Abstract
As extreme weather events enhanced by climate change pose challenges to the resilience of critical infrastructure, the ability to handle disruptions, avoid tipping points, adapt and transform in crises becomes essential. Despite advances in resilience research, there is a need to improve empirical evidence and mathematical models to quantify the systems’ adaptive capabilities to extreme climate-related phenomena, such as floods. This research fills this gap by integrating an agent-based multimodal traffic functional model with a compound failure model to provide valuable insights into adaptation patterns (that is, mode shift and route switching) and risk mitigation in response to flood-related disruptions. The proposed modelling approach not only quantifies the recovery and adaptive capacity against failures, going beyond traditional resilience analyses, but also unveils the key factors that drive adaptation of transportation to flood-induced disasters. These factors include variations in trip demand and network density, which together reveal a universal law of mode shift. The study provides valuable insights into the design of resilient and sustainable critical infrastructure systems, such as transportation, energy and communication systems capable of withstanding severe flood events while maintaining their functionality.
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Data availability
The Nanjing multimodal transport simulation model is available via GitHub at https://github.com/ChunhongLi8/adaptiveCapacityOfUrbanTransportNetwork. The Hamburg multimodal transport simulation model is available via GitHub at https://github.com/matsim-scenarios/matsim-hamburg. The LA multimodal transport simulation model is available via GitHub at https://github.com/matsim-scenarios/matsim-los-angeles. Flood hazard data for a 100-year return period for Nanjing and Hamburg are available from the Joint Research Centre of European Commission61. Flood hazard data for a 100-year return period for LA is available via Zenodo at https://doi.org/10.5281/zenodo.6965044 (ref. 63). The human mobility dataset for LA scenario validation is available via GitHub at https://github.com/GeoDS/COVID19USFlows. For contractual and privacy reasons, we cannot make the vehicle mobility dataset for Nanjing available. One can contact Amap to try to get access to the Nanjing vehicle mobility dataset.
Code availability
The implementation of this work is available via GitHub at https://github.com/ChunhongLi8/adaptiveCapacityOfUrbanTransportNetwork.
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Acknowledgements
C.L., W.W., B.J., Z.L. and Z.G. are supported by the National Natural Science Foundation of China (grant nos. 72288101, 72242102, 72471031, W2411064, 72001018 and 72361137002), the Jiangsu Provincial Scientific Research Center of Applied Mathematics (grant no. BK20233002), Natural Science Foundation of Beijing, China (grant no. 9242012) and Guangdong Provincial Natural Science Foundation (grant no. 2023A1515010604). J.G. is supported by the National Science Foundation of the United States (grant no. 2047488) and by the Rensselaer-IBM AI Research Collaboration. A.S.-R. and J.B.-H. acknowledge financial support from the Ministry of Science and Innovation of Spain, through project no. PID2021-128966NB-I00. J.B.-H. acknowledges financial support from the Ramón y Cajal programme through grant no. RYC2020-030609-I. We sincerely thank L. Zhong, K. Huang, Z. Bai and J. Liu for insightful discussions.
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C.L., W.W., B.J. and J.G. conceived the project and designed the study. C.L., W.W., B.J. and J.G. performed the data analyses. C.L., W.W., A.S.-R., J.B.-H., B.J., Z.G. and J.G. wrote the first draft of the manuscript. C.L., W.W., A.S.-R., J.B.-H., B.J., Z.L., B.Y., Z.G. and J.G. contributed to interpreting the results and improving the manuscript.
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Extended data
Extended Data Fig. 1 The driving factors of adaptability.
We utilize a set of controlled trials to explore the potential drivers for adaptive capacity. Passengers in the treatment group Fa must maintain the same travel routes and modes as in the baseline scenario. In contrast, passengers in the treatment group Fb are allowed to adjust their travel routes but not their modes in response to flood-induced disruptions. Meanwhile, passengers in the control group F have the flexibility to modify both their travel routes and modes without any restrictions. We then compare trips composition for each group and display trips flow with growing adaptability for Nanjing (T=3m) (a), Hamburg (T=4m) (b) and LA (T=0.3 m) (c).
Extended Data Fig. 2 The social dimension of adaptive capacity.
a-d Sankey diagrams display the way that travelers adapt to the adverse effect induced by floods (T = 0.3 m) in Hispanic, HP (a), Non-Hispanic Black, NHB (b), Non-Hispanic Asian, NHAS (c), and Non-Hispanic White, NHW (d). e-h In a similar vein, for travelers divided by household annual income quartiles, with the first quartile representing the poorest (e) and the fourth quartile representing the wealthiest (h). i-l For travelers holding distinct education attainments, including no education (i), below high school (j), completing high school (k), and associate/bachelor or higher (l). Numbers in brackets indicate adaptive capacity metric, κ, for each cluster (see Eq. (8) in Methods).
Extended Data Fig. 3 The model validation.
a-b We extracted and processed Nanjing’s empirical mobility datasets on a typical normal workday (July 18, 2024) and a stormy workday (July 11, 2024) from Amap, an online navigation provider. Panel (a) shows the comparison of cumulative density function (CDF) for travel time between the normal workday and the simulated baseline scenario. Same to panel (a), panel (b) depicts the comparison between the rainy workday (July 11, 2024) and simulated flooding scenario (T=6m). c-d We also compare the travel radius distribution for LA between simulation data and empirical human mobility data derived from SafeGraph, a ___location data service provider. Panel (c) compares the CDF of travel radius between the baseline model and a normal workday (Wednesday, February 27, 2019), while panel (d) compares the CDF of travel radius between the flooding model (T=0) and a stormy workday (Wednesday, March 6, 2019). In all panels, we present the Kolmogorov-Smirnov (KS) test results (*** indicates that the p-value is less than 0.001).
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Supplementary Information
Supplementary Notes 1–13, Figs. 1–33 and Tables 1–15.
Supplementary Video 1
Travel behaviour changes due to flooding.
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Li, C., Wang, W., Solé-Ribalta, A. et al. Adaptive capacity for multimodal transport network resilience to extreme floods. Nat Sustain (2025). https://doi.org/10.1038/s41893-025-01575-z
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DOI: https://doi.org/10.1038/s41893-025-01575-z
