                  <disp-formula specific-use="align" content-type="numbered"><mml:math id="M2" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E1"><mml:mtd><mml:mtext>1</mml:mtext></mml:mtd><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mi>A</mml:mi><mml:mrow><mml:mn mathvariant="normal">100</mml:mn><mml:msup><mml:mi>Q</mml:mi><mml:mi>m</mml:mi></mml:msup></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E2"><mml:mtd><mml:mtext>2</mml:mtext></mml:mtd><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi>d</mml:mi><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mi>Q</mml:mi><mml:mi>d</mml:mi><mml:mi>l</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

              <?xmltex \hack{\newpage}?><?xmltex \hack{\noindent}?>where <inline-formula><mml:math id="M3" display="inline"><mml:mi mathvariant="italic">σ</mml:mi></mml:math></inline-formula> represents the water loss coefficient per unit length per unit flow in the canal (m<inline-formula><mml:math id="M4" 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>); <inline-formula><mml:math id="M5" display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula> is the soil permeability coefficient of the canal bed (m<inline-formula><mml:math id="M6" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">3</mml:mn><mml:mi>m</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> d<inline-formula><mml:math id="M7" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mi>m</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula>), <inline-formula><mml:math id="M8" display="inline"><mml:mi>m</mml:mi></mml:math></inline-formula> is the soil permeability exponent of the canal bed (–), and their values depend on the soil type of the canal bed (please refer to Guo, 1997, for the values). <inline-formula><mml:math id="M9" display="inline"><mml:mi>Q</mml:mi></mml:math></inline-formula> represents the daily net flow in the canal (m<inline-formula><mml:math id="M10" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> d<inline-formula><mml:math id="M11" 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 <inline-formula><mml:math id="M12" display="inline"><mml:mrow><mml:mi>d</mml:mi><mml:mi>Q</mml:mi></mml:mrow></mml:math></inline-formula> represents the daily flow loss of the water conveyance within <inline-formula><mml:math id="M13" display="inline"><mml:mrow><mml:mi>d</mml:mi><mml:mi>l</mml:mi></mml:mrow></mml:math></inline-formula> distance in the canal (m<inline-formula><mml:math id="M14" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> d<inline-formula><mml:math id="M15" 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>).</p>
      <p id="d1e502">Thus, Eq. (1) is equal to Eq. (2), and they can be transformed into
              <disp-formula id="Ch1.E3" content-type="numbered"><label>3</label><mml:math id="M16" display="block"><mml:mrow><mml:msup><mml:mi>Q</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mi>d</mml:mi><mml:mi>Q</mml:mi><mml:mo>=</mml:mo><mml:mi>A</mml:mi><mml:mi>d</mml:mi><mml:mi>l</mml:mi><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
            Integrations of both sides of Eq. (3) give

                  <disp-formula specific-use="align" content-type="numbered"><mml:math id="M17" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E4"><mml:mtd><mml:mtext>4</mml:mtext></mml:mtd><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:munderover><mml:mo movablelimits="false">∫</mml:mo><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mi>L</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:munderover><mml:msup><mml:mi>Q</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mi>d</mml:mi><mml:mi>Q</mml:mi><mml:mo>=</mml:mo><mml:munderover><mml:mo movablelimits="false">∫</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mi>L</mml:mi></mml:munderover><mml:mi>A</mml:mi><mml:mi>d</mml:mi><mml:mi>l</mml:mi></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E5"><mml:mtd><mml:mtext>5</mml:mtext></mml:mtd><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:msub><mml:mi>Q</mml:mi><mml:mi>L</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mfenced open="(" close=")"><mml:mrow><mml:msubsup><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mi>m</mml:mi></mml:msubsup><mml:mo>-</mml:mo><mml:mi>A</mml:mi><mml:mi>L</mml:mi><mml:mi>m</mml:mi></mml:mrow></mml:mfenced><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:mi>m</mml:mi></mml:mrow></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

              where <inline-formula><mml:math id="M18" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the daily gross flow in the head of the canal
(m<inline-formula><mml:math id="M19" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> d<inline-formula><mml:math id="M20" 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 <inline-formula><mml:math id="M21" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mi>L</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the daily net flow in the canal at <inline-formula><mml:math id="M22" display="inline"><mml:mi>L</mml:mi></mml:math></inline-formula> distance from the canal head (m<inline-formula><mml:math id="M23" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> d<inline-formula><mml:math id="M24" 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>). Thus, flow loss in water conveyance process can be calculated as follows:

                  <disp-formula specific-use="align" content-type="numbered"><mml:math id="M25" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E6"><mml:mtd><mml:mtext>6</mml:mtext></mml:mtd><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:msub><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">Ls</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mi>A</mml:mi><mml:mn mathvariant="normal">100</mml:mn></mml:mfrac></mml:mstyle><mml:msup><mml:mfenced open="(" close=")"><mml:mrow><mml:msubsup><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mi>m</mml:mi></mml:msubsup><mml:mo>-</mml:mo><mml:mi>A</mml:mi><mml:mi>L</mml:mi><mml:mi>m</mml:mi></mml:mrow></mml:mfenced><mml:mrow><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mi>m</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E7"><mml:mtd><mml:mtext>7</mml:mtext></mml:mtd><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">ls</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">ls</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">su</mml:mi></mml:msub></mml:mrow></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

              where <inline-formula><mml:math id="M26" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">Ls</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the daily groundwater recharge due to water conveyance loss in the main and submain canals (m<inline-formula><mml:math id="M27" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> d<inline-formula><mml:math id="M28" 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>), <inline-formula><mml:math id="M29" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">ls</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the daily groundwater recharge per unit area due to water conveyance loss in the main and submain canals (m d<inline-formula><mml:math id="M30" 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>), <inline-formula><mml:math id="M31" display="inline"><mml:mi>n</mml:mi></mml:math></inline-formula> represents the total number of HRUs along selected main and submain canals (–), and <inline-formula><mml:math id="M32" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">HRU</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the area of each HRU (m<inline-formula><mml:math id="M33" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula>).</p>
      <p id="d1e893"><?xmltex \hack{\newpage}?>Lateral and field canals are densely distributed in the irrigated area, and
they are intermittently filled with low water flow. Thus, it is assumed that
seepage from these canals uniformly recharges groundwater units within their
control area. The canal seepage is estimated by the following empirical formula:
              <disp-formula id="Ch1.E8" content-type="numbered"><label>8</label><mml:math id="M34" display="block"><mml:mtable columnspacing="1em" class="split" rowspacing="0.2ex" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">as</mml:mi></mml:msub></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">mc</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:mfenced close=")" open="("><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">sbmc</mml:mi></mml:msub></mml:mrow></mml:mfenced><mml:mo>+</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">mc</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">sbmc</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:mfenced open="(" close=")"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">lc</mml:mi></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">mc</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">sbmc</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">lc</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:mfenced open="(" close=")"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">fc</mml:mi></mml:msub></mml:mrow></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
            where <inline-formula><mml:math id="M35" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">as</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> represents daily groundwater recharge per unit area due to water conveyance loss in the lateral and field canals (m d<inline-formula><mml:math id="M36" 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
<inline-formula><mml:math id="M37" display="inline"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the daily irrigation water depth applied per unit area (m d<inline-formula><mml:math id="M38" 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>).
<inline-formula><mml:math id="M39" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">mc</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M40" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">sbmc</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M41" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">lc</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M42" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">fc</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are the utilization coefficients of the main, submain, lateral, and field canals, respectively (–).</p>
</sec>
<sec id="Ch1.S2.SS1.SSS3">
  <label>2.1.3</label><title>Drainage system module</title>
      <?pagebreak page2403?><p id="d1e1121">In the drainage system module, only the groundwater draining into ditches is
considered, as the precipitation directly on ditches is negligible in
arid and semiarid areas. The drainage processes are simulated based on the
spatial distributions of the main, submain, and lateral ditches, which are
grouped into the first-, second-, and third-order ditches, respectively.
Drainage is estimated by comparing local groundwater levels and ditch bottom
elevation. According to Tang et al. (2007), the groundwater drainage was
calculated as follows:
              <disp-formula id="Ch1.E9" content-type="numbered"><label>9</label><mml:math id="M43" display="block"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfenced close="" open="{"><mml:mtable class="array" columnalign="left center"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi mathvariant="italic">γ</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:msub><mml:mo>×</mml:mo><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">db</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:mfenced><mml:mo>;</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">db</mml:mi></mml:msub><mml:mo>&gt;</mml:mo><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mo>;</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">db</mml:mi></mml:msub><mml:mo>&lt;</mml:mo><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mfenced></mml:mrow></mml:math></disp-formula>
            where <inline-formula><mml:math id="M44" display="inline"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the daily groundwater drainage per unit area (m d<inline-formula><mml:math id="M45" 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>). <inline-formula><mml:math id="M46" 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> is the drainage coefficient (–), which describes the groundwater table decline caused by the elevation difference between the groundwater table and the streambed of the drainage ditch, and it depends on the underlying soil conductivity and the average distance between the drainage ditches. <inline-formula><mml:math id="M47" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> represents the daily groundwater table depth (m d<inline-formula><mml:math id="M48" 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 <inline-formula><mml:math id="M49" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">db</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the daily streambed depth of the drainage ditch (m d<inline-formula><mml:math id="M50" 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>).</p>
</sec>
<sec id="Ch1.S2.SS1.SSS4">
  <label>2.1.4</label><title>Groundwater module</title>
      <p id="d1e1291">For a plain irrigation area, groundwater levels are usually relatively flat
on the large scale. In our model, it is assumed that groundwater lateral flow
exists between one HRU and its four adjacent HRUs (Fig. 2). Using the water
table gradient, groundwater flow between the current HRU and its adjacent HRUs
can be calculated as follows:
              <disp-formula id="Ch1.E10" content-type="numbered"><label>10</label><mml:math id="M51" display="block"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">gr</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfenced open="(" close=")"><mml:mrow><mml:mi>K</mml:mi><mml:mo>×</mml:mo><mml:mi>h</mml:mi><mml:mo>×</mml:mo><mml:mi>B</mml:mi><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mi mathvariant="normal">ga</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>L</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow><mml:mi>D</mml:mi></mml:mfrac></mml:mstyle></mml:mrow></mml:mfenced><mml:mo>/</mml:mo><mml:msup><mml:mi>B</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            where <inline-formula><mml:math id="M52" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">gr</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the daily groundwater inflow of the current HRU from
adjacent HRUs (m d<inline-formula><mml:math id="M53" 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 <inline-formula><mml:math id="M54" display="inline"><mml:mi>K</mml:mi></mml:math></inline-formula> is the daily permeability coefficient of
unconfined aquifers in the current HRU (m d<inline-formula><mml:math id="M55" 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>). <inline-formula><mml:math id="M56" display="inline"><mml:mi>h</mml:mi></mml:math></inline-formula> represents the
thickness of the unconfined aquifers, which is the difference between the water
table and the upper confined bed and varies with water table changes (m). <inline-formula><mml:math id="M57" display="inline"><mml:mi>B</mml:mi></mml:math></inline-formula> is
the length of the groundwater unit (m) – here the value is 1 km. <inline-formula><mml:math id="M58" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mi mathvariant="normal">ga</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M59" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> represent the water table level of adjacent HRUs and the current HRU, respectively (m). <inline-formula><mml:math id="M60" display="inline"><mml:mi>D</mml:mi></mml:math></inline-formula> is the distance between the center of the current HRU and the centers of its adjacent HRUs (m). There are three types of groundwater boundary conditions: river head (when the boundary HRU, including the irrigation canal and the daily river flux, equals to the daily canal flux), river flux (when the boundary HRU, including the drainage ditches and the water heads in ditches, is assumed constant and equal to the river head), and constant flux (when the boundary HRU is mainly barren area and no irrigation is applied); thus, in our study, zero flux is assumed.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2"><?xmltex \currentcnt{2}?><label>Figure 2</label><caption><p id="d1e1433">Schematic diagram of groundwater lateral runoff exchange between HRUs.</p></caption>
            <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://hess.copernicus.org/articles/24/2399/2020/hess-24-2399-2020-f02.png"/>

          </fig>

      <p id="d1e1442">Based on the field-scale simulation, groundwater lateral exchange, canal
seepage, and groundwater drainage are added in the daily water and salt
balance calculations of each groundwater unit at the regional scale:
<?xmltex \hack{\newpage}?><?xmltex \hack{\vspace*{-6mm}}?>

                  <disp-formula specific-use="gather" content-type="numbered"><mml:math id="M61" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E11"><mml:mtd><mml:mtext>11</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mtable class="split" columnspacing="1em" rowspacing="0.2ex" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi mathvariant="normal">hg</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="normal">hg</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:mfenced open="(" close=")"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">y</mml:mi></mml:msub></mml:mrow></mml:mfenced><mml:mfenced open="(" close=""><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">wg</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">wg</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="normal">ext</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mfenced close="" open=""><mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi mathvariant="normal">grup</mml:mi><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi mathvariant="normal">grdown</mml:mi><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi mathvariant="normal">grleft</mml:mi><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi mathvariant="normal">grright</mml:mi><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mfenced open="" close=")"><mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi mathvariant="normal">ls</mml:mi><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi mathvariant="normal">as</mml:mi><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant="normal">g</mml:mi><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E12"><mml:mtd><mml:mtext>12</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mtable columnspacing="1em" class="split" rowspacing="0.2ex" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><?xmltex \hack{\hbox\bgroup\fontsize{9.5}{9.5}\selectfont$\displaystyle}?><mml:msub><mml:mi mathvariant="normal">SCa</mml:mi><mml:mi>i</mml:mi></mml:msub><?xmltex \hack{$\egroup}?></mml:mrow></mml:mtd><mml:mtd><mml:mrow><?xmltex \hack{\hbox\bgroup\fontsize{9.5}{9.5}\selectfont$\displaystyle}?><mml:mo>=</mml:mo><mml:msub><mml:mi>Z</mml:mi><mml:mi>a</mml:mi></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mi mathvariant="normal">Sa</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi mathvariant="normal">grup</mml:mi><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mi mathvariant="normal">Sa</mml:mi><mml:mrow><mml:mi mathvariant="normal">up</mml:mi><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi mathvariant="normal">grdown</mml:mi><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><?xmltex \hack{$\egroup}?></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><?xmltex \hack{\hbox\bgroup\fontsize{9.5}{9.5}\selectfont$\displaystyle}?><mml:mo>×</mml:mo><mml:msub><mml:mi mathvariant="normal">Sa</mml:mi><mml:mrow><mml:mi mathvariant="normal">down</mml:mi><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi mathvariant="normal">grleft</mml:mi><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mi mathvariant="normal">Sa</mml:mi><mml:mrow><mml:mi mathvariant="normal">left</mml:mi><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi mathvariant="normal">grright</mml:mi><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><?xmltex \hack{$\egroup}?></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><?xmltex \hack{\hbox\bgroup\fontsize{9.5}{9.5}\selectfont$\displaystyle}?><mml:mo>×</mml:mo><mml:msub><mml:mi mathvariant="normal">Sa</mml:mi><mml:mrow><mml:mi mathvariant="normal">right</mml:mi><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi mathvariant="normal">ls</mml:mi><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi mathvariant="normal">as</mml:mi><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mfenced><mml:mo>×</mml:mo><mml:msub><mml:mi mathvariant="normal">Is</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant="normal">g</mml:mi><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><?xmltex \hack{$\egroup}?></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><?xmltex \hack{\hbox\bgroup\fontsize{9.5}{9.5}\selectfont$\displaystyle}?><mml:mo>×</mml:mo><mml:msub><mml:mi mathvariant="normal">Sa</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">sg</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">sg</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:msub><?xmltex \hack{$\egroup}?><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

              where <inline-formula><mml:math id="M62" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">grup</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M63" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">grdown</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M64" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">grleft</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M65" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">grright</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> represent the daily groundwater lateral runoff per unit area into the current groundwater unit from the up, down, left, and right adjacent groundwater units, respectively (m d<inline-formula><mml:math id="M66" 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>). SCa is the daily soluble salt content in the saturated zone below the transmission soil profile (mg m<inline-formula><mml:math id="M67" 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="M68" 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>). <inline-formula><mml:math id="M69" display="inline"><mml:mrow><mml:msub><mml:mi>Z</mml:mi><mml:mi>a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the thickness of the saturated zone, which is the difference between the groundwater table depth and the depth that groundwater table fluctuations largely cannot reach (m). <inline-formula><mml:math id="M70" display="inline"><mml:mrow><mml:msub><mml:mi>Z</mml:mi><mml:mi>a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> only affects the soluble salt concentration in the groundwater salt balance, while it has no effect on the water balance and groundwater fluctuation simulation. Sa, Sa<inline-formula><mml:math id="M71" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">up</mml:mi></mml:msub></mml:math></inline-formula>, Sa<inline-formula><mml:math id="M72" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">down</mml:mi></mml:msub></mml:math></inline-formula>, Sa<inline-formula><mml:math id="M73" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">left</mml:mi></mml:msub></mml:math></inline-formula>, and
Sa<inline-formula><mml:math id="M74" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">right</mml:mi></mml:msub></mml:math></inline-formula> represent the salt concentration of the current groundwater unit and the up, down, left, and right adjacent groundwater units, respectively (mg m<inline-formula><mml:math id="M75" 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>). “Is” represents the salt concentration of the irrigation water (mg m<inline-formula><mml:math id="M76" 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>). <inline-formula><mml:math id="M77" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> represents the specific yield (–), which is the ratio of the volume of water that can be drained by gravity to the total volume of the saturated soil/aquifer. “ext” is the daily groundwater extraction per unit area (m d<inline-formula><mml:math id="M78" 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>). <inline-formula><mml:math id="M79" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">wg</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the daily percolation water depth to groundwater from the potential root zone (m d<inline-formula><mml:math id="M80" 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 <inline-formula><mml:math id="M81" display="inline"><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mi mathvariant="normal">wg</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the daily water depth supplied to the potential root zone from shallow groundwater due to the rising capillary action (m d<inline-formula><mml:math id="M82" 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>). <inline-formula><mml:math id="M83" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">sg</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M84" display="inline"><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mi mathvariant="normal">sg</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are the quantity of soluble salt in <inline-formula><mml:math id="M85" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">wg</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M86" display="inline"><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mi mathvariant="normal">wg</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, respectively (mg m<inline-formula><mml:math id="M87" 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="M88" 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>). The detailed calculations of the water and salt
exchange components between unsaturated soil and groundwater, such as <inline-formula><mml:math id="M89" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">wg</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M90" display="inline"><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mi mathvariant="normal">wg</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, were described in our previous field-scale water productivity model (Xue et al., 2018).</p>
</sec>
<sec id="Ch1.S2.SS1.SSS5">
  <label>2.1.5</label><title>Field-scale irrigation water productivity module</title>
      <p id="d1e2258">Cropping patterns are complex for each HRU, and sometimes HRUs include
uncultivated land, forest land, and other nonagricultural land. In our
model, using a high-resolution land use map, different cropping patterns can be
separated to simulate soil water and salt processes as well as the responses of ET
and crop yields to the water and salt content of root zone. Here, we employed
our previously developed field IWP model to simulate field water, salt, ET, and crop yield under shallow groundwater conditions (Xue et al., 2018). The
soil profile is vertically divided into four soil zones: the current root
zone, the potential root zone, the transmission zone, and the saturated
zone. In each HRU, the soil water and salt balance processes and the water
productivity are independently<?pagebreak page2404?> simulated for each cropping pattern under its
corresponding groundwater unit condition. For uncultivated lands, only water
and salt balance are simulated, and the IWP is zero. The water and salt
exchange between unsaturated soil and groundwater of different cropping
patterns are then weight-averaged by area proportion. Finally, the weighted
averages are used to update the daily groundwater table and salinity (Fig. 3).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3" specific-use="star"><?xmltex \currentcnt{3}?><label>Figure 3</label><caption><p id="d1e2263">Schematic diagram of coupling soil water and salt dynamics and
groundwater level and salinity. The IWP evaluation in each HRU is also shown.</p></caption>
            <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/articles/24/2399/2020/hess-24-2399-2020-f03.png"/>

          </fig>

</sec>
</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>Module coupling and flowchart calculation</title>
      <p id="d1e2281">The simulation was run using a daily temporal step and a HRU spatial step. The
irrigation system module simulates the canal seepage to the groundwater and the
field irrigation water amount; the canal seepage to the groundwater is the
recharge of the groundwater module, whereas the field irrigation water amount
is the input of the field IWP module. The drainage system module simulates
the groundwater drainage to drainage ditches, which is the discharge from the
groundwater module. The groundwater module is used to simulate the
groundwater table depth, which is the input for the field IWP module and also
the input for the drainage module. In the field-scale IWP module, the deep
percolation to groundwater under different cropping patterns is simulated
independently, and the weighted average value is the recharge of the groundwater
module. The salt exchange is simulated along with the water exchange. The
groundwater module is used to simulate the groundwater lateral movement
between the current HRU and its adjacent HRUs to update the groundwater
level at the next time step. By coupling the irrigation system module, the drainage
system module, and the groundwater module with the field IWP model, this RIWP
model simulates the temporal and spatial distribution of the IWP over the whole
irrigation area from the beginning to the end of the growing season.</p>
      <p id="d1e2284">The model was implemented using a combination of ArcGIS, MATLAB, and Microsoft
Excel (Fig. 4). The HRUs were created in ArcGIS using Create Fishnet, with each grid numbered. In MATLAB, the HRUs were represented using a matrix, and the daily
time step was represented using a vector. At each time step, all of the HRUs were
traversed by a nested loop. The updated information for the current
time step was then used to calculate the next time step. Microsoft Excel stored the
ArcGIS vector layer and its attribute data for MATLAB modeling, and it also
stored MATLAB output results for ArcGIS analysis and visualization.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4" specific-use="star"><?xmltex \currentcnt{4}?><label>Figure 4</label><caption><p id="d1e2289">Procedure chart for the regional irrigation water productivity simulation.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/articles/24/2399/2020/hess-24-2399-2020-f04.png"/>

        </fig>

      <p id="d1e2299">Considering the high spatial heterogeneity, meteorological data need to be
collected from all of the weather stations within or close to the study area.
The distribution of soil physical properties, moisture, and salinity in
unsaturated soil, and the groundwater table depth and salinity need to be collected
from many observation sites, which are uniformly or randomly spread over the
study area. Each data set can then be interpolated in ArcGIS using inverse
distance weighting to obtain a spatial distribution vector layer. For each
layer, the average value in each HRU is calculated by ArcGIS using
geometric division statistics. The vector layer of the irrigation control zones
and the vector layer of drainage control zones are overlaid with
the HRU division layer in ArcGIS, respectively, to obtain the HRU numbers controlled by
each irrigation control zone and each drainage control zone, respectively. The HRU numbers
controlled by the same zone are stored in the same matrix for batch
simulation in MATLAB. In MATLAB, the soil water and salt balances and the field-scale IWP for main crops are simulated simultaneously for each HRU, whereas
groundwater lateral exchange is simulated between adjacent HRUs. At the end
of the model simulation, soil moisture and salinity, groundwater table depth
and salinity, ET, crop yield, and IWP for different land use types in each
HRU can be obtained. The area proportion-weighted average in each HRU
can then be imported into ArcGIS to visualize the spatial distribution.</p>
</sec>
<sec id="Ch1.S2.SS3">
  <label>2.3</label><title>Model evaluation</title>
      <p id="d1e2311">We will provide a case study using the abovementioned new RIWP model in order to
test its applicability; we will also provide a sensitivity analysis of the
parameters.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5" specific-use="star"><?xmltex \currentcnt{5}?><label>Figure 5</label><caption><p id="d1e2316">Location of the Jiefangzha Irrigation District.</p></caption>
          <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://hess.copernicus.org/articles/24/2399/2020/hess-24-2399-2020-f05.png"/>

        </fig>

<sec id="Ch1.S2.SS3.SSS1">
  <label>2.3.1</label><title>Description of study area and data</title>
      <p id="d1e2332">As a typical subdistrict of the Hetao Irrigation District, the Jiefangzha
Irrigation District (JFID) is a typical arid irrigated area with shallow
groundwater that has resulted from its arid continental climate, years of flood
irrigation, and poor drainage systems (Fig. 5). Located on the Hetao Plain,
the JFID is very flat with an average slope of 0.02 % from southeast to
northwest (Xu, 2011). The mean annual precipitation is only 155 mm, 70 % of which  occurs between July to September, and the mean annual potential evaporation is 1938 mm. The mean annual temperature is 7<inline-formula><mml:math id="M91" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>, with the respective lowest and highest monthly average being <inline-formula><mml:math id="M92" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">10.1</mml:mn></mml:mrow></mml:math></inline-formula> and 23.8<inline-formula><mml:math id="M93" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> in January and July. The JFID covers an area of <inline-formula><mml:math id="M94" display="inline"><mml:mrow><mml:mn mathvariant="normal">22</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mn mathvariant="normal">4</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> ha, 66 % of which is irrigated farmland area. Wheat, maize, and sunflower are the main crops in this region, comprising more than 90 % of the irrigated farmland area. The <inline-formula><mml:math id="M95" display="inline"><mml:mrow><mml:mn mathvariant="normal">12</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mn mathvariant="normal">8</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> m<inline-formula><mml:math id="M96" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> <inline-formula><mml:math id="M97" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">yr</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> of irrigation water is diverted from the Yellow River. Due to the poor maintenance of drainage ditches, it is quite common for poor drainage situations to exist in this area. Therefore, the annual average groundwater table depth ranges from 1.5 to 3.0 m during the crop growing season. Soils in the JFID are spatially heterogeneous and are primarily composed of silt loam in the northern region and sandy loam in the southern region. The shallow groundwater table and strong evaporation makes soil salinization a very serious problem in this area, and salinization is becoming the main constraint on crop production.</p>
      <p id="d1e2417">An irrigation and drainage network includes 4 main irrigation canals,
16 submain irrigation canals, 5 main drainage ditches, and 12
submain drainage ditches that control the<?pagebreak page2405?> water movement in the JFID
(Fig. 5). The streambed depths of the regional main, submain, and lateral
ditches were collected by a regional survey in 2016. Daily water flow data
from the main and submain irrigation canals and monthly data from the five main
drainage ditches were obtained from the local irrigation administration
bureau. A total of 55 groundwater observation wells are installed in the
JFID (Fig. 5). The groundwater level was measured on the 1st, 6th, 11th, 16th, 21st, and 26th of each month, and groundwater salinity was measured three times each month. Near the groundwater observation wells, soil moisture was measured four times, and soil electrical conductivity was measured once before wheat sowing and once before autumn irrigation. Due to the spatially homogeneous climate in the JFID, daily meteorological data (air temperature, humidity, wind speed, and precipitation) were obtained from the Hangjinghouqi weather station for the calculation of the regional reference ET.</p>
      <p id="d1e2420">HJ-1A, HJ-1B, and Landsat NDVI images from 2006 to 2013 with a 30 m resolution were downloaded from the official website of the CERSDA (2013) and the USGS (2013) in order to determine the annual cropping pattern distributions. Due to the lack of measured ET values, the ET values estimated by the SEBAL model using MODIS images from NASA (2013) were utilized as a reference for comparison with the simulated ET values (Bastiaanssen et al., 2003b).</p><?xmltex \hack{\newpage}?>
</sec>
<?pagebreak page2406?><sec id="Ch1.S2.SS3.SSS2">
  <label>2.3.2</label><title>Parameterization of the distributed RIWP model</title>
      <p id="d1e2433">The JFID was divided into 2485 1 km <inline-formula><mml:math id="M98" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 1 km HRUs (Fig. S1a in the
Supplement). In terms of boundary conditions, the upper Quaternary aquifer layer was regarded as the phreatic layer in the model. It was modeled as an aquitard with loamy soil. From north to south, the thickness of the aquifer in the JFID varied from 2 to 20 m with an average of 7.4 m (Bai and Xu, 2008). Thus, the initial value of the average thickness of unconfined aquifer was set as 7.4 m. The water level contour maps of the JFID from 1997 to 2002 from Bai (2008) were used to determine the direction of water flow near the groundwater boundary. Based on the topography conditions, land use types, the locations of the main canals and ditches, and the directions of water flow, the regional phreatic layer was divided into five zones with river, drainage, and impervious boundary conditions (Fig. S1b).</p>
      <p id="d1e2443">The JFID was divided into four irrigation control sections and five drainage
control sections, and each section was controlled by one main irrigation canal
or one main drainage ditch. These sections were further divided into 48 irrigation control subareas and 17 drainage control subareas, and each
subarea was controlled by one submain irrigation canal or one submain
drainage ditch (Fig. S2). Sunflower fields, wheat fields, maize fields,
and uncultivated lands were the four cropping patterns, i.e., land use types,
in the RIWP model. When considering the irrigation schedule applied, many other studies on distributed hydrological
models simply set the sowing and
irrigation of a particular crop as occurring on the same day over the
whole study area, which may be a simplification of actual conditions (Singh,
2005). In our study, the irrigation time and the amount of irrigation water for each
HRU were co-determined by both the local irrigation schedule of the three
main crops and the actual water amount flowing into the fields.</p>
      <p id="d1e2446">The simulation period was from 1 April to 20 September, which covers the growing seasons of all of the three main crops. The initial crop parameters were set as the default values suggested for sunflower, wheat, and maize by Allen et al. (1998). The empirical values of the regional canal utilization and the ditch drainage coefficient were obtained from the Jiefangzha administration.</p>
</sec>
<sec id="Ch1.S2.SS3.SSS3">
  <label>2.3.3</label><title>Model calibration and validation</title>
      <p id="d1e2457">To comprehensively evaluate the accuracy and reliability of the model, the
data from 2010 to 2013 and from 2006 to 2009 were used as the
calibration and validation datasets, respectively. The daily measured soil moisture content of the crop root zone (<inline-formula><mml:math id="M99" display="inline"><mml:mi mathvariant="italic">θ</mml:mi></mml:math></inline-formula>), the electrical conductivity of soil water (EC), and
the groundwater table depth (<inline-formula><mml:math id="M100" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) and groundwater salinity, were calibrated using measured data from the 22 soil water and salt observation sites and 55 groundwater observation sites (Fig. 5) mentioned in Sect.  2.3.1. The regional ET simulated by RIWP for each HRU was calibrated using the remote-sensing-based ET images obtained once<?pagebreak page2407?> every 8 d. The regional
drainage processes was calibrated using the monthly groundwater drainage data
from main ditches, in which the simulated drainage of each main ditch was
the sum of the drainage of its controlling HRUs. Overall, the soil hydraulic
parameters, the crop water productivity-related coefficient, and the canal
conveyance and ditch drainage parameters were all calibrated using observed
data from 2010 to 2013 and then validated with observed data from 2006 to 2009.</p>
      <p id="d1e2478">To quantify the model performance, the root-mean-square error (RMSE), the
Nash and Sutcliffe model efficiency (NSE), and the coefficient of
determination (<inline-formula><mml:math id="M101" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>) were used as the indicators. The RMSE was used to
measure the deviation of simulated values from measured values, the NSE is
commonly used to verify the credibility of the hydrological model, and
<inline-formula><mml:math id="M102" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> represented the degree of linear correlation. The indicators were
calculated as follows:

                  <disp-formula specific-use="gather" content-type="numbered"><mml:math id="M103" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E13"><mml:mtd><mml:mtext>13</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mrow><mml:mi mathvariant="normal">RMSE</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mfenced close="]" open="["><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><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:mi>n</mml:mi></mml:munderover><mml:msup><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mi mathvariant="normal">Output</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="normal">Output</mml:mi><mml:mi mathvariant="normal">o</mml:mi></mml:msub></mml:mrow></mml:mfenced><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow><mml:mi>n</mml:mi></mml:mfrac></mml:mstyle></mml:mfenced><mml:mn mathvariant="normal">0.5</mml:mn></mml:msup></mml:mrow></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E14"><mml:mtd><mml:mtext>14</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mrow><mml:mi mathvariant="normal">NSE</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><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:mi>n</mml:mi></mml:munderover><mml:msup><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Output</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="normal">Output</mml:mi><mml:mi mathvariant="normal">o</mml:mi></mml:msub></mml:mrow></mml:mfenced><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow><mml:mrow><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:mi>n</mml:mi></mml:munderover><mml:msup><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Output</mml:mi><mml:mi mathvariant="normal">o</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="normal">Output</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub></mml:mrow></mml:mfenced><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E15"><mml:mtd><mml:mtext>15</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mtable columnspacing="1em" class="split" rowspacing="0.2ex" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><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:mi>n</mml:mi></mml:munderover><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Output</mml:mi><mml:mi mathvariant="normal">o</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mover accent="true"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Output</mml:mi><mml:mi mathvariant="normal">o</mml:mi></mml:msub></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:mrow></mml:mfenced><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mi mathvariant="normal">Output</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mover accent="true"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Output</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:msqrt><mml:mrow><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:mi>n</mml:mi></mml:munderover><mml:msup><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Output</mml:mi><mml:mi mathvariant="normal">o</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mover accent="true"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Output</mml:mi><mml:mi mathvariant="normal">o</mml:mi></mml:msub></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:mrow></mml:mfenced><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:msqrt><mml:msqrt><mml:mrow><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:mi>n</mml:mi></mml:munderover><mml:msup><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mi mathvariant="normal">Output</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mover accent="true"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Output</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:mrow></mml:mfenced><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:msqrt></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

              where <inline-formula><mml:math id="M104" display="inline"><mml:mi>n</mml:mi></mml:math></inline-formula> is the number of simulations; Output<inline-formula><mml:math id="M105" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:math></inline-formula> and Output<inline-formula><mml:math id="M106" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">o</mml:mi></mml:msub></mml:math></inline-formula> are the simulated and observed values of model outputs, respectively; and <inline-formula><mml:math id="M107" display="inline"><mml:mover accent="true"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Output</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:math></inline-formula> and
<inline-formula><mml:math id="M108" display="inline"><mml:mover accent="true"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Output</mml:mi><mml:mi mathvariant="normal">o</mml:mi></mml:msub></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:math></inline-formula> are the average values of the simulated and observed model outputs, respectively. The RMSE indicates a perfect match between observation and simulation values when it equals 0, and increasing RMSE values indicate an increasingly poor match. Singh et al. (2005) stated that RMSE values less than 50 % of the standard deviation of the observed data could be considered low enough to be an indicator of a good model prediction. With a range between <inline-formula><mml:math id="M109" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mi mathvariant="normal">∞</mml:mi></mml:mrow></mml:math></inline-formula> and 1, the NSE indicates a perfect match between observed and predicted values when it is equal to 1. Values between 0 and 1 are generally considered to be an acceptable level of performance, whereas values less than 0.0 indicate that the simulation is worse than taking an average of the observation values, which indicates unacceptable performance. The <inline-formula><mml:math id="M110" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>, which ranges between 0 and 1, describes the proportion of the variance in the observed data, and higher values indicate less error variance. Typically, an <inline-formula><mml:math id="M111" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> value higher than 0.5 is considered acceptable (Santhi et al., 2001).</p>
</sec>
<sec id="Ch1.S2.SS3.SSS4">
  <label>2.3.4</label><title>Global sensitivity analysis</title>
      <p id="d1e2882">To find the key parameters significantly impacting the model output, a
global sensitivity analysis was conducted. The analysis related the changes
in three output variables – RIWP, the groundwater table depth, and the groundwater
salinity – to eight parameters in the RIWP model. Latin hypercube
sampling (LHS; please see Mckay et al., 1979; Muleta and Nicklow, 2005; Wang et al., 2008 for detailed descriptions of the sampling method), which is a typical sampling method for sensitivity and uncertainty analysis, was used to sample the parameter space. Following Dai (2011), the test number was set as 20, more than double the parameter number (which was 8), in order to ensure that the test points were evenly distributed in space and to guarantee the accuracy of the test. For uniform distributions, the parameter range was subdivided into 20 equal intervals. Each interval was sampled only once to generate random values of the possible parameter sets. The possible parameter value ranges referred to the local measurements, the survey data, and relevant research papers. Additionally, considering the spatial heterogeneity of the three output variables, 22 evenly distributed groundwater observation sites in the JFID were selected for the global sensitivity analysis. Based on the LHS method, 20 groups of parameter combinations were obtained, and the simulation was run 20 times. Finally, the sensitivity of the three output variables to the eight parameters were determined in SPSS Statistics. The absolute values of the standardized regression coefficients (SRCs) obtained
quantified the significance of each parameter to each output variable (Table 1; Cannavó, 2012), and the plus or minus sign of the SRCs indicated the positive or negative correlations between the corresponding parameter and output variable pairs.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T1"><?xmltex \currentcnt{1}?><label>Table 1</label><caption><p id="d1e2888">The significance level of the input parameter to the model output
variables.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="2">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">SRC value</oasis:entry>
         <oasis:entry colname="col2">Significance level</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M112" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.8</mml:mn><mml:mo>≤</mml:mo><mml:mo>|</mml:mo><mml:mi mathvariant="normal">SRC</mml:mi><mml:mo>|</mml:mo><mml:mo>≤</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Very important</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M113" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.5</mml:mn><mml:mo>≤</mml:mo><mml:mo>|</mml:mo><mml:mi mathvariant="normal">SRC</mml:mi><mml:mo>|</mml:mo><mml:mo>≤</mml:mo><mml:mn mathvariant="normal">0.8</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Important</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M114" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.3</mml:mn><mml:mo>≤</mml:mo><mml:mo>|</mml:mo><mml:mi mathvariant="normal">SRC</mml:mi><mml:mo>|</mml:mo><mml:mo>≤</mml:mo><mml:mn mathvariant="normal">0.5</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Unimportant</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M115" display="inline"><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mo>≤</mml:mo><mml:mo>|</mml:mo><mml:mi mathvariant="normal">SRC</mml:mi><mml:mo>|</mml:mo><mml:mo>≤</mml:mo><mml:mn mathvariant="normal">0.3</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Irrelevant</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

</sec>
</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Results and discussion</title>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Model performance</title>
      <p id="d1e3040">Good agreement was obtained by the RIWP model in simulating the IWP and hydrological components during the calibration and validation periods. Table 2 shows the calibrated<?pagebreak page2408?> parameters describing crop growth and water
usage, and Table 3 shows the possible variation ranges and calibrated
values of the parameters describing the soil hydraulic characteristics and the irrigation and drainage system. The agreement between the observed and
simulated soil moisture content in the crop root zone in both the calibration (Fig. 6a; RMSE of 2.867 cm<inline-formula><mml:math id="M116" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> cm<inline-formula><mml:math id="M117" 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>, NSE of 0.330, and  <inline-formula><mml:math id="M118" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> of 0.502) and validation (Fig. 6b; RMSE of 2.989 cm<inline-formula><mml:math id="M119" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> cm<inline-formula><mml:math id="M120" 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>, NSE of 0.232, and <inline-formula><mml:math id="M121" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> of 0.548) indicates the reasonable performance of the RIWP model. The good performance of the RIWP model was also indicated by the simulation of the soil salt content in both the calibration (Fig. 6c; RMSE of 1.108 dS m<inline-formula><mml:math id="M122" 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>, NSE of 0.612, and <inline-formula><mml:math id="M123" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> of 0.657) and validation (Fig. 6d; RMSE of 1.205 dS m<inline-formula><mml:math id="M124" 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>, NSE of 0.525, and <inline-formula><mml:math id="M125" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> of 0.590). The simulated and observed groundwater table depth (Fig. 6e: RMSE of 0.786 m, NSE of 0.424, and <inline-formula><mml:math id="M126" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> of 0.509 in calibration; Fig. 6f: RMSE of 0.667 m, NSE of 0.637, and <inline-formula><mml:math id="M127" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> of 0.504 in validation) and groundwater salinity (Fig. 6g: RMSE of less than 10 %, NSE of 0.813, and <inline-formula><mml:math id="M128" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> of 0.815 in calibration; Fig. 6h: RMSE of less than 10 %, NSE of 0.604, and <inline-formula><mml:math id="M129" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> of 0.730 in validation) at 55 observation sites are also in good agreement.</p>

      <?xmltex \floatpos{p}?><fig id="Ch1.F6" specific-use="star"><?xmltex \currentcnt{6}?><label>Figure 6</label><caption><p id="d1e3201">Relationship between the simulated and measured values during the
crop growing season in the calibration and validation periods, respectively.</p></caption>
          <?xmltex \igopts{width=497.923228pt}?><graphic xlink:href="https://hess.copernicus.org/articles/24/2399/2020/hess-24-2399-2020-f06.png"/>

        </fig>

      <p id="d1e3210">The model did not perform very well with respect to simulating groundwater drainage. The
overestimated drainage (Fig. 6i, j) was due to the different operating
conditions of the drainage ditches of different orders. The reader may recall that we
classified the main, submain, and lateral drainage ditches into first-,
second-, and third-order ditches, respectively. In the model, for each year,
we adopt the same drainage coefficient for all of the ditches of the different
orders, assuming well-operated conditions. However, the actual operating
conditions of the ditches of the different orders cannot be the same,
resulting in the simulation discrepancy.</p>
      <p id="d1e3214">The ET simulated by the RIWP model (ET<inline-formula><mml:math id="M130" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">IWP</mml:mi></mml:msub></mml:math></inline-formula>) and the ET estimated by the SEBAL model using MODIS images (ET<inline-formula><mml:math id="M131" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">RS</mml:mi></mml:msub></mml:math></inline-formula>) agree well both in calibration (RMSE of 1.918 mm, NSE of 0.274, and <inline-formula><mml:math id="M132" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> of 0.561) and in validation (RMSE of 2.132 mm, NSE of 0.189, and <inline-formula><mml:math id="M133" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> of 0.498) (Fig. 6l). Furthermore, the comparison of the spatial distribution of cumulative ET<inline-formula><mml:math id="M134" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">IWP</mml:mi></mml:msub></mml:math></inline-formula> and ET<inline-formula><mml:math id="M135" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">RS</mml:mi></mml:msub></mml:math></inline-formula> during the crop growth season showed that ET<inline-formula><mml:math id="M136" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">IWP</mml:mi></mml:msub></mml:math></inline-formula> was lower than ET<inline-formula><mml:math id="M137" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">RS</mml:mi></mml:msub></mml:math></inline-formula> in the uncultivated area, while they agreed well in farmland (Fig. S3). The uncultivated area, which was merely bare soil, accounted for about 34 % of the JFID, and the ET<inline-formula><mml:math id="M138" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">IWP</mml:mi></mml:msub></mml:math></inline-formula> of the uncultivated area was merely soil evaporation; this resulted in the underestimation of actual ET in the uncultivated area compared with the ET acquired by remote sensing images, which was consistent with previous studies (Singh, 2005; Tian et al., 2015). Moreover, the cumulative ET<inline-formula><mml:math id="M139" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">RS</mml:mi></mml:msub></mml:math></inline-formula> was calculated based on eight images of daily ET on eight satellite acquisition dates; thus, using the non-representative ET<inline-formula><mml:math id="M140" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">RS</mml:mi></mml:msub></mml:math></inline-formula> above the average daily value may also result in the underestimation of ET<inline-formula><mml:math id="M141" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">IWP</mml:mi></mml:msub></mml:math></inline-formula>.</p>
      <p id="d1e3331">To test the model performance under different cropping patterns, one
representative site was selected for each cropping pattern to compare the
observed and simulated time series of the groundwater table depth (Fig. 7).
Results indicated that the model can adequately capture the groundwater
dynamics at the four representative sites. Occasionally, the simulated
groundwater table depth declined quickly, while the observed value rose. This
was most likely due to the fact that we ignored the time lag between
groundwater recharge from soil and deep percolation. In the uncultivated
area (Fig. 7a), the simulated groundwater table level presented a slower and more
flat decreasing trend than the measured value. By assuming a completely
nonvegetated coverage condition in the uncultivated area, although this is not
actually the case, the estimated groundwater evapotranspiration driven by
capillarity action will become lower than its actual value; small
vegetation, in comparison, transpires amounts of water from the soil, and soil moisture is
relatively low, meaning that groundwater evapotranspiration is higher.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F7" specific-use="star"><?xmltex \currentcnt{7}?><label>Figure 7</label><caption><p id="d1e3336">The comparison of the simulated and measured groundwater table depth
for four typical sites during the crop growing season from 2006 to 2013. Panel <bold>(a)</bold> shows the uncultivated area from 2006 to 2013; panel <bold>(b)</bold> shows the uncultivated area from 2006 to 2008 and the sunflower field and maize field from 2009 to 2013; panels <bold>(c)</bold> and <bold>(d)</bold>  show the sunflower, wheat, and maize fields from 2006 to 2013.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/articles/24/2399/2020/hess-24-2399-2020-f07.png"/>

        </fig>

      <?xmltex \floatpos{p}?><fig id="Ch1.F8"><?xmltex \currentcnt{8}?><label>Figure 8</label><caption><p id="d1e3359">Parameter sensitivity analysis results of the model for the three output
variables: <bold>(a)</bold> irrigation water productivity, <bold>(b)</bold> groundwater table depth, and <bold>(c)</bold> groundwater salinity.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://hess.copernicus.org/articles/24/2399/2020/hess-24-2399-2020-f08.png"/>

        </fig>

</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Global sensitivity analysis</title>
      <p id="d1e3385">Recall that a global sensitivity analysis was carried out to determine the sensitivity
of the three output variables to the eight parameters. The three output
variables were RIWP, groundwater table depth, and groundwater salinity,
and the eight parameters were those parameters describing soil hydraulic
characteristics and irrigation and drainage system, as shown in Table 3.
The specific yield (<inline-formula><mml:math id="M142" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) and the soil evaporation coefficient (<inline-formula><mml:math id="M143" display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) were the two key parameters influencing the RIWP (Fig. 8a). The specific yield indicated the readily available soil moisture released to the crop root zone from the shallow aquifer under capillary action for crop consumption. Thus, its significant positive influence on the RIWP was explained. The soil evaporation coefficient indicated the proportion of water that was transferred into the atmosphere but was not used by crops. Therefore, a significant negative impact on the RIWP was expected from this parameter. We concluded that the effect of the
groundwater contribution on the IWP would sometimes be greater than that of the irrigation water depth applied for a
shallow groundwater area such as the JFID. Applying lots of shallow irrigation to crops may
reduce the deep percolation and decrease unbeneficial water use due to
evaporation. Applying less and deeper irrigation water will result
in deeper percolation, while a greater groundwater contribution will be
beneficial for crop water use. Thus, compared with applying lots of shallow irrigation, a deeper irrigation schedule involving less water may have greater affect
on the IWP in arid regions with shallow groundwater. For both groundwater
table depth (Fig. 8b) and groundwater salinity (Fig. 8c), specific yield was
the only key parameter. Canal seepage was expected be the cause of the variation in the
groundwater table depth around the canal at the local scale. However, the
results indicated that the variation in the groundwater table depth was
more susceptible to the local groundwater properties, i.e., the specific yield,
than to canal seepage at the regional scale. We speculate that lateral
groundwater movement might compensate for the variation in the groundwater table
depth caused by the canal seepage. Moreover, salt moves with water; thus, the
variation in groundwater salinity was also dominated by the specific yield.
Due to the high sensitivity of the IWP, the groundwater table depth, and the salinity to
the specific yield, it is highly recommended to use spatially variable
values of the specific yield rather than a constant value as a model input if it
is available. This could greatly enhance the evaluation accuracy of the
RIWP model. Furthermore, it is indicated that the permeability coefficient of
unconfined aquifers (<inline-formula><mml:math id="M144" display="inline"><mml:mi>K</mml:mi></mml:math></inline-formula>) did not significantly affect the IWP, groundwater
table depth, or<?pagebreak page2411?> salinity. Due to the lack of measurement data in our study,
we adopted a unified <inline-formula><mml:math id="M145" display="inline"><mml:mi>K</mml:mi></mml:math></inline-formula> value for the whole study area, which also make the
model simulations reasonable, as they are insensitive to this parameter.</p>
</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><title>Regional irrigation water productivity</title>
<sec id="Ch1.S3.SS3.SSS1">
  <label>3.3.1</label><title>The spatial distribution of irrigation water productivity</title>
      <p id="d1e3439">Validated by the measured soil moisture and salinity, the groundwater table
depth and salinity, and the drainage water depth and ET, specifically the 2006–2013 time series of the groundwater table depth under the four cropping patterns, the RIWP model developed can be used to estimate the spatial distribution of IWP for the three main crops over the period from 2006 to 2013 (Fig. 9). Note that these IWP values were based on the simulated water balance and crop yields of individual HRUs, which may deviate to a certain extent from the real values. However, the values can still represent the utilization of water resources at the regional scale. We note that there are “red HRUs” in Fig. 9 that change with time and space due to the different irrigation water depths applied under different groundwater conditions. Even different crop species can result in a big difference in the IWP. As we mentioned previously, the spatial distribution of these three crops is very complex in the JFID, and the field plot is small; thus, we use remote sensing data to obtain the cropping pattern map with a 30 m <inline-formula><mml:math id="M146" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 30 m resolution. Every HRU has these three crops; therefore, we can simulate the IWP for each main crop in every HRU. The RIWP of the three main crops showed a declining trend during the period from 2006 to 2010 (Fig. 9a, b, c, d, e).This was mainly attributed to the increasing irrigation quota, as the excess water lowered the IWP. During the period from 2011 to 2013 (Fig. 9f, g, h), in contrast, the RIWP of the three main crops showed an increasing trend. This was because the irrigation quota was reduced over this period, and the contribution of groundwater compensated for the crop yield losses. When less irrigation water is applied, the number of red HRUs will increase.</p>

      <?xmltex \floatpos{p}?><fig id="Ch1.F9" specific-use="star"><?xmltex \currentcnt{9}?><label>Figure 9</label><caption><p id="d1e3451"> </p></caption>
            <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://hess.copernicus.org/articles/24/2399/2020/hess-24-2399-2020-f09-part01.png"/>

          </fig>

      <?xmltex \floatpos{p}?><fig id="Ch1.F10" specific-use="star"><?xmltex \currentcnt{9}?><label>Figure 9</label><caption><p id="d1e3462">Spatial distribution of irrigation water productivity for the three
main crops from 2006 to 2013. Each line shows the RIWP for each
year in ascending order. The left, middle, and right columns show the RIWP of
wheat, sunflower, and maize, respectively.</p></caption>
            <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://hess.copernicus.org/articles/24/2399/2020/hess-24-2399-2020-f09-part02.png"/>

          </fig>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T2" specific-use="star"><?xmltex \currentcnt{2}?><label>Table 2</label><caption><p id="d1e3475">Calibrated crop parameters for wheat, sunflower, and maize for the regional irrigation water productivity model.</p></caption><oasis:table frame="topbot"><?xmltex \begin{scaleboxenv}{.91}[.91]?><oasis:tgroup cols="4">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:thead>
       <oasis:row>

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

         <oasis:entry rowsep="1" namest="col2" nameend="col4" align="center">Calibrated value </oasis:entry>

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

         <oasis:entry colname="col1"/>

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

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

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

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

         <oasis:entry colname="col1">Rate of yield decrease per unit of excess salts, <inline-formula><mml:math id="M147" display="inline"><mml:mi>b</mml:mi></mml:math></inline-formula> (% md S<inline-formula><mml:math id="M148" 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">7.1</oasis:entry>

         <oasis:entry colname="col3">12</oasis:entry>

         <oasis:entry colname="col4">12</oasis:entry>

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

         <oasis:entry colname="col1">Average fraction of total available water (TAW) that can be depleted from the root zone before moisture stress, <inline-formula><mml:math id="M149" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> (–)</oasis:entry>

         <oasis:entry colname="col2">0.55</oasis:entry>

         <oasis:entry colname="col3">0.45</oasis:entry>

         <oasis:entry colname="col4">0.55</oasis:entry>

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

         <oasis:entry colname="col1">Crop coefficient at crop initial stage, <inline-formula><mml:math id="M150" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">c</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> (–)</oasis:entry>

         <oasis:entry colname="col2">0.3</oasis:entry>

         <oasis:entry colname="col3">0.3</oasis:entry>

         <oasis:entry colname="col4">0.3</oasis:entry>

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

         <oasis:entry colname="col1">Crop coefficient at crop development stage, <inline-formula><mml:math id="M151" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">c</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> (–)</oasis:entry>

         <oasis:entry colname="col2">0.73</oasis:entry>

         <oasis:entry colname="col3">0.8</oasis:entry>

         <oasis:entry colname="col4">0.75</oasis:entry>

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

         <oasis:entry colname="col1">Crop coefficient at mid-season stage, <inline-formula><mml:math id="M152" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">c</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> (–)</oasis:entry>

         <oasis:entry colname="col2">1.15</oasis:entry>

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

         <oasis:entry colname="col4">1.2</oasis:entry>

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

         <oasis:entry colname="col1">Crop coefficient at late season stage, <inline-formula><mml:math id="M153" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">c</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> (–)</oasis:entry>

         <oasis:entry colname="col2">0.4</oasis:entry>

         <oasis:entry colname="col3">0.7</oasis:entry>

         <oasis:entry colname="col4">0.6</oasis:entry>

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

         <oasis:entry colname="col1">Yield response factor, <inline-formula><mml:math id="M154" display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (–)</oasis:entry>

         <oasis:entry colname="col2">1.15</oasis:entry>

         <oasis:entry colname="col3">0.95</oasis:entry>

         <oasis:entry colname="col4">1.25</oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col1">Electrical conductivity of the saturation extract at the threshold of EC<inline-formula><mml:math id="M155" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:math></inline-formula> when crop yield first</oasis:entry>

         <oasis:entry colname="col2" morerows="1">5</oasis:entry>

         <oasis:entry colname="col3" morerows="1">1.7</oasis:entry>

         <oasis:entry colname="col4" morerows="1">2</oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col1">drops below <inline-formula><mml:math id="M156" display="inline"><mml:mrow><mml:msub><mml:mi>Y</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> at the late season stage, EC<inline-formula><mml:math id="M157" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">et</mml:mi></mml:msub></mml:math></inline-formula> (dS m<inline-formula><mml:math id="M158" 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:tbody>
   </oasis:tgroup><?xmltex \end{scaleboxenv}?></oasis:table></table-wrap>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T3" specific-use="star"><?xmltex \currentcnt{3}?><label>Table 3</label><caption><p id="d1e3789">The possible parameter variation ranges and calibrated
values of the parameters that were collected to describe the soil hydraulic characteristics
(<inline-formula><mml:math id="M159" display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M160" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M161" display="inline"><mml:mi>K</mml:mi></mml:math></inline-formula>) and the irrigation and drainage system (<inline-formula><mml:math id="M162" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">lc</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M163" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">fc</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M164" 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>, <inline-formula><mml:math id="M165" display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math id="M166" display="inline"><mml:mi>m</mml:mi></mml:math></inline-formula>).</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="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"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1">Parameters</oasis:entry>
         <oasis:entry colname="col2">Description</oasis:entry>
         <oasis:entry rowsep="1" namest="col3" nameend="col4" align="center">Value range </oasis:entry>
         <oasis:entry colname="col5">Calibrated value</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3">Min</oasis:entry>
         <oasis:entry colname="col4">Max</oasis:entry>
         <oasis:entry colname="col5"/>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M171" display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Soil evaporation coefficient (–)</oasis:entry>
         <oasis:entry colname="col3">0.1</oasis:entry>
         <oasis:entry colname="col4">0.35</oasis:entry>
         <oasis:entry colname="col5">0.25</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M172" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">lc</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Water utilization coefficient of lateral canal (–)</oasis:entry>
         <oasis:entry colname="col3">0.81</oasis:entry>
         <oasis:entry colname="col4">0.91</oasis:entry>
         <oasis:entry colname="col5">0.88</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M173" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">fc</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Water utilization coefficient of field canal (–)</oasis:entry>
         <oasis:entry colname="col3">0.81</oasis:entry>
         <oasis:entry colname="col4">0.86</oasis:entry>
         <oasis:entry colname="col5">0.89</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M174" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Specific yield (–)</oasis:entry>
         <oasis:entry colname="col3">0.02</oasis:entry>
         <oasis:entry colname="col4">0.15</oasis:entry>
         <oasis:entry colname="col5">0.15</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M175" 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></oasis:entry>
         <oasis:entry colname="col2">Drainage coefficient (–)</oasis:entry>
         <oasis:entry colname="col3">0.02</oasis:entry>
         <oasis:entry colname="col4">0.06</oasis:entry>
         <oasis:entry colname="col5">0.03</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M176" display="inline"><mml:mi>K</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Permeability coefficient of unconfined aquifers (mm d<inline-formula><mml:math id="M177" 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="col3">731</oasis:entry>
         <oasis:entry colname="col4">12 701</oasis:entry>
         <oasis:entry colname="col5">1150</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M178" display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Soil water permeability coefficient (–)</oasis:entry>
         <oasis:entry colname="col3">0.7</oasis:entry>
         <oasis:entry colname="col4">3.4</oasis:entry>
         <oasis:entry colname="col5">3.4</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M179" display="inline"><mml:mi>m</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Soil water permeability exponent (–)</oasis:entry>
         <oasis:entry colname="col3">0.3</oasis:entry>
         <oasis:entry colname="col4">0.5</oasis:entry>
         <oasis:entry colname="col5">0.5</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table><table-wrap-foot><p id="d1e3869">Note: The parameter value ranges were collected from local measurements, survey data, and relevant research results. The soil texture of canal bed was silty sandy loam for depths of 0–1 and 2–3 m below the ground and sandy loam for a depth of 1–2 m. For silty sandy loam soil, the bulk density and saturated soil water conductivity were 502.3 mm d<inline-formula><mml:math id="M167" 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 1.42 g cm<inline-formula><mml:math id="M168" 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. For sandy loam soil, the bulk density and saturated soil water conductivity were 1.49 g cm<inline-formula><mml:math id="M169" 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> and 592.6 mm d<inline-formula><mml:math id="M170" 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>, respectively. There was fine sand and sandy soil in the phreatic layer.</p></table-wrap-foot></table-wrap>

      <?pagebreak page2414?><p id="d1e4189">Under a given irrigation water distribution, the spatial distribution of ET
was the key factor controlling the RIWP distribution. The spatial
distribution of ET was also fundamentally determined by the solar energy as well as the
water and salt dynamics of soil. Recall that the climate and, therefore, the
solar energy, was homogeneous in the JFID. The spatial heterogeneity of
RIWP must then be attributed to the water and salt heterogeneity caused by the
spatial heterogeneity of the cropping pattern, the groundwater table depth, and the
irrigation and drainage networks. Particularly, when the farmlands had
a limited supply of irrigation water, the groundwater table depth and salinity
played an important role with respect to the IWP. Groundwater
could drain both water and salt out of the field through the drainage ditches; thus, groundwater evapotranspiration decreased, and the soluble salt content involved in groundwater evapotranspiration also decreased as well. Despite the negative effect of draining water on the IWP, draining
salt out of the field will positively affect the IWP. As we see from Fig. 9,
the simulated IWP values for three crops were lower in the south, west,
north, and northwest of the JFID than in the other regions. The south of the
JFID is the main canal for water diversion, which provides a higher irrigation
quota than other regions and results in a lower IWP. The west of
the JFID, in contrast, is mainly uncultivated area; thus, the IWP is lower than in the other
regions. In the northwest of the JFID, the main drainage ditch received the
drainage water with a high saline content from the four submain ditches and
drained all the way to the north of the region. Ditch seepage water with high
salinity resulted in severe soil salinization in the north and
northwest of the JFID, which will restrict the crop growth and lower the IWP.
Thus, appropriate groundwater drainage management and dealing with salt
accumulation at the end of main drainage ditches in irrigated areas is
also a pressing and unsolved problem with respect to increasing the red HRUs, which
needs to be solved by irrigation managers.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F11" specific-use="star"><?xmltex \currentcnt{10}?><label>Figure 10</label><caption><p id="d1e4194"><bold>(a)</bold> Simulated regional irrigation water productivity under various groundwater table depth (<inline-formula><mml:math id="M180" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) conditions with the application of different irrigation water amounts (<inline-formula><mml:math id="M181" display="inline"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>); <bold>(b)</bold> the results of the statistical analysis. In Fig.10a, W, S, and M represent wheat, sunflower, and maize, respectively.</p></caption>
            <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/articles/24/2399/2020/hess-24-2399-2020-f10.png"/>

          </fig>

      <p id="d1e4230">As the JFID is the major food-producing region of China, improving water productivity
means greater food crop yields with less water usage,
based on local or regional potential. With declining access to water
resources, farmers will need to grow different crops to maintain or increase
crop production profitability in the future. A comparison of the RIWP values
of different crops (comparison of the three columns in Fig. 9) showed that maize
had the highest IWP, wheat had the lowest IWP, and the IWP of sunflower was
in between. Therefore, modestly increasing the planting area of maize
will improve the crop production per unit of irrigation water. In
addition, the RIWP of sunflower is a little higher than that of wheat, and
the salt tolerance of sunflower is much higher than
that of wheat. Thus, planting sunflowers should be promoted in the JFID
if the amount of irrigation water available declines in the future;
this practice will definitely increase the red HRUs.</p><?xmltex \hack{\newpage}?>
</sec>
<?pagebreak page2415?><sec id="Ch1.S3.SS3.SSS2">
  <label>3.3.2</label><title>The impact of the irrigation water depth applied and the groundwater table depth on the irrigation water productivity</title>
      <?pagebreak page2416?><p id="d1e4242">In arid shallow groundwater areas, the irrigation water productivity (IWP) is
affected by the irrigation water depth (IWD) applied and the groundwater table depth (<inline-formula><mml:math id="M182" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>). In all of the four simulated <inline-formula><mml:math id="M183" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> ranges, the IWP decreased when the IWD increased (Fig. 10a), which are findings consistent with Huang et al. (2005). Moreover, the magnitude of the IWP decrease per unit increase of IWD was different for different <inline-formula><mml:math id="M184" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> ranges. The magnitude of the IWP decrease for a shallower <inline-formula><mml:math id="M185" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> was smaller than that for a deeper <inline-formula><mml:math id="M186" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. This effect of increasing <inline-formula><mml:math id="M187" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> on the relationship between IWP and IWD was consistent with Gao et al. (2017). The above results indicate that groundwater can help meet the crop water demand when irrigation water is insufficient. However, when irrigation water is excessive, a large proportion will eventually drain through the drainage ditches, and the IWP will decrease. Additionally, among the four <inline-formula><mml:math id="M188" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> ranges, the highest IWP was obtained between 2 and 3 m (Fig. 10b), which was consistent with Xue et al. (2018). This indicates that a <inline-formula><mml:math id="M189" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> deeper than the abovementioned depth provides insufficient water
for crop growth, whereas a <inline-formula><mml:math id="M190" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> shallower than 2–3 m  will increase the root zone soil salinity and the salt stress of crops. The negative effect of shallow groundwater salinity can also be seen in Fig. 10a when <inline-formula><mml:math id="M191" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is less than 2 m; this indicates that when the amount of irrigation applied decreases from 300 <inline-formula><mml:math id="M192" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> IWD<inline-formula><mml:math id="M193" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 400 mm to 200 <inline-formula><mml:math id="M194" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> IWD <inline-formula><mml:math id="M195" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 300 mm, it leads to decreases in the IWP, which is caused by the faster reduction of ET than the irrigation applied. The shallow groundwater contribution will make up for the ET reduction when a smaller amount of irrigation water is applied; thus, another reason exists to accelerate the reduction of ET. We deduced that less irrigation water will weaken the role of irrigation on salt leaching and result in more severe salinization in the crop root zone. The negative effect of salt stress on the crop water use is greater than the positive effect of the shallow groundwater contribution on the crop water use in this situation. Thus, keeping the groundwater table depth within the optimal range and sustainable is of great importance to reach a higher crop IWP at the regional scale, and irrigation managers may need to reasonably determine the irrigation quota and constantly maintain the drainage system. Groundwater sustainability includes spacing withdrawals to avoid excessive depletion and taking measures to safeguard or improve groundwater quality. To achieve this, regional irrigation managers may need to undertake monitoring efforts to establish historic and current conditions, carry out research to model groundwater systems, forecast future variation, and create policy to manage activities influencing the groundwater table and groundwater quality.</p>
</sec>
</sec>
</sec>
<sec id="Ch1.S4" sec-type="conclusions">
  <label>4</label><title>Conclusions</title>
      <p id="d1e4395">In view of the heterogeneous conditions of irrigated areas, and fully
considering the supply, consumption, and drainage processes of irrigation water and groundwater, a distributed RIWP model was developed to couple the irrigation water flow processes along main canals and the drainage processes, the water and salt transport processes in soil profile, the groundwater water and salt lateral transport, and the agricultural water productivity module. In particular, a new method was designed and incorporated to couple regional soil hydrology process and groundwater flow with the spatial difference of the cropping pattern. Taking advantage of remote sensing and GIS tools, the quantitative distributed RIWP model requires fewer soil and groundwater hydraulic parameters and crop growing parameters, and it needs only readily available data from several observation sites at the regional scale; moreover, regional water and salt process can be simulated on a daily time step. Despite the simplifications involved, the proposed methods of irrigation canal and drainage ditch digitization and groundwater–runoff lateral exchange simulation between grids means that the spatial IWP is simulated in a real distributed way, instead of using a field-scale model applied in a
distributed mode to simulate all simulation units independently. The
calibration and validation results indicate good  RIWP
model performance in this typical study area, and the spatial distribution of IWP for
different crops can be produced.</p>
      <p id="d1e4398">As it was programmed in MATLAB (Mathworks Inc., 2011), the RIWP model can be run on different operating systems. Furthermore, the model includes the capability for the parallelization of simulations to reduce batch run times when conducting simulations over large areas, conditions, and/or time periods. In the near future, enabling the code to be linked quickly with other disciplinary models to support integrated water resource management could be a great improvement over the current RIWP model. Furthermore, we plan to develop a website that can be used for the long-term distribution of the RIWP model and associated documentation. Finally, the RIWP model could improve the knowledge of best practices to enhance water productivity for key irrigation decision-makers. The simplicity of the RIWP model with respect to its required minimum input data, which are readily available or can easily be collected, also makes it user-friendly. Furthermore, it is a very useful model for scenario simulations and for planning purposes, and it can be used by economists, water administrators, and managers working in arid irrigated areas with shallow groundwater.</p>
</sec>

      
      </body>
    <back><notes notes-type="dataavailability"><title>Data availability</title>

      <p id="d1e4406">The JFID water budget simulation results from the simulation period in this study are available from the authors upon request (jiyxue@ucdavis.edu).</p>
  </notes><app-group>
        <supplementary-material position="anchor"><p id="d1e4409">The supplement related to this article is available online at: <inline-supplementary-material xlink:href="https://doi.org/10.5194/hess-24-2399-2020-supplement" xlink:title="pdf">https://doi.org/10.5194/hess-24-2399-2020-supplement</inline-supplementary-material>.</p></supplementary-material>
        </app-group><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e4418">JYX and ZLH conceived the idea to develop the conceptual RIWP model for an irrigated area in an arid region with shallow groundwater and complex cropping patterns. JYX wrote the RIWP model programming code used in this study in MATLAB. JYX collected and processed the multiple datasets with help from SW, GHH, and XX and prepared the paper. The results were extensively commented on and discussed by ZLH, IW, IK, ZPS, and CZW.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e4424">The authors declare that they have no conflict of interest.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e4430">This study was supported by the National Key Research and Development
Program of China (grant no. 2017YFC0403301), the National Natural Science<?pagebreak page2417?> Foundation
of China (grant nos. 51679236 and 51639009), and the International Postdoctoral Exchange
Fellowship Program from the Office of China Postdoctoral Council (grant no. 20180044).
Special thanks also go to the adminstration of the Hetao Irrigation District and the
Shahaoqu experimental station for providing information and data.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d1e4435">This research has been supported by the National Key Research and Development Program of China (grant no. 2017YFC0403301), the National Natural Science Foundation of China (grant nos. 51679236 and 51639009), and the International Postdoctoral Exchange Fellowship Program from the Office of China Postdoctoral Council (grant no. 20180044).</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e4441">This paper was edited by Pieter van der Zaag and reviewed by Zhongyi Qu and one anonymous referee.</p>
  </notes><ref-list>
    <title>References</title>

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    <!--<article-title-html>A novel regional irrigation water productivity model coupling irrigation- and drainage-driven soil hydrology and salinity dynamics and shallow groundwater movement in arid regions in China</article-title-html>
<abstract-html><p>The temporal and spatial distributions of regional irrigation water
productivity (RIWP) are crucial for making decisions related to agriculture,
especially in arid irrigated areas with complex cropping patterns. Thus, in this study, we
developed a new RIWP model for an irrigated agricultural area with complex
cropping patterns. The model couples the irrigation- and drainage-driven soil water and salinity dynamics and shallow groundwater movement in order to quantify the temporal and spatial distributions of the target hydrological and biophysical variables. We divided the study area into 1&thinsp;km&thinsp; × &thinsp;1&thinsp;km hydrological response units (HRUs). In each HRU, we considered four land use types: sunflower fields, wheat fields, maize fields, and uncultivated lands (bare soil). We coupled the regional soil hydrological processes and groundwater flow by taking a weighted average of the water exchange between unsaturated soil and groundwater under different land use types. The RIWP model was calibrated and validated using 8 years of hydrological variables obtained from regional observation sites in a typical arid irrigation area in North China, the Hetao Irrigation District. The model simulated soil moisture and salinity reasonably well as well as groundwater table depths and salinity. However, overestimations of groundwater discharge were detected in both the calibration and validation due to the assumption of well-operated drainage ditch conditions; regional evapotranspiration (ET) was reasonably estimated, whereas ET in the uncultivated area was slightly underestimated in the RIWP model. A sensitivity analysis indicated that the soil evaporation coefficient and the specific yield were the key parameters for the RIWP simulation. The results showed that the RIWP decreased from maize to sunflower to wheat from 2006 to 2013. It was also found that the maximum RIWP was reached when the groundwater table depth was between 2 and 4&thinsp;m, regardless of the irrigation water depth applied. This implies the importance of groundwater table control on the RIWP. Overall, our distributed RIWP model can effectively simulate the temporal and spatial distribution of the RIWP and provide critical water allocation suggestions for decision-makers.</p></abstract-html>
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