A New Approach to Stochastically Generating Six-Monthly Rainfall Sequences Based on Empirical Mode Decomposition

Thomas A. McMahon Department of Civil and Environmental Engineering, University of Melbourne, Victoria, Australia

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Anthony S. Kiem Sinclair Knight Merz, Armadale, Victoria, Australia

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Murray C. Peel Department of Civil and Environmental Engineering, University of Melbourne, Victoria, Australia

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Phillip W. Jordan Sinclair Knight Merz, Armadale, Victoria, Australia

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Geoffrey G. S. Pegram Civil Engineering Programme, University of KwaZulu-Natal, Durban, Republic of South Africa

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Abstract

This paper introduces a new approach to stochastically generating rainfall sequences that can take into account natural climate phenomena, such as the El Niño–Southern Oscillation and the interdecadal Pacific oscillation. The approach is also amenable to modeling projected affects of anthropogenic climate change. The method uses a relatively new technique, empirical mode decomposition (EMD), to decompose a historical rainfall series into several independent time series that have different average periods and amplitudes. These time series are then recombined to form an intradecadal time series and an interdecadal time series. After separate stochastic generation of these two series, because they are independent, they can be recombined by summation to form a replicate equivalent to the historical data. The approach was applied to generate 6-monthly rainfall totals for six rainfall stations located near Canberra, Australia. The cross correlations were preserved by carrying out the stochastic analysis using the Matalas multisite model. The results were compared with those obtained using a traditional autoregressive lag-one [AR(1)], and it was found that the new EMD stochastic model performed satisfactorily. The new approach is able to realistically reproduce multiyear–multidecadal dry and wet epochs that are characteristic of Australia’s climate and are not satisfactorily modeled using traditional stochastic rainfall generation methods. The method has two advantages over the traditional AR(1) approach, namely, that it can simulate nonstationarity characteristics in the historical time series, and it is easy to alter the decomposed time series components to examine the impact of anthropogenic climate change.

Corresponding author address: Thomas A. McMahon, Department of Civil and Environmental Engineering, The University of Melbourne, VIC, 3010, Australia. Email: t.mcmahon@civenv.unimelb.edu.au

Abstract

This paper introduces a new approach to stochastically generating rainfall sequences that can take into account natural climate phenomena, such as the El Niño–Southern Oscillation and the interdecadal Pacific oscillation. The approach is also amenable to modeling projected affects of anthropogenic climate change. The method uses a relatively new technique, empirical mode decomposition (EMD), to decompose a historical rainfall series into several independent time series that have different average periods and amplitudes. These time series are then recombined to form an intradecadal time series and an interdecadal time series. After separate stochastic generation of these two series, because they are independent, they can be recombined by summation to form a replicate equivalent to the historical data. The approach was applied to generate 6-monthly rainfall totals for six rainfall stations located near Canberra, Australia. The cross correlations were preserved by carrying out the stochastic analysis using the Matalas multisite model. The results were compared with those obtained using a traditional autoregressive lag-one [AR(1)], and it was found that the new EMD stochastic model performed satisfactorily. The new approach is able to realistically reproduce multiyear–multidecadal dry and wet epochs that are characteristic of Australia’s climate and are not satisfactorily modeled using traditional stochastic rainfall generation methods. The method has two advantages over the traditional AR(1) approach, namely, that it can simulate nonstationarity characteristics in the historical time series, and it is easy to alter the decomposed time series components to examine the impact of anthropogenic climate change.

Corresponding author address: Thomas A. McMahon, Department of Civil and Environmental Engineering, The University of Melbourne, VIC, 3010, Australia. Email: t.mcmahon@civenv.unimelb.edu.au

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