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

Abstract

A simple guide to the new technique of empirical mode decomposition (EMD) in a meteorologicalclimate 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.

Response of the West African Monsoon to the Madden–Julian Oscillation

“…This suggests that it may be possible to predict part of the variability in the WAM with a 15-20-day lead time, particularly given the recent success of operational statistical forecast models of the MJO (Wheeler and Hendon 2004;Love et al 2008). As modeling capability continues to increase and with an improved representation of the MJO, this may also lead to better forecasting ability over West Africa.…”

On Changing El Niño: A View from Time-Varying Annual Cycle, Interannual Variability, and Mean State

“…The effectiveness of the EMD-EEMD method has been recently documented in many geophysical applications (e.g., Huang and Wu 2008;Wu et al 2008;Wu and Huang 2009;Love et al 2008;Qian et al 2009Qian et al , 2010Qian et al , 2011Ruzmaikin and Feynman 2009;Franzke 2009Franzke , 2010Franzke and Woolings 2011;Breaker and Ruzmaikin 2010). In particular, the capability of EEMD and the advantage of using it to extract the annual cycle component (which has strong amplitude-frequency modulation) from a climate variable have been validated through analyzing synthetic data, monthly SST data, and daily surface air temperature records Qian et al 2011).…”

Modulation of Daily Precipitation over East Africa by the Madden–Julian Oscillation*

“…Significant correlations (0.41 and 20.40 with the MJO indices at 1608 and 208E, respectively) are also found in April at a lead of four pentads. Various studies have developed statistical and/or dynamical prediction models of the MJO with skills extending to about 25 days and beyond (e.g., Waliser et al 2003;Maharaj and Wheeler 2005;Vitart et al 2007;Jiang et al 2008;Lin et al 2008;Love et al 2008;Love and Matthews 2009;Seo 2009;Seo et al 2009;Kang and Kim 2010;Rashid et al 2011). Waliser et al (2003, for example, find that in the Eastern Hemisphere useful predictability of the MJO extends out to about 25-30 days for 200-hPa velocity potential.…”