Freq 
(GHz) 
Depth 
(cm) 
A 
B 
std 
r2 
Model 
1.4 
8.14 
0.98 
6.469 
0.971 
W 
0.5 
-1.48 
1.03 
12.66 
0.906 
F 
1.0 
1.69 
1.01 
12.116 
0.911 
F 
2.0 
6.24 
0.99 
11.814 
0.911 
F 
5.0 
25.16 
0.9 
15.934 
0.823 
F 
5.05 
1.37 
1.01 
5.106 
0.984 
W 
0.5 
-7.72 
1.05 
5.697 
0.982 
F 
1.0 
6.57 
0.99 
6.878 
0.97 
F 
2.0 
24.71 
0.9 
7.53 
0.958 
F 
5.0 
94.8 
0.57 
14.88 
0.698 
F 
10.65 
18.33 
0.94 
5.422 
0.982 
W 
0.5 
13.89 
0.984 
5.215 
0.984 
F 
1.0 
26.98 
0.9 
6.134 
0.975 
F 
2.0 
43.34 
0.82 
6.454 
0.967 
F 
5.0 
107 
0.52 
14.076 
0.712 
F 
Table III: results of statistical 
analysis (linear regression) of 
simulated data, using Wilheit 
(W) and Fresnel (F) models, 
and experimental data. 
with: 
A slope 
B intercept 
std standard deviation 
r2 determination coefficient 
Study 2: surface scattering models 
The figure 3 is a representation, in the ks-kl space (where k = foifk is the wave number), of all roughness 
conditions for the four surfaces and for the three frequencies (1.4, 5.05, 10.65 GHz). The standard height 
deviation and the surface correlation length have been determined using a Gaussian distribution for the surface 
height and the autocorrelation function, respectively. Each validity domain of the SPM, PO, GO models for 
random surfaces are also represented there, assuming a Gaussian autocorrelation function. First, we can note 
for the same test site field 1, 2, 3 or 4, the heterogeneity in the roughness measurements, especially for the 
surface correlation lengths. Then, several surface roughness conditions fall outside all the validity ranges 
(particularly for the lower frequencies). 
Figure 3: Measured 
roughness parameters and the 
validity domains of the SPM, 
PO, GO models. 
So, in order to test the ability of the different models to reproduce the observed data and because of the 
variability of the observed surface parameters, we have kept, in a first step, for the simulations, the measured 
roughness couples (s, 1) which fall into the validity domain of each model. Figures 4, are illustrations of the 
comparisons between the simulated emissivities, using the surface scattering models, and the measured 
emissivities, versus incidence angle, for two contrasted soil moisture conditions. Figures 4 (a) to 4 (b) show a 
good angular behaviour of the simulated emissivities, for both polarizations. A sensitivity study of the SPM 
model (first order) has shown a little effect of the roughness parameters on the emissivity, so that we can 
consider at this level of approximation the model is not different from the equation using the Fresnel