An exploratory study of seasonal rainfall variability in Australia using independent component analysis

Abstract

Component extraction techniques have been used frequently by climate and water resources researchers to analyse high dimensional datasets such as global sea surface temperature (SST) and rainfall time series. The motivation for using these techniques is usually twofold; firstly to reduce the dimension of the dataset, by representing the data using a small number of components that are able to describe a significant proportion of the total variance, and secondly to enhance our understanding of the dynamics of the underlying system, by interpreting these components as representing physically significant ‘modes’ of climate variability. In this study we explore the potential of a relatively new technique known as independent component analysis (ICA), which has been developed as a means to separate mixtures of signals when little is known about either the original signals, or the manner in which they have been mixed. This is a problem that occurs frequently in the climate field, where one wishes to understand the factors that contribute to the dynamical nature of a given set of observations. The premise of ICA is based on central limit theorem, which asserts that if a set of independent random variables is mixed using a linear transformation, the result will be a set of variables that tend towards a Gaussian distribution. Reversing this logic, if one rotates a mixed dataset in a manner that maximises the divergence from a Gaussian distribution, then under certain conditions it is possible to retrieve the original independent variables. Therefore, ICA focuses on higher-order statistics that measure the divergence from a Gaussian distribution. The ICA method is contrasted to the more widely used principal component analysis (PCA), which removes the correlation between the components while at the same time maximising the variance of successive principal components. This latter property in particular has proved to be useful to reduce the dimension of the datasets while retaining much of the information, and in the present study PCA is also used as a pre-processing step for ICA. The primary distinction between ICA and PCA is that while PCA uses only second order statistics to obtain uncorrelated components, ICA maximises the independence between components through the use of higher order statistics. Thus, while PCA may be well suited to variance maximisation and dimension reduction, ICA is fundamentally more suited to ensuring the statistical independence of the components and in certain cases is also capable of determining the underlying causes of this variability. To demonstrate the potential of the ICA technique in highlighting physically ‘interesting’ modes of variability, we apply PCA and ICA to a set of seasonal rainfall time series from over 200 rainfall gauges located around the Australian continent. It is assumed, based on the results of a number of earlier studies, that the El Niño Southern Oscillation (ENSO) phenomenon is an important factor in influencing Australian rainfall. Furthermore, it has been shown that an inter-decadal phenomenon, particularly the Inter-decadal Pacific Oscillation (IPO), may influence the degree of correlation between ENSO and Australian rainfall, with an enhanced link when the IPO is negative, and a reduced link when the IPO is positive. The results of this study consistently show that, for each season of the year, one independent component is significantly correlated with an index of the ENSO phenomenon known as the Southern Oscillation Index (SOI), with the highest correlation occurring during spring. Furthermore, during the IPO negative phase from 1946-1977, the correlation between one of the independent components and the SOI is further enhanced. This is contrasted with the PCA solution, in which t he correlation coefficients for the majority of cases are not statistically significant. These results therefore indicate that ICA may have a significant potential to be applied to a number of altern...