Use of mixed bivariate distributions for deriving inter‐station correlation coefficients of rain rate

Abstract

AbstractEven though rain rate is notorious for its spatial and temporal intermittency, its effect on the second‐order statistics of rain rate, especially the inter‐station correlation coefficients, has not been intensively evaluated before. This study has derived and compared the inter‐station correlation coefficient of rain rate for three cases of data: (1) only the positive measurements at both locations; (2) the positive measurements at either one or both locations; (3) all the measurements including zero measurement at both locations. For these three cases, the inter‐station correlation coefficients are analytically derived by applying the mixed bivariate log‐normal distribution. As an application example, the model parameters are estimated using the rain rate data collected at the Geum River basin, Korea, and the resulting inter‐station correlation coefficients are evaluated and compared with those estimated by applying the Gaussian distribution. We could find that highly biased inter‐station correlation coefficients are unavoidable when simply estimating them under the assumption of Gaussian distribution, or even when using the log‐transformed rain rate data. Copyright © 2007 John Wiley & Sons, Ltd.