Lagged oceanic and atmospheric climate indices are potentially useful predictors of seasonal rainfall totals. A rigorous Bayesian joint probability modeling approach is applied to find the cross-validation predictive densities of gridded Australian seasonal rainfall totals using lagged climate indices as predictors over the period of 1950–2009. The evidence supporting the use of each climate index as a predictor of seasonal rainfall is quantified by the pseudo-Bayes factor based on cross-validation predictive densities. The evidence strongly supports the use of climate indices from the Pacific region with weaker, but positive, evidence for the use of climate indices from the Indian region and the extratropical region. The spatial structure and seasonal variation of the evidence for each climate index is mapped and compared. Spatially, the strongest supporting evidence is found for forecasting in northern and eastern Australia. Seasonally, the strongest evidence is found from August–October to November–January and the weakest evidence is found from March–May to May–July. In some regions and seasons, there is little evidence supporting the use of climate indices for forecasting seasonal rainfall. Climate indices derived from sea surface temperature anomalies in the Pacific region show stronger persistence in the relationship with Australian seasonal rainfall totals than climate indices derived from sea surface temperature anomalies in the Indian region. Climate indices derived from atmospheric variables are also strongly supported, provided they represent the large-scale circulation. Many climate indices are found to show similar supporting evidence for forecasting Australian seasonal rainfall, leading to the prospect of combining climate indices in multiple predictor models and/or model averaging.

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.

GCMs are used by many national weather services to produce seasonal outlooks of atmospheric and oceanic conditions and fluxes. Postprocessing is often a necessary step before GCM forecasts can be applied in practice. Quantile mapping (QM) is rapidly becoming the method of choice by operational agencies to postprocess raw GCM outputs. The authors investigate whether QM is appropriate for this task. Ensemble forecast postprocessing methods should aim to 1) correct bias, 2) ensure forecasts are reliable in ensemble spread, and 3) guarantee forecasts are at least as skillful as climatology, a property called “coherence.” This study evaluates the effectiveness of QM in achieving these aims by applying it to precipitation forecasts from the POAMA model. It is shown that while QM is highly effective in correcting bias, it cannot ensure reliability in forecast ensemble spread or guarantee coherence. This is because QM ignores the correlation between raw ensemble forecasts and observations. When raw forecasts are not significantly positively correlated with observations, QM tends to produce negatively skillful forecasts. Even when there is significant positive correlation, QM cannot ensure reliability and coherence for postprocessed forecasts. Therefore, QM is not a fully satisfactory method for postprocessing forecasts where the issues of bias, reliability, and coherence pre-exist. Alternative postprocessing methods based on ensemble model output statistics (EMOS) are available that achieve not only unbiased but also reliable and coherent forecasts. This is shown with one such alternative, the Bayesian joint probability modeling approach.

We present a new streamflow forecasting system called forecast guided stochastic scenarios (FoGSS). FoGSS makes use of ensemble seasonal precipitation forecasts from a coupled ocean‐atmosphere general circulation model (CGCM). The CGCM forecasts are post‐processed with the method of calibration, bridging and merging (CBaM) to produce ensemble precipitation forecasts over river catchments. CBaM corrects biases and removes noise from the CGCM forecasts, and produces highly reliable ensemble precipitation forecasts. The post‐processed CGCM forecasts are used to force the Wapaba monthly rainfall‐runoff model. Uncertainty in the hydrological modeling is accounted for with a three‐stage error model. Stage 1 applies the log‐sinh transformation to normalize residuals and homogenize their variance; Stage 2 applies a conditional bias‐correction to correct biases and help remove negative forecast skill; Stage 3 applies an autoregressive model to improve forecast accuracy at short lead‐times and propagate uncertainty through the forecast. FoGSS generates ensemble forecasts in the form of time series for the coming 12 months. In a case study of two catchments, FoGSS produces reliable forecasts at all lead‐times. Forecast skill with respect to climatology is evident to lead‐times of about 3 months. At longer lead‐times, forecast skill approximates that of climatology forecasts; that is, forecasts become like stochastic scenarios. Because forecast skill is virtually never negative at long lead‐times, forecasts of accumulated volumes can be skillful. Forecasts of accumulated 12 month streamflow volumes are significantly skillful in several instances, and ensembles of accumulated volumes are reliable. We conclude that FoGSS forecasts could be highly useful to water managers.

[1] Forecasting rainfall at the seasonal time scale is highly challenging. Seasonal rainfall forecasts are typically made using statistical or dynamical models. The two types of models have different strengths, and their combination has the potential to increase forecast skill. In this study, statistical-dynamical forecasts of Australian seasonal rainfall are assessed. Statistical rainfall forecasts are made based on observed relationships with lagged climate indices. Dynamical forecasts are made by calibrating raw outputs from multiple general circulation models. The statistical and dynamical forecasts are then merged using a Bayesian model averaging (BMA) method. The skill and reliability of the forecasts is assessed through cross-validation for the period 1980-2010. We confirm that the dynamical and statistical groups of models give skill in different locations and seasons and the merged statistical-dynamical forecasts represent a significant improvement in terms of maximizing spatial and temporal coverage of skillfulness. We find that the merged statistical-dynamical forecasts are reliable in representing forecast uncertainty.Citation: Schepen, A., Q. J. Wang, and D. E. Robertson (2012), Combining the strengths of statistical and dynamical modeling approaches for forecasting Australian seasonal rainfall,

[1] Long lead rainfall forecasts are highly valuable for planning and management of water resources and agriculture. In this study, we establish multiple statistical calibration and bridging models that use general circulation model (GCM) outputs as predictors to produce monthly rainfall forecasts for Australia with lead times up to 8 months. The statistical calibration models make use of raw forecasts of rainfall from a coupled GCM, and the statistical bridging models make use of sea surface temperature (SST) forecasts of the GCM. The forecasts from the multiple models are merged through Bayesian model averaging to take advantage of the strengths of individual models. The skill of monthly rainfall forecasts is generally low. Compared to forecasting seasonal rainfall totals, it is more challenging to forecast monthly rainfall. However, there are regions and months for which forecasts are skillful. In particular, there are months of the year for which forecasts can be skillfully made at long lead times. This is most evident for the period of November and December. Using GCM forecasts of SST through bridging clearly improves monthly rainfall forecasts. For lead time 0, the improvement is particularly evident for February to March, July and October to December. For longer lead times, the benefit of bridging is more apparent. As lead time increases, bridging is able to maintain forecast skill much better than when only calibration is applied.

Abstract. Rainfall forecasts are an integral part of hydrological forecasting systems at sub-seasonal to seasonal timescales. In seasonal forecasting, global climate models (GCMs) are now the go-to source for rainfall forecasts. For hydrological applications however, GCM forecasts are often biased and unreliable in uncertainty spread, and calibration is therefore required before use. There are sophisticated statistical techniques for calibrating monthly and seasonal aggregations of the forecasts. However, calibration of seasonal forecasts at the daily time step typically uses very simple statistical methods or climate analogue methods. These methods generally lack the sophistication to achieve unbiased, reliable and coherent forecasts of daily amounts and seasonal accumulated totals. In this study, we propose and evaluate a Rainfall Post-Processing method for Seasonal forecasts (RPP-S), which is based on the Bayesian joint probability modelling approach for calibrating daily forecasts and the Schaake Shuffle for connecting the daily ensemble members of different lead times. We apply the method to post-process ACCESS-S forecasts for 12 perennial and ephemeral catchments across Australia and for 12 initialisation dates. RPP-S significantly reduces bias in raw forecasts and improves both skill and reliability. RPP-S forecasts are also more skilful and reliable than forecasts derived from ACCESS-S forecasts that have been post-processed using quantile mapping, especially for monthly and seasonal accumulations. Several opportunities to improve the robustness and skill of RPP-S are identified. The new RPP-S post-processed forecasts will be used in ensemble sub-seasonal to seasonal streamflow applications.

This study evaluates seasonal precipitation forecasts over China produced by statistically postprocessing multiple-output fields from the European Centre for Medium-Range Weather Forecasts' System4 (SYS4) coupled ocean-atmosphere general circulation model (CGCM). To ameliorate systematic deficiencies in the SYS4 precipitation forecasts, we apply a Bayesian joint probability (BJP) modeling approach to calibrate the raw forecasts. To improve the skill of the calibration forecasts, we use six large-scale climate indices, calculated from SYS4 sea surface temperature forecasts, to establish a set of BJP statistical bridging models to forecast precipitation. The calibration forecasts and bridging forecasts are merged through Bayesian model averaging to combine strengths of the different models. The BJP calibration effectively removes bias and improves statistical reliability of the raw forecasts. The calibration forecasts are skillful at a 0 month lead in most seasons, but skill decreases sharply at a 1 month lead. The skill of the bridging forecasts is more stable at different lead times. Consequently, the merged calibration and bridging forecasts at a 1 month lead are clearly more skillful than the calibration forecasts, and the skill is maintained out to a 4 month lead. The forecast framework used in this study can help to better realize the potential of CGCM ensemble forecasts. The increased reliability as well as improved skill of seasonal precipitation forecasts suggests that the system proposed here could be a useful operational forecasting tool.