Application of the Gibbs Sampler to the Conditional Simulation of Rain Fields

The low density of raingauge networks in West-Africa and the availability of climatological variable at large scale only (as outputs of climatological models or remote sensing estimation algorithms) can be bridged by the so-called disagreggation algorithms which are designed to provide rainfall data at any scale given large scale data, and a small set of ground (point scale) measurements. The proposed algorithms is based on a geostatistical model, namely a stochastic model taking explictly into account the spatial structure of the variable. The disagreggation problem is then viewed as a Monte-Carlo simulation problem at the required scale conditionned by all the available information. As the problem of sampling from the multivariate density derived from our model does not have direct solution, the simulation is performed with an iteration of a Markov Chain whose limiting distribution is the desired one. Under the general Metropolis-Hastings scheme we use the well known Gibbs sampler, which allows here to deal with grids with arbitrary large number of points at the cost of small approximations. The behaviour of the model is demonstrated by disagreggation of a few rainfall events observed during the EPSAT-Niger experiment.