1172 
through the concept of Crop Water Stress Index (Jackson et al., 1981) initially designed for crop monitoring 
but also valid for bare soil and sparse vegetation (Moran et al., 1994a): 
E T - T 
— = l-CWSI = 1 5 (6) 
E, T Sma -T Snm 
where Ts is surface temperature and min and max correspond respectively to potential and no evaporation. We 
can assume in a first approximation that T Smin equals air temperature T c and that T Smax can be easily infered 
from energy balance equation (E=0): 
pc p 
where Rn is the net radiation (W/m 2 ), G the soil heat flux (assumed to be 30% of Rn on bare soil, Clothier et 
al., 1986), and r a aerodynamic resistance of bare soil. The only additional input variables needed here is thus 
net radiation. 
4.1.3. Vegetation temperature model (Fig. 4 part (c))\ as a first approximation, the surface radiometric 
temperature observed from space over sparse vegetation can be considered as the area weighted mean of 
vegetation and soil temperatures. However, when using Landsat TM data acquired around lOhOO local, the 
shaded part of the soil must be acounted for because of the low solar elevation. Indices sh and si corresponding 
to shaded and sunlit soil respectively and assuming that Tsl=Ts and Tsh=(Tc+Tsl)/2 we can write: 
Tr = fc.Tc + fsl.Tsl + fsh.Tsh = (fc+fsh/2).Tc + (fsl+fsh/2).Ts (8) 
fsh and fsl are computed according to the Jasinsky model (Jasinski & Eagleson, 1990) as a function of solar 
elevation, vegetation cover and mean shrub height and diameter. 
4.2. Results 
Infrared bare soil temperature collected at MF 5 were used to adjust the model of eq. (6) & (7). Results are 
reported on Fig. 5 and show a good fit to an exponential law. The different parameterizations encountered in 
littérature range in fact from simple linear model (Deardorff, 1977) to more complex sigmoïde shape (Chanzy 
et al., 1993) but these works demonstrated above all that the relationship between E/Ep and soil moisture 
depends essentially on soil texture. Since the texture is nearly similar on the whole watershed this model will 
thus be used on other sites. 
Concerning the Jasinski model, it was run on MF 1 at lOhOO local and it provided estimated 
shaded soil portion ranging from 20% to 50% depending on the day from the beginning to the end of the rainy 
season. Not accounting for this shaded portion in eq. (8) leads here to vegetation temperature sometimes lower 
of more than 15 degrees. 
Two Landsat images (DOY 162, 274) and three additionnai aircraft flights (DOY 290,291,310) 
were finally selected in the dataset close to ERS-1 overpasses (respectively DOY 170, 275 for TM and DOY 
275,310 for aircraft). Estimating soil moisture from a° (mainly dry conditions on these dates), input variables 
Ts and Tc were then computed at the time of satellite/aircraft overpass (between lOhOO and llhOO local) 
according to eq. (6) to (8). The resulting sensible heat fluxes derived from eq. (5) on MF 1 are plotted on Fig. 6 
and display an overall RMSE around 29 W/m 2 corresponding to a slight overestimation. This is to be compared 
with previous modelling approach on Walnut Gulch with one layer models (Moran et al., 1994b) which 
provided RMSE between 40 and 50 W/m 2 . Nevertheless, this quite good agreement between ERS-1 ATM 
estimated and observed fluxes doesn't mean a complete validation of the method because of the limited number 
of points. Particularly wider range of moisture conditions should have better demonstrated the interest of ERS-1 
SAR data to improve fluxes estimation.