The inter-decadal cycles observed in the ensemble forecast from Figure \ref{div-565673} are not present in this case since a seasonal component has not been considered in the model. The El Niño3.4 series and the PDO series are assumed independent for simulation which might not be a valid assumption. Figure \ref{619690} shows a comparison between the observed PDSI value with the mean ensemble forecast for the ES model and the TF model for the validation period, comparing also the mean future projections for both models. The projection of PDSI over the four future decades (2015-2054) for the ES model lies around the “incipient drought” class, with excursions to "mild drought”, while the projections of the TF model remain around the "incipient drought" region.
5. Discussion and concluding remarks
Our results can be useful for water resources planning, and provide and basic knowledge to support further predictive studies beyond the use of Global Climate Models (GCMs, \citealt{Hazeleger2015,Ingram2016} ), which vary their parameters for climatic simulations under alternative GHG emission scenarios. So far, exponential smoothing approaches were applied almost exclusively in econometric and financial domains \citep[see][]{Hyndman2008}. The major potential cause of bias in exponential smoothing approach is that extrapolative forecasts can differ substantially depending on the time period examined \citep[see][]{Armstrong2001}(Armstrong, 1999). However, this bias can be dwindled by identifying long time-series and by comparing forecasts when different starting points are used (ensemble). This is what we have done with an extended series of PDSI data.
Droughts occur over long time spans, and their timing are difficult to identify. This paper takes the challenge to examine a strategy for structuring knowledge about drought dynamics for use in annual PDSI extrapolation for the coming decades.