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Real-Time Extraction of the Madden–Julian Oscillation Using Empirical Mode Decomposition and Statistical Forecasting with a VARMA Model

Barnaby S. LoveSchool of Environmental Sciences, University of East Anglia, Norwich, United Kingdom

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Adrian J. MatthewsSchool of Environmental Sciences, and School of Mathematics, University of East Anglia, Norwich, United Kingdom

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Gareth J. JanacekSchool of Computing Sciences, University of East Anglia, Norwich, United Kingdom

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Abstract

A simple guide to the new technique of empirical mode decomposition (EMD) in a meteorological–climate forecasting context is presented. A single application of EMD to a time series essentially acts as a local high-pass filter. Hence, successive applications can be used to produce a bandpass filter that is highly efficient at extracting a broadband signal such as the Madden–Julian oscillation (MJO). The basic EMD method is adapted to minimize end effects, such that it is suitable for use in real time. The EMD process is then used to efficiently extract the MJO signal from gridded time series of outgoing longwave radiation (OLR) data.

A range of statistical models from the general class of vector autoregressive moving average (VARMA) models was then tested for their suitability in forecasting the MJO signal, as isolated by the EMD. A VARMA (5, 1) model was selected and its parameters determined by a maximum likelihood method using 17 yr of OLR data from 1980 to 1996. Forecasts were then made on the remaining independent data from 1998 to 2004. These were made in real time, as only data up to the date the forecast was made were used. The median skill of forecasts was accurate (defined as an anomaly correlation above 0.6) at lead times up to 25 days.

Corresponding author address: Barnaby Love, School of Environmental Sciences, University of East Anglia, Norwich, NR4 7TJ, United Kingdom. Email: b.love@uea.ac.uk

Abstract

A simple guide to the new technique of empirical mode decomposition (EMD) in a meteorological–climate forecasting context is presented. A single application of EMD to a time series essentially acts as a local high-pass filter. Hence, successive applications can be used to produce a bandpass filter that is highly efficient at extracting a broadband signal such as the Madden–Julian oscillation (MJO). The basic EMD method is adapted to minimize end effects, such that it is suitable for use in real time. The EMD process is then used to efficiently extract the MJO signal from gridded time series of outgoing longwave radiation (OLR) data.

A range of statistical models from the general class of vector autoregressive moving average (VARMA) models was then tested for their suitability in forecasting the MJO signal, as isolated by the EMD. A VARMA (5, 1) model was selected and its parameters determined by a maximum likelihood method using 17 yr of OLR data from 1980 to 1996. Forecasts were then made on the remaining independent data from 1998 to 2004. These were made in real time, as only data up to the date the forecast was made were used. The median skill of forecasts was accurate (defined as an anomaly correlation above 0.6) at lead times up to 25 days.

Corresponding author address: Barnaby Love, School of Environmental Sciences, University of East Anglia, Norwich, NR4 7TJ, United Kingdom. Email: b.love@uea.ac.uk

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