Bayesian analysis of the scatterometer wind retrieval inverse problem: some new approaches

The retrieval of wind vectors from satellite scatterometers is a non-linear inverse problem. A common approach to solving inverse problems is to adopt a Bayesian framework and infer the posterior distribution of the parameters of interest given the observations using a likelihood model relating the observations to the parameters, and a prior distribution over the parameters. In this paper we show how Gaussian process priors can be used efficiently with a variety of likelihood models, using local forward (observation) models and direct inverse models for the scatterometer. We present an enhanced Markov Chain Monte Carlo method to sample from the resulting multi-modal posterior distribution. We go on to show how the computational complexity of the inference can be controlled using a sparse, sequential Bayes algorithm for estimation with Gaussian processes. This helps to overcome the most serious barrier to the use of probabilistic, Gaussian process methods in remote sensing inverse problems, where the size of the data set can become prohibitively large. We contrast the sampling results with the approximations found using the sparse, sequential Bayes algorithm.