Effect of Surface Profile Length on the Backscattering Coefficients of Bare Surfaces

The root mean square (rms) height s and autocorrelation length l are commonly used as the surface roughness input parameters to surface scattering models. Whereas it is well known that the surface roughness parameters of a natural soil surface are underestimated with a short surface profile, it is not clear how much the underestimated surface parameters affect the backscattering coefficients of the surface for various incidence angles and polarizations. In this paper, the backscattering coefficients of simulated and measured surface profiles are computed using the integral equation method and analyzed to answer this question. A 4000lmacr-long rough surface is generated numerically, where lmacr is the true correlation length of the surface, and the backscattering coefficients of the surface are computed and analyzed for various conditions. The rms error of the backscattering coefficient at a medium range of incidence angles is less than 1.5 dB for vv-polarization and 0.5 dB for hh-polarization if the profile length is larger than 5lmacr for a surface with ks=1.0, kl=10.0, and epsiv _r=(10.0,2.0). Similar results are obtained from numerous simulations with various roughness conditions and various wavelengths. It is also shown that the rms error of the backscattering coefficients between 5- and 1-m-long measured surface profiles is 1.7 dB for vv-polarization and 0.5 dB for hh-polarization at a medium range of incidence angle (15deglesthetasles70deg), whereas the surface roughness parameters are significantly reduced from 2.4 to 1.5 cm for the rms height s and from 35.1 to 10.0 cm for the autocorrelation length l