A Semi-Parametric Stochastic Model For Simultaneous Stochastic Simulation Of Daily Precipitation Amounts At Multiple Sites

EXTENDED ABSTRACT A semi-parametric stochastic model for generation of daily precipitation amounts, simultaneously at a collection of stations in a way that preserves realistic spatial correlations, accommodates seasonality, and reproduces a number of key aspects of the distributional and dependence properties of observed rainfall is described and illustrated. Following a conventional weather generator formulation, rainfall occurrences are modeled at the first stage and the rainfall amounts on simulated wet days are modeled subsequently. The rainfall occurrences at each individual site are simulated using a two-state, second-order Markov model. This model is found to produce better results for the statistics of long wet and dry spells. The rainfall amounts on the simulated wet days are generated using a non-parametric kernel density based approach. The amount model is conditioned on the rainfall amount on the previous day. Multisite spatial correlations of rainfall occurrences and amounts are reproduced by driving the single-site models with spatially correlated random numbers following a procedure described in Wilks (1998). The seasonal transition in the generation process is maintained by estimating the correlations on a day-to-day basis using a moving window formulation. The procedure of simulating rainfall at individual station and introducing the spatial dependence by means of spatially correlated random numbers, allows more flexibility to model temporal rainfall attributes of importance at individual station without introducing unnecessary complexity. The model is applied on a network of 30 raingauge stations around Sydney in Australia and the results evaluated. The study region exhibits substantial topographic and spatiotemporal rainfall variations, and thus provides a challenging setting to evaluate the simulation model. The analyses of the results show that the model is able to reproduce successfully the spatial correlations of rainfall occurrence and amounts (as shown by the scatter plots of Figure 1) and temporal rainfall characteristics (for example, number of wet days and average rainfall amount as shown in Figure 2) of general interest to the hydrologists. In addition, rainfall characteristics at higher time scale are also found to be captured well by the model.