Effect of Multicollinearity on the Bivariate Frequency Analysis of Annual Maximum Rainfall Events

Abstract

A rainfall event, simplified by a rectangular pulse, is defined by three components: the rainfall duration, the total rainfall depth, and mean rainfall intensity. However, as the mean rainfall intensity can be calculated by the total rainfall depth divided by the rainfall duration, any two components can fully define the rainfall event (i.e., one component must be redundant). The frequency analysis of a rainfall event also considers just two components selected rather arbitrarily out of these three components. However, this study argues that the two components should be selected properly or the result of frequency analysis can be significantly biased. This study fully discusses this selection problem with the annual maximum rainfall events from Seoul, Korea. In fact, this issue is closely related with the multicollinearity in the multivariate regression analysis, which indicates that as interdependency among variables grows the variance of the regression coefficient also increases to result in the low quality of resulting estimate. The findings of this study are summarized as follows: (1) The results of frequency analysis are totally different according to the selected two variables out of three. (2) Among three results, the result considering the total rainfall depth and the mean rainfall intensity is found to be the most reasonable. (3) This result is fully supported by the multicollinearity issue among the correlated variables. The rainfall duration should be excluded in the frequency analysis of a rainfall event as its variance inflation factor is very high.