Abstract
The Integral Equation Model with multiple scattering (IEMM) represents a well-established method that provides a theoretical framework for the scattering of electromagnetic waves from rough surfaces. A critical aspect is the long computational time required to run such a complex model. To deal with this problem, a neural network technique is proposed in this work. In particular, we have adopted neural networks to reproduce the backscattering coefficients predicted by IEMM at L- and C-bands, thus making reference to presently operative satellite radar sensors, i.e., that aboard ERS-2, ASAR on board ENVISAT (C-band), and PALSAR aboard ALOS (L-band). The neural network-based model has been designed for radar observations of both flat and tilted surfaces, in order to make it applicable for hilly terrains too. The assessment of the proposed approach has been carried out by comparing neural network-derived backscattering coefficients with IEMM-derived ones. Different databases with respect to those employed to train the networks have been used for this purpose. The outcomes seem to prove the feasibility of relying on a neural network approach to efficiently and reliably approximate an electromagnetic model of surface scattering.
Highlights
Modeling the electromagnetic wave scattering from random rough surfaces is an important issue for remotely sensing both land and ocean geophysical parameters from satellite microwave sensors
To assess the proposed approach, we have compared the backscattering coefficients produced by the Integral Equation Model with multiple scattering (IEMM) model and belonging to the test sets with those generated by the neural network (NN) for the same inputs
The backscattering coefficients are represented in dB to be consistent with most of the literature works on surface scattering measurements (e.g., [6,7,8])
Summary
Modeling the electromagnetic wave scattering from random rough surfaces is an important issue for remotely sensing both land (e.g., soil moisture and roughness) and ocean (speed and direction of the wind blowing over the sea surface) geophysical parameters from satellite microwave sensors. The IEMM can be considered as an extension of the Integral Equation based surface scattering model (IEM) With respect to the latter, the IEMM removes the assumption on the phase factor exp(jw|z − z′|), which was neglected in the spectral representations of the Green’s function and of its gradient in the development of the original IEM formulation. The quantity denoted by w is the vertical component of the propagation vector of the generic plane wave in which the electromagnetic field is expanded, j denotes imaginary unit and z and z′ are the random variables representing the heights at different locations, defined by (x,y) and (x′,y′), respectively, on the rough surface This approximation was basically thought in order to obtain a simple algebraic form for the scattering model. The Kirchhoff and complementary field coefficients, fqp and Fqp respectively, are dimensionless, complicated expressions that depend on spatial variables:
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