Tenth U.S. National Conference on Earthquake EngineeringFrontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska 10NCEE

MODELING AND VISUALIZING INFRASTRUCTURE-CENTRIC

COMMUNITY DISASTER RESILIENCE

Scott B. Miles1

ABSTRACT

This paper provides a general overview of four critical forms of representation for understanding and achieving the goal of community resilience to earthquakes. Conceptual representations serve to codify theoretical knowledge that can guide the selection of appropriate indicators. The conceptual representation presented here is founded on an expanded definition of infrastructure: the combination of a wide range of capitals and services derived from those capitals. Theoretically-based indicators can be represented quantitatively in order to communicate relative resilience with respect to that indicator. The theoretical relationships in the conceptual model, together with certain metrics of resilience, can be operationalized using algorithmic representation in order to explore the complex, interdependencies of community resilience. Lastly, visual representations can be created to synthesize and comprehend an assembled suite of conceptual, quantitative, and algorithmic representations to foster improved comprehension of community resilience. The ultimate goal of the types of representations discussed in this paper is the posing and evaluation of hypotheses in both scholarly and professional settings with newly developed analysis and decision support tools.

1 Resilience Institute, Huxley College of the Environment, Western Washington University, 516 High St, Bellingham, WA, 98225, USA. PH (206) 406-9805, email: scott.miles@wwu.edu

Miles, S. Modeling and visualizing infrastructure-centric community disaster resilience. Proceedings of the 10th National Conference on Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

Tenth U.S. National Conference on Earthquake EngineeringFrontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska 10NCEE

MODELING AND VISUALIZING INFRASTRUCTURE-CENTRIC COMMUNITY DISASTER RESILIENCE

Scott B. Miles2

ABSTRACT

This paper provides a general overview of four critical forms of representation for understanding and achieving the goal of community resilience to earthquakes. Conceptual representations serve to codify theoretical knowledge that can guide the selection of appropriate indicators. The conceptual representation presented here is founded on an expanded definition of infrastructure: the combination of a wide range of capitals and services derived from those capitals. Theoretically-based indicators can be represented quantitatively in order to communicate relative resilience with respect to that indicator. The theoretical relationships in the conceptual model, together with certain metrics of resilience, can be operationalized using algorithmic representation in order to explore the complex, interdependencies of community resilience. Lastly, visual representations can be created to synthesize and comprehend an assembled suite of conceptual, quantitative, and algorithmic representations to foster improved comprehension of community resilience. The ultimate goal of the types of representations discussed in this paper is the posing and evaluation of hypotheses in both scholarly and professional settings through the use of newly developed analysis and decision support tools.

Introduction

This paper presents aspects of evolving work on conceptual, quantitative, algorithmic and visual representations of community resilience to earthquakes and other hazards. Conceptual representations are (or need to be) the basis for all other work on improving community resilience. Conceptual representations are critical in assisting what quantitative metrics, simulated relationships, and visual linkages are most important for improving community resilience. Debates around how community resilience can be briefly and succinctly defined, or even if the term is worthwhile, can do little to advance the state of the art with respect to avoiding and dealing with earthquake impacts. Richer conceptual debates and development are needed.

It is argued here and elsewhere [1], [2] that a theoretical framework and its related conceptual model must be founded upon the concept and role of infrastructure. In this paper, infrastructure is defined as any combination of capital and related services—extending beyond just physical lifeline infrastructure like roads and utilities. The following section provides a discussion of the

1 Resilience Institute, Department of Environmental Studies, Western Washington University, 516 High St, MS 9085 Bellingham, WA 98225; email: scott.miles@wwu.edu

Miles, S. Modeling and visualizing infrastructure-centric community disaster resilience. Proceedings of the 10th National Conference on Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

theoretical role of infrastructure. (Due to space constraints, a deep discussion is included in a companion paper within these conference proceedings.)

The second section of this paper deals with how to quantitatively represent community resilience using metrics to describe indicators inspired by the contents of some conceptual model. The section begins by reviewing a common metric for representing the efficiencies related to avoiding loss and speeding recovery. It then presents related metrics to represent adaptation, speed, and inter-indicator relationships. Algorithmic representations are presented in the subsequent section to illustrate how relationships between chosen indicators and associated metrics can be simulated. These representations build upon past work on ResilUS—a prototype simulation model of community disaster resilience [6]. The vast number of conceptual variables, data, and socio-technical infrastructure interdependencies requires research and development of uniquely designed visual representation in order to comprehend the complexities of community resilience. The paper concludes with a brief illustration of the types of visual interfaces that could serve to translate the other types of representations into effective decisions support systems for dealing with potential future earthquake disasters.

Figure 1. (a) Conceptual model of the static constructs of the WISC framework of community

resilience. (b) Resilience across space and time, as influenced by community capital condition and levels of services. The solid polygons represent resilience time-space-paths for infrastructure capitals and services, while the lines represent time-space-paths for indicators of well-being and identity of agents within a community. Points along the time-space-long indicate agent movement across space.

Conceptual Representation

Fig. 1a presents a conceptual representation of a new theoretical framework of community resilience to disasters called WISC. The acronym WISC stands for the four static constructs of

static resilience represented in the framework: well-being, identity, services, and capitals. Under this framework, the constructs of well-being and identity comprise the concept of community, while the constructs of capitals and services comprise the concept of infrastructure. The four static constructs of WISC provide the vocabulary to describe the state of community resilience at any state in time and space before or after an earthquake with respect to some fixed scale (i.e., static). Each construct consists of multiple variables that can be used to suggest indicators for which to develop quantitative metrics (following section) or the inputs/outputs for constructing algorithms (fourth section) for representing dynamic resilience. The variables for each of the four static constructs of WISC are listed in Fig 1a. Due to space constraints, no explanation is provided here for specific variables.

In most of the literature, the goal of community resilience is a functioning system or community. The goal of resilience, however, should go beyond safety or functioning and ultimately ensure the well-being of different communities and their members [3]. The WISC framework incorporates six variables of well-being: material needs, security, health, affiliation, autonomy, and satisfaction [1], [3], [4]. Variables of the construct community identity have been empirically linked to variables of well-being—efficacy, esteem, distinctiveness, and continuity [5]. To these, the WISC framework adds equity, empowerment, diversity, and adaptability, for a total of eight variables. In WISC, the static construct services consists of nine variables that represent service attributes. These variables are universally applicable to all of the capitals variables. Services are typically defined in economic terms as measurable flows, such as perishable goods, that are provided and consumed. The construct of community capital refers to any asset utilized as part of socio-economic activity [2]. For the WISC framework, six variables of community capital are adopted: social, political, human, economic, built, and natural.

Communities suffer loss and achieve recovery dynamically in relation to both space and time [6]. Communities and agents within them exist at some location, at some point in time, with some level of well-being and status in identity. The state of these constructs varies with time, because the state of infrastructure varies with respect to a particular earthquake’s impacts and the time after the event [7]. Fig. 1b presents a conceptual representation of dynamics community resilience—a concept represented in WISC. The figure represents an augmentation of the loss-recovery curves or “resilience triangles” typical of the literature based on the work of [8]. The three-dimensions of the figure are space/scale, time, and some indicator of resilience based on the static constructs of WISC. Within these three dimensions, variables and constructs of community and infrastructure from the static model are plotted. The lines represent the dynamics of well-being and identity (community), while the polygons represent the dynamics of services and capitals (infrastructure). Fig. 1b is necessarily simplified and is described in greater detail elsewhere in the conference proceedings.

Quantitative representation

Bruneau and others [8], as well as many other studies based on their formative ideas, proposed quantitatively representing community resilience to earthquakes as the area under a curve representing the quality or quantity of some indicator over time, Q(t). (Technically, they define resilience based on the area above the curve, but the inverse is more common in the literature.)

Examples of Q(t) curves are shown in Fig. 2. These curves are analogous to those represented in Fig. 1a, but without the dimension of space.

Assuming Q(t) is normalized, resilience with respect to R(t) can be quantitatively represented as the following:

(1)

Perfect resilience is quantitatively represented as R = 1.0. If any loss is suffered, then resilience by definition is less than perfect. A major contribution of [8] is showing that the resilience can only be represented by a single value if time (and space) is fixed. In other words, our knowledge about a community’s resilience changes with time (and across space) after an earthquake event. This is illustrated by plotting R(t) in comparison to Q(t) in Fig 2.

In Fig 2., R(t) is labeled “Efficiency” because the graph reflects the representation that the highest resilience is associated with the most efficient recovery relative to the amount of loss suffered from an earthquake. This can be referred to as efficiency resilience—quantitatively representing resilience as the means and manifestation of maximizing the efficiency of both earthquake-induced loss and recovery speed.

Graphs depicting various indicators as Q(t) are the most common means of quantitatively representing the dynamics of community resilience. Q(t) represents the cumulative amount of recovery that has occurred over time—for example, the number of customers restored. Sampling R(t) at a particular time is likely the second most common means of quantitatively representing the dynamics of resilience. The value of resilience at a point in time singularly describes the unique time-path that resulted in the particular value of the corresponding Q(t). In other words, the same value of Q(t) can be associated with different values of R(t) based on the shape of the Q(t) recovery curve.

The amount of speed and adaptation manifested to get to the same level of recovery matters in understanding a community’s resilience. The speed of recovery for a given unit of time—for example the number of customers restored per day—is simply the first derivative of Q(t) and is illustrated in Fig. 2 with the plot labeled “Speed.” By comparing the change in speed over time—the second derivative of Q(t)—the relative amount of adaptation, A(t), between two states in time can be quantitatively represented. This is illustrated in the graph “Adaptation” in Fig 2. Adaptation can be likened to acceleration in decision-making or actions that result in changes of restoration, reconstruction, or recovery speed—critical components of post-earthquake resilience.

Adaptation, speed, quantity (or quality), and efficiency—Fig. 2.—are metrics that quantitatively contextualize indicators of resilience with respect to time (that can be easily extended to space as in Fig. 1b). It is also important to represent the dynamics of resilience with respect relationships between indicators. Specifically, it is important to put resilience in the context of the interdependencies between infrastructure (writ large) provision and consumption towards the

maintenance of identity and well-being. One way to put individual resilience indicators in context is by analyzing the sufficiency of one indicator with respect to another by quantifying the relationship between supply and demand. Metrics describing the dynamics of supply and demand after an earthquake can be referred to as sufficiency resilience.

The goal of quantitatively representing sufficiency resilience is to minimize the difference between supply and demand indicators over time after an earthquake, while simultaneously maximizing the efficiency resilience with respect to those indicators. The equation below expresses sufficiency resilience, S(t), as the absolute difference between the areas under the supply and demand efficiency curves—Rs(t) and Rd(t), respectively—multiplied by the average of the areas under both curves.

(2)

Two examples of sufficiency resilience curves are shown in Fig. 2. One (Fig. 2a) demonstrates the relationship between supply and demand indicators when both exhibit relatively efficient resilience, while the other (Fig. 2b) demonstrates the relationship when the resilience of demand is significantly more efficient than for supply.

Algorithmic representation

A subset of algorithms based on the simulation model ResilUS [6] are presented here to help illustrate potential algorithmic representations that can be used to operationalize both conceptual and quantitative representations of community resilience. These particular algorithms have not been evaluated to date; however previous versions of these algorithms were calibrated [6].

Building reconstruction, BL(t), for households is represented as a time series of logistic step functions implemented using Monte Carlo simulation. Output values range from 0 to 1, where 1 represents complete reconstruction. ResilUS operates at a time scale, t, of weeks. One step, SS, represents an increment of progress in rebuilding in a respective week. BL at t = 0 is determined by earthquake-induced building damage. Rebuilding progress may temporarily or permanently stall or reach full reconstruction (BL = 1). BL is defined by the following equation. ( + 1) = ( ) + (3)

SS is determined by a generalized building type indicator (BTYPE) that ranges from 0 to 1, with 1 representing the most complex type of building in a particular area. BTYPE has the effect of making the step size smaller for more complex buildings and thus the shortest possible reconstruction time longer.

Figure 2. Quantitative representations of resilience with respect to metrics of adaptation, speed,

quantity, efficiency, and sufficiency in the case of relative balance between supply and demand (a) and relative imbalance (b). = ∙ (4)

The denominator of is the minimum possible rebuilding time for a particular building. SHORT is a parameter that represents the minimum possible time to rebuild the simplest type of building in the area, which could be determined via survey of local professionals. LONG represents the additional time required beyond to rebuild the most complex type.

A step of progress is not guaranteed each week; some weeks rebuilding may stall. Within ResilUS, the probability of making a step of progress each week depends on whether the building has been inspected (INSP), the availability of construction resources (CONSTR), the amount of financial resources (RES), and the service level for transporting construction materials into the respective neighborhood (TRNSn). All values are normalized to range from 0 to 1. Notice that TRNSn is an indicator of service, rather than capital (i.e., the ability to get around, not condition of physical assets). The service of transport of materials is what is important for

reconstruction, not specifically the capital used to provide that service. If no inspection has been done, no progress is possible. The remaining indicators are combined to calculate the probability of progress, Pss, using the following logistic function. ( ) = ( ) (5) ( ) = + ∙ + ∙ ( ) + ∙ ( ) (6)

Logistic regression can be used to determine the best fit linear combination of the three indicators as represented by the � coefficients.

Reconstruction progress is simulated using a Monte Carlo realization for which a uniform random number between 0 and 1 is generated. If the probability of a step, Pss, is greater than the number generated, rebuilding progress increases by one step, SS, for a respective household’s home in the respective week. The process is repeated for each week until ( ) = 1 or the simulation ends. Fig. 3 presents a conceptual illustration of the algorithm described above.

Figure 3. An algorithmic representation of dynamic community resilience based on Monte Carlo

simulation. The probability of recovery progress is determined based on a set of input factors (e.g., CONSTR, RES, and TRNS). For each Monte Carlo realization, the probability is compared to a random number generated at each time step after

modeled earthquake. A single step in recovery progress occurs each instance that the probability exceeds the particular random number.

Households require the service of shelter, which depend on the built capital of residential buildings, in order to maintain basic well-being. In turn, shelter is not serviceable without lifeline infrastructure services derived from various types of built capitals. Complete reconstruction of a building—capital—does not mean that the necessary level of shelter service (SHEL) is available for a household’s well-being. In this case, complete likelihood that the level of shelter service is adequate is only possible if water, WAT, and electricity, ELEC, service is available. ResilUS currently only considers water delivery by truck as an alternate capital for providing lifeline services; this will be expanded in future work (e.g., to consider backup generators). The probability that shelter service level is adequate is assumed to be 1 if a household is placed in short-term housing, STH, while their home is being reconstructed. This is another example of how infrastructure capital can be substituted to provide similar infrastructure services. ( ) = ( ) ∙ ( ) ∙ ( ) = 01 = 1 (7)

Visual representation

Figs. 1 through 3 together with Equations 1 through 7 illustrate the conceptual, quantitative, and algorithmic complexity of representing community resilience to earthquakes. Figure 1 demonstrates that community disaster resilience is hyper-variate with complex, interdependent relationships. Equations 1 and 2 and Fig. 2 deal only with one or two variables of resilience and so are not enough to quantitatively or visually represent resilience. The algorithms of ResilUS currently incorporate 17 pre-event inputs related to a single community with multiple neighborhoods each filled with a large number of households and businesses. Similarly, ResilUS models 19 time-variant recovery outputs [6], [9].

To provide decision support (e.g., for utilities or emergency managers) the hyper-dimensionality and complexity of community resilience can be visually represented in a manageable, comprehendible, and meaningful way. This is true whether indicators are represented empirically or algorithmically. Of the four types of representations discussed in this paper—conceptual, quantitative, algorithmic, and visual—visualization is the least explored to date with respect to research and development on decision support systems for guiding restoration, reconstruction and recovery after earthquakes. Fig. 4 presents a mockup of how visualization techniques can be combined to assist in supporting decision for improving community resilience to earthquakes. Fig. 4 is part of a custom geo-visual interface being designed for utilizing ResilUS. It begins to illustrate the complexity of comprehending the rich array of available and potential conceptual, quantitative, and algorithmic representations and the challenges of visually representing them.

Conclusion

This paper provides a general overview of four critical forms of representation for understanding and achieving the goal of community resilience to earthquakes. Conceptual representations serve

to codify theoretical knowledge that can guide the selection of appropriate indicators. These indicators can be represented quantitatively in order to communicate relative resilience corresponding to that indicator. The theoretical relationships in the conceptual model together with certain metrics of resilience can be operationalized using algorithmic representation in order to explore the complex, interdependencies of community resilience. Lastly, visual representations can be created to synthesize and comprehend an assembled suite of conceptual, quantitative, and algorithmic representations to foster improved comprehension of community resilience. The ultimate goal of the types of representations is the posing and evaluation of hypotheses in both scholarly and professional settings using newly developed analysis and decision support tools.

Figure 4. A mockup of a computer interface for visually representing empirical or modeled

indicators of community resilience to earthquakes.

Acknowledgements

This work is supported by National Science Foundation CMMI grant #0927356.

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