Optimal Exponent Values of Distance and Elevation Based on Hourly Rainfall Data in the Modified Inverse Distance Method

Abstract

Obtaining appropriate, applicable exponent values of distance and elevation in the modified inverse distance method for hourly rainfall interpolation is difficult because the range of the exponent values has not yet been established at existing studies. In this research, an attempt is made to find the optimal exponent values in the modified inverse distance method based on hourly rainfall data. For the purpose of this study, 28 rainfall observation stations providing the data were classified into four groups, which are located at the Han River upstream, the Han River downstream, the Geum River upstream, and the Nakdong River midstream areas in South Korea. A total of 44 cases consisting of one base rainfall station and four index rainfall stations were analyzed. The optimal exponent values of distance and elevation were calculated by a simple nonlinear optimization technique of the steepest gradient method using hourly rainfall data observed for 10 years (2004–2013) and validated using another data for three years (2014–2016) on a case basis across different groups. The proposed modified inverse distance method was found to be superior to the conventional inverse distance method. Worth noting is that the root mean squared error values obtained by the method of this study were smaller than those of the conventional methods in all groups even though they were small in size hydrometeorologically. Therefore, the method proposed in this research can be considered more advanced than the conventional method. The optimal exponent values of distance and elevation obtained in this research were 3.463 and −0.017, 2.559 and 0.741, 2.877 and −0.681, and 3.738 and 2.001, respectively, in the four groups, and the total mean values of the two values were 3.159 and 0.511, respectively. The main factor influencing rainfall between stations when applying the modified inverse distance method with the optimal exponents was found to be the distance, and the altitude is the minor factor.