A note on some methods suitable for verifying and correcting the prediction of climatic anomaly

Abstract

The weighted correlation coefficient of the predicted and observed anomalies and the ratio of the weighted norm of predicted anomaly to the observed one, both together, are suggested to be suitable for the estimating of the correctness of climate prediction. The former shows the similarity of the two patterns, and the later indicates the correctness of the predicted intensity of the anomaly. The weighting function can be different for different emphasis, for example, a constant weight means that the correlation coefficient is the conventional one, but some non-uniform weight leads to the ratio of correct sign of the anomaly, the stepwise weight leads to the formulation of correctness of prediction represented by grades of the anomaly, and so on.

Three methods for making correction to the prediction are given in this paper. After subtracting the mean error of the prediction, one method is developed for maximizing the similarity between the predicted and observed patterns, based on the transformation of the spatial coordinates. Another method is to minimize the mean difference between the two fields. This method can also be simplified as similar to the “optimum interpolation” in the objective analysis of weather chart. The third method is based on the expansion of the anomaly into series of EOF, where the coefficients are the predicted but the EOFs are taken as the “observed” calculated from historical samples.