Estimating Watershed Evapotranspiration with PASS. Part II: Moisture Budgets during Drydown Periods

J. Song Department of Geography, Northern Illinois University, DeKalb, Illinois

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M. L. Wesely Environmental Research Division, Argonne National Laboratory, Argonne, Illinois

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M. A. LeMone Mesoscale and Microscale Meteorology Division, National Center for Atmospheric Research, Boulder, Colorado

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R. L. Grossman Program in Atmospheric and Oceanic Studies, University of Colorado, Boulder, Colorado

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Abstract

The second part of the parameterization of subgrid-scale surface fluxes model (PASS2) has been developed to estimate long-term evapotranspiration rates over extended areas at a high spatial resolution by using satellite remote sensing data and limited, but continuous, surface meteorological measurements. Other required inputs include data on initial root-zone available moisture (RAM) content computed by PASS1 for each pixel at the time of clear-sky satellite overpasses, normalized difference vegetation index (NDVI) from the overpasses, and databases on available water capacity and land-use classes. Site-specific PASS2 parameterizations evaluate surface albedo, roughness length, and ground heat flux for each pixel, and special functions distribute areally representative observations of wind speed, temperature, and water vapor pressure to individual pixels. The surface temperature for each pixel and each time increment is computed with an approximation involving the surface energy budget, and the evapotranspiration rates are computed via a bulk aerodynamic formulation. Results from PASS2 were compared with observations made during the 1997 Cooperative Atmosphere–Surface Exchange Study field campaign in Kansas. The modeled diurnal variation of RAM content, latent heat flux, and daily evapotranspiration rate were realistic in comparison to measurements at eight surface sites. With the limited resolution of the NDVI data, however, model results deviated from the observations at locations where the measurement sites were in fields with surface vegetative conditions notably different than surrounding fields. Comparisons with aircraft-based flux measurements suggested that the evapotranspiration rates over distances of tens of kilometers were modeled without significant bias.

Corresponding author address: Jie Song, Department of Geography, Northern Illinois University, DeKalb, IL 60115.

Email: jsong@geog.niu.edu

Abstract

The second part of the parameterization of subgrid-scale surface fluxes model (PASS2) has been developed to estimate long-term evapotranspiration rates over extended areas at a high spatial resolution by using satellite remote sensing data and limited, but continuous, surface meteorological measurements. Other required inputs include data on initial root-zone available moisture (RAM) content computed by PASS1 for each pixel at the time of clear-sky satellite overpasses, normalized difference vegetation index (NDVI) from the overpasses, and databases on available water capacity and land-use classes. Site-specific PASS2 parameterizations evaluate surface albedo, roughness length, and ground heat flux for each pixel, and special functions distribute areally representative observations of wind speed, temperature, and water vapor pressure to individual pixels. The surface temperature for each pixel and each time increment is computed with an approximation involving the surface energy budget, and the evapotranspiration rates are computed via a bulk aerodynamic formulation. Results from PASS2 were compared with observations made during the 1997 Cooperative Atmosphere–Surface Exchange Study field campaign in Kansas. The modeled diurnal variation of RAM content, latent heat flux, and daily evapotranspiration rate were realistic in comparison to measurements at eight surface sites. With the limited resolution of the NDVI data, however, model results deviated from the observations at locations where the measurement sites were in fields with surface vegetative conditions notably different than surrounding fields. Comparisons with aircraft-based flux measurements suggested that the evapotranspiration rates over distances of tens of kilometers were modeled without significant bias.

Corresponding author address: Jie Song, Department of Geography, Northern Illinois University, DeKalb, IL 60115.

Email: jsong@geog.niu.edu

1. Introduction

Evapotranspiration is an essential component of surface hydrological balances, but obtaining accurate estimates of the water vapor flux over large terrestrial areas can be difficult because of the large temporal and spatial variability that can occur. This variability is often very large in the Great Plains and other portions of the Mississippi River basin because of the unevenness of precipitation and diversity of vegetation. Nevertheless, variations in soil moisture content, groundwater levels, and runoff in streams and rivers cannot be fully assessed without some knowledge of evapotranspiration rates. In this research, a version (PASS2) of the parameterization of subgrid-scale surface fluxes model (Gao 1995; Gao et al. 1998) is developed to estimate evapotranspiration after initial estimates of soil moisture are made with PASS1 [see companion paper by Song et al. (2000)]. The goal is to model satellite–pixel-scale moisture and energy fluxes by coupling satellite remote sensing data with a limited set of surface meteorological measurements. Observations made during the 1997 Cooperative Atmosphere–Surface Exchange Study (CASES) at the Atmospheric Boundary Layer Experiments (ABLE) site in the Walnut River Watershed (WRW) in Kansas (LeMone et al. 2000) are used to implement and evaluate PASS2.

2. Background

Numerous field experiments have employed combinations of visible, near-infrared, and thermal data to examine the use of remote sensing to estimate the land surface fluxes of latent and sensible heat. Although substantial progress has been made, significant problems remain in evaluating the simultaneous spatial and temporal variations of surface fluxes over heterogeneous land surfaces under various weather conditions.

Estimating surface fluxes at high spatial resolution can be difficult because remote sensing data emphasize local land surface conditions, while the surface fluxes can be strongly influenced by surface–atmosphere interactions occurring over substantially larger areas (Friedl 1996). Some studies have assumed certain parameters to be spatially invariant in the region because of the difficulty of describing accurately the horizontal variation of the parameters. For example, Humes et al. (1994) assumed near-surface meteorological variables to be constant horizontally across a study area. These authors compensated by developing equations, based in part on flux measurements at multiple sites, that related horizontal variations in remotely sensed quantities to the differences between energy fluxes at a reference site and fluxes at any other points in the area of interest. The results were quite sensitive to the ability to describe spatial variations in net radiation, the ratio of ground heat flux to net radiation, and the roughness length. Previously, Gash (1987) examined an analytical framework that likewise depended strongly on horizontal variations in a remotely sensed parameter, surface temperature, to infer changes in a surface energy flux of latent heat. Gash (1987) found that the results were affected by spatial variations in aerodynamic transfer resistance and air temperature. Models that utilize remotely sensed data to estimate surface fluxes usually perform better when additional observational inputs on spatial variability are provided. PASS2 relies on data on remotely sensed variables and descriptions of land surface properties to drive simulation of spatial variability.

Evapotranspiration can be estimated by several approaches, the selection of which can influence, or be influenced by, the method chosen for using remote sensing data to evaluate the spatial and temporal variations of evapotranspiration. Because many of the approaches rely on satellite data that are typically not available or usable (e.g., due to cloudiness) every day for observations of surface conditions in a specific area, some set of assumptions or models is needed to extend calculations between times of the satellite observations.

One approach to estimating evapotranspiration relies on finding latent heat flux as a residual of the surface energy budget (Humes et al. 1994; Kustas et al. 1994; Kustas and Norman 1996). Many studies using remote sensing data to infer evapotranspiration rates have adopted the residual method because energy budget calculations are straightforward. Moran et al. (1994b) found that the scatter in observed latent heat flux versus the flux computed as a residual was increased by the cumulative effects of errors associated with estimating net radiation, ground heat flux, and sensible heat flux, a difficulty that has also been seen with PASS1 (Song et al. 2000). The residual approach can, in principle, be used in models to make flux estimates either on a near-instantaneous basis at the time of satellite overpasses or on a continuous basis with more elaborate computational schemes. PASS2 computes the latent and sensible heat fluxes initially with an aerodynamic method and then adjusts each flux value proportionally so that their sum closes the energy balance.

A second approach is to calculate latent heat flux fairly directly with micrometeorological flux-gradient expressions whose inputs include satellite remote sensing data to infer surface conditions and local observations of wind, temperature, and humidity above the surface. With this approach, for example, Zhang et al. (1995) used a one-dimensional resistance model to estimate evapotranspiration rates over a well-instrumented region. PASS1 uses some of the same micrometeorological expressions but relies less heavily on extensive surface observations. This approach is usually not intended for long-term, continuous estimates of evapotranspiration and soil moisture content, and is not used in PASS2.

A third approach applies the “triangle” method for obtaining surface soil moisture content and energy fluxes from remote measurements. The triangle method uses the normalized difference vegetation index (NDVI) and surface radiant temperature derived from remote sensing, as does PASS2, but the triangle method has special techniques to generate empirical and statistical relationships among soil moisture availability, fractional vegetation cover, and the instantaneous surface energy fluxes (e.g., Gillies et al. 1997; Price 1990). This approach requires derivation of several polynomial functions that can be dependent on location. Moran et al. (1994a) evaluated relationships between remotely sensed spectral data and measurements of daily evapotranspiration and other vegetation-related hydrological parameters for semiarid rangeland in southeast Arizona. They found that caution is warranted in deriving the relationships, because measurements of spectral reflectance of surface features can vary significantly with changes in soil characteristics and solar zenith angle, which are considered to some extent in PASS1 and PASS2.

A fourth approach is to use inverse modeling, which usually requires solving a set of several equations iteratively for multiple unknowns to get the best fit. Ottlé and Vidal-Madjar (1994) used inversion techniques with remote sensing data to estimate evapotranspiration and soil moisture content in a vegetated area and then applied the soil moisture estimates for an extended period of time to adjust a hydrological model to improve simulation of stream flow in a river basin. The complexity of inversion models can lead to difficulty in finding reliable solutions (e.g., Feddes et al. 1993), and the iterative calculations can be demanding on computational resources when the number of pixels is large.

The PASS2 model attempts to overcome many of the difficulties in estimating simultaneously the spatial and temporal variation in evapotranspiration rates. PASS2 relies on operational surface meteorological observations and surface solar irradiance data collected continuously and on sets of NDVI data from satellite observations made at least every week or two. The assumption is made that NDVI values and thus the greenness and spatial coverage of the vegetation do not change significantly between the times when the satellite data were collected for PASS1, although future research might lead to useful methods of interpolation. Parameterizations specific to the study area for albedo, the ratio of ground heat flux to net radiation, and surface roughness are applied using the satellite data. The horizontal distribution of key surface meteorological parameters is inferred on the basis of selected surface variables in relation to areally representative values. A fairly elaborate scheme is used to estimate surface temperature and evaporation rates for each time step of 30 min.

3. Description of the PASS2 model

The PASS2 model, like the original PASS model (Gao 1995; Gao et al. 1998), uses a rapid algorithm for computing subgrid-scale surface energy partitioning on the basis of an analytical solution to surface energy budget equations. A rapid computing algorithm is needed because of the large number of pixels associated with the satellite, land use, and soil characteristics data. The scheme of the PASS2 procedure is illustrated in Fig. 1. All variables in the model are described either at the subgrid (SG) scale or the model grid (MG) scale, where SG corresponds to the scales of satellite or land use pixels and MG corresponds to scales of at least 100 km. The MG scale variables are approximated by the average of the observations made at the surface meteorological stations.

a. Step 1, model inputs

Data on NDVIi or simple ratio SRi are obtained along with root-zone available moisture (RAM) content θia for each pixel i from PASS1 outputs for the time of latest suitable clear-day satellite overpass. Arithmetic means of incoming solar irradiance K↓, surface air temperature Ta, relative humidity RH, and wind speed u observed at surface meteorological stations in the area are required to drive the calculations of energy fluxes and RAM content forward in time. Data on land use and available water capacity θA, necessary for various steps in PASS2, are provided from the same sources as those used in PASS1.

b. Step 2, precalculation

The precalculation step focuses on estimating pixel-specific surface temperature Tis and the domain-representative surface temperature Ts, both of which are needed to apply the distribution function for Tia in step 3 (Fig. 1). A means of estimating the surface temperature is required because continuous temperature readings from satellite observations are not available. The surface temperatures are estimated in PASS2 with a second-order approximation involving the energy budget equation (Paw U and Gao 1988; Gao 1995). The approximation is used for Tis and Ts separately; that is, the latter is not just the arithmetic mean of the former. As Fig. 1 shows, the inputs needed to estimate Tis include several subgrid-scale parameters. The surface albedo αi and the ratio Γi of soil heat flux to net radiation are derived from SRi and the solar zenith angle for each land-use class in the same way as in PASS1. The aerodynamic resistance Ria and its embedded parameter of friction velocity ui are found with bulk aerodynamic equations using zi0 and ui (Song et al. 2000). Here ui is estimated with the wind distribution function, which is shown in Fig. 1 and described below as being part of step 3 but is actually calculated before step 2. The surface water vapor conductance gic is found in step 4 except for the first time increment, when the regional average value of the water vapor deficit factor is used because pixel-specific values are not yet available. For computing Ts, the input parameters are averages of those used for Tis. The terms SR and θa represent linear averages of the pixel-specific values, while z0, Ra, u∗, α, Γ, and gc are calculated with nonlinear expressions of other averages.

Estimates of Tis and mean state Ts are made with the corresponding pixel-specific and domain-averaged values. In terms not denoted as pixel-specific or averaged, the surface energy and radiation budgets can be expressed as
i1525-7541-1-5-462-e1
Here the sum of the latent heat (λE), sensible heat (H), and ground heat (ΓRn) is equal to the net radiation Rn;K↓ is the incoming shortwave radiation; and L↓ and L↑ are the incoming and outgoing longwave radiation, respectively. Bulk aerodynamic expressions for λE and H can be written as
i1525-7541-1-5-462-e3
Here ρ is the air density, cp is the air specific heat at constant pressure, and γ is the psychrometric constant. The air vapor pressure and air temperature are represented by ea and Ta, respectively; and Rc = g−1c and Ra are the surface water vapor resistance and aerodynamic resistance, respectively. The outgoing longwave radiation term and the saturation vapor pressure term are parameterized with the following second-order Taylor approximations:
i1525-7541-1-5-462-e5
Here ɛ represents the surface emissivity, Δ and Δ2 are the first and second derivatives of the slope of the saturation vapor pressure curve with respect to temperature, and the incoming longwave radiation is represented by
LσT4aeTa/2016a
Here ea represents water vapor pressure expressed in millibars and Ta is atmospheric temperature in Kelvin. This formula can be used for a wide range of temperatures and humidities (Satterlund 1979).
To derive Ts, the following quadratic equation, a solution for Eqs. (1)–(7) needs to be evaluated:
aTsTa2bTsTac
Here the parameters a, b, and c are defined as
i1525-7541-1-5-462-e9
The term δe represents the atmospheric vapor deficit, equal to esat(Ta) − ea. Only one of the two solutions to Eq. (8) has physical meaning and is used to calculate the surface temperature,
i1525-7541-1-5-462-e12

c. Steps 3–6

Distribution functions are used in step 3 to find wind speed ui for each pixel at a reference height zr of about 10 m above the aerodynamic displacement height d and to find air temperature Tia and water vapor pressure eia at 1.5–2.0 m above the displacement height. These variables are evaluated for each time step throughout the diurnal cycle as follows:
i1525-7541-1-5-462-e13
The roughness length zi0 is found in the same manner as in PASS1 by using land-use data and NDVIi, and z0 is the domain average computed as described by Eq. (3) in the companion paper by Song et al. (2000). For the distribution function for eia, θia is initially provided as an input from PASS1 and is subsequently found via step 6; θa is the arithmetic mean of θa for the entire area. The terms αT and αe represent numerical coefficients both chosen to be equal to 0.57, consistent with PASS1 (Song et al. 2000).

The distribution functions for ui and Tia are identical to those used in PASS1, but the equation for eia differs slightly. That is, the RAM content provides the basis for distribution here instead of a calculated value of the surface vapor pressure in contact with the outer surface of the surface elements. Although this surface vapor pressure is likely to be physically more similar than the RAM content to surface temperature in influencing air–surface exchange, tests using both types of distribution functions showed practically no difference in the resulting estimates of surface latent heat flux. PASS2 uses RAM content only because it involves fewer computational steps than using the surface vapor pressure.

In step 4 (“postcalculation” in Fig. 1), after the pixel-scale variables are estimated by using the distribution functions, gic is recalculated with pixel-specific vapor deficit values and the equations described by Gao (1995). Important variables in this calculation include SRi, derived from the most recent satellite data used, and photosynthetically active radiation, assumed to be equal to 0.5K↓ for each time step. Most importantly, the relative available water content ϒ = θia/θiA for each time step is taken into account in estimating the surface conductance. Values of the available water capacity θiA are obtained from soil survey databases. Also in step 4, ui and Ria could be recalculated with the stability adjustments; however, here, as in PASS1, the stability adjustments sometimes resulted in unrealistic values of Ria and thus were not used.

In step 5, latent heat flux λEi for each pixel is initially estimated with a pixel-specific version of Eq. (3). In the pixel-specific version shown in Fig. 1, δei is the difference between saturation vapor pressure at the pixel-specific surface temperature and air vapor pressure. The sensible heat flux Hi is likewise initially estimated with Eq. (4) for each pixel. The net radiation Rin is found from the radiation balance involving observed K↓ together with the same parameterizations as are used in PASS1 for albedo αi, incoming longwave irradiance Li, and outgoing longwave irradiance Li. The initial estimates of λEi and Hi are then adjusted using Rin(1 − Γi) as shown in Fig. 1 so that the energy balance is properly closed. This adjustment does not change the Bowen ratio, Hi/λEi, and reduces the effects of any poor estimates of aerodynamic resistance Ra in producing unrealistic values of the λEi and Hi. When the Bowen ratio is negative, this approach to closing the energy balance fails, and Hi is found as the residual quantity in the surface energy balance.

In step 6, the decrease in RAM content due to evapotranspiration for each pixel and time increment δt is computed for the root zone (Fig. 1), which is represented by a single layer of soil with depth δz. In principle, increases due to precipitation could also be estimated in this step if adequate precipitation estimates were available (e.g., from calibrated radar data) and if runoff were simulated. The root-zone depth is a crucial variable but is quite difficult to estimate accurately because it is dependent on plant species and the stage of growth, which are not identified well on the basis of the information available to PASS2. That is, only broad categories of vegetation are identified, and only the general state of the vegetation can be inferred on the basis of SR data from satellites. This version of PASS2 assumes that δz is equal to one-third of canopy height h for croplands, where h is estimated as 10z0; 0.2 m for rangeland; 2 m for woodland; and 0.2 m for residential- and urban-related grassy areas. These values account for all of the important land-use classes (Song et al. 2000). The depths might be too small to include the entire root zone of the vegetation, but they include the majority of the roots (e.g., Jackson et al. 1996). Because water extraction at the greater depths can be important when the moisture in the upper layers becomes depleted, this version of PASS2 might underestimate evapotranspiration for dry conditions.

Steps 1–6 are repeated for each time increment after the set of θia values produced by step 6 is supplied as an input to step 1. The amounts of water loss by evapotranspiration can be summed over long periods of time and used in hydrological moisture budgets. PASS2 assumes that initial estimates of θia from PASS1 are correct and timely. Periods of time with precipitation are not covered unless increases in soil moisture due to precipitation are considered, such as during cloudy periods that prevent the use of satellite observations to estimate NDVI immediately after precipitation events. Also, PASS2 currently does not contain a soil hydrological model that considers the movement of moisture through the soil column. For example, PASS2 ignores the effects of excessive soil water after heavy rainfall and assumes that the maximum value of θa is given by θA.

4. Application and results

Data collected during CASES-97 in the WRW were used to evaluate the performance of PASS2. The size of the WRW is sufficiently large to serve as a testbed for MG-scale processes. The initial estimates of θia were provided by PASS1, and the other input data sources for PASS2 were identical to those used in PASS1 (Song et al. 2000). These data consisted of NDVIi derived from the Advanced Very High Resolution Radiometer on the National Oceanic and Atmospheric Administration’s (NOAA) NOAA-14 satellite, land-use data and θiA from available datasets, and surface meteorological observations at stations operated during CASES-97 by the National Center for Atmospheric Research (NCAR) and by ABLE. The pixel size used by PASS1 and PASS2 to process and analyze the data was 200 m by 200 m, which corresponds to the size of the pixels in the land use and θiA datasets but is smaller than the NDVI pixel size of about 1 km. The same value of NDVI for each 1-km pixel was assigned to all of the encompassed 200-m pixels.

PASS2 was applied for continuous simulations for several days following each of the clear-day satellite overpasses that occurred on days of year (DOY) 119, 130 and 140 (29 April, 10 May, and 20 May). The three periods modeled each began with slightly dissimilar conditions of vegetation and soil moisture. On DOY 119, the vegetation was in the early spring green-up stage. This stage corresponded to rather low values of NDVI in cropland, located mostly in the western portions of the WRW, and lower NDVI in rangeland, located mostly in the eastern WRW. The soil was fairly dry in most of the WRW except in the southwestern area, where patches of moist soil persisted after previous scattered precipitation events. By DOY 130, NDVI had increased for both cropland and rangeland. The soils in most of the WRW were fairly moist due to moderate precipitation, especially in the northern and southern portions of the watershed. On DOY 140, the canopies were in the early peak green stage and had high NDVI values, and the soils were mostly saturated in the domain because of the heavy precipitation that occurred during the previous two days.

a. Comparisons with measurements

Surface energy fluxes and soil moisture content were measured in addition to the standard meteorological quantities at the eight NCAR surface sites scattered across the southern WRW (at locations shown in Fig. 3 of Song et al. 2000). The soil moisture content was detected as an average for the soil layer between depths of about 1 and 9 cm below the surface. Figure 2 shows the arithmetic mean and the range of values for the soil moisture content θ measured at the eight NCAR sites and for θa computed by PASS2 for the individual 200-m resolution SG pixels most closely centered on the eight NCAR sites. Because θ is the sum of θa and the wilting point moisture content θw, the two estimates of soil moisture should differ by perhaps 0.13–0.17, values typical of θw for the soils in the area. A value of 0.15 was added to θa for the purpose of displaying the data in Fig. 2 but was not expected to represent field conditions precisely. For only this comparison involving the eight SG pixels, soil moisture was explicitly depleted for four equally sized layers of the root zone so that the results for the top layer could be compared more directly to the observations. The depletion rates were assumed to decrease roughly linearly with the depth of the layer to reflect the diminishment of root density and the changing water potential with depth. Specifically, for each time increment, the fraction of total evapotranspirative loss in each layer from top to bottom was found as the product of 0.4, 0.3, 0.2, or 0.1 times θa for each corresponding layer, all divided by the sum of the product of 0.4, 0.3, 0.2, or 0.1 times θa for each layer.

The changes with time of the model-derived values plotted in Fig. 2 of moisture content for entire root zone are similar to the observed changes for DOY 119–122 and 130–134, but the model-derived values for the upper layer decrease more rapidly than observational data. These variations in trends are related to the model assumption that the soil moisture at the start of each sequence of days is evenly distributed vertically through the root zone. Also, the modeled trends are not expected to be identical to the observed trends because the modeled values of RAM are based on availability for evapotranspiration, not the actual soil moisture content. Finally, the choice of greater root-zone depths would have resulted in smaller modeled moisture depletion rates, which would usually match the observed rates more closely. The selection of root-zone depths and of methods to estimate soil depletion rates as a function of depth remains a subject of future research in PASS modeling.

The ability to evaluate the performance of the model on the basis of Fig. 2 is limited by the spatial variability of soil moisture. Horizontal variability in soil moisture content changes can be large because of variations in vegetative cover, which frequently occur at distances of 200–800 m in the WRW, as well as because of spotty precipitation patterns and locally variable drainage characteristics of the soil. The individual pixel areas of 200 m × 200 m are reasonably small, but estimates of NDVI for each pixel are derived with a resolution of 1 km, and the geographical registration of the NDVI pixels could be in error by as much as 1 km. The ranges shown in Fig. 2 for soil moisture amounts from site to site are wide, indicating much field-to-field variability. For example, two of the measurement sites were on bare soil or very sparse vegetation, where the subsurface soil moisture content tended to remain high and change slowly with time. Three of the sites had winter wheat, which depleted soil moisture rather quickly during the few days after precipitation. The other three sites were rangeland, where the soil moisture decreased with time at a moderate rate. The ranges of the values increased slowly from day to day as soil moisture was depleted differentially at various locations, and the ranges were relatively small when the soil moisture content was large, for example, on DOY 140–142. On DOY 130–133 and 140–142, the ranges of the measured soil moisture were smaller than those of the modeled values, which supports the assertion that PASS2 tends to suppress the effects of field-to-field variability on simulated soil moisture amounts.

Figure 3 shows the means and ranges of latent heat fluxes measured at the NCAR sites and of the fluxes modeled for the nearest SG pixels. The fluxes were measured by eddy correlation at a height of about 3 m; the effective surface “footprint” for the fluxes extended to about 300 m upwind. Both modeled and measured λE values are relatively small for the sequence of days starting on DOY 119, moderately large for the sequence starting on DOY 130, and large for the sequence starting on DOY 140. This variation from sequence to sequence corresponds well with rainfall and soil moisture patterns; solar irradiance amounts and their diurnal variations changed very little from sequence to sequence for the days with cloudless conditions (especially DOY 120, 130, 131, 140, and 141). In comparison to the averages for the eight NCAR sites, PASS2 estimates of λE for mostly cloudless days are lower for the sequence starting on DOY 119 by up to 40 W m−2, but they are higher for the sequence beginning on DOY 140 by up to 60 W m−2. Figure 3 also shows the ranges of λE values across the eight sites, for noon when the ranges are near their maximum values. The ranges for the measurements are large, while the model results have smaller ranges because of the smoothing effects of the limited spatial resolution of the NDVI data.

The differences between model and observational results in Fig. 3 were caused at least in part by the difficulty of obtaining observational sampling for areas where surface conditions vary greatly, coupled with the probable incorporation of several types of fields in the view of each 1-km resolution NDVI pixel. To further investigate issues of spatial and temporal variability, Fig. 4 shows means and standard deviations of the modeled daily evapotranspiration values computed for the 121 200-m pixels within 1 km of the eight measurement sites. For nearly every day, the model-derived values were simultaneously larger than the observed quantities at some sites and smaller at others, with the underestimates being the most significant. The underestimates were consistently the most noticeable for measurement sites where winter wheat grew, and were the most severe on sunny days during moderately dry conditions, for example, on DOY 119. Overestimates tended to occur at other locations and were the strongest for the bare soil at site 3, especially during the relatively wet conditions of DOY 141 and 142. Nevertheless, the average of all of the modeled daily values shown in Fig. 4 was practically identical to the average of 2.48 mm day−1 for the observations. A linear regression analysis yielded a line with a slope of 0.79 and an offset of 0.52 mm day−1, with an R value of 0.77.

Averages of fluxes measured from aircraft during CASES-97 provided spatial averages that could be more readily compared to the model results than could the fluxes measured at the surface stations. The vertical fluxes of water vapor were measured by eddy correlation with fast-response instruments aboard the University of Wyoming King Air research aircraft. The vertical fluxes were obtained with analysis techniques similar to those described by Grossman (1992a). The results from 15 flights on DOY 130, 140, 141, and 142, at heights of 100–300 m above the local terrain along the horizontal paths shown in Fig. 5, were chosen for comparison to PASS2 results. The flights paths were sufficiently long, nearly 60 km, to ensure that statistically reliable estimates of the turbulent eddy fluxes were obtained (e.g., Grossman 1992b). Because the selected 15 flights were carried out during the early afternoon when the planetary boundary layer was deep and well mixed, the aircraft-based measurements of moisture flux were probably good estimates of the surface fluxes if the effects of horizontal advection of moisture were not significant. Figure 6 plots the aircraft flux results in comparison to PASS2 estimates expressed as arithmetic means of the flux values for all of the pixels in a rectangular area 10 km wide with its long axis centered along the flight path. No attempt was made here to select the pixels in the surface footprint of the aircraft fluxes, a practice that might have resulted in some of the scatter in the comparison. The average of all 15 values of λE from PASS2 was 266 W m−2 (standard deviation: 81 W m−2), while the aircraft-based mean was 283 W m−2 (standard deviation: 74 W m−2). The run-to-run variability of the fluxes measured sequentially from aircraft over the same area is typically 20% (one standard deviation) or about 50 W m−2. Overall, the PASS2-derived estimates of λE are not statistically different from the aircraft-based observations. A linear regression analysis applied for all flight tracks resulted in an equation with an offset of 46 W m−2, a slope of 0.78 (with error of 0.21), and an R value of 0.72.

Examination of Figs. 3 and 4 suggests that estimates of λE from PASS2 were slightly smaller than the observations at individual sites when conditions were relatively dry. This difference tended to disappear or even be reversed when the soil moisture content was large. The fluxes from the aircraft observations probably provided the most reliable means of model evaluation (Fig. 6) because they represented averages over extended areas, although the spatial matching to the PASS2 estimates was inexact. A general difficulty is that a precise observational “standard” that is directly comparable to the PASS2 results was not available, primarily because of horizontal variability and the difficulties of matching the sampling areas. Gao et al. (1998) provided some successful evaluation of the long-term evaporation rates from PASS by comparison to antecedent rainfall over a large area, which will also be attempted in future work with PASS2. For the present analysis, additional potential problems in applying PASS2 involved the representativeness of the domain-averaged meteorological parameters, which were derived from the observations at the eight NCAR sites. Finally, evaluation of PASS2 performance cannot be separated from consideration of PASS1 performance, especially with regard to the initial RAM field used in PASS2. As was discussed by Song et al. (2000), the derivation of initial RAM is highly sensitive to the estimates of surface temperature found in PASS1 from the satellite observations, and the application of atmospheric corrections to estimate surface temperatures might have been limited at times by undetected variations in atmospheric particulate content.

b. Daily evapotranspiration

Figure 7 shows images of a primary type of data product that can be derived from PASS2 outputs: cumulative SG-scale water loss by evapotranspiration over the region of interest. The individual pixels are 200 m × 200 m in these images, but the 1-km resolution in the NDVI and SR data lessens contrasts over distances of up to 2 km. The water loss amounts depicted in Fig. 7 are commensurate with the findings that evapotranspiration rates were relatively small on DOY 119, intermediate on DOY 130, and large on DOY 140. The patterns in each image are similar to the soil moisture and rainfall patterns illustrated by Song et al. (2000). Very low evapotranspiration rates occurred in urban and suburban areas, such as in the city of Wichita near the center of the western edge of the model domain, and relatively high evapotranspiration occurred at the lakes, ponds, and creeks.

5. Conclusions and discussion

Application of PASS2 with PASS1 outputs for the times of selected satellite overpasses as initial conditions provides long-term estimates of evapotranspiration over extended areas. PASS2 attempts to account explicitly for the effects of albedo, roughness length, ground heat flux, wind speed, air temperature, and air vapor pressure for each pixel, but it requires surface observational data from only a limited number of standard meteorological stations. PASS2 uses the same land-use, soil available water capacity, and NDVI data as does PASS1, as well as many of the same algorithms. The surface temperature for each pixel and time increment is computed in PASS2 with an approximation involving the surface energy budget. After application of the distribution functions, evapotranspiration rates can be computed via a bulk aerodynamic formulation, because soil moisture and thus surface water vapor conductance are evaluated for the preceding time steps. Thus, estimating evapotranspiration is less susceptible to the cumulative effects of errors in the energy balance than in the PASS1 procedure of finding evapotranspiration as a residual term in the energy budget. Overall, PASS2 links MG and SG variables with rapid algorithms that enable description of spatial heterogeneities and their influence on MG variables throughout the diurnal cycle.

Comparisons of PASS2 results on evapotranspiration with aircraft-based measurements made during CASES-97 indicate that model-derived estimates over distances of tens of kilometers are, on average, without significant bias. Because the individual agricultural fields where the observations were made were small in comparison to the resolution of the NDVI data used, however, soil moisture and evapotranspiration estimates at the pixels closest to individual sites could deviate significantly from local observations. For example, PASS2 tended to overestimate the rate of depletion of soil moisture content for fields of bare soil and to underestimate depletion rates for winter wheat fields in the springtime. For surface sites in rangeland, which were usually surrounded by grassy fields with similar vegetative characteristics, the model-derived estimates agreed quite well with the locally observed values.

Soil moisture available for evapotranspiration is estimated in the current version of PASS2 by tabulating the amount of moisture in a single layer of soil with limited depth, and the influence of soil moisture on evaporation rates is described with a factor that is linearly related to the ratio of available soil moisture content to its moisture capacity. A slightly more sophisticated scheme might be needed for dry conditions, such as a description using a deeper soil column with several layers from which moisture extraction rates and availability for evapotranspiration are assumed to vary with depth. The WRW is currently being instrumented at several locations to measure profiles of moisture content, which will allow some testing of such alternative methods of describing soil moisture with PASS2.

The question sometimes arises on whether data from satellites are necessary for computing surface energy budgets over geographical domains whose characteristic size is approximately 100 km, similar to the size of the WRW or the grid of a large-scale model. This question occurs in part because use of satellite data requires manipulation of fairly large datasets, which adds to the amount of computer resources needed. One possible suggestion is to use the Penman or the Penman–Monteith approach (as summarized by Brutsaert 1982) without satellite data. If an area had ample soil moisture for vegetation and the surfaces of fields with bare soil were wetted, use of the Penman approach and averages of measurements of air temperature and humidity in the area would probably produce good results. During drydown, the Penman–Monteith approach would be needed instead of the Penman approach. With this approach, computation of the evapotranspiration rate requires estimates of the vapor pressure deficit in air, aerodynamic resistance above the surface, and bulk canopy stomatal resistance or conductance for water vapor. Estimates of u∗ and z0 necessary to evaluate aerodynamic resistance could be made on the basis of land-use information and knowledge of seasonal variations in vegetative height. The water vapor deficit could be inferred from surface meteorological station data; the averages for the domain might be used initially. Minimum bulk canopy conductance values for water could be assumed for various categories of vegetative cover and then adjusted for the effects of limited soil moisture. A difficulty with this procedure, however, lies in developing a method to make the adjustments in the conductance values. That is, the Penman–Monteith equation includes two variables, evapotranspiration rate and bulk surface resistance, and a means of fixing one or the other is needed for the case when optimally wet conditions do not exist. In PASS1, estimates of surface temperature Ts remotely sensed from satellites provides the information that can be used to assess surface moisture conditions. In PASS2, Ts is again a key variable but it is calculated analytically with consideration of changes in soil moisture. Also, Eqs. (14) and (15), which depend directly or indirectly on Ts, provide a means of estimating air temperature and vapor pressure over each type of surface. Without information derived from satellites on surface temperature or an alternative key surface variable such as surface soil moisture content, a method of applying the Penman–Monteith approach for extended areas that contain significant variations in surface conditions would be limited. In addition, when measures of the Ts are available, the approximations for bulk aerodynamic relationships used in the Penman–Monteith equations are not needed because they can be replaced by the more complete bulk equations of the type used in PASS.

The PASS2 model is intended for estimating evapotranspiration over extended areas on the basis of remote sensing data and limited surface observations. For CASES-97 and similar types of planetary boundary layer studies, PASS2 can be used to evaluate the spatial and temporal variations of terms in the surface energy balance. For hydrological or other types of studies for which truly continuous estimates of evapotranspiration are needed, estimates of pixel-specific precipitation and runoff are needed. In this regard, the coupling of PASS2 with hydrological models and radar-derived precipitation estimates would be an important step.

Acknowledgments

This work was supported by the National Aeronautics and Space Administration Order S-10133-X directed to the U.S. Department of Energy. Operation of the Atmospheric Boundary Layer Experiments facility was supported by the U.S. Department of Energy, Office of Science, Office of Biological and Environmental Research, Environmental Science Division, under Contract W-30-109-Eng-38. Activities of the first author were funded in part by the National Science Foundation through Grant ATM 97-09948. Data collected on surface meteorology, soil moisture, and evapotranspiration rates at the NCAR measurement sites were provided by the Atmospheric Technology Division of NCAR. The land use and available water capacity data were provided by Alice T. Cialella of Brookhaven National Laboratory as part of activities for the U.S. Department of Energy’s Atmospheric Radiation Measurement program. Barry M. Lesht and Richard L. Coulter of Argonne National Laboratory gave valuable advice and guidance on data retrieval.

REFERENCES

  • Brutsaert, W. H., 1982: Evaporation into the Atmosphere. Theory, History, and Applications. D. Reidel, 299 pp.

    • Crossref
    • Export Citation
  • Feddes, R. A., M. Menenti, P. Kabat, and W. G. M. Bastiaanssen, 1993: Is large-scale inverse modelling of unsaturated flow with areal average evaporation and surface soil moisture as estimated from remote sensing feasible? J. Hydrol.,143, 125–152.

    • Crossref
    • Export Citation
  • Friedl, M. A., 1996: Relationships among remotely sensed data, surface energy balance, and area-averaged fluxes over partially vegetated land surfaces. J. Appl. Meteor.,35, 2091–2103.

    • Crossref
    • Export Citation
  • Gao, W., 1995: Parameterization of subgrid-scale land surface fluxes with emphasis on distributing mean atmospheric forcing and using satellite-derived vegetation index. J. Geophys. Res.,100, 14;th305–14 317.

    • Crossref
    • Export Citation
  • ——, R. L. Coulter, B. M. Lesht, J. Qiu, and M. L. Wesely, 1998: Estimating clear-sky regional surface fluxes in the southern Great Plains Atmospheric Radiation Measurement site with ground measurements and satellite observations. J. Appl. Meteor.,37, 5–22.

    • Crossref
    • Export Citation
  • Gash, J. H. C., 1987: An analytical framework for extrapolating evaporation measurements by remote sensing surface temperature. Int. J. Remote Sens.,8, 1245–1249.

  • Gillies, R. R., T. N. Carlson, J. Cui, W. P. Kustas, and K. S. Humes, 1997: A verification of the triangle method for obtaining surface soil water content and energy fluxes from remote measurements of the normalized difference vegetation index (NDVI) and surface radiant temperature. Int. J. Remote Sens.,18, 3145–3166.

    • Crossref
    • Export Citation
  • Grossman, R. L., 1992a: Convective boundary layer budgets of moisture and sensible heat over an unstressed prairie. J. Geophys. Res.,97, 18 425–18 438.

    • Crossref
    • Export Citation
  • ——, 1992b: Sampling errors in the vertical fluxes of potential temperature and moisture measured by aircraft during FIFE. J. Geophys. Res.,97, 18 439–18 443.

  • Humes, K. S., W. P. Kustas, and M. S. Moran, 1994: Use of remote sensing and reference site measurements to estimate instantaneous surface energy balance components over a semiarid rangeland watershed. Water Resour. Res.,30, 1363–1373.

    • Crossref
    • Export Citation
  • Jackson, R. B., J. Canadell, J. R. Ehleringer, H. A. Mooney, O. E. Sala, and E. D. Shulze, 1996: A global analysis of root distributions for terrestrial biomes. Oecologia,108, 389–411.

    • Crossref
    • Export Citation
  • Kustas, W. P., and J. M. Norman, 1996: Use of remote sensing for evapotranspiration monitoring over land surfaces. Hydrol. Sci.,41, 495–516.

    • Crossref
    • Export Citation
  • ——, M. S. Moran, K. S. Humes, D. I. Stannard, P. J. Pinter Jr., L. E. Hipps, E. Swiatek, and D. C. Goodrich, 1994: Surface energy balance estimates at local and regional scales using optical remote sensing from an aircraft platform and atmospheric data collected over semiarid rangelands. Water Resour. Res.,30, 1241–1259.

    • Crossref
    • Export Citation
  • LeMone, M. A., and Coauthors, 2000: Land–atmosphere interaction research and opportunities in the Walnut River Watershed in southeast Kansas: CASES and ABLE. Bull. Amer. Meteor. Soc.,81, 757–779.

    • Crossref
    • Export Citation
  • Moran, M. S., T. R. Clarke, W. P. Kustas, and M. Weltz, 1994a: Evaluation of hydrologic parameters in a semiarid rangeland using remotely sensed spectral data. Water Resour. Res.,30, 1287–1297.

    • Crossref
    • Export Citation
  • ——, W. P. Kustas, A. Vidal, D. I. Stannard, J. H. Blanford, and W. D. Nichols, 1994b: Use of ground-based remotely sensed data for surface energy balance evaluation of a semiarid rangeland. Water Resour. Res.,30, 1339–1349.

    • Crossref
    • Export Citation
  • Ottl;aae, C., and D. Vidal-Madjar, 1994: Assimilation of soil moisture inferred from infrared remote sensing in a hydrological model over the HAPEX-MOBILHY region. J. Hydrol.,158, 241–264.

    • Crossref
    • Export Citation
  • Paw U, K. T., and W. Gao, 1988: Application of solutions to nonlinear energy budget equations. Agric. For. Meteor.,43, 121–145.

    • Crossref
    • Export Citation
  • Price, J. C., 1990, Using spatial context in satellite data to infer regional scale evapotranspiration. IEEE Trans. Geosci. Remote Sens.,28, 940–948.

    • Crossref
    • Export Citation
  • Satterlund, D. R., 1979: An improved equation for estimating long-wave radiation from the atmosphere. Water Resour. Res.,15, 1649–1650.

    • Crossref
    • Export Citation
  • Song, J., M. L. Wesely, R. L. Coulter, and E. A. Brandes, 2000: Estimating watershed evapotranspiration with PASS. Part I: Inferring root-zone moisture conditions using satellite data. J. Hydrometeor.,1, 447–461.

    • Crossref
    • Export Citation
  • Zhang, L., R. Lemeur, and J. P. Goutorbe, 1995: A one-layer resistance model for estimating regional evapotranspiration using remote sensing data. Agric. For. Meteor.,77, 241–261.

    • Crossref
    • Export Citation

Fig. 1.
Fig. 1.

Scheme of the PASS2 model.

Citation: Journal of Hydrometeorology 1, 5; 10.1175/1525-7541(2000)001<0462:EWEWPP>2.0.CO;2

Fig. 2.
Fig. 2.

Temporal variations of modeled RAM content θa, averaged among the eight pixels that were closest to the eight NCAR sites and of the average soil moisture θ observed at the eight NCAR sites. The vertical bars represent the maximum range of values for the eight pixels or eight sites for the upper layer of soil.

Citation: Journal of Hydrometeorology 1, 5; 10.1175/1525-7541(2000)001<0462:EWEWPP>2.0.CO;2

Fig. 3.
Fig. 3.

Temporal variations of modeled latent heat fluxes λE, averaged among the eight pixels that were closest to the eight NCAR sites and the average λE observed at the eight NCAR sites. The vertical bars represent the maximum ranges of values for the eight pixels or eight sites.

Citation: Journal of Hydrometeorology 1, 5; 10.1175/1525-7541(2000)001<0462:EWEWPP>2.0.CO;2

Fig. 4.
Fig. 4.

Comparison of daily evapotranspiration rates observed on 10 days at the eight NCAR sites with the model estimates averaged among pixels within 1 km of each NCAR site. The error bars indicate one standard deviation on each side of the mean for each set of pixels.

Citation: Journal of Hydrometeorology 1, 5; 10.1175/1525-7541(2000)001<0462:EWEWPP>2.0.CO;2

Fig. 5.
Fig. 5.

Fifteen selected flight tracks of King Air aircraft on DOY 130, 140, 141, and 142.

Citation: Journal of Hydrometeorology 1, 5; 10.1175/1525-7541(2000)001<0462:EWEWPP>2.0.CO;2

Fig. 6.
Fig. 6.

Comparison of modeled versus measured latent heat fluxes for the flight tracks shown in Fig. 5.

Citation: Journal of Hydrometeorology 1, 5; 10.1175/1525-7541(2000)001<0462:EWEWPP>2.0.CO;2

Fig. 7.
Fig. 7.

Examples of the spatial distributions of daily evapotranspiration rates, estimated by using PASS2.

Citation: Journal of Hydrometeorology 1, 5; 10.1175/1525-7541(2000)001<0462:EWEWPP>2.0.CO;2

Save
  • Brutsaert, W. H., 1982: Evaporation into the Atmosphere. Theory, History, and Applications. D. Reidel, 299 pp.

    • Crossref
    • Export Citation
  • Feddes, R. A., M. Menenti, P. Kabat, and W. G. M. Bastiaanssen, 1993: Is large-scale inverse modelling of unsaturated flow with areal average evaporation and surface soil moisture as estimated from remote sensing feasible? J. Hydrol.,143, 125–152.

    • Crossref
    • Export Citation
  • Friedl, M. A., 1996: Relationships among remotely sensed data, surface energy balance, and area-averaged fluxes over partially vegetated land surfaces. J. Appl. Meteor.,35, 2091–2103.

    • Crossref
    • Export Citation
  • Gao, W., 1995: Parameterization of subgrid-scale land surface fluxes with emphasis on distributing mean atmospheric forcing and using satellite-derived vegetation index. J. Geophys. Res.,100, 14;th305–14 317.

    • Crossref
    • Export Citation
  • ——, R. L. Coulter, B. M. Lesht, J. Qiu, and M. L. Wesely, 1998: Estimating clear-sky regional surface fluxes in the southern Great Plains Atmospheric Radiation Measurement site with ground measurements and satellite observations. J. Appl. Meteor.,37, 5–22.

    • Crossref
    • Export Citation
  • Gash, J. H. C., 1987: An analytical framework for extrapolating evaporation measurements by remote sensing surface temperature. Int. J. Remote Sens.,8, 1245–1249.

  • Gillies, R. R., T. N. Carlson, J. Cui, W. P. Kustas, and K. S. Humes, 1997: A verification of the triangle method for obtaining surface soil water content and energy fluxes from remote measurements of the normalized difference vegetation index (NDVI) and surface radiant temperature. Int. J. Remote Sens.,18, 3145–3166.

    • Crossref
    • Export Citation
  • Grossman, R. L., 1992a: Convective boundary layer budgets of moisture and sensible heat over an unstressed prairie. J. Geophys. Res.,97, 18 425–18 438.

    • Crossref
    • Export Citation
  • ——, 1992b: Sampling errors in the vertical fluxes of potential temperature and moisture measured by aircraft during FIFE. J. Geophys. Res.,97, 18 439–18 443.

  • Humes, K. S., W. P. Kustas, and M. S. Moran, 1994: Use of remote sensing and reference site measurements to estimate instantaneous surface energy balance components over a semiarid rangeland watershed. Water Resour. Res.,30, 1363–1373.

    • Crossref
    • Export Citation
  • Jackson, R. B., J. Canadell, J. R. Ehleringer, H. A. Mooney, O. E. Sala, and E. D. Shulze, 1996: A global analysis of root distributions for terrestrial biomes. Oecologia,108, 389–411.

    • Crossref
    • Export Citation
  • Kustas, W. P., and J. M. Norman, 1996: Use of remote sensing for evapotranspiration monitoring over land surfaces. Hydrol. Sci.,41, 495–516.

    • Crossref
    • Export Citation
  • ——, M. S. Moran, K. S. Humes, D. I. Stannard, P. J. Pinter Jr., L. E. Hipps, E. Swiatek, and D. C. Goodrich, 1994: Surface energy balance estimates at local and regional scales using optical remote sensing from an aircraft platform and atmospheric data collected over semiarid rangelands. Water Resour. Res.,30, 1241–1259.

    • Crossref
    • Export Citation
  • LeMone, M. A., and Coauthors, 2000: Land–atmosphere interaction research and opportunities in the Walnut River Watershed in southeast Kansas: CASES and ABLE. Bull. Amer. Meteor. Soc.,81, 757–779.

    • Crossref
    • Export Citation
  • Moran, M. S., T. R. Clarke, W. P. Kustas, and M. Weltz, 1994a: Evaluation of hydrologic parameters in a semiarid rangeland using remotely sensed spectral data. Water Resour. Res.,30, 1287–1297.

    • Crossref
    • Export Citation
  • ——, W. P. Kustas, A. Vidal, D. I. Stannard, J. H. Blanford, and W. D. Nichols, 1994b: Use of ground-based remotely sensed data for surface energy balance evaluation of a semiarid rangeland. Water Resour. Res.,30, 1339–1349.

    • Crossref
    • Export Citation
  • Ottl;aae, C., and D. Vidal-Madjar, 1994: Assimilation of soil moisture inferred from infrared remote sensing in a hydrological model over the HAPEX-MOBILHY region. J. Hydrol.,158, 241–264.

    • Crossref
    • Export Citation
  • Paw U, K. T., and W. Gao, 1988: Application of solutions to nonlinear energy budget equations. Agric. For. Meteor.,43, 121–145.

    • Crossref
    • Export Citation
  • Price, J. C., 1990, Using spatial context in satellite data to infer regional scale evapotranspiration. IEEE Trans. Geosci. Remote Sens.,28, 940–948.

    • Crossref
    • Export Citation
  • Satterlund, D. R., 1979: An improved equation for estimating long-wave radiation from the atmosphere. Water Resour. Res.,15, 1649–1650.

    • Crossref
    • Export Citation
  • Song, J., M. L. Wesely, R. L. Coulter, and E. A. Brandes, 2000: Estimating watershed evapotranspiration with PASS. Part I: Inferring root-zone moisture conditions using satellite data. J. Hydrometeor.,1, 447–461.

    • Crossref
    • Export Citation
  • Zhang, L., R. Lemeur, and J. P. Goutorbe, 1995: A one-layer resistance model for estimating regional evapotranspiration using remote sensing data. Agric. For. Meteor.,77, 241–261.

    • Crossref
    • Export Citation
  • Fig. 1.

    Scheme of the PASS2 model.

  • Fig. 2.

    Temporal variations of modeled RAM content θa, averaged among the eight pixels that were closest to the eight NCAR sites and of the average soil moisture θ observed at the eight NCAR sites. The vertical bars represent the maximum range of values for the eight pixels or eight sites for the upper layer of soil.

  • Fig. 3.

    Temporal variations of modeled latent heat fluxes λE, averaged among the eight pixels that were closest to the eight NCAR sites and the average λE observed at the eight NCAR sites. The vertical bars represent the maximum ranges of values for the eight pixels or eight sites.

  • Fig. 4.

    Comparison of daily evapotranspiration rates observed on 10 days at the eight NCAR sites with the model estimates averaged among pixels within 1 km of each NCAR site. The error bars indicate one standard deviation on each side of the mean for each set of pixels.

  • Fig. 5.

    Fifteen selected flight tracks of King Air aircraft on DOY 130, 140, 141, and 142.

  • Fig. 6.

    Comparison of modeled versus measured latent heat fluxes for the flight tracks shown in Fig. 5.

  • Fig. 7.

    Examples of the spatial distributions of daily evapotranspiration rates, estimated by using PASS2.

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