A new flood estimation paradigm for the design of civil infrastructure systems

Abstract

Methods for quantifying flood risk of civil infrastructure systems such as road and rail networks require considerably more information compared to traditional methods that focus on flood risk at a point. These systems are characterised by multiple interconnected components, whereby a ‘failure’ of the overall system can arise because of complex combinations of failures in system subcomponents. For example, flooding of a single bridge along a railway may leave the entire railway inoperable, and the interest is often in the probability that one or more bridges along a stretch of railway will be flooded, rather than designing each bridge in isolation. Similarly, the viability of evacuation routes often requires an assessment of the probability that the route is flooded, conditional on an evacuation being necessary as a result of floods elsewhere in the system. Conventional design flood estimation processes are ill-equipped to deal with these complex problems. Whereas traditional flood estimation approaches focus on estimating flood risk at a single location, this thesis proposes a new estimation paradigm that focuses on estimating system-wide risk. The approach builds on the traditional intensity-duration-frequency (IDF) methods that are commonly used in engineering practice in Australia and internationally; however, this is implemented in such a way at to provide information on the spatial dependence of design storms. A particular innovation in this thesis is to estimate spatial rainfall dependence across multiple storm durations, allowing it to be used to estimate flood risk across multiple catchments with differing times of concentration. This enables the estimation of both conditional probabilities (e.g. probability of one part of a system being flooded conditional on another part of the system being flooded) and joint probabilities (e.g. the probability of multiple parts of a system experiencing floods simultaneously). Finally, whereas traditional IDF approaches consider conversion from point rainfall to spatial rainfall via areal reduction factors as a post-processing step, the approach proposed herein enables this conversion implicitly as part of the method. The proposed approach is based on two classes of extreme value model: max-stable process models, and inverted max-stable process models. These models differ in their assumption for how spatial dependence scales in the limit, as the rainfall events become increasingly extreme (referred to as “asymptotic dependence”). In particular, max-stable models assume asymptotic dependence (i.e. the spatial dependence converges to a non-zero limit), whereas inverted max-stable models assume asymptotic independence. This assumption has significant implications for very rare events (e.g. the 1% annual exceedance probability event), particularly when the estimates are based on relatively short observational records. Specifically, implementation focuses on the (inverted) Brown-Resnick family of models. This class of model was adjusted by accounting for spatial dependence across multiple storm burst durations. The adjustment used the theoretical pairwise extremal coefficient function as a function of both distance and duration. The integration of multiple durations into the modelling framework was tested on a 21,400 km2 spatial domain in the Greater Sydney region, with data on sub-daily rainfall from 25 stations. The updated model shows a reasonable fit between the observed pairwise extremal coefficients and the theoretical pairwise extremal coefficient function across all durations. The asymptotic dependence and comparison with empirically derived areal reduction factors was tested next, and it was shown that the observed data follow the behaviour of an asymptotically independent process, which leads to ARFs that decrease with an increasing return period. This demonstrates that inverted max-stable process models such as the inverted Brown-Resnick model are the most suitable method for simulating spatial rainfall in the study areas that were investigated. Finally, the outcomes of this research are demonstrated by implementing the spatially dependent IDF approach in a realistic case study that requires information on both conditional and joint dependence. The case study examines a highway upgrade project on the east coast of Australia, containing five bridge crossings with differing contributing catchment areas, and thus differing times of concentration. The results are used to show the differences between conditional-flood and conventional-flood estimates at each bridge, and the relationship between the overall failure of a system and the failure probability of an individual bridge. For example, if one were to design the highway section for a 1% probability of at least one bridge being flooded in any given year, it would be necessary to design each individual bridge to a 𝑋% annual exceedance probability design flood. This research therefore is shown to enable a different paradigm for design flood risk estimation, which focuses attention on the risk of the entire system rather than considering individual system elements in isolation.