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

Even 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.