layer, the model provided an estimate 
for the penetration depth when the 
calculated ratio ’attenuated 
amp 1itude/inei dent amplitude’ equaled 
1/e. For calculations, we used the 
estimated values of the dielectric 
constant given by Hallikainen et al. 
(1985), who used the soil texture and 
the volumetric water content as input. 
3.2 The surface scattering model 
The Kirchhoff’s scattering model under 
the scalar approximation or physical 
optics model is often used to compute 
the backscattering coefficient of bare 
soil (Ulaby et al., 1982 ). Three basic 
hypotheses of the model must be 
remembered: (1) soil surface has gentle 
ondulations with average horizontal 
dimensions which are large compared to 
the incident wave length, (2) the model 
takes into account the surface 
scattering only and the contribution of 
volume scattering was neglected, (3) 
soi 1 roughness was assumed to be 
isotropic and randomly distributed. 
This model exhibits a decreasing 
angular dependence that characterizes 
relatively smooth surfaces. The 
backscattering coefficient oopp (p 
denotes the polarization state) is the 
sum of a non-coherent scattering term 
(ooppn) and a slope term (oopps). These 
two scattering terms consist of the 
product of two independent functions. 
The "dielectric" function accounts for 
the dependence of the scattering 
coefficient on the dielectric constant, 
which is very sensitive to soil 
moisture and less sensitive to soil 
texture.For calculations, we used the 
estimated values of the dielectric 
constant given by Hallikainen et al. 
(1985). The "roughness" function is 
governed by the soil surface roughness, 
which is characterized by two 
parameters: (1) the standard deviation 
of heights (s), and (2) the correlation 
1ength (1 ). 
4 RESULTS AND DISCUSSION 
4.1 Soil moisture estimation from 
microwave measurements 
All measurements were perfomed during 
three experiments on a slightly rough 
surface (s ranging from 0.006 to 0.010 
m). A wide range of soil moisture was 
studied. Figure 1 shows results 
obtained with a 15 angle of incidence 
and a HH polarization (configuration 
I). This configuration is often 
recommanded as an optimal one for soil 
moisture estimation. A second 
configuration (configuration II) of the 
future radar satellite ERS-1 (23 angle 
of incidence, VV polarization) was also 
tested (Figure 2). 
According to previous works (Ulaby et 
al 1978, Bernard et al 1982), we have 
obtained linear relationships. Results 
of the regression analysis are given in 
Table 1. The both configurations (I, 
II) give similar accuracy ( about 
0.02 m 3 . rrr 3 ) on the predicted 
volumetric water contents. 
Table 1 : Results of the backscattering 
coefficient - volumetric 
water content (0-5cm) linear 
relationship. 
Parameter 
Radar 
Configuration 
15 -HH 23 -VV 
S 1 ope 
0.031 
0.034 
Intercept 
0.221 
0.328 
r 3 
0.94 
0.97 
Resi dual 
0.020 
0.017 
The methodology of determination of 
soil moisture influences the accuracy 
of observed field data which are to be 
correlated with remote data. It can 
modify the values of fitted parameters 
of the calibration relationships. For 
example, in dry or and wet conditions, 
the accuracy of volumetric water 
content estimated over the field area 
from 50 samples was found to be equal 
to 0.013 m 3 .rrr 3 . Averaging data 
spatially located in the surface foot 
print seen by the radar will increase 
the accuracy of soil moisture 
determination. It was found to be equal 
to 0.005 m 3 . rrr 3 . 
The quality of results presented in 
this section could be considered to be 
optmistic compared to future 
operational applications. We shall 
analyse in the following sections how 
the results are affected when 
penetration depth, roughness variations 
and soil moisture heterogeneity are 
taken into account. 
4.1.1 Penetration depth effects. 
In the previous section, we took the 
mean volumetric water content (Go - 5 ) 
over the 0-5 cm layer for soil moisture 
determination. But, on one hand, we 
can see on Figure 3 that the near 
surface water profiles present 
sometimes high water gradients. On the 
other hand, it is well known that the 
penetration depth of the microwaves 
depends on the soil moisture. Thus Go - 5 
does not always describe the physical 
properties of the soil layer which 
effectively affected the microwave 
scattering. 
A set of 17 measurements was used for 
this analysis. For each measurement, 
penetration depth was computed with the 
model el ectomagnetic wave propagation 
described in section 3.1. Figure 4 
shows the computed values of 
penetration depth for configuration I. 
Note that, in spite of the 
heterogeneity on the shape of the soil 
moisture profile, there is almost an 
univoque relationship between the 
penetration depth and mean volumetric 
water content over the 0-penetration 
depth layer (Go - 6 ) . 
A new soil moisture-backscattering 
coefficient (oo) relationship have been 
707