## 1. Introduction

[2] The demand for accurate and reliable forecasts of seasonal climate, particularly rainfall, continues to be strong. Objective seasonal rainfall forecasts are produced using either statistical models or dynamical models such as general circulation models (GCMs). In Australia, the Bureau of Meteorology issues its operational seasonal rainfall forecasts based on a statistical model [*Fawcett et al.*, 2005; *Fawcett*, 2008], which uses climate indices as predictors. The climate indices represent the El Niño Southern Oscillation (ENSO) and the status of the Indian Ocean. In line with international trends, the Bureau is also developing a GCM with the view that it will eventually replace the statistical model as the operational model. The coupled ocean–atmosphere GCM, the Predictive Ocean Atmosphere Model for Australia (POAMA), is tailored to seasonal forecasting.

[3] Statistical models have been used extensively throughout the world to forecast seasonal climate [e.g., *Barnston et al.*, 1999; *Fawcett et al.*, 2005; *Folland et al.*, 1991; *Landsea and Knaff*, 2000; *Rajeevan et al.*, 2007; *Shabbar and Barnston*, 1996]. They are based on observational relationships, and their main advantage is that they are simple to implement and operate. The main concern with statistical models is the fact that they are reliant on stationary relationships between the predictor and predictand variables, which is not guaranteed in a changing climate.

[4] GCMs are increasingly being used to forecast seasonal climate [e.g., *Lim et al.*, 2009; *Palmer et al.*, 2004; *Saha et al.*, 2006; *Yasuda et al.*, 2007]. They are based on the laws of physics and their main advantages are that they have the ability to capture nonlinear interactions of the atmosphere, land and ocean, and are adaptable to shifts in climate. GCMs also provide spatially and temporally coherent forecasts of multiple variables (e.g., temperature, pressure) at high temporal resolution (e.g., daily). However, they suffer from the general problem that the spread of ensemble members tends to be too narrow (overconfident) [e.g., *Graham et al.*, 2005, *Lim et al.*, 2011] and the climatology of the simulations is not always aligned with that of the corresponding observations. It is therefore common to apply statistical models to calibrate raw GCM output for bias correction and variance adjustment so that the forecast climatology more closely matches the observed and the forecasts are statistically reliable [e.g., *Doblas-Reyes et al.*, 2005; *Feddersen et al.*, 1999; *Landman and Goddard*, 2002]. Of course, statistical calibration also assumes stationary predictor-predictand relationships and thus can be viewed as interim solution while GCMs continue to be improved.

[5] Given their unique strengths, both statistical and dynamical models are attractive approaches for seasonal climate forecasting. Recently, *Barnston et al.* [2012]compared the real-time performance of 12 GCMs and 8 statistical models for forecasting ENSO (Niño3.4) from 2002 to 2011. At this large scale, the group of GCMs was able to outperform the group of statistical models during the onset or transition phases of ENSO events, suggesting dynamical models may be starting to edge ahead in terms of skill. However, a general conclusion was that there remains a place in operational climate prediction for statistical modeling when GCMs fail to provide useful information. There is also potential to improve seasonal forecasts by objectively combining the information from statistical and dynamical models, particularly for sub-grid scale processes such as rainfall.

[6] Some recent studies have investigated Bayesian approaches for combining statistical forecasts with raw GCM output. *Coelho et al.* [2004]developed a Bayesian methodology for combining statistical forecasts with raw GCM output to provide improved and well-calibrated long lead Niño3.4 predictions. A statistical forecast was used as an informative prior distribution, which was updated with raw GCM output.*Luo et al.* [2007] adopted a similar approach to update a climatology model with raw output from multiple GCMs, but assumed model independence for simplicity. A more flexible Bayesian approach to combine multiple models, which does not assume model independence, is to establish the models individually and weight and merge forecasts based on past predictive performance through Bayesian Model Averaging (BMA) [*Hoeting et al.*, 1999; *Raftery et al.*, 2005]. *Wang et al.* [2012] developed a BMA method for merging multiple statistical seasonal rainfall forecasting models based on climate indices. Here, we apply the method to merge multiple statistical forecasts with calibrated dynamical forecasts from multiple GCMs.

[7] In this paper, we combine statistical and dynamical forecasts of Australian seasonal rainfall. We use a consistent Bayesian modeling approach to establish statistical models based on lagged climate indices and to calibrate raw rainfall forecasts from dynamical models. We demonstrate that the statistical and dynamical models have different strengths and weaknesses. In particular, they produce skillful seasonal rainfall forecasts in different Australian regions and seasons. We further demonstrate that by weighting and merging the forecasts from the different models, we take advantage of their respective strengths, and achieve greater spatial and temporal coverage of skillfulness.

[8] The remainder of this paper is structured as follows. In the next section, we present the statistical and dynamical forecasting models and data. In section 3, we outline the BMA method for merging forecasts and verification methods for assessing the skill and reliability of probabilistic forecasts. In section 4, we present maps and diagrams showing the skill and reliability of the forecasts and show some examples of model weights. Section 5 provides some supplementary discussion. Section 6 completes the paper with a summary and conclusions.