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  • View in gallery

    False color imagery for an area of 314 km × 344 km of the SGP CART site derived from surface reflectances detected in the red channel 1 (0.58–0.68 μm), the near-infrared channel 2 (0.73–1.10 μm), and radiances in the thermal infrared channel 4 (10.5–11.5 μm) of the AVHRR on the NOAA-14 satellite. The locations of the CART surface EBBR stations, the CART eddy correlation stations, and the Oklahoma Mesonet stations are indicated.

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    Diurnal cycle of (a) sensible heat flux, (b) latent heat flux, (c) net radiation, and (d) soil heat flux measured on 12 July 1995 by the 10 EBBR stations (indicated by different station identification numbers).

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    (a) Comparison between ground-level NDVI values corrected using LOWTRAN7 and a linear scaling method for AVHRR data from NOAA-14 on 12 July and 14 October 1995. Only 1 out of every 100 pixels across the CART site were plotted. (b) Comparison between ground-level surface temperature values corrected using LOWTRAN7 and by the split-window method. Only 1 out of every 100 pixels across the CART site were plotted.

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    Spatial distributions of AVHRR-derived NDVI at 1-km spatial resolution across the CART area of 314 km × 344 km for clear days selected in different seasons.

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    (a) Comparison of surface albedo calculated by (2a) with measurements taken over a tallgrass prairie in Kansas and (b) changes of the ratio of soil heat flux to net radiation with spectral vegetation index SR. The function derived from the regression of the data (solid squares and associated regression curve) taken at the EBBR stations was compared with the curve (line with open circles) derived by Kustas et al. (1993).

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    (a) Variations of local midday air temperature and relative humidity measured on 12 July 1995, at 2 m above the ground with local vegetation conditions described by AVHRR-derived SR. (b) Relationship between the local air temperature and the local temperature forcing ΔTi (defined in the text) induced by surface changes.

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    (a) Relationship of AVHRR NDVI to surface temperature for all satellite pixels across the CART site from AVHRR observations at 1407 LT 12 July 1995. (b) Stressed surface conductances (for different SR values), inferred from AVHRR surface temperature, in comparison with unstressed surface conductance calculated for cases with sufficient water supply in the soil.

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    Coefficients of correlation between derived soil moisture from satellite pass on 12 July 1995, and accumulated previous rainfall measured at the 58 Oklahoma Mesonet stations along with accumulated previous rainfall averaged for these stations.

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    Comparison of the spatial distribution of derived soil moisture with the spatial distribution produced with previous rainfall accumulated within the previous 100 days.

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    Schematic diagram of the PASS model and associated computing procedure.

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    Spatial distributions of calculated surface albedo, net radiation, surface temperature, surface sensible heat flux, surface latent heat flux, and soil moisture across the CART site for 1400 LT 12 July 1995.

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    (Continued)

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    Comparison between modeled and measured average values of surface fluxes for the 10 EBBR stations on 12 July and 14 October 1995.

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    Comparison of (a) air temperature and (b) relative humidity calculated with estimated surface sensible and latent heat fluxes with corresponding midday values measured at 1.5 m above 58 ground stations on 12 July 1995.

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    Comparison of CART average values of surface energy budget components derived from pixel-specific calculations with average values from the 10 EBBR stations for (a) 12 July and (b) 14 October 1995.

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Estimating Clear-Sky Regional Surface Fluxes in the Southern Great Plains Atmospheric Radiation Measurement Site with Ground Measurements and Satellite Observations

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  • 1 Environmental Research Division, Argonne National Laboratory, Argonne, Illinois
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Abstract

The authors compared methods for estimating surface fluxes under clear-sky conditions over a large heterogeneous area from a limited number of ground measurements and from satellite observations using data obtained from the southern Great Plains Cloud and Radiation Testbed (CART) site, an area of approximately 350 km × 400 km located in Kansas and Oklahoma. In situ measurements from 10 energy balance Bowen ratio (EBBR) stations showed large spatial variations in latent and sensible heat fluxes across the site because of differences in vegetation and soil conditions. This variation was reproduced by a model for parameterization of subgrid- scale (PASS) surface fluxes that was developed previously and extended in the present study to include a distribution of soil moisture inferred from combined visible and thermal infrared remote sensing data. In the framework of the PASS model, the satellite-derived normalized difference vegetation index and surface temperature were used to derive essential surface parameters including surface albedo, surface conductance, soil heat flux ratio, surface roughness length, and soil moisture, which were then used to calculate a surface energy budget at satellite-pixel scales with pixel-specific surface meteorological conditions appropriately distributed from their mean values using a distribution algorithm. Although the derived soil moisture may be influenced by various uncertainty factors involved in the satellite data and the model, spatial variations of soil moisture derived from the multichannel data from the Advanced Very High Resolution Radiometers on the NOAA-14 satellite appeared to have some correlation (the correlation coefficient is as large as 0.6) with the amount of accumulated previous rainfall measured at the 58 Oklahoma Mesonet stations located within the CART area. Surface net radiation, soil heat flux, and latent and sensible heat fluxes calculated at a spatial resolution of 1 km (the size of a satellite pixel) were evaluated directly by comparing with flux measurements from the EBBR stations and indirectly by comparing air temperature and humidity inferred from calculated sensible and latent heat fluxes with corresponding values measured at 1.5 m above the 58 meteorological stations. In calculating regional fluxes, biases caused by the sampling uncertainty associated with point measurements may be corrected by application of the satellite data.

Corresponding author address: Dr. W. Gao, Bldg 203, Rm. J159, Argonne National Laboratory, 9700 South Cass Ave., Argonne, IL 60439.

Gao%anler.bitnet@anlvm.anl.gov

Abstract

The authors compared methods for estimating surface fluxes under clear-sky conditions over a large heterogeneous area from a limited number of ground measurements and from satellite observations using data obtained from the southern Great Plains Cloud and Radiation Testbed (CART) site, an area of approximately 350 km × 400 km located in Kansas and Oklahoma. In situ measurements from 10 energy balance Bowen ratio (EBBR) stations showed large spatial variations in latent and sensible heat fluxes across the site because of differences in vegetation and soil conditions. This variation was reproduced by a model for parameterization of subgrid- scale (PASS) surface fluxes that was developed previously and extended in the present study to include a distribution of soil moisture inferred from combined visible and thermal infrared remote sensing data. In the framework of the PASS model, the satellite-derived normalized difference vegetation index and surface temperature were used to derive essential surface parameters including surface albedo, surface conductance, soil heat flux ratio, surface roughness length, and soil moisture, which were then used to calculate a surface energy budget at satellite-pixel scales with pixel-specific surface meteorological conditions appropriately distributed from their mean values using a distribution algorithm. Although the derived soil moisture may be influenced by various uncertainty factors involved in the satellite data and the model, spatial variations of soil moisture derived from the multichannel data from the Advanced Very High Resolution Radiometers on the NOAA-14 satellite appeared to have some correlation (the correlation coefficient is as large as 0.6) with the amount of accumulated previous rainfall measured at the 58 Oklahoma Mesonet stations located within the CART area. Surface net radiation, soil heat flux, and latent and sensible heat fluxes calculated at a spatial resolution of 1 km (the size of a satellite pixel) were evaluated directly by comparing with flux measurements from the EBBR stations and indirectly by comparing air temperature and humidity inferred from calculated sensible and latent heat fluxes with corresponding values measured at 1.5 m above the 58 meteorological stations. In calculating regional fluxes, biases caused by the sampling uncertainty associated with point measurements may be corrected by application of the satellite data.

Corresponding author address: Dr. W. Gao, Bldg 203, Rm. J159, Argonne National Laboratory, 9700 South Cass Ave., Argonne, IL 60439.

Gao%anler.bitnet@anlvm.anl.gov

Introduction

Surface fluxes of heat and moisture have important roles in the boundary forcing of various atmospheric processes. Large spatial variations of surface fluxes are usually observed, however, and are caused by differences in soil, vegetation, and other surface properties. This variability makes it difficult to obtain reliable estimates of surface fluxes representative of large areas. For example, direct measurements of flux from surface towers typically represent averages over a distance of 1 km or less and are thus inadequate to provide data for atmospheric models addressing scales with a minimum cell of 10–100 km.

At least two types of indirect approaches can be usedfor estimating regional surface fluxes. One approach is to use measurements of the thermal or water vapor structure of the planetary boundary layer to infer surface fluxes representing the surface area extending 1–10 km upwind. For example, Brutsaert and Sugita (1992) used measurements of vertical profiles of temperature and humidity and boundary layer similarity theory to estimate regional surface fluxes over a moderately hilly area in Kansas. Diak (1990) used the information on boundary layer height and satellite-derived surface temperature, together with a one-dimensional boundary layer model, to derive regional surface heat fluxes. Another approach is to evaluate the spatial variations in the surface parameters that control surface energy partitioning and then estimate the corresponding spatial variation in surface fluxes by using a model of atmosphere–surface exchange processes. Spatial variations of surface fluxes and their relationships with satellite-derived surface properties have been extensively addressed by Sellers et al. (1992) and Smith et al. (1992) for a tallgrass prairie15 km × 15 km in area located in Kansas. Other investigations have also addressed the influence of surface heterogeneity on regional surface fluxes (e.g., Mason 1988; Avissar 1992; Koster and Suarez 1992; Seth et al. 1994; Gao 1995), but many practical issues concerning the application of atmosphere–surface exchange models for regional scales are not well understood, and an effective method for routinely estimating regional- scale surface fluxes with satellite observations and minimal ground measurements has not been developed.

One of the difficult tasks in applying an atmosphere–surface exchange model over regional scales is to estimate values of the essential model parameters at scales characteristic of the heterogeneous surface. These parameters may include surface albedo, surface conductances, surface roughness length, and soil moisture content. The spatial variability in these parameters is responsible for the differences in surface flux, especially when the spatial variability in cloud and incoming solar radiation is not important. Another problem associated with the application of surface models over a regional scale is spatial variability in the near-surface meteorology. The air temperature, humidity, and wind speed in the atmospheric surface layer over different surfaces will differ from their areally averaged values because of the effects of the local surface and the localized meteorological conditions will influence the local atmosphere–surface exchange. Some of these practical problems were addressed with a model framework for parameterizing subgrid-scale (PASS) surface fluxes (Gao 1995). Although the PASS model uses a simplified treatment of the surface energy balance of a plant–soil system, the model includes both (a) methods for using high- resolution satellite remote sensing data to derive the essential parameters for individual types of surfaces over large areas and (b) algorithms for deriving the interactions of near-surface atmospheric conditions with surface processes.

This paper describes the continued research with the PASS model to estimate regional surface fluxes over the southern Great Plains (SGP) Cloud and Radiation Testbed (CART) site operated by the Atmospheric Radiation Measurement Program of the U.S. Department of Energy (Stokes and Schwartz 1994). In this study, the PASS model is extended by adding a module for inferring soil moisture conditions over a regional scale from a combination of satellite observations and a minimal set of ground measurements. Soil moisture is one of the most important parameters that control the surface energy balance, but it is difficult to estimate reliably over regional scales.

Ground measurements and satellite observations over the SGP CART site

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 Rn, 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 Ts wasobtained by adjusting the raw Ts 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 − NDVIn)/(NDVIυ − NDVIn) = (NDVI0 − NDVI0n)/(NDVI0υ − NDVI0n), where NDVI and NDVI0 represent the NDVI value used in the surface model and the uncorrected NDVI value, respectively; where NDVIn and NDVI0n represent the corrected and uncorrected NDVI values, respectively, for a nonvegetated surface; and where NDVIυ and NDVI0υ 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 = (NDVIυ −NDVIn)(NDVI0 − NDVI0n)/(NDVI0υ − NDVI0n) + NDVIn.

Price (1984) suggested a split-window method for adjusting at-sensor Ts to ground-level Ts 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 Ts can be calculated from the AVHRR brightness temperature of channel 4 (T4) and channel 5 (T5) using Ts = 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 NDVI0n = 0, NDVIn = 0.2, NDVI0υ = 0.5, and NDVIυ = 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 NDVIn. 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 Ts 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 Ts 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.

Energy budget for heterogeneous surfaces and the PASS model

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
i1520-0450-37-1-5-e1a
where
i1520-0450-37-1-5-e1b
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 (Rin); δi is the surface shortwave albedo; Ki is the total incoming shortwave radiation; Ii and Ii are the incoming and outgoing longwave radiation, respectively; ρ is the air density; Cp is the air-specific heat at constant pressure; γ is the psychrometric constant; es(Tis) is the saturation vapor pressure at surface temperature (Tis); eia and Tia are the local air vapor pressure and air temperature, respectively; and Ric and Ria 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 (Gic = [Ric]−1), soil heat flux ratio (Γi), and surface roughness length (zi0), are expressed by the following functions:
i1520-0450-37-1-5-e2a
and
i1520-0450-37-1-5-e2d
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 θir in the plant root zone defined as f1 = (1 + β3δe) and f2 = 1 − exp(−β4θr) (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 θs 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) (KiPAR), 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 z0h 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 Γi 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, Gc, 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*, is, and êia, 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 + αu(ûi**)/*], Tia = Ta + αT(iss), and eia = ea + αq(êiaa), where u, Ta and ea 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 = iss) calculated by the automatic distributing scheme described above. The value of coefficient αT (0.57) was obtained for this dataset by a linear regression. In the original PASS model, the coefficients αu, αT, and αq 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 forαT = {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 αT = 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 Ts 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 Ts). 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(Ts − 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–Ts 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 Ts for a given NDVI to the decrease in soil moisture content and have developed methods to infer soil moisture from NDVI–Ts 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 Tis 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 = ρCp(TisTia)/Ria, where Ria is the aerodynamic resistance and was computed by the surface-layer relationship Ria = 0.74(k2ui)−1{ln[(zd)/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 Ra, in which case, iteration is required to include surface heat flux in the calculation of Ra 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 = Rin(1 − Γi) − Hi. Here, under the clear-sky condition, Rin 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 Tis, pixel- specific Tia and eia. The Γi was estimated with function (2c), also using observed SRi. The surface conductancefor each pixel was then estimated from the derived LE byGic = {ρCp(γLE)−1[e(Tis) − eia] − Ria}−1.

The resulting values of surface conductance are shown in Fig. 7b in relation to observed SRi values. The theoretical Gic 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 Gc–SR graph should have a near-linear relationship because both Gc and SR increase with canopy density in a similar manner. Gao et al. (1992a) confirmed the existence of the Gc–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 Gc–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, Gic = Gi*f2(θir) = Gi*[1 − exp(−1.7θir)], of Kim and Verma (1991) was used to infer the proportion of extractable soil water or relative soil moisture θir on the basis of the stressed conductance Gic 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 Tis 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 Ts 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 of calculated surface fluxes with ground measurements

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 Rn, G, LE, and H, respectively, for the case of 12 July 1995, and 55, 19, 42, and 25 W m−2 for Rn, G, LE, and H, respectively, for the case of 14 October 1995. The relative error, however, is the smallest for Rn 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 Rn 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.

Conclusions

The spatial variabilities among the EBBR stations distributed across the SGP CART site are fairly large for LE, H, and G but are relatively small for Rn. Thesampling of various surface conditions by the ground stations is limited and could sometimes be biased when it is used to represent the whole CART area. Satellite observations of the surface spectral vegetation index NDVI and Ts at 1-km spatial resolution from AVHRRs on the NOAA-12 and NOAA-14 satellites may provide a much more complete coverage of the surface conditions.

A modeling method that combines high-resolution satellite observations and limited ground measurements to estimate the area-representative surface fluxes was extended to include the distribution of surface moisture. The information on the spatial variability of soil moisture was inferred from the combined visible and thermal infrared remote sensing data on the basis of the hypothesis that the increase in AVHRR-derived Ts for a given NDVI is caused by the decrease in the soil moisture. Although the derived soil moisture may be influenced by the accuracy of model parameterization, the spatial distribution of soil moisture derived at 1-km resolution has a correlation (with a correlation coefficientof about 0.6) with the accumulated previous rainfall amount measured at the 58 Oklahoma Mesonet stations. By including determination of the soil moisture distribution, the current version of the model was used for operational calculations of surface fluxes with the AVHRR data and limited ground data. The minimal input data include AVHRR NDVI, Ts, mean wind speed, mean air temperature, mean humidity for the whole region of interest (when mesoscale horizontal gradient is not significant), and total solar radiation (single-point data can be used for clear days; data on the spatial variation are required for cloudy days).

The calculated surface fluxes follow the trend of diurnal, seasonal, and spatial variations measured at ground stations. The modeled fluxes agree within 13–55 W m−2 with corresponding measurements made at the EBBR stations. The difference may be partially caused by the possible mismatch between the extracted satellite pixels and the surface measured by the EBBR stations because of scale difference and partially by the uncertainties in model parameterization. The near-surface temperature and humidity calculated with estimated surface sensible and latent heat fluxes agree within 1.3°C and 0.06, respectively, with their corresponding values independently measured at the 58 ground stations located within the Oklahoma Mesonet. This comparison validates the spatial variation of heat fluxes estimated by the present method.

The CART-representative surface fluxes, which were calculated by averaging fluxes modeled for all pixels covering the site, were compared with the average fluxes from the EBBR stations for two clear days in summer and fall. The differences identified between the CART- average and the EBBR-average fluxes, to some degree, may indicate the possible contribution of surface fluxes caused by the difference between the site-wide surface covered by satellite observations and the limited surfaces covered by the EBBR ground stations.

Acknowledgments

This work was supported by the U.S. Department of Energy, Office of Energy Research, Office of Health and Environmental Research, Environmental Sciences Division, under Contract W-31-109- Eng-38 through the Atmospheric Radiation Measurement (ARM) Program, and by the U.S. Department of Defense, Strategic Environmental Research and Development Program, through the ARM Unmanned Aerospace Vehicle (UAV) Program.

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Fig. 1.
Fig. 1.

False color imagery for an area of 314 km × 344 km of the SGP CART site derived from surface reflectances detected in the red channel 1 (0.58–0.68 μm), the near-infrared channel 2 (0.73–1.10 μm), and radiances in the thermal infrared channel 4 (10.5–11.5 μm) of the AVHRR on the NOAA-14 satellite. The locations of the CART surface EBBR stations, the CART eddy correlation stations, and the Oklahoma Mesonet stations are indicated.

Citation: Journal of Applied Meteorology 37, 1; 10.1175/1520-0450(1998)037<0005:ECSRSF>2.0.CO;2

Fig. 2.
Fig. 2.

Diurnal cycle of (a) sensible heat flux, (b) latent heat flux, (c) net radiation, and (d) soil heat flux measured on 12 July 1995 by the 10 EBBR stations (indicated by different station identification numbers).

Citation: Journal of Applied Meteorology 37, 1; 10.1175/1520-0450(1998)037<0005:ECSRSF>2.0.CO;2

Fig. 3.
Fig. 3.

(a) Comparison between ground-level NDVI values corrected using LOWTRAN7 and a linear scaling method for AVHRR data from NOAA-14 on 12 July and 14 October 1995. Only 1 out of every 100 pixels across the CART site were plotted. (b) Comparison between ground-level surface temperature values corrected using LOWTRAN7 and by the split-window method. Only 1 out of every 100 pixels across the CART site were plotted.

Citation: Journal of Applied Meteorology 37, 1; 10.1175/1520-0450(1998)037<0005:ECSRSF>2.0.CO;2

Fig. 4.
Fig. 4.

Spatial distributions of AVHRR-derived NDVI at 1-km spatial resolution across the CART area of 314 km × 344 km for clear days selected in different seasons.

Citation: Journal of Applied Meteorology 37, 1; 10.1175/1520-0450(1998)037<0005:ECSRSF>2.0.CO;2

Fig. 5.
Fig. 5.

(a) Comparison of surface albedo calculated by (2a) with measurements taken over a tallgrass prairie in Kansas and (b) changes of the ratio of soil heat flux to net radiation with spectral vegetation index SR. The function derived from the regression of the data (solid squares and associated regression curve) taken at the EBBR stations was compared with the curve (line with open circles) derived by Kustas et al. (1993).

Citation: Journal of Applied Meteorology 37, 1; 10.1175/1520-0450(1998)037<0005:ECSRSF>2.0.CO;2

Fig. 6.
Fig. 6.

(a) Variations of local midday air temperature and relative humidity measured on 12 July 1995, at 2 m above the ground with local vegetation conditions described by AVHRR-derived SR. (b) Relationship between the local air temperature and the local temperature forcing ΔTi (defined in the text) induced by surface changes.

Citation: Journal of Applied Meteorology 37, 1; 10.1175/1520-0450(1998)037<0005:ECSRSF>2.0.CO;2

Fig. 7.
Fig. 7.

(a) Relationship of AVHRR NDVI to surface temperature for all satellite pixels across the CART site from AVHRR observations at 1407 LT 12 July 1995. (b) Stressed surface conductances (for different SR values), inferred from AVHRR surface temperature, in comparison with unstressed surface conductance calculated for cases with sufficient water supply in the soil.

Citation: Journal of Applied Meteorology 37, 1; 10.1175/1520-0450(1998)037<0005:ECSRSF>2.0.CO;2

Fig. 8a.
Fig. 8a.

Coefficients of correlation between derived soil moisture from satellite pass on 12 July 1995, and accumulated previous rainfall measured at the 58 Oklahoma Mesonet stations along with accumulated previous rainfall averaged for these stations.

Citation: Journal of Applied Meteorology 37, 1; 10.1175/1520-0450(1998)037<0005:ECSRSF>2.0.CO;2

Fig. 8b.
Fig. 8b.

Comparison of the spatial distribution of derived soil moisture with the spatial distribution produced with previous rainfall accumulated within the previous 100 days.

Citation: Journal of Applied Meteorology 37, 1; 10.1175/1520-0450(1998)037<0005:ECSRSF>2.0.CO;2

Fig. 9.
Fig. 9.

Schematic diagram of the PASS model and associated computing procedure.

Citation: Journal of Applied Meteorology 37, 1; 10.1175/1520-0450(1998)037<0005:ECSRSF>2.0.CO;2

Fig. 10.
Fig. 10.

Spatial distributions of calculated surface albedo, net radiation, surface temperature, surface sensible heat flux, surface latent heat flux, and soil moisture across the CART site for 1400 LT 12 July 1995.

Citation: Journal of Applied Meteorology 37, 1; 10.1175/1520-0450(1998)037<0005:ECSRSF>2.0.CO;2

Fig. 10.
Fig. 10.

(Continued)

Citation: Journal of Applied Meteorology 37, 1; 10.1175/1520-0450(1998)037<0005:ECSRSF>2.0.CO;2

Fig. 11.
Fig. 11.

Comparison between modeled and measured average values of surface fluxes for the 10 EBBR stations on 12 July and 14 October 1995.

Citation: Journal of Applied Meteorology 37, 1; 10.1175/1520-0450(1998)037<0005:ECSRSF>2.0.CO;2

Fig. 12.
Fig. 12.

Comparison of (a) air temperature and (b) relative humidity calculated with estimated surface sensible and latent heat fluxes with corresponding midday values measured at 1.5 m above 58 ground stations on 12 July 1995.

Citation: Journal of Applied Meteorology 37, 1; 10.1175/1520-0450(1998)037<0005:ECSRSF>2.0.CO;2

Fig. 13.
Fig. 13.

Comparison of CART average values of surface energy budget components derived from pixel-specific calculations with average values from the 10 EBBR stations for (a) 12 July and (b) 14 October 1995.

Citation: Journal of Applied Meteorology 37, 1; 10.1175/1520-0450(1998)037<0005:ECSRSF>2.0.CO;2

Table 1a.

Inputs and outputs of empirical equations and associated constants.

Table 1a.
Table 1b.

Values of empirical constants.

Table 1b.
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