Policy Research Working Paper 10049 Mobility and Resilience A Global Assessment of Flood Impacts on Road Transportation Networks Yiyi He Jun Rentschler Paolo Avner Jianxi Gao Xiangyu Yue John Radke Urban, Disaster Risk Management, Resilience and Land Global Practice May 2022 Policy Research Working Paper 10049 Abstract This study provides the first global evaluation of both direct flood impact (both direct and indirect). Compared with and indirect flood hazard impacts on road transportation direct flood hazard exposure, the indirect impact of floods networks. It constructs topological road networks for 2,564 on mobility is more prominent and heterogeneous. The human settlements, representing over 14 million kilome- average share of the road network that is flooded by at ters of urban roads. It assesses their exposure to pluvial least 0.3 meters is 3.64 percent (or 24.84 percent) under and fluvial flood risks under 10 scenarios, corresponding the 5-year (or 1,000-year) return period, yet 11.58 percent to different flood intensities (1:5 year to 1:1,000 year return (or 65.67 percent) of the simulated trips fail in the same periods). Under each scenario, the study analyzes direct scenario. The results enable comparisons of exposure and infrastructure exposure and assesses the indirect effects of vulnerability of road networks to flood hazards across coun- flood-induced mobility disruptions: route failures, travel tries, allowing the identification and prioritization of urban delays, and travel distance increases. The results document transport resilience measures. a positive relationship between flood return period and This paper is a product of the Urban, Disaster Risk Management, Resilience and Land Global Practice. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at yiyi_he@berkeley.edu, jrentschler@worldbank.org, and pavner@worldbank.org. The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent. Produced by the Research Support Team Mobility and Resilience: A Global Assessment of Flood Impacts on Road Transportation Networks Yiyi Hea*, Jun Rentschlerb, Paolo Avnerc, Jianxi Gaod, Xiangyu Yuee, John Radkea,f a College of Environmental Design, University of California, Berkeley, USA. b Office of the Chief Economist for Sustainable Development, The World Bank, Washington, D.C., USA. c The Global Facility for Disaster Reduction and Recovery, The World Bank, Washington, D.C., USA. d Department of Computer Science, Rensselaer Polytechnic Institute, Troy, New York, USA. e Department of Electrical Engineering and Computer Science, University of California, Berkeley, USA. f Department of City and Regional Planning, University of California, Berkeley, USA. * Corresponding author Keywords: Floods, Global road network, Infrastructure network resilience, Travel simulation JEL codes: Q54, R41, R12, C63 Introduction Road transportation networks are lifelines for cities around the world, providing people with access to markets, jobs, and critical services, including emergency medical services, primary health care and fuel1,2. However, climate change, rapid urbanization, coupled with increasing interdependencies among various infrastructure systems are putting road transportation networks under increasing pressure2–5. An increasing number of studies document the growing risk and vulnerability of these networks to climate-change- induced extreme weather events such as floods6–10, wildfires11–13, and earthquakes14–16. Among them, floods, especially as a result of intense precipitation, are the predominant cause of weather-related disruption in the transportation sector7. Such events are particularly acute on urban road networks owing to the high proportion of impermeable surfaces that prevents fast infiltration and reduces flow resistance17. Roads naturally become preferential paths for stormwater runoff. Such floods compromise the vital functionality of road transportation networks, either directly through flood water accumulation or indirectly through physical destruction resulting in decreases in local network capacity. According to the Intergovernmental Panel on Climate Change (IPCC), the frequency of climate-change- induced extreme precipitation events is expected to increase globally18–21. Between 1900 and 2021, a total of 5,501 reported flood disasters had been recorded around the world, affecting more than three billion people (48.4% of the total number of people affected by all weather-related disasters) and claiming more than six million lives ①. In the past 30 years, the world has witnessed an alarming increase in the number of reported flood disasters, mainly driven by steady population growth and economic activities in flood-prone areas23,24. In many developing countries, the challenges associated with transport disruptions due to floods are aggravated by a lack of systematic urban planning, adequate flood control infrastructure (e.g., drainage systems), regular maintenance, technical capacity, and financial resources25. Without proactive flood risk management planning and adaptation, risks could continue to intensify as the absolute flood damage may increase up to a factor of 20 by the end of century26. When taking network complexity and cross-sector interconnectivity into consideration, such impacts will likely cascade through the networks causing system- level failures, severe delays, and prolonged socioeconomic damages. To date, many studies have investigated the impact of floods on road networks in terms of hazard exposure to historical or modeled flood events27,28, travel delay as a result of flood disruption19,29, economic cost estimation2,30, and road network resilience evaluation31,32 at local and regional scales. However, several challenges and limitations have so far prevented an analysis at a global level. First, the lack of publicly accessible high-resolution global flood maps capable of capturing flood events of varying intensities hinders a worldwide evaluation of flood hazard impacts on road transportation networks. Although the development of global flood models has been facilitated by advances in satellite data, numerical algorithms, computing ① Historical flood records are extracted from the Emergency Events Database (EM-DAT22). Four flood hazard types are included: coastal flood, flash flood, ice jam flood and riverine flood. It should be noted that the number of deaths and the number of affected people are both conservative estimations. Three entry criteria need to be fulfilled to be entered into the database: ten or more deaths, 100 or more people affected/injured/homeless, and declaration by the country of a state of emergency and/or an appeal for international assistance. For more information refer to EM-DAT data entry guidelines at https://public.emdat.be/about. To calculate the percentage of people that were affected by floods over all weather related disasters from 1900 to 2021, we extracted the number of people affected by four types of floods: 3,879,727,358 and divide by the number of people that were affected by meteorological (extreme temperature, fog, storm), hydrological (wave action, landslide, flood), and climatological disasters (wildfire, glacial lake outburst, drought): 8,015,008,050. 2 power, and coupled modeling frameworks, several limitations still exist33. Information on globally available discharge estimates, specifically, the estimation of high flows in ungauged catchments remains one of the most fundamental challenges in catchment hydrology34,35. In addition, the quality of digital elevation models, the accuracy of boundary conditions used to force inundation models, along with inadequate knowledge of river morphology have hindered the development of high-quality global flood models36,37. Second, many studies use administrative or self-defined boundaries to extract spatially embedded infrastructure networks in local and regional studies38–40. However, due to the misalignment between functional network structure41 and spatial network structure42, the aforementioned approach often cuts through critical road segments leaving out network components that many residents rely on for daily commuting. Third, the emergent risk that arises from indirect, transboundary, and system-level flood disruptions is difficult to quantify and therefore rarely investigated in past studies43. The potential indirect impacts induced by floods span the social, environmental, and economic spheres, vary across different cultural contexts, and contain uncertainties surrounding the behavioral responses of individuals and communities19. More often than not, these impacts extend beyond the context of the hazard or location, reaching interdependent or interconnected networks. In this study, we tackle the three challenges mentioned above and evaluate both direct flood hazard exposure and indirect travel disruptions of pluvial and fluvial floods on road networks in 2,564 populated settlement clusters spanning 177 countries and regions ② around the world. We spatially overlay high-resolution flood inundation maps for ten flood return periods: 5-year, 10-year, 20-year, 25-year, 50-year, 75-year, 100-year, 250-year, 500-year, and 1000-year (based on Fathom global flood models at 3 arc-seconds spatial resolution, equivalent to about 90×90 meters at the equator ③) with worldwide road networks extracted from Open Street Map (OSM) to better understand local hazard exposure. For each return period, we simulate travel trajectories between potential origins and destinations (generated with a probability-based spatial sampling approach) within each settlement cluster and record trip details such as travel time, distance and trajectory. Our study fills a gap in the current literature by providing the first global evaluation of both direct (impacts due to the physical contact with floodwater) and indirect (impacts not due to physical contact or that occur outside the inundated area in space or time such as travel disruptions and cascading failures in interconnected or interdependent infrastructures) flood hazard impact on road transportation networks. Literature Review Floods are the predominant cause of weather-related disruptions to the transport sector44. Specifically, floods reduce transportation network capacity, either directly through physical destruction rendering roads unusable or through flood water accumulation on the road surface rendering the road impassable2. These local network disruptions often cause increases in travel demand on distant road segments leading to severe traffic congestion that could later propagate to regional scales25,45,46. In the following sections, we present a review of existing literature on understanding direct flood hazard exposure and vulnerability and resilience of transportation networks to floods. Understanding exposure ② Here we used the World Bank-approved administrative boundaries (Admin 0) as reference. In sum, there are 251 countries and regions worldwide and the settlement clusters identified in our study spatially intersect with 177. ③ Fathom uses MERIT-DEM and MERIT-Hydro. 3 The United Nations Office for Disaster Risk Reduction defines exposure as “a situation of people, infrastructure, housing, production capacities and other tangible human assets located in hazard-prone areas”47. To understand infrastructure network exposure to floods, the most widely used method in the literature is spatial overlay—a geospatial approach first proposed by Ian McHarg in his landmark book Design with Nature48. Many studies in the past used this method to understand flood exposure for different asset types at national and regional scales49. For example, Narayanan et al. leveraged the flood hazard layer provided by the Federal Emergency Management Agency (FEMA) to evaluate flood exposure across five infrastructure sectors including transportation in the contiguous United States50. Jongman et al. used a similar approach to measure long-term trends and changes in hazard exposure to river and coastal flooding at the global scale23. To achieve optimal outcomes with minimum errors in measurement, explicit and high- resolution spatial data sets for infrastructure assets and well-established flood hazard zones or flood inundation maps are often required. In the past decades, increased computing power and precision of remote sensing data sets have led to the development of multiple high-resolution global flood models37,51. In addition, open-access road transportation network mapping and transportation data surveys (e.g., dual- condition General Transit Specification Survey) enable new research efforts that aim to understand direct transportation network exposure to floods across multiple temporal and spatial scales. For example, He et al. leveraged high-resolution flood maps for both pluvial and fluvial floods from Fathom and spatially overlaid on multimodal transportation network assets to evaluate flood exposure2. Understanding vulnerability and resilience Early research on evaluating the vulnerability and resilience of transportation networks focuses on network topology52. When viewing the transportation system as a network of nodes and links, the vulnerability and resilience of the transportation systems can be measured by key topological features. Metrics that are used to understand vulnerability include network efficiency53, normalized average edge betweenness54, network autocorrelation55, cascading network failure proportion56, and average shortest path length57. Metrics that are used to understand resilience include the existence of giant connected component58, redundancy and fracture coefficient59, average degree, diameter, and cyclicity60. In recent years, more and more studies turned to mathematical models, simulation models, and data-driven models, namely, demand and supply models61–63, systems dynamic models, stochastic and optimization processes64, and data-driven approaches52, to understand the vulnerability and resilience of transportation networks65. Compared with traditional topology analysis, these models can more truly reflect the changes in system performance, which has attracted the attention of an increasing number of researchers. The mathematical models along with simulation and data-driven approaches are collectively referred to as system structure-based performance analysis. They mainly consider the impact of dynamic travel supply and demand on transportation network vulnerability and resilience52. Methods To understand the impact of pluvial and fluvial floods of varying intensities on road transportation networks worldwide under multiple climate scenarios, we develop a framework with three main components: network boundary delineation and network model creation, global flood mapping, and travel simulation (Fig. 1). First, we extract the boundaries of settlement clusters around the world leveraging the global human settlement mapping effort by the European Commission. These boundaries delineate all human settlements, from hamlets and villages, to towns, cities, and metropolitan areas. The size of these clusters 4 ranges from a small number of dwellings in rural areas to conurbations comprising multiple cities. These cluster boundaries function as spatial masks for which road networks were extracted from OSM and modeled as directed graphs/digraphs (a set of vertices and a collection of directed edges that each connects an ordered pair of vertices). An evaluation of the OSM road networks in different functional hierarchies reveals high heterogeneity in the completeness of mapping. We focus on drivable road networks with higher functional hierarchy due to incomplete mapping of roads with lower hierarchy–namely residential roads and local pathways. Next, we integrate both pluvial and fluvial flood maps under 10 return periods from Fathom’s latest global flood modeling effort and overlay them on road networks to evaluate local and network-level flood hazard exposure35. We disrupt the road network based on location-specific flood inundation conditions and run travel simulations from sampled origins and destinations recording travel trajectory, travel time, and travel distance. Finally, we compare the simulation results between dry and wet (flooded) conditions and across different flood intensities (i.e., return periods) to evaluate the resilience of road transportation networks to flooding. The following sections detail our approach for network boundary delineation, road network model creation, flood mapping, and travel simulation. Fig. 1: Overall workflow diagram. This study consists of three main components: 1) delineate network boundaries leveraging global settlement dataset and generate convex hulls based on these boundaries (later used as spatial masks for extracting the road network from OSM dataset), 2) process global pluvial and fluvial flood mapping products from Fathom global flood models, and 3) simulate travel activities in dry as well as disrupted networks under 10 flood scenarios. Network boundary delineation To tackle the aforementioned challenge of defining network boundaries that capture the functional network structure, we use settlement cluster boundaries as a proxy. Since the goal of this study is to evaluate how floods of different intensities impact the movement of people on road transportation networks, choosing the settlement cluster boundaries allows us to focus on areas with relatively higher population density and travel activity. We do so in a consistent manner, thereby overcoming common challenges in comparing across urban areas with inconsistent national definitions of what constitutes a city. In this study, we extract boundaries for a total of 2,564 settlement clusters worldwide leveraging the global human settlement model grid (GHS-SMOD66) data set developed and maintained by the European Commission (Fig. 2). It provides a validated and complete representation of the spatial distribution of population with global coverage67. Specifically, it delineates and classifies 1×1 km grid cells into 8 settlement classes defined based on 5 population size and built-up area densities, thus refining the “degree of urbanization”68 method by Eurostat69. These settlement typologies include water (class 10), very low density rural (class 11), low density rural (class 12), rural cluster (class 13), suburban or peri-urban (class 21), semi-dense urban cluster (class 22), dense urban cluster (class 23), and urban center (class 30). Detailed information on the classification rules and methods is offered by the European Commission’s Joint Research Centre67. Among these classes, we exclude grid cells with “water bodies” (code 10) and “very low density” (code 11) due to extremely low population density (fewer than 50 inhabitants per 1×1 km grid cell). The extraction process yields 1,222,827 settlement boundaries of varying area and population sizes. An additional screening criterion is applied to select boundaries whose area is greater than 100 km2 which yields 4,237 settlement clusters. This initial screening process enables a better focus on medium and large settlements with more complex road networks. The 100 km2 cutoff threshold allows each settlement cluster to contain a minimum number of 100 grid cells (1×1 km), creating a sufficient sample size for the subsequent travel simulations. Among these clusters, 8 giant clusters (ranging between 47,218 km2 and 762,144 km2 in area) are excluded due to multiple considerations (Supplementary Figure 1). First, extremely large clusters prevent meaningful travel simulations. Since the spatial extent of these giant clusters spans multiple cities and, in some cases, countries, long-distance trips between origin and destination pairs will be overrepresented using the sampling approach proposed in this study. Under such cases, rail or air is considered as the main mode of transportation. Second, when portions of the road network close due to severe flood inundation and the long-distance trips can no longer be completed, travelers are more likely to cancel the trip rather than taking an alternative route that is significantly longer in travel time and distance. Potential solutions include imposing a maximum travel duration constraint which is individual-dependent. In addition, convex hulls (smallest convex polygon enclosing clusters’ boundary) are created for the remaining 4,229 clusters and they are used as masks in the road networks extraction process from the OSM data set. We choose convex hulls over the original settlement cluster boundaries to preserve critical road networks or road segments that connect peripheral locations within the settlement cluster that would have been left out otherwise (Fig. 2a). Fig. 2: Settlement cluster boundaries developed from GHS-SMOD. a. Settlement cluster boundary of the greater Phoenix metropolitan area, United States, developed from GHS-SMOD and the corresponding convex hull. The road network extracted from OSM using the convex hull as a mask is shown in grey. b. Map of the GHS-SMOD global 6 settlement layer illustrating the spatial distribution of 8 pixel classifications: water, very low density (rural), low density, rural cluster, suburban or per-urban, semi-dense urban cluster, dense urban cluster, and urban cluster. Road network model We extract road networks from the OSM data set using convex hulls created from settlement cluster boundaries as spatial masks. OSM provides a free, openly licensed, volunteer-contributed repository of geographic information with a focus on streets and roads. As of August 2021, approximately 7.9 million contributors had created this database with more than 796 million roads, coastlines, administrative boundaries, and other linear features known as “ways”70. Barrington-Leigh et al.71 assessed the completeness of OSM road network data in countries around the world as of 2017. They found that globally, OSM is 83% complete, and more than 40% of countries–including several in the developing world–have a fully mapped street network ④. However, there still exists a significant discrepancy in the completeness of road networks—countries with good internet access tend to be more complete. The completeness of the OSM road network has a U-shaped relationship with population density—smaller towns and villages with medium population density are likely to have missing roads71. In addition, past studies71–73 revealed relatively lower levels of completeness in road networks that are lower in the road hierarchy such as tertiary and residential roads. Such discrepancy will introduce selection bias which could potentially invalidate the subsequent travel simulations in this study. To address this issue, we first extract all drivable roads ⑤ from the OSM data set for all clusters at the global scale and then evaluate the relative completeness of tertiary and residential roads based on the extracted road network. For each settlement cluster, we compare road network density (total road length divided by the area of the cluster’s convex hull, unit: km/sqkm) between two types of road network: a) drivable road network excluding tertiary and residential road types and b) tertiary and residential road networks only. We evaluate the percentile rank of network density for both types among all clusters as well as the percentile ratio–the quotient of road network density percentile rank (tertiary and residential roads excluded) and its tertiary and residential network density percentile rank) (Fig. 3a). Percentile rank measures the percentage of network density values in the frequency distribution that are equal to or lower than it. For example, if a cluster’s tertiary and residential road network density is greater than 50% of the densities of all clusters, then it is at the 50th percentile, where 50 is the percentile rank. A higher percentile rank suggests higher network density relative to other settlement clusters. Percentile ratio measures the inequality between the two network types aforementioned based on the distribution of network densities. A percentile ratio of 1 suggests no difference between the percentile ranks of the two network types. A percentile ratio greater than 1 suggests that the percentile rank of road network density excluding tertiary and residential roads is higher than that of tertiary and residential roads alone. This translates to the potential of insufficient ④ It should be noted that only roads with the following tags in the OSM road database were included in the completeness evaluation study: “motorway”, “motorway_link”, “trunk”, “trunk_link”, “primary”, “primary_link”, “secondary”, “secondary_link”, “tertiary”, “residential”, “road”, “unclassified”, and “living_street”. ⑤ OSM uses a “key-value” framework for data labeling and organization. The highway key/tag is the primary tag used for any kind of street or way. To extract, download and create graphs for road networks for each settlement cluster, we use the graph module of OSMnx specifying the network type parameter as “drive_service”. The built-in query within the graph module under this specification returns all roads with the “highway” key/tag and further filters out roads with the following values: “abandoned”, “bridleway”, “bus_guideway”, “construction”, “corridor”, “cycleway”, “elevator”, “escalator”, “footway”, “path”, “pedestrian”, “planned”, “platform”, “proposed”, “raceway”, “service”, “steps”, “track”, and any roads with “no motor” specification. 7 mapping of tertiary and residential road networks. Here, we make two hypothesises: 1) settlement clusters with denser highways/motorways also have denser tertiary/residential roads and 2) strong differences in percentile rankings between the two network types, speficially lower percentile ranks for tertiary and residential roads, suggest incompleteness in the OSM road network. Our results show that approximately 44.7% of the clusters have percentile ratios greater than one, with a maximum ratio of 21.3. This suggests that the density of tertiary and residential roads for many settlement clusters is relatively lower compared to the network density of higher-level roads. Therefore, we decided to exclude tertiary and residential road types in this study due to incompleteness in the mapping of tertiary and residential roads (3.3% and 92.7% of the clusters contain no records for tertiary and residential roads respectively) as well as imbalance in network density distribution. In addition, we examine the same percentile rank patterns for clusters that belong to economies at different development stages and find that clusters that belong to developed regions (e.g., G7 ⑥ countries) have relatively higher road network densities than those that belong to emerging and less developed economies (Fig. 3c-i). Such results are aligned with the findings from Barrington-Leigh et al. and raise the issue of data bias in this study. To minimize the error introduced by this bias, we remove clusters with inadequate network coverage in addition to excluding tertiary and residential roads from extracted OSM. For each cluster, we calculate the percentage difference between the area of the convex hull created from the OSM data set and that created from the original settlement cluster boundaries. Clusters with percentage differences above the inflection point or “knee”74 are removed, resulting in 3,128 clusters (Supplementary Figure 2). Furthermore, 564 clusters (among the 3,128 clusters) have insufficient speed limit assignment and are left out in the subsequent travel simulation. Consequently, a total of 2,564 settlement clusters distributed across 177 countries are included in the subsequent travel simulation analysis. To summarize, we use the following criteria to narrow down the total number of clusters from 1,222,827 to 2,564: (1) area larger than 100 km2 (1,218,590 clusters removed), (2) not extremely large clusters (eight clusters removed), (3) sufficient network coverage within convex hull (1,101 clusters removed), and (4) complete speed limit assignment (564 clusters removed). For each of the 2,564 clusters, we create directed graphs in which road intersections are represented as nodes and road segments are represented as links. Key information about road segment geometry, road type, segment length, number of lanes, one-way restrictions, and speed assignment is embedded in the link attributes. ⑥ The G7 (Group of Seven) is an informal grouping of seven of the world’s advanced economies: Canada, France, Germany, Italy, Japan, the United Kingdom, the United States, and the European Union. 8 Fig. 3: Road network density percentile rank comparison. a. Scatter plot of tertiary and residential network density percentile rank and road network density percentile rank (tertiary and residential roads excluded). Each point represents a cluster, and it is color-coded by the percentile ratio. The points in the lower right section below the 45- degree separation line have percentile ratios above 1. Within this group, we observe a portion of the clusters (represented by red points) with a very high percentile ratio. This suggests more incompleteness in tertiary and residential roads compared with higher level roads. b. World map of 247 countries or territories color-coded by development stages, ranging from developed region to least developed region including the G7, non G7, BRIC ⑦, MIKT ⑧ and G20 ⑨ countries. c-i. Scatter plots combined with kernel density estimation plots of road network density percentile ranks for 7 development groups. Countries and regions with higher development levels (developed region: G7, developed region: non G7) have higher road network density than those with lower development levels (emerging region: G20, least developed region). ⑦ BRIC is a country grouping referring to Brazil, Russia, India, and China75. ⑧ MIKT is an acronym referring to the economies of Mexico, Indonesia, the Republic of Korea, and Turkey. ⑨ The G20 (Group of Twenty) is an intergovernmental forum comprising 19 countries and the European Union (EU). As of 2021 there are 20 members of the group: Argentina, Australia, Brazil, Canada, China, the European Union, France, Germany, India, Indonesia, Italy, Japan, Mexico, Russia, Saudi Arabia, South Africa, the Republic of Korea, Turkey, the United Kingdom, and the United States. 9 Fig. 4: Country level summary of cluster attributes. a. Global distribution of settlement cluster convex hulls and total number of settlement clusters by country. We spatially overlaid the cluster convex hulls on worldwide country boundaries and summarized the total number of clusters within each country. b. Scatter plot of cluster population and cluster convex hull area (km2). The population count for each cluster is calculated by summarizing the pixel values from the GHS-POP dataset that spatially intersect with the cluster’s convex hull. Global flood mapping Advances in numerical algorithms76, new global data sets77, and high-performance computing have enabled the development of flood hazard models at high resolution that solve hydrodynamic equations36. In recent years, many research groups and institutions have focused on developing global flood models to examine current and future flood risk at global scales under a changing climate33. To understand the exposure of road networks to floods, we use the latest high resolution (90 meters) pluvial and fluvial flood map products (in raster spatial data format) for 10 flood return periods from Fathom35. For each cluster and for every return period, we mosaic the pluvial and fluvial flood map rasters that overlap the cluster’s spatial boundary. The maximum mosaic operator is used so that the maximum inundation depth value is preserved from either the pluvial or fluvial flood model. We clip the mosaic using the cluster’s boundary as a spatial mask. Travel simulation To understand the impact of floods on the travel activities along the road transportation network, we run travel simulations between origin-destination (OD) pairs within every settlement cluster under both dry and wet conditions. For the dry condition simulations, we probabilistically sample the origin and destination location points based on the population density raster data set extracted from the latest 2015 estimate layer from the GHS-POP multitemporal population grid. This data set depicts the distribution of population expressed as the number of people per cell66. The average sampling percentage (measured as the total number of unique OD node locations divided by the total number of unique nodes in the road network) for all settlement clusters is 7.95%. We use the clusters’ spatial boundaries as spatial masks in the extraction process and apply the min-max scaler to the resulting population raster. By doing so, all headcount values from the original GHS-POP raster are transformed into the range [0, 1]. Since the cluster boundaries are defined based on settlement patterns instead of administrative boundaries such as city limits, both inter- and intra-city travels are represented in the travel simulation. In the simulation process, OD points are sampled based on the normalized population raster. Pixels with higher population count will therefore have a higher chance of housing an origin or destination point location. The exact locations of the OD points are aligned with the centroid (geometric center) of the designated pixels. The locations of these sampled OD points are often misaligned with the nodes in the graph. Therefore, we reassign the OD points to their closest 10 neighbors in the graph by calculating the haversine distance between the OD point and all other nodes in the graph. In each travel simulation run, we compute the shortest path (i.e., fastest route) using the Dijkstra’s algorithm78 (minimizing total travel time along the network) and record the travel trajectory, time, and distance of the optimal route between each OD pair. We leverage the free-flow travel speed for all road types that are currently available from the OSM data set and assign it to the road segments in the network. � ℎ During the simulation process, we calculate the average travel time = ∑=1 after the simulation run and track its change ∆= � ������ − −1 over time. When ∆ reaches a threshold =0.01s , the simulation ⑩ runs are suspended (Fig. 5b). This approach achieves a stable or highly converged solution with reasonable computational effort for large urban road networks. The mean travel time across all clusters is 18.25 min (1,095.46 s) with a maximum of 545.39 min (32,723.47 s or 9 hrs.), a minimum of 1.77 min (106 s), and 23.22 min (1,393.26 s) as the standard deviation. In general, we find that the average travel time and distance increase with population less than proportionately (Supplementary Figure 3). Specifically, when population doubles, average travel time and distance increase by a factor of 1.35 and 1.38 respectively. This is globally aligned with the key findings from Angel and Blei79 which demonstrate that when US cities double in population, travel time and distance only increase by a factor of 1.07 and 1.13 respectively. The authors explain the less than proportional increase as the result of the effects of spatial adjustments including increasing residential density, locational adjustments of residences and workplaces, and increasing commuting speeds brought about by transit system shifts on the average travel distance and time. This supports our OD sampling approach as a reasonable method to capture representative trips within settlement clusters. Initial aggregated summaries of mean travel time at the country level reveal a discrepancy between developed and developing regions: countries in less developed (Tanzania, Mozambique, Zambia, Niger, Zimbabwe) and emerging economies (China, India, Philippines, Cambodia, Indonesia) have longer mean travel time compared to those in developed regions (United States, Canada, Sweden, Finland) (Fig. 5d). The standard deviation of mean travel time summarized at the country level shows a higher dispersion of average travel time values in developing countries, especially in East Asia, Southeast Asia, and Africa (Fig. 5e). Due to the discrepancies in the total number of settlement clusters in different countries (Fig. 4), country-level result summaries are more robust in countries with more clusters and less robust in countries with few clusters (e.g., African countries). ⑩ Results from sensitivity tests on show that the threshold value of 0.1 s or below yields the most consistent (variance of average travel time between 100 runs < 1s) across 100 sampled clusters. The chosen value of 0.01 s in relatively conservative. 11 Fig. 5: Statistics of travel simulation results. a. Histogram of mean travel time for 2,564 clusters. b. The change in average travel time in the simulation process. We designed an iterative travel simulation and track mean trip travel � time � . When the marginal change in is smaller than =0.01 s, the simulation process is suspended. c-e. Country- level summaries of mean simulation steps, travel time (mean), and travel time (standard deviation). In terms of flooded condition simulations, we overlay 10 flood maps of different return periods on the dry road networks to identify road intersections (nodes) or segments (links) with flood water inundation in each scenario. The floodwater inundation depth of a road segment is determined by the maximum inundation depth of all points along the segment. We denote , (1 , 2 ) as the distance between node 1 and node 2 when traveling along road segment (, ). Define as a point on segment (, ) that satisfies the following condition (Eq.(1) and () as the inundation depth at . The inundation depth for segment (, ) is max () ∈[0,1] , (, ) = , (, ), ∈ [0,1] (1) We assume that road segments become impassable if they exceed a certain inundation depth . The National Weather Service in the United States highlights 6 in. (15 cm) of floodwater inundation as posing a threat to individuals and 12 in. (30 cm) as sufficient to sweep most cars off the road80. Pregnolato et al. studied the relationship between vehicle speed and floodwater depth for cases around the world and found that an inundation depth as low as 15 cm could render a road impassable for vehicles7. In this study, we conduct a sensitivity test by considering four threshold values for : 15 cm, 20 cm, 25 cm, and 30 cm and run travel simulations for each threshold. For all wet condition simulations, we disrupt the road network by removing road intersections or segments with inundation depth greater than the critical threshold . For road segments with an inundation depth smaller than the critical threshold , we modify the speed assignment according to the empirical relationship between inundation depth and maximum driving speed proposed by Pregnolato et al. in 20177. The relationship function of limit vehicle speed and flood water 12 depth was constructed by fitting a curve to video analysis supplemented by a range of quantitative data that has been extracted from 36 experimental, observational, and modeling studies around the world spanning four continents, making it the best available model for understanding flood impact on travel speed at the global scale. The calculated speed is the maximum acceptable velocity that ensures safe control of the vehicle given the depth of flood water. Results Indirect impacts on mobility far exceed direct infrastructure exposure We measure the direct impact of floods on the road network in terms of total road network length inundated across all settlement clusters and percent inundation per cluster. Our results show that more than 1 million kilometers of roads are exposed to greater than 1-meter floodwater inundation under the 100-year return period scenario. The exposure profile for all settlement clusters considered in this study, with respect to the length of road network inundation, consistently increases with flood return periods regardless of the inundation depth threshold (Fig. 6a). On average, 14.73% of road network is inundated under the 30 cm inundation threshold, 100-year return period scenario. In some extreme corner cases, almost all of the road network (99.04%) is inundated by flood water (1000-year return period, 15 cm inundation threshold). In addition, we measure indirect disruptions on mobility: failed routes (unable to find viable paths between OD pairs), travel delay, and travel distance increase due to road closures and speed reduction under multiple flood return periods and floodwater inundation thresholds. Our results highlight the differences between direct and indirect flood impacts on roads. The interconnected nature of road networks allows local flood disruptions to propagate through the network extending far beyond the exposure areas and inducing regional travel delays and failures. In general, the percentage of roads that are directly exposed to floodwater measured as share of road length inundated by floodwater is relatively low compared with the percentage of route failure (Fig. 6b), especially for smaller flood return periods. The average flood exposure levels under 5-year and 1000-year return periods for the 30 cm inundation threshold are 3.64% and 24.84% respectively. By contrast, the results from the travel simulations show that on average 11.58% and 65.97% of routes from trip origins to destinations fail due to flood disruption under the 5-year and 1000-year flood return periods respectively. For complete summary statistics on flood exposure and route failures under 10 flood return periods and four inundation thresholds, refer to Supplementary Table 3. 13 Fig. 6: Road network exposure to floodwater inundation. a. Total road network length exposed to floodwater under different inundation thresholds for 10 flood return periods. The lines in the plot are smoothed using B-spline interpolation with degree k=9. The raw input data can be found in Supplementary Table 2. b. Scatterplot of percentage road inundation and percentage failed routes for the 30 cm inundation threshold scenario for all 10 flood return periods. Each dot in the scatterplot represent a settlement cluster. Most dots (92.04%) fall above the 45-degree separation line which suggest that for most cases, the percentage of failed routes is greater than percentage of road inundation. Route failures are more evident in travel simulations under higher return periods than under lower return periods (Fig. 7). When comparing both the percentage of failed routes and the percentage of exposure under four different flood inundation thresholds , we observe a negative relationship between and the percentage of failed routes overall. Lower translates directly to lower resilience to floodwater inundation—under the same flood event, more road segments would be closed due to flooding. Consequently, it is less likely to find a viable route between trip origin and destination under such circumstances. 14 Fig. 7: Direct and indirect flood impact on road networks measured as percentage of flooded roads and percentage of failed routes. For 2,564 clusters, we simulate trips along the clusters’ road networks under both dry and wet conditions (the latter include 10 flood return period scenarios) and for four different critical inundation depth assumptions: 15 cm, 20 cm, 25 cm, and 30 cm. a. Box and whisker plot of percentage of failed routes for 10 flood return periods and four critical inundation depths. b. Box and whisker plot of the direct exposure of road networks to floods. For each settlement cluster, we measure the length of road segments that are exposed to flood water above the critical inundation threshold . c-d. Average percentage of failed routes and road inundation summarized at the country level (1000-year flood scenario, = 30 cm). Asymmetrical impact of floods on mobility We measure changes in travel time and travel distance under dry and wet conditions among successful trips and compare the differences between multiple flood impact scenarios (Fig. 8a). Our results reveal increasing trends for both measures. Increases in travel time and distance are experienced in all settlement clusters but with varying magnitudes. In Fig. 8, we show the distribution of travel delay and travel distance increase for different flood return periods and critical inundation depth thresholds . Scenarios with higher return periods and lower inundation depth thresholds experience longer travel times and distances. It should be noted that to compute travel delays and distance increases, we excluded trips that fail due to flooding. The inclusion of failed trips introduces bias to the measurement: the probability of failure for longer trips is higher than that for shorter trips leading to a reduction in average travel time and distance (assuming failed trips are attributed a 0 km travel distance and 0 minute travel time). Supplementary Figure 5 shows the average travel delay and distance change with complete records. It shows the distribution of negative values for both measures (travel time and distance) under the same flood impact scenarios. The uncertainty in flood impact on road networks measured as the variance of travel time and distance increase has a positive association with flood return period. Travelers, on average, experience a 5-minute delay in travel time (over an average of 18.26 minutes) and a 4-kilometer increase in travel distance (over an average of 18.53 km) across all scenarios considered in this study. There exist many extremes where the average travel delay can 15 be as long as 2.61 hrs. and the distance increases by as much as 82.26 km. It should be noted again that due to the scale of this study, we assume free-flowing traffic speeds across all regions and traffic nor congestion are considered in the simulation process. The reported travel times and travel delays provide conservative estimations. Fig. 8: Indirect flood impact measured as average travel delay (min) and travel distance increase (km). a. Distribution of average travel delay and travel distance increase for four different critical inundation depth assumptions and 10 flood return periods. These records are calculated from subtracting the cluster-wise average travel time under dry conditions from that under flooded conditions. Due to varying percentages of failed routes, the sample population based on which the average travel time and distance are calculated changes across clusters and scenarios. For scenarios with high percentages of route failures, the average travel time is calculated with a limited number of simulation records. The increasing trend in both the median and interquartile range for travel time and distance values suggests that trips with longer commute distances and times are affected more than those with shorter commute distances and times. b. Spatial distribution of average travel delay (min) for critical inundation depth =30 cm, 1000- year return period summarized at the country level. c. Spatial distribution of average travel distance increase (km) for critical inundation depth =30 cm, 1000-year return period summarized at the country level. Global mapping of the percentage failed routes aggregated to countries and regions reveals high heterogeneity and complex spatial patterns. In general, we observe a positive relationship between countries’ average percentage of failed routes and flood intensity. Flood scenarios with higher return periods are more likely to correspond to higher percentages of route failures. Countries in Central Africa (Mali and Sudan), Southeast Asia (Bangladesh, Myanmar, Thailand, the Lao People’s Democratic Republic, Cambodia, China, Vietnam, Malaysia, and the Philippines), and Latin America (Honduras, Costa Rica, Ecuador, Colombia, Venezuela, Guyana, and Suriname) have road networks that are more sensitive to flood hazard impacts. In these countries, floods of lower intensities induce more than 50% failure rates in road networks. Mali in West Africa, Latvia in Northern Europe, and Lao PDR in Southeast Asia are some of the few countries with high levels of route failures under low flood magnitudes. According to the World Bank Poverty Global Practice and Development Research Group, the average daily per capita income/consumption in both Mali and Lao PDR is below 5 USD. In fact, many countries and regions in Africa, South Asia, East Asia, Southeast Asia, and South America where the levels of failed routes are high also have high poverty rates. Several high- and medium-income countries, namely Canada, South Africa, Australia, and the United States, 16 have road networks that are relatively resilient to flood hazards. However, in the 1000-year flood scenario, more than half of the routes would be affected for most of the countries and regions around the globe (Fig. 9). Figure Fig. 10 shows the spatial distribution of the average travel delay measured in minutes for countries worldwide. Similar to the pattern that is observed for route failure levels, we observe a positive correlation between flood return period and average travel delay. Countries in Africa (Algeria, Niger, Libya, Egypt, Zambia, Malawi, Mozambique, Tanzania, and Kenya), South Asia (India), East Asia (China, Philippines, and Indonesia), and the Middle East (Lebanon, Israel, Syria, and Jordan) are more susceptible to flood hazard impact than other countries. For many developed and developing countries in the Americas, Eastern Europe, Central Asia, and Oceania, the average travel delay does not exceed 5 minutes. It should be noted that many countries in Africa, South America, East Asia, and Southeast Asia have fewer than 10 settlement clusters, which may lead to uncoverage bias. Fig. 9: Country-level percentage average of failed routes. The spatial distribution of the percentage of failed routes averaged by country for 10 flood return periods under the 30 cm critical inundation depth assumption . A complete mapping with all four critical inundation depth assumptions can be found in Supplementary Figure 4. 17 Fig. 10: Country-level travel delay in minutes. The spatial distribution of travel delay in minutes averaged by country for 10 flood return periods under the 30 cm critical inundation depth assumption . Resilience as a function of network density and flood exposure Many factors can contribute to high routing failure rates observed in the travel simulation, including network topology, flood hazard exposure patterns and the spatial distribution of travel demand. Past studies have documented the role of network topology in explaining road network resilience. Gao et al. discovered a universal resilience pattern in complex networks and suggested that network density, heterogeneity, and symmetry were the three key structural factors affecting a system’s resilience81. Specifically, high network density could enhance a system’s resilience under local or global disturbances through topological redundancy. Using the San Francisco Bay Area as a case study, Kasmalkar et al. leveraged the fix-demand incremental traffic assignment model and simulated local residents’ trips between home and work locations to measure the resilience of a road network under flooded scenarios19. They discovered that metric reach 11, a measure of network density, has high explanatory potential for understanding traffic resilience to coastal 11 Metric reach is defined as the number of unique road miles that can be covered starting from a specific road segment within a service radius82. 18 flooding. From a logical standpoint, higher road network density correlates well with network redundancy– defined as the number of behaviorally effective routes between OD pairs83. Under a disruptive event such as flooding, road networks with higher redundancy are more likely to provide alternative routes to travelers. Bruneau et al.84, De Bruijne and Van Eeten85 both consider redundancy as one of the principal features of resilient infrastructures due to their ability to resist or absorb the potential impacts brought by local and network-level disruptions. In this study, we explore a similar relationship between network density (measured as the quotient of the total road network length and the area of the bounding convex hull) and the percentage of failed routes under flood hazard impact scenarios for seven economies and 10 flood return periods (Fig. 11). Assuming a linear relationship between the percentage of failed routes (dependent variable) and network density (independent variable), we calculate the R-squared (R2) between every pair for different return periods and economy groups. Overall, the proportion of the variance in the percentage of failed routes that can be explained by road network density is 0.0824 (8.24%) at the average, 0.2055 (20.55%) as the maximum (Emerging region G20, 50-year flood), and 0.0011 (0.11%) as the minimum (Least developed region, 10- year flood) across all flood impact scenarios. However, the R2 values for emerging regions, namely BRIC and G20 as well as developing regions, are relatively higher than those for developed and least developed regions. These results suggest that the underlying relationship between failure rate and potential causal factors is complex and varies across space. Although network density metrics provide useful insights into the redundancy of road networks, there still exist topologic, structural, political, environmental, and socio- economic factors that influence the rate of routing failures. For instance, differences in geography translate to differences in the friction of movements across space, impacting the development and evolution of road networks86,87. 19 20 Fig. 11: Relationship between road network density and percentage failed routes grouped by countries and regions with different development stages. a-g. Scatter plots combined with kernel density estimation plots of road network density and percentage failed routes under five selected flood return periods (5-year, 50-year, 100-year, 500-year, and 1000-year) and categorized by economies’ development levels. The R-squared (R2) value the dependent variable– percentage failed routes and the independent variable–road network density for each subplot is labeled on the top right corner. h. World map of the distribution of 247 countries and territories color coded by their development stages. In addition, the flood exposure pattern varies across different geographies as well. When overlaying flood hazard maps with different road network topologies, the direct and indirect impacts are a function of both the infrastructure layer and the hazard layer. To account for both flood exposure patterns and network density, we perform a log-transformed linear regression of direct flood exposure percentage and network density for 10 flood return periods under the =30 cm inundation threshold (Supplementary Table 4). The results of the analysis show a positive relationship between percentage failed routes and direct flood exposure and a negative relationship between percentage failed routes and network density. Such pattern remains consistent across all 10 flood return periods considered in the analysis. Assuming a significance threshold of =0.05, both direct flood exposure percentage and network density is statistically significant (P value=0.000; Supplementary Table 4). The proportion of the variance for percentage failed routes explained by the independent variables—flood exposure and network density, increase with flood return period. As is shown in Supplementary Table 4, flood scenarios with higher return periods exhibit higher 2 values ( 2=0.677 for 1000-year flood scenario) than lower return periods ( 2=0.221 for 5-year flood scenario). Furthermore, we observe that network density and flood exposure influence network resilience in different ways. As is shown in Supplementary Table 4, the absolute values of network density coefficients decrease with flood return period. That is, the change (negative) in average percentage of failed routes decreases given a one-unit increase in network density. This suggests that road density, as an indicator of network redundancy, contributes positively to overall network resilience yet the level of contribution decreases with higher flood intensity. As flood return period increases, the absolute values of the flood exposure coefficients first increase and then decrease with the 75-year flood as the inflection point. This agrees with the exposure pattern observed in Fig. 7a and suggests the diminishing impact of flood exposure on network resilience. Discussion This study provides the first global evaluation of both direct (hazard exposure) and indirect (mobility and travel behavior) impact of flood hazards on road transportation networks. We define settlement cluster boundaries around the world based on global settlement distribution instead of administrative or self- defined boundaries. We use these urban clusters as spatial masks to extract meaningful road networks from OSM. In addition, we leverage the latest global high-resolution flood maps which detail the extent and depth of pluvial and fluvial floods for 10 return periods. Combining these data sets with exposure mapping, travel simulation, and vulnerability analysis, we are able to better understand the far-reaching impacts of floods on road network resilience to flood hazards. The impact of flood hazards on road networks in terms of both infrastructure exposure and mobility disruption (measured as the percentage of failed routes, travel delay, and travel distance increase) is heterogeneous across space. Specifically, the road networks in Africa, South Asia, East Asia, Southeast Asia, Central America, and South America are less resilient to pluvial and fluvial floods. Flood disruptions on road networks are costly for local residents and households as they give rise to longer travel times, wasted fuel, and missed work opportunities25. Compared with direct flood exposure, the indirect impact of 21 floods on mobility is more prominent and discrepant. The average share of the road network that is flooded by at least 30 cm is 3.64% (or 24.84%) under the 5-year (or 1000-year) return period–yet 11.58% (or 65.67%) of simulated trips fail in the same scenario. Past case studies on city or regional road networks proposed a positive correlation between road network resilience and graph-theoretic metrics, such as network density. Our study at the global scale, examining a total number of 2,564 road networks shows that network density helps partially understand network resilience to floods. The degree to which the variance of network resilience can be explained by network density alone varies case by case. When combining network density with flood exposure patterns, we show an increase in the overall explainability of network resilience. Furthermore, the proportion of the variance for percentage failed routes that can be explained by flood exposure and network density increases with flood return period. Nevertheless, it should be noted that the underlying governing factors that influence network resilience are inherently complex and vary across space. In locations where the political, socio- economic, environmental, and cultural conditions for road infrastructure development are complex, additional factors need to be taken into the equation to fully understand road network resilience to floods. Considering the scale of this study, we made several generalizations and assumptions when modeling the impact of floods on the mobility within settlement clusters. Due to limitations in data availability, we are unable to fully consider traffic congestion, local travel behavior patterns, or road conditions in the disruption simulation process. In addition, the exclusion of tertiary and residential road networks is able to reduce but not exclude selection bias that stems from the incompleteness of the OSM data set at the global scale. 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Data Availability GHS-SMOD global human settlement layer is available online for download by tiles or as a single file. • Download by tile: https://ghsl.jrc.ec.europa.eu/download.php?ds=smod • Download as single file: https://cidportal.jrc.ec.europa.eu/ftp/jrc- opendata/GHSL/GHS_SMOD_POP_GLOBE_R2019A/GHS_SMOD_POP2015_GLOBE_R2019 A_54009_1K/V2-0/GHS_SMOD_POP2015_GLOBE_R2019A_54009_1K_V2_0.zip GHS-POP global population multitemporal grid raster data is available online for download by tiles or as a single file. • Download by tile: https://ghsl.jrc.ec.europa.eu/download.php?ds=pop • Download as a single file: https://cidportal.jrc.ec.europa.eu/ftp/jrc- opendata/GHSL/GHS_POP_MT_GLOBE_R2019A/GHS_POP_E2015_GLOBE_R2019A_5400 9_250/V1-0/GHS_POP_E2015_GLOBE_R2019A_54009_250_V1_0.zip Code Availability The Python code used to complete the analysis and produce the figures in this study will be available in the following online repository [https://github.com/jesuslovesyiyi/global-road-network-resilience-to-floods]. 26 Acknowledgments The authors thank Nick Jones, Natalia Romero, Mersedeh Tariverdi, and Fred Pedroso for helpful feedback on a previous version of this study. Supplementary Information Supplementary Figure 1: Boundaries for top eight largest settlement clusters. There are a total of eight giant settlement cluster boundaries identified in the initial extraction process based on GHS-SMOD. The population count shown in the figure is calculated by spatially overlaying the cluster boundary on the GHS population estimate grid (in raster format with 250×250 m grid cells/pixels) for year 2015 and calculating the sum of all pixel values. Supplementary Table 1: OSM road network types. Link type OSM dataset type Description High-speed motorway A restricted access major divided highway, normally with two or (HS) highways more running lanes plus emergency hard shoulder. Highways trunk The most important roads in a country’s system that aren’t motorways. Primary roads primary The next most important roads in a country’s system (often link larger towns). Secondary secondary The next most important roads in a country’s system (often link roads towns). HS highway motorway_link The link roads (sliproads/ramps) leading to/from a motorway ramps from/to a motorway or lower class highway. Normally with the same motorway restrictions. Highway ramps trunk_link The link roads (sliproads/ramps) leading to/from a trunk road from/to a trunk road or lower class highway. Primary ramps primary_link The link roads (sliproads/ramps) leading to/from a primary road from/to a primary road or lower class highway. Secondary secondary_link The link roads (sliproads/ramps) leading to/from a secondary road ramps from/to a secondary road or lower class highway. 27 Service roads service For access roads to, or within an industrial estate, camp site, business park, car park, alleys, etc. Can be used in conjunction with service=* to indicate the type of usage and with access=* to indicate who can use it and in what circumstances. Supplementary Figure 2: Cumulative sum of number of clusters by convex hull percentage difference. The horizontal axis shows the percentage difference between the area of the convex hull created from the OSM dataset and that created from the original settlement cluster boundaries. The vertical axis shows the number of clusters whose percentage difference is the same or lower. The kneedle algorithm was implemented to find the point of maximum curvature (21% at 3128 clusters)74. 28 Supplementary Figure 3: Scatter plots of the relationships between average cluster travel times and distances with cluster sizes and population counts. Each point in the scatter plot represent a settlement cluster. We fit a power function p(x) = axb to the points (x, y) and retrieve coefficients (a, b) that minimizes the squared error. The red solid line correspond to the power fit and the grey solid line correspond to the reference function y=x. Supplementary Table 2: Total road length exposed to floodwater inundation under 10 flood return periods. The first column is floodwater inundtion depth threshold in meters. The subsequent columns store the total length of road network exposed to floodwater (unit: meters) under each inundation threshold for 10 flood return periods: 5, 10, 20, 50, 75, 100, 200, 250, 500, and 1000. 5 10 20 50 75 100 200 250 500 1000 0.1 1.02E+09 1.60E+09 2.25E+09 3.21E+09 3.58E+09 3.88E+09 4.44E+09 4.57E+09 5.09E+09 5.59E+09 0.2 6.88E+08 1.09E+09 1.56E+09 2.27E+09 2.56E+09 2.80E+09 3.27E+09 3.39E+09 3.85E+09 4.31E+09 0.3 5.36E+08 8.55E+08 1.23E+09 1.82E+09 2.07E+09 2.27E+09 2.70E+09 2.81E+09 3.23E+09 3.66E+09 0.4 4.43E+08 7.07E+08 1.02E+09 1.53E+09 1.75E+09 1.94E+09 2.33E+09 2.43E+09 2.83E+09 3.23E+09 0.5 3.81E+08 6.04E+08 8.77E+08 1.33E+09 1.53E+09 1.69E+09 2.06E+09 2.16E+09 2.53E+09 2.92E+09 0.6 3.34E+08 5.27E+08 7.66E+08 1.17E+09 1.35E+09 1.50E+09 1.84E+09 1.94E+09 2.29E+09 2.66E+09 0.7 2.97E+08 4.66E+08 6.77E+08 1.04E+09 1.21E+09 1.35E+09 1.67E+09 1.76E+09 2.10E+09 2.45E+09 29 0.8 2.69E+08 4.17E+08 6.06E+08 9.36E+08 1.09E+09 1.22E+09 1.52E+09 1.61E+09 1.93E+09 2.27E+09 0.9 2.45E+08 3.76E+08 5.45E+08 8.47E+08 9.91E+08 1.11E+09 1.40E+09 1.48E+09 1.79E+09 2.12E+09 1 2.24E+08 3.42E+08 4.94E+08 7.71E+08 9.05E+08 1.02E+09 1.28E+09 1.37E+09 1.66E+09 1.98E+09 1.1 2.06E+08 3.13E+08 4.50E+08 7.04E+08 8.29E+08 9.33E+08 1.19E+09 1.26E+09 1.55E+09 1.85E+09 1.2 1.92E+08 2.88E+08 4.12E+08 6.46E+08 7.62E+08 8.59E+08 1.10E+09 1.17E+09 1.45E+09 1.74E+09 1.3 1.79E+08 2.66E+08 3.79E+08 5.93E+08 7.02E+08 7.93E+08 1.02E+09 1.09E+09 1.35E+09 1.64E+09 1.4 1.67E+08 2.47E+08 3.50E+08 5.47E+08 6.48E+08 7.35E+08 9.51E+08 1.02E+09 1.27E+09 1.54E+09 1.5 1.57E+08 2.31E+08 3.25E+08 5.07E+08 6.01E+08 6.83E+08 8.87E+08 9.52E+08 1.19E+09 1.46E+09 1.6 1.49E+08 2.15E+08 3.02E+08 4.71E+08 5.58E+08 6.34E+08 8.29E+08 8.92E+08 1.12E+09 1.38E+09 1.7 1.42E+08 2.03E+08 2.83E+08 4.39E+08 5.21E+08 5.90E+08 7.76E+08 8.36E+08 1.05E+09 1.31E+09 1.8 1.35E+08 1.91E+08 2.65E+08 4.10E+08 4.87E+08 5.51E+08 7.27E+08 7.85E+08 9.93E+08 1.24E+09 1.9 1.28E+08 1.80E+08 2.48E+08 3.83E+08 4.55E+08 5.16E+08 6.82E+08 7.37E+08 9.38E+08 1.17E+09 2 1.23E+08 1.71E+08 2.34E+08 3.59E+08 4.27E+08 4.85E+08 6.42E+08 6.94E+08 8.88E+08 1.11E+09 2.1 1.18E+08 1.62E+08 2.21E+08 3.38E+08 4.01E+08 4.55E+08 6.04E+08 6.54E+08 8.41E+08 1.06E+09 2.2 1.13E+08 1.54E+08 2.09E+08 3.19E+08 3.78E+08 4.29E+08 5.70E+08 6.17E+08 7.96E+08 1.01E+09 2.3 1.09E+08 1.47E+08 1.98E+08 3.01E+08 3.57E+08 4.05E+08 5.39E+08 5.84E+08 7.55E+08 9.57E+08 2.4 1.06E+08 1.40E+08 1.88E+08 2.84E+08 3.37E+08 3.82E+08 5.09E+08 5.52E+08 7.16E+08 9.11E+08 2.5 1.02E+08 1.34E+08 1.79E+08 2.69E+08 3.20E+08 3.62E+08 4.82E+08 5.23E+08 6.80E+08 8.68E+08 2.6 9.90E+07 1.29E+08 1.70E+08 2.55E+08 3.03E+08 3.43E+08 4.58E+08 4.96E+08 6.46E+08 8.28E+08 2.7 9.63E+07 1.24E+08 1.63E+08 2.43E+08 2.88E+08 3.26E+08 4.35E+08 4.72E+08 6.15E+08 7.89E+08 2.8 9.34E+07 1.20E+08 1.56E+08 2.31E+08 2.73E+08 3.09E+08 4.13E+08 4.49E+08 5.86E+08 7.53E+08 2.9 9.09E+07 1.16E+08 1.49E+08 2.21E+08 2.60E+08 2.95E+08 3.94E+08 4.28E+08 5.59E+08 7.19E+08 3 8.87E+07 1.12E+08 1.43E+08 2.11E+08 2.48E+08 2.81E+08 3.75E+08 4.08E+08 5.33E+08 6.88E+08 3.1 8.67E+07 1.08E+08 1.38E+08 2.01E+08 2.36E+08 2.68E+08 3.58E+08 3.90E+08 5.09E+08 6.58E+08 3.2 8.48E+07 1.05E+08 1.33E+08 1.93E+08 2.26E+08 2.56E+08 3.42E+08 3.72E+08 4.87E+08 6.30E+08 3.3 8.28E+07 1.02E+08 1.28E+08 1.85E+08 2.17E+08 2.45E+08 3.27E+08 3.55E+08 4.66E+08 6.04E+08 3.4 8.10E+07 9.90E+07 1.23E+08 1.77E+08 2.07E+08 2.35E+08 3.13E+08 3.40E+08 4.47E+08 5.78E+08 3.5 7.95E+07 9.64E+07 1.19E+08 1.70E+08 1.99E+08 2.25E+08 3.00E+08 3.26E+08 4.29E+08 5.55E+08 3.6 7.82E+07 9.37E+07 1.15E+08 1.64E+08 1.91E+08 2.16E+08 2.88E+08 3.13E+08 4.12E+08 5.33E+08 3.7 7.69E+07 9.16E+07 1.12E+08 1.58E+08 1.84E+08 2.08E+08 2.76E+08 3.01E+08 3.95E+08 5.12E+08 3.8 7.56E+07 8.95E+07 1.09E+08 1.52E+08 1.77E+08 2.00E+08 2.65E+08 2.89E+08 3.80E+08 4.92E+08 3.9 7.45E+07 8.75E+07 1.06E+08 1.47E+08 1.71E+08 1.92E+08 2.55E+08 2.78E+08 3.65E+08 4.74E+08 4 7.32E+07 8.57E+07 1.03E+08 1.42E+08 1.65E+08 1.86E+08 2.46E+08 2.68E+08 3.52E+08 4.56E+08 4.1 7.23E+07 8.41E+07 1.00E+08 1.37E+08 1.59E+08 1.79E+08 2.37E+08 2.58E+08 3.39E+08 4.40E+08 4.2 7.14E+07 8.24E+07 9.80E+07 1.33E+08 1.54E+08 1.73E+08 2.29E+08 2.49E+08 3.27E+08 4.25E+08 4.3 7.06E+07 8.12E+07 9.58E+07 1.28E+08 1.49E+08 1.67E+08 2.21E+08 2.40E+08 3.16E+08 4.11E+08 4.4 6.98E+07 7.98E+07 9.37E+07 1.25E+08 1.44E+08 1.62E+08 2.13E+08 2.32E+08 3.05E+08 3.96E+08 4.5 6.90E+07 7.84E+07 9.18E+07 1.21E+08 1.39E+08 1.56E+08 2.06E+08 2.24E+08 2.95E+08 3.83E+08 4.6 6.85E+07 7.72E+07 8.99E+07 1.18E+08 1.35E+08 1.51E+08 1.99E+08 2.17E+08 2.85E+08 3.71E+08 4.7 6.79E+07 7.59E+07 8.81E+07 1.15E+08 1.31E+08 1.46E+08 1.92E+08 2.10E+08 2.76E+08 3.59E+08 4.8 6.74E+07 7.49E+07 8.65E+07 1.12E+08 1.27E+08 1.42E+08 1.86E+08 2.03E+08 2.67E+08 3.48E+08 4.9 6.67E+07 7.41E+07 8.48E+07 1.09E+08 1.23E+08 1.38E+08 1.80E+08 1.96E+08 2.59E+08 3.37E+08 5 6.61E+07 7.29E+07 8.34E+07 1.06E+08 1.20E+08 1.34E+08 1.75E+08 1.90E+08 2.51E+08 3.27E+08 Supplementary Table 3: Summary statistics for percentage flood exposure and percentage failed routes. Average Minimum Median Maximum Flood Average Minimum Median Maximum percentage percentage percentage percentage return percentage percentage percentage percentage failed failed failed failed period exposure exposure exposure exposure routes routes routes routes 5 3.58% 0.00% 2.40% 60.18% 11.58% 0.00% 4.64% 97.95% 10 5.60% 0.00% 3.96% 76.37% 18.03% 0.00% 8.54% 100.00% 30 20 7.98% 0.00% 6.01% 81.79% 25.42% 0.00% 14.81% 100.00% 50 11.73% 0.00% 9.21% 84.83% 36.29% 0.00% 27.27% 100.00% 75 13.35% 0.00% 10.68% 85.94% 40.98% 0.00% 34.29% 100.00% 30 100 14.73% 0.00% 11.95% 87.01% 44.83% 0.00% 40.36% 100.00% 200 17.58% 0.00% 14.40% 91.14% 51.99% 0.00% 52.31% 100.00% 250 18.35% 0.00% 15.09% 92.34% 53.83% 0.00% 54.99% 100.00% 500 21.26% 0.00% 17.75% 94.80% 60.09% 0.00% 63.79% 100.00% 1000 24.28% 0.00% 20.68% 97.96% 65.97% 0.00% 72.26% 100.00% 5 4.02% 0.00% 2.72% 61.72% 13.00% 0.00% 5.43% 98.97% 10 6.29% 0.00% 4.48% 78.00% 20.12% 0.00% 10.36% 100.00% 20 8.95% 0.00% 6.91% 82.82% 28.45% 0.00% 17.65% 100.00% 50 13.09% 0.00% 10.63% 85.82% 40.42% 0.00% 33.40% 100.00% 75 14.85% 0.00% 12.19% 87.14% 45.40% 0.00% 41.61% 100.00% 25 100 16.35% 0.00% 13.63% 87.99% 49.66% 0.00% 48.23% 100.00% 200 19.38% 0.00% 16.34% 92.83% 56.93% 0.00% 59.35% 100.00% 250 20.18% 0.00% 17.00% 93.43% 58.67% 0.00% 62.16% 100.00% 500 23.26% 0.00% 19.86% 95.81% 64.76% 0.00% 70.35% 100.00% 1000 26.43% 0.00% 22.96% 98.29% 70.64% 0.00% 77.34% 100.00% 5 4.66% 0.00% 3.28% 64.28% 15.02% 0.00% 6.76% 98.97% 10 7.30% 0.00% 5.48% 79.33% 23.06% 0.00% 12.76% 100.00% 20 10.36% 0.00% 8.28% 83.85% 32.53% 0.00% 22.39% 100.00% 50 15.06% 0.00% 12.55% 86.94% 45.84% 0.00% 41.93% 100.00% 75 17.05% 0.00% 14.44% 88.37% 51.22% 0.00% 50.87% 100.00% 20 100 18.71% 0.00% 16.01% 91.47% 55.63% 0.00% 57.63% 100.00% 200 22.00% 0.00% 19.09% 94.00% 62.91% 0.00% 68.51% 100.00% 250 22.86% 0.00% 19.87% 94.47% 64.47% 0.00% 70.35% 100.00% 500 26.14% 0.00% 23.05% 96.94% 70.71% 0.00% 78.15% 100.00% 1000 29.51% 0.00% 26.59% 98.54% 75.74% 0.00% 84.16% 100.00% 5 5.58% 0.00% 4.02% 66.19% 17.65% 0.00% 8.32% 100.00% 10 8.72% 0.00% 6.82% 80.92% 27.14% 0.00% 16.50% 100.00% 20 12.38% 0.00% 10.28% 84.83% 38.07% 0.00% 29.98% 100.00% 50 17.87% 0.00% 15.49% 88.25% 53.10% 0.00% 53.99% 100.00% 75 20.10% 0.00% 17.58% 91.91% 58.72% 0.00% 63.21% 100.00% 15 100 21.99% 0.00% 19.63% 92.97% 63.26% 0.00% 68.72% 100.00% 200 25.61% 0.00% 23.06% 95.19% 70.23% 0.00% 77.66% 100.00% 250 26.52% 0.00% 23.88% 95.57% 71.65% 0.00% 79.68% 100.00% 500 30.04% 0.00% 27.31% 97.68% 77.08% 0.00% 85.40% 100.00% 1000 33.57% 0.00% 31.18% 99.04% 81.34% 0.00% 89.26% 100.00% Supplementary Table 4: Linear regression with log-transformed data of percentage failed routes versus percent flood exposure and network density for 10 flood return periods under the =30 cm inundation threshold. R-squared 0.221 F-statistic 362.5 Adj. R-squared 0.220 Prob (F-statistic) 2.43e-139 Condition number 110 Log-Likelihood -8570.7 5-year Independent variables Coefficients Standard error t-score p-value (P>||) flood Constant -14.8727 1.884 7.893 0.000 Log percent flood exposure 0.7753 0.030 25.543 0.000 Log network density -2.0335 0.242 -8.395 0.000 R-squared 0.254 F-statistic 435.8 Adj. R-squared 0.253 Prob (F-statistic) 1.23e-163 10- Condition number 111 Log-Likelihood -7893.7 year Independent variables Coefficients Standard error t-score p-value (P>||) flood Constant 10.7672 1.450 7.427 0.000 Log percent flood exposure 0.8563 0.030 28.203 0.000 Log network density -1.3878 0.186 -7.454 0.000 R-squared 0.340 F-statistic 659.8 20- Adj. R-squared 0.340 Prob (F-statistic) 7.45e-232 year Condition number 113 Log-Likelihood -7106.9 flood Independent variables Coefficients Standard error t-score p-value (P>||) Constant 7.9570 1.070 7.436 0.000 31 Log percent flood exposure 0.9536 0.027 35.106 0.000 Log network density -0.9671 0.137 -7.052 0.000 R-squared 0.375 F-statistic 767.3 Adj. R-squared 0.374 Prob (F-statistic) 8.08e-262 50- Condition number 116 Log-Likelihood -5969.0 year Independent variables Coefficients Standard error t-score p-value (P>||) flood Constant 4.7635 0.694 6.867 0.000 Log percent flood exposure 0.9217 0.024 37.988 0.000 Log network density -0.4896 0.088 -5.546 0.000 R-squared 0.452 F-statistic 1055.0 Adj. R-squared 0.451 Prob (F-statistic) 0.00 75- Condition number 117 Log-Likelihood -5483.8 year Independent variables Coefficients Standard error t-score p-value (P>||) flood Constant 3.7319 0.575 6.491 0.000 Log percent flood exposure 0.9336 0.021 44.941 0.000 Log network density -0.3455 0.073 -4.729 0.000 R-squared 0.515 F-statistic 1358.0 Adj. R-squared 0.514 Prob (F-statistic) 0.00 100- Condition number 117 Log-Likelihood -5068.1 year Independent variables Coefficients Standard error t-score p-value (P>||) flood Constant 3.5865 0.489 7.335 0.000 Log percent flood exposure 0.9068 0.018 51.124 0.000 Log network density -0.3090 0.062 -4.976 0.000 R-squared 0.612 F-statistic 2024.0 Adj. R-squared 0.612 Prob (F-statistic) 0.00 200- Condition number 118 Log-Likelihood -44 year Independent variables Coefficients Standard error t-score p-value (P>||) flood Constant 3.0979 0.382 8.114 0.000 Log percent flood exposure 0.8699 0.014 62.739 0.000 Log network density -0.2226 0.048 -4.595 0.000 R-squared 0.613 F-statistic 2025.0 Adj. R-squared 0.612 Prob (F-statistic) 0.00 250- Condition number 118 Log-Likelihood -4425.7 year Independent variables Coefficients Standard error t-score p-value (P>||) flood Constant 3.0062 0.381 7.897 0.000 Log percent flood exposure 0.8685 0.014 62.824 0.000 Log network density -0.2091 0.048 -4.329 0.000 R-squared 0.676 F-statistic 2677.0 Adj. R-squared 0.676 Prob (F-statistic) 0.00 500- Condition number 119 Log-Likelihood -4012.2 year Independent variables Coefficients Standard error t-score p-value (P>||) flood Constant 2.8180 0.324 8.697 0.000 Log percent flood exposure 0.8508 0.012 72.394 0.000 Log network density -0.1740 0.041 -4.234 0.000 R-squared 0.677 F-statistic 2685.0 Adj. R-squared 0.677 Prob (F-statistic) 0.00 1000- Condition number 120 Log-Likelihood -3987.1 year Independent variables Coefficients Standard error t-score p-value (P>||) flood Constant 2.6101 0.321 8.133 0.000 Log percent flood exposure 0.8445 0.012 72.654 0.000 Log network density -0.1440 0.041 -3.540 0.000 32 33 Supplementary Figure 4: Percentage of failed routes averaged at country level. Supplementary Figure 5: Indirect flood impact measured as average travel delay (min) and travel distance increase (km). a. Average travel delay calculated from subtracting the cluster-wise average travel time under dry conditions from that under flooded conditions. The boxplots on the upper panel show the distribution of non-negative travel delay values under 10 flood return periods and four inundation threshold scenarios. The boxplots on the lower panel show the distribution of negative travel delay values i.e., reduction in average travel time. b. Average increase in travel distance calculated from subtracting the cluster-wise average travel distance under dry conditions from that under flooded conditions. The boxplots on the upper panel show the distribution of increases in travel distance under 10 flood return periods and four inundation threshold scenarios. The boxplots on the lower panel show the distribution of decreases in travel distance. 34