Additional regressions were performed by combination of 
the principal factors and parameters like land-use, soil type 
classes, etc. The best results were obtained with the linear 
combination of the vegetation coverage density and the fifth 
principal factor. The derived values correlated strongly with 
the soil moisture measurements (r — 0.98 and r = 0.79) 
made in the 4-8cm and 0—4cm layers respectively. 
To sum up, most of the correlation coefficients obtained in 
the regression analyses were relatively small. It was how- 
ever predictable through the multitude of parameters influ- 
encing the backscatter coefficient. 
4 MODEL APPLICATION AND FIRST RESULTS 
Many models have been developed in the active microwave 
domain to explain backscatter as a function of soil mois- 
ture: theoretical models, like GO (Geometrical Optics), PO 
(Physical Optics), SPM (Small Perturbation Model) or IEM 
(Integral Equation Model), empirical models (Ulaby et al., 
1981, 1982 and 1986), and semi-empirical models (Oh et 
al., 1992), (Shi et al., 1995), (Dubois et al., 1995). The 
semi-empirical models have been applied with promising 
results in previous work, see e.g. (Wang et al., 1995). 
Therefore we have decided to apply the DUBOIS- (Dubois 
et al., 1995) and the OH- (Oh et al., 1992) models to our 
dataset. 
4.1 The DUBOIS-model 
This algorithm (Dubois et al., 1995) was derivated using 
scatterometer data and has been tested with several data- 
sets acquired with spaceborne (SIR-C) and airborne (AIR- 
SAR) systems. The inversion of the algorithm can also be 
applied successfully to areas with sparse vegetation. 
The model expresses the like polarized radar backscatter- 
ing as a function of radar characteristics (local incidence 
angle, frequency) and field parameters (dielectric constant, 
surface roughness). The HH- and VV-polarized backscat- 
tering cross-sections were found to follow the equations : 
i 1.5 ; 
o, = 10 2775 ce A 100-028€ eli sin 9)14507 
(1) 
0 = te 3 ; : 
ol, = 10 2.35 A ? 10? 046€ tan 8 (kh sip g)! 140.7 
where 8 : the incidence angle, « : the real part of the dielec- 
tric constant, h : the RMS height of the surface, k : the wave 
number, À : the wavelength. Best results were achieved 
by (Dubois et al., 1995) with bare and sparsely vegetated 
areas (NDVI« 0.4), at a frequency between 1.5GHz and 
11G Hz, for kh « 2.5, and incidence angles 9 > 30°. 
The inversion accuracy reaches an RMS error from 4.2% for 
the estimates of soil moisture and 0.34cm for the estimate 
of the RMS height. 
4.2 The OH-model 
The main difference to the previous model is the presence 
of the HV-polarized return. The model was derivated us- 
ing a truck-mounted network-analyzer-based scatterometer 
(LCX POLARSCAT)(Oh et al., 1992). The examination of 
the cross- and co-polarized ratios, defined respectively by 
552 
g = he andp = Zhh leaded to the empirical expressions 
vv Tov 
ineq. (2). 
The inversion model is defined by the nonlinear equation 
(4), which can be solved using an iterative technique. The 
solved I'? can then be introduced in eq. (3) to determine 
the real part of the dielectric constant € and the surface 
roughness kh. 
t 
| 
o 1 : 2 
p= - (r- GT ean) 
(2) 
q= Lis = 0.23VF°(1 — exp”**) 
1- €42 
h I’ =|—"— 3 
where nv. (3) 
20 | 37 1 q 1=0 4) 
(3) ^ 0.23VT? *typ-iz (4) 
where 6 : the incidence angle, ¢ : the real part of the di- 
electric constant, h : the RMS height of the surface, k : the 
wave number, A : the wavelength. 
Best results were achieved here with bare areas, at fre- 
quencies 1.5GHz « f « 11GHz (L, C, X), for RMS heights 
0.1cm « kh « 6cm and at incidence angles 10? « 8 « 70°. 
To estimate the capability of the inversion technique, (Oh et 
al., 1992) made a comparison between the values of sur- 
face parameters estimated by the inversion technique and 
those measured in situ for the roughness and the soil mois- 
ture, including the data measured in support of his study. 
The RMS errors in this case are 496 for the estimate of soil 
moisture and 0.23cm for the surface roughness (excluding 
the surfaces for which kh » 3). 
4.3 First results 
4.3.1 Application of the DUBOIS-model From the avail- 
able o2, and oJ, measurements in each image, we derived 
the surface roughness and the real part of the dielectric 
constant. Using the sand and clay fractions, the dielectric 
constant values were converted into soil moisture values 
through the set of Hallikainen empirical curves (Hallikainen, 
M. and Ulaby, F. and Dobson, M. and El-Rayes, M. and Wu, 
L., 1985). 
The field measurements have first been averaged over each 
field and then been compared with the estimated values. 
The results are presented in Fig. 4 and Fig. 5. 
We note, that the RMS heights for the bands C and L are 
much better estimated than the soil moisture. The RMS er- 
rors with the C-band represent respectively 0.36cm for the 
estimates of surface roughness and 7.4vol% for the esti- 
mates of soil moisture. 
The figure 4 shows an extreme underestimation of the soil 
moisture with L-band. Moreover, our results for the C-band 
confirm what (Dubois et al., 1995) predicts : the presence 
of vegetation on the fields 1, 6 and 7 results in an over- 
estimated surface roughness and an underestimated soil 
moisture. 
The whole results show a better fitting for the data of the 
second campaign. This is probably due to the co-polarized 
Intemational Archives of Photogrammetry and Remote Sensing. Vol. XXXII, Part 7, Budapest, 1998 
  
  
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