Structured Coupling of Probability Loss Distributions: Assessing Joint Flood Risk in Multiple River Basins

Losses due to natural hazard events can be extraordinarily high and difficult to cope with. Therefore, there is considerable interest to estimate the potential impact of current and future extreme events at all scales in as much detail as possible. As hazards typically spread over wider areas, risk assessment must take into account interrelations between regions. Neglecting such interdependencies can lead to a severe underestimation of potential losses, especially for extreme events. This underestimation of extreme risk can lead to the failure of riskmanagement strategies when they are most needed, namely, in times of unprecedented events. In this article, we suggest a methodology to incorporate such interdependencies in risk via the use of copulas. We demonstrate that by coupling losses, dependencies can be incorporated in risk analysis, avoiding the underestimation of risk. Based on maximum discharge data of river basins and stream networks, we present and discuss different ways to couple loss distributions of basins while explicitly incorporating tail dependencies. We distinguish between coupling methods that require river structure data for the analysis and those that do not. For the later approach we propose a minimax algorithm to choose coupled basin pairs so that the underestimation of risk is avoided and the use of river structure data is not needed. The proposed methodology is especially useful for large-scale analysis and we motivate and apply our method using the case of Romania. The approach can be easily extended to other countries and natural hazards.