Modeling of daily precipitation at multiple locations using a mixture of distributions to characterize the extremes

A stochastic model for the generation of daily time series of rainfall at multiple locations in which the amount of daily rainfall is modeled by a mixture of two different probability distribution functions is presented. A mixture model is implemented with the specific objective of characterizing extremes of daily precipitation. The approach is based on the assumption that the extremes within a time series have a different stochastic behavior compared to the normal regime of precipitation. A multivariate autoregressive model is used to model the local probability of occurrence of rainfall and the amount while keeping the intersite covariance structure using a truncated normal distribution. The amount simulated using the truncated normal distribution is further transformed so that it can be regarded as coming from the actual distribution fitted to the daily precipitation at each station using the probability integral transformation. The seasonal cycles of the amount as well as the temporal and spatial correlations of the daily precipitation are incorporated by fitting the model on the monthly basis. Application was made on 122 stations within the Unstrut catchment with an area of 6343 km(2) in central eastern Germany. Results show that the model can fairly well reproduce a number of statistical features of daily precipitation including the extreme value distribution of the annual maximum daily and 3 day total precipitation, both at individual stations and at the catchment scale.