Ground measurements

The SGP CART site is located in an area of about 350 km × 400 km in Kansas and Oklahoma (Fig. 1),where a large number of observational instruments are operated routinely and special field campaigns are conducted (Stokes and Schwartz 1994). The data used in this study include (a) surface fluxes of energy and radiation and other micrometeorological parameters measured by 10 energy balance Bowen ratio (EBBR) stations and (b) air temperature, humidity, and precipitation measured by 58 ground stations of the Oklahoma Mesonet located within the CART area. The meteorological parameters from the EBBR stations were used as model inputs, and the flux measurements from the EBBR stations and the meteorological parameters from the Oklahoma Mesonet stations were used to evaluate the output of the model. The measurements at the EBBR stations provide continuous 30-min-averaged values for each component of the surface energy budget, including net radiation R_n, soil heat flux G, latent heat flux (LE), and sensible heat flux (H) (Wesely et al. 1995).

Figures 2a–d show the diurnal variations of each surface flux measured at the EBBR stations on 12 July 1995. Although the differences in net radiation among the different stations were relatively small, differences in daytime latent, sensible, and soil heat fluxes are substantial. The midday H and LE across the CART site varied by as much as 250 W m⁻² and 350 W m⁻², respectively. The large spatial differences measured on this specific day are consistent with those found by Wesely et al. (1995), who examined a month of data from the EBBR stations across the CART site.

Satellite data

The data from the Advanced Very High Resolution Radiometers (AVHRRs) used in this study were obtained by direct reception of the NOAA-12 and NOAA- 14 satellites’ high-resolution picture transmission (HRPT). The HRPT data were calibrated into NOAA level-1b data in the form of reflectance for channels 1 and 2 and of radiance for channels 3, 4, and 5 (Kidwell 1991). Figure 1 shows the combined imagery of channels 1, 2, and 4 received from the NOAA-14 satellite at 1407 LST 12 July 1995. The image covers an overall outline of latitudes 34°53′–38°35′N and longitudes 95°30′–99°33′W. The data were rectified and mapped to a geographic coordinate system by using ground control points determined by the global positioning system.

The process of rectification involves resampling the data by using a third-order nearest neighbor algorithm in which the output pixel size is fixed at 1.0 km × 1.0 km. The accuracy of georectification was checked against some known ground targets such as visible water bodies. This check is especially important for extracting satellite pixels for the EBBR stations, which measure the surface fluxes representing only a small area. Two ground locations clearly visible in the images were used to perform ground reference checks. One of these ground references is the water body in the small bay measuring about 1 km × 1 km east of Kaw City, whichis clearly visible in the east-central portion of the image (36.7635°N, 96.8069°W) (a black patch west of station 12 in Fig. 1). A pixel with a higher channel 1 reflectance than channel 2 reflectance, typical for a water surface, can be identified for the bay. Another reference location is the water body in the eastern portion of the Great Salt Plains Lake (36.7500°N, 98.1383°W), which is clearly visible north of station 15 in the west-central portion of the image as a circular patch that is partially yellow (high reflectance in channel 1), indicating a salt plain, and nearly black, where a lake exists. The offsets between the locations for the ground reference points in the image and those determined from geographic maps are less than one pixel.

The reflectances in the red waveband (channel 1: 0.58–0.68 μm) and the near-infrared waveband (channel 2: 0.73–1.10 μm) were used to calculate the normalized difference vegetation index (NDVI) as NDVI = (ch2 − ch1)/(ch1 + ch2), while the radiances for channel 4(10.3–11.3 μm for NOAA-12 and 10.5–11.5 μm for NOAA-14) and channel 5 (11.50–12.50 μm) in the thermal infrared range were converted to brightness surface temperature by the standard procedure documented in the NOAA satellite user’s manual (Kidwell 1991).

To derive ground-level spectral reflectances and surface temperature from the satellite-derived at-sensor values, the calculations of atmospheric scattering, absorption, transmission, and emission in the layer from the satellite altitude to the altitude of the site were made using a commonly used atmospheric radiation transfer model LOWTRAN7, with radiosonde and aerosol data taken at the CART site (Lesht 1995; Michalsky et al. 1995). The calculated atmospheric quantities were used to estimate the differences in reflectances between satellite-level values and corresponding ground-level values by using the algorithm suggested by Fraser et al. (1992), and thus appropriate adjustments can be made to obtain corrected reflectances. The ground-level T_s wasobtained by adjusting the raw T_s with calculated atmospheric transmittance and radiance in the thermal region associated with AVHRR channels 4 and 5.

The atmospheric correction with LOWTRAN7 was compared with some alternative simple methods that do not require complicated atmospheric calculations, which may not be feasible for many applications. To linear scale the uncorrected NDVI to corrected NDVI without performing atmospheric calculations, we use a normalization in the form of (NDVI − NDVI_n)/(NDVI_υ − NDVI_n) = (NDVI0 − NDVI0_n)/(NDVI0_υ − NDVI0_n), where NDVI and NDVI0 represent the NDVI value used in the surface model and the uncorrected NDVI value, respectively; where NDVI_n and NDVI0_n represent the corrected and uncorrected NDVI values, respectively, for a nonvegetated surface; and where NDVI_υ and NDVI0_υ represent the corrected and uncorrected NDVI values, respectively, for a full canopy. This relationship allows the range of the change in uncorrected NDVI to represent the actual change in NDVI at surface level as used in the surface model. Thus, the ground-level NDVI values may be estimated using NDVI = (NDVI_υ −NDVI_n)(NDVI0 − NDVI0_n)/(NDVI0_υ − NDVI0_n) + NDVI_n.

Price (1984) suggested a split-window method for adjusting at-sensor T_s to ground-level T_s without using atmospheric calculations. The split-window method assumes that atmospheric effects are similar between the two AVHRR thermal channels and they can cancel each other by using an appropriate rearrangement of radiation transfer equations for the two channels so that the ground-level T_s can be calculated from the AVHRR brightness temperature of channel 4 (T₄) and channel 5 (T₅) using T_s = 4.33T₄ − 3.33T₅.

Figure 3a compares NDVI values corrected with LOWTRAN7 and by the linear scaling method. The linear scaling appears to closely describe the linear trend between ground-level NDVI and NDVI at the top of the atmosphere (TOA). In this case, the constant values of NDVI0_n = 0, NDVI_n = 0.2, NDVI0_υ = 0.5, and NDVI_υ = 0.98 were used for the two datasets collected on different days. The slopes of the regression of the corrected NDVI values using LOWTRAN7 are slightly different from those for the linear scaling, with minimumNDVI values being smaller than the given NDVI_n. More studies are needed to investigate the stability of this scaling method and effects of changes in atmospheric conditions, satellite, and solar angles. In the present study, the NDVI values corrected with LOWTRAN7 were used. Figure 3a shows that the corrected T_s values with the split-window method are about 9 K (root-mean- square difference) higher than those calculated using the LOWTRAN7 method for the data for 12 July, but the two methods agree closely (within about 2 K) for the data for 14 October. It is unclear whether the relatively lower temperature in the lower troposphere for October data is beneficial to the split-window method, which was originally used for oceanic conditions. While further studies with more data may be needed to address this issue, the T_s values corrected with LOWTRAN7 calculations were used in the present paper.

Surface changes described by AVHRR data

Figure 4 shows the spatial distributions of uncorrected NDVI derived from the AVHRR observations by the NOAA-12 and NOAA-14 satellites across theCART site on different clear days selected to represent different seasons. Comparison with a land use map from the U.S. Geological Survey (not shown) indicates that on 13 April the area with a large NDVI from the central to the southwest was covered primarily by winter wheat, the northeast quadrant and west side were primarily rangeland, and the southeast corner was mostly woodland mixed with rangeland (Gao 1994b). On 12 July, the central wheat area had changed to low NDVI, representing matured or harvested winter wheat by this time of year. The rangeland in the eastern portion appeared to be greener, with higher NDVI, than the rangeland in the western portion, probably because of the difference in precipitation between the two areas. In addition, valley areas along riverbeds lying approximately from the northwest to the southeast had a relatively higher vegetation density than nearby areas. On 14 October, most of the CART site had a small NDVI, except for the southeast woodland areas. As the season progressed, NDVI values decreased to near zero in winter, indicating little green vegetation existing in the area.

Heterogeneous surface energy budget

In the PASS model, the surface energy budget is calculated for individual cells that represent the satellite pixels at the 1-km scale used in the present study or the subgrid cells that are sometimes used in large-scale atmospheric models. The surface energy budget at a given cell i is expressed as

View Expanded

where

View Expanded

Here, each of the terms has the conventional meaning except that the terms are applied to individual cells within a large area of interest; the value of Γⁱ is the ratio of soil heat flux (Gⁱ) to net radiation (Rⁱ_n); δⁱ is the surface shortwave albedo; K↓ⁱ is the total incoming shortwave radiation; I↓ⁱ and I↑ⁱ are the incoming and outgoing longwave radiation, respectively; ρ is the air density; C_p is the air-specific heat at constant pressure; γ is the psychrometric constant; e_s(Tⁱ_s) is the saturation vapor pressure at surface temperature (Tⁱ_s); eⁱ_a and Tⁱ_a are the local air vapor pressure and air temperature, respectively; and Rⁱ_c and Rⁱ_a are the local bulk surface resistance and aerodynamic resistance, respectively.

Module for estimating surface parameters from remotely sensed spectral indices

The PASS model consists of four interconnected modules developed to calculate the surface energy balance at the resolution of satellite observations. The first module was developed for estimating essential surface parameters at the pixel level from a satellite-derived vegetation index, the simple ratio (SRⁱ) of the reflectance in the near-infrared band to the reflectance in the red band or NDVI (SR and NDVI are interchangeable through SR = [1 + NDVI]/[1 − NDVI]). The surface parameters, including surface albedo (δⁱ), surface conductance (Gⁱ_c = [Rⁱ_c]⁻¹), soil heat flux ratio (Γⁱ), and surface roughness length (zⁱ₀), are expressed by the following functions:

View Expanded

and

View Expanded

Here α₁, α₂, K, δ₂, G₀, β₁, β₂, μ₁, μ₂, π₀, π₁, and π₂ are empirically determined numerical constants, and functions f₁ and f₂ describe the influence on the surface conductance by the atmospheric water vapor deficit δeⁱ and available soil water content θⁱ_r in the plant root zone defined as f₁ = (1 + β₃δe) and f₂ = 1 − exp(−β₄θ_r) (Kim and Verma 1991). The physical basis and methodology used for developing these functions were described in detail by Gao (1995). Most of them were derived by fitting these empirical functions with the results from calculations based on more complex canopy models and previous field measurements.

Function (2a) describes the surface albedo as a combined function of solar zenith angle θ_s and surface vegetation density described by SRⁱ. Function (2b) calculates the total surface conductance, with the first term contributed by nonvegetated surfaces and the second term contributed by the vegetation canopy, for the transfer of water vapor from the surface to the atmosphere. The conductance for the vegetation term is described as a function of the solar radiation within the photosynthetically active radiation (PAR) wave band (about 0.4–0.7 μm) (K↓ⁱ_PAR), which was assumed to be 50% of the total solar radiation measured at the site, the vegetation density or SR, and atmospheric and soil moisture conditions. Function (2c) describes the ratio of soil heat flux to net radiation as a function of the solar zenith angle and the vegetation density because the radiation penetrating to the soil surface to generate surface heat flux would increase with the decreasing solar zenith angle and the decreasing vegetation density (Kustas and Daughtry 1990). Function (2d) was designed to allow the surface roughness length to vary according to local NDVI. The values of three constants π₀, π₁, and π₂ listed in Table 1 allow z₀ = 0.01 cm for water surface (Brutsaert 1988) with NDVI = 0, z₀ = 0.1–5 cm for grass prairie (Gao et al. 1992b) with NDVI = 0.4–0.6, and z₀ = 1–6.5 cm for more vegetated areas of grass mixed with trees with NDVI = 0.7–0.98. The determination of these constants is empirical and subject to uncertainties when vegetation density is not consistent with surface roughness. Thus, while (2d) may only catch large spatial differences such as the difference between water bodies and grass, it may not be accurate for sparse canopies and wooded areas with mixed grass and trees. For the same reason, the possible difference between z₀ for momentum and z_0h for heat (Stewart 1995) is not considered in the present function. This difference may cause an uncertainty in estimating surface roughness for surface heat transfer and affect modeling results of the surface energy budget.

Figure 5a compares the values for surface albedo calculated by function (2a) with those measured over atallgrass prairie site in Kansas. Figure 5b shows the change of the measured soil heat flux ratio Γ_i with site- specific AVHRR-derived SR values for the selected EBBR stations at the CART site. The Γ–SR relationship derived from the present dataset is close to that obtained by Kustas et al. (1993).

Module for parameterizing the feedback of the near-surface meteorology to local surface energy balance

The second module implements a distribution scheme, described in detail by Gao (1995), that is designed to assign different values of air temperature, humidity, and wind speed to different pixels according to local conditions of the surface. The basis of the scheme is the variation of local near-surface air temperature and relative humidity with SR (Fig. 6a). To implement this scheme, the PASS model was first run with average surface meteorology and average surface parameters [δ, G_c, Γ, and z₀ estimated by functions (2a)–(2d), with SR averaged for the whole CART area] to produce estimates of average friction velocity _*, average surface temperature _s, and average vapor pressure (_a). The model was then run again with pixel-specific SRⁱ but still with average surface meteorological parameters to obtain first-order estimates of pixel-specific surface parameters ûⁱ_*, T̂ⁱ_s, and êⁱ_a, which result from partial influence of local surfacechanges. Finally, pixel-specific wind speed, air temperature, and vapor pressure were estimated with the outputs from the previous two model runs as uⁱ = u[1 + α_u(ûⁱ_* − _*)/_*], Tⁱ_a = T_a + α_T(ⁱ_s − _s), and eⁱ_a = e_a + α_q(êⁱ_a − _a), where u, T_a and e_a are the average wind speed, air temperature, and vapor pressure derived from measurements at the EBBR stations.

Figure 6b shows the relation of the 2-m air temperature at the EBBR stations with the temperature difference (ΔTⁱ = T̂ⁱ_s − _s) calculated by the automatic distributing scheme described above. The value of coefficient α_T (0.57) was obtained for this dataset by a linear regression. In the original PASS model, the coefficients α_u, α_T, and α_q were assumed to have an equal value and were calculated on the basis of the knowledge of turbulent mixing in the atmospheric boundary layer, and their values should represent the degree of influence by the footprint of the upwind surface. The expression forα_T = {1 − z[d + ln(1.11)·kDu_*/u]⁻¹} was derived from equations for the turbulence mixing in the atmospheric boundary layer, where d is the mean displacement height representing an elevated source or sink for a plant canopy; the constant 1.11 was the inverse of 90%, which was the assumed flux contribution by the surface-source upwind; k is the von Kármán constant; and D is a dimension factor. For α_T = 0.57 derived from the present data, the dimension factor D was estimated to be about 870 m, which by definition represents the horizontal distance over which the surface condition can influence the air temperature at 2 m.

Note that under circumstances where a substantial mesoscale gradient exists, the distributing scheme described above should be used only for smaller areas, where the mesoscale gradient should be much smaller than the micrometeorological gradient because of surface variabilities within the area of interest. In this case, a studied area should be divided into several subdomains and then the distributing scheme should be applied within the individual subdomains. Such a strategy is not addressed here but could be adopted by coupling the PASS model with a mesoscale meteorological model.

Module for deriving soil moisture from visible and thermal infrared remote sensing data

The most difficult aspect of applying an atmosphere–surface exchange model over a regional scale is the lack of information on evaporation from the soil surface and the soil water content, which influences evapotranspiration and surface conductance by adjusting the openingof plant leaf stomata, a major pathway for water vapor and other gaseous exchange. When sufficient soil water content exists, the surface conductance can be estimated fairly accurately by function (2b) to describe the effects of solar radiation, green leaf amount, and local atmospheric moisture conditions (Gao 1994a). Under natural conditions when the soil water is limited, however, the surface conductance is strongly modulated by the amount of soil water available to plant uptake in the plant root zone.

Figure 7a shows the uncorrected NDVI values plotted against T_s for all of the 1-km resolution pixels across the CART site derived from the AVHRR observations by the NOAA-14 satellite on a clear day (12 July 1995). Most of the pixels are located within a triangle-shaped area, while a smaller number of points are scattered to the lower left (relatively small NDVI and T_s). Comparing with land use and geographic maps shows that the points within the triangular area are from the pixels representing land areas, while the points scattered over the lower left are from the pixels that either represent water bodies or boundaries between water bodies and land areas. Water surfaces are relatively cool and have negative NDVI because of high reflectance in channel 1. A linear boundary expressed as NDVI = 0.54–0.026(T_s − 300) appears to separate the water pixels from land pixels and, when applied, indicates that less than 1% of the 107055 pixels examined represented areas with water surfaces.

The triangle-shaped NDVI–T_s distribution is typical for land pixels and has been reported by other investigators (Hope 1988; Nemani and Running 1989; Carlson et al. 1994; Gillies and Carlson 1995). The surface temperature range for a given NDVI has been attributed to differences in soil moisture, with higher temperatures associated with lower soil moisture content (Hope and McDowell 1990). Carlson et al. (1994) have also attributed the increase in T_s for a given NDVI to the decrease in soil moisture content and have developed methods to infer soil moisture from NDVI–T_s relationships.

In this paper, we use a different method to explicitly calculate soil moisture from combined AVHRR observations and minimal ground measurements. In this method, the AVHRR-derived Tⁱ_s air temperature at 2 m, and the wind speed at 2 m distributed to each pixel by the method discussed in section 3c, are used to compute surface-sensible heat flux by using Hⁱ = ρC_p(Tⁱ_s − Tⁱ_a)/Rⁱ_a, where Rⁱ_a is the aerodynamic resistance and was computed by the surface-layer relationship Rⁱ_a = 0.74(k²uⁱ)⁻¹{ln[(z − d)/zⁱ₀]}², where neutral conditions were assumed for the near-surface atmosphere, without using a more complicated iteration procedure to include thermal effects for possibly unstable conditions. The thermal stability may have some effects on pixel-specific R_a, in which case, iteration is required to include surface heat flux in the calculation of R_a with a surface layer relationship for unstable conditions. This will significantly increase computation when 314 × 344 pixels are involved (some effective method should be added to consider this problem in the future). Although a large percentage of surface cover is rangeland and pasture, some cropland and woodland also exist in the CART area (Gao 1994b). In this model application, a fixed canopy height was assumed to be 0.4 m, which is close to the canopy height for tallgrass prairie (Gao et al.1992a). Improvements could be made by using land use types to assign canopy heights for each satellite pixel. The surface zero displacement height d was estimated as 0.67 of the mean canopy height (Brutsaert 1988). The surface latent heat flux was then calculated as a residual term, that is, LEⁱ = Rⁱ_n(1 − Γⁱ) − Hⁱ. Here, under the clear-sky condition, Rⁱ_n was estimated with Eq. (1b). Downwelling solar radiation measured by the ground stations at the time of satellite pass was used with surface albedo δⁱ estimated with function (2a) by using observed SRⁱ; incoming and outgoing longwave radiation were estimated by using AVHRR-derived Tⁱ_s, pixel- specific Tⁱ_a and eⁱ_a. The Γⁱ was estimated with function (2c), also using observed SRⁱ. The surface conductancefor each pixel was then estimated from the derived LE byGⁱ_c = {ρC_p(γLE)⁻¹[e(Tⁱ_s) − eⁱ_a] − Rⁱ_a}⁻¹.

The resulting values of surface conductance are shown in Fig. 7b in relation to observed SRⁱ values. The theoretical Gⁱ_c values for an unstressed condition, as calculated with function (2b) by assuming a sufficient soil water supply [or no influence of soil moisture, i.e., f₂ = 1 in function (2b)], were also shown for comparison in Fig. 7b. The estimated values can be considered to represent stressed conductance most typical with real soil moisture conditions, while the latter calculations represent unstressed conductance. Theoretical studies by Sellers (1987) have shown that the G_c–SR graph should have a near-linear relationship because both G_c and SR increase with canopy density in a similar manner. Gao et al. (1992a) confirmed the existence of the G_c–SR linearity with a limited number of field experimental data, and the surface conductance derived from AVHRR data presented in Fig. 7b tends to support the existence of the G_c–SR linearity.

For a given SR, the inferred surface conductance has a range of values, largely reflecting the influence of the variation in soil moisture. Kim and Verma (1991) derived an empirical function describing the relationship between the surface conductance of a tallgrass canopy in Kansas and the percentage of the extractable soil water in the primary plant root zone (the extractable water is determined by comparing soil water potential with plant water potential). The function, Gⁱ_c = Gⁱ_*f₂(θⁱ_r) = Gⁱ_*[1 − exp(−1.7θⁱ_r)], of Kim and Verma (1991) was used to infer the proportion of extractable soil water or relative soil moisture θⁱ_r on the basis of the stressed conductance Gⁱ_c derived from AVHRR data and the unstressed conductance Gⁱ_* calculated by function (2b). An inversion calculation was made to obtain one soil moisture value for every pixel, with 0 and 1 representing completely dry and saturated soil, respectively.

Figure 8a shows the correlation between the derived soil moisture and the amount of total accumulated previous rainfall monitored at the 58 Oklahoma Mesonet stations. The correlation was calculated by pairing the derived soil moisture values extracted for each Mesonet station with the corresponding rainfall data at the same station accumulated for different periods of time just prior to the satellite pass (12 July 1995). The correlation coefficient increases rapidly to 0.5 in response to the rainfall accumulated approximately within a previous month. The correlation coefficient drops sharply, however, with the rainfall during the period from 30 to 60 days before the satellite pass, possibly because the heavy rain or scattered thunderstorms that occurred in this period (indicated by a sharp increase in the accumulated rainfall amount) were less efficient in penetrating into the soil. The increase in correlation coefficients reaching approximately 0.6 at periods longer than 2 months before the satellite pass may reflect a long-term effect of the precipitation on the soil water content reserved inthe deep plant root zone, which typically extends to 1–2 m in depth.

Figure 8b shows the spatial distribution of the derived soil moisture and the previous rainfall accumulated for the previous 100 days. The satellite-derived distribution of soil moisture values was shown for every 1-km pixel. The rainfall pattern was produced with the data at the 58 ground stations by using appropriate interpolation between the stations. The pixels with extremely high soil moisture close to 1 (red color) represent water bodies and surrounding areas. The patterns of spatial variation from these two independent sources match quite well, and the large amount of rainfall in the northeast corner corresponds to the high soil moisture in the same region. Generally speaking, the eastern portion of the CART site has a higher soil moisture associated with a relatively large amount of accumulated rainfall, compared to the soil moisture and rainfall in the western portion of the site.

It should be mentioned that the products of soil moisture derived on the basis of the satellite optical remote sensing are primarily related to the radiometric surface temperature, which is partially controlled by soil moisture conditions. The empirical equation we used was derived by Kim and Verma from the measurements of soil moisture in the deep soil (up to 1 m) in the tallgrass prairie in Kansas, which has similarities to the soil in many CART locations. Thus, theoretically, the derived soil moisture should represent the soil moisture content in the plant root zone, but any uncertainties in developing the empirical equation and the differences in soil conditions between the First ISLSCP (International Satellite Land-Surface Climatology Project) Field Experiment site and the CART site and other factors involved in calculating surface temperature from surface energy budget and in deriving surface temperature from satellite thermal infrared measurements will cause uncertainties in the derived soil moisture. Further validation of this remote–sensing-based soil moisture algorithm is needed.

Module for fast computation of the surface energy balance at satellite-pixel scale

The last module was designed to compute the surface energy budget for every satellite pixel (for every 1-km area in the present case) with the results from the first three modules. An analytical solution obtained for the surface energy budget equation of (1a) (Paw U and Gao 1989; Gao 1995) was used to compute surface temperature for each pixel Tⁱ_s without numerical iteration so that fast calculations can be made for a large number of pixels. The calculated surface temperature then was used to calculate latent and sensible heat fluxes using (1c) and (1d), respectively. The detailed procedure for solving the energy budget equation system (1a)–(1d) was described in detail by Gao (1995).

Figure 9 shows an overall schematic diagram for thePASS model and associated modeling procedures. The input data include average meteorological conditions derived from a limited number of ground meteorological stations and pixel-specific data of NDVI and T_s derived from high-resolution AVHRR remote sensing. The empirical constants used in (2a)–(2d) are listed in Table 1 along with their values derived from previous experiments primarily for grassland conditions. Their possible variations among different land use types are not included here for simplicity but should be further considered when more field data can be summarized in the future work.

The four modules of the PASS model were combined into a single procedure that can be used to calculate surface energy fluxes with AVHRR observations and a limited set of ground measurements. Under clear-sky conditions, only ground measurements of solar radiation, air temperature, humidity, and wind speed measured at a few representative stations are needed to compute the fluxes for different times of day over the large areas covered by satellite remote sensing. Under cloudy conditions, the situation is more complicated. Spatial variation in the incoming total solar radiation must be included in the calculations, and surface conditions need to be derived from composite clear-sky pixels from satellite observations on the other days [i.e., the satellite data for clear-sky pixels must be derived by combining a number of daily images and by choosing pixels that have maximum NDVI (clouds usually have smaller NDVI than land)]. The flux estimation under cloudy conditions is not presented here and needs to be further investigated. The performance of the model for flux calculations made for clear-sky conditions is evaluated below with ground data from different sources.

Figure 10 shows spatial distributions of the calculated surface albedo, net radiation, surface temperature, surface-sensible and latent heat fluxes, along with the derived soil moisture for the entire CART area (calculated for 1400 LST 12 July 1995). The surface energy balance for the water bodies, which accounts for less than 1% of the total area, was calculated by assuming very large surface conductance and Γⁱ = 0.1 (close to the value for saturated soft). The vegetated area in the easternCART site generally had lower albedo than the western portion. The net radiation for land pixels ranged from 400 W m⁻² to about 650 W m⁻² for some densely vegetated areas in the eastern portion. This range is much larger than that detected by the EBBR stations (Fig. 2). The water bodies appear to have a relatively smaller net radiation compared with surrounding land surfaces because of estimated higher surface albedo. The distribution of sensible and latent heat fluxes for the land pixels by and large follows the change in surface temperature.

Evaluation with flux measurements at individual EBBR stations

Uncertainties in matching satellite pixels with the EBBR stations can be caused by the fact that satellite pixels have a size of 1 km, with a georectification error of about 1 km, and the measurements at the EBBR stations represent surface fluxes over a much smaller area. To reduce the noise, the fluxes modeled for individual EBBR stations were averaged to produce EBBR-average modeled fluxes, which then are compared with the average fluxes from the measurements made at the 10 EBBR stations, as shown in Fig. 11.

The root-mean-square (rms) differences between modeled and measured values of EBBR-average fluxes are approximately 26, 13, 39, and 21 W m⁻² for R_n, G, LE, and H, respectively, for the case of 12 July 1995, and 55, 19, 42, and 25 W m⁻² for R_n, G, LE, and H, respectively, for the case of 14 October 1995. The relative error, however, is the smallest for R_n because it has a much larger value than other fluxes and the largest for G because it has the smallest magnitudes. The rms errors seem to be small for midday large fluxes but are still quite significant for smaller fluxes in the early morning and late afternoon.

There are several factors that may contribute to the differences between modeled and measured fluxes: 1) the mismatch between surface areas covered by satellitepixels and measured by the EBBR stations as described earlier, 2) the other important meteorological and biophysical factors that are not included in parameterization functions (2a)–(2d), 3) the uncertainties in empiricalconstants used in the parameterization and their variations among different land use types, 4) the uncertainties in surface meteorology redistribution scheme and soil moisture scheme, and 5) the uncertainties in satellite-based remote sensing measurements and atmospheric correction calculations. These uncertainties should be further investigated with field data and model sensitivity studies.

Evaluation with surface meteorology measured at the Oklahoma Mesonet stations

To further validate the spatial variation of modeled surface heat fluxes, an independent dataset for air temperature and humidity measured at 1.5 m above the ground at the 58 Oklahoma Mesonet stations covering the southern half of the SGP CART site was used. The surface latent and sensible heat fluxes calculated for the pixels covering these ground stations were used to compute the air humidity and temperature at 1.5 m with (1c) and (1d), respectively, together with other intermediate outputs from the PASS model including surface conductance, aerodynamic resistance, and surface temperature. Figure 12 compares calculated air temperature and relative humidity at the midday of 12 July 1995 with corresponding measurements. The rms difference between modeled and measured values are small, equal to 1.29°C for air temperature and 0.06 for relative humidity. Because the air temperature and humidity at the Mesonet stations were not used in the flux calculations, the comparisons shown in Fig. 12 should provide an independent evaluation of modeling results. We note that because air temperature and relative humidity are less sensitive to local conditions than are LE and H, the point-by-point comparisons shown in Fig. 12 are reasonable and may be less influenced by uncertainties in matching ground stations with satellite pixels than the comparison for LE and H.

Comparison of the estimated CART average surface fluxes with EBBR-derived average surface fluxes

The modeling method described above was used to compute the surface fluxes for all 1-km resolution pixels covering the CART area. The resulting fluxes for 108016 pixels (314 × 344) were averaged to produce CART average fluxes. These fluxes were then compared in Fig. 13 with the fluxes averaged from the measurements made at the 10 EBBR stations for 12 July and 14 October 1995, respectively. The net radiation was larger on 12 July than on 14 October, largely because of the higher incoming solar radiation. The latent heat flux was larger than the sensible heat flux on 12 July, but the opposite was true on 14 October because the surface had less vegetation (see Fig. 4). The modeled CART average LE and H followed this seasonal change in the relative magnitudes between LE and H.

The net radiation estimated by the two different methods is very close except for the afternoon on 14 October, when CART-average R_n was up to 100 W m⁻² higher than the EBBR averages. The modeled CART-average G values were close to EBBR averages for 12 July, but the CART averages were higher for 14 October. The CART-average LE values were up to about 50 W m⁻² higher than the EBBR averages in the afternoon of bothdays. The difference between the sensible heat fluxes by the two methods is within the range of the model uncertainty for H and thus is not significant.

The difference between the CART-average fluxes and the EBBR-average fluxes may be caused partially by the uncertainties in the model parameterization, as discussed in section 4a, and partially by the difference in spatial coverage by the satellite data and the EBBR stations. As shown in Fig. 1 and Fig. 4, a few EBBR stations in the eastern part of the CART site represent wet surfaces and the smaller wet area in the southeastern quadrant is not sampled at all. This disparity could result in the EBBR-derived average LE being lower than the CART-average LE in the afternoon, although further validation is needed to evaluate the representativeness of the EBBR-derived surface fluxes.