Vulnerability of California roadways to post-wildfire debris flows

Post-wildfire debris flows represent a significant hazard for transportation infrastructure. The location and intensity of post-fire debris movements are difficult to predict, and threats can persist for several years until the watershed is restored to pre-fire conditions. This situation might worsen as climate change forecasts predict increasing numbers of wildfire burned areas and extreme precipitation intensity. New insights are needed to improve understanding of how roadways are vulnerable to post-fire flows and how to prioritize protective efforts. Using California as a case study, the vulnerability of transportation infrastructure to post-fire debris flow was assessed considering geologic conditions, vegetation conditions, precipitation, fire risk, and roadway importance under current and future climate scenarios. The results showed significant but uneven statewide increases in the number of vulnerable roadways from the present to future emission scenarios. Under current climate conditions, 0.97% of roadways are highly vulnerable. In the future, the ratio of vulnerable roadways is expected to increase 1.9–2.3 times in the representative concentration pathways (RCPs) 4.5 emission scenarios, and 3.5–4.2 times in the RCP 8.5 emission scenarios. The threat of post-fire debris flow varies across the state, as precipitation changes are uneven. The vulnerability assessment is positioned to (a) identify, reinforce, and fortify highly vulnerable roadways, (b) prioritize watershed fire mitigation, and (c) guide future infrastructure site selection.


Introduction
Characterizing the vulnerability of infrastructure to climate change represents an important new frontier in theory, research, and practice. Infrastructure systems-the human-engineered structures that deliver essential and critical services, such as transportation, power, and water-are caught between design processes that largely emphasize historical weather and those that emphasize future climate uncertainty . As infrastructure managers are increasingly required to confront climate change to ensure the reliability of services into the future, new methods are needed for understanding risks, vulnerabilities and adaptation options.
Post-wildfire debris flows represent a particularly challenging problem for infrastructure. Wildfires change the soil water infiltration capacity in the burned scar. Common precipitation events (i.e. a once every 10 year storm) are capable of producing powerful floods and debris flows in the fire-burned region (Gartner et al 2008), and the threat could last years until the watershed returns to pre-fire conditions (Ice et al 2004). These post-fire debris flows represent significant hazards for transportation infrastructures where landslides, debris movement, and exacerbated water flows cut across roadways (Garfin et al 2016). For example, the 2017-2018 Thomas Fire debris flow hit Highway 101 in Santa Barbara and Ventura counties, California, after a 50 year recurrence storm triggered the event. The debris flow contributed to an inundation zone more extensive than the once in 100 years floodplain and created a 500 m-wide flow path across the highway (Kean et al 2019). Climate change in many places across California is expected to worsen wildfires and extreme precipitation (Westerling 2018, Pierce et al 2018a. Post-fire debris flow is a combined hazard from fire and rainfall, and evaluating transportation vulnerability under climate change scenarios could help stakeholders identify future hotspots. Post-fire flow hazard assessment has been under the domain of geologists for decades, and there are few efforts to estimate how such hazards translate to infrastructure vulnerability. Geophysical studies have utilized statistical models to predict post-fire debris flows based on the likelihood or magnitude of the event and the rainfall intensity threshold (Gartner et al 2008, Cannon et al 2010. These predictive models estimate debris flow risk on small watersheds up to about 30 km 2 (Gartner et al 2014) and require wildfire severity associated information, including the differenced normalized burn ratio (dNBR) and field-validated soil burn severity (Staley et al 2017), which are obtained after the fire. Although statistical models have been well-developed for post-fire debris flows, the data required for large-scale assessment (i.e. dNBR, soil burn severity, and high-resolution watersheds data) for future wildfires remains onerous .
Initial efforts to study infrastructure vulnerability to post-fire debris flow events are just emerging. For small regions such as Arizona's forested North, Fraser et al (2020) combined the empirical post-fire debris flow model (Cannon et al 2010) with a roadway network criticality assessment to estimate transportation infrastructure vulnerability. Moftakhari and AghaKouchak (2019) studied California's energy infrastructure's post-fire debris flow vulnerability. However, both studies avoided predicting the fire burned severity associated metrics required in post-fire debris flow assessment models. Fraser et al (2020) used fire threat to represent soil burned severity, while Moftakhari and AghaKouchak (2019) used fire intensity to represent the location and likelihood of debris flow.
New opportunities have emerged to characterize infrastructure post-fire debris flow vulnerability at large scales with recently developed high-resolution watershed datasets and debris flow predictions for future fire events. The high resolution NHDPlus (NHDPlus HR) dataset, built with the 10 m 3D elevation data and adjusted to reduce the uncertainties in the flat terrain, depicts the watershed morphology and water flows for the whole California state (Viger et al 2016). Staley et al (2018) combined the vegetation, watershed morphology, historical fire severity, and precipitation data to predict debris flow hazards for future wildfires.
This study advanced the method used by Fraser et al (2020) to estimate the vulnerability of transportation infrastructure for the entire state of California, using a state-of-the-art debris flow assessment model from Staley et al (2018), the high-resolution watershed dataset from NHDPlus HR (Viger et al 2016), and considering the uncertainty in climate change. The climate forecasts for future wildfire burned areas and precipitation intensities are included in a future debris flow estimation. The post-fire debris flow model is combined with design-storm intensity data for hazard estimation. High-resolution watershed data are used to carry out statewide assessments. Lastly, the resilience of the infrastructure network and individual roadway links are considered in a vulnerability assessment.

Methodology
The vulnerability assessment in this study identified critical roadway sections exposed to post-fire debris flow threats. Roadway criticality used the betweenness centrality of the transportation network to measure the importance of each link. The post-fire debris flow threat was estimated as the frequency of rainfall threshold (design-storm recurrence level) that generates the debris flow events. Downscaled climate predictions were included to assess future post-fire debris flow threats. Four future scenarios were considered to capture the uncertainty of climate change effects on post-fire debris flow threat. The selected future scenarios were defined by two greenhouse representative concentration pathways (RCPs), 4.5 and 8.5, and two General Circulation Models (GCMs), the Canadian Earth System Model (CanESM2) and the Hadley Centre Global Environment Model version 2 (HadGEM2-ES). RCP 4.5 represents a scenario in which greenhouse gas (GHG) emissions are stabilized and begin to decline in the middle of the 21st century. RCP 8.5 describes a scenario in which GHG emissions increase rapidly until the end of the century. According to the California Energy Commission, compared to other GCM models, CanESM2 is an average future while HadGEM2-ES is a 'warmer and drier' future for the state (Pierce et al 2018a).
The assessment consisted of three major parts (figure 1): (a) a current and future (climate change) post-fire debris flow threat characterization for each watershed in California; (b) a roadway criticality analysis which gave the criticality score for each link in the transportation network; and (c) watershed-level post-fire debris flow results are combined with the roadway criticality score, to identify the vulnerable locations.

Post-fire debris flow threat assessment 2.1.1. Rainfall threshold estimation
The rainfall threshold represents the precipitation value, calculated from empirical models, above which there is a high probability of debris flow (Staley et al 2017). This study adopted the state-of-art post-fire debris flow model from (Staley et al 2017) to estimate the 15 min duration rainfall threshold (TH i15 ) under current and future climate conditions as equation (1): (1) P represents the statistical likelihood of post-fire debris flow occurrence, which ranges between 0% and 100%. Staley et al (2017) pointed out that the selection of P depends on the application. A lower P value, such as 50%, can be used to estimate a more conservative TH i15 and vice versa.
X 1 , X 2 , and X 3 represent the watershed steepness, burned severity, and soil erosion characteristics in the studied watershed. X 1 is the ratio of watershed area with a medium to high burned severity and has gradients ⩾23 • . Gradients were calculated from 30 m resolution digital elevation models (U.S. Geological Survey 2017). The burned severity is derived from simulated dNBR. X 2 is the dNBR value divided by 1000. X 3 is the soil erodibility index obtained from the State Soil Geographic (STATSGO) database (Schwartz and Alexander 1995). φ f is the percentage increase of future wildfire burned area derived from the 6 km resolution localized constructed analogs (LOCA) downscaled climate estimation obtained from Cal-Adapt (2017). The projected fire burned area and rainfall intensity from 2010 to 2099 resemble the future, while the simulated 1960-2009 data represent current conditions. φ f equals zero under current climate conditions.

dNBR simulation
The dNBR (used to calculate X 1 and X 2 ) is estimated prior to fire events using the empirical model from  (equation (2)): k and λ are the shape and scale parameters of the historical dNBR fitting Weibull cumulative distribution functions (CDFs) for different vegetation types . The vegetation type and distribution information are from the LandFire EVT dataset (LANDFIRE 2018). P dsim , which is the cumulative percentile of the Weibull CDF, is the frequency of fire severity. For instance, P dsim = 0.5 represents a moderate frequency and medium fire burn severity, while P dsim = 0.9 means a less frequent but higher severity wildfire. The current fire threat map (FRAP 2017), which classifies the fire potential from very low to very high, is introduced to determine the value of P dsim . The P dsim is assumed to be 0.15 when the fire threat level is very low. Moreover, P dsim increases incrementally by 0.15 each time the fire threat goes up. There are six fire threat levels in (FRAP 2017), so the highest P dsim value is 0.90. As such, regions with high to extreme fire threats are assumed to burn with medium to high severity, while areas with low fire threats are assumed to burn at low severity.

Post-fire debris flow threat estimation
The post-fire debris flow threat considers the magnitude and frequency of the rainfall threshold by comparing the TH i15 with the local design storm intensity. The threat level is classified based on 10, 50, and 100 year design storm events. The post-fire debris flow threat is high when TH i15 is smaller than the local 10 year design storm intensity. The post-fire debris flow threat is moderate when TH i15 is between the 10 year and 50 year design storm intensity. The debris flow threat is elevated when TH i15 is between the 50 year and 100 year design storm intensity. Furthermore, the threat is low when TH i15 is larger than the 100 year design storm intensity. The post-fire debris flow threat estimation considers the climate change effects on the design storm and the rainfall threshold intensity. The threat assessment under current climate conditions uses design storm data from the National Oceanic and Atmospheric Administration (NOAA) precipitation frequency estimation service (Bonnin et al 2006). Scripps Institution of Oceanography (Pierce et al 2018b) provides 24 h duration design storm intensities under various recurrence intervals for the selected climate change scenarios. The 24 h storm projections are disaggregated into 15 min design storm intervals to get the future debris flow threat (equation (3)): where current_i15 prc is the current 15 min design storm intensity obtained from NOAA. prc represents the storm recurrence interval, such as 10, 50, and 100 year. future_i15 prc is the estimated future 15 min design storm intensity at a given recurrence interval. φ i is the percentage increase of future design storm intensity. The future design storm data is obtained from LOCA downscale estimation (Cal-Adapt 2017, Pierce et al 2018b).

Roadway criticality and vulnerability assessment
Betweenness centrality-a measure of how important each link is to a network-is used to analyze the topological connectivity of networks. Criticality of roadways can be measured in many different ways, e.g. as link capacity (Li and Ozbay 2012) or traffic delay when disruption occurs (Dowds et al 2017). But traffic data, while a useful measure of how intensively a roadway is used, does not capture dynamics related to how important a link is in the overall network (Dowds et al 2017, Yang et al 2018, Fraser et al 2020. Nor is traffic data uniformly available for remote roads that may be more at risk to post-fire debris flows. In addition, if a high traffic link is disabled and the traffic can be accommodated on nearby links at minimal to no cost, then the link should not necessarily be considered critical. Transportation resilience studies often rely on measures of betweenness centrality in order to describe network criticality (Zhang et al 2015, Kermanshah andDerrible 2016). Therefore, the roadway criticality is analyzed as betweenness centrality. Betweenness centrality is combined with the post fire debris flow risk to measure the roadway vulnerability. The betweenness centrality is estimated using the network analysis toolkit NetworkX (Hagberg et al 2020). The roadway network, including interstates, arterials, and collectors, is retrieved from OpenStreetMap (OSM 2019). In total, 94 752 km (59 220 miles) of roadways are included in the study, which is 93% of the California public road (excluding the local road) (State of California et al 2020). Roadway vulnerability considers its spatial criticality (betweenness centrality) and its post-fire debris flow threat. The highly vulnerable corridors are those with high betweenness centrality (i.e. the top 10% betweenness centrality) and high post-fire debris threat (i.e. TH i15 is smaller than a 10 year design storm intensity). As such, the identified roadways are all spatially critical to the network with many parts of the system dependent on them, and they are also vulnerable to post-fire debris flow when rainfall occurs. The location where post-fire debris flow occurs is assumed to be the roadway and stream intersections. We also assume that: (a) roadway sections with no streamflow interactions would not experience debris flow, and (b) roadways would have the same degree of risk as the catchment areas at their intersections with the streamflow. As such, while post-fire debris flow threat was calculated for each watershed where corridors passed through, roadway risk was assigned equal to the watershed's risk. The Caltrans District map (shown in figure 2) was introduced to describe risk management regions.  Figure 2 demonstrates the locations and sizes of wildfires used in validation. Based on the field validation, the historical observations offer X 1 , X 2 , and X 3 for the burned watersheds (U.S. Geological Survey 2018). The observed rainfall threshold (TH i15 (obs) ) is calculated using the observed X 1 , X 2 , X 3 , and equation (1).

Validation
The validation examines the model performance from three perspectives. The first test follows Staley et al (2018) to compare the similarity of the simulated and the observed rainfall threshold (TH i15 ) using equation (4): ∆TH i15 is sensitive to X 1 , X 2 , and X 3 , but is irrelevant to the post-fire debris flow likelihood P. The second test checks the similarity of post-fire debris threats between simulation and observation using equation (5): where N is the total number of watersheds in each previous fire burned region.N is the number of watersheds with the same simulated and observed post-fire debris flow threat. When R equals 100%, simulation and observation predict the same post-fire debris flow threat for all watersheds in the fire burned region. Lastly, the validation compared the ratio of high threat watersheds in all 35 898 validated basins between the simulations and observations. The validation process considers P values ranging from 0.1 to 0.9 to check the model sensitivity. Validation outcomes are discussed in the Results section.

Results
The results describe the post-fire debris flow threat, validation, and roadway vulnerability under current and future conditions. The current and future debris flow threat discussion and the validation focus on the  figure 3). These regions have high simulated dNBR, medium to high-level burn severity on steep slopes, high soil erosion susceptibility, and intense precipitation for common rainfall events (i.e. 10 year recurrence design storm). In the west part of Caltrans District 2, the simulated dNBR and burn severity are both high, but the soil is relatively stable. In such a case, precipitation intensity determines the debris flow susceptibility. Meanwhile, in the Mojave Desert (Caltrans Districts 8 and 9) and Central Valley (Districts 3, 6, and 10) have little fire and vegetation, and a low post-fire debris flow threat.
Most roadways passing through high post-fire debris flow threat watersheds tend to be service or recreational roads, but some crucial highways are also identified. The service roads connect cities-such as Los Angeles, San Diego, and metropolitan areas in Central Valley-with the wildland-urban interface. These highways include Interstate-5 at Redding in District 2, Interstate-80 between Colfax and Blue Canyon in District 3, and Highway 101 in Ventura and Santa Barbara counties in Caltrans Districts 5 and 7. The highly susceptible roadways identified align with the previous post-fire debris flow records, including the 2017-2018 Thomas Fire debris flow event that hit Highway 101 in Santa Barbara and Ventura counties (figure 3).

Validation
The simulated rainfall threshold (TH i15 ) has low predictive accuracy, which aligns with Staley et al (2018) findings. When ∆TH i15 is within a ±0.2 range, the TH i15(sim) is close to the observed TH i15(obs) . Only 44% of the 35 656 validated watershed has ∆TH i15 within a ±0.2 range. Group the watershed based on fires, 28 of previous wildfires have less than 50% watersheds with∆TH i15 between ±0.2 range. 2020 Ranch Fire has the highest level of accuracy as over 94% of the burned basins have their ∆TH i15 within ±0.2. The least precise simulations were associated with the 2017 Creek and Canyon fires.
Model accuracy is significantly improved by converting the rainfall threshold to a post-fire debris flow threat. The simulated post-fire debris flow threat compared favorably with the estimations from the historical wildfire regions, especially when the P value is in the lower range (figure 4). The simulated results perfectly match (R equals 100%) with the historical estimations when P = 0.1 for all 49 validated historical wildfires. The discrepancy between simulation and observed post-fire debris flow threat increases with  increasing P values. When P = 0.9, 26 wildfires have over 55% of their watersheds with the same simulated and observed post-fire debris flow threat.
Post-fire debris flow threats are overestimated when the P value is small, even though the simulation is compared favorably with the historical estimation (figure 5). The TH i15 is small when P is small according to equation (1). And a small rainfall threshold value means the precipitation event triggers the debris flow is frequent. For instance, when P = 0.1, the mean TH i15(sim) was 2.87 mm h −1 , and TH i15(obs) was 3.68 mm h −1 . The 99% of the validated watersheds have their TH i15 smaller or equal to the 10 year design storm intensity-high post-fire debris flow threat. On the contrary, when P = 0.9, the mean TH i15(sim) was 11.7 mm h −1 , and TH i15(obs) was 15 mm h −1 . The 48% of watersheds in the observation and 65% in the simulation have TH i15 smaller or equal to a 10 year design storm intensity. The discrepancies between the observation and simulations reached the maximum when P = 0.7 and started to converge when P > 0.7.
From the validation, converting the rainfall threshold to post-fire debris flow threat significantly improved the model accuracy. The post-fire debris flow threat level and accuracy are sensitive to the P value. Although the simulation has the highest accuracy when P = 0.1, the result tends to overestimate the debris flow threat. P = 0.9, selected for the rainfall threshold estimation in this study, reasonably controlled the uncertainties between the simulation and historical observations and prevented over-estimating the high-threat watersheds.

Climate unevenness and future post-fire debris flow threat
In the climate change scenarios debris flow threat is expected to increase in watersheds where either precipitation intensity or wildfire size is projected to increase. Climate change is expected to increase the total fire-burned area size and change rainfall event intensity. Downscaled climate models show the unevenness of effects across California. In some locations, precipitation and wildfire are expected to worsen, while in other places, they are expected to improve. For example, under the HadGEM2-ES RCP 8.5 scenario, climate change could lead to up to a 4600% increase in the fire burn area in the mountain forest regions of Caltrans Districts 1-3, 6, and 10 (yellow, orange, red, and maroon colors in figure 6(a)) (Westerling 2018). Climate projections estimate that most of California's design storm intensities are increasing ( figure 6(b)). The increasing debris threat from climate change is identified in the already high threat region along the mountain forest and coastal line in Caltrans Districts 1-7 and 10 ( figure 6(c)). In such regions, the future fire burn size (figure 6(a)) and the storm intensity ( figure 6(b)) are expected to increase.
The number of roadways in high post-fire debris flow threat regions will dramatically increase in the future, especially under RCP 8.5 (Deep blue color bars in figure 6(d)). About 14.7% of roadways are currently under high post-fire debris flow threat and this could increase to 17.7%-21.3% in the RCP 4.5 scenarios and 31.6%-34.5% in the RCP 8.5 scenarios. The increased risky roadways are clustered in and around currently moderate to high post-fire debris threat problematic areas (Blue to deep blue colors in figure 3). In the meantime, the ratio of low threat roadways will decrease as we move from the current climate to the future climate scenarios. Approximately 55% of roadways have a low post-fire debris threat in the current climate. The ratio of low likely debris flow threat roadways is expected to be stabilized around 51%-55% in RCP 4.5 but decrease to 35.9%-39.6% in RCP 8.5 scenarios. The post-fire debris flow threat for all climate scenarios are shown in appendix B.

Roadway vulnerability and district priority
Roadway vulnerability considers its spatial criticality and post-fire debris flow threat. The calculated roadway betweenness centrality ranges between 0 to 0.002, and interstate highway No. 5 has the highest betweenness centrality. Roadways with top 10% betweenness centrality values are considered most critical to the network (appendix C). Under current climate conditions, 0.97% of the total roadways have high post-fire debris flow threats and are highly vulnerable. Climate change is expected to increase the ratio of highly vulnerable roadways to up to 4.15%. Table 1 shows the system's number and percentage of highly vulnerable roadways. Under the RCP 4.5 scenarios, the number of highly vulnerable roadways will increase 1.9-2.3 times and could increase to 3.5-4.2 times under the RCP 8.5 scenarios.
As climate change will affect the future fire burn areas and precipitation differently, the vulnerability profile of the Caltrans districts will change. The vulnerability ranking is defined as the rank of the number of highly vulnerable roadways in each Caltrans district. In current climate condition, more than 70% of the highly vulnerable corridors are in Caltrans districts 2, 5, 7, and 11 (figure 7). In future scenarios, more vulnerable roadway hotspots are anticipated to appear in Southern California and along the West Coast. For comparison, the debris flow vulnerability ranking chart in figure 8 shows Caltrans districts based on the number of hotspots in each region. Districts 3, 9, and 10 are ranked as the least vulnerable, while districts 2 and 7 are expected to have the most perturbations in current and future scenarios. Half of the districts have vulnerability profile shifts between different climate scenarios. Districts 1 and 6 are anticipated to increase their vulnerability rankings. The debris flow threat ranking of district 8 is expected to decrease because other districts will become riskier. The changing ranking could signal a shift in the distribution of roadway impacts from post-fire flows, warranting consideration of how resources are invested between different districts.

Policy implications
This research demonstrates a method to proactively estimate transportation infrastructure post-fire debris flow threat and the system's vulnerability prior to wildfire. Both current and future climate conditions are considered when estimating watershed post-fire debris flow threat and roadway system vulnerability. Several key takeaways emerge that warrant further discussion: how to (a) identify, reinforce, and fortify highly vulnerable roadways, (b) prioritize watershed fire mitigation, and (c) assist future transportation infrastructure site selection.
Reinforcement and fortification should be targeted at highly vulnerable roadways to increase infrastructure robustness to post-fire debris flow. Currently, the estimated highly vulnerable roadways are concentrated along coastal regions in California and the west rim of the Sierra Nevada Mountains. Engineering techniques to increase roadway resilience include expanding culvert capacity, installing lateral berms, building debris flow basins, and planning extra routes to increase transportation network redundancy.
Transportation planning efforts can use the results to assist the site selection of new roadways. In the modelling, the roadway network was assumed to be static through end-of-century, and planning efforts should minimize the expansion of critical infrastructure where large debris flow hazards are estimated. The assessment under four climate models demonstrates a significant spread of vulnerability across the state. There are 2.2 times more highly vulnerable roadways in California when comparing the HadGEM2-ES RCP8.5 and CanESM2 RCP 4.5 results. Decisionmakers will need to use novel approaches to balance the costs, risks to infrastructure, and regrets of overcommitting, and can leverage emerging frameworks to do so, such as Decision making Under Deep Uncertainty, Robust Decision Making, and Safe-to-Fail (Kim et al 2019).

Limitations
The limitations come from the uncertainties embedded in the empirical debris flow risk model, network simplifications, the exclusion of non-direct hazards, and the uncertainty of future conditions. The debris flow assessment model is regressed based on historical wildfire records in Southern California and has least accuracy when implemented in Northern California . Besides, the transportation infrastructure is simplified to only consider interstates, arterials, and collectors, due to the computation challenges for calculating betweenness centrality for every roadway in California. The local roads, which account for 64% of the total California roads (State of California et al 2020), are not included in this study. The simplification of transportation infrastructures causes an overestimation of roadways criticality in the urban region. Moreover, this study only considers locations of direct physical disruptions although both direct and indirect hazards can create critical damage to the roadway system. The direct physical disturbances on transportation infrastructure from post-wildfire hazards include but are not limited to roadway washout, flash flooding, bridge scour, debris flows, culvert flood with debris, and mudslides (Valentin and Stormont 2019). There are also indirect impacts of post-fire hazards on roadway infrastructure, including the deterioration of roadway embankments and pavement foundations and, eventually, pavement and roadway damage (Vennapusa et al 2013). However, modelling of the indirect post-fire debris flow impact on roadways is still a topic under development (Vennapusa et al 2013). This study underestimates the number of vulnerable roadways by considering direct disruption exclusively. Lastly, there is no meaningful approach for forecasting future infrastructure in the long term to assess climate change scenarios. Instead of guessing the configuration of future infrastructure systems, current infrastructure was assessed against future climate to elucidate how today's infrastructure is vulnerable and how adaptation planning can be targeted.

Resilience strategies
The findings have broad implications for how California approaches the resilience of roadways to post-wildfire debris flows. As California and other communities develop strategies for preparing infrastructures for climate change, they must confront a concurrent set of challenges that affect their ability to deploy solutions . This includes limited (and possibly insufficient) funding, large uncertainty about where and how climate impacts will manifest, and limited insights into the radically changing landscape regarding how we will use transportation services in the future. These forces are emerging and appear to contradict the state-of-the-art design and operation principles of infrastructure, which remain rooted in certainty and intentionally long design lifetimes. In an uncertain future, our systems rigidity and emphasis on predictability are potentially problematic (Chester and Allenby 2018). Reconciling future conditions with current ones with an emphasis on how infrastructure is designed and operated is paramount to adapting for resilience .
Much of our engineered infrastructure is designed to control or push back the environment , and the uncertainty inherent in post-fire debris flows and climate change raises serious questions about the efficacy of this approach as we move into the future. As such, California should deploy a multi-tiered strategy to address post-fire debris flow roadway adaptation, which, in many ways, contrasts completely with the models of infrastructure design today . Hardening assets (through armouring or strengthening) have their place, most likely at the asset level, but systemic strategies that consider failure inevitable and provide alternative ways of satisfying function are also needed (Markolf et al 2018). The systemic strategies might include shifting from physical to virtual connectivity through investments in high bandwidth cybertechnologies or rapid and large-scale mode shifting as particular assets go offline, embracing agility and flexibility in how they design, operate, and govern their transportation systems (Chester and Allenby 2018). Establish processes and governance models that commit to reassessing the conditions and needs surrounding infrastructure and a willingness to change systems rapidly as the environment changes.
Upgrading roadway infrastructure across California's entirety in order to better manage future post-fire debris flows should consider the inherent complexity in the confluence of uncertainties in infrastructure design . The majority of California's infrastructure was built in the past century. Environmental sensor networks that detect, for example, precipitation events, were first deployed in the middle of the twentieth century. At this time, infrastructure design was informed by relatively limited data streams as sensor networks were still in their infancy. As such, there may have been significant uncertainty around the frequency and intensity of local events. Guidelines that specified return periods by which to design infrastructure assets (e.g. a 50 year event) may have over-or under-estimated these critical events, leading to assets that were over-and under-designed. While under-designed assets may have been corrected over the past decades, this has not been universally true, and over-designed assets also exist. Today, climate change represents an additional layer of uncertainty, in which conditions in some regions worsen and in other regions improve. The confluence of these complexities and uncertainties can be characterized by three domains that can aid decisionmakers in surgically investing limited resources . The three domains are as follows: the severe domain, the guarded domain, the elevated domain. In the severe domain, infrastructure has already experienced conditions that surpass its design. Climate change is expected to worsen the severity of this. Here, a roadway designed to withstand a low-intensity post-fire flow may experience much more intense flows, and climate change is forecast to elevate flow risk. For this reason, roadways in the severe domain should be the top priority. At the other end of the spectrum is the guarded domain where roadways were overdesigned for what they experienced. When it comes to these roadways, climate change is expected to lessen the hazard. The most difficult and troubling assets are found in the elevated domains, where the asset is experiencing conditions that contradict climate change predictions. For instance, the asset is experiencing more severe conditions than those they were designed for, and climate change is weakening the hazard. The elevated domains are problematic because they do not provide a clear picture of the asset's future robustness. Assets in these domains require new knowledge and insights to be able to make decisions regarding their future. As California looks to prepare its roadways against post-fire debris flows, taking stock of past design conditions relative to future climate becomes critically important for deciding how to prioritize investments.
Given the uncertainties of future climate, the massive investments required to adapt infrastructure, and the long lifetimes of assets, California should consider safe-to-fail strategies. Safe-to-fail is a resilience framework that calls for the impacts of failure to be internalized in the design process toward minimizing and better managing failure consequences (Kim et al 2017). Infrastructure failure under climate change may be inevitable, so planning for its eventuality is prudent. Assessment of roadway vulnerability to post-fire debris flow provides opportunities for California to identify novel ways of avoiding or compensating for such failures. Given the remoteness and low use of some post-fire flow-vulnerable roads, for example, the state may allow such roads to fail rather than investing in keeping them functional when climate strikes. However, since this will inevitably mean certain services being inaccessible, it may be prudent to identify alternatives to these services. Such graceful extensibility may be cheaper in the long term than traditional robustness-centric approaches (Woods 2015, Kim et al 2017.

Conclusion
This study developed a roadway post-fire debris flow vulnerability assessment method to evaluate California roadway vulnerability. The results show a significant increase in vulnerability levels of roadways to post-fire debris flow due to climate change impacts on fire and rainfall intensities. Adapting California's roadways to future post-fire debris flows will likely require extensive planning and novel investment strategies for the diverse conditions and needs of the state. A one-size-fits-all approach may not be prudent; what works in the Mojave Desert may be fundamentally different than what works in the forested High Sierra. Adaptation strategies should therefore embrace agility and flexibility, recognizing that diverse and rapidly changing conditions are not conducive to rigid and single-vision strategies (Chester and Allenby 2018). Preparing roadways for future post-fire debris flows will require new outlooks, innovative financing models, and possibly improved governance models that embrace agility and flexibility.

Data availability statement
The data that support the findings of this study are openly available at the following URL/DOI: Chester et al 2023.