## Approaches for Determining Available Energy

A number of approaches using remote sensing have been developed for estimating the available energy components in Eq. (10). Generally, Rn is evaluated in terms of its four radiation components (Sellers et al., 1990), namely,

where Rs is the incoming shortwave solar radiation (W/m2), is the incoming longwave radiation (W/m2), a is the surface shortwave albedo, ss is the surface

Spectral Region

Reflective Thermal Microwave Satellite Sensor (pm) (pm) (GHz)

GOES-8

Imager

METEOSAT VISSR NOAA-12,14

Landsat-5

Landsat-7

SPOT-1 to SPOTS

Advanced Very High-Resolution Radiometer (AVHRR-2) Thematic Mapper (TM)

Enhanced Thematic Mapper Plus (ETM+)

High Resolution Visible (HRV)

0.50-0.90 10.4-12.5 0.45-0.52 0.52-0.60 0.63-0.69 0.76-0.90 1.55-1.75 2.08-2.35 0.50-0.75 0.50-0.59 0.62-0.66 0.77-0.87

Pixel Resolution (PR)

Orbital

Characteristics Repeat Cycle

Time of Data Acquisition

Delivery time from acquisition to user (Td)

Geostationary

Stationary

Every 30min

Instantaneous at ground station

Acquired at 1 km Geostationary Archived at 8 km

1.1 km (local area Near-polar, coverage) sun-

4 km (global area synchronous coverage)

120 m (thermal IR) synchronous

Stationary

12 h,every 9.2 days

Near-polar, sun- 16 days

Every 30min Instantaneous at ground station 19.30 (ascending) Instantaneous at and 07.30 (descending)

Midmorning ground station

72 hours at best, generally 2 weeks to 1 month

30 m (Vis-IR) Near-polar, sun- 16 days Midmorning 48 h

60 m (thermal, IR) synchronous 15m (panchromatic)

(panchromatic) 20m

(multi spectral)

Near-polar, sun-synchionous

26 days, and pointing capability provide shorter cycles

Late morning

48 hours at best, generally 2 weeks to 1 month

ERS-1 to Active Microwave ERS-2 (AM-I) Along-

Track Scanning Radiometer (ATSR)

RADARSAT Synthetic Aperture Radar (SAR)

(C-band) 30 m (3 looks, SAR) 100 m (@ radiometric resolution of 1 dB)

JERS-l

Space Imaging

OPtical Sensor

(OPS) Visible and Near IR (VNIR) Radiometer Short wavelength

InfraRed (SWIR) Radiometer Synthetic Aperture Radar SAR) IKONOS

20 m (OPSVNIR

(panchromatic) 4m

(multispectral)

Near-polar, sun- 3 days synchronous

Midmorning and 48 h at best, late evening generally

2 weeks to 1 month

Near-polar, sun-synchronous

Near-polar, sun-synchronous

24 days

44 days

Midmorning and late evening

Midmorning and late evening

48 h at best, generally 2 weeks to

1 month 48 h at best, generally

2 weeks to 1 month

Inclination 1-3 days Late morning 24-^18 h

98.1

sun-synchronous

(continued)

TABLE 2 (continued)

Satellite

Spectral Region

Sensor

Reflective (pm)

Thermal (pm)

Microwave (GHz)

Pixel Resolution (PR)

Orbital Characteristics

Repeat Cycle

Time of Data Acquisition

Delivery time from acquisition to user (Td)

Terra

Moderate Resolution Imaging Spectrometer (MODIS-N) Advanced Space-borne Thermal Emission and Reflectance Radiometer (ASTER) Multiangle Imaging Spectro Radiometer (MISR)

MODIS 0.66-0.87

MODIS 0.25 km (Visible,

15 m (Visible,

Polar orbiting, sun-

synchronous

MODIS 1-2 days

10:30

48 h

### ASTER VNIR 5 days

SWIR&T 16 days MISR 9 days emissivity, a is the Stefan-Boltzman constant (5.67x 10-8 W/m2K4), rsh is the hemispherical radiometric temperature (K) as defined by Norman and Becker (1995), so that the quantity rr/represents the upwelling longwave radiation flux, Rkr The radiometric temperature measured by an infrared radiometer from a space-borne platform, is assumed to approximate Tsh.

Both Rs and a have been estimated from Geosynchronous operational environmental satellites (GOES) using empirical/statistical and physically based models (Pinker et al., 1995). On a daily basis, the estimate of Rs from satellite data has an uncertainty of approximately 10%, but at shorter time scales, for example hourly, the uncertainty may be greater (probably on the order of 20 to 30%, on average), especially for partly cloudy conditions (Pinker et al., 1994). Validating Rs at hourly or shorter time scales under partly cloudy skies is especially difficult due to sampling problems associated with the limited network of ground-based measurements typically available from field experiments (Pinker et al., 1994).

Satellite estimates of the contribution of the net longwave flux at the surface have been developed using sounding data (Darnell et al., 1992). The Tiros Operational Vertical Sounder (TOVS) of the National Oceanic and Atmospheric Administration (NOAA) satellites contains infrared and microwave sensors that can be used for estimating both R[(j and Tmd. Other approaches have utilized meteorological data collected near ground level with semiempirical relationships for estimating R](i, and then used Trdd for calculating the upwelling longwave component (Jackson et al., 1987). Sellers et al. (1990) raise the concern that estimating the four components of Rn could lead to error accumulation, especially in estimating the net longwave flux because both R{li and are large components, so the difference would be small and prone to significant uncertainty. This has led some to estimate surface Rn from the top of the atmosphere (TOA) Rn (Pinker and Tarpley, 1988). While it has been shown that there is little correlation between surface and TOA net longwave flux (Harshvardhan et al., 1990), there is a strong correlation between Rs and Rn at the surface. This has lead to statistical approaches using slowly varying surface properties such as surface albedo and soil moisture with remotely sensed estimates of Rs for estimating Rn (Kustas et al., 1994b). Other techniques use narrow-band reflectance data and Trdd from aircraft and satellite-based platforms for estimating the upwelling components iRs and Riu and use meteorological data for estimating the downwelling components Rs and R]A (e.g., Moran et al., 1989; Daughtry et al., 1990). Comparisons with ground-based observations at meteorological time scales (i.e., half-hourly to hourly) indicate that the differences are within the uncertainty in the measurements, namely 5 to 10%.

The soil heat flux (G) can be solved as a function of the thermal conductivity of the soil and the vertical temperature gradient. This temperature gradient cannot be measured remotely, hence numerical models solve for G by having several soil layers (Campbell, 1985). This requires detailed information about soil properties. Models using routine weather data may provide satisfactory predictions of soil heat flux (e.g., Camillo, 1989). An alternative approach takes G/Rn as a constant under daytime conditions that varies as a function of the amount of vegetation cover or leaf area index (LAI), which can be estimated by use of remotely sensed vegetation indices (VI)* (Choudhury et al., 1994). Several studies have shown that the value of G/Rn typically ranges between 0.4 for bare soil and 0.05 for full vegetation cover (Choudhury et al., 1987). Observations (Clothier et al., 1986; Kustas et al., 1993a) indicate that a linear relationship between VI and G/Rn exists, although analytically it has been shown that the relationship should be nonlinear (Kustas et al., 1993a).

### Statistical Approaches for Determination of AE

Statistical methods for estimating ).E have mainly been developed to predict daily ).E using instantaneous remote-sensing observations and assumptions about the relationship between midday H and ).E and Rn + G. One of the most widely applied approaches, using a Trad observation near midday, was pioneered by Jackson et al. (1977) whereby they observed that daily differences between ).E and Rn could be approximated by this linear expression:

where the subscript i and d represent instantaneous and daily values, respectively, A and B are statistical regression coefficients, and Ta is the air temperature (°C) at about 2 m above the surface. A more general form of this expression was proposed by Seguin and Itier (1983) based on theoretical and experimental observations; namely,

where B' was dependent on surface roughness and the value of n depended on stability (n — 1 for stable and 1.5 for unstable conditions). A variant of Eq. (13) was introduced by Nieuwenhuis et al. (1985) where they replaced Ta i and Rnd with a reference canopy temperature (Tcj) corresponding to conditions of potential ).E ().Edp). The linear form of Eq. (12) has been verified experimentally and theoretically (Carlson and Buffum, 1989; Lagouarde, 1991). Carlson et al. (1995) used a soil vegetation atmospheric transfer (SVAT) model to show that a systematic relationship exists between the B! and n parameters in Eq. (13) and fractional cover, which can be estimated with remotely sensed data. Theoretical and experimental work by Lagouarde and McAneney (1992) resulted in the derivation of an equation for estimating daily sensible heat flux (Hd) using Trad measured around the time of the NOAA-AVHRR (advanced very high resolution radiometer) overpass (1400 local standard time) and maximum Ta. The equation is similar in form to Dalton's evaporation equation (see Brutsaert, 1982) and requires the determination of two empirical parameters relating instantaneous to daytime average values of wind speed and surface-air temperature differences. On a daily basis the above techniques appear to have an uncertainty of ±1 mm/day or 20 to 30%.

* Spectral vegetation indices (VI) are a ratio or linear combination of reflectances in the red and NIR wavebands that is particularly sensitive to vegetation amount (Jackson and Huete, 1991) or the amount of photosynthetically active plant tissue in the plant canopy (Wiegand et al., 1991).

The approaches described above attempt to extrapolate "instantaneous" remote-sensing observations of the derived fluxes to daily totals, which is required for many hydrological and agricultural applications. Interest in daily fluxes led Jackson et al. (1983) to develop a procedure using the assumption that the temporal trend in XE would follow the course of solar radiation during the daylight period. They showed that for a clear day the ratio of daily to midday Rs (Rsm) could be approximated by an analytical expression:

where N is the daylength in hours, and t is the time starting at sunrise. Several studies have shown this technique can yield satisfactory estimates of XE using the assumed equivalence XEd/XEm = Rsd/Rsm (Brutsaert and Sugita, 1992).

Experimental observations analyzed by Hall et al. (1992) suggest that the evaporative fraction [EF = —XE/(Rn + G)] remains fairly constant over the daytime period. With this assumption, an instantaneous estimate of the fluxes and hence EF from a remote-sensing observation would have the potential to provide daily XE as long as one can estimate the daytime average available energy (Rn + G). Several studies have found this technique can give reasonable results with differences in daily E* of less than lmm/d (Sugita and Brutsaert, 1991; Brutsaert and Sugita, 1992; Hall et al., 1992; Kustas et al., 1994a). The estimates of daily XE derived from either Eq. (14) or from assuming EF is constant, however, should be adjusted for the contribution of nighttime XE. Nighttime XE can be anywhere from 10 to 30% of the daily total (Owe and van de Griend, 1990). This percentage of the daily total will largely depend upon the climate and season. For temperate climates in the summer, 10 to 20% of the daily total is probably typical (Brutsaert and Sugita, 1992).

Recently, Zhang and Lemeur (1995) examined the underlying assumptions of both Eq. (14) and constant EF using the Penman-Monteith equation, and compared the results to measurements from a mixed agricultural and forested region during HAPEX-MOBILHY (Hydrological Atmospheric Pilot Experiment-Modelisation du Bilan Hydrique; see, e.g., André et al., 1986) under clear skies. They found that EF is fairly constant for short vegetation but may not be for forests. Furthermore, the midday values of EF tended to be smaller than the daytime average and the daytime total available energy is required to use this method. Therefore they felt the approach of Jackson et al. (1983) was more suitable since it required only one instantaneous estimate of XE and Eq. (14) to compute daily XE. However, Eq. (14) will only be suitable for clear-day conditions whereas Sugita and Brutsaert (1991) and Kustas et al. (1994a) found that EF was reasonably constant under a wider variety of conditions.

### Analytical Approaches for Determination of H and AE

Price (1980) proposed a model for obtaining daily integrated fluxes directly by integrating Eq. (10) over a 24-h period with some simplifying assumptions. The result is an analytical expression for computing daily XE. It requires as primary input a 24-h max-min difference in Tnd and daily average climate data obtained by routine weather station observations (i.e., wind speed, air temperature, and vapor pressure). This model readily lends itself to the NOAA AVHRR series of satellites, which provide day—night pairs of radiometric surface temperature. Further refinements to the technique were made by Price (1982) resulting in a prognostic model that appears to give appropriate XE values when compared to local estimates using standard meteorological and pan evaporation data. However, the amplitude of the max-min difference in 7j.ad is affected by more than surface soil moisture when vegetation is present and therefore it is less directly coupled to the relative magnitude of XE (Norman et al., 1995a).

Other methods generally compute XE by evaluating Rn, G and H and solving for XE by residual in Eq. (10). At least one radiometric surface temperature observation is required. Unfortunately, most of the approaches that are described below provide only an instantaneous estimate of the fluxes because these models require Trai, which means that only one estimate of XE can be computed during the daytime except when using Tm] observations from satellites such as GOES or METEOSAT.

With Rn and G estimated by the remote-sensing methods described earlier, sensible heat flux is normally computed using the following expression:

where Taero is the surface aerodynamic temperature (°C) (Norman and Becker, 1995) and Ta is the air temperature (°C) either measured at screen height or the potential temperature in the mixed layer (Brutsaert and Sugita, 1991; Brutsaert et al., 1993). The resistance to heat transfer (ra) is affected by windspeed, atmospheric stability, and surface roughness (Brutsaert, 1982).

Since Taero cannot be measured by remote sensing, it is usually replaced by TmV For uniform canopy cover, the difference between Taero and Tmi is typically less than 2°C (Choudhury et al., 1986; Huband and Monteith, 1986), but for partial vegetation cover the differences can reach 10°C (Kustas, 1990). This has forced many investigators to adjust ra via empirical methods related to the scalar roughness for heat (Kustas et al., 1989; Sugita and Brutsaert, 1990; Kohsiek et al., 1993) or to use an additional resistance term (Stewart et al., 1994). However, these adjustments to Eq. (15) are not generally applicable because they have not been related to physical quantities causing differences between momentum and scalar transport (McNaugh-ton and Van den Hurk, 1995). This is supported by Sun and Mahrt (1995) who analyzed TmA observations collected over heterogeneous surfaces and found that existing scalar roughness parameterizations for predicting reliable H fluxes with Eq. (15) were not generally applicable. Efforts have been made to develop dual-source models (Norman et al., 1995b; Lhomme et al., 1994; Chehbouni et al., 1996) to account for differences between Taero and Trad, and thus avoid the need for empirical adjustments to ra. As a result, dual-source models may have broader application for heterogeneous surfaces (Kustas et al., 1996).

In dual-source modeling approaches, the energy exchange is partitioned between the soil/substrate and the vegetation. An example of a dual-source model was presented by Norman et al. (1995b), based on the assumption that soil surface and vegetation canopy fluxes can be taken in parallel, where

H = Hc + Hs = -f>Cp\[{Tc - Ta)/ra] + [(Ts - Ta)/{ra + rs)]} (16)

and Hc and Hs are the sensible heat fluxes from the canopy and soil, respectively, rs is the resistance to heat flow in the boundary layer immediately above the soil surface, and Tc and Ts are the canopy and soil temperatures, respectively. Though a dual-source approach such as that presented in Eq. (16) has the advantage over single-source approaches [represented by Eq. (15)] of accounting for different sources and sinks of energy fluxes, difficulties arise in specifying the resistances to sensible and latent heat transport from the soil and vegetation. However, relatively simple parameterizations have been proposed. For example, Norman et al. (1995b) proposed that the value of rs be computed from the equation developed by Sauer et al. (1995)

where us is the wind speed (m/s) about 5 cm above the soil surface, estimated with equations of Goudriaan (1977), and a ^ 0.004 m/s and b ~ 0.012. Further, they proposed that values of Tc and Ts be derived from Tmà using the expression

where ^g,. is the fraction of green vegetation viewed by the radiometer; and that the absorbed net radiation by the plant canopy, Rnc, be partitioned between Hc and kEc according to the Priestley-Taylor approximation (Priestley and Taylor, 1972), where

where f is the fraction of green or actively transpiring vegetation.

A recent study by Zhan et al. (1996) compared several single- and dual-source models for computing H with TTià over different land cover types. They showed that models containing the least empiricism to account for the differences between Tni and T.icro gave the best results with differences less than 30%, on average. The dual-source model by Norman et al. (1995b) generally gave the smallest differences with measured H fluxes. The average difference was around 20%, which is considered the level of uncertainty in eddy correlation and Bowen ratio techniques for determining the surface fluxes in heterogeneous terrain (Nie et al., 1992).

Another approach to solve this problem relates to performing detailed simulations using microclimate and radiative transfer models that can predict the relationship between TTià and T,icm as a function of surface conditions such as vegetation cover or LAI and surface soil moisture and solar zenith and azimuth angles (Prévôt et al., 1994). Some preliminary results from the simulations indicate that LAI is a major factor in determining the order of magnitude of the scalar roughness needed in Eq. (15) if T.dcm is replaced by Trdd. A similar result using a Lagrangian approach was obtained by McNaughton and Van de Hurk (1995) who represented the difference between momentum and scalar transport using an excess resistance term.

The analytical approaches outlined above require an estimate of Ta. Air temperature is not measured in many regions, and where it is measured it only represents local conditions near the site of the measurement and not at each satellite image pixel. With most current satellite observations of TnA at the 0.10- 1-km pixel scale, significant variations in near surface meteorological conditions may exist depending on surface conditions. Methods using satellite data indicate at least ±3°C uncertainty in the estimate of Ta when compared to standard weather station observations (Goward et al., 1994). Zhan et al. (1996) showed that two-source models are generally more sensitive to errors in TnA — Ta than to most other model parameters; thus it is a major advantage for a model not to require a measurement of Ta. Kustas and Norman (1997) revised the Norman et al. (1995b) dual-source model for computing the turbulent fluxes without the need for Ta via the use of Trdd observations at two sensor viewing angles, and ~50° zenith angles. Such viewing angles from a satellite-based platform have been available from the along track scanning radiometer (ATSR) instrument aboard the ERS-1 satellite (Prata et al., 1990; Prata, 1993). With the ATSR data, there would be no need to extrapolate Ta from a sparse network of meteorological observations to each satellite pixel, a very unreliable approach. Moreover, the model is essentially unaffected by the typical 1 to 2°C error in estimating Tr!lA from satellites. With these two attributes, the model is well suited for computing regional-scale surface fluxes with an ATSR type of sensor.

Other methods avoid the need for estimating Ta on a pixel-by-pixel basis by relying on air temperature in the ABL, which is much more uniform over a region (Brutsaert and Sugita, 1991; Brutsaert et al., 1993). However, the variability of evaporation is more difficult to quantify. Other approaches attempt to use remotely sensed data in the optical wavebands to define variation in meteorological conditions (Bastiaanssen et al., 1998; Gao et al., 1998). It remains to be seen how universal these relationships are for different climates.

Modeling Approaches That Use Remote-Sensing Data to Define Boundary Conditions

Numerical Models. Several numerical models have been developed over the past decade to simulate surface energy flux exchanges using remote sensing data (usually observations of 7^) for updating the model parameters (Camillo et al., 1983; Carlson et al., 1981; Soer, 1980; Taconet et al., 1986). The advantage of these approaches is that the temporal trend of the fluxes can be simulated and periodically updated with the remote-sensing data. Taconet et al. (1986) show the feasibility of using this approach with AVHRR data and, more recently, included the geostationary satellite data (METEOSAT) to increase the stability of the model inversion and atmospheric correction of the satellite observations (Taconet and Vidal-Madjar, 1988).

Unfortunately, these models require many input parameters related to soil and vegetation properties not readily available at regional scales. This has prompted some to simplify numerical models in order that remote sensing could potentially be used to estimate most of them (Bougeault et al., 1991). Ail extreme example of this is given by Brunet et al. (1991) who use an atmospheric boundary layer (ABL) model to calculate regional-scale energy fluxes with a Penman-Montieth equation for parameterizing the energy transport across the soil-vegetation-atmosphere interface. The surface resistance is the main adjustable parameter and is adjusted in order for the model to match the early afternoon infrared surface temperature observation from the NOAA-AVHRR satellite. Preliminary tests using observations under different moisture and crop conditions and surface temperatures from ground-based stations indicate the model adequately simulates the temporal trace and magnitudes of both the energy fluxes and surface temperature.

Numerical models have several advantages over the statistical and analytical approaches. First, they typically better represent the physics of energy transport in the soil-vegetation-atmosphere system. Second, with initial and boundary conditions, they can simulate the energy fluxes continuously. Yet many numerical models still require continuous weather data such as wind speed, air temperature, and vapor pressure, or in the case of atmospheric models that can simulate the near-surface weather, they require radiation data. In practice, few of these models can be used at regional scales with remote-sensing data because of the large amount of vegetation and soils information required to evaluate necessary parameters. Some success in bridging this gap has been achieved by combining a physically based robust model simulating the energy fluxes with remote-sensing data, which provides necessary information for determining key surface parameters in an operational mode (Sellers et al., 1992; Crosson et al., 1993). Two such approaches that appear to have great potential for estimating XE operationally are discussed below in some detail.

Atmospheric Climate Models. An important conceptual step in improving the procedure for estimating soil moisture and the surface energy balance came with the idea of using the time rate of change of Tm] from a geostationary satellite such as GOES with an atmospheric boundary layer model (Wetzel et al., 1984). By using time rate of change of TmA, one reduces the need for absolute accuracy in satellite sensing and atmospheric corrections, both major challenges. Diak (1990) improved this approach further with a method for partitioning the available energy (Rn + G) into H and XE by using the rate of rise of Tmi from the GOES satellite and ABL rise from the 12 Greenwich mean time (GMT) synoptic sounding to the 00 GMT sounding. The model is initialized with the 12 GMT sounding of temperature, humidity, and wind speed. Then the surface Bowen ratio (i.e., the ratio of the turbulent fluxes H/XE) and the "effective" surface roughness are varied until the predicted 12-h rise in ABL height and TmA match the observations. This effective surface roughness combines the effects of the surface aerodynamic roughness, viewing angle, and fractional vegetative cover. Estimates of surface albedo and emissivity are required by the model.

Diak and Whipple (1993) further refined the model by including a procedure to account for effects of horizontal and vertical temperature advection and vertical motions above the ABL. Sensitivity of the model to the determination of the surface energy balance and to the effective roughness was performed with a case study using data from the Midwest and Great Plains areas in the continental United States. They also verified their model estimates of the surface energy balance with in situ measurements from the FIFE (First ISLSCP Field Experiment; see Sellers et al., 1988) site for 2 days. The model-derived XE values were within 10% of the measurements, suggesting this technique may provide reliable XE estimates at regional scales. Additional comparisons of 12-h averages of sensible heat flux with FIFE observations support the utility of their model (see Fig. 2 from Diak et al., 1995). They also found that temperature advection usually does not significantly impact the surface energy balance estimates given by the model on a daily basis, although for areas that are routinely affected by advection the biasing could impact longer term averages of XE (i.e., at climate time scales).

In a related approach, Anderson et al. (1997) recently developed and tested a two-source surface energy balance model requiring measurements of the time rate of change of surface temperature and an early morning ABL sounding. With this model, many of the problems associated with the use of radiometric surface temperature were avoided. The model accommodated the first-order dependence of the radiometric surface temperature on view angle, avoided the need for atmospheric corrections and precise emissivity evaluation, and did not require in situ measurements of air temperature. The performance of the model was evaluated with experimental data from FIFE and from a semiarid rangeland experiment (Monsoon'90; see Kustas and Goodrich, 1994). The model yielded uncertainties in flux estimates comparable to models needing in situ air temperature observations and were comparable to the uncertainties in surface energy flux measurements.

Recognizing the fact that using Tmá requires detailed information on the characteristics of the surface and the structure of the overlying atmosphere, which is often incomplete for many regions, Diak et al. (1994) have proposed a method that employs the High Resolution Interferometer-Sounder (HIS) for estimating the turbulent heat fluxes, H and XE. The premise is that the temporal changes in the radiances observed by the HIS implicitly measure changes in the lower atmosphere, which are a measure of the absolute amount of energy added to the ABL. The HIS radiance changes were described by coefficients obtained by an eigenvalue decomposition procedure. These coefficients were in turn related to various components of the surface energy balance equation using multiple linear regression. Diak et al. (1994) provide convincing evidence that this method responds to temperature changes in the lower atmosphere as well as surface temperature changes. Consequently, this method is equivalent to the method of Diak (1990), but without requiring any ancillary data, just two remote radiance measurements. However, even when HIS becomes operational, co-located flux measurements will be required to establish a database to use the HIS technique. One possible solution is to identify sites that have sufficiently detailed surface information to permit some of the other techniques described above to be used to calibrate this procedure. In any event, the HIS tech nique offers tremendous potential since it can evaluate the surface energy balance relying only on remotely sensed data.

Alternative Approach: Exploiting the Vl/Trad Relation. Numerous studies have found a significant negative correlation between the normalized difference vegetation index (NDVI) and rrad over a variety of surfaces (Goward et al., 1985; Hope and McDowell, 1992; Nemani and Running, 1989; Nemani et al., 1993), where

and pNIR and pRed are the measured reflectance factors of the surface in the near-infrared (NIR) and red spectrum, respectively. They suggest that this relationship is related to the amount of available energy partitioned into XE, which is driven by variation in transpiration or evaporative cooling. Hope et al. (1986) showed theoretically that with VI and Tmi one can extract canopy resistance. However, this assumes complete canopy cover, which does not usually exist in most natural land surfaces.

Nemani and Running (1989) used an ecological model for forested regions and observed a nonlinear relationship between the slope of the NDVI-7^ curve and the canopy resistance. Goward and Hope (1989) also proposed that the slope was a measure of the surface resistance. These approaches will be difficult to apply to most landscapes with partial canopy cover since variability in fractional cover and surface soil moisture cause significant scatter in the VI/Tni relationship. Furthermore, studies suggest that the relationship between surface resistance and the NDVI/7;ad slope will vary significantly with vegetation type. Nemani et al. (1993) showed that the NDVI/rrad slope responded to changes in water status of forested areas, but not of the grasslands. The variability in slope for the grasslands appeared to be mainly caused by variation in fractional cover rather than in XE. Smith and Choudhury (1991) used a coupled dual-source soil-vegetation model to show that the NDVI/slope largely depended on whether the drying soil surface is the source of the decline in XE or whether it was the vegetation. They also observed that the linear relationship between NDVI and did not exist for forests but only for agricultural and native pastures.

Others have used an energy balance model for computing spatially distributed fluxes from the variability within the NDVI-plot from a single scene (Price, 1990). Price (1990) used NDVI to estimate the fraction of a pixel covered by vegetation. From the NDVI/plot Price (1990) showed how one could derive bare soil and vegetation temperatures and, with enough spatial variation in surface moisture, estimate daily XE for the limits of full cover vegetation, dry and wet bare soils.

Following Price (1990), Carlson et al. (1990, 1994) combined an ABL model with a SVAT for mapping surface soil moisture, vegetation cover, and surface fluxes. Model simulations were run for two conditions: 100% vegetative cover with the maximum NDVI being known a priori, and with bare soil conditions knowing the minimum NDVI. Using ancillary data (including a morning atmospheric sounding, vegetation and soil-type information) root-zone and surface soil moisture were varied, respectively, until the modeled and measured Tmd were closely matched for both cases, and fractional vegetated cover and surface soil moisture were derived. Further refinements to this technique have been developed by Gillies and Carlson (1995) for potential incorporation into climate models. Comparisons between modeled-derived fluxes and observations have been made recently by Gillies et al. (1997) using high-resolution aircraft-based remote-sensing measurements from a grassland ecosystem during FIFE and Monsoon'90. Approximately 90% of the variance in the fluxes was explained by the model.

In a related approach, Moran et al. (1994) defined theoretical boundaries in the SAVI/(rrad — Ta) two-dimensional space using the Penman-Monteith equation, where SAVI is the soil-adjusted vegetation index proposed by Huete (1988). The boundaries define a trapezoid, which has at the upper two corners unstressed and stressed 100% vegetated cover and at the lower two corners wet and dry bare soil conditions. To calculate the vertices of the trapezoid, measurements of Rn, vapor pressure, Ta, and wind speed are required as well as vegetation-specific parameters; these include maximum and minimum SAVI for the full-cover and bare soil case, maximum leaf area index, and maximum and minimum stomatal resistance. Moran et al. (1994) analyzed and discussed several of the assumptions underlying the model, especially those concerning the linearity between variations in canopy-air temperature and soil-air temperatures and transpiration and evaporation. Information about XE rates is derived from the location of the SAVI/(Trad - Ta) measurements within the date and time-specific trapezoid. This approach permits the technique to be used for both heterogeneous and uniform areas and thus does not require having a range of NDVI and surface temperature in the scene of interest as required by Carlson et al. (1990) and Price (1990). Moran et al. (1994) compared the method for estimating relative rates of XE with observations over agricultural fields and showed it could be used for irrigation scheduling purposes. More recently, Moran et al. (1996) showed that the technique had potential for computing XE over natural grassland ecosystems.

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