A Bayesian framework to improve seasonal rainfall forecasts through a combination of calibration and bridging of GCM outputs

Seasonal rainfall forecasting is highly challenging. Although research efforts continue to deliver incremental improvements, the skill of general circulation models (GCMs) for seasonal rainfall forecasting remains modest. Skill improvement is therefore a major focus of the climate modeling community. Another problem from an operational or a user perspective is that GCMs tend to produce forecasts that are biased and/or overconfident. Here, we present a sophisticated Bayesian framework to overcome this problem and to improve forecast skill through statistical post-processing of GCM outputs.

The GCM used in Australia for seasonal forecasting is the Predictive Ocean Atmosphere Model for Australia (POAMA). POAMA is a coupled ocean-atmosphere GCM and as such it produces concurrent forecasts of rainfall and sea surface temperatures (SST). In some regions of Australia and in certain seasons, it has been observed that SST-based climate indices (e.g. NINO3.4) forecast by POAMA have higher correlations with observed rainfall than the rainfall forecast by POAMA. Using our Bayesian statistical post-processing framework, it is possible to exploit such empirical relationships to improve the overall skill of Australian seasonal rainfall forecasts.

Firstly, we establish multiple single-predictor models to forecast seasonal rainfall. If the predictor variable is raw GCM rainfall, we refer to the model as a forecast calibration model. If the predictor variable is an SST-based climate index, we refer to the model as a forecast bridging model. Three calibration models are established using seasonal mean rainfall from three variants of POAMA. Six bridging models are established using POAMA forecasts of well known climate indices in the Pacific and Indian oceans. A Bayesian joint probability modelling approach is used to infer the parameters of each model and to produce probabilistic forecasts.

Secondly, forecasts from each model are weighted and merged using a robust Bayesian model averaging method. Forecast skill and reliability are assessed using leave-one-out cross-validation for the period 1980-2010. Skill is also analysed in the short independent period 2011-2012.

We compare the forecasting skill of the calibration and bridging models separately, and also their combined skill. As separate groups, the calibration and bridging forecasts are skilful in certain seasons and locations. Whilst there are overlaps in skill, there are seasons and locations where the calibration or bridging forecasts are uniquely skilful. The merged calibration and bridging forecasts represent a significant improvement in terms of spatiotemporal coverage of skilfulness. The merged forecasts are also statistically reliable and have climatologies aligned with the observed. They are therefore suitable for use in further modelling such as seasonal streamflow forecasting. The merged calibration and bridging forecasts are also shown to outperform the calibration forecasts in the short independent period (2011-2012).

The Bayesian framework has also been applied to merging rainfall forecasts from multiple international GCMs, showing potential for further increases in skill.