A Bayesian model for stochastic generation of daily precipitation using an upper-bounded distribution function

Parametric and non-parametric approaches for rainfall generation have been widely used in hydrological simulation. Both approaches, however, show inherent limitations for representing precipitation extremes. Hence, a stochastic generator able to represent all the range of precipitation amounts is desired. This paper presents a mixed stochastic generator designed for this purpose: the low to moderate rainfall amounts are modeled by the non-parametric approach, avoiding the adjustment of theoretical probability density functions to this range of precipitation and, the extreme rainfall amounts are modeled by the parametric approach, employing the upper-bounded 4-parameter log-normal (LN4) distribution function, with the upper bound estimated under a Bayesian framework, having the at-site probable maximum precipitation (PMP) as a reference value. The mixed generator was used for simulating a 10,000-year long series in the Para river catchment, in the Brazilian state of Minas Gerais. Results showed that mean daily rainfall, the correspondent standard deviation, coefficient of skewness, number of wet days, and mean monthly and annual rainfall are adequately reproduced. Furthermore, by combining in a logical structure of analysis a prior distribution describing the uncertainties about the PMP estimates and the rainfall data, one can expect more reliable estimates of rare and extreme quantiles and their related uncertainties.