Multiday Rainfall Simulations for Malaysian Monsoons

This study examines the suitability of the discrete autoregressive and moving average [DARMA(1,1)] model to simulate the sequences of daily rainfall data in Malaysia. The daily monsoon rainfall data recorded at Subang Airport are used to test this modeling approach. The autocorrelation function and probability distributions of wet and dry run lengths estimated from the DARMA(1,1) model matched the sample values quite well. Both theoretical and sample autocorrelation functions slowly decay to zero at day 15. The theoretical probability distribution for two consecutive wet days estimated for the DARMA(1,1) is 0.1966, while the observed rainfall data give a probability of 0.2066. Additionally, the sum of squared errors for the DARMA(1,1) model were very small, i.e., 0.0015. Furthermore, two simulations were done, i.e., 100 samples of 9,600 days (simulation A) and a very long sequence of 1,000,000 days (simulation B). This was done to test the capability of DARMA(1,1) to model a long sequence of daily rainfall. The statistics examined in this study include the lag-1 autocorrelation coefficient (lag-1 ACF) and the maximum wet and dry run lengths. Generally, the statistics of generated rainfall for simulation A fall within two standard deviations from the sample. The diversions of these statistics were reasonable, considering the sample size used in this study. The estimated lag-1 ACF for simulation B was slightly lower than the sample. The maximum wet and dry run lengths were much higher than the observed data because of the different sample sizes. It is concluded that the DARMA(1,1) model is able to simulate the long sequences wet and dry days and preserving the statistics within reasonable accuracy.