528 
temperature Tj, it emits the same radiations as it absorbs. Therefore, according to the Rayleigh-Jeans 
approximation, the energy radiated by the jth layer is Fj*Tj. By applying this condition to all the layers, the 
Surface scattering models 
The other part of the study presents three basic surface scattering models based on the theory of 
electromagnetic waves from random rough surfaces (Beckman and Spizzichino 1963, Ulaby et al. 1982, Tsang 
et al. 1985). Each analytical formula derivation of the bistatic scattering coefficients results from 
approximations which are surface roughness and wavelength dependent. They involve two surface roughness 
parameters: the surface height standard deviation (s), and the surface correlation length (1). The integration of 
the bistatic scattering coefficients, over the upper hemisphere, gives the soil surface reflectivity (albedo) of the 
medium. The Small Perturbation Model as SPM (Rice et al. 1951, Schiffer et al. 1987), to the first order, the 
Kirchoff model, under the scalar approximation - Physical Optics as PO - (Fung and Eom 1981) and under the 
stationnary phase approximation - Geometrical Optics as GO - (Wu and Fung 1972) are briefly presented here. 
In the small perturbation theory, which concerns surfaces with slight roughness (slope, and s to wavelength 
ratio, much smaller than unity), scattering from a smooth surface is considered with perturbative terms arising 
from slight surface roughness. For the first order, only the contribution of the specular intensity reflected by a 
smooth surface and the diffuse incoherent intensity are taken into account. In the Kirchoff approximation, 
electromagnetic field on the surface is estimated using the tangent plane approximation (i.e. every point on the 
surface is treated as though it were part of an infinite plane parallel to the local tangent surface). Hence, the 
theory is applicable for large scale roughness, where s and radii of curvature of the surface are much larger 
than the wavelength. For small s (rms slope lower than 0.25), the PO model is used. Increasing the surface 
EXPERIMENT 
The experiment was carried out at the test site of INRA Montfavet, France, during the period of April to June 
1993. The multifrequency radiometric measurements have been collected with the Portos radiometer (Table I), 
over bare soils surfaces, for both polarization and incidence angles ranging from 0° to 50°. Bare soils test sites 
were prepared to cover an extensive range of soil moisture (from 0.03 to 0.36 cm3/cm3) and roughness surface 
conditions (from very smooth to rough, Table II). The gravimetric soil moisture vertical profile (5 repetitions) 
were collected, for the following depths: 0-0.5, 0-1, 0-2, 2-3, 3-4,4-5, 5-7, 7-10, 10-15 cm, as well as the soil 
surface temperature (thermal infrared measurement) and the soil temperature profile down to 25 cm of depth 
(ten platinum resistance thermocouples). The time interval between the soil moisture sampling and microwave 
observations never exceeds two hours. The profiling of the soil dry bulk density (Bertuzzi et al. 1987) was 
performed over each field. The surface roughness characteristics were determined by laser profile meter 
technics (4 four profiles on average) (Bertuzzi et al. 1990). 
Frequency 
1.4GHz 
5.05GHz 
10.65Ghz 
23.8Ghz 
36.5GHz 
90.0GHz 
-3dB beamwidth 
12°.5 
12°.l 
13°.25 
10°. 15 
9°.6 
11°.0 
-20dB beamwidth 
30°.0 
29°.0 
39°. 1 
31°.8 
32°. 1 
32°.8 
Polarization 
Horizontal / Vertical 
Platform Height 
20 m | 20 m | 20 m | 20 m | 20 m I 20 m 
Table I: PORTOS radiometer characteristics 
N 
total radiations emitted by the soil medium (brightness temperature TB) is equal to 
where N is 
the total numbers of layers. 
roughness (i.e increasing s to wavelength ratio), scattering consists of only diffuse contribution, so the GO 
model, which represents the short wavelength limit of the PO model, is used. In this case, the surface 
reflectivity is a function of the slope distribution of the surface and thus non frequency dependent. Shadowing 
functions for the PO model (Smith 1967) and the GO model (Sancer 1969) are taken into account.