4. Estimation of Surface Characteristics

The inversion of the Oh-Model is based on the solution of relations introduced in the former paragraph. In the absence of an analytic solution, ks and ε ′ have to be estimated by an iterative procedure. In a first step, Γ° is evaluated from 0 1 23. 0 1 2 1 = − +       ° Γ       ° Γ p q π θ (1) Using the measured co-and cross-polarised ratios, Γ° can be estimated from (1) using an iterative technique. In this study, the Newton iteration approach was applied. Accordingly, the n-th Newton iteration for Γ° is given by () () () () x n n n x n a b x b a x c x b a x (2) Where 0 1 : Γ = x , π θ 2 := a , 23. 0 : q b = , 1 : − = p c (3) In a second step, from the approximated value 0 1 : Γ = x , Γ 0 is extracted as 2 0 1         = n x Γ and used to retrieve directly from Eq. (11.26) the real part of the dielectric constant 0 0 1 1 Γ − Γ + = ′ ε (4) The obtained values for ε ′ are converted into m v values after TOPP et al. (1980). Finally, Γ 0 is used again in Eq. (11.58) to derive the surface roughness value ks as 1 2 1 ln π θ p ks (5) The iterative procedure converges rather slowly after about 30 iterations. 4.2.1.2 Inverting Dubois-Model The inversion of the empirical algorithm addressed by DUBOIS et al.(1995) is much simpler than the inversion of the model proposed by OH et al.(1992). Both, dielectric constant as well as surface roughness, can be retrieved directly from the model using the co-polarised backscatter coefficient and the local incidence angle by using the following two step inversion algorithm. The first step is to retrieve the dielectric constant as () θ θλ θ σ σ ε tan 024. 0 sin cos 10 10 log 15. 0 93. 0 82. 1 19. 0 0 7857. 0 0 −                 = ′ − VV HH (6) and using the estimated …