Info-gap assessment of cost-effectiveness for flood-mitigation scenarios: Haigh Beck case study

A graphical cost-effectiveness tool has been developed to communicate flood-mitigation plans and measures to decision-makers. In its simplest form, the tool is based on flood hydrograph and water level data at a critical location along a river stretch, for a design flood expressed in terms of its return period. A three-panel graph is made with water-level data in quadrant three, a rating curve in quadrant two and a hydrograph in quadrant one, sharing axes with the adjacent quadrant(s). After establishing a water-level threshold of flooding, a discharge-threshold follows. The discharge over time above that threshold defines the flood-excess volume to be mitigated to avoid flood damage. Expressed as a square lake of 2m depth and 100m’s or 1000m’s side length, the fraction of each flood-mitigation method is overlayed on this square-lake chart, plus its costs, costs per percentage and total costs. Choices can be made by comparing square-lake graphs for each mitigation scenario [1]. Where possible, more complicated cost-effectiveness assessments can be based on ensemble simulations of flood forecasts with various flood-mitigation measures, and made by including uncertainties.

Info-gap theory [2] will be applied in an idealised Haigh Beck case study, a stream of ~2000m length and ~100m decline that flows into the River Aire (UK). The beck has caused floods with combined-sewer overflows during severe rainfall, in a neighbourhood near the beck’s mouth and upstream of the Leeds-Liverpool canal, flooding several apartments (e.g., on May 6^th, 2024). Proposed mitigation measures are inflow into canal C1, an upstream bund B2 and flood-plain storage FP3, combined into cost-competitive mitigation scenarios C1 and a B2-FP3 combination [3]. Challenging is that crucial pieces of information, on costs and risks (of failure), are missing for informed decision-making, either because organisations refuse to provide the information, the data are lost or do not exist. Info-gap theory will be used to deal with these true or Knightian uncertainties. An info-gap is the gap between what one knows and what one needs to know for reliable decision-making. Info-gap theory aims to quantify decisions with a high robustness, concerning decisions on flood-mitigation scenarios that satisfy performance requirements over a range of unanticipated eventualities. In this study, it is comprised of (a) a cost model, (b) a performance criterion (costs below a threshold) and (c) model uncertainty intervals. Furthermore, costs of scenario B2-FP3 are known, but the value of co-benefits for scenario C1 are unknown while its base costs are somewhat known. This use of info-gap theory to facilitate cost-effectiveness decisions is novel and practical. Alternatively, the unknown uncertainty (pertaining to (c)) in the flood-excess volume can be used as decision support, a type of application of info-gap theory found in, e.g., [4].

[1] Bokhove, Kelmanson, Kent, Piton, Tacnet 2020: Water 12(3), 652. https://doi.org/10.3390/w12030652
[2] Marchau, Walker, Bloemen, Popper 2019: Decision making under deep uncertainty. Chapters 1, 5 and 10 (e.g. by Y. Ben-Haim) on info-gap theory. Springer. 405 pp. https://doi.org/10.1007/978-3-030-05252-2
[3] Knotters, Bokhove, Lamb, Poortvliet 2024: Cambridge Prisms: Water 2, e6. https://doi.org/10.1017/wat.2024.4
[4] Hine, Hall 2010: Water Resources Research 46. W01514. https://doi:10.1029/2008WR007620