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Is unequal weighting significantly better than equal weighting for multi-model forecasting?



This article proposes a statistical test for whether a multi-model combination with unequal weights has significantly smaller errors than a combination with equal weights. A combination with equal weights includes the case of a no-skill model, in which all weights equal zero, and the multi-model mean, in which all weights equal 1/M, where M is the number of models. The test is applied to seasonal hindcasts of 2 m temperature and precipitation generated by five state-of-the-art coupled atmosphere–ocean models. The hypothesis of equal weights could not be rejected over 75% the globe for temperature and 90% of the land for precipitation, implying that strategies for unequal weighting of forecasts may be of value only over a relatively small fraction of the globe. The fact that the test does not require pre-specifying a specific strategy for weighting forecasts suggests that it should be useful for exploring a wide range of multi-model strategies. Copyright © 2012 Royal Meteorological Society