Gibbs sampling for conditional spatial disaggregation of rain fields

Abstract

Gibbs sampling is used to simulate Sahelian rain fields conditional to an areal estimate provided either as the output of an atmospheric model or by a satellite rainfall algorithm. Whereas various methods are widely used to generate simulated rain fields conditioned on point observations, there are many fewer simulation algorithms able to produce a spatially disaggregated rain field of known averaged value. The theoretical and practical aspects of Gibbs sampling for the purpose of conditional rain field simulation are explored in the first part of the paper. It is proposed to used a so‐called acceptation‐rejection algorithm to ensure convergence of the conditional simulation. On a Sahelian case study, it is then showed that Gibbs sampling performs similarly to the well‐known turning band method in an unconditional mode. A preliminary validation of the method in conditional mode is presented. Several rain fields are simulated conditionally on an observed rainfield, whose only the spatial average over a 100 × 100 km2 area is supposed to be known. These conditional simulations are compared with the observed rain field and to other rain fields of similar magnitude. For a given class of events, the conditional rain fields have a distribution of point values similar to the distribution of observed point values. At the same time, the model is producing a wide range of spatial patterns corresponding to a single area average, giving an idea of the variety of possible fields of equal areal value.