Coupling a Neural Network-Based forward Model and a Bayesian Inversion Approach to Retrieve Wind Field from Spaceborne Polarimetric Radiometers

Abstract

A simulation study to assess the potentiality of sea surface wind vector estimation based on the approximation of the forward model through Neural Networks and on the Bayesian theory of parameter estimation is presented. A polarimetric microwave radiometer has been considered and its observations have been simulated by means of the two scale model. To perform the simulations, the atmospheric and surface parameters have been derived from ECMWF analysis fields. To retrieve wind speed, Minimum Variance (MV) and Maximum Posterior Probability (MAP) criteria have been used while, for wind direction, a Maximum Likelihood (ML) criterion has been exploited. To minimize the cost function of MAP and ML, conventional Gradient Descent method, as well as Simulated Annealing optimization technique, have been employed. Results have shown that the standard deviation of the wind speed retrieval error is approximately 1.1 m/s for the best estimator. As for the wind direction, the standard deviation of the estimation error is less than 13° for wind speeds larger than 6 m/s. For lower wind velocities, the wind direction signal is too weak to ensure reliable retrievals. A method to deal with the non-uniqueness of the wind direction solution has been also developed. A test on a case study has yielded encouraging results.

Neural Network Emulation of the Integral Equation Model with Multiple Scattering

“…With subscript meas , we denote the IEMM σ 0 to which the noise was added thus simulating a radar sensor measurement, while with subscript NN we indicate the outputs of the trained network. The minimization of (13) has been performed by applying a simulated annealing technique (e.g., [ 29 ]). Note that since this is only a theoretical exercise aiming at proving the suitability of our methodology for a typical remote sensing problem such as soil moisture estimation, the knowledge of the roughness parameters ( i.e., s and l ) has been supposed to generate the NN outputs, while it is well known that in real cases the uncertainty on the roughness parameters affects the quality of soil moisture estimates inducing retrieval errors that may be quite large [ 30 , 31 ].…”