Comparison of Two Nonparametric Alternatives for Stochastic Generation of Monthly Rainfall

Monthly rainfall data are needed in the simulation of water resources systems, and in the estimation of water yield from large catchments. Models to generate monthly streamflow data can be applied to generate monthly rainfall data, but this presents problems for most regions, which have significant months of no rainfall. This paper compares two established approaches for generation of monthly hydrological variables. These approaches are (1) the method of fragments modified so as to ensure accurate representation of over-year variability and persistence between the last month of the year and the first month of the next year, and (2) the nonparametric order-1 simulation model with long-term dependence, that considers aggregate variables representing the previous 12 months to impart long-term persistence in addition to the representation of a short-term order-1 Markovian dependence. The first of the two methods, while simpler to implement, has the limitation that it represents a disaggregation of an annual aggregate variable that is generated using a separate stochastic model. The second method, while more mathematically complex, introduces over-year or longer-term persistence through the use of an internally accounted aggregate variable, thereby removing the need to generate aggregate values separately. In this study both the methods are applied to generate rainfall data from ten rainfall stations located in various parts of Australia, and results compared to evaluate performance at both monthly and annual time scales. In the comparison performed both the models were found to preserve the annual and monthly characteristics adequately.