Simulation of rainfall with different temporal resolution by stochastic pulse models

Various modifications of clustered rectangular point process models are applied to represent temporal rainfall processes at a single site. Besides comparing observed and simulated properties of the precipitation time series, an assessment of fit is carried out using difierent methodologies. Thus the possibilities of downscaling of daily rainfall series and the identification of some limiting ranges of application are investigated. Modifications of the fitting procedure are also considered. The generalized extreme value analysis is used to test whether the incorporation of third order moments in the fitting indicates an improvement and better agreement for small time intervals. Former investigations have revealed some dificulties in applying these kind of models for sub-hourly levels of aggregation. Therefore a difierent distribution of the cell depths, namely the generalized Pareto distribution is tested. The methodology of wavelet transformation is applied to investigate the self similarity and fractal pattern of rainfall time series. Furthermore a method called Wavelet transform modulus maxima is taken into account to draw inferences about the multifractal properties of the observed and the simulated rainfall data. This thoroughly analysis of the synthetically generated time-series show some very good agreement with the properties of the observed precipitation processes pointing out the good applicability of the rectangular point process models for a range of time scales. This paper is intended to give a general overview of some work carried out most recently by the authors, whereas the details will be presented somewhere else.