How to Improve Accuracy by Combining Independent Forecasts

Abstract

It is shown that the ensemble mean-square error of forecasts constructed from a particular linear combination of independent and imperfectly correlated predictions is less than that of any of the individual predictions. The weights to be attached to each prediction are determined by the Gaussian method of least squares and depend on the covariances between independent predictions and between prediction and verification. At the present stage of development of numerical prediction methods, it appears possible to reduce the error variance by about 20%, simply by the optimum combination of two independent predictions.