Optimal stochastic multi-states first-order Markov chain parameters for synthesizing daily rainfall data using multi-objective differential evolution in Thailand

Stochastic Multi-states First-order Markov Chain (SMFOMC) models have been used to describe occurrence of daily rainfall. This paper describes optimization of SMFOMC parameters through the generation of synthetic daily rainfall sequences. Three SMFOMC parameters were the number of states (NS), the preserved proportion in the last state (PPL) and the state divider (SD). The multi-objective differential evolution (MODE) was used to find the Pareto-optimal line (POL) of two conflicting objectives; (1) minimization of total monthly absolute total relative error (TMATRE), and, (2) minimization of NS. Three probability distributions functions (PDFs) for generating daily rainfall amounts in the last Markov Chain state were compared. They were: (1) the shifted exponential distribution (SE), (2) the exponential distribution (E), and, (3) the two-parameter gamma distribution (G-2). The optimal SMFOMC parameters were applied to generate the daily rainfall sequences of 44 rainfall stations located in five regions of Thailand. Reliability of the optimal SMFOMC parameters for each PDF was measured by TMATRE and coefficient of determination (R²). Performance of PDFs was analysed by a ranking method. Results showed that the three PDFs were mostly found to be fitted well with the synthetic daily rainfall sequences. However, highest error was found in case of monthly average minimum daily rainfall values. Out of the three PDFs, the SE demonstrated the lowest performance, while G-2 performed the best.