Flood risk management decisions in many countries are based on decision-support frameworks which rely on cost-benefit analyses. Such frameworks are seldom informative about the geographical distribution of risk, raising questions on the fairness of the proposed policies. In the present work, we propose a new decision criterion that accounts for the distribution of risk reduction and apply it to support flood risk management decisions on a transboundary stretch of the Rhine River. Three types of interventions are considered: embankment heightening, making Room for the River, and changing the discharge distribution of the river branches. The analysis involves solving a flood risk management problem according to four alternative formulations, based on different ethical principles. Formulations based on cost optimization lead to very poor performances in some areas for the sake of reducing the overall aggregated costs. Formulations that also include equity criteria have different results depending on how these are defined. When risk reduction is distributed equally, very poor economic performance is achieved. When risk is distributed equally, results are in line with formulations based on cost optimization, while a fairer risk distribution is achieved. Risk reduction measures also differ, with the cost optimization approach strongly favoring the leverage of changing the discharge distribution and the alternative formulations spending more on embankment heightening and Room for the River, to rebalance inequalities in risk levels. The proposed method advances risk-based decision-making by allowing to consider risk distribution aspects and their impacts on the choice of risk reduction measures.

Most alluvial plains in the world are protected by flood defences, for example, embankments, whose primary aim is to reduce the probability of flooding of the protected areas. At the same time, however, the presence of embankments at one area influences hydraulic conditions of downstream areas located on the same river. These hydraulic interactions are often neglected in current flood risk management. The aim of this study is to explicitly acknowledge hydraulic interactions and investigate their impact on establishing optimal embankment heights along a stretch of the IJssel River. We find that the current approach leads to a single solution, while taking into account hydraulic interactions substantially expands the number of promising solutions. Furthermore, under a reference scenario, the current approach is in fact suboptimal with respect to both downstream locations and the system as a whole. Under uncertainty, it performs adequately from a system viewpoint, but poorly for individual locations, mostly due to risk overestimation downstream. Overall, the current approach proves to be too short-sighted, because spatial trade-offs among locations are neglected and alternative solutions remain hidden. Acknowledging the effect of hydraulic interactions provides policy makers with a broader and more comprehensive spectrum of flood risk management strategies.

Rivers typically flow through multiple flood-protected areas which are clearly interconnected, as risk reduction measures taken at one area, e.g. heightening dikes or building flood storage areas, affect risk elsewhere. We call these interconnections 'hydraulic interactions'. The current approach to flood risk management, however, neglects hydraulic interactions for two reasons: They are uncertain and, furthermore, considering them would require the design of policies not only striving for risk reduction, but also accounting for risk transfers across flood-protected areas. In the present paper, we compare the performance of policies identified according to the current approach with those of two alternative formulations: One acknowledging hydraulic interactions and the other also including an additional decision criterion to account for equity in risk distribution across flood-protected areas. Optimal policies are first identified under deterministic hydraulic interactions, and, next, they are stress-tested under uncertainty. We found that the current approach leads to a false sense of equal risk distribution. It does, however, perform efficiently when a risk-averse approach towards uncertain hydraulic interactions is taken. Accounting for hydraulic interactions in the design of policies, instead, increases efficiency and both efficiency and equity when hydraulic interactions are considered deterministically and as uncertain, respectively.