No abstract

Determining the probability of a flood event in a catchment given that another flood has occurred in a nearby catchment is useful in the design of infrastructure such as road networks that have multiple river crossings. These conditional flood probabilities can be estimated by calculating conditional probabilities of extreme rainfall and then transforming rainfall to runoff through a hydrologic model. Each catchment's hydrological response times are unlikely to be the same, so in order to estimate these conditional probabilities one must consider the dependence of extreme rainfall both across space and across critical storm durations. To represent these types of dependence, this study proposes a new approach for combining extreme rainfall across different durations within a spatial extreme value model using max‐stable process theory. This is achieved in a stepwise manner. The first step defines a set of common parameters for the marginal distributions across multiple durations. The parameters are then spatially interpolated to develop a spatial field. Storm‐level dependence is represented through the max‐stable process for rainfall extremes across different durations. The dependence model shows a reasonable fit between the observed pairwise extremal coefficients and the theoretical pairwise extremal coefficient function across all durations. The study demonstrates how the approach can be applied to develop conditional maps of the return period and return level across different durations.

Abstract. Conventional flood risk methods typically focus on estimation at a single location, which can be inadequate for civil infrastructure systems such as road or railway infrastructure. This is because rainfall extremes are spatially dependent; to understand overall system risk, it is necessary to assess the interconnected elements of the system jointly. For example, when designing evacuation routes it is necessary to understand the risk of one part of the system failing given that another region is flooded or exceeds the level at which evacuation becomes necessary. Similarly, failure of any single part of a road section (e.g., a flooded river crossing) may lead to the wider system's failure (i.e., the entire road becomes inoperable). This study demonstrates a spatially dependent intensity–duration–frequency (IDF) framework that can be used to estimate flood risk across multiple catchments, accounting for dependence both in space and across different critical storm durations. The framework is demonstrated via a case study of a highway upgrade comprising five river crossings. The results show substantial differences in conditional and unconditional design flow estimates, highlighting the importance of taking an integrated approach. There is also a reduction in the estimated failure probability of the overall system compared with the case where each river crossing is treated independently. The results demonstrate the potential uses of spatially dependent intensity–duration–frequency methods and suggest the need for more conservative design estimates to take into account conditional risks.

Abstract. Conventional flood risk methods typically focus on estimation at a single location, which is inadequate for civil infrastructure systems such as road or railway infrastructure. This is because rainfall extremes are spatially dependent, so that to understand overall system risk it is necessary to assess the interconnected elements of the system jointly. For example, when designing evacuation routes it is necessary to understand the risk of one part of the system failing given that another region is flooded or exceeds the level at which evacuation becomes necessary. Similarly, failure of any single part of a road section (e.g., a flooded river crossing) may lead to the wider system’s failure (i.e. the entire road becomes inoperable). This study demonstrates a spatially dependent Intensity-Duration-Frequency curve framework that can be used to estimate flood risk across multiple catchments, accounting for dependence both in space and across different critical storm durations. The framework is demonstrated via a case study of a highway upgrade, comprising five bridge crossings where the upstream contributing catchments each have different times of concentration. The results show that conditional and unconditional design flows can differ by a factor of two, highlighting the importance of taking an integrated approach. There is also a reduction in the failure probability of the overall system compared with the case of no spatial dependence between storms. The results demonstrate the potential uses of spatially dependent Intensity-Duration-Frequency curves and suggest the need for more conservative design estimates to take into account conditional risks.