A probabilistic approach to the prediction of area weather events, applied to precipitation

In meteorology it is important to compute the probabilities of certain weather events occurring. There are a number of numerical and statistical methods for estimating the probability that a weather event occurs at a fixed location (a point). However, there are no widely applicable techniques for estimating the probability of such an event occurring in a geographical region (an area). In this paper, we propose a model-based approach for the computation of area probabilities using point probabilities. We develop this approach in the context of estimating the probability of the meteorological event ‘occurrence of precipitation’. We treat the point and area probabilities as coverage probabilities of a germ–grain model, where the grains can roughly be interpreted as precipitation cells. The germ–grain model is completely characterized by a sequence of local intensities and a grain size. We compute these model characteristics using available point probabilities. A non-negative least-squares approach is used to determine the local intensities and a semivariogram estimation technique is used to find the grain size. We are then able to determine area probabilities either analytically or by repeated simulation of the germ–grain model. We validate our model, using radar observations to assess the precision of the computed probabilities.