A POINT PROCESS APPROACH FOR SPATIAL STOCHASTIC MODELING
OF THUNDERSTORM CELLS
Bjoern Kriesche
Reinhold Hess
Volker Schmidt
Abstract: In this paper we consider two different approaches for spatial stochastic modeling of
thunderstorms. Thunderstorm cells are represented using germ-grain models from stochastic
geometry, which are based on Cox or doubly-stochastic cluster processes. We present
methods for the operational fitting of model parameters based on available point probabilities
and thunderstorm records of past periods. Furthermore, we derive formulas for the
computation of point and area probabilities according to the proposed germ-grain models. We
also introduce a conditional simulation algorithm in order to increase the model’s ability to
precisely predict thunderstorm events. A systematic comparison of area probabilities, which
are estimated from the proposed models, and thunderstorm records conclude the paper.
2010 AMS Mathematics Subject Classification: Primary: 60D05; Secondary: 60G55,
86A10.
Keywords and phrases: Stochastic modeling, Cox process, cluster process, germ-grain
model, Monte Carlo simulation, thunderstorm cell.