metadata: authors: 0: author: He,Yiyi
1: author: Maruyama Rentschler,Jun Erik
2: author: Avner,Paolo
3: author: Gao,Jianxi
4: author: Yue,Xiangyu
5: author: Radke,John
count: World
docna: 0: docna: Mobility and Resilience : A Global
            Assessment of Flood Impacts on Road Transportation Networks
docty: Policy Research Working Paper
abstracts: cdata!: This study provides the first global
            evaluation of both direct and indirect flood hazard impacts
            on road transportation networks. It constructs topological
            road networks for 2,564 human settlements, representing over
            14 million kilometers of urban roads. It assesses their
            exposure to pluvial and fluvial flood risks under 10
            scenarios, corresponding to different flood intensities (1:5
            year to 1:1,000 year return periods). Under each scenario,
            the study analyzes direct infrastructure exposure and
            assesses the indirect effects of flood-induced mobility
            disruptions: route failures, travel delays, and travel
            distance increases. The results document a positive
            relationship between flood return period and flood impact
            (both direct and indirect). Compared with direct flood
            hazard exposure, the indirect impact of floods on mobility
            is more prominent and heterogeneous. The average share of
            the road network that is flooded by at least 0.3 meters is
            3.64 percent (or 24.84 percent) under the 5-year (or
            1,000-year) return period, yet 11.58 percent (or 65.67
            percent) of the simulated trips fail in the same scenario.
            The results enable comparisons of exposure and vulnerability
            of road networks to flood hazards across countries, allowing
            the identification and prioritization of urban transport
            resilience measures.
display_title: Mobility and Resilience : A Global
            Assessment of Flood Impacts on Road Transportation Networks
listing_relative_url: /research/2022/05/33820434/mobility-resilience-global-assessment-flood-impacts-road-transportation-networks
topicv3: Urban Transport m1327133 788,Resilient Cities m1327412 809,Flood m1503315 3216
publishtoextweb_dt: 2022-05-17T00:00:00Z
dois: 10.1596/1813-9450-10049
origu: Off of Sr VP Dev Econ/Chief Econ (DECVP)
author_keys: 0: author_key: 1896944
1: author_key: 1217979
2: author_key: 1256219
3: author_key: NA
4: author_key: NA
5: author_key: NA
model_extractions: 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 and indirect flood hazard impacts on road transportation networks. It constructs topological road networks for 2,564 human settlements, representing over 14 million kilometers of urban roads. It assesses their exposure to pluvial and fluvial flood risks under 10 scenarios, corresponding to different flood intensities (1:5 year to 1:1,000 year return periods). Under each scenario, the study analyzes direct infrastructure exposure and assesses the indirect effects of flood-induced mobility disruptions: route failures, travel delays, and travel distance increases. The results document a positive relationship between flood return period and flood impact (both direct and indirect). Compared with direct flood hazard exposure, the indirect impact of floods on mobility is more prominent and heterogeneous. The average share of the road network that is flooded by at least 0.3 meters is 3.64 percent (or 24.84 percent) under the 5-year (or 1,000-year) return period, yet 11.58 percent (or 65.67 percent) of the simulated trips fail in the same scenario. The results enable comparisons of exposure and vulnerability of road networks to flood hazards across countries, allowing the identification and prioritization of urban transport resilience measures.

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 He**<sup>**a***</sup> **, Jun Rentschler**<sup>**b**</sup> **, Paolo Avner**<sup>**c**</sup> **, Jianxi Gao**<sup>**d**</sup> **, Xiangyu Yue**<sup>**e**</sup> **, John Radke**<sup>**a,f**</sup>

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 fuel<sup>1,2</sup> . However, climate change, rapid urbanization, coupled with increasing interdependencies among various infrastructure systems are putting road transportation networks under increasing pressure<sup>2–5</sup> . An increasing number of studies document the growing risk and vulnerability of these networks to climate-changeinduced extreme weather events such as floods<sup>6–10</sup> , wildfires<sup>11–13</sup> , and earthquakes<sup>14–16</sup> . Among them, floods, especially as a result of intense precipitation, are the predominant cause of weather-related disruption in the transportation sector<sup>7</sup> . Such events are particularly acute on urban road networks owing to the high proportion of impermeable surfaces that prevents fast infiltration and reduces flow resistance<sup>17</sup> . 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-changeinduced extreme precipitation events is expected to increase globally<sup>18–21</sup> . 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<sup>1</sup> . 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 areas<sup>23,24</sup> . 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 resources<sup>25</sup> . 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 century<sup>26</sup> . When taking network complexity and cross-sector interconnectivity into consideration, such impacts will likely cascade through the networks causing systemlevel 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 events<sup>27,28</sup> , travel delay as a result of flood disruption<sup>19,29</sup> , economic cost estimation<sup>2,30</sup> , and road network resilience evaluation<sup>31,32</sup> 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.

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power, and coupled modeling frameworks, several limitations still exist<sup>33</sup> . Information on globally available discharge estimates, specifically, the estimation of high flows in ungauged catchments remains one of the most fundamental challenges in catchment hydrology<sup>34,35</sup> . 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 models<sup>36,37</sup> . Second, many studies use administrative or self-defined boundaries to extract spatially embedded infrastructure networks in local and regional studies<sup>38–40</sup> . However, due to the misalignment between functional network structure<sup>41</sup> and spatial network structure<sup>42</sup> , 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 studies<sup>43</sup> . 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 communities<sup>19</sup> . 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<sup>2</sup> 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<sup>3</sup> ) 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 sector<sup>44</sup> . 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 impassable<sup>2</sup> . 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 scales<sup>25,45,46</sup> . 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”<sup>47</sup> . 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 Nature_<sup>48</sup> . Many studies in the past used this method to understand flood exposure for different asset types at national and regional scales<sup>49</sup> . 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 States<sup>50</sup> . 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 scale<sup>23</sup> . To achieve optimal outcomes with minimum errors in measurement, explicit and highresolution 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 models<sup>37,51</sup> . In addition, open-access road transportation network mapping and transportation data surveys (e.g., dualcondition 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 exposure<sup>2</sup> .

## **Understanding vulnerability and resilience**

Early research on evaluating the vulnerability and resilience of transportation networks focuses on network topology<sup>52</sup> . 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 efficiency<sup>53</sup> , normalized average edge betweenness<sup>54</sup> , network autocorrelation<sup>55</sup> , cascading network failure proportion<sup>56</sup> , and average shortest path length<sup>57</sup> . Metrics that are used to understand resilience include the existence of giant connected component<sup>58</sup> , redundancy and fracture coefficient<sup>59</sup> , average degree, diameter, and cyclicity<sup>60</sup> . In recent years, more and more studies turned to mathematical models, simulation models, and data-driven models, namely, demand and supply models<sup>61–63</sup> , systems dynamic models, stochastic and optimization processes<sup>64</sup> , and data-driven approaches<sup>52</sup> , to understand the vulnerability and resilience of transportation networks<sup>65</sup> . 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 resilience<sup>52</sup> .

# **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
<!-- Start of picture text --> Network boundary delineation + road network model Global flood mapping<br>| GHS global settlement dataset i | Fathom global flood model<br>: f Giant clusters -—_—_<br>Settlement Clusters {_ Normal clusters tfi Pluvial flood mapping Fluvial flood mapping i:<br>Convex hull masks OSM road network dataset | | Maximum operator<br>Extracted road networks 5-year flood 10-year flood 20-year flood --- 1000-year flood<br>Travel simulation EFaerTEOAn>wrmTHT—rvr<br>Spatial overlay<br>Baseline/dry network Disrupted network 1 Disrupted network 2 Disrupted network 3: Disrupted network n<br>Travel simulation<br><!-- End of picture text -->
<!-- Start of picture text --> a al " b Ps = pate: Re ”<br>NORTH o_o| a. PAM; aS 2.9 Aesa aN —<br>0 5 10km eo P a iene < j a O She Se<br>oo] weiy NeBs ae rely i 9 yeFES Sey}Sena GF? zyau<br>Step Me ~ EEA ee<br>BEG ~ a7 gral * ROS { AE : A) oe<br>En : yc a € , Xt i Os \ b 4 ‘Vi ds bo. a<br>oly a Phoenix Me — Pao , me? S _ " Re<br>= es Gilbert TY ben) . \ . .<br>pA L+. ol aeu J a op OSM road network \ Ocode 10—water . ” . [Bl Code 21—Suburbanid or per-urban ZA<br>SSSa~ ey +r, CCO SettlementSettlement clustercluster boundary convex hull (C1(i Code Code 11—Very 12—Low lowdensity density (rural) (rural) 1Hl Code 22—Semi-denseCode 23—Dense urbanurbanclustercluster<br>= 0 O Country boundaries GB Code 13—Rural cluster 1 Code 30—Urban center<br><!-- End of picture text -->
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”<sup>70</sup> . Barrington-Leigh et al.<sup>71</sup> 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<sup>4</sup> . 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 roads<sup>71</sup> .

In addition, past studies<sup>71–73</sup> 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<sup>5</sup> 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 50<sup>th</sup> 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.

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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<sup>6</sup> 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”<sup>74</sup> 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 km<sup>2</sup> (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.

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<!-- Start of picture text --> a WER He ., Com : Numberof clusters © TF<br>—- Se eae ale — ZA 0 mo ,<br>| .<br>‘ Se- i ]‘S . aba“aanj 11-15oer - 104 PPvanea ae<br>ey m4 “4g LS 16-25 & diphe |<br>er cl ny ‘ Wt 26-50 S gE<br>“Y yf tS ss an @@ 51-100 < » Bere Vase<br>; SS \B WB Cluster convex hull Rts Seer<br>h 5 Disputed territories “eer stad<br>\ ; . 4 Zz 10?<br>~ . 104 108 108 107<br>S : Population<br><!-- End of picture text -->
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 algorithm<sup>78</sup> (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. During the simulation process, we calculate the average travel time = ∑ after the simulation run and track its change ������ over time. When ∆ reaches a threshold nn =0.01s<sup>10</sup> , the simulation<sup>�</sup> nn ii=1 ii tt tt nn<sup>tth</sup> runs are suspended (Fig. 5b). This approach achieves a stable or highly converged solution with reasonable<sup>�</sup> nn nn−1 ∆= tt −tt εε 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 Blei<sup>79</sup> 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. εε

11
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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
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flooding. From a logical standpoint, higher road network density correlates well with network redundancy– defined as the number of behaviorally effective routes between OD pairs<sup>83</sup> . Under a disruptive event such as flooding, road networks with higher redundancy are more likely to provide alternative routes to travelers. Bruneau et al.<sup>84</sup> , De Bruijne and Van Eeten<sup>85</sup> 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 (R<sup>2</sup> ) 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, 10year flood) across all flood impact scenarios. However, the R<sup>2</sup> 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 socioeconomic 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 networks<sup>86,87</sup> .

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 (R<sup>2</sup> ) 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 cc exposure and a negative relationship between percentage failed routes and network density. Such pattern γγ 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 αα period. As is shown in Supplementary Table 4, flood scenarios with higher return periods exhibit higher values ( =0.677 for 1000-year flood scenario) than lower return periods ( =0.221 for 5-year flood scenario). Furthermore, we observe that network density and flood exposure influence network resilience RRin different ways. As is shown in Supplementary Table 4, the absolute values of network density coefficients<sup>2</sup> RR<sup>2</sup> RR<sup>2</sup> 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 selfdefined 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 opportunities<sup>25</sup> . 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, socioeconomic, 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. In locations where primary and secondary road network data is incomplete, our approach will likely overestimate the adverse impact of flood hazard on mobility.

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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/jrcopendata/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/jrcopendata/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
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|**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|
|<br>**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.

|γc|**Flood**<br>**return**<br>**period**|**Average**<br>**percentage**<br>**exposure**|**Minimum**<br>**percentage**<br>**exposure**|**Median**<br>**percentage**<br>**exposure**|**Maximum**<br>**percentage**<br>**exposure**|**Average**<br>**percentage**<br>**failed**<br>**routes**|**Minimum**<br>**percentage**<br>**failed**<br>**routes**|**Median**<br>**percentage**<br>**failed**<br>**routes**|**Maximum**<br>**percentage**<br>**failed**<br>**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%|
|<br>75|14.85%|0.00%|12.19%|87.14%|45.40%|0.00%|41.61%|100.00%|
|25<br>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%|
|<br>75|17.05%|0.00%|14.44%|88.37%|51.22%|0.00%|50.87%|100.00%|
|20<br>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%|
|<br>75|20.10%|0.00%|17.58%|91.91%|58.72%|0.00%|63.21%|100.00%|
|15<br>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. **<u>R-squared</u>** <u>0.221</u> **<u>F-statistic</u>** γγcc <u>362.5</u>

||**R-squared**|0.221|**F-statistic**||362.5|
|---|---|---|---|---|---|
||**Adj. R-squared**|0.220|**Prob (F-statistic)**||2.43e-139<br>|
|5|**Condition number**|110|**Log-Likelihood**||-8570.7<br>|
|-year<br>flood|**Independent variables**|**Coefficients**|**Standard error **|**t-score**|**p-value (P>**|t|**)**|
||Constant|-14.8727|1.884|7.893|0.000|
||Log percent flood exposure|0.7753|0.030|25.543|0.000|
||Lognetwork 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<br>|
|10-|**Condition number**|111|**Log-Likelihood**||-7893.7<br>|
|year|**Independent variables**|**Coefficients**|**Standard error**|**t-score**|**p-value (P>**|t|**)**|
|flood|Constant|10.7672|1.450|7.427|0.000|
||Log percent flood exposure|0.8563|0.030|28.203|0.000|
||Lognetwork 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<br>|
|year|**Condition number**|113|**Log-Likelihood**||-7106.9<br>|
|flood|**Independent variables**|**Coefficients**|**Standard error**|**t-score**|**p-value (P>**|t|**)**|
||Constant|7.9570|1.070|7.436|0.000|

31
||Log percent flood exposure|0.9536|0.027|35.106|0.000|
|---|---|---|---|---|---|
||<br>Lognetwork 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<br>|
|50-|**Condition number**|116|**Log-Likelihood**||-5969.0<br>|
|year|**Independent variables**|**Coefficients**|**Standard error**|**t-score**|**p-value (P>**|t|**)**|
|flood|Constant|4.7635|0.694|6.867|0.000|
||Log percent flood exposure|0.9217|0.024|37.988|0.000|
||Lognetwork 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<br>|
|75-|<br>**Condition number**|117|<br>**Log-Likelihood**||-5483.8<br>|
|year|**Independent variables**|**Coefficients**|**Standard error**|**t-score**|**p-value (P>**|t|**)**|
|flood|Constant|3.7319|0.575|6.491|0.000|
||Log percent flood exposure|0.9336|0.021|44.941|0.000|
||<br>Lognetwork 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<br>|
|100-|<br>**Condition number**|117|**Log-Likelihood**||-5068.1<br>|
|year|**Independent variables**|**Coefficients**|**Standard error **|**t-score**|**p-value (P>**|t|**)**|
|<br>flood|Constant|3.5865|0.489|7.335|0.000|
||Log percent flood exposure|0.9068|0.018|51.124|0.000|
||<br>Lognetwork 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<br>|
|200-|**Condition number**|118|**Log-Likelihood**||-44<br>|
|year|**Independent variables**|**Coefficients**|**Standard error**|**t-score**|**p-value (P>**|t|**)**|
|flood|Constant|3.0979|0.382|8.114|0.000|
||Log percent flood exposure|0.8699|0.014|62.739|0.000|
||<br>Lognetwork 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<br>|
|250-|**Condition number**|118|**Log-Likelihood**||-4425.7<br>|
|year|**Independent variables**|**Coefficients**|**Standard error**|**t-score**|**p-value (P>**|t|**)**|
|flood|Constant|3.0062|0.381|7.897|0.000|
||Log percent flood exposure|0.8685|0.014|62.824|0.000|
||Lognetwork 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<br>|
|500-|<br>**Condition number**|119|<br>**Log-Likelihood**||-4012.2<br>|
|year|**Independent variables**|**Coefficients**|**Standard error**|**t-score**|**p-value (P>**|t|**)**|
|<br>flood|Constant|2.8180|0.324|8.697|0.000|
||Log percent flood exposure|0.8508|0.012|72.394|0.000|
||<br>Lognetwork 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<br>|
|1000-|<br>**Condition number**|<br>120|<br>**Log-Likelihood**||<br>-3987.1<br>|
|year|**Independent variables**|**Coefficients**|**Standard error**|**t-score**|**p-value (P>**|t|**)**|
|flood|Constant|2.6101|0.321|8.133|0.000|
||Log percent flood exposure|0.8445|0.012|72.654|0.000|
||Lognetwork density|-0.1440|0.041|-3.540|0.000|

32
33
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