Nonlinear analysis of rainfall variability in Australia
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ORIGINAL PAPER
Nonlinear analysis of rainfall variability in Australia Bellie Sivakumar • Fitsum M. Woldemeskel Carlos E. Puente
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Springer-Verlag Berlin Heidelberg 2013
Abstract This study examines the utility of nonlinear dynamic concepts for analysis of rainfall variability across Western Australia. The correlation dimension method, which involves data reconstruction and nearest neighbor concepts, is employed to estimate the dimensionality of rainfall time series and assess the degree of variability (or complexity) of rainfall dynamics. Monthly rainfall data observed over a period of 67 years (January 1937– December 2003) from each of 62 raingage stations across Western Australia are analyzed. The results indicate the utility of the dimensionality concept for identification of rainfall variability at point locations and rainfall patterns across space. The dimension estimates (ranging from 4.63 to 8.29) suggest a medium-level complexity in rainfall dynamics at each of the 62 stations and, hence, across Western Australia. Rainfall dynamics are generally more complex in the southwest part of Western Australia than in other parts of the state, with the far south exhibiting a greater complexity. Also, the mid-western region exhibits slightly more complex rainfall dynamics when compared to the northeast. The reliability of the correlation dimension estimates with respect to data size (i.e. number of data points in time series) is also discussed. The outcomes of the present study, the first ever based on nonlinear dynamic and chaos theories for rainfall in Australia and also across a far more extensive network of raingages, can provide new B. Sivakumar F. M. Woldemeskel School of Civil and Environmental Engineering, The University of New South Wales, Sydney, NSW 2052, Australia e-mail: [email protected] B. Sivakumar (&) C. E. Puente Department of Land, Air and Water Resources, University of California, Davis, CA 95616, USA e-mail: [email protected]
avenues for rainfall (and other hydrologic) studies in Australia and for spatial/spatio-temporal analysis. Keywords Rainfall variability Nonlinear dynamics Phase space reconstruction Correlation dimension Australia
1 Introduction Australia is the driest inhabited continent in the world, with a mean annual rainfall of only about 465 mm. As a consequence, water is a critical resource, and its proper planning and management is vital for sustaining the nation’s people, ecosystems, environment, and economy. However, the extreme variability of rainfall in both space and time brings tremendous challenges to this, considering also the significant variability in the distribution of population across the country (e.g. very high density in a few big cities in the coastal regions vs. very low density in the largely rural towns in the interior regions). For instance: (1) coastal regions generally receive far greater rainfalls than interior regions; (2) northeast Australia generally gets significantly higher rainfalls than the rest of the country, especially centr
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