Merging Seasonal Rainfall Forecasts from Multiple Statistical Models through Bayesian Model Averaging

Abstract

Merging forecasts from multiple models has the potential to combine the strengths of individual models and to better represent forecast uncertainty than the use of a single model. This study develops a Bayesian model averaging (BMA) method for merging forecasts from multiple models, giving greater weights to better performing models. The study aims for a BMA method that is capable of producing relatively stable weights in the presence of significant sampling variability, leading to robust forecasts for future events. The BMA method is applied to merge forecasts from multiple statistical models for seasonal rainfall forecasts over Australia using climate indices as predictors. It is shown that the fully merged forecasts effectively combine the best skills of the models to maximize the spatial coverage of positive skill. Overall, the skill is low for the first half of the year but more positive for the second half of the year. Models in the Pacific group contribute the most skill, and models in the Indian and extratropical groups also produce useful and sometimes distinct skills. The fully merged probabilistic forecasts are found to be reliable in representing forecast uncertainty spread. The forecast skill holds well when forecast lead time is increased from 0 to 1 month. The BMA method outperforms the approach of using a model with two fixed predictors chosen a priori and the approach of selecting the best model based on predictive performance.

The challenge of forecasting high streamflows 1–3 months in advance with lagged climate indices in southeast Australia

“…Some studies suggest that these interactions may be important in understanding concurrent relationships (e.g. Kiem et al, 2003); however, results from our previous work demonstrate that adding a second joint predictor does not result in any improvement in forecast skill of seasonal total rainfalls or streamflows when using lagged climate indices (Robertson and Wang, 2012;Wang et al, 2012a).…”

“…3b). The BMA method we use is described in detail by Wang et al (2012a). For a set of models M k , k = 1, 2, .…”

“…α−1 is from the symmetric Dirichlet prior distribution used by Wang et al (2012a). We use α values greater than 1 to distribute weights more evenly among models, which helps to stabilise the weights when there is significant sampling variability.…”

“…Wang et al (2012a) showed that Bayesian model averaging (BMA) outperformed predictor selection methods for merging rainfall forecast models generated with the BJP. In addition, predictor selection can lead to artificially inflated estimates of cross-validation skill if the predictor selection is not included in the cross-validation (DelSole and Shukla, 2009;Robertson and Wang, 2013), a problem that is not present with the BMA method we use in this study.…”

“…To achieve this, we build a set of forecast models with the BJP by combining an estimate of initial catchment wetness with a suite of climate indices derived from oceanic and atmospheric variables. We combine the models with the BMA method described by Wang et al (2012a) to maximise predictive power.…”