Study on Poisson Cluster Stochastic Rainfall Generators

The purpose of this dissertation is to enhance the applicability and the accuracy of the Poisson cluster stochastic rainfall generators. Firstly, the 6 parameters of the Modified Bartlett-Lewis Rectangular Pulse (MBLRP) stochastic rainfall simulation model were regionalized across the contiguous United States. Each of the parameters of MBLRP model estimated at 3,444 National Climate Data Center (NCDC) rain gages was spatially interpolated based on the Ordinary Kriging technique to produce the parameter surface map for each of the 12 months of the year. Cross-validation was used to assess the validity of the parameter maps. The results indicate that the suggested maps reproduce well the statistics of the observed rainfall for different accumulation intervals, except for the lag-1 autocorrelation coefficient. The estimated parameter values were also used to produce the maps of storm and rain cell characteristics. Secondly, the relative importance of the rainfall statistics in the generation of watershed response characteristics was estimated based on regression analyses using the rainfall time series observed at 1099 NCDC rain gages. The result of the analyses was used to weigh the rainfall statistics differently in the parameter calibration process of MBLRP model. It was observed that synthetic rainfall time series generated weighing the precipitation statistics according to their relative importance outperformed those generated weighing all statistics equally in predicting watershed runoff depths and peak flows. When all statistics were given the same weight, runoff depths and peak flows were underestimated by 20 percent and 14 percent, respectively; while, when the statistics were weighed proportionally to their relative importance, the underestimation was reduced to 4 percent and 3 percent, which confirms the advantage of weighing the statistics differently. In general, the value of the weights depends on the hydrologic process being modeled. Lastly, a stochastic rainfall generation model that can integrate year-to-year variability of rainfall statistics is suggested. The new framework consists of two parts. The first part generates the short-term rainfall statistics based on the correlation between the observed rainfall statistics. The second part generates the rainfall time series using the modified Bartlett-Lewis rectangular pulse model based on the simulated rainfall statistics. The new approach was validated at 104 NCDC gages across the United States in its ability to reproduce rainfall and watershed response characteristics. The result indicates that the new framework outperformed the traditional approach in reproducing the distribution of monthly maximum rainfall depths, monthly runoff volumes and monthly peak flows.