Rough paths theory applied to analyze the electromagnetic field scattered by a time varying sea surface

International audienceDue to complex non-linear fluid dynamics, sea surfaces can be considered as time-varying random rough surfaces. For the sake of simplicity, statistical approaches model the complex surface as a set of random discrete scatterers. Assuming a great number of random scatterers (phase screens) following a birth-death Markov process, Field and al. [1], [2] proved that the dynamics of the electrical field scattered by these scatterers can be described by a stochastic differential model. More precisely [3], [4], the electrical scattered field is described by two processes, a normalized amplitude Psi {text{t}} and a Radar Cross Section (RCS) Xt, that are given by the following set of non-linear coupled stochastic differential equations (NLCSDE)