V. Stergiou, Investigation of the stochastic structure of the rainfall intermittency, Diploma thesis, 195 pages, Department of Water Resources, Hydraulic and Maritime Engineering – National Technical University of Athens, Athens, September 2005.
The most significant property of the rainfall process, in comparison to other hydrological processes, is its intermittent character. Many and various stochastic processes have been proposed and represent more or less successfully the rainfall occurrence process. In discrete time representation, the most typical model widely used until nowadays is the Markov chain model. In continuous time, the point process models dominate. At the present study, a binary stochastic model of order k non Markovian is investigated. The model aims at a better representation of the rainfall process in combination with a parsimonious use of parameters. This approach is based on the dominant physical and mathematical principle of maximum entropy, interpreted has maximum uncertainty in the theory of stochastic processes. The theoretical framework results in a parametric expression of the probability of a sequence of consecutive dry time intervals. The Markov chain model is α specific case of the parametric expression. The binary stochastic model was applied to the daily rainfall data set of 28 stations in U.S.A., U.K., France and Italy. Multiple time series were examined; the time series for the entire year, the monthly time series, the seasonal time series as well as the time series for the dry and the wet period of the year. The results of the application to the empirical data indicated good agreement of the model and the historical rainfall time series. The proposed model was used for order 7 with satisfactory accuracy in order to generate synthetic binary rainfall series reproducing the order 8 joint probability mass function of the historical rainfall process. The results of the application to the empirical data verified the proposed model.
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