Generation of rainfall sequence using fourier series

Abstract

The generation of rainfall sequence at subdaily scale is needed for various applications in hydrology. In this study a clustered point process model the Neyman Scott Rectangular Pulse Model (NSRP) with mixed exponential distribution for cell intensity is selected to produce synthetic hourly rainfall sequence of the Klang Valley, Malaysia. In the NSRP model, storms arrive following a Poisson process. Each storm generates rain cells with the position of cells relative to storm origin are determined by the exponential distribution. Individual cell has width and height which correspond to the cell’s duration and intensity respectively. The NSRP model with mixed exponential distribution has seven parameters, X, v , B, n, a, and 0 that characterize respectively the storm origin, number of cells, positions of cells, duration of cells, mixing probability and the intensity of cells. The model’s parameters were estimated by employing the Shuffle Complex Evolution (SCEMJA) method. The model’s setback which requires the parameters to be estimated monthly to account for seasonality is dealt with by incorporating Fourier Series. Fourier coeftlcients for each paranieter were derived based on significant harmonics which best describe the parameter. Historical hourly data of ten years were used for model assessment. Results indicate that statistical properties of the simulated rainfall series were able to match most of those of the historical series. The preservation of these properties exhibits the ability of Fourier Series to capture the seasonal pattern of rainfall process.