To compute lite radar back scattering coefficient, the IEM model need the radar parameters(frequency,
polarisation state, incidence angle, azimulal angle), and the surface parametersfdielectric constant and the
surface correlation function). The expression of the backscaUering coefficient is (in co-polarised case):
C PP = ~| i pp| C x p(- 4 S 2 k 2 COS 2 e)^ 4S k C ^ S ^ W (n) (2ksin9cos«I).2ksinesin
k2 " / -* - ' ‘ ^ o\V (4s 2 k 2 cos 2 9) n
— Re(f’ppFpp)cxp(-3s 2 k 2 cos 2 0)£-
n=l
k | c I 2 / _ 2, 2 2 a) V 1 (S 2 k 2 COS 2 0) n ,
+ |Fpp| exp^-2s k COS GJ^ W' J (2ksinecos,2ksinesin)
n=l
n!
-W (n) (2ksine cos )
where:
- s : Heigth RMS
2n
• k = — wave number
X
- 0,C>: incidence and azimutal angle
- W (n) (u,v) = -L/|p n (x,y) e - i(ux+vy) dxdy
2n
- p(x,y) : surface correlation function
-e r , p r : dielectric constant and relative pennitivity
* R II > R 1 : Parallel and perpendicular fresnel coefficient for the incidence angle 0
3, A SURFACE MODEL FOR AGRICULTURAL SURFACE OF BARE SOIL:
Before, we have seen that the IEM model needs the two dimensional correlation function of the surface
(i.e. the height distribution in 2 dimensions of the surface) to compute the backscattering coefficient The
difficulty of measuring the two dimensional height distribution of the surface on a large area leads us to
define a model of surface based on the profile of heights measured by the "profile-meter" in two
directions, parallel and perpendicular to the row direction. As a result, we have to determine parameters
of the surface model.
The complexity of agricultural surface is due to the fact that the surface can represents more than one
spatial scale. In general, clods and rows represent two separate spatial scales: a small spatial structure
(clods) and a large spatial structure (rows). On sowing fields, the row structure introduce an anisotropy of
the surface and gives a preferential direction of the surface structure.
The surface model used in this study was presented by Kong in 1984 [4]. The height distribution is given
by:
Z = f(x,y) = £(x,y) + A(x) cos(^x +
- 4(x,y) represents the small scale (clods) and is a gausian random variable with zero mean
- A(x)cos(^fx +
centered around the spatial frequency of , where the variation of the enveloppe A(x) and
the phase tp(x) is slow compared to those of cos(-^?- x)
The correlation function corresponding to this height distribution is
424
