Model averaging methods to merge statistical and dynamic seasonal streamflow forecasts in Australia

The Australian Bureau of Meteorology operates a statistical seasonal streamflow forecasting service. It has also developed a dynamic seasonal streamflow forecasting approach. The two approaches produce similarly reliable forecasts in terms of ensemble spread but can differ in forecast skill depending on catchment and season. Therefore, it may be possible to augment the skill of the existing service by objectively weighting and merging the forecasts.

Bayesian model averaging (BMA) is first applied to merge statistical and dynamic forecasts for 12 locations using leave-five-years-out cross-validation. It is seen that the BMA merged forecasts can sometimes be too uncertain, as shown by ensemble spreads that are unrealistically wide and even bi-modal. The BMA method applies averaging to forecast probability densities (and thus cumulative probabilities) for a given forecast variable value. An alternative approach is quantile model averaging (QMA), whereby forecast variable values (quantiles) are averaged for a given cumulative probability (quantile fraction). For the 12 locations, QMA is compared to BMA.

BMA and QMA perform similarly in terms of forecast accuracy skill scores and reliability in terms of ensemble spread. Both methods improve forecast skill across catchments and seasons by combining the different strengths of the statistical and dynamic approaches. A major advantage of QMA over BMA is that it always produces reasonably well defined forecast distributions, even in the special cases where BMA does not. Optimally estimated QMA weights and BMA weights are similar; however, BMA weights are more efficiently estimated.