Inter-station correlation and estimation errors of areal average rain rate

In this study an equation for estimating the error involved in the areal average rain rate considering the inter-station correlation was derived and applied for two cases: the first compared two storm events with different inter-station correlations, and the second evaluated the seasonal variation of estimation error of monthly rainfall. Similar cases, but without considering the rainfall seasonality, were also investigated for the comparison. This study was applied to the Geum River Basin with 28 rain gauge measurements, each having more than 30 years of rainfall data. A summary of the application results follows: (1) When considering the inter-station correlation, the estimation error involved in the areal average rain rate became significantly decreased proportional to the inter-station correlation. (2) The estimation error of monthly areal average rainfall showed strong seasonality with high ones during the wet season and lower ones during the dry season. (3) The estimation error was well proportional to the areal average rain rate as well as to its standard deviation. The ratio of estimation error to the areal average rain rate itself was estimated to be about 0.1 for the case of assuming no inter-station correlations, but decreased to 0.06 for the case of considering the inter-station correlations between measurements. (4) The relation between the standard deviation of areal average rain rate and the estimation error became much stronger than that between the areal average rain rate itself and the estimation error. The ratio of estimation error to the standard deviations of rain rate amount was estimated to be about 0.2 for the case of assuming no inter-station correlations, but decreased to 0.1 for the case of considering the inter-station correlations. This relation was found to be valid for any case of accumulation time such as in daily, monthly, or annual rainfall data.