Spatial-Temporal Modeling of Occurrence and Amount of Winter Rainfall using Hidden Markov Model

Multi site modeling of rainfall is one of the most important issues in environmental sciences especially in watershed management. For this purpose, different statistical models have been developed which involve spatial approaches in simulation and modeling of daily rainfall values. The hidden Markov is one of the multi-site daily rainfall models which in addition to simulation of daily rainfall values, explores the spatial and temporal pattern of rainfall events. In this study, the winter (January to April) rainfall pattern of 130 rain gauges have been modeled using hidden Markov approach during a 21 years period (1990-2010). The aim of this study was finding temporal and spatial distribution of weather patterns and stochastic simulation of occurrence and amount of rainfall, simultaneously. To achieve this goal, different hidden Markov algorithms including, Viterbi decoding algorithm, Expectation-Maximization (EM) algorithm and a stochastic simulation approach with the probability transformation were applied. It is expected that extracted patterns, using hidden Markov model, are consistent with synoptic patterns and accordingly eight different weather pattern as the definite set of possible cases were recognized. The most frequent rainfall pattern extracted from hidden Markov model was the dry pattern (stable condition) in which the rainfall occurrence probability is low in most of the stations. This pattern has the maximum initial probability of 0.429 and maximum Markov transfer probability of 0.637 Besides, multi-site simulation of winter rainfall keeping the basic statistic of mean, standard deviation of total seasonal rainfall and percentile values in each station and also spatial correlation of occurrence or non-occurrence of rainfall produced reasonable result. In general this approach can be recommended for regional studies.