抄録
It is shown that a similarity parameter has new mathematical structure. Heretofore, the correlation coefficient is used for quantifying the correlation relationship between two ensemble members. Koster et al1 introduced a statistical parameter, called Ω to quantify the similarity among several ensemble members with calculating the ensemble numbers and the two types of variances. However the mathematical structure of Ω had not been revealed in their studies. The present authors applied to derivate Ω for understanding the mathematical meaning of it. As results, we could have a knowledge that Ω consists of mainly two terms. One is the average value of cross correlation coefficients (ACCC) across all ensemble members. Another is the similarity of the mean value and the variance across all ensemble members. Therfore, the authorscan conclude that Ω shows the similarity of the ‘shape’ of all ensemble members and the mathematical characteristics is more capacious than the correlation coefficient. The paper ends with some remarks on the mathematical characteristics of ‘as a new evaluation methodology for the predictabity of numerical forecast.’ in monthly or seasonal time scale.
