Development of a stochastic rainfall generator and its uncertainty quantification for the Kelantan River Basin, Malaysia - Ng, Jing Lin (2017)
Stochastic simulation of rainfall is challenging due to incomplete rainfall series and high variability of rainfall. Furthermore, the quantification of uncertainty is often ignored in the current practice of hydrological modelling and lead to inappropriate decisions. Accordingly, this research intends to develop a stochastic rainfall generator, consisting of rainfall occurrence models and rainfall amount models and perform its uncertainty quantification for the Kelantan River Basin, Malaysia. Seventeen rainfall stations with rainfall series within the period from 1954 to 2013 were selected. The first until fifth order Markov chains were utilized to simulate the rainfall occurrences. The results showed that the first until fourth order Markov chains gave similarly good performances in simulating the mean, frequency distribution, standard deviation and extreme values of wet spells, dry spells, wet day frequency and dry day frequency, while the fifth order Markov chain gave poor results. The first until fourth order Markov chains passed most of the Wilcoxon rank sum (82.4 – 100% passing rate), Kolmogorov-Smirnov (K-S) (70.6 – 100% passing rate) and squared ranks tests (70.6 – 100% passing rate). They reproduced lower values of mean absolute percentage error (MAPE) for the mean (0.4 – 5.2%), standard deviation (1.4 – 7.5%) and extreme values (2.3 – 16.4%). However, the results of the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) suggested that the monthly, seasonal and yearly rainfall occurrences were simulated fairly using the second (35.3 – 82.4% selection rate), fourth (58.8 – 100% selection rate) and third (100% selection rate) order Markov chains. The exponential, gamma, log-normal, skew normal, mixed exponential and generalized Pareto distributions were used to simulate the rainfall amounts. It was found that all the distributions were capable of simulating the mean, frequency distribution and standard deviation of the rainfall amounts by reproducing high passing rates of the Wilcoxon rank sum (100%), K-S (86.8 – 100%) and squared ranks tests (88.2 – 100%). They obtained relatively low values of MAPE for the mean (2.5 – 4.7%), standard deviation (2.8 – 10.4%) of rainfall amounts and low values of variance overdispersion (-7.9 – -1.7%). For the extreme rainfall amounts, the exponential, gamma, log-normal and mixed exponential distributions were consistently better than the skew normal and generalized Pareto distributions. The log-normal distribution (41.2 – 100% selection rate) was chosen as the best fitting distribution based on the results of AIC and BIC. The uncertainty quantification was performed on the synthetic rainfall series simulated from the best formulations for the monthly, seasonal and yearly rainfall series. The uncertainty of the rainfall depth duration frequency (DDF) curves was quantified using the 95% confidence interval. The results showed that there was uncertainty ranged from -10.0% to 12.4% for return periods up to 100 years in the DDF curves. The uncertainty increases with the return period. Overall, the stochastic rainfall generator is considered a convenient tool to simulate the rainfall characteristics over the Kelantan River Basin and the uncertainty quantification framework is straightforward and useful. The outcomes of this study can be used for flood control, climate change assessment, hydrological modelling and decision making.