Using the Apriori Algorithm and Copula Function for the Bivariate Analysis of Flash Flood Risk

Abstract

Flash flooding is a phenomenon characterized by multiple variables. Few studies have focused on the extracted variables involved in flash flood risk and the joint probability distribution of the extracted variables. In this paper, a novel methodology that integrates the Apriori algorithm and copula function is presented and used for a flood risk analysis of Arizona in the United States. Due to the various rainfall indices affecting the flash flood risk, when performing the Apriori algorithm, the accumulated 3-h rainfall and accumulated 6-h rainfall were extracted as the most fitting rainfall indices. After comparing the performance of copulas, the Frank copula was found to exhibit the best fit for the flash flood hazard; thus, it was used for a bivariate joint probability analysis. The bivariate joint distribution functions of P–Q, PA–Q, PB–Q, and D–Q were established, and the results showed an increasing trend of flash flood risk with increases in the rainfall indices and peak flow; however, the risk displayed the least significant relation with the duration of the flash flood. These results are expected to be useful for risk analysis and decision making regarding flash floods.