Investing in Transportation Resilience: A Framework for Informed Choices (2021)

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

75 In 2013 the White House defined resilience as “the ability to prepare for and adapt to changing conditions and withstand and recover rapidly from disruption,” adding that “resilience includes the ability to withstand and recover from deliberate attacks, accidents, or naturally occurring threats or incidents.”1 The first formal definition of resilience was provided in 1973 and focused on the ability of a system to absorb unusual disturbances and remain func- tional.2 Over the years, many other definitions of resilience have been pro- posed in science and engineering.3,4 Likewise, the field of resilience research has diversified into several areas of study (see Box 4-1). Despite the variety of approaches, resilience research has emphasized two important features: the inclusion of the post-event recovery phase and the use of functionality— at the component and system levels—as the primary framework for analysis. Most resilience metrics used in research relate to the “functionality recovery 1 The White House. 2013. Presidential Policy Directive—Critical Infrastructure Security and Resilience. PPD-21. http://www.whitehouse.gov/the-press-office/2013/02/12/presidential- policy-directive-critical-infrastructure-security-and-resil. 2 Holling, C.S. 1973. “Resilience and Stability of Ecological Systems.” Annual Review of Ecology and Systematics 4:1–23. https://doi.org/10.1146/annurev.es.04.110173.000245. 3 Bruneau, M., S.E. Chang, R.T. Eguchi, G.C. Lee, T.D. O’Rourke, A.M. Reinhorn, M. Shinozuka, K. Tierney, W.A. Wallace, and D.V. Winterfeldt. 2003. “A Framework to Quan- titatively Assess and Enhance the Seismic Resilience of Communities.” Earthquake Spectra 19:733–752. 4 Bocchini, P., D.M. Frangopol, T. Ummenhofer, and T. Zinke. 2014. “Resilience and Sustainability of Civil Infrastructure: Toward a Unified Approach.” Journal of Infrastructure Systems 20:04014004. https://doi.org/10.1061/(ASCE)IS.1943-555X.0000177. 4 Contemporary Research on Resilience and Resilience Metrics

76 INVESTING IN TRANSPORTATION RESILIENCE BOX 4-1 Areas of Resilience Research Resilience research of the decline in functionality after disruptive events is divided into four different types of academic studies: system reliability, vulner- ability, survivability, and recoverability. Reliability—Research on reliability is useful in transportation resilience as a way to understand the occurrence of a hazard or disruptive event and the time interval between disruptions. When disruptive events are of a stochastic nature, research in reliability theory provides methods and techniques to analyze, model, and optimize system behavior.a Vulnerability—Current vulnerability research is developing approaches that describe the interaction between a disruptive event and system performance so as to quantify the degradation of specific system components and their functions.b The aim is to identify the system elements that generate the highest damage when disrupted. These elements are known as points of system vulnerability. Survivability—Survivability focuses on techniques that maintain system service continuity in the face of potential disruptive events. Research in survivability develops approaches that can help the system become robust through adapt- ability (i.e., ability to change the system so it can perform for new requirements) and flexibility (i.e., ability to adapt to a range of adverse events without having to anticipate the particular response in advance).c Although research on surviv- ability typically examines telecommunications systems, the similarities between transportation systems and telecommunication services makes the research applicable to transportation as well. Recoverability—Research in recoverability deepens understanding of the abil- ity of systems to recover after a disruptive damaging event. For example, Rose describes dynamic recoverability as related to “the speed at which an entity or system recovers from a severe shock to achieve a desired state.”d While there are many studies related to recoverability, especially in socioecological or sociotechnical resilience, most are management or lessons-learned oriented and thus generally unquantifiable. Moreover, except for the analysis presented for intermodal freight systems by a few researchers, there is a void in research related to the stochastic behavior of recovery in general networked systems.e

CONTEMPORARY RESEARCH ON RESILIENCE AND RESILIENCE METRICS 77 a Elsayed, E.A. 2012. Reliability Engineering. Hoboken, New Jersey: John Wiley & Sons. b Crucitti, P., V. Latorak, W. Ebeling, and B. Spagnolo. 2005. “Locating Critical Lines in High-Voltage Electric Power Grids.” Fluctuation and Noise Letters 5(2):L201–L208. https://doi.org/10.1142/S0219477505002562; Zhang, S., D. Caragea, and X. Ou. 2011. “An Empirical Study on Using the National Vulnerability Database to Predict Software Vul- nerabilities.” Database and Expert Systems Applications 6860. https://link.springer.com/ chapter/10.1007/978-3-642-23088-2_15; Nagurney, A., and Q. Qiang. 2008. “An Efficiency Measure for Dynamic Networks Modeled as Evolutionary Variational Inequalities with Appli- cation to the Internet and Vulnerability Analysis.” Netnomics 9:1–20. https://doi.org/10.1007/ s11066-008-9008-z; Zio, E., G. Sansavini, R. Maja, and G. Marchionni. 2008. “An Analytical Approach to the Safety of Road Networks.” International Journal of Reliability, Quality and Safety Engineering 15(1):67–76. https://www.worldscientific.com/doi/abs/10.1142/ s0218539308002939. c Westmark, V.R. 2004. “A Definition for Information System Survivability.” Proceedings of the 37th Annual Hawaii International Conference on System Sciences, 2004. https://doi. org/10.1109/HICSS.2004.1265710. d Rose, A. 2007. “Economic Resilience to Natural and Man-Made Disasters: Multi- Disciplinary Origins and Contextual Dimensions.” Environmental Hazards 7(4):383–398. https://doi.org/10.1016/j.envhaz.2007.10.001. e Nair, R., H. Avetisyan, and E. Miller-Hooks. 2010. “Resilience Framework for Ports and Other Intermodal Components.” Transportation Research Record 2166(1):54–65. https:// doi.org/10.3141/2166-07; Ta, C., A.V. Goodchild, and K. Pitera. 2009. “Structuring a Defini- tion of Resilience for the Freight Transportation System.” Transportation Research Record 2097(1):19–25. https://doi.org/10.3141/2097-03; Pant, R., K. Barker, F. Grant, and T. Landers. 2011. “Interdependent Impacts of Inoperability at Multi-Modal Transportation Container Terminals.” Transportation Research Part E: Logistics and Transportation Review 47:722–737. https://doi.org/10.1016/j.tre.2011.02.009. Sy st em F un ct io na lit y, F( t) 100% 75% 50% 25% 0% Time to te td tf Reliability Vulnerability & survivability Recoverability Stable recovered system state Disruptive event Disrupted state

78 INVESTING IN TRANSPORTATION RESILIENCE curve,” which describes the evolution of functionality (or performance or level of service) over time after a disruptive event.5 The approach to resilience presented in this chapter builds on research into safety, reliability, and risk. Metrics related to safety and reliability account for the hazard and the probability of a component/system falling below a performance threshold, and risk-based metrics consider the conse- quences associated with performance failures. Resilience-related metrics are used to examine when and how a system can maintain or regain its ability to function after a disruptive event and account for a system’s inherent coping capacity and adaptability. Figure 4-1 describes this approach, con- necting safety and reliability, risk, and resilience. The research literature reviewed here uses functionality recovery curves and their associated metrics to measure resilience. Although resilience met- rics based on functionality recovery curves are not yet in common practice and more research is needed in some areas, the foundational concepts represented by functionality recovery curves and their metrics are useful for framing the analysis of transportation’s resilience to natural hazards. In addition, the metrics required by functionality recovery curves will often be useful to conduct the analysis outlined in the framework presented in Chapter 5. This chapter begins with an introduction to functionality recovery curves and how they are used to measure resilience. To apply functional- ity recovery curves to transportation, the chapter provides an overview of fragility curves and transportation-specific functionality metrics. The results of a comprehensive review of functionality metrics for the surface, air, and water modes are provided in Table 4-2 at the end of the chapter. Because the analysis of natural hazards requires methods to deal with uncertainty, the chapter also covers probabilistic approaches to functionality recovery curves and resilience metrics. The chapter concludes with research on tools that are useful for analyzing investments that are intended to increase the resilience of transportation systems. 5 Sun, W., P. Bocchini, and B.D. Davison. 2020. “Resilience Metrics and Measurement Methods for Transportation Infrastructure: The State of the Art.” Sustainable and Resilient Infrastructure 5:168–199. https://doi.org/10.1080/23789689.2018.1448663.

CONTEMPORARY RESEARCH ON RESILIENCE AND RESILIENCE METRICS 79 FIGURE 4-1 Relationship among safety and reliability, risk, and resilience.6 FUNCTIONALITY RECOVERY CURVES The resilience of a transportation system is related to its functionality during and after a harmful event. A common way to illustrate a system’s resilience is to represent its functionality (or performance or level of service) over time with a functionality recovery curve. Functionality recovery curves can be ap- plied to almost any system and any disruption. For an electric utility after a hurricane, functionality could be measured as a percentage of power demand satisfied over time. For a school district during a pandemic, functionality could be measured as the number of student-hours delivered over time. To apply functionality recovery curves to transportation, the analyst must first select the metrics that best describe the important functions of the system under study. For a given transportation system, multiple metrics may be required to fully describe its services. For example, the carried and crossed traffic flow capacities of a bridge are two different metrics that can evolve differently over time, generating two different functionality recovery curves. For a transportation network, some metrics focus on the traffic flow capacity (e.g., traffic volumes or tons of freight moved per time period) and others capture the degree of connectedness (e.g., number or types of places connected).7,8 Therefore, when performing a resilience assessment, multiple functionality recovery curves may be needed, each capturing dif- ferent aspects of the system functionality and each generating a different value of the resilience metric associated with performance during the event and recovery. 6 Bocchini, P. 2021. “Regional-Level Approach to Resilience Assessment.” NIST (National Institute of Standards and Technology) Center of Excellence Seminar Series, Colorado State University, March 25. http://resilience.colostate.edu/seminar/Paolo-Bocchini%202.mp4. 7 Faturechi, R., and E. Miller-Hooks. 2015. “Measuring the Performance of Transporta- tion Infrastructure Systems in Disasters: A Comprehensive Review.” Journal of Infrastructure Systems 21(1):04014025. https://doi.org/10.1061/(ASCE)IS.1943-555X.0000212. 8 Zhang, X., E. Miller-Hooks, and K. Denny. 2015. “Assessing the Role of Network Topology in Resilience of Transportation Systems.” Journal of Transport Geography 46:35–45.

80 INVESTING IN TRANSPORTATION RESILIENCE FIGURE 4-2 General functionality recovery curve. Figure 4-2 presents an example of a functionality recovery curve, where time (t)—typically measured starting from the occurrence of the first dis- ruption—is represented in the horizontal axis, and a metric representing the functionality of the component/system under study, F(t), is presented in the vertical axis. When the system is disrupted, the system’s functionality shifts from its original state, S0, to a disrupted state, Sd. Functionality re- mains in its disrupted state for a period of time until recovery activity begins. Eventually, recovery activity yields a stable system state, Sf. The stable, recovered system state may not be at the same level of functionality as the original state. For instance, in Figure 4-2, functionality after recovery is flat at a level that is worse than its performance before the disruptive event. However, in recent years there has been a strong push to leverage the post-disaster recovery and reconstruction period to build more resilient and better performing systems. The United Nations has formally promoted this approach since 2015 in its Sendai Framework for Disaster Risk Reduction under the “Build Back Better” motto.9 In Figure 4-2, there are four notable time points on the horizontal axis of the functionality recovery curve: the time when the disruptive event starts (te), the time when the maximum disrupted functionality first occurs (td), the time recovery activity commences (ts), and the time of achieving the stable, recovered state (tf). When the impact on functionality is nearly 9 United Nations. 2015. Sendai Framework for Disaster Risk Reduction 2015–2030. https:// www.undrr.org/publication/sendai-framework-disaster-risk-reduction-2015-2030. Sy st em F un ct io na lit y, F( t) 100% 75% 50% 25% 0% Time to te ts tf th Original system state, So Disrupted state, Sd Stable recovered system state, Sf Disruptive event Recovery activity Figure 1

CONTEMPORARY RESEARCH ON RESILIENCE AND RESILIENCE METRICS 81 instantaneous, like earthquakes, te and td occur nearly simultaneously. For events such as hurricanes or wildfires, however, the loss of functionality may occur more gradually over an interval of time. Figure 4-2 illustrates the gradual loss of functionality with a decreasing curve from the time of the event to the time when the maximum disrupted functionality, (td), first occurs.10 Finally, th represents the extent of the time horizon of the analysis, which is set by the analyst and used to standardize some popular resilience metrics.11,12,13 During the recovery process, improvements in functionality may hap- pen in fits and starts and functionality may even temporarily worsen. For example, a partially functioning bridge may need to be closed for repairs. In addition, recent studies have challenged the practice of setting the pre- event functionality level at 100%. Instead, pre-event functionality varies. Functionality as designed or built (at t0) is set to 100% and then decreases (or jumps around) due to aging, deterioration, demand, environmental factors (including climate change stressors), maintenance, and other dis- ruptions. Thus, the functionality at the time of the event may be less than 100%. Figure 4-3 illustrates both pre-event deterioration of functionality and nonlinear recovery.14 Performance at the system level is usually the most important re- sult for resilience planning and society. A system-level performance model uses the functionality recovery curves of individual components to calculate the functionality recovery curve for the system.15 Functionality recovery curves can take many shapes. For complex systems, such as a transit system, 10 Henry, D., and J.E. Ramirez-Marquez. 2012. “Generic Metrics and Quantitative Ap- proaches for System Resilience as a Function of Time.” Reliability Engineering and System Safety 99(1):114–122. 11 Reed, D.A., K.C. Kapur, and R.D. Christie. 2009. “Methodology for Assessing the Resil- ience of Networked Infrastructure.” IEEE Systems Journal 3:174–180. https://doi.org/10.1109/ JSYST.2009.2017396. 12 Frangopol, D.M., and P. Bocchini. 2011. “Resilience as Optimization Criterion for the Rehabilitation of Bridges Belonging to a Transportation Network Subject to Earthquake.” In Proceedings of the 2011 Structures Congress (D. Ames, T.L. Droessler, and M. Hoit, eds.). Las Vegas, Nevada: ASCE. April 14–16, pp. 2044–2055. https://doi.org/10.1061/41171(401)178. 13 Faturechi, R., and E. Miller-Hooks. 2014. “Mathematical Framework for Quantifying and Optimizing Protective Actions for Civil Infrastructure Systems.” Computer-Aided Civil and Infrastructure Engineering Systems: Special Issue on Sustainability and Resilience of Spatially Distributed Civil Infrastructure Systems 29:572–589. 14 Levenberg, E., E. Miller-Hooks, A. Asadabadi and R. Faturechi. 2016. “Resilience of Net- worked Infrastructure with Evolving Component Conditions.” ASCE Journal of Computing in Civil Engineering 31(3). https://doi.org/10.1061/(ASCE)CP.1943-5487.0000629. 15 Karamlou, A., and P. Bocchini. 2017. “From Component Damage to System-Level Proba- bilistic Restoration Functions for a Damaged Bridge.” Journal of Infrastructure Systems 23(3). https://doi.org/10.1061/(ASCE)IS.1943-555X.0000342.

82 INVESTING IN TRANSPORTATION RESILIENCE FIGURE 4-3 Resilience curve illustrating non-uniform, pre-event system perfor- mance due to component deterioration and maintenance actions and nonlinear recovery phase. they tend to be continuous curves,16 which can be modeled analytically17 or through experimental observations and post-event measurements. For individual components, a functionality measure may only have a small set of discrete values (e.g., number of open lanes in a bridge) or be binary (e.g., a traffic light is working or not working).18 RESILIENCE METRICS BASED ON FUNCTIONALITY RECOVERY CURVES Because functionality recovery curves condense information about the resil- ience of a system, they can be applied to a wide range of assets, systems, and types of disruptions. Although the measures of functionality need to be 16 Continuity is due to the fact that complex systems typically have a large set of possible functionality levels, so recovery curves tend to vary in a gradual way. For instance, the total travel time over a rush hour is affected by a multitude of factors, and each road closure/opening has a tiny impact on it. A simple system, instead, has a much simpler set of possible states (often only two—functional or not), so the functionality curve shifts from one state to the other. For in- stance, a small, single lane bridge is either closed or open, so the functionality shifts from 0 to 1. 17 Decò, A., P. Bocchini, and D.M. Frangopol. 2013. “A Probabilistic Approach for the Prediction of Seismic Resilience of Bridges.” Earthquake Engineering and Structural Dynamics 42(10):1469–1487. https://doi.org/10.1002/eqe.2282. 18 Padgett, J.E., and R. DesRoches. 2007. “Bridge Functionality Relationships for Improved Seismic Risk Assessment of Transportation Networks.” Earthquake Spectra 23:115–130. th Sy st em F un ct io na lit y, F( t) 100% 75% 50% 25% 0% Time to te td ts tf Wear-and-tear and maintenance Disrupted state Disruptive event Recoveryphase Figure 3

CONTEMPORARY RESEARCH ON RESILIENCE AND RESILIENCE METRICS 83 specific for each system, the associated resilience metrics can be defined in a general way and are said to be “event agnostic” and “system (or mode) ag- nostic.” It is important to stress again that functionality metrics need to be specific to the area being studied, the mode of transportation, and in some cases even the hazard scenario. When appropriate, multiple functionality metrics may be needed to capture the performance of an asset/system. On the other hand, the resilience metrics discussed in this section are general enough to be applicable to virtually any asset, system, region, mode of transportation, and hazard. Resilience Index A commonly used resilience metric is called the “resilience index,” Fmean, and it is simply the mean value of functionality during the time horizon of analysis, which starts with the beginning of the perturbative event at te and lasts to a time th defined by the analyst in such a way as to include the recovery phase.19 The resilience index can be also seen as the normalized (over time) area under the functionality recovery curve (see Figure 4-4). The resilience index has the advantage of being easy to assess and interpret, while also capturing different aspects of resilience. For example, a system will have a high resilience index if it is capable of preserving a high level of functionality after the disruptive event. Similarly, the resilience index is high if a system suffers a substantial functionality loss but recovers very quickly. Resilience Triangle The “resilience triangle” measures the total loss of functionality from the time of the event to the end of the recovery process. Bruneau and colleagues defined “robustness” as the amount of residual functionality after the initial drop, “rapidity” as the average slope of the functionality recovery curve during the recovery phase, and the “resilience triangle” (see Figure 4-5) as the area over the recovery curve that is representative of the loss of functionality.20 19 Reed, D.A., K.C. Kapur, and R.D. Christie. 2009. “Methodology for Assessing the Resil- ience of Networked Infrastructure.” IEEE Systems Journal 3:174–180. https://doi.org/10.1109/ JSYST.2009.2017396. 20 Bruneau, M., S.E. Chang, R.T. Eguchi, G.C. Lee, T.D. O’Rourke, A.M. Reinhorn, M. Shinozuka, K. Tierney, W.A. Wallace, and D.V. Winterfeldt. 2003. “A Framework to Quan- titatively Assess and Enhance the Seismic Resilience of Communities.” Earthquake Spectra 19:733–752.

84 INVESTING IN TRANSPORTATION RESILIENCE FIGURE 4-4 Representation of resilience index as the normalized area under the functionality recovery curve. FIGURE 4-5 Illustration of the concept of “resilience triangle.” th Sy st em F un ct io na lit y, F( t) 100% 75% 50% 25% 0% Time te Fmean F(t)th te te th = – 1 Recovery activity Disruptive event ∫ ADDITIONAL Figure th Sy st em F un ct io na lit y, F( t) 100% 75% 50% 25% 0% Time te “Resilience triangle” ADDITIONAL2 Figure (7B?)

CONTEMPORARY RESEARCH ON RESILIENCE AND RESILIENCE METRICS 85 FIGURE 4-6 Example of a functionality recovery curve that includes the resilience metrics “minimum level of functionality” (Fmin), “level of functionality restored at the end of the recovery process” (Ff), and “time to reach a target level of function- ality” (Ftarget). Other Functionality-Based Metrics There are additional resilience metrics that represent variations on function- ality. For example, the minimum level of functionality at any time during the recovery, Fmin, is a useful metric for analyzing the worst-case scenario (see Figure 4-6). Similarly, the level of functionality restored at the end of the recovery process, Ff, can be used to represent the degree of reparability of the system and, indirectly, the resourcefulness of the operator. Time to Complete Recovery An even simpler metric is the “time to complete recovery.” While this metric is appealing because of its simplicity, it conveys only limited information about the severity of the loss of functionality and the path to recovery. Moreover, for systems that never recover to 100% of their pre-event func- tionality, the metric would remain undefined. It is also important to dif- ferentiate between public recovery (i.e., when services are partially or fully restored) and full recovery (i.e., when the systems are restored to their origi- nal functionality or enhanced). While public recovery can be accomplished within days, weeks, or months, full recovery often entails longer terms. Sy st em F un ct io na lit y, F( t) 100% 75% 50% 25% 0% Time to te td tf tht75ts Fmin Ftarget = 75% Ff Figure 5

86 INVESTING IN TRANSPORTATION RESILIENCE Time to Reach a Target Level of Functionality Metrics for “time to reach a target level of functionality” report the time to reach a level of functionality that is less than 100% but still an impor- tant threshold. In Figure 4-6, the target functionality, Ftarget, is 75%, and t75 corresponds to the point in time when recovery activities have restored functionality to 75%. In addition to being useful in cases where recovery never reaches 100% of pre-event functionality, this type of metric can be particularly relevant to disaster management planning and reporting. For example, the San Francisco Planning and Urban Research As- sociation (SPUR) introduced and popularized the concept of “resilience tables” that use time to target functionality metrics. In Table 4-1, each row of the resilience table lists a community facility, type of infrastructure, or critical system and a target level of functionality (e.g., 90% of roads and highways). The columns represent time, and the resulting matrix identifies both the official goal of local disaster response planning (shaded areas) and SPUR’s assessment of current recovery time (marked “X”).21 More generally, this metric is useful for analyzing gaps between the desired time to reach a target level of functionality set by policy makers and the estimate produced by engineers and planners of the most likely time to reach the target. The discrepancy between the desired and the most likely times can be used to assess which assets or locations are most in need of mitigation actions. This gap analysis has been used in numerous resilience assessments done by state and local governments.22,23,24 Metrics for Recovery Activities Functionality recovery curves can also be used to analyze the impact of actions designed to increase resilience. The curves can assess actions to be taken before or during an event and during the recovery activity phase. In Figure 4-7, the dotted line at the bottom illustrates the baseline resilience 21 Poland, C.D. 2009. The Resilient City: Defining What San Francisco Needs from Its Seismic Mitigation Policies. San Francisco, CA: San Francisco Planning and Urban Research Association. 22 Oregon Seismic Safety Policy Advisory Commission. 2013. Oregon Resilience Plan. https://www.oregon.gov/oem/documents/oregon_resilience_plan_final.pdf. 23 Washington State Emergency Management Council: Seismic Safety Committee. 2012. Resil- ient Washington State—A Framework for Minimizing Loss and Improving Statewide Recovery After an Earthquake. https://mil.wa.gov/asset/5bac1790e2d29#:~:text=THE%20RESILIENT%20 WASHINGTON%20STATE%20INITIATIVE,-This%20report%20is&text=The%20initiative %20was%20spearheaded%20by,before%20the%20next%20damaging%20event. 24 NIST (National Institute of Standards and Technology). 2016. Community Resilience Planning Guide for Buildings and Infrastructure Systems. https://nvlpubs.nist.gov/nistpubs/ SpecialPublications/NIST.SP.1190v2.pdf.

CONTEMPORARY RESEARCH ON RESILIENCE AND RESILIENCE METRICS 87 TABLE 4-1 SPUR Model of Measuring Recovery from Earthquakes25 made up of the inherent coping capacity of the asset (or system) and base- line recovery response activities. The three top curves indicate the changes to functionality recovery from adding redundancy, retrofitting to reduce the 25 Poland, C. 2009. “Defining Resilience: What San Francisco Needs from Its Seismic Mitiga- tion Policies.” The Urbanist 479. https://www.spur.org/publications/spur-report/2009-02-01/ defining-resilience.

88 INVESTING IN TRANSPORTATION RESILIENCE FIGURE 4-7 Illustration of the contribution to resilience from different actions: retrofitting, adding redundancy, providing effective recovery response, and increas- ing the resources available for recovery activities.26 vulnerability of components or assets, and increasing the resources avail- able for recovery response activities. MODELS INCORPORATING UNCERTAINTY The metrics discussed in the previous section are deterministic—they do not account for randomness. Because uncertainty is a significant part of natural hazard analysis and resilience assessments, analysis approaches and metrics have been developed that address these uncertainties. Significant uncertainties for measuring resilience are (1) what hazards will strike the assets in the future and (2) how the assets will respond. The first will gradually be reduced as the future climate reveals itself over time and as climate prediction models continue to improve. The second—the un- certainty in the performance of infrastructure systems—will be reduced with research on system performance in the face of hazards, including learning from natural experiments as we observe the performance of real systems in the face of natural hazards. Relevant current approaches are presented here. 26 Adapted from Faturechi, R., and E. Miller-Hooks. 2014. “Mathematical Framework for Quantifying and Optimizing Protective Actions for Civil Infrastructure Systems.” Computer- Aided Civil and Infrastructure Engineering Systems: Special Issue on Sustainability and Resil- ience of Spatially Distributed Civil Infrastructure Systems 29:572–589. Sy st em F un ct io na lit y, F( t) 100% 75% 50% 25% 0% Time to te tfts Resource availability Retrofit Adding redundancy Response Inherent coping capacity Figure 6

CONTEMPORARY RESEARCH ON RESILIENCE AND RESILIENCE METRICS 89 Probabilistic hazard analysis is the science that studies the exposure of a region to hazards and assesses the probability of hazard events occurring and of reaching a certain level of intensity at each site.27,28,29 For transpor- tation systems, it is important to know both the probability of exceeding a certain intensity level at each site and the probability of having a certain intensity occur simultaneously at various locations of the system. For this reason, the science of scenario selection was developed to pick specific ex- treme event scenarios in a way that is representative of all of the possible scenarios that a hazard source can generate.30,31,32,33 For a given scenario, the damage and recovery process also includes large amounts of uncertainty. For instance, for a given level of ground shaking, the probability that a specific earthquake leads a bridge to col- lapse depends on the duration and frequency content of the earthquake, as well as the materials (random to some extent) used in its construction, the potential for imperfections in the construction phase, and the deterio- ration that the bridge has suffered over time. For transportation systems, these uncertainties can be captured using fragility curves that describe the probability of a component or system falling below a specified performance threshold for a given level of hazard intensity.34,35,36 Similarly, vulnerability 27 McGuire, R.K. 2008. “Probabilistic Seismic Hazard Analysis: Early History.” Earthquake Engineering and Structural Dynamics 37:329–338. https://doi.org/10.1002/eqe.765. 28 Han, Y., and R.A. Davidson. 2012. “Probabilistic Seismic Hazard Analysis for Spatially Distributed Infrastructure.” Earthquake Engineering and Structural Dynamics 41:2141–2158. 29 Baker, J.W. 2008. An Introduction to Probabilistic Seismic Hazard Analysis (PSHA). https://www.jackwbaker.com/Publications/Baker_(2013)_Intro_to_PSHA_v2.pdf. 30 Christou, V., P. Bocchini, M.J. Miranda, and A. Karamlou. 2017. “Effective Sampling of Spatially Correlated Intensity Maps Using Hazard Quantization: Application to Seismic Events.” ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering 4(1):1–13. 31 Manzour, H., R.A. Davidson, N. Horspool, and L.K. Nozick. 2016. “Seismic Hazard and Loss Analysis for Spatially Distributed Infrastructure in Christchurch, New Zealand.” Earthquake Spectra 32:697–712. https://doi.org/10.1193/041415eqs054m. 32 Jayaram, N., and J.W. Baker. 2009. “Correlation Model for Spatially Distributed Ground- Motion Intensities.” Earthquake Engineering and Structural Dynamics 38:1687–1708. https:// doi.org/10.1002/eqe.922. 33 Jayaram, N., and J.W. Baker. 2010. “Efficient Sampling and Data Reduction Techniques for Probabilistic Seismic Lifeline Risk Assessment.” Earthquake Engineering and Structural Dynamics 39:1109–1131. https://doi.org/10.1002/eqe.988. 34 Anelli, A., F. Mori, and M. Vona. 2020. “Fragility Curves of the Urban Road Network Based on the Debris Distributions of Interfering Buildings.” Applied Sciences 10(4):1289. https://doi.org/10.3390/app10041289. 35 Lupoi, G., P. Franchin, A. Lupoi, and P. Pinto. 2006. “Seismic Fragility Analysis of Structural Systems.” Journal of Engineering Mechanics 132:385–395. https://doi.org/10.1061/ (ASCE)0733-9399(2006)132:4(385). 36 Ghosh, J., and J.E. Padgett. 2010. “Aging Considerations in the Development of Time- Dependent Seismic Fragility Curves.” Journal of Structural Engineering 136:1497–1511.

90 INVESTING IN TRANSPORTATION RESILIENCE curves relate the intensity measure of an event at one location (e.g., the peak ground acceleration of an earthquake or the water depth in a storm surge) with the expected level of damage for a component or system. Fragil- ity curves are an explicitly probabilistic tool, whereas vulnerability curves hide the uncertainties and present mean values of damage. Uncertainties in implementing the recovery plan (e.g., duration of the various recovery tasks or resource availability) can also be captured through analytical models or numerical simulation (see Box 4-2).37,38,39 Each realization or sample of an extreme event scenario, a damage scenario, a recovery plan scenario, and a specific implementation scenario results in a different sample of functionality recovery curve. If the analysis is repeated for different samples, it is possible to obtain a set of recovery curves for the system. In Figure 4-8, the set of scenarios contains four sam- ple functionality recovery curves marked in purple, yellow, green, and blue. A direct approach to building probabilistic resilience metrics is to compute the statistics of the deterministic resilience metrics (discussed in the previous section of this chapter) assessed for each sample functionality recovery curve. For instance, it is possible to compute the mean, standard 37 Decò, A., P. Bocchini, and D.M. Frangopol. 2013. “A Probabilistic Approach for the Prediction of Seismic Resilience of Bridges.” Earthquake Engineering and Structural Dynamics 42(10):1469–1487. https://doi.org/10.1002/eqe.2282. 38 Karamlou, A., and P. Bocchini. 2017. “Functionality-Fragility Surfaces.” Earthquake Engineering and Structural Dynamics 46:1687–1709. https://doi.org/10.1002/eqe.2878. 39 Sun, W., P. Bocchini, and B.D. Davison. 2020. “Model for Estimating the Impact of Inter- dependencies on System Recovery.” Journal of Infrastructure Systems 26:04020031. https:// doi.org/10.1061/(ASCE)IS.1943-555X.0000569. BOX 4-2 What Is a Numerical Simulation? Numerical simulations enable computer-based testing of a complex system un- der a range of input factors that replicate aspects of the real world to produce a range of output predictions that show designers and decision makers how that system may perform under many different conditions. Therefore, they facilitate testing the performance of systems under a wide variety of circumstances— for example, hazards—to understand the range of possible performance out- comes (functionalities) given that the hazard occurrence and intensity are highly uncertain. For example, a simulation model might assess the damage suffered by a bridge under a range of flood conditions, varying the assumptions on the strength of key components such as foundations, erosion protection, and struc- tural strength.

CONTEMPORARY RESEARCH ON RESILIENCE AND RESILIENCE METRICS 91 FIGURE 4-8 Examples of probabilistic resilience metrics based on the functionality recovery curve. The gray curves in (b) and (c) represent distributions of all of the functionalities in the simulation scenarios at the selected point in time.40 40 Used with permission from Paolo Bocchini. Sy st em F un ct io na lit y, F( t) Time, t 100% 75% 50% 25% 0% Minimum acceptable functionality recovery path Figure 8 Sy st em F un ct io na lit y, F( t) Time, t 100% 75% 50% 25% 0% 25th percentile Figure 9 Sy st em F un ct io na lit y, F( t) Time, t 100% 75% 50% 25% 0% Ftarget Figure 10 (a) (b) (c)

92 INVESTING IN TRANSPORTATION RESILIENCE deviation, and quartiles of the resilience index. The same applies to the time to complete recovery, the time to reach a target level of functionality, the minimum functionality, and the other deterministic resilience measures. The probability of observing an unsatisfactory recovery curve has direct applications in evaluating resilience probabilistically. For example, a railroad company may decide that at no time, even after extreme events, should their capacity drop below 20% (which may correspond to the ability to transport highly perishable items), and that 2 weeks after a disruptive earthquake their functionality should be at least back to 70%. These constraints de- fine a “minimum acceptable functionality recovery path” (dashed line in Figure 4-8a). The percentage of the recovery curves that at any time dip below the minimum acceptable functionality recovery path is a probabilistic metric of failing to achieve the target. Conversely, the probabilistic metric of resilience is the percentage of sample recovery curves that are always above the minimum path. In Figure 4-8 only the yellow curve is always above the red dashed curve, so in this case, if the four curves are equally likely, the probability of resilience metric would be 25%. In actual assessments, simulations of thousands or millions of recovery curves are used. A probabilistic metric that results from calculating the distribution of the functionality at each point in time can be used to focus attention on the worst performing cases. In Figure 4-8b, the red curve is made up of the 25th percentile of functionality at each point in time. Once created, this recovery curve—made up of functionality from a range of curves—can be analyzed like any other recovery curve. The metric represented in Figure 4-8c uses the probabilistic distribution of functionality to create a probabilistic recovery curve for a target level of functionality. For a specified target level of functionality, the probability of having a functionality level equal to or larger than the target is computed for each point in time. As represented in Figure 4-8c, for the target level of 50%, the red areas are the percentage of recovery samples equal to or above 50% functionality at that point in time. Plotting these percentages (or probabilities) over time builds the probabilistic recovery curve for the target functionality.41 Other probabilistic metrics can be built in similar ways, starting from the recovery curve samples and focusing on the statistics that are most rel- evant for the problem at hand. Expanding on this, a multi-hazard approach that protects against multiple probable disaster scenarios can be taken as well (see Box 4-3). Because the condition of an asset (e.g., due to sufficient/ lack of maintenance) can affect both its and the system’s performance after 41 Karamlou, A., and P. Bocchini. 2017. “Functionality-Fragility Surfaces.” Earthquake Engineering and Structural Dynamics 46:1687–1709. https://doi.org/10.1002/eqe.2878.

CONTEMPORARY RESEARCH ON RESILIENCE AND RESILIENCE METRICS 93 BOX 4-3 Multi-Hazard Approach A multi-hazard analysis approach is essential if the best action to improve resil- ience to one hazard type may make the system less resilient to other possible hazards.a Consider, for example, a resilience enhancing action of locating power switches for generators in a secure, low-lying location. Given this decision, the facility might be more resilient to a human-made attack but could be more likely to fail under a flooding event. In fact, a resilience measure is a function of the scenario(s) considered in the analysis. A system may be highly resilient under one scenario and much less so under another. A multi-hazard approach can be exercised using a performance metric (of relevance to the studied system) that normalizes to the system’s routine condi- tions. A multi-hazard approach can be taken through expectation or other strate- gic operator, such as maximizing worst-case performance.b In many cases, this may require a multi-stage stochastic modeling conceptualization where stages correspond with periods of the disaster cycle. a Argyroudis, S.A., S.A. Mitoulis, M.G. Winter, and A.M. Kaynia. 2019. “Fragility of Trans- port Assets Exposed to Multiple Hazards: State-of-the-Art Review Toward Infrastructural Resilience.” Reliability Engineering & System Safety 191:106567. https://doi.org/10.1016/j. ress.2019.106567. b Nair, R., H. Avetisyan, and E. Miller-Hooks. 2010. “Resilience of Ports, Terminals and Other Intermodal Components.” Transportation Research Record 2166:54–65; Chen, L., and E. Miller-Hooks. 2012. “Resilience: An Indicator of Recovery Capability in Intermodal Freight Transport.” Transportation Science 46:109–123; Miller-Hooks, E., X. Zhang, and R. Faturechi. 2012. “Measuring and Maximizing Resilience of Freight Transportation Networks.” Computers and Operations Research 39(7):1633–1643. a disruptive event, a probabilistic analysis can account for the effects of asset conditions at the time of the disruptive event. Probabilistic analysis is particularly important because it allows for incorporating the crucial effects of climate change in the resilience assess- ment. Climate change has important impacts on three aspects of resilience assessment. First, it affects the frequency and severity of weather-related events, which can be reflected in the selection of representative scenarios for resilience analysis. The current practice tends to select scenarios based on past occurrences, but given the dynamism of climate change, scenarios for hazards affected by climate change should be selected based on their predicted frequency and severity in the future. Second, climate change affects the deterioration process of the infra- structure, by changing the mean environmental conditions (e.g., temperature,

94 INVESTING IN TRANSPORTATION RESILIENCE humidity, salinity of the air) as well as the magnitude of their fluctuations. This, in turn, affects the fragility curves discussed earlier in the chapter. Third, climate change affects the context in which extreme events occur. For instance, sea level rise, because it can lead to changes to the subsurface and groundwater tables, may impact the ability to access specific loca- tions and hinder proper emergency response. Moreover, different environ- mental conditions will affect the speed and effectiveness of the emergency response crews. Extreme temperatures will affect power demand, exacer- bating potential interdependencies among power, transportation, and other systems in the wake of a disaster. All of these aspects can be reflected in appropriate recovery models. The metrics discussed in this chapter can account for these three effects of climate change through proper scenario selection that accounts for future trends, advanced fragility curves that factor in accelerated deteriora tion, and comprehensive recovery models that account for the future climate. However, integrating climate change into resilience assess ment requires combining resilience modeling with climate model- ing, which increases the uncertainty in the results. Although the concept of resilience is typically defined around a short but impactful perturbing event, resilience is also affected by the slow but equally important per- turbation that climate change can impose on infrastructure assets and transportation systems. FUNCTIONALITY METRICS FOR TRANSPORTATION SYSTEMS The deterministic and probabilistic metrics discussed in the previous sec- tions require that the analyst defines and assesses the performance of a transportation asset or system using one or more functionality metrics. Functionality metrics are also critical in measuring the consequences of hazard events and the benefits of resilience interventions, as discussed in Chapter 5. As mentioned, functionality metrics are typically specific to the mode or service and the scale of the analysis. In engineering, transportation networks are often described using theories and various algorithms that find the best routes and distribute traffic to them. These same theories and algorithms can also be used to analyze the loss of functionality associated with asset damage and travel disruption.42,43 The appropriate functionality metric for assessing resil- 42 Bocchini, P., and D.M. Frangopol. 2011. “A Stochastic Computational Framework for the Joint Transportation Network Fragility Analysis and Traffic Flow Distribution Under Extreme Events.” Probabilistic Engineering Mechanics 26:182–193. 43 Bocchini, P., and D.M. Frangopol. 2012. “Optimal Resilience- and Cost-Based Post- Disaster Intervention Prioritization for Bridges Along a Highway Segment.” Journal of Bridge Engineering 17:1–13.

CONTEMPORARY RESEARCH ON RESILIENCE AND RESILIENCE METRICS 95 ience should be related to the performance and services most relevant to the mission of the transportation agency. Moreover, functionality might be computed based on stakeholder perspectives and from either the engineer- ing or user level.44,45 Typically, these functionality metrics relate to business continuity. Some examples used for resilience analysis include through- put of cargo via rail46 or maritime systems;47 takeoffs and landings at airports;48 berths on arrival,49 throughput,50 and minimum throughput51 at ports; travel time or delay on roadways;52,53 and service levels in transit.54,55 While an exhaustive list of these metrics is beyond the scope of this report and can be found in scientific papers, some illustrative examples of these metrics follow.56 44 Asadabadi, A., and E. Miller-Hooks. 2018. “Co-opetition in Enhancing Global Port Network Resiliency: A Multi-Leader, Common-Follower Game Theoretic Approach.” Trans- portation Research Part B 108:281–298. 45 Vodopivec, N., and E. Miller-Hooks. 2019. “Transit System Resilience: Quantifying the Impacts of Disruptions on Diverse Populations.” Reliability Engineering & Systems Safety 191(11):106561. 46 Chen, L., and E. Miller-Hooks. 2012. “Resilience: An Indicator of Recovery Capability in Intermodal Freight Transport.” Transportation Science 46:109–123. 47 Asadabadi, A., and E. Miller-Hooks. 2018. “Co-opetition in Enhancing Global Port Network Resiliency: A Multi-Leader, Common-Follower Game Theoretic Approach.” Trans- portation Research Part B 108:281–298. 48 Faturechi, R., and E. Miller-Hooks. 2014. “Travel Time Resilience of Roadway Networks Under Disaster.” Transportation Research Part B 70:47–64. 49 Zhou, C., J. Xu, E. Miller-Hooks, W. Zhou, C. Chen, L. Lee, E. Chew, and H. Li. 2021. “Analytics with Digital-Twinning: A Decision Support System for Maintaining a Resilient Port.” Decision Support Systems 143. https://doi.org/10.1016/j.dss.2021.113496. 50 Nair, R., H. Avetisyan, and E. Miller-Hooks. 2010. “Resilience of Ports, Terminals and Other Intermodal Components.” Transportation Research Record 2166:54–65. 51 Asadabadi, A., and E. Miller-Hooks. 2020. “Maritime Port Network Resiliency and Reli- ability Through Co-opetition.” Transportation Research Part E 137:101916. 52 Faturechi, R., and E. Miller-Hooks. 2014. “Travel Time Resilience of Roadway Networks Under Disaster.” Transportation Research Part B 70:47–64. 53 Fotouhi, H., S. Moryadee, and E. Miller-Hooks. 2017. “Quantifying the Resilience of an Urban Traffic Signal-Power Coupled System.” Reliability Engineering & Systems Safety 163:79–94. 54 Vodopivec, N., and E. Miller-Hooks. 2019. “Transit System Resilience: Quantifying the Impacts of Disruptions on Diverse Populations.” Reliability Engineering & Systems Safety 191(11):106561. 55 Chan, R., and J. Schofer. 2015. “Measuring Transportation System Resilience: Re- sponse of Rail Transit to Weather Disruptions.” Natural Hazards Review 17(1). https://doi. org/10.1061/(ASCE)NH.1527-6996.0000200. 56 Sun, W., P. Bocchini, and B.D. Davison. 2020. “Resilience Metrics and Measurement Methods for Transportation Infrastructure: The State of the Art.” Sustainable and Resilient Infrastructure 5:168–199. https://doi.org/10.1080/23789689.2018.1448663.

96 INVESTING IN TRANSPORTATION RESILIENCE Weighted Sum of Assets in Service The functionality metric “weighted sum of assets in service” is especially useful for networks where not all links are equally important. For example, for the resilience tables mentioned in the previous section, if the target is set to “90% of roads open,” it is necessary to specify what “90%” means. Is it 90% of the road capacity or 90% of the road lengths? One way to address this question is to assign a “weight” or “importance factor” to each road segment. A weight could be number of lanes, flow capacity, average daily traffic, traffic flow in peak hours, or some combination of these. The weight of the roads that are open divided by the total weight of the system is a way to assess the percentage of the system that is functional, while also partially accounting for the system topology and traffic capacity.57 Total Travel Time Metrics such as “total travel time” track functionality from the perspective of the ability of the transportation network to handle flows of vehicles, passengers, or goods. These metrics still need to be defined in terms specific to the analysis. For example, the functionality metric total travel time of trips originating during the peak hour of weekday travel in a city measures the effects of the hazard when the highway network is already congested.58 Changes in total travel time capture the effects of damage and disruptions and the resulting congestion that may occur even on highway segments that are not directly damaged by the extreme event. If a bridge is closed because of an earthquake, part of the traffic that was supposed to cross the bridge will be rerouted to other portions of the highway network and to secondary routes. Detours and delays from additional congestion increase travel time.59 Connectivity Connectivity metrics capture the ability to reach every node from every other node in a network. The degree of connectivity can be measured by 57 Karamlou, A., P. Bocchini, and V. Christou. 2016. “Metrics and Algorithm for Optimal Retrofit Strategy of Resilient Transportation Networks.” In Maintenance, Monitoring, Safety, Risk and Resilience of Bridges and Bridge Networks (T.N. Bittencourt, D.M. Frangopol, and A. Beck, eds.). London: Taylor & Francis Group, pp. 1121–1128. 58 Bocchini, P., and D.M. Frangopol. 2011. “A Stochastic Computational Framework for the Joint Transportation Network Fragility Analysis and Traffic Flow Distribution Under Extreme Events.” Probabilistic Engineering Mechanics 26:182–193. 59 Bocchini, P., and D.M. Frangopol. 2012. “Optimal Resilience- and Cost-Based Post- Disaster Intervention Prioritization for Bridges Along a Highway Segment.” Journal of Bridge Engineering 17:117–129. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000201.

CONTEMPORARY RESEARCH ON RESILIENCE AND RESILIENCE METRICS 97 the percentage of connected node pairs. More elaborate approaches weight each origin–destination pair by the corresponding volume of trips.60 Aver- age added distance between locations above the pre-disruption value can also serve as a measure of connectivity.61 Metrics for Interdependent Systems or Facilities In infrastructure, the functionality of one system often affects the function- ality of other systems. Power lines and water infrastructure may be located in the rights-of-way for road and rail networks, while many transportation services depend on electric, water, and communications services gener- ated by outside vendors. For instance, the operation, safety, and security of transportation systems are dependent on communications networks that support control, monitoring, data storage, and safety and security functions. These communication services are commonly purchased from vendors (such as telecom and cloud service providers) that own and main- tain such networks. Access to transportation connecting a labor force to employment centers in high-density urban centers is also critical for other industries, such as health care and retail. Therefore, to assess the resilience of one system, it becomes necessary to account for the functionality of other interdependent systems. The buildings that house and facilitate the operation of all transpor- tation systems are a special case of systems, the functionality of which is interdependent. The functionality of buildings—airport terminals, train stations, port operation centers, etc.—is vulnerable to disruptions caused by structural and non-structural damage, loss of critical services such as electricity, or impeded access. Therefore, the vulnerability of the support- ing buildings should be assessed and described in relation to their potential for disrupting operations, and functionality metrics should be chosen that directly or indirectly relate to post-event recovery.62 Tools and methods for the assessment of post-earthquake building functionality and recovery are currently being used in practice.63,64 For other hazards such as hurricanes, 60 Bocchini, P., and D.M. Frangopol. 2013. “Connectivity-Based Optimal Scheduling for Maintenance of Bridge Networks.” Journal of Engineering Mechanics 139:760–769. https:// doi.org/10.1061/(ASCE)EM.1943-7889.0000271. 61 Zhang, X., E. Miller-Hooks, and K. Denny. 2015. “Assessing the Role of Network Topology in Resilience of Transportation Systems.” Journal of Transport Geography 46:35–45. 62 Burton, H.V., G. Deierlein, D. Lallemant, and T. Lin. 2016. “Framework for Incorporat- ing Probabilistic Building Performance in the Assessment of Community Seismic Resilience.” Journal of Structural Engineering 142(8):C4015007. 63 FEMA (Federal Emergency Management Agency). 2012. Seismic Performance Assessment of Buildings. FEMA P58 Report, Applied Technology Council. 64 Almufti, I., and M. Wilford. 2013. REDi™: Resilience-Based Earthquake Design (REDi) Rating System. London: Arup Group.

98 INVESTING IN TRANSPORTATION RESILIENCE tornadoes, flooding, and fire, methods for assessing post-event building functionality are still in the research stage.65 METHODS AND TOOLS FOR ANALYZING HAZARD MITIGATION To improve resilience, transportation agencies need methods to analyze investments designed to prevent damage and disruption and speed recovery. Off-the-shelf and ad hoc software tools developed for a specific purpose can assist investment analysis. Investment Decision-Making Process The focus of research on resilience analysis has been on characterizing the processes of disruption, response, and recovery, that is, given a disruption, how does the system perform? For resilience analysis to be useful for ana- lyzing investments designed to prevent loss, the chosen models and metrics must be sensitive to the proposed investment. For example, to analyze a proposed structural retrofit for a bridge, a model that uses fragility curves66 must be able to predict the changes in the associated fragility curve resulting from the retrofit. If the model could reflect the change in the fragility curve resulting from the preventive action, then the impact of the proposed action on resilience could be assessed by running the model twice, with and with- out the preventive action, producing metrics with and without the changes induced by the preventive action. The difference between the two metrics is an estimate of the preventive action’s impact on resilience. While the use of functionality recovery curves to analyze investments in resilience is easy to explain in theory, the transition to practice is only in the beginning stages. There is still much work to be done on developing implementable models and metrics, specifically models that relate in fragil- ity curves to mitigation investments. In addition, the data needs are quite intensive. Agency studies of past disruptions and hazard events are needed that describe, measure, and evaluate the recovery process and characterize resilience. Such studies enable agencies to analyze their own performance, identify weaknesses, and prioritize improvements. Studies are also needed that relate types of infrastructure assets, contexts, and hazard characteris- tics to general recovery curves, thus enabling predictions of the impacts of asset design and context changes on resilience. 65 Abdelhady, A.U., S.M. Spence, and J. McCormick. 2020. “A Framework for the Probabi- listic Quantification of the Resilience of Communities to Hurricane Winds.” Journal of Wind Engineering and Industrial Aerodynamics 206:104376. 66 Fragility curves display the probability of a component/system to reach a certain low performance threshold for a given level of the intensity measure.

CONTEMPORARY RESEARCH ON RESILIENCE AND RESILIENCE METRICS 99 Mitigation Analysis Tools The Interdependent Networked Community Resilience Modeling Environ- ment (IN-CORE)67 and the Probabilistic Resilience Assessment of Inter- dependent Systems (PRAISys)68 are examples of the next generation of community resilience analysis tools. IN-CORE is designed to model the impact of natural hazards and community resilience and recovery. PRAISys is designed to conduct post-event resilience analysis of communities by address ing the interdependencies among infrastructure systems in a proba- bilistic way. These tools can also effectively capture the resilience outcomes of detailed mitigation actions, preparedness actions, and general opera- tional changes (e.g., changes in the disaster response policies, investments in equipment and personnel for emergency response, and coordination of mutual aid agreements). The tools can be used to conduct specific analyses to assess many of the functionality metrics described in this chapter. How- ever, the analyst has to perform a preliminary data collection from sources external to the tools before conducting any analyses. Because of the com- plexity of the associated data collection and, to some extent, the software programs, their application is warranted only when other approaches are deemed insufficient and the magnitude of the investment justifies a thorough resilience analysis. Sufficient data availability is also a challenge for the private and propri- etary resilience software tools developed over the past decade. These tools rely on artificial intelligence (AI) and data-driven approaches to bypass the engineering modeling efforts that more well-established analysis approaches have built over time. These AI approaches, however, require vast amounts of data to train the AI models; by definition, data on extreme natural haz- ards and their effects are scarce. CHAPTER SUMMARY The research literature on measuring resilience with functionality recovery curves and their associated metrics, as presented in this chapter, is currently useful for helping transportation agencies conceptualize the performance of their assets and systems during and after a natural hazard event and to com- municate resilience concepts with stakeholders. Research into functionality recovery curves also emphasizes the importance of robust fragility curves and functionality metrics, both of which are useful and sometimes neces- sary for the types of resilience analysis that would be conducted as part of 67 Center of Excellence for Risk-Based Community Resilience Planning. 2018. IN-CORE Manual 1.0.0. https://incore.ncsa.illinois.edu/doc/incore. 68 Bocchini, P., B.D. Davison, A.-M. Esnard, A.J. Lamadrid, D. Mitsova, A. Sapat, R. Sause, L.V. Snyder, and W. Sun. 2020. “The PRAISys Platform.” www.praisys.org.

100 INVESTING IN TRANSPORTATION RESILIENCE the framework presented in Chapter 5. Table 4-2 summarizes functionality metrics for a variety of modes and services. This summary is based on the committee’s review of metrics used in resilience research and practice. TABLE 4-2 Functionality Metrics in Use in Resilience Research and Practice69 All Modes and Some Facilities System level/facilities Capacity, delay (travel time), safety Roadways System level Connectivity, lengths of network links Pavement Serviceability Facilities/information technology (IT)/ communication systems Up/down, downtime Regional Passenger Rail Signal systems/power/IT/communication systems/maintenance facilities Up/down, downtime Power Fraction with/without power Stations Open/closed Bus; Heavy, Light, and Commuter Rail; Last-Mile Transit System level On-time performance, number of transfers Track Serviceability Signal systems/power/IT/communication systems/maintenance facilities Up/down, downtime Stations Open/closed Freight Rail Track Serviceability Signal systems/power/IT/communication systems/maintenance facilities Up/down, downtime Terminals Open/closed, service time Intermodal Transit Terminals Node level Connectivity, number of modes operating Terminal Open/closed, throughput Power/IT/communications systems Up/down, downtime Power Fraction with/without power 69 From the committee’s review of metrics used in resilience research and practice.

CONTEMPORARY RESEARCH ON RESILIENCE AND RESILIENCE METRICS 101 Walking/Bicycling/Rolling Special-purpose lanes/trails Open/closed Sidewalks Accessibility Parking/shared mobility infrastructure Accessibility Air Transportation System level Connectivity, number of transfers, take-offs/ landings, throughput, number of travelers served Terminal/control tower/taxiway/ apron/ramps/aircraft stands/facilities (maintenance)/freight/parking/hangars Up/down, downtime Runways Open/closed, downtime, number of take-offs/ landings, on-time performance Fuel systems Availability IT/lighting/communications systems Up/down Waterways System level Connectivity, speed Docks/ports Open/closed Links Speed Locks Throughout capacity, open, closed Pipelines System level Flow rate Storage facilities Capacity, open, closed Surface-Aviation-Water Intermodal Terminals Facility Berth/to gate on arrival, open/closed, throughput, service times Power/IT/communication systems/ maintenance facilities Up/down, downtime Operators Throughput, service time, berth on arrival However, to use the concept of recovery curves for making investment decisions (i.e., in an a priori context), agencies would need to estimate, quantitatively, the curve before and after an investment in the face of a disruption. While the curves can be measured ex post for a specific, experi- enced disruption, there are currently no operational tools to estimate them after an investment in resilience has been made. In part, this is because the future recovery curve depends not only on the design of the system but also on the effectiveness of the investment in mitigation actions, the specific characteristics of the disruption, and the response and restoration

102 INVESTING IN TRANSPORTATION RESILIENCE resources deployed after a future disruption. Recovery curves also presume a perturbing or hazard event and thus require additional work to adapt them to the gradual, chronic, and likely permanent changes associated with climate change. Significant work still needs to be done on developing functionality metrics for transportation and incorporating case study data that chart haz- ard recovery over time. Research is also needed to develop practical ways to predict changes in functionality recovery curves brought about by specific mitigation measures to support investment to prevent future disruptions. While research is creating mitigation analysis tools that go beyond the high- level resilience investment analysis possible with the Federal Emergency Management Agency’s Hazus-MH (described in Chapter 3), these new tools still require significant amounts of data that may not be accessible to transportation agencies today.