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<article xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:oasis="http://docs.oasis-open.org/ns/oasis-exchange/table" xml:lang="en" dtd-version="3.0">
  <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-23-4891-2019</article-id><title-group><article-title>Spatial variability of mean daily estimates of actual evaporation from
remotely sensed imagery and surface reference data</article-title><alt-title>Spatial variability of mean daily estimates of actual evaporation</alt-title>
      </title-group><?xmltex \runningtitle{Spatial variability of mean daily estimates of actual evaporation}?><?xmltex \runningauthor{R.~N.~Armstrong et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1 aff2">
          <name><surname>Armstrong</surname><given-names>Robert N.</given-names></name>
          <email>r.armstrong1@uq.edu.au</email>
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Pomeroy</surname><given-names>John W.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-4782-7457</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Martz</surname><given-names>Lawrence W.</given-names></name>
          
        </contrib>
        <aff id="aff1"><label>1</label><institution>Centre for Hydrology, University of Saskatchewan, Saskatoon, S7N 1K2, Canada</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Queensland Alliance for Agriculture and Food Innovation, The
University of Queensland, <?xmltex \hack{\break}?> Gatton Campus, Gatton, 4343, Australia</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Robert N. Armstrong (r.armstrong1@uq.edu.au)</corresp></author-notes><pub-date><day>29</day><month>November</month><year>2019</year></pub-date>
      
      <volume>23</volume>
      <issue>12</issue>
      <fpage>4891</fpage><lpage>4907</lpage>
      <history>
        <date date-type="received"><day>30</day><month>November</month><year>2018</year></date>
           <date date-type="rev-request"><day>12</day><month>December</month><year>2018</year></date>
           <date date-type="rev-recd"><day>2</day><month>October</month><year>2019</year></date>
           <date date-type="accepted"><day>16</day><month>October</month><year>2019</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2019 Robert N. Armstrong et al.</copyright-statement>
        <copyright-year>2019</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/23/4891/2019/hess-23-4891-2019.html">This article is available from https://hess.copernicus.org/articles/23/4891/2019/hess-23-4891-2019.html</self-uri><self-uri xlink:href="https://hess.copernicus.org/articles/23/4891/2019/hess-23-4891-2019.pdf">The full text article is available as a PDF file from https://hess.copernicus.org/articles/23/4891/2019/hess-23-4891-2019.pdf</self-uri>
      <abstract><title>Abstract</title>
    <p id="d1e106">Land surface evaporation has considerable spatial variability that
is not captured by point-scale estimates calculated from meteorological data
alone. Knowing how evaporation varies spatially remains an important issue
for improving parameterisations of land surface schemes and hydrological
models and various land management practices. Satellite-based and aerial
remote sensing has been crucial for capturing moderate- to larger-scale
surface variables to indirectly estimate evaporative fluxes. However, more
recent advances for field research via unmanned aerial vehicles (UAVs) now allow
for the acquisition of more highly detailed surface data.</p>
    <p id="d1e109">Integrating models that can estimate “actual” evaporation from higher-resolution imagery and surface reference data would be valuable to better examine potential impacts of local variations in evaporation on upscaled estimates. This study introduces a novel approach for computing a normalised ratiometric index from surface variables that can be used to obtain more-realistic distributed estimates of actual evaporation. For demonstration purposes the Granger–Gray evaporation model (Granger and Gray, 1989) was applied at a rolling prairie agricultural site in central Saskatchewan, Canada. Visible and thermal images and meteorological reference data required to parameterise the model were obtained at midday.</p>
    <p id="d1e112">Ratiometric indexes were computed for the key surface variables albedo and
net radiation at midday. This allowed point observations of albedo and mean
daily net radiation to be scaled across high-resolution images over a large
study region. Albedo and net radiation estimates were within 5 %–10 % of measured values. A daily evaporation estimate for a grassed surface was 0.5 mm (23 %) larger than eddy covariance measurements. Spatial variations in key factors driving evaporation and their impacts on upscaled evaporation estimates are also discussed. The methods applied have two key advantages for estimating evaporation over previous remote-sensing approaches: (1) detailed daily estimates of actual evaporation can be directly obtained using a physically based evaporation model, and
(2) analysis of more-detailed and more-reliable evaporation estimates may lead to improved methods for upscaling evaporative fluxes to larger areas.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Background and introduction</title>
      <p id="d1e124">“Actual” evaporation is the water vapour physically transferred from a
surface (e.g. plants, soil, or water) to the atmosphere over a given time
period (e.g. hourly or daily). Reliable estimates of actual evaporation are
often needed over large spatial scales for applications such as water
resource management, agriculture, ecology, and forecast modelling of weather
and climate. However, estimates (or measurements) are often calculated at
point scales with footprints that can range from centimetres to several
kilometres or more (Brutsaert, 1982). Consequently, point-scale footprints
in heterogeneous landscapes may contain large variability that needs to be
considered more appropriately.</p>
      <p id="d1e127">From an ecological standpoint, heterogeneous landscapes are comprised of
distinct topographic features, land cover types, biological attributes, and
other physical properties that exhibit observable patterns in the order of
metres (e.g. Yates et al., 2006; Zhang and Guo, 2007). Therefore, variable
surface properties and state conditions exert a strong control on<?pagebreak page4892?> local
surface energy fluxes. As a result, “scaling” evaporation estimates over
large areas must consider a potential loss of information due to upscaling
processes. The potential impacts of spatial variability on larger-scale
estimates of evaporation are still not well understood, and previous
estimation and scaling methods have not examined this issue in detail.</p>
      <p id="d1e130">For example, hydrologic and atmospheric modelling applications often require
large- to regional-scale evaporation estimates, but the underlying variability
is difficult to examine practically (e.g. Avvisar and Pielke, 1989;
Baldocchi et al., 2005; Brutsaert, 1998; Claussen, 1991, 1995; Klaassen, 1992; Klaassen and Claussen, 1995). Courault et al. (2005) and Gowda et al. (2007) have also reviewed remote-sensing approaches which integrate surface images to derive key variables needed to parameterise various energy-balance-type evaporation models. This generally results in estimates at moderate scales of input images (e.g. Bisht et al., 2005). Purely empirical methods have also correlated evaporation with vegetation indices (e.g. Nagler et al., 2005).</p>
      <p id="d1e133">A common remote-sensing method has been to calculate evaporation indirectly
as a residual of a simplified energy balance (e.g. Jackson et al., 1977;
Seguin et al., 1989; Bussières et al., 1996). In such cases surface
temperatures derived from thermal imagery is a critical input. More complex
resistance-type formulations also exist based on developments by Monteith (1965), e.g. Norman et al. (1995), Anderson et al. (1997, 2007), Boegh et al. (2002) and Houborg and Soegaard (2004). However, such approaches are computationally intensive and parameterising the resistance terms is difficult without detailed data.</p>
      <p id="d1e137">Colaizzi et al. (2006) reviewed scaling approaches based on an evaporative
fraction determined through complex solar-radiation modelling. Mu et al. (2007) and Fisher et al. (2008) discuss advanced methods for deriving global-scale estimates based on expert knowledge and detailed data sets obtained from the AmeriFlux network in association with the global FLUXNET (Baldocchi et al., 2001). As an alternative to more complex methods, Granger (2000) integrated a complementary feedback approach with Penman's combination model and remote-sensing imagery that can directly estimate actual evaporation, even in data-sparse regions.</p>
      <p id="d1e140">Previous remote-sensing methods have been valuable for integrating
generalised representations of moderate- to larger-scale variability.
However, most methods fail to include fundamental interactions governing the
evaporation process which can be more realistically captured with an energy
balance and aerodynamic combination model approach. More importantly, few
(if any) have addressed the issue of how detailed surface variability may
impact upscaled evaporation estimates over larger areas. The acquisition of
high-resolution imagery from a plane (or even unmanned aerial vehicles;
UAVs) combined with new methods of obtaining detailed surface information
could be valuable for examining the spatial variability of point-scale
evaporation estimates. Such analysis could then help advance understanding
how the underlying surface variability may impact upscaling of point
evaporation estimates to larger areas.</p>
      <p id="d1e143">The goal of this study is to examine the spatial variability of key surface
variables driving point-scale evaporation estimates and their impact on
upscaled evaporation estimates to larger areas, and this includes two objectives.
The first is to use the spatial variability captured from high-resolution
one-time-of-day visible and thermal images taken at midday to scale (i.e. distribute) energy-balance factors that drive combination evaporation
models. This objective required the development of a scaling method that
derives a ratiometric index of surface variables from the midday images. The
resulting information can then be used to distribute a measured value of
mean daily net radiation which can be used as an input for deriving detailed
estimates of evaporation. The second objective is to examine impacts of
variations of the key surface variables on daily estimates of evaporation,
including point-scale and larger areal estimates.</p>
      <p id="d1e146">Methods applied here integrated high-spatial-resolution images with an
initial pixel size of less than 5 m taken during a flight on 5 August 2007
over a rolling prairie agricultural landscape. It also included point
measurements of surface reference data, a physically based evaporation
model, and analysis using ArcGIS (v9.x) software. Estimates of mean daily
actual evaporation were calculated with the Granger–Gray complementary feedback model (G–D) (1989). The model is a useful alternative to more
complex methods that require resistance parameters and is well suited for a
variety of Canadian environments (e.g. agricultural, prairie, and boreal).</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Study area</title>
      <p id="d1e157">A case study was conducted on 5 August 2007 at St. Denis National Wildlife
Area (SDNWA) located in the parkland ecoregion of the Canadian Prairies in
central Saskatchewan (see Armstrong et al., 2008). Figure 1 shows a photo of
the study region taken during the study flight on 5 August to capture visible
and thermal images from handheld cameras. The landscape was characterised
by hummocky, gently rolling terrain and a few slopes of 1 %–10%. Elevations ranged from 540 to 565 m, and the land use consisted of mixed
cool-season grasses, tall brome grass, cultivated land, and wetlands
surrounded by trees or dense grass; all grasses and crops were <inline-formula><mml:math id="M1" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> types. The soil region is classified as dark-brown chernozem, and the soil texture is predominately silty loam (van der Kamp et al., 2003).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1"><?xmltex \currentcnt{1}?><label>Figure 1</label><caption><p id="d1e173">Photo of the study area at St. Denis National Wildlife Area taken during the flight on 5 August 2007 and locations of micrometeorological measurement stations.</p></caption>
        <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://hess.copernicus.org/articles/23/4891/2019/hess-23-4891-2019-f01.png"/>

      </fig>

<?xmltex \hack{\newpage}?>
</sec>
<?pagebreak page4893?><sec id="Ch1.S3">
  <label>3</label><title>Data and methods</title>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Granger–Gray evaporation model (G–D model)</title>
      <p id="d1e199">Granger and Gray (1989) developed the G–D model from the complementary
relationship of the combination model of Bouchet (1963) and Penman (1948). The
G–D model extends the potential evaporation model to non-saturated surfaces
using the relative evaporation term, <inline-formula><mml:math id="M2" display="inline"><mml:mi>G</mml:mi></mml:math></inline-formula>. This is defined as a ratio of actual to potential evaporation which depends on the relative drying power of the air, <inline-formula><mml:math id="M3" display="inline"><mml:mi>D</mml:mi></mml:math></inline-formula>. The underlying theory is based on the reduction of water availability as a surface dries, but the “potential” evaporation increases due to a subsequent rise in surface temperature.</p>
      <p id="d1e216">The development of <inline-formula><mml:math id="M4" display="inline"><mml:mi>G</mml:mi></mml:math></inline-formula> eliminated the need for observations of surface
temperature and vapour pressure. As a result, estimates of actual evaporation were obtainable for non-saturated surfaces with atmospheric data alone (Granger, 1989). The general form of the equation is
            <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M5" display="block"><mml:mrow><mml:mi>E</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>G</mml:mi><mml:mfenced open="(" close=")"><mml:mrow><mml:msup><mml:mi>Q</mml:mi><mml:mo>*</mml:mo></mml:msup><mml:mo>-</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:mfenced><mml:mo>+</mml:mo><mml:mi mathvariant="italic">γ</mml:mi><mml:mi>G</mml:mi><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">A</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>G</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="italic">γ</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          The available energy term is driven by net radiation, <inline-formula><mml:math id="M6" display="inline"><mml:mrow><mml:msup><mml:mi>Q</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> (W m<inline-formula><mml:math id="M7" 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>),
calculated as a sum of the net shortwave and longwave radiation components
and the ground heat flux, <inline-formula><mml:math id="M8" 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> (W m<inline-formula><mml:math id="M9" 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>), and the slope of the saturation vapour pressure curve, <inline-formula><mml:math id="M10" display="inline"><mml:mi mathvariant="normal">Δ</mml:mi></mml:math></inline-formula>.</p>
      <p id="d1e333">The aerodynamic term includes the psychrometric constant, <inline-formula><mml:math id="M11" display="inline"><mml:mi mathvariant="italic">γ</mml:mi></mml:math></inline-formula>, and
“drying power of the air”, <inline-formula><mml:math id="M12" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">A</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, calculated using a Dalton-type formula.
            <disp-formula id="Ch1.E2" content-type="numbered"><label>2</label><mml:math id="M13" display="block"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">A</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi>u</mml:mi><mml:mo>)</mml:mo><mml:mfenced open="(" close=")"><mml:mrow><mml:msubsup><mml:mi>e</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mo>*</mml:mo></mml:msubsup><mml:mo>-</mml:mo><mml:msub><mml:mi>e</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M14" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi>u</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is a vapour transfer function, and the atmospheric vapour pressure deficit at 2 m height is derived from <inline-formula><mml:math id="M15" display="inline"><mml:mrow><mml:msubsup><mml:mi>e</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mo>*</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> (saturated) and <inline-formula><mml:math id="M16" display="inline"><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (actual). Pomeroy et al. (1997) empirically derived <inline-formula><mml:math id="M17" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi>u</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> as a function of wind speed and aerodynamic roughness length and <inline-formula><mml:math id="M18" display="inline"><mml:mrow><mml:msub><mml:mi>Z</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (m) from extensive field data
collected for prairie, boreal forest, and northern cold-region environments
in western Canada.
            <disp-formula id="Ch1.E3" content-type="numbered"><label>3</label><mml:math id="M19" display="block"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi>u</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mn mathvariant="normal">8.19</mml:mn><mml:mo>+</mml:mo><mml:mn mathvariant="normal">22</mml:mn><mml:msub><mml:mi>Z</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mfenced close=")" open="("><mml:mrow><mml:mn mathvariant="normal">1.16</mml:mn><mml:mo>+</mml:mo><mml:mn mathvariant="normal">8</mml:mn><mml:msub><mml:mi>Z</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:mfenced><mml:mi>u</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M20" display="inline"><mml:mi>u</mml:mi></mml:math></inline-formula> is the mean daily wind speed (m s<inline-formula><mml:math id="M21" 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="d1e523">The G–D complementary feedback method is driven by the non-linear
relationship between <inline-formula><mml:math id="M22" display="inline"><mml:mi>G</mml:mi></mml:math></inline-formula> and the relative drying power of the air, <inline-formula><mml:math id="M23" display="inline"><mml:mi>D</mml:mi></mml:math></inline-formula>.
            <disp-formula id="Ch1.E4" content-type="numbered"><label>4</label><mml:math id="M24" display="block"><mml:mrow><mml:mi>G</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:mn mathvariant="normal">0.793</mml:mn><mml:mo>+</mml:mo><mml:mn mathvariant="normal">0.2</mml:mn><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mn mathvariant="normal">4.902</mml:mn><mml:mi mathvariant="normal">D</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:mn mathvariant="normal">0.006</mml:mn><mml:mi>D</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M25" display="inline"><mml:mi>D</mml:mi></mml:math></inline-formula> is a function of the humidity deficit and available energy is given by
            <disp-formula id="Ch1.E5" content-type="numbered"><label>5</label><mml:math id="M26" display="block"><mml:mrow><mml:mi>D</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">A</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">A</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mfenced close=")" open="("><mml:mrow><mml:msup><mml:mi>Q</mml:mi><mml:mo>*</mml:mo></mml:msup><mml:mo>-</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:mfenced></mml:mrow><mml:mi mathvariant="italic">λ</mml:mi></mml:mfrac></mml:mstyle></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          and <inline-formula><mml:math id="M27" display="inline"><mml:mi mathvariant="italic">λ</mml:mi></mml:math></inline-formula> is the latent heat of vaporisation (kJ kg<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>).</p>
      <p id="d1e652">The feedback model approach is generally applicable for regions indicated
above and can be used when detailed soil moisture information is lacking,
except under conditions of severe moisture stress. Armstrong et al. (2008)
evaluated point-scale evaporation estimates obtained with the G–D model over
mixed grasses at the same study area under conditions of non-limiting soil
moisture using field data collected during 2006. Estimates obtained with the
G–D model compared well with eddy covariance (EC) measurements and was less
data intensive than the Penman–Monteith model, which also performed well in
that study.</p>
      <p id="d1e655">Armstrong et al. (2010), however, found that the use of appropriate soil moisture
constraints was required to obtain reliable estimates with the G–D model
when applied under drought conditions to a mixed-prairie site at Lethbridge,
Alberta, Canada.</p>
</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Field observations</title>
      <p id="d1e666">Inputs needed to parameterise Eqs. (1)–(5) included mean daily net radiation, air temperature, humidity, wind speed, and surface roughness length. Outgoing radiation components were derived from high-resolution digital (Canon PowerShot A70 camera) and thermal (FLIR ThermaCAM P20 imaging
radiometer) images taken on 5 August 2007 during a Cessna flight at midday.
Meteorological and surface observations (radiation components, temperature,
humidity, and wind speed) were recorded at two station locations. Figure 1 shows
the relative locations, which included one reference site and one validation
site. An independent station operated by the National Water Research
Institute (Environment Canada, Saskatoon) was also available which provided
a second validation site for estimates of daily net radiation.<?pagebreak page4894?> Air
temperature, humidity, wind speed, incoming radiation, and surface
temperature were recorded as 15 min averages. Incoming and outgoing
shortwave and longwave radiation were measured with a CNR1 net radiometer
(Kipp &amp; Zonen, Delft, the Netherlands). Air temperature and humidity were
measured at 2 m height using a shielded Vaisala HMP45C (Campbell Scientific,
Inc., Logan, Utah, USA). A shielded Exergen infrared (IR) temperature sensor (IRTC; Exergen, Watertown, Massachusetts, USA) was used to measure surface temperature.</p>
      <p id="d1e669">Canopy spectral reflectance was independently sampled on 21 August 2007 for
validating albedo estimates derived from the visible images taken on 5 August. Canopy reflectance was collected according to the methods of Disney et al. (2004) and Zhang and Guo (2007). Samples were taken at 4.5 m intervals along a site transect at 1 m height at the nadir (25<inline-formula><mml:math id="M29" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> field of view) with an ASD FR Pro spectroradiometer (Analytical Spectral Devices, Inc., Boulder, Colorado, USA); the spectral range was 350–2500 nm with a 1 nm resolution. Samples were taken between 12:00 LT (local time) and solar noon. Reflectance was recalibrated every 10 min using a white Spectralon reflectance panel (Labsphere Inc., North Sutton, New Hampshire, USA).</p>
      <p id="d1e681">Eddy covariance observations were sampled at approximately 2 m height with a CSAT3
three-dimensional sonic anemometer (Campbell Scientific, Inc., Logan,
Utah, USA) and a KH20 ultraviolet krypton hygrometer (Campbell Scientific, Inc., Logan, Utah, USA). The raw EC data were reported as 15 min averages and
post-processing was done with MATLAB (Mathworks, Natick, Massachusetts, USA) which
included flux corrections using a standard planar-fit axis rotation
algorithm (Wilczak et al., 2001). Data filtering indicated there were no missing or bad data values on the study day, and station positioning was not considered to be an issue. EC data collected at the validation site were used for a comparison against a mean estimate obtained from the G–D model upwind of the EC station.</p>
      <p id="d1e684">Given the higher frequency of flux reporting (15 min averages), axis
rotation, and data filtering applied, and a potential mismatch in measurement
footprints, no further corrections were used to force an energy balance closure
on the 15 min averages.</p>
</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><title>Surface reference meteorological parameters</title>
      <p id="d1e695">At midday, reference observations of the shortwave, <inline-formula><mml:math id="M30" display="inline"><mml:mrow><mml:mi>K</mml:mi><mml:mo>↓</mml:mo></mml:mrow></mml:math></inline-formula> (835 W m<inline-formula><mml:math id="M31" 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>), and longwave, <inline-formula><mml:math id="M32" display="inline"><mml:mrow><mml:mi>L</mml:mi><mml:mo>↓</mml:mo></mml:mrow></mml:math></inline-formula> (320 W m<inline-formula><mml:math id="M33" 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>), irradiance and albedo (0.153 over grass) were obtained from the CNR1. Both <inline-formula><mml:math id="M34" display="inline"><mml:mrow><mml:mi>K</mml:mi><mml:mo>↓</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M35" display="inline"><mml:mrow><mml:mi>L</mml:mi><mml:mo>↓</mml:mo></mml:mrow></mml:math></inline-formula> were assumed to be uniform over the field given the images used for calculations were cloud free. The reference values were used in the calculation of midday normalised ratiometric indexes for albedo and net radiation. A mean daily reference value of 155 W m<inline-formula><mml:math id="M36" 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> was obtained for <inline-formula><mml:math id="M37" display="inline"><mml:mrow><mml:msup><mml:mi>Q</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> which was the input for distributing the final estimates of the mean daily net radiation using the ratiometric index (discussed in Sect. 3.4).</p>
      <p id="d1e786">The daily ground heat flux measured at two locations was relatively small, 8 and 2 W m<inline-formula><mml:math id="M38" 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>, due to the continuous and tall grass canopy
cover. For this study the ground heat flux was ignored, in part due to the
small measured values, but this was also to limit errors introduced from using a
numerical solution to estimate ground heat flux, which would require more-detailed cover information at each image pixel. To standardise the parameterisation of the G–D model for calculating the mean daily estimates of
evaporation, the reference values of mean daily air temperature  (19.6 <inline-formula><mml:math id="M39" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C), humidity deficit (1.1 kPa), and wind speed (3 m s<inline-formula><mml:math id="M40" 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>) were also taken to be uniform. Differences in mean daily air temperature between the measurement locations were approximately 1 <inline-formula><mml:math id="M41" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C.</p>
      <p id="d1e831">Potential impacts of assuming uniform humidity and wind speed for
parameterising the aerodynamic term was also considered. This was done by
examining G–D evaporation estimates derived from 2006 field data collected
over different surfaces at the same study area (Armstrong et al., 2008).
During 2006 a fixed station obtained continuous measurements over a mixed-grass upland, and a portable EC station was moved periodically to obtain
concurrent measurements over different land covers. Meteorological
observations from the fixed station were initially used to estimate
evaporation with the G–D model. Another estimate was obtained after
substituting observations of humidity and wind speed taken from the portable
EC station. This resulted in only minor variations in the respective
evaporation estimates (root mean square deviation (RMSD) of 0.02 mm) derived from the concurrent
measurements of humidity and wind speed taken from the different sites.</p>
      <p id="d1e834">Implications of neglecting the ground heat flux and treatment of the
meteorological parameters (above) with respect to modelling uncertainty are
given in the discussion.</p>
</sec>
<sec id="Ch1.S3.SS4">
  <label>3.4</label><title>Deriving key surface variables from one-time-of-day images</title>
<sec id="Ch1.S3.SS4.SSS1">
  <label>3.4.1</label><title>Theoretical basis for a normalised ratiometric index for surface properties</title>
      <?pagebreak page4895?><p id="d1e852">Remotely sensed images contain valuable information that characterise highly
variable surface properties (e.g. reflectance, temperature, RGB (red–green–blue) and
greyscale digital numbers (DNs), etc.). Theoretically, relative variations in these properties
can be quantified using a “normalised” ratiometric index. For example,
consider the “evaporation ratio” (<inline-formula><mml:math id="M42" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), defined simply as the ratios of individual evaporation rates at different spatial locations (<inline-formula><mml:math id="M43" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) to a reference rate obtained at a specified location (<inline-formula><mml:math id="M44" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">ref</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>).
              <disp-formula id="Ch1.E6" content-type="numbered"><label>6</label><mml:math id="M45" display="block"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">R</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">ref</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:math></disp-formula>
            <?xmltex \hack{\newpage}?><?xmltex \hack{\noindent}?>At the reference location <inline-formula><mml:math id="M46" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is 1 and will be the same at any other
locations where <inline-formula><mml:math id="M47" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">ref</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, but it will vary from unity at all other spatial locations.</p>
      <p id="d1e948">For obvious reasons the theory integrates well for computations with
pixel-based images. Subsequently, an evaporation rate measured at the
reference pixel could be scaled to all other pixels by multiplication with
the value of <inline-formula><mml:math id="M48" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> at each pixel. The concept may be extended to other surface variables (e.g. albedo, net radiation, etc.) required to parameterise an evaporation model.</p>
</sec>
<sec id="Ch1.S3.SS4.SSS2">
  <label>3.4.2</label><title>Distributing surface variables using a normalised index of relative surface ratios</title>
      <p id="d1e970">Methods described here assume spatial variations in surface variables
driving net radiation (and driving evaporation) are near their maximum
around solar noon. This is likely to be valid within 2 h from the actual
time of solar noon (Colaizzi et al., 2006). Net radiation is the major
component needed to determine available energy for the conversion of water
to an equivalent depth of water vapour. Net radiation is determined from the
shortwave and longwave radiation components measured in the electromagnetic
spectrum between approximately 0.3 and 4 and 4 and 14 <inline-formula><mml:math id="M49" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>m, respectively (Zoran and Stefan, 2006).</p>
      <p id="d1e981">Traditionally, radiative terms needed for estimating evaporation are derived
from satellite-based imagery, e.g. Landsat, AVHRR (Advanced Very High
Resolution Radiometer), and MODIS (Moderate Resolution Imaging
Spectroradiometer). However, satellite-based methods are often limited by
cloud contamination, varying spatial and temporal resolutions, and sensor
footprint mismatches. Under clear skies it can be assumed shortwave and
longwave irradiance are uniform over an agricultural field area. Very-high-resolution images taken near the surface could be used to derive the much
more variable surface-reflected shortwave and emitted longwave radiation
components.</p>
      <p id="d1e984">For example, normalised ratiometric indexes for albedo, <inline-formula><mml:math id="M50" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>,
emitted longwave, <inline-formula><mml:math id="M51" display="inline"><mml:mrow><mml:mi>L</mml:mi><mml:msub><mml:mo>↑</mml:mo><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, and roughness length, <inline-formula><mml:math id="M52" display="inline"><mml:mrow><mml:msub><mml:mi>Z</mml:mi><mml:mrow><mml:msub><mml:mn mathvariant="normal">0</mml:mn><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, can be calculated at every pixel location within visible and thermal images using

                  <disp-formula specific-use="align" content-type="numbered"><mml:math id="M53" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E7"><mml:mtd><mml:mtext>7</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:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">R</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">ref</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E8"><mml:mtd><mml:mtext>8</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:mi>L</mml:mi><mml:msub><mml:mo>↑</mml:mo><mml:mi mathvariant="normal">R</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi>L</mml:mi><mml:msub><mml:mo>↑</mml:mo><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mi>L</mml:mi><mml:msub><mml:mo>↑</mml:mo><mml:mi mathvariant="normal">ref</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E9"><mml:mtd><mml:mtext>9</mml:mtext></mml:mtd><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:msub><mml:mi>Z</mml:mi><mml:mrow><mml:msub><mml:mn mathvariant="normal">0</mml:mn><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>Z</mml:mi><mml:mrow><mml:msub><mml:mn mathvariant="normal">0</mml:mn><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>Z</mml:mi><mml:mrow><mml:msub><mml:mn mathvariant="normal">0</mml:mn><mml:mi mathvariant="normal">ref</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

              where the subscript “i” is an individual value at each pixel and “ref” is the value at the reference pixel. Incoming shortwave (<inline-formula><mml:math id="M54" display="inline"><mml:mrow><mml:mi>K</mml:mi><mml:mo>↓</mml:mo></mml:mrow></mml:math></inline-formula>) and longwave radiation (<inline-formula><mml:math id="M55" display="inline"><mml:mrow><mml:mi>L</mml:mi><mml:mo>↓</mml:mo></mml:mrow></mml:math></inline-formula>) components can reasonably be assumed to be uniform over the field under clear skies, so <inline-formula><mml:math id="M56" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and
<inline-formula><mml:math id="M57" display="inline"><mml:mrow><mml:mi>L</mml:mi><mml:msub><mml:mo>↑</mml:mo><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> can be further integrated to derive a ratiometric index of the midday net radiation, <inline-formula><mml:math id="M58" display="inline"><mml:mrow><mml:msubsup><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">R</mml:mi><mml:mo>*</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>.
<?xmltex \hack{\newpage}?><?xmltex \hack{\vspace*{-1mm}}?>
              <disp-formula id="Ch1.E10" content-type="numbered"><label>10</label><mml:math id="M59" display="block"><mml:mrow><mml:msubsup><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">R</mml:mi><mml:mo>*</mml:mo></mml:msubsup><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msubsup><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mo>*</mml:mo></mml:msubsup></mml:mrow><mml:mrow><mml:msubsup><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">ref</mml:mi><mml:mo>*</mml:mo></mml:msubsup></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:mi>K</mml:mi><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">α</mml:mi><mml:mi mathvariant="normal">R</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">ref</mml:mi></mml:msub></mml:mrow></mml:mfenced><mml:mo>+</mml:mo><mml:mi>L</mml:mi><mml:mo>↓</mml:mo><mml:mo>-</mml:mo><mml:mi>L</mml:mi><mml:msub><mml:mo>↑</mml:mo><mml:mi mathvariant="normal">R</mml:mi></mml:msub><mml:mi>L</mml:mi><mml:msub><mml:mo>↑</mml:mo><mml:mi mathvariant="normal">ref</mml:mi></mml:msub></mml:mrow></mml:math></disp-formula>
            Subsequently, single measured values of albedo and mean daily net radiation
taken at a reference pixel can be scaled (i.e. distributed) across all other
pixels via multiplication with the surface ratios derived for <inline-formula><mml:math id="M60" display="inline"><mml:mrow><mml:msubsup><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">R</mml:mi><mml:mo>*</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>. The next section illustrates the indexing method for deriving accurate estimates of albedo.</p>
</sec>
<sec id="Ch1.S3.SS4.SSS3">
  <label>3.4.3</label><title>Ratiometric-index method for albedo estimates from digital visible images</title>
      <p id="d1e1307">Surface albedo (<inline-formula><mml:math id="M61" display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula>) represents a crucial radiation loss term for
radiative transfer calculations and surface–atmosphere energy and mass
exchanges (Sellers et al., 1997; Liang, 2000; Lucht et al., 2000; Roberts, 2001; Liang et al., 2003; Disney et al., 2004). Its calculation can be complex and is typically a major source of uncertainty (Yang et al., 2008).</p>
      <p id="d1e1317">In this case, a measured value of broadband albedo obtained at a reference
pixel location could be scaled to every other pixel within a high-resolution
visible image. In 2007, digital photos were taken with a Canon PowerShot A70
camera with a maximum resolution of <inline-formula><mml:math id="M62" display="inline"><mml:mrow><mml:mn mathvariant="normal">2048</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">1536</mml:mn></mml:mrow></mml:math></inline-formula> pixels, a CCD (charge-coupled device)
imager, and a DIGIC (Digital Imaging Core) processor. This resulted in very-high-resolution (<inline-formula><mml:math id="M63" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> m pixels) “visible images” without cloud cover issues.</p>
      <p id="d1e1342">While digital cameras may not cover the full visible and near-infrared
spectrum of advanced measurement sensors, the imaging techniques are based
on the same principles. Corripio (2004) demonstrated how accurate estimates
of snow albedo could be obtained from digital images using a linear scaling
technique applied to a measured albedo at a reference pixel location. A key
step for our analysis was to transform an RGB digital photo to a single-band
8 bit greyscale image with DNs ranging from 0 to 255.</p>
      <p id="d1e1345">This resulted in higher DNs associated with more-reflective surfaces (i.e. brighter) and lower DNs with less-reflective surfaces (i.e. darker) in
accordance with the principles for calculating albedo. The resulting albedo map
was aggregated to a pixel size of 5 m for a practical analysis and
georectified to 100 GPS ground control points. The study area included some
dried wetlands and others containing open water. This allowed for
application of a simple dark-object subtraction (DOS) method to correct
potential atmospheric effects (Song et al., 2001; Liang, 2000).</p>
      <?pagebreak page4896?><p id="d1e1349">Applying Eq. (11) made it possible to accurately estimate albedo at individual pixel locations, <inline-formula><mml:math id="M64" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, from a measured broadband value taken at the reference location, <inline-formula><mml:math id="M65" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">ref</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, and a ratiometric index for DNs calculated at each pixel.
              <disp-formula id="Ch1.E11" content-type="numbered"><label>11</label><mml:math id="M66" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">ref</mml:mi></mml:msub><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi mathvariant="normal">DN</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="normal">DN</mml:mi><mml:mi mathvariant="normal">ref</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            where DN<inline-formula><mml:math id="M67" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:math></inline-formula> is the digital number of an individual pixel and DN<inline-formula><mml:math id="M68" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">ref</mml:mi></mml:msub></mml:math></inline-formula> is the reference pixel value.</p>
      <p id="d1e1426">Angular measurements of broadband albedo from 0.3 to 3.0 <inline-formula><mml:math id="M69" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>m with a
hemispherical CNR1 directly accounted for bidirectional reflectance
properties of the mixed grassed surface. Therefore, the point observations
satisfied the bidirectional reflectance considerations related to albedo
estimation techniques (Nicodemus et al., 1977; Lucht et al., 2000; Roberts,
2001).</p>
      <p id="d1e1437">Figure 2 shows a sample of measured reflectance values from a grassed upland
area. The spectral reflectance from the mixed grasses was virtually
identical to the response for healthy (green) winter wheat (see Disney et
al., 2004). For wheat, they concluded reflectance was directionally
invariant and reasonably could be assumed to behave as a Lambertian surface
(i.e. scattering light equally in all directions). The field-measured
spectral reflectance over the grassed surface was therefore treated similar
to a Landsat-measured reflectance and divided into respective wavelengths
for Landsat wavebands 1, 3, 4, 5, and 7.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2"><?xmltex \currentcnt{2}?><label>Figure 2</label><caption><p id="d1e1442">Reflectance spectra collected at four sample points over mixed-grassland vegetation at the upland area on 5 August 2007. Reflectance values
affected by noise at corresponding wavelengths were removed.</p></caption>
            <?xmltex \igopts{width=170.716535pt}?><graphic xlink:href="https://hess.copernicus.org/articles/23/4891/2019/hess-23-4891-2019-f02.png"/>

          </fig>

      <p id="d1e1451">An empirical linear approximation for narrow-to-broadband albedo conversion
applicable to Landsat imagery (see Liang, 2000) was then applied to the
field-measured spectral reflectance data. This allowed for a direct
comparison of albedo estimates and measurements along the sampling transect
shown in Fig. 3. Due to the 4.5 m sampling distance some pixels contained a
single value, whilst others contained two values, in which case the mean
value was used for comparison.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3"><?xmltex \currentcnt{3}?><label>Figure 3</label><caption><p id="d1e1457">Albedo map (5 m resolution) derived from visible images taken at
midday. Also shown are the location of reference and validation sites; letter codes
indicate major land cover types: fallowed (F), mixed grass (MG), brome grass (BG), cultivated (C), and wetlands (W).</p></caption>
            <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://hess.copernicus.org/articles/23/4891/2019/hess-23-4891-2019-f03.png"/>

          </fig>

</sec>
<sec id="Ch1.S3.SS4.SSS4">
  <label>3.4.4</label><title>Surface temperature (emitted longwave radiation)</title>
      <p id="d1e1474">For the case of surface temperatures the indexing method was not needed
because high-resolution observations were obtained directly with a handheld
forward-looking infrared (FLIR) ThermaCAM P20 imaging radiometer. The P20 used a focal plane array uncooled microbolometer with a maximum image
resolution of <inline-formula><mml:math id="M70" display="inline"><mml:mrow><mml:mn mathvariant="normal">320</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">240</mml:mn></mml:mrow></mml:math></inline-formula> pixels, a 24<inline-formula><mml:math id="M71" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> <inline-formula><mml:math id="M72" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 18<inline-formula><mml:math id="M73" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> field of
view, and a spatial resolution of 1.3 mrad. The spectral range was 7.5–13 <inline-formula><mml:math id="M74" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>m, which is similar to traditional satellite sensors (e.g. Landsat, MODIS, and AVHRR with a spectral range of 10–12.5 <inline-formula><mml:math id="M75" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>m and ASTER with a spectral range of 8–12 <inline-formula><mml:math id="M76" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>m).</p>
      <p id="d1e1539">A standard emissivity of 0.98 was assumed for the cover types encountered,
and ambient air temperature and humidity and the distance between the surface and
camera detector were set based on observations. The Stefan–Boltzmann
equation was applied to transform surface temperatures into values of
outgoing longwave radiation needed to estimate the net radiation. For the
flight height of approximately 1 km the FLIR produced a surface pixel
resolution of approximately 3 m. The longwave radiation map was then
aggregated to a 5 m resolution and georectified using the resulting map of
albedo estimates as the reference.</p>
</sec>
<sec id="Ch1.S3.SS4.SSS5">
  <label>3.4.5</label><title>Surface roughness length</title>
      <p id="d1e1551">The study area is characterised by a complex landscape with rolling terrain
covered by tall grasses, cultivated land, and narrow rings of tall grasses,
tall shrubs, or tall trees surrounding ponds and dried wetlands (see Fig. 1). Such surface characteristics (e.g. discontinuities and protrusions) are
expected to produce variations in wind speed and turbulent<?pagebreak page4897?> energy through
interactions with the different surface types and roughness.</p>
      <p id="d1e1554">Variations in the aerodynamic roughness length, <inline-formula><mml:math id="M77" display="inline"><mml:mrow><mml:msub><mml:mi>Z</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, and wind speed are
important factors considered in the turbulent transfer function used for
calculating the aerodynamic terms of the G–D model (Eqs. 2 and 3). Previous
developments (e.g. Pomeroy et al., 1997) have considered boundary layer
(friction velocity) and surface parameters (roughness length) estimated from
EC measurements and wind profiles over boreal forests and Canadian Prairie
land covers such as bare soil and <inline-formula><mml:math id="M78" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>-type crop and grasses.</p>
      <p id="d1e1579">Due to the general surface complexity at the study area, roughness classes
for <inline-formula><mml:math id="M79" display="inline"><mml:mrow><mml:msub><mml:mi>Z</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> were needed to adjust the vapour transfer function to reflect
potential increases or decreases in turbulent exchanges as result of
variations in surface properties and local roughness. For example, lower
values of <inline-formula><mml:math id="M80" display="inline"><mml:mrow><mml:msub><mml:mi>Z</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> associated with fallowed areas and crops would imply
increased wind speeds near the ground and a reduction in turbulent energy.
In contrast, larger <inline-formula><mml:math id="M81" display="inline"><mml:mrow><mml:msub><mml:mi>Z</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> values associated with taller dense grasses,
shrubs, and trees would effectively reduce wind speeds and increase turbulent
exchanges.</p>
      <p id="d1e1615">For the purposes here, a roughness length classification map for <inline-formula><mml:math id="M82" display="inline"><mml:mrow><mml:msub><mml:mi>Z</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> was
derived from the 8 bit grayscale image used for estimating surface albedo.
This was achieved based on knowledge of the various land covers at the site
and segmentation analysis using the IDRISI Kilimanjaro surface analysis tool
(Clark Labs, Clark University, Worcester, Massachusetts, USA). Greyscale DNs were
initially classified into 13 zones of similarity, and a segmentation analysis
was applied. The method computes a standard deviation for each pixel using a
<inline-formula><mml:math id="M83" display="inline"><mml:mrow><mml:mn mathvariant="normal">3</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:math></inline-formula> moving window filter. The standard deviation and associated DN for each pixel are then sorted (low to high), and a bin range is assigned. A class width tolerance was set for pixels having similar standard deviations, and all
values within a specified range were assigned to the same class. Where pixel
values were outside the range, but class boundaries overlapped, a midpoint
was determined and a new class was created.</p>
      <p id="d1e1642">The initial 13 classes were manually reclassified into three general classes
(fallowed/cropped, grass, and trees) based on the extents of the dominant
land cover types observed in the original and classified images.
Characteristic roughness lengths, <inline-formula><mml:math id="M84" display="inline"><mml:mrow><mml:msub><mml:mi>Z</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, were then selected for each class
based on values reported for similar surface types (Brutsaert, 1982). In
this case, a value of 0.05 m was used for the fallowed/cropped class, and
0.10 m was used for the taller- and denser-grass class. Narrow rings of shrubs and
trees around wetlands were also dense and much taller than the surrounding
cover with heights varying from 3 to 10 m. Brutsaert (1982) reported
roughness lengths between 0.2 and 0.4 m for similar type surface elements.
The value of 0.40 m was chosen to reflect an expected increase in roughness
and turbulent exchange due to a likely reduction in wind speed compared to
the surrounding cover types.</p>
</sec>
</sec>
<sec id="Ch1.S3.SS5">
  <label>3.5</label><title>Exploratory analysis of surface variables and evaporation estimates</title>
      <p id="d1e1666">Exploratory analysis of key surface variables and evaporation estimates was
conducted using the R software environment (Grunsky, 2002). Data analysis consisted of boxplot summaries giving the 25th and 75th quartiles (i.e. the interquartile range) defined by the box, and an inner solid line indicating the median value was also given. Data points were plotted with jitter to reflect the density of outliers greater than 1.5 times larger or smaller than the interquartile range with the upper and lower limits defined by box whiskers.</p>
</sec>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>Results and discussion</title>
      <p id="d1e1678">Calculating detailed daily evaporation estimates and examining spatial
scaling issues required the midday inputs and temporal-scaling function to
be computed first. Analysis of midday inputs are described in Sect. 4.1–4.4. Section 4.5 and 4.6 discuss the sensitivity of the G–D model to the
midday evaporation ratio and the temporal transfer function required for
scaling a single measured value of mean daily radiation across a midday
image. Section 4.7–4.9 discuss the accuracy of the resulting evaporation
estimates, variations in statistical distributions of key driving components, and scaling implications for larger-scale evaporation estimates.</p>
<sec id="Ch1.S4.SS1">
  <label>4.1</label><title>Validation of albedo estimates</title>
      <p id="d1e1688">At midday on 5 August 2007 a reference albedo of <inline-formula><mml:math id="M85" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">ref</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.153</mml:mn></mml:mrow></mml:math></inline-formula>
was obtained from observed irradiance and the reflectance of shortwave radiation
over the mix of green grasses. The albedo map resulting from Eq. (11) and
locations of reference and validation points is shown in Fig. 3. Vegetation
was similar at both EC station locations, and the scaled albedo estimate (0.164) agreed well with the measured value (0.167) at the validation site.</p>
      <p id="d1e1706">The validation of the mean and range of albedo estimates obtained for major land
covers in Fig. 3 is summarised in Table 1. Estimates of albedo from the image
compared well with values expected for grasses, agricultural crops,
deciduous trees, and bare soils reported in Brutsaert (1982). The root mean
square error (RMSE) of albedo estimates from the pixels and measured albedo
values was approximately 3.5 %, which is within an expected error of 2 % to 5 % for research purposes (Liang, 2000).</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T1"><?xmltex \currentcnt{1}?><label>Table 1</label><caption><p id="d1e1712">Approximate mean values and ranges of albedo for the major land cover types.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="3">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="center"/>
     <oasis:colspec colnum="3" colname="col3" align="center"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Land cover</oasis:entry>
         <oasis:entry colname="col2">Mean</oasis:entry>
         <oasis:entry colname="col3">Range</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Wetland vegetation (W)</oasis:entry>
         <oasis:entry colname="col2">0.11</oasis:entry>
         <oasis:entry colname="col3">0.05–0.16</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Brome grass (BG)</oasis:entry>
         <oasis:entry colname="col2">0.15</oasis:entry>
         <oasis:entry colname="col3">0.13–0.17</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Mixed grass (MG)</oasis:entry>
         <oasis:entry colname="col2">0.17</oasis:entry>
         <oasis:entry colname="col3">0.15–0.19</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Cultivated (C)</oasis:entry>
         <oasis:entry colname="col2">0.18</oasis:entry>
         <oasis:entry colname="col3">0.17–0.20</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Fallowed (F)</oasis:entry>
         <oasis:entry colname="col2">0.20</oasis:entry>
         <oasis:entry colname="col3">0.17–0.23</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p id="d1e1805">The 5 m resolution albedo map highlighted surface information within the
landscape that would be more generalised using coarser data. For example,
the albedo map depicted distinct boundaries separating regions dominated by
brome (BG) and mixed grasses (MG), cultivated or crop area (C), sparsely
vegetated, fallow area (F), and wetland fringe vegetation (W). Also, wetland
extents and fringe vegetation were observable in areas surrounded by other
vegetation types (see Fig. 1 for reference). The detailed variations<?pagebreak page4898?> are
expected to impact evaporation estimates through relative increases at
pixels with relatively lower values of albedo, which results in an increase
in the available energy, whereas relatively higher values will reduce the
available energy and estimates of evaporation.</p>
</sec>
<sec id="Ch1.S4.SS2">
  <label>4.2</label><title>Validation of longwave radiation estimates</title>
      <p id="d1e1816">Figure 4 shows the resulting map of emitted longwave radiation, <inline-formula><mml:math id="M86" display="inline"><mml:mrow><mml:mi>L</mml:mi><mml:mo>↑</mml:mo></mml:mrow></mml:math></inline-formula>, derived from the image of observed surface temperatures, with estimates ranging between 380 to 480 W 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>. At the two EC station
locations a comparison was made among the midday surface longwave measurements from the P20 camera, a narrow-beam Exergen infrared
thermocouple (IRTC) radiometer, and surface-emitted longwave values obtained from
the CNR1.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4"><?xmltex \currentcnt{4}?><label>Figure 4</label><caption><p id="d1e1843">Surface-emitted longwave radiation (W m<inline-formula><mml:math id="M88" 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>) map (5 m resolution) derived from a thermal image taken at midday.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://hess.copernicus.org/articles/23/4891/2019/hess-23-4891-2019-f04.png"/>

        </fig>

      <p id="d1e1864">The P20 measurement compared well with the IRTC values with differences less
than <inline-formula><mml:math id="M89" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">12</mml:mn></mml:mrow></mml:math></inline-formula> W m<inline-formula><mml:math id="M90" 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>. Compared with the CNR1 values, the differences were
slightly larger at <inline-formula><mml:math id="M91" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">30</mml:mn></mml:mrow></mml:math></inline-formula> W m<inline-formula><mml:math id="M92" 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> but was still within 8 % error.
Generally, the differences were small considering relative changes in midday
surface net radiation, and the magnitude of incoming radiation components is
considerably larger. The variable footprints of the different measurements
and absorption properties of water vapour, which can reduce the signal, are
likely sources of error. Also, dust and heating of the CNR1 downward-facing
pyrgeometer may introduce another source of error.</p>
      <p id="d1e1912">For estimating evaporation, the smaller emitted longwave values resulting
from lower surface temperatures will increase the available energy relative
to larger values which imply reduced water availability and evaporative
cooling.</p>
</sec>
<sec id="Ch1.S4.SS3">
  <label>4.3</label><title>Surface roughness length map</title>
      <p id="d1e1923">Figure 5 shows the resulting classified surface roughness length, <inline-formula><mml:math id="M93" display="inline"><mml:mrow><mml:msub><mml:mi>Z</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>,
map. A visual comparison with the study area map (Fig. 1) and albedo map
(Fig. 3) suggests that the classification map provides a physically realistic
representation of variations in roughness over a large portion of the study
area. Notable changes in the reflected surface properties and roughness
length classification among the key land cover types can be observed.
This is particularly true where distinct boundaries separate the transition between the
dominant cover types such as where taller shrubs and trees surround ponds,
compared to more broad regions of the fallow, cropped areas and grasses.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5"><?xmltex \currentcnt{5}?><label>Figure 5</label><caption><p id="d1e1939">Classification map of aerodynamic surface roughness length derived
from a visible image taken at midday and typical values found in Brutsaert (1982).</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://hess.copernicus.org/articles/23/4891/2019/hess-23-4891-2019-f05.png"/>

        </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6" specific-use="star"><?xmltex \currentcnt{6}?><label>Figure 6</label><caption><p id="d1e1950">Sensitivity of the evaporation ratio to key inputs at midday. The
measured range of input values is shown to demonstrate potential variation in this case study.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/articles/23/4891/2019/hess-23-4891-2019-f06.png"/>

        </fig>

<?xmltex \hack{\newpage}?>
</sec>
<?pagebreak page4899?><sec id="Ch1.S4.SS4">
  <label>4.4</label><title>Sensitivity of the evaporation ratio to key variables at midday</title>
      <p id="d1e1970">Normalised indexes for albedo, surface temperature, and roughness were
considered to examine the relationships of variations in these variables
compared to the evaporation ratio. Figure 6 shows the expected physical
behaviour of these variables within the G–D model. Only the actual range of
values computed for the ratiometric index was considered so that the physical
variations could be shown more clearly. In this case, the impacts of
relative changes in the apparent inverse linear relationships between <inline-formula><mml:math id="M94" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M95" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M96" display="inline"><mml:mrow><mml:mi>L</mml:mi><mml:msub><mml:mo>↑</mml:mo><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and slight non-linear relationship between <inline-formula><mml:math id="M97" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M98" display="inline"><mml:mrow><mml:msub><mml:mi>Z</mml:mi><mml:mrow><mml:msub><mml:mn mathvariant="normal">0</mml:mn><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> on evaporation estimates can be computed. The results can be used to illustrate the impacts of required changes in key driving variables to produce notable changes in the evaporation ratio.</p>
      <p id="d1e2034">For example, a relative increase in the surface temperature via <inline-formula><mml:math id="M99" display="inline"><mml:mrow><mml:mi>L</mml:mi><mml:msub><mml:mo>↑</mml:mo><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of 0.18 (or 18 %) was shown to reduce <inline-formula><mml:math id="M100" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> by 10 %. By comparison, an increase in reflected shortwave radiation via <inline-formula><mml:math id="M101" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of 0.30 (or 30 %) reduced <inline-formula><mml:math id="M102" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> by only 5 %. In the case of surface roughness, an increase of 250 % was needed to reduce <inline-formula><mml:math id="M103" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> by 10 %.
Consequently, a relative reduction in evaporation rates may be expected
where albedo, surface temperature, and surface roughness tend to be larger.
In the latter case, step changes in surface roughness would increase the
relative drying power, <inline-formula><mml:math id="M104" display="inline"><mml:mi>D</mml:mi></mml:math></inline-formula>, but the relative evaporation, <inline-formula><mml:math id="M105" display="inline"><mml:mi>G</mml:mi></mml:math></inline-formula>, results in a relative decrease due to the inverse non-linear relationship. The increased
sensitivity of <inline-formula><mml:math id="M106" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> to <inline-formula><mml:math id="M107" display="inline"><mml:mrow><mml:mi>L</mml:mi><mml:msub><mml:mo>↑</mml:mo><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> also indicates that detailed spatial variations in surface longwave radiation is an important factor for estimating evaporation.</p>
</sec>
<sec id="Ch1.S4.SS5">
  <label>4.5</label><title>Temporal transfer function: normalised ratiometric radiation index</title>
      <p id="d1e2141">Net radiation is known to vary dynamically on a sub-daily basis. Equation (10) shows how a radiation ratio, <inline-formula><mml:math id="M108" display="inline"><mml:mrow><mml:msubsup><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">R</mml:mi><mml:mo>*</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, can be used as a temporal transfer function to scale estimates of mean daily net radiation over an image. In order to scale the normalised net radiation ratios from a temporal “point” at midday to a mean daily value, it was necessary to examine whether a stable proportionality existed between measured values at midday and mean daily net radiation. Verification of a proportionality under clear skies would eliminate the need for an empirical scaling function.</p>
      <p id="d1e2157">Historical records were examined for a period from 1 May to 1 September at three Canadian Prairie locations at similar latitudes (49–52.2<inline-formula><mml:math id="M109" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>). The analysis included two field seasons at the SDNWA study site (2006–2007). Archived data were also obtained at two short grass prairie locations, an AmeriFlux network site at Lethbridge, Alberta, Canada (1999–2004), and Kernen Farm located at Saskatoon, Saskatchewan, Canada (1999–2000). Figure 7 shows a moderately strong relationship at each location even with the <inline-formula><mml:math id="M110" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> intercept set to 0, and <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> is equal to 0.54–0.62.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F7" specific-use="star"><?xmltex \currentcnt{7}?><label>Figure 7</label><caption><p id="d1e2189">Relationship between the midday and mean daily net radiation for a
range of years at two Canadian Prairie sites and one Parkland site for the
period 1 May through 1 September. <inline-formula><mml:math id="M112" 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> values shown for fitted line with the <inline-formula><mml:math id="M113" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> intercept set to 0.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/articles/23/4891/2019/hess-23-4891-2019-f07.png"/>

        </fig>

      <p id="d1e2217">This result confirms that a general proportionality exists and suggests that
daily net radiation, <inline-formula><mml:math id="M114" display="inline"><mml:mrow><mml:msubsup><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">d</mml:mi><mml:mo>*</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, could be scaled to all pixels across an image from a single measured reference value, <inline-formula><mml:math id="M115" display="inline"><mml:mrow><mml:msubsup><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">dref</mml:mi><mml:mo>*</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, as a function of the normalised ratio index for <inline-formula><mml:math id="M116" display="inline"><mml:mrow><mml:msubsup><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">R</mml:mi><mml:mo>*</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> at midday, stated here as
            <disp-formula id="Ch1.E12" content-type="numbered"><label>12</label><mml:math id="M117" display="block"><mml:mrow><mml:msubsup><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">d</mml:mi><mml:mo>*</mml:mo></mml:msubsup><mml:mo>=</mml:mo><mml:msubsup><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">dref</mml:mi><mml:mo>*</mml:mo></mml:msubsup><mml:msubsup><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">R</mml:mi><mml:mo>*</mml:mo></mml:msubsup><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          <inline-formula><mml:math id="M118" display="inline"><mml:mrow><mml:msubsup><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">dref</mml:mi><mml:mo>*</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> was assigned a daily measured reference value of 155 W m<inline-formula><mml:math id="M119" 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>, which was obtained from the CNR1 at the reference station. <inline-formula><mml:math id="M120" display="inline"><mml:mrow><mml:msubsup><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">R</mml:mi><mml:mo>*</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> was derived from Eq. (10) using the measured reference values of incoming shortwave and longwave radiation components, and albedo and emitted longwave maps are used as inputs. The resulting mean daily net radiation map and a comparison of estimated and measured <inline-formula><mml:math id="M121" display="inline"><mml:mrow><mml:msubsup><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">d</mml:mi><mml:mo>*</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> at two validation locations are shown in Fig. 8. The main validation site was equipped with a CNR1 and a second independent site maintained by Environment Canada was equipped with an NR Lite radiometer (Kipp &amp; Zonen, Delft, the Netherlands).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F8"><?xmltex \currentcnt{8}?><label>Figure 8</label><caption><p id="d1e2344">Resulting input map of mean daily net radiation derived from the
normalised index of midday net radiation and a single reference value of mean daily net radiation (155 W m<inline-formula><mml:math id="M122" 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>). Also shown are the location of validation sites for comparing measured and estimated values of mean daily net radiation.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://hess.copernicus.org/articles/23/4891/2019/hess-23-4891-2019-f08.png"/>

          <?xmltex \hack{\vspace*{2mm}}?>
        </fig>

      <?pagebreak page4900?><p id="d1e2367">The distributed estimates of daily net radiation ranged from approximately
120 to 190 W m<inline-formula><mml:math id="M123" 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>. The <inline-formula><mml:math id="M124" display="inline"><mml:mrow><mml:msubsup><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">d</mml:mi><mml:mo>*</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> estimates at the validation sites were 6 W m<inline-formula><mml:math id="M125" 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> higher (4 % error) compared to the CNR1 measurement and 11 W m<inline-formula><mml:math id="M126" 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> lower (8 % error) compared to the NR Lite observation. These results indicate that accurate estimates of net radiation can be scaled across detailed midday images from a single measured value of mean daily net radiation. More importantly, detailed accurate estimates of net radiation would be valuable for improving point-scale evaporation estimates.</p>
</sec>
<sec id="Ch1.S4.SS6">
  <label>4.6</label><title>Calculating direct estimates of actual evaporation with the G–D model</title>
      <p id="d1e2427">The mean daily net radiation map derived from Eq. (12) was supplied as input
to the G–D model to estimate the mean daily actual evaporation at every
land surface pixel. The reference humidity and wind speed values (discussed
earlier) and the surface roughness length map were used for calculating the
aerodynamic terms in Eqs. (2) and (3). An estimate of mean daily evaporation
was then calculated at every pixel location based on Eq. (1).</p>
      <p id="d1e2430">The resulting map of distributed actual evaporation estimates is shown in
Fig. 9. Due to the level of detail captured in the net radiation map of Fig. 8, the map shows a physically realistic pattern of evaporation for the range of land cover types. For example, areas where vegetation was less dense
(e.g. fallowed/cropped) and soil surface conditions were drier showed lower
rates of mean daily evaporation, and higher rates were associated with the
more-densely grassed areas. The highest evaporation estimates were obtained
where water availability is expected to be higher, e.g. among wetland
fringes and depressions where albedo and surface<?pagebreak page4901?> temperatures were lower,
which can be attributed to increased water availability and evaporative
cooling.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F9"><?xmltex \currentcnt{9}?><label>Figure 9</label><caption><p id="d1e2435">Map of distributed estimates of mean daily evaporation at a 5 m pixel resolution.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://hess.copernicus.org/articles/23/4891/2019/hess-23-4891-2019-f09.png"/>

        </fig>

      <p id="d1e2445">The prevailing wind direction for the day (<inline-formula><mml:math id="M127" display="inline"><mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mi mathvariant="normal">dir</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) was from a
north-northwest direction. A mean evaporation estimate of 2.7 mm was
obtained along a linear transect for pixels containing a brome grass surface
immediately upwind of the EC station (Fig. 9). The estimate of 2.7 mm was
0.5 mm or 23 % higher than the EC-measured mean evaporative flux of
2.2 mm d<inline-formula><mml:math id="M128" 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>. Based on the cumulative flux model of Schuepp et al. (1990), it is expected that 80 % of the cumulative flux would come from within an upwind distance of 100 m from the EC station along a similar path to the linear transect. The estimate of 2.7 mm d<inline-formula><mml:math id="M129" 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> might be lower if ground heat flux was found to be a factor for reducing the available energy. However this would need to be reliably accounted for at every 5 m pixel.</p>
      <p id="d1e2483">On the study day the mean daily energy fluxes in W m<inline-formula><mml:math id="M130" 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> (including
latent (LE) and sensible heat (HE)), and the ratio of the energy balance closure at
the validation site was (LE <inline-formula><mml:math id="M131" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> HE)<inline-formula><mml:math id="M132" display="inline"><mml:mrow><mml:mo>/</mml:mo><mml:mo>(</mml:mo><mml:msup><mml:mi>Q</mml:mi><mml:mo>*</mml:mo></mml:msup><mml:mo>-</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">63</mml:mn><mml:mo>+</mml:mo><mml:mn mathvariant="normal">55</mml:mn><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">144</mml:mn><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>.
This results in an energy balance closure of approximately 83 %. The
resulting Bowen ratio of 0.87 was reasonable for the drying conditions and
later timing in the growing season for the grasses in this semi-arid region.
In this case it is expected there will be uncertainty in both estimated and
measured EC fluxes due to modelling and measurement errors and different
footprint scales. For instance, it is possible that LE and HE could be
under-measured or the ground heat flux could be more variable upwind of the EC station than estimated.</p>
      <p id="d1e2554"><?xmltex \hack{\newpage}?>Measured evaporation rates were not available for trees (dominated by aspen)
in 2007, but the G–D estimates were compared against archived values from
Boreal Ecosystem–Atmosphere Study (BOREAS) data for an old-aspen site from August 1996. The G–D mean daily
values in the order of 3 mm were reasonable compared to evaporation from
similar trees reported by Hogg et al. (2001).</p>
      <p id="d1e2558">In general, the results are instructive because the G–D method has been
demonstrated to provide a reasonable estimate of evaporation from the remote-sensing images taken over a complex landscape. Armstrong et al. (2008) have
also shown similar accuracy for daily and multi-day periods from
meteorological data alone during the 2006 field season at the same study
area. More importantly, the ratiometric-index method of scaling may be valid
for distributing surface radiation components across remote-sensing imagery
obtained from satellites, planes, or near-surface aerial platforms such as UAVs.</p>
</sec>
<sec id="Ch1.S4.SS7">
  <label>4.7</label><title>Distributions of evaporation and driving surface variables</title>
      <p id="d1e2569">The following sections briefly discuss the statistical distributions of the
driving variables obtained from the images used for estimating evaporation
and their impacts on the resulting evaporation estimates. The benefit here
is the statistical distributions of evaporation and key driving factors are
considered to be physically meaningful.</p>
      <p id="d1e2572">Figure 10 shows the frequency distributions of evaporation estimates and
relative contributions for the energy balance and aerodynamic components.
G–D model evaporation estimates appear normally distributed with a mean of
2.8 mm d<inline-formula><mml:math id="M133" 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 a relatively low coefficient of variation (cv of 0.07). Distributions for the energy and aerodynamic terms were notably different due to interactions among the driving variables and different roughness classes. For the energy component, the distribution was continuous with a mean of 1.1 mm and a cv of 0.11. The distribution mean for the aerodynamic term was 1.7 mm and was bimodal due to the differences in magnitude of the discrete roughness classes used.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F10" specific-use="star"><?xmltex \currentcnt{10}?><label>Figure 10</label><caption><p id="d1e2589">Distribution of daily evaporation estimates over the field area and relative contributions of evaporation for the energy and aerodynamic terms.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/articles/23/4891/2019/hess-23-4891-2019-f10.png"/>

        </fig>

      <?pagebreak page4902?><p id="d1e2599">Figure 11 shows boxplot summaries of distributions for albedo (<inline-formula><mml:math id="M134" display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula>),
surface temperature (<inline-formula><mml:math id="M135" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), net radiation (<inline-formula><mml:math id="M136" display="inline"><mml:mrow><mml:msup><mml:mi>Q</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>), relative evaporation (<inline-formula><mml:math id="M137" display="inline"><mml:mi>G</mml:mi></mml:math></inline-formula>), mean daily evaporation (<inline-formula><mml:math id="M138" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula>), and <inline-formula><mml:math id="M139" display="inline"><mml:mi>G</mml:mi></mml:math></inline-formula> plotted against net radiation. In the case of <inline-formula><mml:math id="M140" display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula>, values below approximately 0.10 and lower “outliers” can be attributed to uncertainty associated with the wetland vegetation and likely where surface water was not completely masked out near the edges of ponds. In general, the distributions for <inline-formula><mml:math id="M141" display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M142" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> which drive the net radiation appear to show more notable variability compared to <inline-formula><mml:math id="M143" display="inline"><mml:mrow><mml:msup><mml:mi>Q</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> and the resulting estimates of <inline-formula><mml:math id="M144" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula>. For example, the distributions of <inline-formula><mml:math id="M145" display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M146" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> showed opposite skewness, <inline-formula><mml:math id="M147" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.83</mml:mn></mml:mrow></mml:math></inline-formula> and 0.36, respectively. The variability for <inline-formula><mml:math id="M148" display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula> (cv of 0.19) was larger than <inline-formula><mml:math id="M149" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (cv of 0.14), which is also much larger than apparent variability of both <inline-formula><mml:math id="M150" display="inline"><mml:mrow><mml:msup><mml:mi>Q</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> (cv of 0.65) and <inline-formula><mml:math id="M151" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula> (cv of 0.66). Mean values of the distributions for <inline-formula><mml:math id="M152" display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math id="M153" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M154" display="inline"><mml:mrow><mml:msup><mml:mi>Q</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M155" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula> were close to the median values shown within the boxes depicting the interquartile ranges.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F11"><?xmltex \currentcnt{11}?><label>Figure 11</label><caption><p id="d1e2800">Distribution of key surface variables, mean daily evaporation estimates, and relative evaporation over the field area and the relationship
between G and net radiation within the roughness classes.</p></caption>
          <?xmltex \igopts{width=199.169291pt}?><graphic xlink:href="https://hess.copernicus.org/articles/23/4891/2019/hess-23-4891-2019-f11.png"/>

        </fig>

      <p id="d1e2809">The resulting boxplot for <inline-formula><mml:math id="M156" display="inline"><mml:mi>G</mml:mi></mml:math></inline-formula> and the plot of <inline-formula><mml:math id="M157" display="inline"><mml:mi>G</mml:mi></mml:math></inline-formula> against net radiation reflects the interaction across the discrete roughness length classes. The statistical
distribution of <inline-formula><mml:math id="M158" display="inline"><mml:mi>G</mml:mi></mml:math></inline-formula> was not continuous due to the larger step change in
roughness length from 10 to 40 cm. Plots of <inline-formula><mml:math id="M159" display="inline"><mml:mi>G</mml:mi></mml:math></inline-formula> against net radiation
resulted in three distinct linear relationships which can be attributed to
using a uniform mean daily wind speed and humidity deficit for calculating
the drying power of the air, <inline-formula><mml:math id="M160" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">A</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. In this case, the potential variability of <inline-formula><mml:math id="M161" display="inline"><mml:mi>G</mml:mi></mml:math></inline-formula> associated with the relative drying power, <inline-formula><mml:math id="M162" display="inline"><mml:mi>D</mml:mi></mml:math></inline-formula>, is limited to variations in roughness length, but this may vary more with changes in wind speed and the humidity deficit.</p>
      <p id="d1e2866">Generally, despite the larger variability of key factors driving the energy
component the complex interactions within the G–D model appear to reduce the
overall variability of evaporation estimates.</p>
<sec id="Ch1.S4.SS7.SSSx1" specific-use="unnumbered">
  <title>Spatial variations within roughness length classes</title>
      <p id="d1e2874">Boxplots shown in Fig. 12 further characterise the spatial variability of <inline-formula><mml:math id="M163" display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math id="M164" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M165" display="inline"><mml:mrow><mml:msup><mml:mi>Q</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M166" display="inline"><mml:mi>G</mml:mi></mml:math></inline-formula>, and <inline-formula><mml:math id="M167" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula> within the three roughness length classes. In general, the plots depict notable shifts in the interquartile ranges of the distributions across the classes. Results of paired Kolmogorov–Smirnov tests for each variable showed statistical differences among the distributions for each roughness class were highly significant (<inline-formula><mml:math id="M168" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> value <inline-formula><mml:math id="M169" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 0.001). General increases in albedo and surface temperature are clearly shown across the 20 to 40 cm and 10 cm roughness length classes.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F12"><?xmltex \currentcnt{12}?><label>Figure 12</label><caption><p id="d1e2937">Distributions of albedo, surface temperature, net radiation, evaporation, and relative evaporation within each roughness class.</p></caption>
            <?xmltex \igopts{width=199.169291pt}?><graphic xlink:href="https://hess.copernicus.org/articles/23/4891/2019/hess-23-4891-2019-f12.png"/>

          </fig>

      <p id="d1e2946">Consequently, there was a notable reduction in net radiation and similar
reduction in evaporation estimates moving from the higher to lower roughness
length classes. Figure 12 also clearly shows evidence of a non-linear,
inverse relationship between <inline-formula><mml:math id="M170" display="inline"><mml:mi>G</mml:mi></mml:math></inline-formula> and net radiation across the roughness length classes. In this case, the interaction between <inline-formula><mml:math id="M171" display="inline"><mml:mi>G</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M172" display="inline"><mml:mrow><mml:msup><mml:mi>Q</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> appears to offset the potential increase in mean estimates of <inline-formula><mml:math id="M173" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula> associated with increases in available energy. As a result, a large reduction in the variability of the evaporation estimates is clearly evident when compared to the same plot for net radiation.</p>
</sec>
</sec>
<sec id="Ch1.S4.SS8">
  <label>4.8</label><title>Scaling implications</title>
      <p id="d1e2990">There is a potential for areal estimates of evaporation to vary depending on
how upscaled estimates are calculated from the underlying driving factors or
the smaller point-scale estimates. For example, a mean areal estimate of
evaporation calculated from all image pixels was 2.8 mm d<inline-formula><mml:math id="M174" 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>, which accounts for all of the variability available from 5 m pixels. An areal estimate may also be calculated as a weighted mean<?pagebreak page4903?> of evaporation estimates obtained for each roughness length class. This is similar to the mosaic approach used within land surface schemes based on fractional land cover areas. The mean daily evaporation rates for the 5, 10, and 40 cm roughness length classes increased with each step change in roughness class as 2.6, 2.8, and 3.0 mm d<inline-formula><mml:math id="M175" 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. The distribution of land area associated with each roughness class was 48 % (10 cm roughness), 30 % (5 cm roughness), and 22 % (40 cm roughness). The weighted areal evaporation (<inline-formula><mml:math id="M176" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">areal</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) can be obtained as
            <disp-formula id="Ch1.E13" content-type="numbered"><label>13</label><mml:math id="M177" display="block"><mml:mrow><?xmltex \hack{\hbox\bgroup\fontsize{8.5}{8.5}\selectfont$\displaystyle}?><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">areal</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">0.30</mml:mn><mml:mo>⋅</mml:mo><mml:mn mathvariant="normal">2.6</mml:mn><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">0.48</mml:mn><mml:mo>⋅</mml:mo><mml:mn mathvariant="normal">2.8</mml:mn><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">0.22</mml:mn><mml:mo>⋅</mml:mo><mml:mn mathvariant="normal">3.0</mml:mn><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mn mathvariant="normal">2.78</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">mm</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">d</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>.</mml:mo><?xmltex \hack{$\egroup}?></mml:mrow></mml:math></disp-formula>
          In this case there was only a small difference in areal estimates obtained
based on the distribution mean or a weighted mean based on fractional areas
of each roughness class. This may be partly due to the relatively small
variation in evaporation rates across the roughness length classes and the
level of detailed variability captured by the 5 m pixel resolution.
<inline-formula><mml:math id="M178" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">areal</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> was recalculated using Eq. (13) with different combinations of the fractional areas, which only produced a minor difference of <inline-formula><mml:math id="M179" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.1</mml:mn></mml:mrow></mml:math></inline-formula> mm. In other words, in order for there to be a larger difference between the areal estimates, greater variability may either be required in the evaporation estimates distributed over the field or among the mean rates for each roughness class.</p>
      <p id="d1e3119">The mean areal estimate, <inline-formula><mml:math id="M180" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">areal</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of 2.8 mm d<inline-formula><mml:math id="M181" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> for all pixels, was also 0.3 mm higher than a G–D model estimate of 2.5 mm d<inline-formula><mml:math id="M182" 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> obtained from station meteorological observations of net radiation, air temperature, humidity, and wind speed. Variations among the estimates and measurements vary by approximately 22 % to 27 %, which is not surprising given the differences in calculation techniques and potential mismatches in associated footprint scales.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T2" specific-use="star"><?xmltex \currentcnt{2}?><label>Table 2</label><caption><p id="d1e3160">Areal evaporation estimates within each roughness class from the G–D model and for the entire area based on mean values. E_energy and E_aero are the contributions from the energy and aerodynamic components, and E_total is the combined total. The mean value of the distributed estimates is given in the column “Expected”, and the difference between the total and expected is given in the column “Diff”.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="12">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="center"/>
     <oasis:colspec colnum="3" colname="col3" align="center"/>
     <oasis:colspec colnum="4" colname="col4" align="center"/>
     <oasis:colspec colnum="5" colname="col5" align="center"/>
     <oasis:colspec colnum="6" colname="col6" align="center"/>
     <oasis:colspec colnum="7" colname="col7" align="center"/>
     <oasis:colspec colnum="8" colname="col8" align="center"/>
     <oasis:colspec colnum="9" colname="col9" align="center"/>
     <oasis:colspec colnum="10" colname="col10" align="center"/>
     <oasis:colspec colnum="11" colname="col11" align="center"/>
     <oasis:colspec colnum="12" colname="col12" align="center"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M183" display="inline"><mml:mrow><mml:msub><mml:mi>Z</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M184" display="inline"><mml:mi mathvariant="normal">Δ</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M185" display="inline"><mml:mi>G</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M186" display="inline"><mml:mrow><mml:msup><mml:mi>Q</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M187" display="inline"><mml:mi mathvariant="italic">γ</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M188" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">A</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7"><inline-formula><mml:math id="M189" display="inline"><mml:mi>D</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col8">E_energy</oasis:entry>
         <oasis:entry colname="col9">E_aero</oasis:entry>
         <oasis:entry colname="col10">E_total</oasis:entry>
         <oasis:entry colname="col11">Expected</oasis:entry>
         <oasis:entry colname="col12">Diff</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">cm</oasis:entry>
         <oasis:entry colname="col2">kPa</oasis:entry>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4">mm d<inline-formula><mml:math id="M190" 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="col5">kPa</oasis:entry>
         <oasis:entry colname="col6">mm d<inline-formula><mml:math id="M191" 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="col7"/>
         <oasis:entry colname="col8">mm d<inline-formula><mml:math id="M192" 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="col9">mm d<inline-formula><mml:math id="M193" 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="col10">mm d<inline-formula><mml:math id="M194" 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="col11">mm d<inline-formula><mml:math id="M195" 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="col12">mm</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">5</oasis:entry>
         <oasis:entry colname="col2">0.134</oasis:entry>
         <oasis:entry colname="col3">0.132</oasis:entry>
         <oasis:entry colname="col4">4.88</oasis:entry>
         <oasis:entry colname="col5">0.063</oasis:entry>
         <oasis:entry colname="col6">12.99</oasis:entry>
         <oasis:entry colname="col7">0.73</oasis:entry>
         <oasis:entry colname="col8">1.07</oasis:entry>
         <oasis:entry colname="col9">1.34</oasis:entry>
         <oasis:entry colname="col10">2.40</oasis:entry>
         <oasis:entry colname="col11">2.59</oasis:entry>
         <oasis:entry colname="col12"><inline-formula><mml:math id="M196" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.18</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">10</oasis:entry>
         <oasis:entry colname="col2">0.134</oasis:entry>
         <oasis:entry colname="col3">0.124</oasis:entry>
         <oasis:entry colname="col4">5.27</oasis:entry>
         <oasis:entry colname="col5">0.063</oasis:entry>
         <oasis:entry colname="col6">15.13</oasis:entry>
         <oasis:entry colname="col7">0.74</oasis:entry>
         <oasis:entry colname="col8">1.10</oasis:entry>
         <oasis:entry colname="col9">1.48</oasis:entry>
         <oasis:entry colname="col10">2.58</oasis:entry>
         <oasis:entry colname="col11">2.77</oasis:entry>
         <oasis:entry colname="col12"><inline-formula><mml:math id="M197" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.19</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">40</oasis:entry>
         <oasis:entry colname="col2">0.134</oasis:entry>
         <oasis:entry colname="col3">0.085</oasis:entry>
         <oasis:entry colname="col4">5.69</oasis:entry>
         <oasis:entry colname="col5">0.063</oasis:entry>
         <oasis:entry colname="col6">27.97</oasis:entry>
         <oasis:entry colname="col7">0.83</oasis:entry>
         <oasis:entry colname="col8">0.87</oasis:entry>
         <oasis:entry colname="col9">2.01</oasis:entry>
         <oasis:entry colname="col10">2.88</oasis:entry>
         <oasis:entry colname="col11">3.02</oasis:entry>
         <oasis:entry colname="col12"><inline-formula><mml:math id="M198" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.14</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M199" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">areal</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">0.134</oasis:entry>
         <oasis:entry colname="col3">0.113</oasis:entry>
         <oasis:entry colname="col4">5.28</oasis:entry>
         <oasis:entry colname="col5">0.063</oasis:entry>
         <oasis:entry colname="col6">18.70</oasis:entry>
         <oasis:entry colname="col7">0.77</oasis:entry>
         <oasis:entry colname="col8">1.03</oasis:entry>
         <oasis:entry colname="col9">1.71</oasis:entry>
         <oasis:entry colname="col10">2.73</oasis:entry>
         <oasis:entry colname="col11">2.77</oasis:entry>
         <oasis:entry colname="col12"><inline-formula><mml:math id="M200" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.03</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p id="d1e3599">An upscaled areal mean estimate of evaporation can also be obtained from
mean values of the key factors driving the energy and aerodynamic terms. The
general form of Eq. (1) can be restated to derive the individual components
more directly as
            <disp-formula id="Ch1.E14" content-type="numbered"><label>14</label><mml:math id="M201" display="block"><mml:mrow><mml:mi>E</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>G</mml:mi><mml:msup><mml:mi>Q</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:mrow><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>G</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="italic">γ</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi mathvariant="italic">γ</mml:mi><mml:mi>G</mml:mi><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">A</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>G</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="italic">γ</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          For the entire area and also each roughness length class, mean values of the
driving factors were derived and evaporation estimates were recalculated
using Eq. (14). The relative evaporative contributions attributed to the
energy and<?pagebreak page4904?> aerodynamic terms are provided in Table 2. For the different
roughness length classes, the range of evaporation estimates attributed to
E_energy was only 0.2 mm d<inline-formula><mml:math id="M202" 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 nearly 0.7 mm d<inline-formula><mml:math id="M203" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> for
E_aero, and the difference in total evaporation, E_total was 0.5 mm d<inline-formula><mml:math id="M204" 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>. A bias toward larger evaporation estimates might be expected given the increase in energy availability and enhanced turbulence with an increase in roughness. However, the potential bias was offset by the interaction of <inline-formula><mml:math id="M205" display="inline"><mml:mi>G</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M206" display="inline"><mml:mrow><mml:mi>Q</mml:mi><mml:mo>*</mml:mo></mml:mrow></mml:math></inline-formula> and also <inline-formula><mml:math id="M207" display="inline"><mml:mi>G</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M208" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">A</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>.</p>
      <p id="d1e3730">Table 2 also compares evaporation estimates calculated from only mean values
of <inline-formula><mml:math id="M209" display="inline"><mml:mi>G</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M210" display="inline"><mml:mrow><mml:msup><mml:mi>Q</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M211" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">A</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> to the “expected” rates for each roughness length class. Expected rates were calculated from the mean values for all pixels assigned within each roughness length class. Evaporation rates derived from the mean input values alone were only between 0.14 and 0.2 mm less than the expected mean rates for each roughness length class. Upscaling the driving factors to the entire area also had no impact on the resulting estimate as the difference was just 0.1 mm.</p>
</sec>
<sec id="Ch1.S4.SS9">
  <label>4.9</label><title>Examining spatial covariance among key variables</title>
      <p id="d1e3770">Whether evaporation estimates might be influenced by a spatial covariance
between driving factors was also examined. The Pearson correlation
coefficient, <inline-formula><mml:math id="M212" display="inline"><mml:mi>r</mml:mi></mml:math></inline-formula>, was used to evaluate correlations among the driving factors
distributed over the field area. By definition, Pearson's correlation is the
ratio of the covariance (the numerator) between two variables normalised by
the product of their standard deviations as follows:
            <disp-formula id="Ch1.E15" content-type="numbered"><label>15</label><mml:math id="M213" display="block"><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mo>∑</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mover accent="true"><mml:mi>X</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:mrow></mml:mfenced><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mi>Y</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mover accent="true"><mml:mi>Y</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:mrow></mml:mfenced></mml:mrow><mml:mi>n</mml:mi></mml:mfrac></mml:mstyle></mml:mrow><mml:mrow><mml:msqrt><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mo>∑</mml:mo><mml:msup><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mover accent="true"><mml:mi>X</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></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:msqrt><mml:msqrt><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mo>∑</mml:mo><mml:msup><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mi>Y</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mover accent="true"><mml:mi>Y</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></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:msqrt></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M214" display="inline"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M215" display="inline"><mml:mrow><mml:msub><mml:mi>Y</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are the respective values of the variables, the overbar denotes the mean value, and <inline-formula><mml:math id="M216" display="inline"><mml:mi>n</mml:mi></mml:math></inline-formula> is the number of pairs. A strong correlation between two variables might suggest the existence of covariance that could influence upscaled estimates of evaporation. Given that the roughness classes used represent discrete data and there is a lack of more detailed meteorological data to parameterise the aerodynamic term, further evaluation related to climate factors would not be meaningful. Therefore only an examination of the factors driving the energy term are considered here.</p>
      <p id="d1e3910">In this case, a potential covariance between <inline-formula><mml:math id="M217" display="inline"><mml:mi>G</mml:mi></mml:math></inline-formula> (dimensionless) and <inline-formula><mml:math id="M218" display="inline"><mml:mrow><mml:msup><mml:mi>Q</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> (expressed in mm d<inline-formula><mml:math id="M219" 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>) can be considered directly. By rearranging Eq. (15) the covariance can be obtained by multiplying the correlation coefficient and the product of the standard deviations of
<inline-formula><mml:math id="M220" display="inline"><mml:mrow><mml:msup><mml:mi>Q</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> (0.34 mm d<inline-formula><mml:math id="M221" 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="M222" display="inline"><mml:mi>G</mml:mi></mml:math></inline-formula> (0.021 mm d<inline-formula><mml:math id="M223" 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 correlation between <inline-formula><mml:math id="M224" display="inline"><mml:mrow><mml:msup><mml:mi>Q</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M225" display="inline"><mml:mi>G</mml:mi></mml:math></inline-formula> over the field area produced a coefficient, <inline-formula><mml:math id="M226" display="inline"><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.67</mml:mn></mml:mrow></mml:math></inline-formula>.</p>
      <p id="d1e4018">When multiplied in series (<inline-formula><mml:math id="M227" display="inline"><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.67</mml:mn><mml:mo>)</mml:mo><mml:mo>⋅</mml:mo><mml:mn mathvariant="normal">0.34</mml:mn><mml:mo>⋅</mml:mo><mml:mn mathvariant="normal">0.02</mml:mn></mml:mrow></mml:math></inline-formula> this results in a
covariance of approximately <inline-formula><mml:math id="M228" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0049</mml:mn></mml:mrow></mml:math></inline-formula> mm d<inline-formula><mml:math id="M229" 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>. This suggests interactions between <inline-formula><mml:math id="M230" display="inline"><mml:mrow><mml:msup><mml:mi>Q</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M231" display="inline"><mml:mi>G</mml:mi></mml:math></inline-formula> for the methods applied here would have no further statistical influence on upscaled evaporation estimates. Unfortunately, no comment can be made regarding covariance between <inline-formula><mml:math id="M232" display="inline"><mml:mi>G</mml:mi></mml:math></inline-formula> and the turbulent flux component in the G–D model. Such analysis would require more detailed observations of air temperature, humidity, and wind speed and possibly a more sensitive combination model. Nevertheless, the impact of combined interactions within the G–D model effectively reduced the overall variability of point-scale evaporation estimates and also upscaled estimates derived from different computation methods for parameterising the model.</p>
</sec>
<sec id="Ch1.S4.SS10">
  <label>4.10</label><title>General uncertainty of the methods applied</title>
      <p id="d1e4102">Implications of general modelling assumptions and the uncertainty of the methods
applied are briefly discussed here. The daily ground heat flux was
considered to be negligible for the study day as the mean daily flux was
relatively small at the two stations where there was good canopy coverage.
Where local cover properties are similar (e.g. brome grass and mixed-grass
areas) the ground heat flux may be of a similar magnitude, but it would be
greater where surface cover is less dense or where water availability is
limited, due to differences in the surface properties.</p>
      <p id="d1e4105">Further, the relative evaporation, <inline-formula><mml:math id="M233" display="inline"><mml:mi>G</mml:mi></mml:math></inline-formula>, which is based on the relative drying
power, <inline-formula><mml:math id="M234" display="inline"><mml:mi>D</mml:mi></mml:math></inline-formula>, integrates available energy which in this case directly includes the spatial variability of surface temperature. As such, evaporation might be
overestimated in areas with more ground exposure and higher surface
temperatures, where ground heat flux may be appreciably larger (e.g. fallowed/crop area). This interaction could result in a<?pagebreak page4905?> further reduction in the energy available for the evaporation estimate.</p>
      <p id="d1e4122"><inline-formula><mml:math id="M235" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>-type vegetation was at the study area, but the model behaviour may differ for <inline-formula><mml:math id="M236" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> plants and may require new vapour transfer equations for surface types and plants other than which the G–D model was developed on. In the current study representative roughness lengths were selected based on reported values for surfaces of a similar type and height. A larger uncertainty in evaporation estimates may be expected for the roughness
length class associated with the shrub/tree areas which could result in
variable changes in wind speed and enhanced turbulence associated with larger roughness lengths.</p>
</sec>
</sec>
<sec id="Ch1.S5" sec-type="conclusions">
  <label>5</label><title>Summary and conclusions</title>
      <p id="d1e4156">This study examined spatial associations and physical interactions amongst
key surface variables driving actual evaporation estimates and impacts of
their variations on various methods of upscaling estimates to a larger area.
The methods applied demonstrate how measured reference values of albedo and
mean daily net radiation can be scaled accurately across a large field area
for the purpose of deriving point-scale estimates of evaporation at each
pixel. This was achieved by computing a normalised ratiometric index of
surface radiation from highly detailed midday visible and thermal images. At
two validation sites estimates of daily net radiation showed good agreement
with measured values to within 4 % and 8 % error.</p>
      <p id="d1e4159">Estimates of mean daily actual evaporation were calculated at 5 m resolution
with the G–D model. The daily evaporation rate estimated for a transect
upwind of the EC station was 2.7 mm for 5 August 2007 which was 23 % larger than the EC measured flux of 2.2 mm. Offsetting interactions between the relative evaporation term and key surface variables effectively reduce the spatial variability of evaporation estimates. As a result, differences
amongst computed areal evaporation estimates were relatively small
regardless of the different methods used to derive representative average
values of driving factors to parameterise the model or the average
evaporation rate derived from detailed estimates across the field. There was
no evidence of a spatial covariance between the spatial distributions of net
radiation and <inline-formula><mml:math id="M237" display="inline"><mml:mi>G</mml:mi></mml:math></inline-formula>, so no correction factor was identified for improving
upscaled evaporation estimates.</p>
      <p id="d1e4169">The scaling methods applied to the energy terms using ratiometric indexes
derived from detailed images could generate useful diagnostic information at
other study locations and potentially over much larger areas. The methods
applied here may also be instructive toward improving techniques for
upscaling evaporation estimates to larger areas via traditional remote
sensing or climate modelling or using a different combination model. It is
expected that the methods can be applied to visible and thermal images taken from
cameras and sensors on a variety of sensing platforms (e.g. satellites,
planes, and UAVs).</p>
</sec>

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

      <p id="d1e4176">Data used for this study can be accessed at <ext-link xlink:href="https://doi.org/10.20383/101.0192" ext-link-type="DOI">10.20383/101.0192</ext-link> (Armstrong et al., 2019).</p>
  </notes><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e4185">RA conducted the field investigation and modelling under the co-supervision of JP and LM. RA prepared the paper with contributions from all co-authors.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e4191">The authors declare that they have no conflict of interest.</p>
  </notes><notes notes-type="sistatement"><title>Special issue statement</title>

      <p id="d1e4197">This article is part of the special issue “Understanding and predicting Earth system and hydrological change in cold regions”. It is not associated with a conference.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e4203">We would like to extend our gratitude to the reviewers for their valuable feedback and suggested edits.</p></ack><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e4208">This paper was edited by Sean Carey and reviewed by two anonymous referees.</p>
  </notes><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d1e4214">This research has been supported by the Canadian Foundation
for Climate and Atmospheric Sciences through the Drought Research Initiative (DRI), the Natural Sciences and Engineering Research Council of Canada through its Discovery Grants, and the Canada Research Chairs (CRC)
programme.</p>
  </notes><ref-list>
    <title>References</title>

      <ref id="bib1.bib1"><label>1</label><?label 1?><mixed-citation>
Anderson, M. C., Norman, J. M., Diak, G. R., Kustas, W. P., and Mecikalski, J. R.: A two-source time-integrated model for estimating surface fluxes using thermal infrared remote sensing, Remote Sens. Environ., 60, 195–216, 1997.</mixed-citation></ref>
      <ref id="bib1.bib2"><label>2</label><?label 1?><mixed-citation>
Anderson, M. C., Kustas, W. P., and Norman, J. M.: Upscaling flux observations from local to continental scales using thermal remote sensing,
Agron. J., 99, 240–254, 2007.</mixed-citation></ref>
      <ref id="bib1.bib3"><label>3</label><?label 1?><mixed-citation>Armstrong, R., Pomeroy, J., and Lawrence, M.: Evaporation modelling gridded data and meteorological station data for a case study at a rolling prairie landscape at St. Denis National Wildlife Area, Saskatchewan, Canada, <ext-link xlink:href="https://doi.org/10.20383/101.0192" ext-link-type="DOI">10.20383/101.0192</ext-link>, 2019.</mixed-citation></ref>
      <ref id="bib1.bib4"><label>4</label><?label 1?><mixed-citation>
Armstrong, R. N., Pomeroy, J. W., and Martz, L. W.: Evaluation of three
evaporation estimation methods in a Canadian prairie landscape, Hydol. Process., 22, 2801–2815, 2008.</mixed-citation></ref>
      <ref id="bib1.bib5"><label>5</label><?label 1?><mixed-citation>
Armstrong, R. N., Pomeroy, J. W., and Martz, L. W.: Estimating Evaporation in a Prairie Landscape under Drought Conditions, Can. Water Resour. J., 35,
173–186, 2010.</mixed-citation></ref>
      <ref id="bib1.bib6"><label>6</label><?label 1?><mixed-citation>
Avissar, R. and Pielke, R. A.: A parameterization of heterogeneous
land-surface for atmospheric numerical models and its impact on regional
meteorology, Mon. Weather Rev., 117, 2113–2136, 1989.</mixed-citation></ref>
      <ref id="bib1.bib7"><label>7</label><?label 1?><mixed-citation>
Baldocchi, D., Falge, E., Gu, L., Olson, R., Hollinger, D., Running, S.,
Anthoni, P., Bernhofer, C., Davis, K., Evans, R., Fuentes, J., Goldstein, A., Katul, G., Law, B., Lee, X., Malhi, Y., Meyers, T., Munger, W., Oechel, W., Paw, K. T., Pilegaard, K., Schmid, H. P., Valentini, R., Verma, S., Vesala, T., Wilson, K., and Wofsy, S.: FLUXNET: A new tool to study the temporal and spatial variability of ecosystem-scale carbon dioxide, water vapour and energy flux densities, B. Am. Meteorol. Soc., 82, 2415–2434, 2001.</mixed-citation></ref>
      <ref id="bib1.bib8"><label>8</label><?label 1?><mixed-citation>
Baldocchi, D., Krebs, T., and Leclerc, M. Y.: `Wet/Dry Daisyworld': A
Conceptual Tool for Quantifying Sub-Grid Variability of Energy Fluxes over
Heterogeneous Landscapes, Tellus B, 57, 175–188, 2005.</mixed-citation></ref>
      <ref id="bib1.bib9"><label>9</label><?label 1?><mixed-citation>
Bisht, G., Venturini, V., Islam, S., and Jiang, L.: Estimation of the net
radiation using MODIS (Moderate Resolution Imaging Spectroradiometer) data for clear sky days, Remote Sens. Environ., 97, 52–67, 2005.</mixed-citation></ref>
      <ref id="bib1.bib10"><label>10</label><?label 1?><mixed-citation>
Boegh, E., Soegaard, H., and Thomsen, A.: Evaluating evapotranspiration rates and surface conditions using Landsat TM to estimate atmospheric resistance and surface resistance, Remote Sens. Environ., 79, 329–343, 2002.</mixed-citation></ref>
      <ref id="bib1.bib11"><label>11</label><?label 1?><mixed-citation>
Bouchet, R. J.: Evapotranspiration réelle et potentielle: Signification climatique, General Assembly, Berkeley, Int. Assoc. Sci. Hydrol., 62, 134–142, 1963.</mixed-citation></ref>
      <ref id="bib1.bib12"><label>12</label><?label 1?><mixed-citation>
Brutsaert, W.: Evaporation into the Atmosphere, D. Reidel, Hingham, Massachussetts, 299 pp., 1982.</mixed-citation></ref>
      <ref id="bib1.bib13"><label>13</label><?label 1?><mixed-citation>
Brutsaert, W.: Land-surface water vapor and sensible heat flux: Spatial
variability, homogeneity, and measurement scales, Water Resour. Res., 34,
2233–2442, 1998.</mixed-citation></ref>
      <ref id="bib1.bib14"><label>14</label><?label 1?><mixed-citation>
Bussières, N., Granger, R., and Strong, G.: Estimates of Regional
Evapotranspiration using GOES-7 Satellite Data: Saskatchewan Case Study,
July 1991, Can. J. Remote Sens., 23, 3–14, 1996.</mixed-citation></ref>
      <ref id="bib1.bib15"><label>15</label><?label 1?><mixed-citation>
Claussen, M.: Estimation of areally averaged surface fluxes, Bound.-Lay.
Meteorol., 54, 387–410, 1991.</mixed-citation></ref>
      <ref id="bib1.bib16"><label>16</label><?label 1?><mixed-citation>
Claussen, M.: Flux aggregation at large scales: on the limits of validity of
the concept of blending height, J. Hydrol., 166, 371–382, 1995.</mixed-citation></ref>
      <ref id="bib1.bib17"><label>17</label><?label 1?><mixed-citation>
Colaizzi, P. D., Evett, S. R., Howell, T. A., and Tolk, J. A.: Comparison of
five models to scale daily evapotranspiration from one-time-of-day
measurements, Am. Soc. Agr. Biol. Eng., 49, 1409–1417, 2006.</mixed-citation></ref>
      <ref id="bib1.bib18"><label>18</label><?label 1?><mixed-citation>
Corripio, J. G.: Snow surface albedo estimation using terrestrial photography, Int. J. Remote Sens., 25, 5705–5729, 2004.</mixed-citation></ref>
      <ref id="bib1.bib19"><label>19</label><?label 1?><mixed-citation>
Courault, D., Seguin, B., and Olioso, A.: Review on estimation of
evapotranspiration from remote sensing data: From empirical to numerical
modelling approaches, Irrig. Drain. Syst., 19, 223–249, 2005.</mixed-citation></ref>
      <ref id="bib1.bib20"><label>20</label><?label 1?><mixed-citation>
Disney, M., Lewis, P., Thackray, G., Quaife, T., and Barnsley, M.:
Comparison of MODIS broadband albedo over an agricultural site with ground
measurements and values derived from Earth observation data at a range of
spatial scales, Int. J. Remote Sens., 25, 5297–5317, 2004.</mixed-citation></ref>
      <ref id="bib1.bib21"><label>21</label><?label 1?><mixed-citation>
Fisher, J. B., Tu, K. P., and Baldocchi, D. D.: Global estimates of the
land-atmosphere water flux based on monthly AVHRR and ISLSCP-II data,
validated at 16 FLUXNET sites, Remote Sens. Environ., 112, 901–919, 2008.</mixed-citation></ref>
      <ref id="bib1.bib22"><label>22</label><?label 1?><mixed-citation>
Gowda, P. H., Chavez, J. L., Colaizzi, P. D., Evett, S. R., Howell, T. A., and Tolk, J. A.: ET mapping for agricultural water management: present status and challenges, Irrig. Sci., 26, 223–237, 2007.</mixed-citation></ref>
      <ref id="bib1.bib23"><label>23</label><?label 1?><mixed-citation>
Granger, R. J.: A complementary relationship approach for evaporation from
nonsaturated surfaces, J. Hydrol., 111, 31–38, 1989.</mixed-citation></ref>
      <ref id="bib1.bib24"><label>24</label><?label 1?><mixed-citation>
Granger, R. J.: Satellite-derived estimates of evapotranspiration in the
Gediz Basin, J. Hydrol., 229, 70–76, 2000.</mixed-citation></ref>
      <ref id="bib1.bib25"><label>25</label><?label 1?><mixed-citation>
Granger, R. J. and Gray, D. M.: Evaporation from natural nonsaturated
surfaces, J. Hydrol., 111, 21–29, 1989.</mixed-citation></ref>
      <ref id="bib1.bib26"><label>26</label><?label 1?><mixed-citation>
Grunsky, E.: R: A data analysis and statistical programming environment – an emerging tool for the geosciences, Comput. Geosci., 28, 1219–1222, 2002.</mixed-citation></ref>
      <ref id="bib1.bib27"><label>27</label><?label 1?><mixed-citation>
Hogg, E. H., Price, D. T., and Black, T. A.: Postulated Feedbacks of Deciduous Forest Phenology on Seasonal Climate Patterns in the Western
Canadian Interior, J. Climate, 13, 4229–4243, 2001.</mixed-citation></ref>
      <ref id="bib1.bib28"><label>28</label><?label 1?><mixed-citation>Houborg, R. M. and Soegaard, H.: Regional simulation of ecosystem
<inline-formula><mml:math id="M238" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and water vapor exchange for agricultural land using NOAA AVHRR and Terra MODIS satellite data. Application to Zealand, Denmark, Remote Sens. Environ., 93, 150–167, 2004.</mixed-citation></ref>
      <ref id="bib1.bib29"><label>29</label><?label 1?><mixed-citation>
Jackson, R. D., Reginato, R. J., and Idso, S. B.: Wheat canopy temperature: a practical tool for evaluating water requirements, Water Resour. Res., 13, 651–656, 1977.</mixed-citation></ref>
      <ref id="bib1.bib30"><label>30</label><?label 1?><mixed-citation>
Klaassen, W.: Average fluxes from heterogeneous vegetated regions, Bound.-Lay. Meteorol., 58, 329–354, 1992.</mixed-citation></ref>
      <ref id="bib1.bib31"><label>31</label><?label 1?><mixed-citation>
Klaassen, W. and Claussen, M.: Landscape variability and surface flux
parameterization in climate models, Agr. Forest Meteorol., 73, 181–188, 1995.</mixed-citation></ref>
      <ref id="bib1.bib32"><label>32</label><?label 1?><mixed-citation>
Liang, S.: Narrowband to broadband conversions of land surface albedo: I. Algorithms, Remote Sens. Environ., 76, 213–238, 2000.</mixed-citation></ref>
      <ref id="bib1.bib33"><label>33</label><?label 1?><mixed-citation>
Liang, S. L., Shuey, C. J., Russ, A. L., Fang, H. L., Chen, M. Z., Walthall,
C. L., Daughtry, C., and Hunt, R.: Narrowband to broadband conversions of land surface albedo: II. Validation, Remote Sens. Environ., 84, 25–41, 2003.</mixed-citation></ref>
      <ref id="bib1.bib34"><label>34</label><?label 1?><mixed-citation>
Lucht, W., Schaaf, C. B., and Strahler, A. H.: An algorithm for the retrieval of albedo from space using semiempirical BRDF models, IEEE T. Geosci. Remote, 38, 977–998, 2000.</mixed-citation></ref>
      <ref id="bib1.bib35"><label>35</label><?label 1?><mixed-citation>
Monteith, J. L.: Evaporation and environment, Symp. Soc. Exp. Biol., 19, 205–234, 1965.</mixed-citation></ref>
      <ref id="bib1.bib36"><label>36</label><?label 1?><mixed-citation>
Mu, Q., Heinsch, F. A., Zhao, M., and Running, S. W.: Development of a global evapotranspiration algorithm based on MODIS and global meteorology data, Remote Sens. Environ., 111, 519–536, 2007.</mixed-citation></ref>
      <ref id="bib1.bib37"><label>37</label><?label 1?><mixed-citation>
Nagler, P. L., Cleverly, J. R., Glenn, E. P., Lampkin, D., Huete, A. R., and
Wan, Z.: Predicting riparian evapotranspiration from MODIS vegetation indices and meteorological data, Remote Sens. Environ., 94, 17–30, 2005.</mixed-citation></ref>
      <ref id="bib1.bib38"><label>38</label><?label 1?><mixed-citation>
Nicodemus, F. E., Richmond, J. C., Hsia, J. J., Ginsberg, I. W., and Limperis, T.: Geometrical considerations and nomenclature for reflectance,
Report, National Bureau of Standards, Washington, D.C., p. 67, 1977.</mixed-citation></ref>
      <ref id="bib1.bib39"><label>39</label><?label 1?><mixed-citation>
Norman, J. M., Kustas, W. P., and Humes, K. S.: Source approach for estimating soil and vegetation energy fluxes in observations of directional
radiometric surface temperature, Agr. Forest Meteorol., 77, 263–293, 1995.</mixed-citation></ref>
      <ref id="bib1.bib40"><label>40</label><?label 1?><mixed-citation>
Penman, H. L.: Natural evaporation from open water, bare soil and grass, P. Roy. Soc. Lond. A, 193, 120–146, 1948.</mixed-citation></ref>
      <?pagebreak page4907?><ref id="bib1.bib41"><label>41</label><?label 1?><mixed-citation>Pomeroy, J. W., Granger, R. J., Pietroniro, A., Elliott, J. E., Toth, B., and Hedstrom, N.: Hydrological Pathways in the Prince Albert Model Forest, Final Report to the Prince Albert Model Forest Association, NHRI Contribution Series No. CS-97004, Environment Canada, NHRI, Saskatoon, p. 154 <inline-formula><mml:math id="M239" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> appendices, 1997.</mixed-citation></ref>
      <ref id="bib1.bib42"><label>42</label><?label 1?><mixed-citation>
Roberts, G.: A review of the application of BRDF models to infer land cover
parameters at regional and global scales, Prog. Phys. Geogr., 25, 483–511, 2001.</mixed-citation></ref>
      <ref id="bib1.bib43"><label>43</label><?label 1?><mixed-citation>
Schuepp, P. H., Leclerc, M. Y., McPherson, J. I., and Desjardin, R. L.:
Footprint prediction of scalar fluxes from analytical solutions of the diffusion equation, Bound.-Lay. Meteorol., 50, 355–374, 1990.</mixed-citation></ref>
      <ref id="bib1.bib44"><label>44</label><?label 1?><mixed-citation>
Seguin, B., Assad, E., Freaud, J. P., Imbernon, J. P., Kerr, Y., and Lagouarde, J. P.: Use of meteorological satellite for rainfall and evaporation monitoring, Int. J. Remote Sens., 10, 1001–1017, 1989.</mixed-citation></ref>
      <ref id="bib1.bib45"><label>45</label><?label 1?><mixed-citation>
Sellers, P. J., Dickinson, R. E., Randall, D. A., Betts, A. K., Hall, F. G.,
Berry, J. A., Collatz, G. J., Denning, A. S., Mooney, H. A., Nobre, C. A.,
Sato, N., Field, C. B., and Henderson-Sellers, A.: Modelling the exchanges of energy, water, and carbon between continents and the atmosphere, Science, 275, 502–509, 1997.</mixed-citation></ref>
      <ref id="bib1.bib46"><label>46</label><?label 1?><mixed-citation>Song, C., Woodcock, C. E., Seto, K. C., Lenney, M. P., and Macomber, S. A.:
Classification and Change Detection Using Landsat TM Data: When and How to
Correct Atmospheric Effects?, Remote Sens. Environ., 75, 230–244, 2001.
 </mixed-citation></ref><?xmltex \hack{\newpage}?>
      <ref id="bib1.bib47"><label>47</label><?label 1?><mixed-citation>
van der Kamp, G., Hayashi, M., and Gallén, D.: Comparing the hydrology of
grassed and cultivated catchments in the semi-arid Canadian prairies, Hydrol. Process., 17, 559–575, 2003.</mixed-citation></ref>
      <ref id="bib1.bib48"><label>48</label><?label 1?><mixed-citation>
Wilczak, J. M., Oncley, S. P., and Stage, S. A.: Sonic anemometer tilt correction algorithms, Bound.-Lay. Meteorol., 99, 127–150, 2001.</mixed-citation></ref>
      <ref id="bib1.bib49"><label>49</label><?label 1?><mixed-citation>
Yang, F., Mitchell, K., Hou, Y.-T., Dai, Y., Zeng, X., Wang, Z., and Liang,
X.-Z.: Dependence of Land Surface Albedo on Solar Zenith Angle: Observations
and Model Parameterization, J. Appl. Meteorol. Clim., 47, 2963–2982, 2008.</mixed-citation></ref>
      <ref id="bib1.bib50"><label>50</label><?label 1?><mixed-citation>
Yates, T. T., Si, B. C., Farrell, R. E., and Pennock, D. J.: Probability
distribution and spatial dependence of nitrous oxide emission: temporal change in a hummocky terrain, Soil Sci. Soc. Am. J., 70, 753–762, 2006.</mixed-citation></ref>
      <ref id="bib1.bib51"><label>51</label><?label 1?><mixed-citation>
Zhang, C. and Guo, X.: Measuring biological heterogeneity in the northern mixed grassland: A remote sensing approach, Can. Geogr., 51, 462–474, 2007.</mixed-citation></ref>
      <ref id="bib1.bib52"><label>52</label><?label 1?><mixed-citation>
Zoran, M. and Stefan, S.: Atmospheric and spectral corrections for estimating surface albedo from satellite data, J. Optoel. Adv. Mater., 8, 247–251, 2006.</mixed-citation></ref>

  </ref-list></back>
    <!--<article-title-html>Spatial variability of mean daily estimates of actual evaporation from remotely sensed imagery and surface reference data</article-title-html>
<abstract-html><p>Land surface evaporation has considerable spatial variability that
is not captured by point-scale estimates calculated from meteorological data
alone. Knowing how evaporation varies spatially remains an important issue
for improving parameterisations of land surface schemes and hydrological
models and various land management practices. Satellite-based and aerial
remote sensing has been crucial for capturing moderate- to larger-scale
surface variables to indirectly estimate evaporative fluxes. However, more
recent advances for field research via unmanned aerial vehicles (UAVs) now allow
for the acquisition of more highly detailed surface data.</p><p>Integrating models that can estimate <q>actual</q> evaporation from higher-resolution imagery and surface reference data would be valuable to better examine potential impacts of local variations in evaporation on upscaled estimates. This study introduces a novel approach for computing a normalised ratiometric index from surface variables that can be used to obtain more-realistic distributed estimates of actual evaporation. For demonstration purposes the Granger–Gray evaporation model (Granger and Gray, 1989) was applied at a rolling prairie agricultural site in central Saskatchewan, Canada. Visible and thermal images and meteorological reference data required to parameterise the model were obtained at midday.</p><p>Ratiometric indexes were computed for the key surface variables albedo and
net radiation at midday. This allowed point observations of albedo and mean
daily net radiation to be scaled across high-resolution images over a large
study region. Albedo and net radiation estimates were within 5&thinsp;%–10&thinsp;% of measured values. A daily evaporation estimate for a grassed surface was 0.5&thinsp;mm (23&thinsp;%) larger than eddy covariance measurements. Spatial variations in key factors driving evaporation and their impacts on upscaled evaporation estimates are also discussed. The methods applied have two key advantages for estimating evaporation over previous remote-sensing approaches: (1) detailed daily estimates of actual evaporation can be directly obtained using a physically based evaporation model, and
(2) analysis of more-detailed and more-reliable evaporation estimates may lead to improved methods for upscaling evaporative fluxes to larger areas.</p></abstract-html>
<ref-html id="bib1.bib1"><label>1</label><mixed-citation>
Anderson, M. C., Norman, J. M., Diak, G. R., Kustas, W. P., and Mecikalski, J. R.: A two-source time-integrated model for estimating surface fluxes using thermal infrared remote sensing, Remote Sens. Environ., 60, 195–216, 1997.
</mixed-citation></ref-html>
<ref-html id="bib1.bib2"><label>2</label><mixed-citation>
Anderson, M. C., Kustas, W. P., and Norman, J. M.: Upscaling flux observations from local to continental scales using thermal remote sensing,
Agron. J., 99, 240–254, 2007.
</mixed-citation></ref-html>
<ref-html id="bib1.bib3"><label>3</label><mixed-citation>
Armstrong, R., Pomeroy, J., and Lawrence, M.: Evaporation modelling gridded data and meteorological station data for a case study at a rolling prairie landscape at St. Denis National Wildlife Area, Saskatchewan, Canada, <a href="https://doi.org/10.20383/101.0192" target="_blank">https://doi.org/10.20383/101.0192</a>, 2019.
</mixed-citation></ref-html>
<ref-html id="bib1.bib4"><label>4</label><mixed-citation>
Armstrong, R. N., Pomeroy, J. W., and Martz, L. W.: Evaluation of three
evaporation estimation methods in a Canadian prairie landscape, Hydol. Process., 22, 2801–2815, 2008.
</mixed-citation></ref-html>
<ref-html id="bib1.bib5"><label>5</label><mixed-citation>
Armstrong, R. N., Pomeroy, J. W., and Martz, L. W.: Estimating Evaporation in a Prairie Landscape under Drought Conditions, Can. Water Resour. J., 35,
173–186, 2010.
</mixed-citation></ref-html>
<ref-html id="bib1.bib6"><label>6</label><mixed-citation>
Avissar, R. and Pielke, R. A.: A parameterization of heterogeneous
land-surface for atmospheric numerical models and its impact on regional
meteorology, Mon. Weather Rev., 117, 2113–2136, 1989.
</mixed-citation></ref-html>
<ref-html id="bib1.bib7"><label>7</label><mixed-citation>
Baldocchi, D., Falge, E., Gu, L., Olson, R., Hollinger, D., Running, S.,
Anthoni, P., Bernhofer, C., Davis, K., Evans, R., Fuentes, J., Goldstein, A., Katul, G., Law, B., Lee, X., Malhi, Y., Meyers, T., Munger, W., Oechel, W., Paw, K. T., Pilegaard, K., Schmid, H. P., Valentini, R., Verma, S., Vesala, T., Wilson, K., and Wofsy, S.: FLUXNET: A new tool to study the temporal and spatial variability of ecosystem-scale carbon dioxide, water vapour and energy flux densities, B. Am. Meteorol. Soc., 82, 2415–2434, 2001.
</mixed-citation></ref-html>
<ref-html id="bib1.bib8"><label>8</label><mixed-citation>
Baldocchi, D., Krebs, T., and Leclerc, M. Y.: `Wet/Dry Daisyworld': A
Conceptual Tool for Quantifying Sub-Grid Variability of Energy Fluxes over
Heterogeneous Landscapes, Tellus B, 57, 175–188, 2005.
</mixed-citation></ref-html>
<ref-html id="bib1.bib9"><label>9</label><mixed-citation>
Bisht, G., Venturini, V., Islam, S., and Jiang, L.: Estimation of the net
radiation using MODIS (Moderate Resolution Imaging Spectroradiometer) data for clear sky days, Remote Sens. Environ., 97, 52–67, 2005.
</mixed-citation></ref-html>
<ref-html id="bib1.bib10"><label>10</label><mixed-citation>
Boegh, E., Soegaard, H., and Thomsen, A.: Evaluating evapotranspiration rates and surface conditions using Landsat TM to estimate atmospheric resistance and surface resistance, Remote Sens. Environ., 79, 329–343, 2002.
</mixed-citation></ref-html>
<ref-html id="bib1.bib11"><label>11</label><mixed-citation>
Bouchet, R. J.: Evapotranspiration réelle et potentielle: Signification climatique, General Assembly, Berkeley, Int. Assoc. Sci. Hydrol., 62, 134–142, 1963.
</mixed-citation></ref-html>
<ref-html id="bib1.bib12"><label>12</label><mixed-citation>
Brutsaert, W.: Evaporation into the Atmosphere, D. Reidel, Hingham, Massachussetts, 299&thinsp;pp., 1982.
</mixed-citation></ref-html>
<ref-html id="bib1.bib13"><label>13</label><mixed-citation>
Brutsaert, W.: Land-surface water vapor and sensible heat flux: Spatial
variability, homogeneity, and measurement scales, Water Resour. Res., 34,
2233–2442, 1998.
</mixed-citation></ref-html>
<ref-html id="bib1.bib14"><label>14</label><mixed-citation>
Bussières, N., Granger, R., and Strong, G.: Estimates of Regional
Evapotranspiration using GOES-7 Satellite Data: Saskatchewan Case Study,
July 1991, Can. J. Remote Sens., 23, 3–14, 1996.
</mixed-citation></ref-html>
<ref-html id="bib1.bib15"><label>15</label><mixed-citation>
Claussen, M.: Estimation of areally averaged surface fluxes, Bound.-Lay.
Meteorol., 54, 387–410, 1991.
</mixed-citation></ref-html>
<ref-html id="bib1.bib16"><label>16</label><mixed-citation>
Claussen, M.: Flux aggregation at large scales: on the limits of validity of
the concept of blending height, J. Hydrol., 166, 371–382, 1995.
</mixed-citation></ref-html>
<ref-html id="bib1.bib17"><label>17</label><mixed-citation>
Colaizzi, P. D., Evett, S. R., Howell, T. A., and Tolk, J. A.: Comparison of
five models to scale daily evapotranspiration from one-time-of-day
measurements, Am. Soc. Agr. Biol. Eng., 49, 1409–1417, 2006.
</mixed-citation></ref-html>
<ref-html id="bib1.bib18"><label>18</label><mixed-citation>
Corripio, J. G.: Snow surface albedo estimation using terrestrial photography, Int. J. Remote Sens., 25, 5705–5729, 2004.
</mixed-citation></ref-html>
<ref-html id="bib1.bib19"><label>19</label><mixed-citation>
Courault, D., Seguin, B., and Olioso, A.: Review on estimation of
evapotranspiration from remote sensing data: From empirical to numerical
modelling approaches, Irrig. Drain. Syst., 19, 223–249, 2005.
</mixed-citation></ref-html>
<ref-html id="bib1.bib20"><label>20</label><mixed-citation>
Disney, M., Lewis, P., Thackray, G., Quaife, T., and Barnsley, M.:
Comparison of MODIS broadband albedo over an agricultural site with ground
measurements and values derived from Earth observation data at a range of
spatial scales, Int. J. Remote Sens., 25, 5297–5317, 2004.
</mixed-citation></ref-html>
<ref-html id="bib1.bib21"><label>21</label><mixed-citation>
Fisher, J. B., Tu, K. P., and Baldocchi, D. D.: Global estimates of the
land-atmosphere water flux based on monthly AVHRR and ISLSCP-II data,
validated at 16 FLUXNET sites, Remote Sens. Environ., 112, 901–919, 2008.
</mixed-citation></ref-html>
<ref-html id="bib1.bib22"><label>22</label><mixed-citation>
Gowda, P. H., Chavez, J. L., Colaizzi, P. D., Evett, S. R., Howell, T. A., and Tolk, J. A.: ET mapping for agricultural water management: present status and challenges, Irrig. Sci., 26, 223–237, 2007.
</mixed-citation></ref-html>
<ref-html id="bib1.bib23"><label>23</label><mixed-citation>
Granger, R. J.: A complementary relationship approach for evaporation from
nonsaturated surfaces, J. Hydrol., 111, 31–38, 1989.
</mixed-citation></ref-html>
<ref-html id="bib1.bib24"><label>24</label><mixed-citation>
Granger, R. J.: Satellite-derived estimates of evapotranspiration in the
Gediz Basin, J. Hydrol., 229, 70–76, 2000.
</mixed-citation></ref-html>
<ref-html id="bib1.bib25"><label>25</label><mixed-citation>
Granger, R. J. and Gray, D. M.: Evaporation from natural nonsaturated
surfaces, J. Hydrol., 111, 21–29, 1989.
</mixed-citation></ref-html>
<ref-html id="bib1.bib26"><label>26</label><mixed-citation>
Grunsky, E.: R: A data analysis and statistical programming environment – an emerging tool for the geosciences, Comput. Geosci., 28, 1219–1222, 2002.
</mixed-citation></ref-html>
<ref-html id="bib1.bib27"><label>27</label><mixed-citation>
Hogg, E. H., Price, D. T., and Black, T. A.: Postulated Feedbacks of Deciduous Forest Phenology on Seasonal Climate Patterns in the Western
Canadian Interior, J. Climate, 13, 4229–4243, 2001.
</mixed-citation></ref-html>
<ref-html id="bib1.bib28"><label>28</label><mixed-citation>
Houborg, R. M. and Soegaard, H.: Regional simulation of ecosystem
CO<sub>2</sub> and water vapor exchange for agricultural land using NOAA AVHRR and Terra MODIS satellite data. Application to Zealand, Denmark, Remote Sens. Environ., 93, 150–167, 2004.
</mixed-citation></ref-html>
<ref-html id="bib1.bib29"><label>29</label><mixed-citation>
Jackson, R. D., Reginato, R. J., and Idso, S. B.: Wheat canopy temperature: a practical tool for evaluating water requirements, Water Resour. Res., 13, 651–656, 1977.
</mixed-citation></ref-html>
<ref-html id="bib1.bib30"><label>30</label><mixed-citation>
Klaassen, W.: Average fluxes from heterogeneous vegetated regions, Bound.-Lay. Meteorol., 58, 329–354, 1992.
</mixed-citation></ref-html>
<ref-html id="bib1.bib31"><label>31</label><mixed-citation>
Klaassen, W. and Claussen, M.: Landscape variability and surface flux
parameterization in climate models, Agr. Forest Meteorol., 73, 181–188, 1995.
</mixed-citation></ref-html>
<ref-html id="bib1.bib32"><label>32</label><mixed-citation>
Liang, S.: Narrowband to broadband conversions of land surface albedo: I. Algorithms, Remote Sens. Environ., 76, 213–238, 2000.
</mixed-citation></ref-html>
<ref-html id="bib1.bib33"><label>33</label><mixed-citation>
Liang, S. L., Shuey, C. J., Russ, A. L., Fang, H. L., Chen, M. Z., Walthall,
C. L., Daughtry, C., and Hunt, R.: Narrowband to broadband conversions of land surface albedo: II. Validation, Remote Sens. Environ., 84, 25–41, 2003.
</mixed-citation></ref-html>
<ref-html id="bib1.bib34"><label>34</label><mixed-citation>
Lucht, W., Schaaf, C. B., and Strahler, A. H.: An algorithm for the retrieval of albedo from space using semiempirical BRDF models, IEEE T. Geosci. Remote, 38, 977–998, 2000.
</mixed-citation></ref-html>
<ref-html id="bib1.bib35"><label>35</label><mixed-citation>
Monteith, J. L.: Evaporation and environment, Symp. Soc. Exp. Biol., 19, 205–234, 1965.
</mixed-citation></ref-html>
<ref-html id="bib1.bib36"><label>36</label><mixed-citation>
Mu, Q., Heinsch, F. A., Zhao, M., and Running, S. W.: Development of a global evapotranspiration algorithm based on MODIS and global meteorology data, Remote Sens. Environ., 111, 519–536, 2007.
</mixed-citation></ref-html>
<ref-html id="bib1.bib37"><label>37</label><mixed-citation>
Nagler, P. L., Cleverly, J. R., Glenn, E. P., Lampkin, D., Huete, A. R., and
Wan, Z.: Predicting riparian evapotranspiration from MODIS vegetation indices and meteorological data, Remote Sens. Environ., 94, 17–30, 2005.
</mixed-citation></ref-html>
<ref-html id="bib1.bib38"><label>38</label><mixed-citation>
Nicodemus, F. E., Richmond, J. C., Hsia, J. J., Ginsberg, I. W., and Limperis, T.: Geometrical considerations and nomenclature for reflectance,
Report, National Bureau of Standards, Washington, D.C., p. 67, 1977.
</mixed-citation></ref-html>
<ref-html id="bib1.bib39"><label>39</label><mixed-citation>
Norman, J. M., Kustas, W. P., and Humes, K. S.: Source approach for estimating soil and vegetation energy fluxes in observations of directional
radiometric surface temperature, Agr. Forest Meteorol., 77, 263–293, 1995.
</mixed-citation></ref-html>
<ref-html id="bib1.bib40"><label>40</label><mixed-citation>
Penman, H. L.: Natural evaporation from open water, bare soil and grass, P. Roy. Soc. Lond. A, 193, 120–146, 1948.
</mixed-citation></ref-html>
<ref-html id="bib1.bib41"><label>41</label><mixed-citation>
Pomeroy, J. W., Granger, R. J., Pietroniro, A., Elliott, J. E., Toth, B., and Hedstrom, N.: Hydrological Pathways in the Prince Albert Model Forest, Final Report to the Prince Albert Model Forest Association, NHRI Contribution Series No. CS-97004, Environment Canada, NHRI, Saskatoon, p. 154&thinsp;+&thinsp;appendices, 1997.
</mixed-citation></ref-html>
<ref-html id="bib1.bib42"><label>42</label><mixed-citation>
Roberts, G.: A review of the application of BRDF models to infer land cover
parameters at regional and global scales, Prog. Phys. Geogr., 25, 483–511, 2001.
</mixed-citation></ref-html>
<ref-html id="bib1.bib43"><label>43</label><mixed-citation>
Schuepp, P. H., Leclerc, M. Y., McPherson, J. I., and Desjardin, R. L.:
Footprint prediction of scalar fluxes from analytical solutions of the diffusion equation, Bound.-Lay. Meteorol., 50, 355–374, 1990.
</mixed-citation></ref-html>
<ref-html id="bib1.bib44"><label>44</label><mixed-citation>
Seguin, B., Assad, E., Freaud, J. P., Imbernon, J. P., Kerr, Y., and Lagouarde, J. P.: Use of meteorological satellite for rainfall and evaporation monitoring, Int. J. Remote Sens., 10, 1001–1017, 1989.
</mixed-citation></ref-html>
<ref-html id="bib1.bib45"><label>45</label><mixed-citation>
Sellers, P. J., Dickinson, R. E., Randall, D. A., Betts, A. K., Hall, F. G.,
Berry, J. A., Collatz, G. J., Denning, A. S., Mooney, H. A., Nobre, C. A.,
Sato, N., Field, C. B., and Henderson-Sellers, A.: Modelling the exchanges of energy, water, and carbon between continents and the atmosphere, Science, 275, 502–509, 1997.
</mixed-citation></ref-html>
<ref-html id="bib1.bib46"><label>46</label><mixed-citation>
Song, C., Woodcock, C. E., Seto, K. C., Lenney, M. P., and Macomber, S. A.:
Classification and Change Detection Using Landsat TM Data: When and How to
Correct Atmospheric Effects?, Remote Sens. Environ., 75, 230–244, 2001.

</mixed-citation></ref-html>
<ref-html id="bib1.bib47"><label>47</label><mixed-citation>
van der Kamp, G., Hayashi, M., and Gallén, D.: Comparing the hydrology of
grassed and cultivated catchments in the semi-arid Canadian prairies, Hydrol. Process., 17, 559–575, 2003.
</mixed-citation></ref-html>
<ref-html id="bib1.bib48"><label>48</label><mixed-citation>
Wilczak, J. M., Oncley, S. P., and Stage, S. A.: Sonic anemometer tilt correction algorithms, Bound.-Lay. Meteorol., 99, 127–150, 2001.
</mixed-citation></ref-html>
<ref-html id="bib1.bib49"><label>49</label><mixed-citation>
Yang, F., Mitchell, K., Hou, Y.-T., Dai, Y., Zeng, X., Wang, Z., and Liang,
X.-Z.: Dependence of Land Surface Albedo on Solar Zenith Angle: Observations
and Model Parameterization, J. Appl. Meteorol. Clim., 47, 2963–2982, 2008.
</mixed-citation></ref-html>
<ref-html id="bib1.bib50"><label>50</label><mixed-citation>
Yates, T. T., Si, B. C., Farrell, R. E., and Pennock, D. J.: Probability
distribution and spatial dependence of nitrous oxide emission: temporal change in a hummocky terrain, Soil Sci. Soc. Am. J., 70, 753–762, 2006.
</mixed-citation></ref-html>
<ref-html id="bib1.bib51"><label>51</label><mixed-citation>
Zhang, C. and Guo, X.: Measuring biological heterogeneity in the northern mixed grassland: A remote sensing approach, Can. Geogr., 51, 462–474, 2007.
</mixed-citation></ref-html>
<ref-html id="bib1.bib52"><label>52</label><mixed-citation>
Zoran, M. and Stefan, S.: Atmospheric and spectral corrections for estimating surface albedo from satellite data, J. Optoel. Adv. Mater., 8, 247–251, 2006.
</mixed-citation></ref-html>--></article>
