On the computation of area probabilities based on a spatial stochastic model for precipitation cells and precipitation amounts

  • Björn Kriesche
  • Antonín Koubek
  • Zbyněk Pawlas
  • Viktor Beneš
  • Reinhold Hess
  • Volker Schmidt
Original Paper


A main task of weather services is the issuing of warnings for potentially harmful weather events. Automated warning guidances can be derived, e.g., from statistical post-processing of numerical weather prediction using meteorological observations. These statistical methods commonly estimate the probability of an event (e.g. precipitation) occurring at a fixed location (a point probability). However, there are no operationally applicable techniques for estimating the probability of precipitation occurring anywhere in a geographical region (an area probability). We present an approach to the estimation of area probabilities for the occurrence of precipitation exceeding given thresholds. This approach is based on a spatial stochastic model for precipitation cells and precipitation amounts. The basic modeling component is a non-stationary germ-grain model with circular grains for the representation of precipitation cells. Then, we assign a randomly scaled response function to each precipitation cell and sum these functions up to obtain precipitation amounts. We derive formulas for expectations and variances of point precipitation amounts and use these formulas to compute further model characteristics based on available sequences of point probabilities. Area probabilities for arbitrary areas and thresholds can be estimated by repeated Monte Carlo simulation of the fitted precipitation model. Finally, we verify the proposed model by comparing the generated area probabilities with independent rain gauge adjusted radar data. The novelty of the presented approach is that, for the first time, a widely applicable estimation of area probabilities is possible, which is based solely on predicted point probabilities (i.e., neither precipitation observations nor further input of the forecaster are necessary). Therefore, this method can be applied for operational weather predictions.


Area probability Stochastic model Occurrence of precipitation Precipitation amount Probabilistic weather prediction Monte Carlo simulation 



The authors gratefully acknowledge the financial supports from the German Academic Exchange Service (DAAD) and the Czech Ministery of Education, project 7AMB14DE006. Antonín Koubek was supported by the Grant SVV-2015-260225.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Björn Kriesche
    • 1
  • Antonín Koubek
    • 2
  • Zbyněk Pawlas
    • 2
  • Viktor Beneš
    • 2
  • Reinhold Hess
    • 3
  • Volker Schmidt
    • 1
  1. 1.Institute of StochasticsUlm UniversityUlmGermany
  2. 2.Department of Probability and Mathematical Statistics, Faculty of Mathematics and PhysicsCharles University in PraguePragueCzech Republic
  3. 3.Deutscher Wetterdienst, Research and DevelopmentOffenbachGermany

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