Testing the Multivariate Hüsler–Reiss Model as a Practical Parametric Approach for Multiple River Flood Risk Assessment Using d4PDF Data: A Case Study in Kyushu Island, Japan

Compound flood disaster risks are increasing due to multiple river floods within a single storm event. Many studies targeted dependence structure based on multivariate extreme value theory; however, fewer studies focused on the sum of subset joint probabilities (SSJP), defined as the probability that any combination of rivers are flooded over the target area as an integral index of compound flooding risks. Modeling multivariate extremes at high dimensions faces two challenges: model complexity and sample size. In this study, as a classical asymptotic dependence model, the Hüsler–Reiss (HR) model was explored to resolve the former issue owing to its simplicity. From the multivariate HR model, any subset joint probability is explicitly obtained without numerical integration of angular measure, and dependence parameters are constructed from only pairwise parameters. The latter challenge was addressed using a large ensemble (50 members of 60-year simulation) of the database for policy decision-making for future climate change (d4PDF), which is consequently regarded as the annual maximum flow data of 3,000 years. This study analytically derived SSJP based on the HR model and tested its applicability using annual maximum flow data simulated from d4PDF for 20 rivers in Kyushu Island, Japan. The simulated SSJP based on the HR model and empirical SSJP were compared as the probability plot of the number of river basins where peak discharge exceeds the design level. As a result, under the constraint of HR that the partial correlation must range from $-1$ to 1, the estimated SSJP by the HR model was in agreement with the empirical SSJP. The case study presents promising results of the proposed HR model–based approach.