An information-theoretical perspective on weighted ensemble forecasts

This paper presents an information--theoretical method for weighting ensemble forecasts with new information. Weighted ensemble forecasts can be used to adjust the distribution that an existing ensemble of time series represents, without modifying the values in the ensemble itself. The weighting can, for example, add new seasonal forecast information in an existing ensemble of historically measured time series that represents climatic uncertainty. A recent article in this journal compared several methods to determine the weights for the ensemble members and introduced the pdf-ratio method. In this article, a new method, the minimum relative entropy update (MRE-update), is presented. Based on the principle of minimum discrimination information, an extension of the principle of maximum entropy (POME), the method ensures that no more information is added to the ensemble than is present in the forecast. This is achieved by minimizing relative entropy, with the forecast information imposed as constraints. From this same perspective, an information--theoretical view on the various weighting methods is presented. The MRE-update is compared with the existing methods and the parallels with the pdf-ratio method are analysed. The paper provides a new, information--theoretical justification for one version of the pdf-ratio method that turns out to be equivalent to the MRE-update. All other methods result in sets of ensemble weights that, seen from the information--theoretical perspective, add either too little or too much (i.e. fictitious) information to the ensemble.