Spatial and temporal torrential rainfall guided cluster pattern based on dimension reduction methods

Abstract

This thesis identifies the spatial and temporal cluster patterns for torrential rainfall data in Peninsular Malaysia. Two dimension reduction methods are used to improve the cluster patterns of the torrential rainfall data. Firstly, a robust dimension reduction method in Principal Component Analysis (PCA) is used to rectify the issue of unbalanced clusters in rainfall patterns due to the skewed nature of rainfall data. A robust measure in PCA using Tukey’s biweight correlation to downweigh observations is introduced and the optimum breakdown point to extract the number of components in PCA using this approach is proposed. The simulated data indicates a breakdown optimum point of at 70% cumulative percentage of variance to give a good balance in extracting the number of components to avoid variations of low frequency or insignificant spatial scale in the clusters. The results show a significance improvement with the robust PCA than the PCA based Pearson correlation in terms of the average number of clusters obtained and its cluster quality. Secondly, based on the decomposing properties in Singular Spectrum Analysis (SSA), a two-way approach to identify the range of local time scale for a cluster of torrential rainfall pattern by discriminating the noise in a time series trend is introduced. Firstly, appropriate window length for the trajectory matrix and adjustments on the coinciding singular values obtained from the decomposed time series matrix based on a restricted singular value decomposition (SVD) using iterative oblique SSA (Iterative O-SSA) is proposed. In addition, a guided clustering method called Robust Sparse k-means (RSk-means) to discriminate the eigenvectors from this iterative procedure is suggested to identify the trend and noise components more objectively. The modified SSA indicates strongest separability between the reconstructed components based on a simulated skewed and short time series rainfall data to effectively identify the local time scale.