Bjoern Kriesche (University Ulm)

Stochastic modeling of spatially resolved data, with applications to the
prediction of  area  weather events

Praha, 21.10.2014
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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 talk, we present 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 from stochastic geometry, where
the grains are random sets which can roughly be interpreted as precipitation
cells. The germs form a (spatially non-homogeneous) Cox point process.

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.