## Introduction

Evapotranspiration (ET) plays a significant role in regional and global climate through the hydrological cycle, and its estimation has important applications in agriculture—in areas such as runoff prediction, recharge, crop yield prediction, land use planning, etc. (Kustas and Norman 1996; Kalma and Calder 1994). Thus, how to monitor ET efficiently has become an interdisciplinary research topic. Most conventional techniques that use point measurements to estimate ET are representative only of local areas and cannot be extended to large areas because of the dynamic nature and regional variation of ET. Remote sensing has proven to be the only suitable approach for large-area estimates of ET because satellite remote sensing is the only technology that can provide representative parameters such as radiometric surface temperature, albedo, and vegetation index in a globally consistent and economically feasible manner (Choudhury 1989; Kustas and Norman 1996).

A variety of methods and models have been developed that use remote sensing techniques to estimate ET. Physically based analytical approaches based on the Penman–Monteith resistance model and surface energy balance equations are the most common methods. They either use radiometric surface temperature to calculate the sensible heat flux *H* then use the energy balance equation to obtain ET, or they use radiometric surface temperature to calculate the so-called crop water stress index, then get ET. However, using radiometric surface temperature as a substitute for the aerodynamic temperature in the original Penman–Monteith model leads to substantial error, especially over partial vegetation cover, because the radiometric surface temperature is the composite temperature of soil and vegetation. This error can be reduced by introducing an extra resistance (Kustas et al. 1989, 1996), changing from single-resistance models to a two-source model, using more complicated multilayer models (Choudhury and Monteith 1988; Lhomme et al. 1994a,b; Norman et al. 1995), or developing an empirical formula to estimate the aerodynamic temperature (Huang et al. 1993), and by incorporating a vegetation index within the model (Moran et al. 1994, 1996).

The primary purpose of this paper is to evaluate models that predict ET using satellite and routine meteorological data. Three different models that are widely used are tested against aircraft observations over the Lake King area of Western Australia over both agricultural and native vegetation. Model performance is evaluated over the two different landscapes.

## Model descriptions

### Model 1: kB^{−1} extra-resistance model (Kustas et al. 1989)

*H*can be expressed as

*ρ*is the air density,

*C*

_{p}is the specific heat of air at constant pressure,

*r*

_{ah}is the resistance to heat transfer,

*T*

_{r}is the radiometric surface temperature,

*T*

_{a}is the air temperature at reference height, and

*r*

_{x}is the extra resistance. The resistances are defined as

*d*

_{0}and

*z*

_{0m}are the displacement height and roughness length for momentum,

*k*is von Kármán’s constant,

*u*is the wind speed at height

*z,*and Ψ

_{h}and Ψ

_{m}are stability corrections for heat and momentum, respectively (Businger 1973; Beljaars and Holtslag 1991).

^{−1}takes into account a combination of effects: the difference between aerodynamic and radiometric temperatures, the vertical distribution of thermal radiation within the vegetation, the angular effect of radiometric temperature, energy exchanges between different surfaces, etc. Strictly speaking, this definition of kB

^{−1}is a radiometric one, in contrast to the original aerodynamic definition of kB

^{−1}wherein the sensible heat flux was defined in terms of the temperature difference between the surface and the atmosphere (Troufleau et al. 1997). The aerodynamic kB

^{−1}is identical to ln(

*z*

_{0m}/

*z*

_{0h}), where

*z*

_{0h}is the roughness length for heat. Kustas et al. (1989) found that the radiometric kB

^{−1}could be expressed empirically as

^{−1}

*S*

_{kb}

*u*

*T*

_{r}

*T*

_{a}

*S*

_{kb}is a constant between 0.05 and 0.25. The original value used by Kustas et al. (1989) was 0.17 based on their field data, but Kustas et al. (1996) later suggested that

*S*

_{kb}may be lower, at about 0.13. The average value of 0.15 has been adopted as a reference value.

*R*

_{n}

*H*

*G,*

*R*

_{n}is the net radiation and

*G*is the soil heat flux.

The accuracy of this model for estimating ET is dependent not only on the estimate of *H* but also on the method used for estimating *R*_{n} and *G,* and all residual errors are incorporated in the estimate of ET.

*R*

_{n}

*α*

_{t}

*R*

_{s}

*ϵσ*

*ϵ*

_{a}

*T*

^{4}

_{a}

*T*

^{4}

_{r}

*R*

_{s}is the incoming shortwave solar radiation,

*α*

_{t}is the surface shortwave albedo,

*ϵ*is the surface emissivity,

*σ*is the Stefan–Boltzmann constant, and

*ϵ*

_{a}is the effective atmospheric emissivity, and with (Brutsaert 1975)

*e*

_{a}is the atmospheric vapor pressure. The surface emissivity is calculated as a weighted average between bare soil and vegetation, such that

*ϵ*

*ϵ*

_{υ}

*V*

_{c}

*ϵ*

_{s}

*V*

_{c}

*ϵ*

_{υ}is the emissivity of vegetation (assumed to be 0.95),

*ϵ*

_{s}is the emissivity of bare soil (assumed to be 0.85), and

*V*

_{c}is the fractional vegetation cover.

*G*/

*R*

_{n}is a function of the amount of vegetation cover or the leaf area index (LAI) (Choudhury 1989). Kustas et al. (1993) indicated that a relationship existed between vegetation indices and

*G*/

*R*

_{n}. Therefore, the soil heat flux can be estimated empirically using the net radiation and LAI or a satellite-derived vegetation index such as the normalized difference vegetation index (NDVI). For instance, Kustas and Daughtry (1990) proposed a linear formula and Moran et al. (1989) proposed an exponential function. Here, the Moran et al. (1989) model has been adopted as

*G*

*R*

_{n}

### Model 2: Soil-adjusted vegetation index model (Moran et al. 1994, 1996)

Moran et al. (1994, 1996) derived a vegetation index–temperature (VIT) trapezoid, which combines satellite vegetation indices with radiometric surface temperature, and extended crop water stress index theory (Jackson et al. 1981) to partial vegetation cover. The method is based on the hypothesis that a trapezoid shape comes from a plot of the difference between radiometric surface temperature and air temperature (*T*_{r} − *T*_{a}) against vegetation cover. The method assumes (Moran et al. 1994) that

- the difference
*T*_{r}−*T*_{a}is a linear function of*V*_{c}and the temperature differences*T*_{c}−*T*_{a}and*T*_{s}−*T*_{a}, such thatwhere*T*_{r}*T*_{a}*V*_{c}*T*_{c}*T*_{a}*V*_{c}*T*_{s}*T*_{a}*T*_{c}is the crop foliage temperature and*T*_{s}is the soil surface temperature; and - for a given
*R*_{n}, vapor pressure deficit of air (VPD), and aerodynamic resistance, the temperature differences*T*_{c}−*T*_{a}and*T*_{s}−*T*_{a}are linearly related with evaporation*E*and transpiration*T*such thatwhere*a, b, a*_{11}, and*b*_{11}are semiempirical coefficients.

_{p}is the potential evapotranspiration; and the subscripts

*m, x,*and

*r*in this case refer to the minimum, maximum, and measured values, respectively. Estimation of the maximum and minimum values is discussed by Moran et al. (1994), and Fig. 1 illustrates the model graphics, wherein WDI is equal to the ratio of the distances AC/AB.

_{p}

*γ*is the psychrometric constant, and

*r*

_{cp}is the canopy resistance at potential evapotranspiration.

*V*

_{c}in Fig. 1 is substituted for by a special vegetation index that is linearly related to

*V*

_{c}. They suggested that the soil-adjusted vegetation index (SAVI) proposed by Huete (1988) is appropriate because SAVI is sensitive to increases in vegetation cover and insensitive to spectral changes in soil background as compared with other vegetation indices. SAVI can be expressed as

*L*is a dimensionless constant assumed to be 0.5 for a wide variety of LAI values (Huete 1988).

### Model 3: Two-source resistance model (Lhomme et al. 1994a,b)

*r*

_{af}is the bulk boundary layer resistance of the foliage per unit ground area, and

*r*

_{as}is the aerodynamic resistance between the substrate and canopy source height. Here,

*r*

_{as}and

*r*

_{af}were calculated following Choudhury (1989) and Choudhury and Monteith (1988). The parameter kB

^{−1}is not included in the aerodynamic resistance term because Lhomme et al. (1994a,b) assumed that the two-source model accounted for the bluff-body correction. Hence,

*ω*is the leaf width,

*z*

_{0s}is the aerodynamic roughness height for the soil surface,

*h*

_{c}is the crop canopy height,

*u*

_{h}is the wind speed at crop height,

*K*

_{H}is the eddy diffusivity at crop height, and here

*α*is a damping coefficient for eddy diffusivity and wind speed within the canopy.

*δT*is very difficult to obtain, Lhomme et al. (1994a) assumed that

*δT*

*a*

_{2}

*T*

_{r}

*T*

_{a}

^{m}

*a*

_{2}and

*m*by comparison with field observations of

*H.*They found that values of 0.1 and 2 for

*a*

_{2}and

*m,*respectively, provided the best fit. Later Lhomme et al. (1994b) found that a good linear relationship existed between

*δT*and the temperature difference

*T*

_{r}−

*T*

_{a}, such that

*δT*

*a*

_{1}

*b*

_{1}

*T*

_{r}

*T*

_{a}

*a*

_{1}and

*b*

_{1}, respectively.

At a temperature difference of approximately 10°C, these two *δT* calculations [(26), (27)] converge. Since our field site is in a semiarid region where these temperature differences are usually on the order of 10°C, we have adopted (26).

As with model 1, this model can estimate only *H.* The ET is obtained from the surface energy balance equation by eliminating *R*_{n} and *G* as before.

## Data source

The models were validated against aircraft data from the Bunny Fence Experiment (buFex) conducted in the Lake King district of the Great Southern region of Western Australia (Fig. 2) (Lyons et al. 1993). This semiarid site is characterized by an abrupt boundary between the native and agricultural vegetation. The native vegetation is characteristically a woodland called a mallee, with *Eucalyptus eremophila* the most consistent species. Patches of eucalypt woodland occur on lower ground, and scrub heath and casuarina thickets are found on the residual plateau soil. The native vegetation is between 0.5 and 6 m high, with more than 75% of this vegetation between 0.5 and 2 m. The adjoining farmlands cultivate winter-growing annual species. Wheat is the major crop in the agricultural area and grows between May and November. Crops are generally less than 1 m high during the growing season, and, after harvest, stubbles of about 20 cm or bare soil are common (Lyons et al. 1993; Huang et al. 1993, 1995b).

Previous studies (Huang et al. 1995b; Lyons et al. 1996) have shown that the NDVI over the native vegetation is relatively constant throughout the year. In contrast, over the agricultural region, it undergoes a marked variation as transpiration increases from that of the bare soil conditions of summer to that of a developing wheat crop and then decreases with the drying out after anthesis. These studies also have shown that over the native vegetation the sensible heat flux dominates throughout the year, in marked contrast to the agricultural region where the latent heat flux is dominant throughout the growing season.

During buFex, infrared surface temperature (bandwidth 8–14 *μ*m), humidity, potential temperature, and the three-dimensional wind components were measured by a GROB G 109B single-engine motor glider (Hacker and Schwerdtfeger 1988) at a sampling rate of 13 Hz (Lyons et al. 1993). Sensible and latent heat fluxes were evaluated by eddy correlation methods. NDVI data were obtained from the daily overpass of the National Oceanic and Atmospheric Administration satellite carrying the Advanced Very High Resolution Radiometer, using postflight calibrations for channels 1 and 2 (Smith et al. 1992).

Table 1 lists the datasets used. Preliminary aircraft data processing produced temperature, humidity, 3D wind speed, and surface temperature as a space series with an interval of 2.5 m during April and September 1992 and 2.0 m during October 1993. Aircraft measurements also provided solar radiation and albedo along the flight path, shown in Fig. 2, at altitudes between 10 and 200 m.

In analyzing the aircraft data, an 8-km cutoff wavelength was used and all aircraft observations were averaged over 20 km for both native and agricultural vegetation based on the analysis of Huang (1994). Hence, this aircraft dataset not only simulates satellite data, but provides measurements of the surface fluxes for model evaluation. Naturally, the *T*_{r} observations are essentially linear transects whereas the eddy flux data are representative of an upwind footprint, and thus there is a much larger area associated with these latter measurements. Nevertheless, the buFex site is very homogeneous on either side of the abrupt boundary.

_{g}is the surface value of the NDVI obtained from the satellite by incorporating an atmospheric correction following Paltridge and Mitchell (1990) and by assuming aerosol optical depths of 0.1 for channel 1 and 0.07 for channel 2, respectively (Huang et al. 1995a). NDVI

_{so}and NDVI

_{vg}are representative values of the NDVI for bare soil and dense vegetation, respectively, obtained from direct surface observations (Huang et al. 1995a; Smith et al. 1992).

## Results and discussion

Figure 3 shows *H* as estimated by model 1 over both agricultural and native vegetation. In the agricultural area, the model performed fairly well, with the scatter mainly falling around the 1:1 line. Over the native vegetation, the results illustrate much more scatter. The ET estimation (Fig. 4) shows different results. Over the agricultural area, ET estimation is slightly better than it is over the native vegetation although it is not as good as the *H* estimation. Since ET is the residual of the surface energy balance, these results depend on the closure of that balance.

*H*+ ET) against the estimated (

*H*+ ET) expressed as (

*R*

_{n}−

*G*) based on closure of the surface energy balance model. This comparison indicates that the model is consistently underestimating the total available energy. Since the radiation penetrating to the soil surface, which generates the surface heat flux, would increase with decreasing solar zenith angle and decreasing vegetation density, Gao et al. (1998) described the ratio of soil heat flux to net radiation as a function of solar zenith angle and the vegetation density as

*G*

*R*

_{n}

*μ*

_{1}

^{μ2}

*K*

*θ*

_{s}

*μ*

_{1},

*μ*

_{2}, and

*K*are empirically determined numerical constants and

*θ*

_{s}is the solar zenith angle. Incorporation of this correction did not improve the model results, suggesting that the empirical constants have regional limitations.

In theory, model 2 would be expected to give better results as it estimates ET directly rather than via the surface energy balance. However, the fluxes from this model (Fig. 6) show that the ET estimation is not very different from model 1 over both agricultural and native vegetation.

Tables 3 and 4 illustrate how the estimated fluxes changed with *S*_{kb} as it ranged from its reference value of 0.15, incorporating a 10% variation up and down. In deriving these tables the following statistical parameters were defined: mean absolute difference (mad) between measured and estimated values, root-mean-square difference (rmsd) between measured and estimated values, intercept of the linear regression of measured and estimated values (*a*), slope of the linear regression of measured and estimated values (*b*), and linear correlation coefficient of measured and estimated values (*r*^{2}).

*S*

_{kb}is slightly larger than 0.15. The mad and rmsd decrease with an increase of

*S*

_{kb}, whereas over the native vegetation, the results are the opposite. The smaller the

*S*

_{kb}, the better the agreement, with the best

*S*

_{kb}being smaller than 0.15. From the tables, it can be seen that the larger the

*S*

_{kb}is, the smaller is

*b*for

*H.*Hence, the estimated

*H*is lower when

*S*

_{kb}is higher. With an increase in

*S*

_{kb}, the extra resistance will increase, leading to a decrease in

*H*and an increase in estimated ET. The reason for different results between agricultural and native vegetation is related to their different surface characteristics. The

*S*

_{kb}constant theoretically depends on the roughness length, displacement height, and sensible heat flux. According to Kustas et al. (1989), kB

^{−1}can be expressed as the following, based on a one-source resistance model, where

*H*

_{obs}is the measured sensible heat flux and

*u*∗ is the friction velocity:

*S*

_{kb}can be expressed as

From (32), it can be seen that the surface roughness has a positive effect on *S*_{kb}, whereas the sensible heat flux has a negative effect. In the study area, both *z*_{0m} and *H*_{obs} are larger over the native than over the agricultural vegetation. The results shown in Tables 3 and 4 suggest that the impact of *H* is more significant on *S*_{kb} than is that of *z*_{0m}. Hence, *S*_{kb} is smaller over native vegetation than over agricultural vegetation.

*S*

_{kb}and the temperature difference was found in the dataset (correlation coefficient = 0.42, number of observations = 56), such that

*S*

_{kb}

*T*

_{r}

*T*

_{a}

Substituting *S*_{kb} values from (33) into models 1 and 2 leads to slightly better results over both areas. The rmsd decreased for both models, especially over the native vegetation (Tables 3 and 4). Model 1 had the best result over the agricultural vegetation whereas model 2 had the best result over the native vegetation.

Compared to the agricultural area, the results over the native vegetation are not as good, especially in estimating *H.* Choudhury (1989) suggested that for equivalent errors in estimating aerodynamic surface temperature, the resulting errors in estimating *H* would be larger over forests than over short vegetation, primarily because of the smaller values of aerodynamic resistance for the forest. Lyons et al. (1993) and Smith et al. (1992) also found similar results in southwestern Australia.

Since aerodynamic surface temperature is very difficult to obtain, Huang et al. (1993) developed an empirical model to estimate aerodynamic temperature and used it in a one-source resistance model to reduce the *H* estimation error. However, an empirical model is not uniformly applicable.

Recently, Verhoef et al. (1997) suggested that kB^{−1} over bare soil could be less than zero. However, kB^{−1} is consistently larger than zero. This result would lead to underestimating *H* and overestimating ET in April when the ground in the agricultural area is generally bare soil. Figure 7 shows kB^{−1} calculated from (31) compared with the results from Kustas et al.’s (1989) empirical model (4) over two different landscapes. In arriving at Fig. 7, the following criteria used by Burke and Stewart (1997) were applied: Monin–Obukhov length scale *L* [different from the *L* constant of Huete (1988)] < −1, (*T*_{r} − *T*_{a}) > 2 K and *u* > 1.0 m s^{−1}. When these criteria were not satisfied, data were eliminated. The average values of kB^{−1} over the agricultural and native vegetation are almost the same, at 5.16 and 5.18, respectively. These results are very different from Burke and Stewart (1997), who suggested that kB^{−1} will increase with increasing mean canopy height and with increasing *z*_{0m}, based on Hydrologic and Atmospheric Pilot Experiment and Sahelian Energy Balance Experiment datasets over different landscapes from a semiarid region to crops and forest. However, the diurnal variation of kB^{−1}, evident in the observations, is consistent with Verhoef et al. (1997).

Figure 8 represents *H* as estimated by model 3. It obviously overestimates *H* and the results are not as good as were achieved with models 1 and 2. These results are consistent with Zhan et al.’s (1996) analysis of the First International Satellite Land Surface Climatology Project (ISLSCP) Field Experiment (FIFE), Monsoon 90, and Washita ’92 data. Model 3 also suffers from its dependence on a large number of parameters, many of which must be obtained empirically.

*S*

_{x}is the sensitivity of a model to a parameter (here denoted by

*x*), defined by Zhan et al. (1996) as

*H*

_{0}(ET

_{0}),

*H*(ET)

_{+}, and

*H*(ET)

_{−}are the estimated sensible heat fluxes (evapotranspiration) when the parameter

*x*

_{0}equals its reference value or is 1.1

*x*

_{0}and 0.9

*x*

_{0}, respectively.

*H*or ET values are very small,

*S*

_{x}is very large even if the absolute differences are very small. Therefore, another parameter

*A*

_{x}also is used to analyze parameter sensitivity and is defined as

*A*

_{x}

*H*

_{+}

*H*

_{−}

The results indicate that, over both agricultural and native vegetation, the radiometric surface temperature and air temperature are very sensitive in all three models. The temperatures *T*_{r} and *T*_{a} not only directly influence *H* and ET estimation but also affect *R*_{n} and *G,* which in turn influence *H* and ET. Of the other measured meteorological data, wind speed is sensitive in model 3 but not in models 1 and 2.

In model 2, the difference between net radiation and soil heat flux is very sensitive to the ET estimation in both areas. However, the *H* estimation changed very little with (*R*_{n} − *G*). Therefore, even though the model estimates ET directly, it still needed to estimate the net radiation and soil heat flux correctly in order to improve the ET accuracy. From this finding, it can be explained why the results of models 1 and 2 are so similar. Over both the agricultural and native vegetation, the crop parameter SAVI has little influence on the estimated ET in comparison with other parameters.

Tables 5 and 6 also indicate that in models 1 and 2 all the parameters are more sensitive to the results over the native than over the agricultural vegetation. Over the agriculture area, the results are better than over the native vegetation, since the fluxes over the native vegetation are more sensitive to parameter error.

The roughness length *z*_{0m} has different effects in the three models. In models 1 and 2, ET and *H* change little with the variation of *z*_{0m}, whereas model 3 is very sensitive, leading to an *A*_{x} of 29.5 W m^{−2} over the native vegetation. Crop height and vegetation cover play important roles in determining *H* and ET in model 3, leading to *A*_{x} values of 88 and 27 W m^{−2}, respectively, over the native vegetation. Thus, reliable estimates of these parameters are essential for improved accuracy in the application of model 3.

For the empirical parameters *a*_{2} and *m, S*_{x} and *A*_{x} are very small in comparison with their values for other parameters, in both areas. Therefore, the figures that Lhomme et al. (1994a) obtained are suitable over a wide region.

## Conclusions

Models 1 and 2 have similar performance over both native and agricultural vegetation, although model 2 directly calculated ET whereas model 1 arrived at it via closure of the surface energy balance. Both models provided better estimates than did the more sophisticated model 3.

Both models 1 and 2 depend on *S*_{kb}, which was found to have a weak relationship with the temperature difference between radiometric surface temperature and air temperature. Incorporating this relationship led to slightly improved results, with model 1 giving the best result over the agricultural area and model 2 giving the best result over the native vegetation.

Tables 5 and 6 highlight the limitations of these models when air temperature is not measured or if it varies much over a region. For regional-scale applications, it may be difficult to use these approaches in areas where there is a very sparse network of air temperature and wind speed observations. The application of single-source approaches over various landscapes will be tenuous because kB^{−1} as formulated in models 1 and 2 is affected not only by the aerodynamic properties of the surface but also by *H* itself. Furthermore, other factors that affect the *T*_{r} observation, such as the amount of bare soil/substrate viewed by the radiometer, have been shown to be uncorrelated to the flux (Sun and Mahrt 1995).

The results for model 3 are more dependent on the empirical parameters within the model. These results are consistent with the recent analysis of Zhan et al. (1996) based on FIFE, Monsoon 90, and Washita ’92 data.

## Acknowledgments

The buFex was a joint field experiment funded by the Australian Research Council, Murdoch University’s Special Research Grant, the CSIRO–Flinders University Collaborative Grant Scheme, the Western Australian Department of Agriculture, and the Leeuwin Remote Sensing Centre. Throughout this research, Fuqin Li was in receipt of an Overseas Postgraduate Research Award and associated Murdoch University Research Scholarship. The comments of anonymous referees also benefited this work. All of this assistance is gratefully acknowledged.

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Date and time of experimental flights undertaken at Lake King, where WST is local standard time (UTC + 0800).

Statistical comparison between modeled and measured *R _{n}* −

*G.*

Impact of changes in *S*_{kb} on model results for the agricultural vegetation for sensible heat flux and evapotranspiration. Statistics are defined in the text.

Impact of changes in *S*_{kb} on model results for the native vegetation.

Average *S _{x}* and

*A*values of the three models over the agricultural vegetation. Variables and statistics are defined in the text.

_{x}Average *S _{x}* and

*A*values of the three models over the native vegetation.

_{x}