418 
where t 2 is given by eq. (4) and the soil direct backscatter (in dB units) is expressed as a linear function 
of its volumetric surface moisture m ,: 
cr° = C + Dm, ( 7 ) 
For each of the 36 vegetation data points of the AgriscaTT’88 campaign, 4 soil points defined by 
m, = 0.125, 0.200,0.275,0.350 were used to generated a 144 data points database on which Mimics was run. 
The simplified model defined by eq. (6), (4) and (7) was fitted on the output of Mimics and figure 6 presents 
the result of this fitting. Keeping in mind that a unique set of the 3 parameters B, C and D is used to 
represent 11 different fields and that only 2 variables m„ and m, respectively represents the vegetation and 
the soil, the agreement is fairly good. 
6 Inversion 
The simplified model presented in the previous section (eq. 6, 4 and 7) is linear when expressed in dB units: 
<r°(dB) = —B'm v + C + Dm, (8) 
with B' = 20/(ln(lO) cos 6). 
When radar measurements are done with 2 incidence angles at the same time, it has been shown [9] 
that it can be inverted. With measurements done at 20° and 40°, the following linear system is obtain, which 
can be solved in m„ or in m,. 
o = -Bio™* + C 2 o + D 2 om. (9) 
(740 = - 04 O m„ + C 40 + D 40 m, (10) 
Figure 7 and 8 present the result of the inversion for the surface soil moisture m, and the total 
canopy water content m v respectively, using radar data in C-band HH at 20° and 40°, for the Agriscatt’88 
experiment data. This method is based upon the difference between attenuations at 20° and 40°. C-band 
is not providing enough difference in attenuations to give accurate estimations of the canopy water content, 
but the same method has been previously applied in X-band VV, at 20° and 40°, giving better estimates of 
m„ [9]. 
7 Concluding remarks 
In this study, we have shown that MIMICS can adequately simulated the signal backscattered by winter wheat 
canopies in C-band. In X-band, the agreement is less good but still reasonable at low incidence angle (20°) 
or when the biomass is not too high. At high incidence angle (40°) and when the biomass is high, Mimics 
strongly underestimates the signal backscattered. This might be related to the first order resolution of the 
radiative transfer equations in Mimics, which does not allow accounting for multiple scattering. 
We then demonstrated that it is possible to summarize Mimics outputs with “water-cloud” derived 
models, function of bulk canopy variables (LAI and total canopy water content) and involving a limited 
number of parameters. 
As it. has been shown previously that these semi-empirical model can be inverted, this allows the 
inversion a complex model such as Mimics. The method presented here could be applied to any complex 
model of canopy backscatter, providing a way to make them invertible. 
Further work should be done in this way. In particular, simplified forms for the surface-volume inter 
actions are yet to be found. This will allow a full application of our approach to the X-band. 
References 
[1] F. T. Ulaby, K. Sarabandi, K. McDonald, M. Whitt, and M. C. Dobson, “Michigan microwave canopy 
scattering model,” International Journal of Remote Sensing, vol. 11, no. 7, pp. 1223-1253, 1990. 
[2] M. A. Karam, A. K. Fung, R. H. Lang, and N. S. Chauman, “A microwave scattering model for layered 
vegetation,” IEEE Tansactions on Geoscience and Remote Sensing, vol. GE-30, no. 4, pp. 767-784, 
1992. 
[3] E. P. W. Attema and F. T. Ulaby, “Vegetation modeled as a water cloud,” Radio Science, vol. 13, no. 2, 
pp. 357-364, 1978. 
[4] F. T. Ulaby, C. T. Allen, G. Eger, and E. Kanemasu, “Relating microwave backscattering coefficient to 
leaf area index,” Remote Sensing of Environment, vol. 14, pp. 113-133, 1984.