The Interplay between Duration and Intensity: Robust Planning Against Extreme Rainfalls

70 Pages Posted: 18 Oct 2022 Last revised: 3 Nov 2023

See all articles by Sheng Liu

Sheng Liu

Rotman School of Management

Wei Qi

Tsinghua University - Department of Industrial Engineering; McGill University - Desautels Faculty of Management

Aiqi Zhang

Wilfrid Laurier University - School of Business & Economics

Date Written: October 1, 2022

Abstract

Climate changes inflict prolonged and intensified rainfalls on cities around the world. Unfortunately, existing efforts hardly meet the urgent need for climate-adaptive stormwater management. Urban stormwater infrastructure is typically planned based on empirically predetermined rainfall scenarios on the intensity-duration-frequency (IDF) curve, which fails to capture the worst-case scenarios that should be planned against. This paper identifies the worst-case rainfall scenarios that cause the most severe flooding loss through robust optimization, which constructs a new type of uncertainty set that builds upon IDF curves. Our analysis reveals that not all rainfalls on the same IDF curve are equal in terms of the incurred flooding loss. If the planners fail to account for the city's intrinsic infrastructure capabilities, they may pick a wrong 50-year rainfall to target and end up barely surviving a 2-year rainfall. Hence, we construct cost-indifferent isocurves that classify rainfall events according to the severity of the flooding loss, providing city planners with interpretable flooding risk mitigation guidelines. We demonstrate that cities should be savvy in achieving a balance between investments in stormwater retention flow rate and investments in stormwater retention capacity, as reflected in the composition of green and grey infrastructures. Under a budget constraint, green infrastructures should give way to grey ones, exchanging flow rates for a larger retention capacity to withstand severe rainfalls that have a longer duration and larger volume. Finally, we show that flooding loss ramps up quickly as the climate change risks are exacerbated, underscoring the urgency of taking the proposed integrated measures.

Keywords: extreme rainfalls; stormwater retention; robust optimization; climate adaptation

Suggested Citation

Liu, Sheng and Qi, Wei and Zhang, Aiqi, The Interplay between Duration and Intensity: Robust Planning Against Extreme Rainfalls (October 1, 2022). Rotman School of Management Working Paper No. 4238919, Available at SSRN: https://ssrn.com/abstract=4238919

Sheng Liu

Rotman School of Management ( email )

105 St. George st
Toronto, ON M5S 3E6
Canada

Wei Qi

Tsinghua University - Department of Industrial Engineering ( email )

Beijing
China

McGill University - Desautels Faculty of Management ( email )

1001 Sherbrooke Street West
Montreal, Quebec H3A 1G5
Canada

Aiqi Zhang (Contact Author)

Wilfrid Laurier University - School of Business & Economics ( email )

Waterloo, Ontario N2L 3C5
Canada

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