Evaluation of the synthetic annual maximum storms

Abstract

Long term historical records of hydrological information such as rainfall and runoff data form the basis of planning and design of major water resources projects. However, in most cases such historical records are unavailable, and in situations where they are available, the records are too short to have any statistically significant meaning. One approach that has been adopted to overcome this difficulty is to generate long-term data synthetically. In this study, the outcome of an attempt to generate synthetic rainfall data is presented. The Monte Carlo method is used, which is an experimental statistical method in generating samples for solving some probability problems as old as probability theory itself. In this study, synthetic annual maximum storms distributed as Type-1Extremal (or Gumbel) with random effective durations and specific time distribution for given population mean and variance are generated using the method. Effective durations of the synthetic annual maximum storms are related to the basin characteristics, length (L) and harmonic slope (S) of the main course, by Kirpich's time of concentration relationship. After synthetic annual maximum storms are generated, sample statistics and frequency distributions of the generated annual maximum storms of random effective durations are investigated. Eight well-known probability distribution models, (Normal (N), LogNormal with two and three parameters (LN2 and LN3), Gumbel (GUM), LogGumbel (LGUM), Gamma with two and three parameters (G2 and G3), and LogPearson 3 (LP3), with moment and maximum likelihood parameters are used for synthetic storm series by chi-square and probability plot correlation goodness of fit tests. The results of the study reveal that the probability distribution of the rainfall input may even diverge from their parent (Type-I Extremal) distributions because of the sampling, and since the generated input series is a mixture of rainfall events of variable durations.