Interpolation of Rainfall Fields Through Expectation Conditionally On Ground and Satellite Measurements

We consider the problem of spatially interpolating rainfall fields at small scale from rain gauge measurements with the additional information provided by infrared satellite channels. Namely, to produce rainfall values at any arbitrary site r(x) given point mea- surements r(x1), ..., r(xn) and remote sensing measurements s(p1), ..., s(pm), each s(pi) standing for a radiance integrated over pixel pi.

Formally, the best statistical prediction is given by the conditional expectation E[r(x)|r(x1), ..., r(xn), s(p1), ..., s(pm)] which can be computed only within a fully prescribed model of random function. We propose to perform the computation in the framework of the so-called transformed-Gaussian model with the additional specifica- tion that s = (r) + (the link function and the noise being modeled separately).

The transform-Gaussian model have proved to be a reasonable model for rainfall in the Sahel (which is the climatological application that we have in mind for these the- oretical developments) and provides an optimal solution different from the classical kriging predictor. As a counterparts, it involves computational difficulties as it may requires MCMC simulations to obtain numerical approximation of the conditional ex- pectation.

Theoretical results obtained are compared to those of more classical spatial and non spatial algorithms previously described in the literature.