[en] This work consists of a presentation and applications of a forecasting methodology based on a mode decomposition performed through a continuous wavelet transform. The idea is comparable to the Fourier series decomposition but where the amplitudes of the components are not constant anymore: the signal is written as a sum of periodic components with smooth time-varying amplitudes. This leads to a drastic decrease in the number of terms needed to decompose and rebuild the original signal without loss of precision.
Once the decomposition is performed, the components are separately extrapolated, which leads to an extrapolation of the reconstructed signal that stands for a forecast of the original one. The quality of the forecast is assessed through a hindcast procedure (running retroactive probing forecasts) and Pearson correlations and root mean square errors are computed as functions of the lead time.
This technique is first illustrated in details with a toy example, then with the El Niño Southern Oscillation (ENSO) time series. This signal consists of monthly-sampled sea surface temperature (SST) anomalies in the Eastern Pacific Ocean and is well-known to be one of the most influential climate patterns on the planet, inducing many consequences worldwide (hurricanes, droughts, flooding,…) and affecting human activities. Therefore, short-term predictions are of first importance in order to plan actions before the occurrence of these phenomena.
As far as the ENSO time series is concerned, the wavelet-based mode decomposition leads to four components corresponding to periods of about 20, 31, 43 and 61 months respectively and the reconstruction recovers 97% of the El Niño/La Niña events (anomalous warming/cooling of the SST) of the last 65 years. Also, it turns out that more than 78% of these extreme events can be retrieved up to three years in advance. Finally, a forecast of the ENSO index is issued: the next La Niña event should start early in 2018 and should be followed soon after by a strong El Niño event in the second semester of 2019.
