A Comparison of Four Precipitation Distribution Models Used in Daily Stochastic Models

Abstract: Stochastic weather generators are statistical models that produce random numbers that resemble the observed weather data on which they have been fitted; they are widely used in meteorological and hydrological simulations. For modeling daily precipitation in weather generators, first-order Markov chain--dependent exponential, gamma, mixed-exponential, and lognormal distributions can be used. To examine the performance of these four distributions for precipitation simulation, they were fitted to observed data collected at 10 stations in the watershed of Yishu River. The parameters of these models were estimated using a maximum-likelihood technique performed using genetic algorithms. Parameters for each calendar month and the Fourier series describing parameters for the whole year were estimated separately. Bayesian information criterion, simulated monthly mean, maximum daily value, and variance were tested and compared to evaluate the fitness and performance of these models. The results indicate that the lognormal and mixed-exponential distributions give smaller BICs, but their stochastic simulations have overestimation and underestimation respectively, while the gamma and exponential distributions give larger BICs, but their stochastic simulations produced monthly mean precipitation very well. When these distributions were fitted using Fourier series, they all underestimated the above statistics for the months of June, July and August.

Keywords:
• weather generators,
• gamma distribution,
• mixed-exponential distribution,
• Markov chain,
• Fourier series