Stochastic Simulation for Dry and Wet Spell

Rainfall models are the most important component in stochastic weather generator. Two-state, firstorder Markov chain model is generally applied to simulate rainfall occurrence.The monthly statistics of time series of dry and wet days simulated by the model shows it may work well, but it is not satisfying when focusing on the persistent drought or prolonged wet in the series, although the difference between the simulated monthly mean of rainy days and the actually observed one are not marked.A stochastic model of dry and wet spells (DWS) is described, in which defined stochastic variables are the length of dry or wet spells, numbering in days, other than dry and wet day state. It is obvious that the variable itself has expressed the persistency of rainy or drought weather. Data modeling method is applied too. The related techniques include designing an algorithm for obtaining observed data of dry and wet spells from history records of daily rainfall; constructing empirical distribution function of the length of dry and wet spells monthly, and creating the parameter tables mapping the accumulated frequency distribution monthly; deriving a stochastic sampling formula for generating a dry or wet spell based on direct sampling principle and an algorithm of daily weather (dry or wet) on computer based on Monte Carlo simulation technique with previous sampling formula and parameter tables. Dry and wet spell simulation has been implemented using Java language. Users can select some run time parameters, for example, the name of observed location, the thread value for rainy day, and so on.Model validation test are done using history data from three locations, Beijing, Taiyuan and Zhengzhou. 100 years of rainfall data are generated for each location with the help of DWS simulator respectively. Its statistic items monthly includes : maximum of spell, mean of spell, variance of spell and mean number of rainy days. The mean absolute deviation of simulated value from observed one for all statistical items are about 1.8—2.0, 0.1—0.4, 0.4—0.6, 0.08—0.09 and 0.2—0.4, respectively.The t-tests are done in order to detect significant differences between observed and simulated value for maximum, mean and variance. No significant differences are found at α=0.01. For comparison betw een dry and wet spell model and two-state, first-order Markov chain model, the same statistics are obtained by running Markov chain model. Results indicate that the accuracy of dry and wet spell model is higher than two-state, first-order Markov chain for all statistical items, especially for maximum dry spells.Although dry and wet spell model is available and better than two-state, first-order Markov chain, its weakness is that the parameters in dry and wet spell model are more than those in Markov chain model, lacking in aesthetic feeling of mathematics.