IMPACTS OF HUMAN BEHAVIORAL HETEROGENEITY ON THE BENEFITS OF

PROBABILISTIC FLOOD WARNINGS: AN AGENT-BASED MODELING FRAMEWORK1

Erhu Du, Samuel Rivera, Ximing Cai, Laura Myers, Andrew Ernest, and Barbara Minsker2

ABSTRACT: Flood forecasts and warnings are intended to reduce flood-related property damages and loss ofhuman life. Considerable research has improved flood forecasting accuracy (e.g., more accurate prediction of theoccurrence of flood events) and lead time. However, the delivery of improved forecast information alone is notnecessarily sufficient to reduce flood damage and loss of life, as people have varying responses and reactions toflood warnings. This study develops an agent-based modeling framework that evaluates the impacts of hetero-geneity in human behaviors (i.e., variation in behaviors in response to flood warnings), as well as residentialdensity, on the benefits of flood warnings. The framework is coupled with a traffic model to simulate evacuationprocesses within a road network under various flood warning scenarios. The results show the marginal benefitassociated with providing better flood warnings is significantly constrained if people behave in a more risk-toler-ant manner, especially in high-density residential areas. The results also show significant impacts of humanbehavioral heterogeneity on the benefits of flood warnings, and thus stress the importance of considering humanbehavioral heterogeneity in simulating flood warning-response systems. Further study is suggested to moreaccurately model human responses and behavioral heterogeneity, as well as to include more attributes of resi-dential areas to estimate and improve the benefits of flood warnings.

(KEY TERMS: agent-based modeling; behavioral heterogeneity; decision support systems; evacuation; floodwarning; flooding; simulation.)

Du, Erhu, Samuel Rivera, Ximing Cai, Laura Myers, Andrew Ernest, and Barbara Minsker, 2017. Impacts ofHuman Behavioral Heterogeneity on the Benefits of Probabilistic Flood Warnings: An Agent-Based Model-ing Framework. Journal of the American Water Resources Association (JAWRA) 53(2):316-332. DOI: 10.1111/1752-1688.12475

INTRODUCTION

Flooding is a common weather disaster in the Uni-ted States (U.S.) that has caused significant socialand economic loss (Smith and Matthews, 2015). Floodwarnings have been shown to be effective in reducingflood-related deaths and economic loss from flood

damages (Estrela et al., 2001). Some studies suggestthat as little as 1 h of lead time can reduce flooddamages by 10-20%, with potential savings of $1.62billion annually in the U.S. (National HydrologicWarning Council, 2002). In addition, many case stud-ies around the world have reported the impact ofearly flood warning systems on saving human lives(Golnaraghi et al., 2008).

1Paper No. JAWRA-16-0041-P of the Journal of the American Water Resources Association (JAWRA). Received January 30, 2016; acceptedAugust 25, 2016. © 2016 American Water Resources Association. Discussions are open until six months from issue publication.

2Ph.D. Student (Du, Rivera) and Professor (Cai, Minsker), Ven Te Chow Hydrosystems Laboratory, Department of Civil and Environmen-tal Engineering, University of Illinois at Urbana-Champaign, 205 North Mathews Avenue, Urbana, Illinois 61801; and Professor (Myers),Center for Advanced Public Safety, and Professor (Ernest), Environmental Institute, University of Alabama, Tuscaloosa, Alabama 35487(E-Mail/Du: erhudu2@illinois.edu).

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Flood warning systems, which have often beendescribed as a combination of tools and processesembedded in different institutional, organizational,and infrastructure systems, are composed of (1)knowledge-based modeling and forecasting of flood-ing; (2) a monitoring and warning system; (3) aninformation dissemination system; and (4) public pre-paredness and response. It is argued that the effec-tiveness of these systems is often rooted in theaccuracy of the forecast, the lead time of the warning,and stakeholder’s understanding of how the risk istranslated and interpreted by the public, which ulti-mately will translate into direct actions (World Bank,2010). Naturally, a considerable amount of researchand development has focused on providing floodwarnings that have both high prediction accuracyand sufficient warning lead time (Siccardi et al.,2005; Verkade and Werner, 2011). Recent advancesin predictions have allowed the public to obtain morereliable information in a timely manner, and longertime for planning and strategizing by emergencyresponders (Cloke and Pappenberger, 2009; Golding,2009; Arheimer et al., 2011).

Nevertheless, improvements in these areas do notin themselves reduce risk in disaster situations asreliable and timely warnings do little good if not fol-lowed by (early) actions. Research has demonstratedthat people’s behavior during disaster events canhave major impacts on the effectiveness of emergencyresponse and evacuation plans (Starcke and Brand,2012; Durage et al., 2014). These studies have hadlimited consideration of how human’s heterogeneousresponse to flood warnings affect the evacuation pro-cesses (i.e., considering how people respond differ-ently to flood warnings). There is a need for a morecomprehensive understanding of how human evacua-tion processes are affected by interpretations of floodwarning information and, ultimately, how thesetranslate into actions (Dash and Gladwin, 2007).

Evacuation decision-making processes remain com-plex and uncertain. This is especially true when onetries to understand human cognition processes underdisaster situations, which are affected by risk aver-sion, interpretation of warning systems, preparednessand education on evacuation procedures, etc. (Dashand Gladwin, 2007). Moreover, to better understandhow human behavior systemically affects evacuationprocesses, one must consider the socioeconomicaspects of households (e.g., residential location, accessto evacuation transportation, previous experienceswith floods, etc.) that affect all stages of evacuationprocesses. Considering all of these human behavioraland social-economic factors and their heterogeneitieshas often been identified as one of the primary chal-lenges for effective flood warning systems (Pan et al.,2007; Dawson et al., 2011).

Considerations such as what level of warning and/or with how much lead time the warning should beissued are critical to the effectiveness of flood warn-ing systems. Earlier lead times have not proven tonecessarily reduce the level of flood damages or lossof life, as the uncertainty with the forecast at thosetimes is often quite high (Schr€oter et al., 2008). Atthe same time, people have different risk aversionaptitudes that create difficulty in understanding whatlevel of warning should be issued. High-risk warningswith high uncertainty could result in loss of trust inthe flood warning system, whereas a low-risk warn-ing can result in catastrophic consequences if people’srisk aversion levels are above it. Thus, there is aneed for a framework that allows for a better under-standing of how the heterogeneity of response to floodwarnings influences the effectiveness of flood warningsystems.

This study proposes an agent-based modelingframework to incorporate human behavioral hetero-geneity into flood warning-response systems. Theobjective is to test the hypothesis that the benefits offlood warnings will vary depending on heterogeneousresponses to flood warnings. Furthermore, this studyalso explores the relationships between the benefitsof flood warnings and residential density (RD) of floodzones. This will improve the understanding of priori-ties in developing evacuation plans for a specific com-munity, and also provide insights that will allow formore effective flood warning systems.

The remainder of this study is structured asfollows. The next section will introduce the state-of-the-art of knowledge related to this study. The thirdsection will provide a detailed description of themethodology of this study, including how the agent-based modeling framework is set up and how it is cou-pled with the traffic model. The coupled model is testedby a hypothetical case study and the preliminaryresults are presented in the fourth section, followedwith conclusions and future work in the final section.

THE STATE-OF-THE-ART KNOWLEDGE

Previous studies that explored the effects of humanbehaviors on the benefits of flood warnings mainlyfocused on gathering empirical data, often throughsurveys (Zhang et al., 2007; Lazo et al., 2010; Starckeand Brand, 2012), or simulated the evacuation pro-cess using a complex mathematical model represent-ing human rationale (Ferrell, 1983). These studieshave mostly concentrated on exploring the effective-ness of different evacuation plans under differentflooding and traffic scenarios. These studies allow the

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inclusion of traffic dynamics on different road net-works, and explicit modeling of rules that mimichuman rationale and adaptability during emergencysituations, and they have enabled a better under-standing of which factors influence the effectivenessof evacuation procedures. For example, Dawson et al.(2011) integrated a dynamic agent-based model witha hydrodynamic model and a traffic model, with theobjective of understanding the probability of an indi-vidual being exposed to flood under different stormsurge conditions and warning lead times. The resultsof this study demonstrated that the number of peopleexposed to dangerous water depths increases mono-tonically as the storm surge height increases as thewarning time becomes shorter. For a case study inthe United Kingdom, there was almost a fourfoldreduction in the number of agents exposed to floodwhen an effective flood warning system is used thatconsiders the dynamics of the decision-making pro-cesses and consequential behaviors within the trans-portation system.

Among the studies that have explored the value ofthe warning information as a function of its ownattributes is the analysis presented by Schr€oter et al.(2008). This study analyzed the effectiveness and effi-ciency of an early warning system for flash floods. Byusing historical data in two river basins, the authorsanalyzed the relationship between the reliability ofinformation and the potential damage reduction as afunction of the warning lead time. In addition, theauthors compared the benefits and costs associatedwith using an early warning system as a function ofthe warning lead time. The authors found that longerlead times did not necessarily result in larger benefitsas the reliability of the information at these timeswas often low. Finally, the study concluded thatamong the main factor affecting the effectiveness ofthe warning systems was stakeholder awareness, andthat perhaps this was as important as improvementsin flood forecast accuracy.

Similarly, Verkade and Werner (2011) assessed thecost-benefit ratio of providing flood warning informa-tion. Using a case study in White Cart Water in Glas-gow, United Kingdom, the authors presented aframework to estimate the flood risk reduction whenusing flood forecasting, warning, and response sys-tems. Using a hydro-economic model of expectedannual damage due to flooding, combined with theconcept of Relative Economic Value, the method wasable to estimate the benefits associated with reduc-tion in flood losses while considering the cost of pro-viding the warnings and the cost associated withforecast uncertainty. The study demonstrated thatthe use of a probabilistic forecast had the potential togain higher benefits for any given lead time. It alsodemonstrated that the lead time of the warning

information should be a function of the forecastuncertainty and the cost-loss ratio of the peoplereceiving and responding to the warning, as longerlead times do not necessarily lead to a larger reduc-tion in flood risk.

These previous studies have provided informationon how the effectiveness of using flood warning infor-mation is affected by the accuracy of the predictionand the warning lead time, and/or have providedmodels of human decision-making processes and theireffects on evacuation processes. Nevertheless, none ofthe previous studies has integrated the heterogeneityin people’s behaviors with the effectiveness of floodwarning information. Moreover, these studies haverelied mostly on historical data to draw conclusionsabout the cost-benefit of using flood warning systems.There is still a need for a framework that bridges thegap between these elements, where the empiricaldata gathered in previous studies would informhuman decision-making rules and their interactions,while at the same time consider uncertainties in theflood warning information. The central premise ofthis study is to explore how interpretation andresponse to flood warnings affect the benefits of theinformation provided by the flood warning systems.In other words, the study aims to understand themarginal benefit of providing a more accurate fore-cast and/or longer lead times given the heterogeneityin risk aversion aptitudes and their socioeconomicenvironments.

METHODOLOGY

Responses to flood warnings are very diverse asthey are often influenced by many socioeconomicaspects (e.g., social class, age, gender, past experiencewith floods, flood insurance, etc.) and by the valuesand beliefs of family and neighbors (Mileti, 1995;Parker et al., 2009). The interactions among peoplewith such diverse behaviors will eventually form acomplex and dynamic system (human community) inwhich all its subsystem components (individuals) areinterconnected with and affected by each other (Liuet al., 2007; An, 2012). This property of the complexsystem imposes challenges to the use of traditional,top-down, centralized simulation approaches (e.g.,optimization). Agent-based modeling has often beensuggested as an appropriate solution to this kind ofproblem for capturing the dynamic feedback of sub-system components and their inherent complexities(Heath et al., 2009). Unlike top-down approaches,which assume centralized control of decision-makingprocesses, agent-based modeling takes a bottom-up

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approach in which each system component is simu-lated as an autonomous, interdependent, and adap-tive agent with heterogeneous attributes and decisionrules (Bonabeau, 2002; Macy and Willer, 2002).

However, simulating such complex systematicinteractions can be quite computationally expensive,which has constrained the application of agent-basedmodels in simulating complex systems. With moreadvanced high-performance computing technologiesdeveloped in recent years, agent-based modeling hasbeen more widely applied to simulating humanbehaviors in many areas, such as river basin manage-ment (Cai et al., 2011; Hu et al., 2015), land use andland cover change (Kelley and Evans, 2011; Ralhaet al., 2013), agriculture and ecosystems (Doran,2001; Ng et al., 2011), economic and financial mar-kets (Raberto et al., 2001; Zhao et al., 2013), and sim-ulation of flood and other natural disaster events (Shiet al., 2009; Zhang et al., 2009; Aschwanden et al.,2012). These studies have shown that an agent-basedmodeling approach can potentially better representempirical systems and improve understanding of therelationships among different system components.Therefore, this study adopts an agent-based modelingapproach to simulate flood warning-response systems.The model simulates (1) a geographical system thatconsists of a group of residents (defined as agents)and a transportation network; (2) probabilistic floodwarnings that indicate the probability of flood withina specified lead time (e.g., 80% chance of having aflood within 5 h); and (3) decision-making processesthat describe how the agents make evacuation deci-sions after receiving the flood warnings and how theyevacuate to the safe area through the transportationnetwork following certain evacuation rules (Fig-ure 1a). The architecture of the proposed agent-basedmodel is shown in Figure 1b. The upper level of themodel describes the geographical environment andflood warning information that all of the agentsreceive. The lower level of the model describes howan agent is defined by its attributes and behaviors.

Responses to flood warnings result from integra-tion of a set of decision-making processes thatincludes reception of flood warning information,social psychological processes for understanding thisinformation, and actions to reduce flood damage(e.g., moving valuables to flood-free places, evacuat-ing to safe areas) (Mileti, 1995). Transportation net-works are important factors that affect both people’sevacuation strategies and the total time needed forevacuation during emergencies (Chen and Zhan,2008). Thus, the proposed agent-based modeltakes both human components (people and theirdecision-making processes after receiving flood warn-ings) and evacuation transportation networks intoconsideration.

Transportation Network and Traffic Rules

The transportation system plays a pivotal role inevacuation planning and management and is framedin the National Response Framework (NRF) as a crit-ical infrastructure during natural disasters and otheremergencies (Department of Homeland Security,2013; Murray-Tuite and Wolshon, 2013). The trans-portation system is an integrated system includingtransportation networks, vehicles in the networks,and traffic rules that regulate the movements andinteractions of the vehicles. Thus, modeling a trans-portation system includes simulating two compo-nents: (1) the transportation network itself; and (2)the traffic rules of the transportation network thatall vehicles should follow. Regarding the first compo-nent, the complexities associated with transportationnetworks make it challenging to explicitly include allof their features in simulation model. To manage thiscomplexity, many studies have suggested the use ofsimplified representations of transportation networks,such as a directed graph (Sheffi et al., 1982; Covaand Johnson, 2003; Zhang et al., 2009), which con-tains a set of nodes, edges, and weights associatedwith edges.

Edges and nodes in a directed graph represent atransportation networks’ routes and route intersec-tions. The weight of an edge represents the cost ofusing the route it represents (e.g., distance of theroute, speed limit, route capacity, etc.). Mathemati-cally, a graph can be represented as a matrix. Forexample, the row and column of a matrix elementcan represent the starting and ending nodes of anedge, respectively, whereas the value of the elementrepresents the cost (i.e., length) of the edge. Edgesassociated with nodes that are not directly connectedare assigned an infinite cost to represent that nodirect evacuation route exists between them. Figure 2is an example representation of a transportation net-work as a graph. The transportation network in Fig-ure 2a consists of four nodes (node 1, 2, 3, and 4); thedirected edges among these nodes represent connec-tions among them. The matrix in Figure 2b is themathematical representation of the directed graph.Note that no direct edge connects node 3 to node 4; inthe matrix, the length from 3 to 4 is therefore set tobe infinite.

Traffic rules, as mentioned above, are also impor-tant components in transportation system simulation.Traffic rules regulate the movements and interactionsof each individual vehicle in the network. Among avariety of traffic simulation methods developed inrecent decades, individual-oriented methods havebeen suggested as powerful simulation tools for repre-senting individual interactions and systematic trafficflow pattern in a transportation system (Chen and

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Zhan, 2008). The Nagel-Schreckenberg model (N-Smodel), first proposed in 1992 by Nagel and Schreck-enberg (1992), is a widely used, individual-orientedmethod in both theoretical and empirical studies. TheN-S model divides a road into cells and categorizes avehicle’s actions on the road into four groups in atime unit: acceleration, deceleration, randomization,and movement. As demonstrated in Figure 2a, forvehicle i and vehicle j traveling from node 1 to node 3with traveling speed vi and vj, respectively, the speedof vehicle i is determined by the following rules foreach time step:

1. If the distance between vehicle i and vehicle j isgreater than a safe distance, the vehicle willaccelerate, increasing moving speed by a unit. As

there is a speed limit on each edge, the vehicle’smoving speed would not exceed the road’s maxi-mum limit speed.

2. If the distance between vehicle i and vehicle j isless than a safe distance, the vehicle willdecrease its moving speed by a unit.

3. A vehicle will randomly change its speed by oneunit with a certain probability.

4. At the end of each time step, a vehicle will moveone time step and update its location on its cur-rent route.

Because the N-S model can capture empirical traf-fic phenomena and allow for parallel computing, ithas been widely applied in many studies and hasbeen developed as the Transportation Analysis and

FIGURE 1. Illustration of (a) the Main Components of the Flood Warning-Response System and (b) the Architecture of the Agent-BasedModel. The four figures in Figure (a) represent: (1) flood warning managers issue a flood warning to residents, (2) residents receive the floodwarning and make evacuation decisions (stay or evacuate), (3) residents evacuate through the transportation network, and (4) agents’ finalevacuation status, respectively. Figure (b) illustrates the structure of the model. The upper level of the structure represents agents’ environ-ment (i.e., geographical system and flood warning information). The lower level represents the attributes and behaviors that are used todefine agents (see Table 1).

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Simulation System for regional transportation systemanalysis (Smith et al., 1995; Nagel and Rickert, 2001;Lee et al., 2014). In our study, we use the N-S modelto simulate evacuation processes on transportationnetworks, assuming that they will follow the rulesdefined in the N-S model. We assume that individualsfollow the all-way stop rule when multiple vehiclesarrive at a road intersection at the same time: a vehi-cle that arrives first has precedence over vehiclesthat arrive later.

Household Agents

In the face of flood risk, we assume that all familymembers in a household will affect each other inarriving at final evacuation decisions. Both empiricaland theoretical flood warning studies are typicallyconducted at the household level (Parker et al.,2007). Household demographics (e.g., location, educa-tion, income, etc.) are therefore assumed to providesufficient information regarding socioeconomicaspects of each agent. Therefore, each household issimulated as an agent in this study. An agent isdefined by the attributes and decision rules thatrelate it to flood warning responses and actions (Fig-ure 1b). We assume that all agents share a trans-portation network for evacuation during emergenciesand will receive a flood warning at the same time.

The agents will need to make decisions regardingwhether to evacuate to a flood-free area outside ofthe neighborhood. The decision-making processesdepend on each agent’s attributes and decision rules.The following sections introduce how we define theagent’s attributes and decision rules in this study.

Agent Attributes. Agent attributes are definedas a set of parameters that describe the characteris-tics of an agent. In this particular study, in whicheach household is defined as an agent, agent attri-butes refer to the characteristics of each householdthat relate to flood warning responses and evacuationprocesses. Previous studies have shown that floodwarning responses and evacuation processes areaffected by many physical, psychological, andsocioeconomic factors (Drabek, 1999; Gladwin et al.,2009; Parker et al., 2009). However, representing allof these factors in a model is challenging when lack-ing empirical data. Therefore, in this study, we sim-plify the representation of these factors and classifyan agent’s attributes as physical attributes that arerelated to its evacuation process, and psychologicalattributes that are related to its response to floodwarnings (Table 1).

Physical attributes describe an agent’s physicalcharacteristics related to flood warning responsesand evacuation actions (e.g., location of a house,house type, construction material of the house, etc.).

FIGURE 2. Illustration of (a) a Transportation Network Represented by a Directed Graph and (b) Matrix Representation of the Network. InFigure (a), numbers inside nodes denote node numbers. Arrows of edges denote connections between nodes. Single arrow denotes one-way

edge (e.g., agents can only move from node 4 to node 3, not in the other direction).

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To capture the attributes that are essential for simu-lating the agents’ evacuation processes and evaluatingthe benefits of flood warnings, three types of physicalattributes are included: agent’s geographical location(G), maximum evacuation speed (Vmax) in the trans-portation network, and evacuation status (ES) at theend of the simulation period. An agent’s geographicallocation in the transportation network is representedby three variables (i.e., Ns, Ne, d) that indicate theagent’s movement from starting node (Ns) to endingnode (Ne) and the distance between its current loca-tion and Ns (d). For example, the geographical locationof agent i in Figure 2a can be denoted by [1, 3, di]. Anagent’s maximum evacuation speed defines its maxi-mum moving speed on a route in a transportation net-work, which is assumed to be the maximum speedlimit of the evacuation route in this study. ES repre-sents an agent’s evacuation status at the end of thesimulation period. ES is a categorical variable forwhich there are only three values: 1 (denotes that anagent stays at its initial location without consideringevacuation); 2 (denotes that the agent is currentlyevacuating but has not arrived at the safe area), and 3(denotes that the agent has arrived at the safe area).

Psychological attributes measure an agent’s risktolerance (RT) to flood risk in flood warning systems.Many studies have shown that responses to floodwarnings are affected by sociopsychological factorssuch as understanding of flood warnings, interpreta-tion of risk, rationality in decision making, past expe-riences with floods, etc. (Weinstein and Klein, 1995;Brewer et al., 2004; Zhang et al., 2007). When a floodwarning is issued, an agent will consider all of thesefactors in making evacuation decisions. Lackingempirical data to represent the complex intercon-nected relationships among these factors, in thisstudy we summarize all of these factors into a singleparameter, RT threshold, to measure an agent’s max-imum tolerance level for flood risk, where flood riskis represented by the probability of floods in theneighborhood. The agent will decide to evacuate to asafe area if the flood risk exceeds his or her tolerance

threshold. We introduce quantification of RT in thecase study section of this article.

Naturally, the agents will behave differently inaddressing these flood risks. Risk-tolerant agents willnot respond as actively as risk-averse agents. Twocommon methods for representing the heterogeneityof an agent’s decision are (1) to classify agents intoseveral categories (e.g., Li and Liu (2007) dividedhousehold agents in a city into six groups based onthe agents’ income and household size; Ng et al.(2011) divided farmer agents into bold and cautiousgroups based on the agents’ adaptation of biofuelcrops), and (2) to continuously vary agent’s behav-ioral parameters (e.g., Benenson (1999) continuouslyvaried agents’ income to study residential distribu-tion in a community; Huang et al. (2013) variedagent’s purchasing budgets and preference for loca-tion parameters to study the spatial patterns ofurban land markets). This study applies the secondmethod, continuously varying agents’ behavioralparameters, with the aim of evaluating how thesedecision parameters affect model output across abroad range of parameter settings.

Agent Behaviors. Understanding flood warninginformation and making evacuation decisions are verycomplex processes (Mileti, 1995). Simplified decision-making processes have been applied by many studiesto simulate evacuation behaviors during natural disas-ters (Shi et al., 2009). In our work, an agent’s responseto flood warnings is simplified into three steps: (1)decide if evacuation action should be taken based onthe flood risk; (2) choose an evacuation path if theagent decides to evacuate; and (3) evacuate throughthe selected path following traffic rules.

Based on these three decision-making processes,three types of behaviors are simulated in this work:evacuation decision, evacuation path search, andreal-time evacuation speed (Figure 1). Evacuationdecision describes the process of an agent receivingflood warnings and deciding if the agent wants toevacuate to a safe area or not. An agent’s evacuationdecision depends on the probability of flooding andthe agent’s RT threshold. An agent will decide toevacuate if the probability of flooding exceeds its RTthreshold. Otherwise, agents will choose not to evacu-ate even if there is a flood warning. The second typeof behavior describes how an agent selects its evacua-tion path to the safe area. In this study, it is assumedthat all of the agents have good knowledge about thetransportation network and they will choose theshortest path from their current locations to the safearea as their evacuation path.

Besides evacuation route selection, the thirdimportant behavior is deciding on the evacuationspeed at each time step. As an agent evacuates on a

TABLE 1. List of Agents’ Attributes

Factors Variables Description of the Variable [unit]

Physical i Agent’s unique identificationnumber [-]1

ES Agent’s evacuation status at the endof simulation [-]

G Agent’s geographical location inneighborhood [-]

Vmax Maximum evacuation speed intransportation network [L/T]

Psychological RT Risk threshold to flood risk [-]

1[-] denotes dimensionless parameter.

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route, its speed is contained by (1) its own maximumevacuation speed; (2) maximum speed limits on theroute; and (3) the location and evacuation speed ofother agents on the same route. In this study, theagents’ real-time evacuation speed is regulated by theN-S traffic model; for more details of how the movingspeed of an agent is determined, see Nagel andSchreckenberg (1992).

Model Implementation

We implement the agent-based model using anobject-oriented programming language, Java. Themodel execution process can be summarized in threesteps (Figure 3): (1) prepare input data to constructagents; (2) execute agent-based model; and (3) ana-lyze and output model execution results. The follow-ing sections introduce more details on theimplementation of each of these steps.

Step 1. Prepare Input Data to ConstructAgents. Two types of input data are needed to ini-tialize the model: input data for agents and inputdata for evacuation transportation network. Inputdata for agents define each individual agent’s attri-butes and behavior parameters, which are listed inTable 1. One of this study’s main objectives is tounderstand how the agent’s risk threshold will affectthe benefits of flood warnings. Without empiricalknowledge about the distribution of human behaviorparameters, it is often assumed that people’s behav-ioral parameters (i.e., risk threshold in this study) fol-low probability distributions. Uniform (Hu et al.,2015) and normal distribution (Huang et al., 2013)

are two commonly applied assumptions for modelingagents’ behavior through parameter distributions.Because the coefficient of variation is a standardmeasurement of the dispersion of a distribution, thisstudy applies the normal distribution to generateagents’ risk threshold. The mean value of the nor-mal distribution measures the agents’ overall riskthreshold for floods (lRT), whereas the coefficient ofvariation (CVRT) measures agents’ behavioral hetero-geneity. Coefficient of variation is set to be zero tosimulate agents with homogeneous risk threshold.

Input data for the evacuation transportation net-work define the number of nodes and how the nodesconnect with one another in the network. One ofthese nodes is set as the evacuation destination torepresent the safe area without flood risk. To improvecomputational speed, the shortest path from anygiven location to this evacuation destination is calcu-lated before model execution and is stored in a Javahashtable with keys and values. The hashtable key isthe location of an agent in the transportation net-work. The hashtable value is the shortest path fromany given location to the evacuation destination. Thehashfunction of the hashtable will return the shortestevacuation path from the agent’s current location tothe evacuation destination.

Step 2. Execute Model. The model executionprocess starts with a probabilistic flood warning thatindicates the probability of flooding within a specifiedlead time. All of the agents will receive this floodwarning and make evacuation decisions based on thedecision rules described in the previous sections. Forthe agents who decide to evacuate through the trans-portation network, their evacuation processes are

FIGURE 3. Flowchart of the Agent-Based Model. The items along the left hand are the three model execution steps. In the final step, thebenefits of flood warnings are measured by the percentage of agents who have evacuated to safe area.

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simulated by the N-S traffic model at discrete timesteps within the flood warning lead time.

Step 3. Analyze the Benefits of Flood Warn-ings. At the end of the model execution process, themodel will return the evacuation status of eachagent. The benefits of flood warnings can be mea-sured by multiple criteria such as total flood damagereduction or saving of human life. In this study, wemeasure the benefits of flood warning by the percent-age of agents that have evacuated to the safe area atthe end of the model simulation.

Model Validation

Model validation is an essential step in the modeldevelopment process. The main objective of modelvalidation is to demonstrate that the model simula-tion results can reasonably represent or approximatethe behaviors observed in the real systems (Heathet al., 2009). A variety of model validation methodsand techniques have been proposed for agent-basedmodels (Ngo and See, 2011). Among them, structurevalidation and output validation are two of the mostimportant and common methods. The objective ofstructural validation is to demonstrate that theagent-based models can correctly represent thebehaviors and the operation rules of the real systems.Outcome validation compares the model output withobservations from real systems when empirical dataare available (Huang et al., 2013).

When empirical data are not available to quantita-tively show the interactions among the autonomousagents in the system, model validation becomes chal-lenging. To address this challenge, many studies haveused expert’s knowledge for a qualitative assessmentof the model performance (Heath et al., 2009). In thistheoretical study, with no empirical data about themodel outputs, the model validation is conducted froma qualitative perspective with empirical findings fromprevious studies (Mileti, 1995; Parker et al., 2007,2009; Paul, 2012). The output validation was done bycomparing the model output with the expert’s knowl-edge about flood warning-response systems. The nextsection gives more details about the model validation.

CASE STUDY

Transportation Network and Scenario Design

Transportation Network. A hypothetical geo-graphical system is designed as the case study. The

geographical system consists of a transportation net-work and a number of household agents (Figure 4).To consider flood warning-response systems with dif-ferent spatiotemporal scales, we use general units tomeasure length and time, following the approachadopted by Zhang et al. (2009). The length and timeunits are represented by L and T, respectively. Theevacuation transportation network has 16 nodes, withone node selected as the evacuation destination, and16 routes. Each evacuation route is assumed to be atwo-way road with one lane for each traveling direc-tion (Chen and Zhan, 2008). The total length of thetransportation network is 2,210 L. We assume thatall lanes in this network have the same speed limit(10 L/T in this study) and all route intersectionshave an all-way stop sign to regulate traffic, whichmeans that an agent arriving at the intersection firstwill take precedence over agents arriving later. Morecomplex transportation networks could be used togenerate more complex evacuation phenomena, whichare discussed further in the Conclusions and FutureWork section. The household agents are assumed tobe uniformly distributed along the transportationroutes. The RD of the neighborhood is defined as thetotal number of agents in the transportation systemdivided by the number of nodes in the network. Inthis study, the total number of agents in the trans-portation network ranges from 320 to 640 (i.e., RDranges from 20 agents/node to 40 agents/node) toexplore how RD affects agents’ evacuation processes.

Scenario Design. With the aforementionedtransportation network as a case study area, thisstudy aims to investigate how human’s heterogeneousbehaviors (i.e., RT threshold) and residential densitycould affect the benefits of flood warnings. We designthree scenarios. The first scenario is for model valida-tion, which we conduct by comparing the results of aset of experiments with empirical knowledge aboutflood warning systems. The second scenario exploreshow agent’s heterogeneous behaviors affect the bene-fits of flood warnings. The third scenario investigatesthe potential interplay between RD and flood forecastaccuracy and its effect on the benefits of flood warn-ings. Table 2 shows the parameters of these threescenarios.

This study focuses on simulating agents’ evacua-tion processes during flood events, without considera-tions of false alarms (i.e., the agents receive floodwarnings, but eventually there is no flood). Therefore,we consider flood forecast accuracy only in terms ofthe predicted flood probability. For example, for aflood forecast indicating 85% probability of having aflood in 3 h, the associated forecast accuracy and leadtime will be 0.85 and 3 h, respectively. We alsoassume that the agents will receive a flood warning

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at the beginning of model execution, and will notreceive any other flood warning information duringthe following simulation periods. In other words, theagents only receive one piece of flood warning infor-mation during the entire simulation.

RESULTS AND DISCUSSION

Scenario 1: Model Validation

In this section, we test whether our model can cap-ture the following findings of previous empirical

studies: (1) that the benefits of flood warnings have apositive relationship with flood forecast accuracy; and(2) that the benefits of flood warnings have a positiverelationship with flood warning lead time (Estrelaet al., 2001; National Hydrologic Warning Council,2002; Golnaraghi et al., 2008). The results of modelvalidation are shown in Figures 5a-5c.

Figure 5a shows that the benefits of flood warningsincrease as flood warning lead time increases. Fig-ure 5b shows that the benefits of flood warningsincrease as predicted flood probability increases. Fig-ure 5c further suggests that the benefits of floodwarnings are constrained by both predicted floodprobability and flood warning lead time. The benefitsof flood warnings are always low if predicted flood

FIGURE 4. The Transportation Network and Household Agents for the Hypothetical Case Study Area. (Numbers along routes denote thelength of routes. The number of agents in the network ranges from 320 to 640. Agents are uniformly distributed along the routes.)

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IMPACTS OF HUMAN BEHAVIORAL HETEROGENEITY ON THE BENEFITS OF PROBABILISTIC FLOOD WARNINGS: AN AGENT-BASED MODELING FRAMEWORK

probability or lead time reaches its lower limit (0.7for predicted flood probability and 200 T for floodwarning lead time). In addition to the lower limits forflood warnings, upper limits also exist beyond whichthe benefits of flood warnings will not increase signif-icantly (0.75 for predicted flood probability and 500 Tfor flood warning lead time in the case study). The

results from Figures 5a-5c demonstrate that themodel is able to capture the empirical findingsfrom experts’ domain knowledge of flood warninginformation.

Scenario 2: Relationships between the Benefits ofFlood Warnings and Agents’ Heterogeneous Behaviors

This scenario aims to explore the relationshipsbetween the benefits of flood warnings and agents’flood warning response behaviors. To be specific, thisscenario addresses two questions: (1) Will agents’flood warning response behaviors (i.e., agents’ RTthreshold) affect the benefits of flood warnings? (2)How will agents’ behavioral heterogeneity (i.e., varia-tion in agents’ RT threshold) affect the benefits offlood warnings? The first question aims to demon-strate that the benefits of flood warnings can beaffected by agents’ behaviors; the second question isintended to evaluate the importance of consideringthe characteristic of behavioral heterogeneity in sim-ulating agents’ behaviors.

Agents’ behavioral heterogeneity implies that dif-ferent agents will behave differently under identical

TABLE 2. Parameters for the Three Simulated Scenarios in theCase Study Area

Parameter [unit] Scenario 1 Scenario 2 Scenario 3

Mean value of agents’risk threshold [-]1

0.75 0.6:0.05:0.92 0.75

Coefficient of variation inrisk threshold [-]

0.1 0:0.05:0.3 0.1

Predicted floodprobability [-]

0.6:0.05:0.9 0.75 0.6:0.05:0.9

Flood forecast leadtime [T]

100:100:700 200:200:600 400

Residential density[number of agents/node]

30 30 20:10:40

1[-] denotes dimensionless parameter.2X:d:Y denotes a numeric vector from X to Y with increment of d.For example, vector [1, 3, 5, 7] can be represented by 1:2:7.

Lead time (T)0 200 400 600 800

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(c)

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-)

0.6

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0.9

FIGURE 5. (a) The Relationship between the Benefits of Flood Warnings and Flood Warning Lead Time When Predicted Flood ProbabilityIs 80%; (b) the Relationship between the Benefits of Flood Warnings and Predicted Flood Probability When Flood Warning Lead

Time Is 400 T; and (c) Contour Plot of the Benefits of Flood Warnings Associated with Predicted Flood Probability (Y-axis)and Flood Warning Lead Time (X-axis).

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environment conditions (i.e., flood warnings). In thisstudy, we measure behavioral heterogeneity by thecoefficient of variation in the agents’ risk threshold.Four groups of agents are investigated: two groups ofrisk-tolerant agents with average risk thresholdhigher than predicted flood risk, and two groups ofrisk-averse agents with average risk threshold lowerthan the predicted flood risk. We set seven levels ofbehavioral heterogeneity, with coefficient of variationin risk threshold varying from 0 to 0.3. Agents arehomogeneous when the coefficient of variation is 0.

Figure 6 shows the simulation results for a sce-nario in which the predicted flood probability (pf) is0.75 and flood warning lead time is 400 T. Theresults show that the benefits of flood warningsincrease as agent heterogeneity increases for risk-tol-erant agents (lRT > pf). The opposite phenomena holdtrue for risk-averse agents (lRT < pf). Given that theresidents’ RT follows normal distribution with meanvalue (lRT) and coefficient of variation CVRT (RT ~ N(lRT, lRTCVRT) | RT 2 [0,1]), the percentage of resi-dents (pe) who decide to evacuate after receiving floodwarning can be represented by:

pe ¼Z pf

0

pRTdRT ¼ Upf � lRTlRTCVRT

� �

where pf is the predicted flood probability of theissued flood warnings, pRT is the probability

distribution function of RT, and Φ( • ) is the cumula-tive distribution function of a standard normaldistribution. For risk-tolerant agents (lRT > pf),

pe ¼ Uð pf�lRTlRTCVRT

Þ increases as CVRT increases, indicat-

ing that more agents decide to evacuate as behavioralheterogeneity indicator (CVRT) increases. Therefore,the benefits of flood warnings increase as agentbehavioral heterogeneity increases. The oppositeholds true for risk-averse agents. This finding agreeswith previous studies that the relationship betweenagent heterogeneity and model output is not uni-formly monotonic (Huang et al., 2013). This findingsuggests that, when providing the public with floodwarning information, flood warning managers shouldnot expect that all of the public will interpret andrespond to the information in the same way. Instead,special information and consideration should be givenfor certain groups of people. For example, people whohave no past experience with floods are less likely torespond to flood warnings compared with people whohave past experience. This past experience includesnot only experiences of evacuation during actual floodevents with different flood warning systems but alsoexperiences in practicing evacuation as part of emer-gency preparedness. It has been shown that practic-ing evacuation drills is effective to enhance theawareness of flood risk and mitigate flood damages(Yamada et al., 2011). Social class, gender, and levelof education might also affect people’s understandingof flood warnings and evacuation actions (Parkeret al., 2007). These findings show that flood warningmanagers should take the heterogeneity of humanattributes into consideration when issuing floodwarnings. For example, the model results suggestthat risk-tolerant agents will not take actions to evac-uate unless they are provided with warnings of highflood probability. Thus, it is important for flood warn-ing managers to identify risk-tolerant agents in thecommunity and provide additional information orresources to aid their decision making.

Besides risk threshold heterogeneity, agents’ aver-age risk threshold is also an important factor affect-ing the benefits of flood warnings. To understand therelationship between flood warning benefits andagents’ average risk threshold levels, we investigatethree different flood warnings with the same pre-dicted flood probability but different lead times (Fig-ure 7). The results provide at least two insights.First, as expected, modeled flood warnings withlonger lead times outperform those with relativelyshorter lead times, as longer lead times allow theagents more time to respond to flood warnings andevacuate to safe areas. However, the results alsoshow that the marginal benefit from the improvementin lead time depends, to a great extent, on the agents’

Coeffient of variation of agents' risk threshold (-)0 0.05 0.1 0.15 0.2 0.25 0.3

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war

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(-)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

(RT) = 0.6(RT) = 0.7(RT) = 0.8(RT) = 0.9

FIGURE 6. The Relationship between the Benefits of Flood Warn-ings and Agent’s Behavioral Heterogeneity When Predicted FloodProbability (pf) is 75% and Flood Warning Lead Time is 400 T.Results for risk-tolerant agents (lRT > pf) are shown by dottedlines. Results for risk-averse agents (lRT < pf) are shown by solidlines.

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risk threshold. More benefits could be achieved byincreasing warning lead times for risk-averse agentsthan for risk-tolerant agents. However, even a longerwarning lead time yields no additional benefits if theagents’ risk threshold exceeds a limit (0.85 in thiscase). This suggests that risk-tolerant agents will notbenefit from flood warnings with longer lead times iftheir risk thresholds do not change. This findingleads to the second insight of the results: in additionto providing the public with better flood warninginformation, informing them about how to respond toflood warnings could be an effective way to reduceflood-related damage. For example, the model resultshere show that there are almost no additional bene-fits if the flood warning lead time is increased from200 T to 400 T when the agents’ average risk thresh-old is 0.80. However, a benefit increase of 0.22 isachieved if the agents become more risk averse, withthe risk threshold reduced from 0.8 to 0.75 (from A toB in Figure 7). Empirical studies have shown thatpeople’s understanding of flood risk is often not nec-essarily logical, leading to misjudgment of flood risk(Tversky and Kahneman, 1973; Weinstein and Klein,1995); educating them how to respond appropriatelycould be beneficial. Thus, combining appropriate floodwarning response with reliable information can makeflood warnings more valuable.

Scenario 3: Impact of Residential Density on theBenefits of Flood Warnings

This scenario aims to understand how the attri-butes of residential properties affect agent’s

evacuation process and ultimately affect the benefitsof flood warnings. The attributes of residentialproperties can be measured by multiple matrices,such as distribution, density, educational level, andsocial class of residents, etc. In this particularstudy, we only focus on RD, which may signifi-cantly affect traffic load during an emergency evac-uation process.

Figure 8 explores the impacts of RD on the bene-fits of flood warnings under different flood warningscenarios. In general, flood warnings with higher pre-dicted flood probability are associated with greaterbenefits, especially in low-density residential areas.However, the benefits associated with more accurateflood warnings is constrained in high residentialareas because a large fraction of the agents that takeevacuation actions may not successfully evacuate to asafe area as a result of traffic congestion caused byhigh traffic loads. In other words, the marginal bene-fit of providing higher predicted flood probability ishigher in low residential areas than in high residen-tial areas. Therefore, the model results show that itis more effective to increase predicted flood probabil-ity in low residential areas. In contrast, in high resi-dential areas, increase in predicted flood probabilitydoes not yield a significant increase in the benefits offlood warnings. Instead of working on increasing pre-dicted flood probability, increasing flood warning leadtime or improving evacuation routes may be morebeneficial.

Figure 9 summarizes agents’ evacuation statusand evacuation times under different residential den-sities. As RD increases, the number of agents whodecide to evacuate through the transportation

Agent's average risk threshold (-)0.6 0.65 0.7 0.75 0.8 0.85 0.9

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(-)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Lead time = 200 TLead time = 400 TLead time = 600 T

A

B

FIGURE 7. The Relationship between the Benefits of FloodWarnings and Agents’ Average Risk Threshold Under Three FloodWarning Scenarios in Which Predicted Flood Probability Is 75%

and Lead Times Are 200 T, 400 T, and 600 T, Respectively.

0.10.10.1

0.20.20.2

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Residential density (number of agents/node)10 20 30 40 50 60 70

Pre

dict

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prob

abili

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-)

0.6

0.65

0.7

0.75

0.8

0.85

0.9

FIGURE 8. Contour Plot of the Benefits of FloodWarnings, ResidentialDensity, and Predicted Flood Probability When Agents’ Average RiskThreshold Is 0.75 and Coefficient of Variation in Risk Threshold Is 0.1

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network increases. This results in two phenomena asshown in Figure 9. First, the percentage of agentswho successfully evacuate to the safe area decreasesas RD increases. For example, 100% of the agentsthat decide to evacuate can successfully evacuate tothe safe area when the RD is 20 agents/node. How-ever, this value decreases to 81 and 68% when theRD is 30 agents/node and 40 agents/node, respec-tively (Figure 9a). Second, the average evacuationtime for all of the agents increases as RD increases,which is 150.2 T, 162.3 T, and 169.6 T when RD is 20agents/node, 30 agents/node, and 40 agents/node,respectively (Figures 9b-9d). The model results sug-gest that RD is an important factor that affects theagents’ evacuation process in the transportation net-work. Flood warning managers need to pre-estimatethe total time needed for the people to evacuate tothe safe area when issuing flood warnings, especiallyin high residential areas where traffic load can behigh when all people decide to evacuate.

To further investigate how RD affects agents’ evac-uation processes, we simulate the evacuation processwhen RD is 20 agents/node, 30 agents/node, and 40agents/node, respectively. The simulation results areshown in Figure 10. The time needed for 50% (100%)of the agents to evacuate to the safe area is approxi-mately 200 T (580 T) when RD is 30 agents/node.This time is approximately 150 T (430 T) and 250 T

(785 T) when the RD is 20 agents/node and 40agents/node, respectively. The results suggest thatmore evacuation time is needed to achieve high floodwarning benefits when RD increases. For example,when RD increases by 33% (from 30 agents/node to40 agents/node), the time needed for 50% of theagents to evacuate to the safe area increases by 25%

Scenario1 2 3

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ES = 1 (stay at home)ES = 2 (is evacuating)ES = 3 (has evacuated)

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Evacuation Time (T)0 100 200 300 400

Num

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s (-

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50(d)

FIGURE 9. Agents’ Evacuation Statistics When Predicted Flood Probability Is 80% with Flood Warning Lead Time of 400 T. (a) Summary ofthe agents’ evacuation status when residential density is 20 agents/node (scenario 1), 30 agents/node (scenario 2), and 40 agents/node(scenario 3), respectively; (b-d) distribution of agents’ evacuation time (i.e., the time that an agent takes to evacuate to safe area) for

scenarios 1, 2, and 3.

Time (T)0 100 200 300 400 500 600 700 800

Per

cent

age

of e

vacu

ated

age

nts

(%)

0

20

40

60

80

100

20 (agents/node)30 (agents/node)40 (agents/node)

Residential Density (RD)

FIGURE 10. Simulation of Agents’ Evacuation Processes WhenResidential Density Is 20 Agents/Node (dashed line), 30 Agents/Node (solid line), and 40 Agents/Node (dotted line), Respectively.

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(from 200 T to 250 T). However, the time for 100% ofthe agents to evacuate to the safe area increases by35% (from 580 T to 785 T). Similar conclusion can bedrawn when RD increases from 20 agents/node to 30agents/node. This implies that achieving high benefitsfrom flood warnings is much more challenging inhigh residential areas than in low residential areasbecause the increase in evacuation time is largerthan the increase in agent population.

CONCLUSIONS AND FUTURE WORK

This study proposes an agent-based modelingframework for incorporating the quality of floodwarnings (i.e., predicted flood probability and leadtime), the heterogeneous nature of response to floodwarnings (i.e., the mean and coefficient of variationin agents’ risk threshold), and RD in flood warning-response systems. The framework is coupled with atraffic model to evaluate how these components inter-play with each other to affect agents’ evacuation pro-cesses in the face of flood warnings. There are threeimportant findings from this study: (1) the benefits offlood warnings are affected not only by the quality offlood warning information but also by responses tosuch information; (2) the marginal benefit associatedwith providing better flood warnings is significantlyconstrained if people behave in a more risk-tolerantmanner; and (3) RD plays an important role in evacu-ation effectiveness and ultimately the benefits of floodwarnings. This highlights the need for different floodwarnings depending on the specific RD of flood zones.

While tremendous efforts have focused on provid-ing better flood warning information to the public,this study suggests that collecting and using informa-tion on human behaviors and residential characteris-tics of flood-threatened areas will make floodwarnings more beneficial. Such information can helpflood warning managers increase warning efficiencyby enabling them to determine when and how torelease flood warnings to the public. With advancedinformation delivery technologies such as socialmedia, it is not beyond the realm of reality that all ofthis information could be available and accessible inreal time. Twitter, Facebook, and cell phone locationservices could provide real-time information aboutflood situations and recommended actions in floods.Flood warning managers could also collect and useinformation from social media to update the currentflood forecast with increased detail and accuracy(Smith et al., 2015). Such information may also assistemergency managers to rescue people during floods.For example, in the 2011 Thai flood, Twitter was

used by local citizens to collect and disseminate up-to-the-minute flood information and requests forassistance. It was quite beneficial to emergency man-agers to analyze and use this Twitter information toprovide assistance in a timely manner according tospecific needs (Kongthon et al., 2012).

This study is a theoretical modeling framework toinvestigate the complexities of flood warning-responseand evacuation systems and inevitably has some limi-tations. First, we simulate a single flooding eventwithout considering the public’s behavioral changesresulting from past experiences of flood events. Inreality, people might change their flood RT based ontheir past experiences. For example, after experienc-ing several flooding events and high flood-relatedcosts, risk-tolerant agents might become risk-averseagents. Future work can obtain residents’ socioeco-nomic and demographic data and their responses toflood warnings to understand the decision-makingprocesses during flood events. Second, in this study,we assume that all of the agents remaining in thearea at the end of model execution will be flooded,and the agents who have evacuated to the safe areabefore the end of model execution will not be flooded.Thus, we did not specify the direction, speed, or tim-ing of the flood inundation processes. In future work,we will simulate the gradual inundation processes tobetter model flood behaviors in the real world. Third,some assumptions of the theoretical model may notapply to real-world situations. For example, weassume that all of the households are knowledgeableabout evacuation paths and will choose the shortestone. However, in reality the agents might dynami-cally change evacuation paths based on real-timetraffic conditions and warning information. Furtherexploration of the impact of individual’s route choicebehaviors on transportation conditions during evacu-ations has been previously suggested (Pel et al.,2011) and our study concurs with this need. Finally,this study assumes that agents make independentevacuation decisions without communicating witheach other. In the real world, relatives, neighbors,and friends greatly affect evacuation decisions (Par-ker et al., 2009). In general, interactions amongagents affect not only individual behaviors but alsothe emergence of the overall system. Future workmay explore how an agent’s decisions are related tothe agent’s geographical location in the residentialarea (e.g., agents who are more close to safe areasmay be more likely to behave in a risk-tolerant man-ner). Other socioeconomic household characteristics(e.g., size of household, economic value of the home,pet ownership) might also affect agents’ behaviors.This study can be expanded by incorporating addi-tional socioeconomic heterogeneities into the model.These improvements can better capture the complex

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behaviors of flood warning-response systems and helpemergency managers with more informed decisionmaking during flood events.

ACKNOWLEDGMENTS

This study was conducted during the inaugural National FloodInteroperability Experiment (NFIE) Summer Institute of 2015. Theauthors would like to acknowledge the National Weather Service,the National Science Foundation, and the Consortium of Universi-ties for the Advancement of Hydrologic Science (CUAHSI), theUniversity of Alabama and the National Water Center for support-ing this event. We would like to thank Dr. David Maidment, Fer-nando Salas, Emily Clark, and many others for their coordinationand advice during NFIE. Lastly, the authors thank the reviewersand Associate Editor Sandra Fox for their helpful comments thatsignificantly improved this study.

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