A novel agent‑based model for tsunami evacuation simulation and risk assessment

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ORIGINAL PAPER

A novel agent‑based model for tsunami evacuation simulation and risk assessment

Zhenqiang Wang¹ · Gaofeng Jia¹

Received: 29 March 2020 / Accepted: 17 October 2020 / Published online: 1 November 2020

Abstract

Tsunami evacuation is an effective way to save lives from the near-field tsunami. Real- istic evacuation simulation can provide valuable information for accurate evacuation risk assessment and effective evacuation planning. Agent-based modeling is ideal for tsunami evacuation simulation due to its capability of capturing the emergent phenomena and modeling the individual-level interactions among agents and the agents’ interactions with the environment. However, existing models usually neglect or simplify some important factors and/or mechanisms in tsunami evacuation. For example, uncertainties in seismic damages to the transportation network are not probabilistically considered (e.g., by simply removing the damaged links (roads/bridges) from the network). Typically a relatively small population (i.e., evacuees) is considered (due to computational challenges) while neglecting population mobility. These simplifications may lead to inaccurate estimation of evacuation risk.

Usually, only single traffic mode (e.g., on foot or by car) is considered, while pedestrian speed adjustment and multi-modal evacuation (e.g., on foot and by car) are not considered concurrently. Also, pedestrian–vehicle interaction is usually neglected in the multi-modal evacuation. To address the above limitations, this study proposes a novel and more realistic agent-based tsunami evacuation model for tsunami evacuation simulation and risk assessment. Uncertainties in seismic damages to all links in the transportation network as well as uncertainties in other evacuation parameters are explicitly modeled and considered. A novel and more realistic multi-modal evacuation model is proposed that explicitly considers the pedestrian–vehicle interaction, walking speed variability, and speed adjustment for both the pedestrian and car according to traffic density. In addition, several different population sizes are used to model population mobility and its impact on tsunami evacuation risk. The proposed model is applied within a simulation-based framework to assess the tsunami evacuation risk assessment for Seaside, Oregon.

Keywords Agent-based model · Tsunami evacuation · Risk assessment · Seismic damage · Transportation network · Pedestrian–vehicle interaction

* Gaofeng Jia

[email protected]

1 Department of Civil and Environmental Engineering, Colorado State University, Fort Collins, CO, USA

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1 Introduction

An earthquake-induced tsunami can damage infrastructure, injure, or even kill people.

Evacuation to safety zones is an effective way to save lives from tsunami strikes due to the short time for the tsunami to arrive after the earthquake, especially for near-field tsunami tsunamis (Katada and Kuwasawa 2006; Wang et al. 2016; Park et al. 2017). An appropri- ate evacuation plan is important to support effective evacuation due to the complexity of tsunami evacuation in emergency (Mas et al. 2015; Xie et al. 2017). Evacuation simulation is regarded as an alternative way to provide important information for evacuation planning considering the difficulty of conducting emergency disaster drills due to the complexity of evacuation (Xie et al. 2017; Usman et al. 2017). For developing the optimal evacuation planning, however, evacuation simulation needs to be implemented more realistically and accurately to investigate evacuation behavior, assess evacuation risk, and develop more resilient communities (González-Riancho et al. 2013; Wang et al. 2016).

To model tsunami evacuation, many techniques can be employed such as geographic information system (GIS) (Katada and Kuwasawa 2006; Clerveaux et al. 2008; González- Riancho et al. 2013), distinct element method (DEM) (Abustan et al. 2012), and system dynamics approach (Simonovic and Ahmad 2005). Each of these modeling methods might have its advantages; however, they typically lack the capacity to capture the complexity of evacuees’ decision and behavior and hence the dynamics of emergency evacuation (Mas et al. 2015). As an alternative, agent-based modeling (ABM) is preferred for tsunami evacuation simulation due to its capability of capturing the emergent phenomena through characterizing the natural and human system dynamics and modeling the individual-level interactions among agents and the agents’ interactions with the environment (Mas et al.

2012; Wang et al. 2016; Jacob et al. 2014). ABM is a modeling technique to simulate the behaviors of a system of autonomous decision-making entities named agents as well as the interactions between them and with the environment (Bonabeau 2002). ABM has several benefits over other modeling techniques, e.g., it can capture emergent phenomena, provide a natural description of a system, and is flexible. Due to these benefits, ABM is regarded as ideal to simulate disaster emergency evacuations (Munadi et al 2012). Since one of the first agent-based tsunami evacuation models was introduced using a network modeling approach that is widely used for evacuation simulations of other natural hazards such as hurricanes, floods, nuclear disasters, and fires in buildings (Usuzawa et al 1997), many tsunami evacuation models have been developed using ABM (Mas et al. 2015), including some recently developed advanced agent-based tsunami evacuation models. For example, a multi-agent- based tsunami evacuation model was introduced to simulate more complex human behaviors in tsunami evacuation (Fujioka et al. 2002); the agent-based tsunami evacuation model presented in Katada et al. (2004) started the application of tsunami evacuation simulations for tsunami mitigation, particularly for disaster education; a GIS model called the Tsunami Scenario Simulator was developed (Katada et al. 2000) and incorporated into the Tsunami Dynamic Hazard Map for disaster education (Katada and Kuwasawa 2006), after which the study on tsunami evacuation models using ABM increase significantly; the tsunami evacuation model uses Multi-Agent Transport Simulation (MATSim) to implement large-scale agent-based simulation (Lämmel 2011); the tsunami evacuation model was developed with finer levels of details with the development of high-performance computing (Wijerathne et al. 2013).

Each agent-based tsunami evacuation model has its characteristics, while a sophisti- cated model typically consists of the evacuation environment model (including natural

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hazard analysis, transportation network, tsunami shelters, and population distribution), the evacuation decision and behavior model, and the evacuation performance model (e.g., risk/casualty model) (Alabdouli 2015; Mostafizi et al. 2019). For each component, different agent-based models might emphasize different advantages; however, some important factors and/or mechanisms in the evacuation are usually neglected or simplified in the tsunami evacuation simulation using ABM. To simulate evacuation and assess evacuation risk more accurately, it is important to consider various uncertainties (Taflanidis et al. 2016) associated with evacuation. The earthquake-induced damage to the transportation network could lead to a significant increase in evacuation time and thus life loss if the network is not resilient enough (Murray-tuite 2007; Mostafizi et al.

2017; Do et al. 2016; Attary et al. 2017). However, few research takes into account seismic damages to the transportation network in evacuation simulation or neglects the uncertainty in seismic damages by simply removing the damaged links from the network. Even if seismic damages to links are considered, it is usually assumed the seismic damages eliminate the connectivity of corresponding links (Mostafizi et al. 2017; Jacob et al. 2014). In reality, seismic damages of links could lead to a significant reduction in the traffic capacity of corresponding links, but not necessarily eliminate the usability of the links. Moreover, usually only seismic damages to bridges rather than roads are considered. However, damaged roads would also affect evacuation severely, especially for evacuation by car. Besides the uncertainty in seismic damage of links, various other uncertainties in evacuation such as departure time need to be considered for more accurate risk assessment.

For the population distribution, a relatively small number of evacuees (e.g., residents) are usually considered and population mobility is neglected, which might be not realistic (Mostafizi et al. 2017; Priest et al. 2016). However, the population distribution throughout the region of interest can be of high spatiotemporal variability and the number of evacuees might be very large in some peak season. The smaller population considered in simulation might underestimate the evacuation risk significantly due to the underestimation of traffic congestion. Considering the highly nonlinear nature of the evacuation, results from simulations using smaller than actual population may not give a good indication of the results under more realistic, large populations. Also, evacuees by car are usually assumed to be in cars when starting evacuation (Mas et al. 2012), or change to cars after reaching the link of the transportation network (Wang et al. 2016). However, these assumptions might be not realistic because evacuees need to first reach their cars on foot when the cars cannot be accessed easily and then evacuate by car.

Multi-modal evacuation (e.g., on foot and by car) using ABM has been gaining more attention. Compared to single-modal evacuation, multi-modal evacuation is more realistic (Wang et al. 2016; Goto et al 2012); however, few research considers the interaction between the pedestrian and vehicle, i.e., assuming that the pedestrian walks on the side- walk and the vehicle moves on the lane while they evacuate separately. Such an assumption may not be realistic since the pedestrian and vehicle might use the shared space on the same road based on the traffic condition (Mauro et al. 2014). In reality, the walking speed and vehicle speed need to be adjusted according to surrounding traffic conditions (e.g., speed up when the traffic density is low while slow down when the traffic density is high or even stop when the traffic jam is caused); however, in many existing models, the walking/

vehicle speed is usually assumed to be constant throughout simulation (Fujioka et al. 2002;

Mostafizi et al. 2017; Xie et al. 2017). Furthermore, to the best of our knowledge, no existing models consider the walking speed variability and walking speed adjustment concurrently; multi-modal evacuation considering pedestrian–vehicle interaction has never been

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incorporated with walking speed variability and speed adjustment for both the pedestrian and vehicle in previous studies.

This paper develops a novel agent-based tsunami evacuation model to simulate tsunami evacuation more realistically and assess evacuation risk more accurately. In the model, seismic damages to links are considered and uncertainties in the damage state of links are quantified through corresponding fragility functions (both roads and bridges). Other uncertainties in evacuation are also explicitly taken into account in the evacuation model.

Several different populations are simulated in the model to consider population mobility.

Some parking lots are placed in the regions where cars cannot be easily accessed when evacuation starts and evacuees first reach their cars on foot before evacuating by car. A novel and more realistic multi-modal evacuation model (i.e., evacuation on foot and by car) is proposed, in which pedestrian–vehicle interaction is modeled by traffic stage transition according to the volume ratio of the pedestrian and car on the same link. Walking speed variability and speed adjustment for both the pedestrian and car are also incorporated in the multi-modal evacuation model. The novel modification introduced in the proposed evacuation model can provide a more realistic simulation of the evacuation procedure.

The remainder of this paper is organized as follows. Section 2 discusses tsunami evacuation risk assessment. Section 3 proposes the novel agent-based model for tsunami evacuation, including modeling of evacuation environment considering seismic damages to the transportation network, evacuation decision and behavior, and evacuation performance.

Sections 4 and 5 present an illustrative example. Section 6 summarizes the research findings.

2 Tsunami evacuation risk assessment

Tsunami evacuation simulation typically involves evacuation environment (e.g., natural hazards, transportation network, tsunami shelters, and population distribution), evacuation decision and behavior, and evacuation performance (Alabdouli 2015; Mostafizi et al.

2019). Uncertainties exist for each component due to the natural and inherent variability of the model input or lack of knowledge (Taflanidis et al. 2016). To measure the output of evacuation simulation accurately, various uncertainties need to be considered in the simulation. Here, we use 𝜽= [𝜽_eem,𝜽_ebm,𝜽_epm] to characterize the uncertainties in the tsunami evacuation simulation, where 𝜽

eem,𝜽

ebm,𝜽

epm represents the model parameters for evacuation environment model (EEM), evacuation decision and behavior model (EBM), and evacuation performance model (EPM), respectively. We use 𝜣 to represent the space of potential values for all the parameters, then 𝜽∈𝜣 . Let p(𝜽) represent the probability density function (PDF) for continuous variables and the probability mass function (PMF) for discrete variables. The performance (or output) of the tsunami evacuation can be charac- terized through a performance function h(𝜽) . Here, we use the casualty rate as the performance indicator h(𝜽) and three types of casualty rates are defined for the multi-modal evacuation, i.e., the total casualty rate (TCR), the pedestrian casualty rate (PCR), and the car casualty rate (CCR). The TCR is calculated by total casualties including both casualties on foot and by car divided by the population; the PCR is the proportion of the casualties on foot to the population; the CCR is the proportion of the casualties by car to the population.

In the above context, propagating the uncertainties in all model parameters 𝜽 , the tsunami evacuation risk H (corresponding to the expected value of the casualty rate) can be written as the following multi-dimensional integral

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To estimate the multi-dimensional integral, general stochastic simulation techniques (e.g., MCS) can be used (Robert and Casella 2004; Taflanidis and Beck 2008). Using N samples from p(𝜽) , H can be estimated as (Taflanidis and Jia 2011; Jia et al. 2016)

The coefficient of variation (CoV) of the estimate 𝛿_CoV can be calculated as (Robert and Casella 2004)

where 𝜽^k represents the kth sample of the uncertain parameters generated from p(𝜽).

3 Agent‑based tsunami evacuation model

ABM is used to develop the tsunami evacuation model in NetLogo considering that the integrated ABM environment can use modern data with a high level of detail, capture the emergent phenomena, and tune the complexity of the agent’s behavior (Wilensky 2001).

The agent-based tsunami evacuation model consists of the evacuation environment model (EEM, including the multi-hazard model, transportation network, tsunami shelters, and population distribution), the evacuation decision and behavior model (EBM), and the evacuation performance model (EPM). Several novelties are proposed and incorporated into the agent-based tsunami evacuation model. In particular, in the EEM, (1) the earthquake- induced damage to the transportation network is considered to simulate the interactions between the evacuees and the updated environment, (2) uncertainties in the seismic damage are quantified using fragility curves of bridges/roads, (3) several different populations are considered to investigate the impact of the population on evacuation, and (4) some parking lots are placed close to the beach to simulate the evacuation by car more realistically. In the EBM, to capture the complexities of evacuation more realistically, (1) a novel and more realistic multi-modal evacuation (i.e., on foot and by car) is proposed, in which the interaction between the pedestrian and car is explicitly simulated by introducing dynamic traffic stage transition based on the volume ratio of the pedestrian and car, and (2) walking speed variability and speed adjustment for both the pedestrian and car according to the traffic density ahead are also incorporated in the multi-modal evacuation model. The following sections discuss in detail the EEM, the EBM, and the EPM, with a focus on the novel contributions of the proposed models.

3.1 Evacuation environment model (EEM)

The evacuation environment model consists of the multi-hazard model, transportation network, tsunami shelters, and population distribution.

(1) H=∫𝜣

h(𝜽)p(𝜽)d𝜽

(2) Ĥ = 1

N

∑

k=1

h(𝜽^k)

(3) 𝛿_CoV= 1

√N

�

1 N

∑N k=1h²(𝜽^k)

Ĥ² −1

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3.1.1 Multi‑hazard model

For the earthquake-induced tsunami, we consider the multiple hazards including tsunami inundation as well as seismic damages to the transportation network for a more realistic evacuation simulation using ABM. The tsunami inundation is simulated using ComMIT/

MOST, which is the tsunami model of NOAA Center for Tsunami Research (NCTR) and capable of simulating three processes of tsunami evolution: generation, propagation, and inundation (Titov and González 1997). In the model, three series of nested grids (A, B, and C) can be used to optimize the simulation for the three tsunami processes. The inundation model provides time series of flow depth and speed at different locations of the area under investigation.

In tsunami evacuation simulation, few research considers the impacts of seismic damages to the environment (e.g., transportation network) and the evacuees’ interactions with the updated environment (Jacob et al. 2014). However, when an earthquake occurs and generates a tsunami, it may change the environment, e.g., it may cause damage to the transportation network and thus reduce the traffic capacity of the damaged links, which might affect the evacuation. In our evacuation model, seismic damages to links of the transportation network are considered for simulating the evacuation more realistically. Uncertain- ties in intensity measures at each link site and damage states of each link are quantified for assessing the evacuation risk more accurately. The spatially distributed ground-motion intensities are estimated by selection of the proper ground-motion model (Campbell and Bozorgnia 2008; Abrahamson et al 2018) and the correlation model for intensity measures (Loth and Baker 2013; Weatherill et al. 2015). Taking the predicted intensity measures at each site as inputs, the fragility functions of corresponding bridges and roads are then used to estimate the probability of damage states for the corresponding links (DHS 2009; Sotiris et al 2015).

3.1.2 Transportation network

The transportation network used for evacuation is extracted from OpenStreetMap and saved as shapefile in which intersections and road segments (or bridges) are represented by nodes and links, respectively. The characteristics of the transportation network such as the coordinates of intersections, cross sections of roads, bridge types are included in the shapefiles. As presented in Sect. 3.1.1, the seismic damage to the link of the transportation network (denoted 𝜽

d ) will be considered for a more realistic simulation. Different reduction rates are defined to estimate the reduction in traffic capacity based on different levels of damage for the link (Wang and Jia 2019, 2020b). In the context of considering seismic damages to the transportation network, the parameter vector 𝜽

d is included in 𝜽

eem.

3.1.3 Tsunami shelter

Both horizontal and vertical evacuation shelters are regarded as effective to reduce the number of casualties (Mostafizi et al. 2019). Typically, all the shelters are assumed to be capable of withstanding earthquake and tsunami hazard (FEMA 2019). For the capacity of the shelter, either a limited or an unlimited capacity can be used in different simulations (Mostafizi et al. 2019; Goto et al 2012).

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3.1.4 Population distribution

The population distribution throughout the community can be of high spatiotemporal variability in terms of types (e.g., residents and tourists), genders, or ages (Mostafizi et al.

2017). Existing research usually considers a relatively small population in evacuation simulation, which might be unrealistic (Mostafizi et al. 2017; Priest et al. 2016). We consider population mobility and use different populations in simulation to investigate the impact of the population on the evacuation risk. To simulate the evacuation by car more realistically, we place some parking lots in the areas where cars are not likely to be accessed in seconds and simulate the process of evacuees reaching their cars on foot first and then evacuating by car. For the distribution scenario, we use the normal and uniform distribution to simulate the uncertainty in the population distribution over the study regions.

3.2 Evacuation decision and behavior model (EBM)

Multiple criteria need to be considered in evacuation decision and behavior due to the complexity of the decision making and behavior in an emergency. The following important aspects are taken into account for evacuees to make the evacuation decisions and evacuate.

3.2.1 Departure time

There is few research on the departure time for tsunami evacuation (Council 2006). We adjust the Rayleigh distribution suggested in Wang et al. (2016) to characterize the uncertainty in departure time in which the probability of action for each individual evacuee is considered by

where t is the departure time after the earthquake occurrence (unit: min); t₀ is the time when being notified the tsunami warning after the earthquake ground shaking (unit: min); 𝜏 is the delay time after receiving the tsunami warning (unit: min); 𝜎_t is the scale parameter.

t₀ is considered to be uncertain and included in 𝜽_ebm due to the complexity of the warning process (US IOTWS 2007). Both 𝜏 and 𝜎_t can vary with the population due to the complexity of decision-making process and are treated as part of 𝜽

ebm. 3.2.2 Evacuation mode

Most of the tsunami evacuations are modeled using single traffic mode, e.g., either on foot or by car, which is not realistic. Here, we simulate the multi-modal evacuation including on foot and by car. In the simulation, we treat the proportion of evacuation by car (denoted p_c ) as uncertain considering that in an emergency the individual selection of evacuation mode (i.e., choose to evacuate on foot or by car) may vary for each evacuee. It is assumed that p_c follows the normal distribution with uncertain mean 𝜇_c and constant standard deviation (SD) 𝜎_c , and lies within some given range. Therefore, 𝜇_c is included in 𝜽

ebm . For multi- modal evacuation models, typically limited interactions between the pedestrian and vehicle are considered (Mauro et al. 2014), which might not be realistic. In this study, the hybrid (4) P(t) =

{0 0<t<t₀+𝜏 1−e^−(t−t⁰^−𝜏)²^∕(2𝜎^t²⁾ t≥t₀+𝜏

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evacuation mode in Mauro et al. (2014) is adjusted to capture different evacuation traffic modes and interactions between them more realistically. In the model, the pedestrian–vehicle interaction is simulated through the dynamic transition of three traffic stages, which are vehicle-dominated, balanced, and pedestrian-dominated. On each link, the transition of the three traffic stages is determined by the ratio between the pedestrian volume and vehicle volume

where V_p and V_v represents the pedestrian volume and vehicle volume (unit: person) on the same link, respectively; for comparison, one vehicle can be assumed to be equivalent to some number of pedestrians based on the average space occupied; w_p and w_v represents the road width occupied by the pedestrian and vehicle (unit: m), respectively; w is the total road width (unit: m); w_wmin is the minimum road width used by the pedestrian (unit: m); w_w is the road width that can be used by the pedestrian including sidewalks, multi-use path, and roadway shoulders (unit: m); w_r is the width of vehicle lane (unit: m); n_l is the number of vehicle lanes occupied by the vehicle, which are typically smaller than the total number of vehicle lanes in the car-dominated stage; T₁ and T₂ are the thresholds for different traffic stages, both of which can vary due to the dynamics of the multi-modal traffic, i.e., T₁ and T₂ are included in 𝜽_ebm.

3.2.3 Shelter selection

Basically, there are two alternative selections for shelters. One choice is the closest shelter, while the other is any shelter based on the evacuees’ preference or experience. The search of the closest shelter can be simulated using the shortest path algorithm in terms of distance or time.

3.2.4 Evacuation speed

Simulation of evacuation speed is critical to estimate the casualty and ultimately the evacuation risk (Wood and Schmidtlein 2012). Variability can be assigned to the walking speed v_p to consider the uncertainty in the pedestrian’s characteristics such as age and physical condition (Wang et al. 2016). In evacuation, v_p may adjust according to the surrounding traffic condition, e.g., the pedestrian density 𝜌_p (Goto et al 2012). Similarly, the car speed v_c may adjust according to the surrounding car density 𝜌_c (Goto et al 2012; Mostafizi et al.

2017). However, to the best of our knowledge, there are no tsunami evacuation models considering both the speed variability and speed adjustment for the pedestrian; no tsunami evacuation models incorporate different traffic stages in Sect. 3.2.2 and speed adjustment in the multi-modal evacuation. To model the dynamics of evacuation more realistically, we consider the walking speed variability, the speed adjustment for the pedestrian and car, which are simulated under any of the different traffic stages. To consider the uncertainty in v_p , we assume that it follows normal distribution with mean 𝜇_p and SD 𝜎_p , and lies within some range (Wang et al. 2016). Both 𝜇_p and 𝜎_p can vary considering the uncertain population distribution, and therefore are treated as part of 𝜽_ebm.

(5) V_p∕V_v≤ T₁→w_p=w_wmin; w_v =w−w_wmin

T₁<V_p∕V_v≤ T₂→w_p=w_w; w_v=w−w_w V_p∕V_v>T₂→w_p=w−w_r×n_l; w_v=w_r×n_l

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3.3 Evacuation performance model (EPM)

The evacuation performance can be measured using different quantities of interest such as casualty, evacuation time, etc. We use the casualty rate (i.e., the proportion of casualties to the total number of evacuees) as the evacuation performance indicator. The flow characteristics such as depth and velocity determine the casualty through impacting the human body (Lind et al. 2004; Jonkman et al. 2008), while many other factors including evacuee’s age, gender, and mental and physical state also have an impact on casualty in tsunami inundation (Yeh 2010). Usually, critical water depth is used to approximate the casualty without considering other factors (Wang et al. 2016; Mostafizi et al. 2017), or the casualty probability is estimated as a function of depth and velocity, which are limited to given intervals (Mas et al. 2012). In this study, the evacuee is considered to be a casualty when the water depth is larger than the given critical depth of h_c . To consider the varied characteristics of different evacuees, h_c is treated as uncertain and included in the evacuation performance model parameters 𝜽_epm.

3.4 General applicability of the proposed agent‑based model for tsunami evacuation simulation and evacuation risk assessment

The proposed agent-based tsunami evacuation model is developed with a modular pro- gramming paradigm and sub-models (i.e., the EEM, EBM, and EPM) including components in each sub-model. These components are general and can capture the nature of tsunami evacuation through characterizing the evacuation system dynamics and modeling the individual-level interactions among evacuees and the evacuees’ interactions with the multi-hazard environment. Due to the above characteristics, the proposed agent-based evacuation model is general, and each sub-model can be adapted to different settings by changing/updating the EEM, EBM, and EPM accordingly. For example, for a different site, we can update the EEM by using the seismic hazard model for the site to simulate the earthquake, using numerical models such as ComMIT/MOST along with topography for the site to simulate tsunami generation and propagation, by using the corresponding ground motion prediction equations and fragility functions of roads and bridges to estimate and update the seismic damages, and by updating the transportation network, shelters, and the population distribution throughout the community. When modeling the departure time, evacuation mode, and evacuation speed in the EBM, different distributions of evacuation model parameters could be updated to model the uncertainties in the evacuation decision and behavior based on the characteristics of the population. In the EPM, depending on the performance of interest, besides the casualty rate, other performance quantities could be also used to measure the evacuation performance. Therefore, the proposed agent-based tsunami evacuation model can be used in different geographic locations for tsunami evacuation simulation and evacuation risk assessment.

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4 Illustrative example

The proposed agent-based evacuation model (described in Sect. 3) is applied to tsunami evacuation simulation and risk assessment for Seaside, Oregon. In addition, cases with different considerations of seismic damage to the transportation network, pedestrian–vehicle interaction, and pedestrian speed adjustment are considered for comparison to highlight the advantages of the proposed model.

4.1 Study area

We select Seaside, Oregon (shown in Fig. 1b) as the study area for the tsunami evacuation simulation. The city is identified with a high risk to a combined Cascadia Subduc- tion Zone (CSZ, shown in Fig. 1a) seismic and tsunami hazard due to its proximity to the CSZ (Mostafizi et al. 2017; González et al. 2009; Priest et al. 2016). The fairly flat topography and two rivers flowing through make the city more vulnerable to tsunami inundation. In addition to shelters are located more than 1.5 km away from the shore- line, ten bridges over the two rivers cause bottlenecks in the transportation network, which makes the tsunami evacuation more complex.

4.2 Agent‑based tsunami evacuation model details

The agent-based model for tsunami evacuation simulation in Seaside, including evacuation environment, evacuation decision and behavior, and evacuation performance, will be discussed in the following sections. In particular, the proposed novel improvements to each component will be described in detail. Figure 2 shows a snap-shot of the agent- based tsunami evacuation model interface in NetLogo.

Fig. 1 a Cascadia subduction zone (CSZ), and b Seaside, Oregon

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4.2.1 Evacuation environment

We consider the seismic hazard and earthquake-induced tsunami generation from the 1000 km long CSZ (USGS 2017). The CSZ stretches from northern Vancouver Island to Cape Mendocino in northern California. The last great seismic event on the CSZ is full-rupture and occurred on January 26, 1700, with moment magnitude estimated between 8.7 and 9.2, and a slip of 19 m (Satake 2003). The average return period for the full-length CSZ event is 530 years. Despite low levels of seismicity since the last megathrust earthquake, it was reported that partial rupture events on the north or south margins of the CSZ became more frequent (Goldfinger et al 2012; Atwater and Griggs 2012; Park et al. 2017). There is a 9.0 M_w earthquake with about 10% probability of occurrence at the CSZ over a 35-year time frame (Goldfinger et al 2012). In this study, we use the historical seismic event in 1700 as the hypothetical seismic and tsunami hazard inputs, under which M_w=9.0 and the focal depth of 40 km are considered.

The transportation network consists of 700 nodes and 896 links (i.e., n = 896). Based on the existing transportation conditions and transportation system plan (Clatsop 2010), each link is considered to consist of a roadway and walkway that is used by the car and pedestrian, respectively. The parameters used for determining the road width occupied by the car or pedestrian in Sect. 3.2.2 are assumed to be w=10.5 m, w_wmin=2 m, w_w=3 m, w_r=2.75 m, and n_l=2 . The roadway used by the car is considered to be two-way.

To consider the impact of the earthquake-induced damage to the transportation network on evacuation, the fragility functions of roads and bridges in HAZUS DHS (2009) are used to estimate the probabilities for seismic damages to roads and bridges, respectively.

In HAZUS, permanent ground deformation (PGD) and spectral acceleration (Sa) are used as intensity measures in the fragility curves for roads and bridges, respectively. Based on Stewart et al. (2015), we select the ground-motion prediction equations (GMPEs) in Camp- bell and Bozorgnia (2008) to estimate the PGD at each road site and Sa at each bridge site, respectively. According to HAZUS DHS (2009), five damage states (i.e., none, slight, moderate, extensive, and complete) are defined for both bridges and roads. Therefore, the damage state of the i th link 𝜃_di corresponds to a discrete variable 𝜃_di=DS_j with j=1,…, 5 . Except for the bridges with complete damage over the two rivers, the reduction of traffic capacity of links due to the seismic damage is considered only for the car since evacuation by car is more likely to be affected by the damage of links compared to evacuation on foot.

Fig. 2 The agent-based tsunami evacuation model interface

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Different reduction rates are used for bridge and road considering that for the same damage level bridges typically have a more significant impact on the traffic than roads. For all the bridges, the residual traffic capacity is assumed to be 100% (none/slight), 75% (moderate), and 50% (extensive). When the damage corresponds to complete damage, for bridges that are not over the two rivers the residual traffic capacity is assumed to be 25%, and for the ten bridges over the two rivers, the residual traffic capacity is assumed to be zero (for both evacuation on foot and by car) considering the bottleneck effect. For road, the residual traffic capacity is assumed to be 100% (none/slight/moderate) and 75% (extensive/complete).

The traffic capacity reduction of the damaged links for the car is modeled by reducing the jam density in the speed adjustment model (discussed in Sect. 4.2.2).

For the shelters, we adopt the eight horizontal shelters outside the inundation zone identified by the Oregon Department of Geology and Mineral Industries (Priest et al 2013), which are shown in Fig. 1b. It is assumed that all the shelters can hold the evacuees that reach them.

We use the population density model in Mostafizi et al. (2017) to simulate the population distribution throughout the study area, which corresponds to the noontime of some weekend in the summer. The evacuees including residents and tourists are distributed across the beach, downtown, and residential area with a proportion of 40%, 30%, and 30%, respectively. Both the populations on the beach and in the downtown are assumed to dis- tribute following the normal distribution around the corresponding centroid of each region.

The population is distributed uniformly throughout the residential area. As to the population size, the up-to-date residential population of Seaside is 6795 in 2018 according to US Census; however, the net daytime residential population decreases to about 3000 (Sleeter and Wood 2006), while the number of tourists can be up to 10,000 per day in the peak summer (Mostafizi et al. 2017). To consider the impact of population mobility on evacuation risk assessment, we consider three different populations (i.e., n_e = 5000, 10,000, 15,000) in simulation, where n_e = 5000 and n_e = 15,000 represents the population in the early summer and peak summer, respectively; n_e = 10,000 represents the population during the time between the early summer and peak summer. To simulate the evacuation by car more realistically, we place one parking lot beside each subregion of the beach, which is used to park for the evacuees on the beach. For the evacuation by car in the two regions other than the beach, cars with four evacuees per car are distributed throughout the regions considering the easier access to their cars for the evacuees in these two regions. The classification of different regions and corresponding population distributions are shown in Fig. 3.

4.2.2 Evacuation decision and behavior

For the modeling of the departure time described in Eq. (4), we consider t₀ to follow the uniform distribution on the interval [3, 10] (unit: min) for the local tsunami (US IOTWS 2007); 𝜏 and 𝜎_t are considered to follow the uniform distribution on the interval [0, 10]

(unit: min) and [1, 5], respectively.

In the multi-modal evacuation simulation presented in Sect. 3.2.2, we model the uncertainty in p_c by assigning to it a truncated within (0, 1) normal distribution with mean 𝜇_c and SD 𝜎_c . It is further assumed that 𝜇_c follows the uniform distribution on the interval [0, 1] and 𝜎_c = 0.15. As to the evacuation by car, it is assumed that four passen- gers take one car. In the calculation of the pedestrian volume and car volume, one car is assumed to be equivalent to ten pedestrians in terms of space occupied. To consider the variability of the thresholds for different traffic stages in Eq. (5), we use the uniform

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distribution on the interval [0.3, 0.7] and [1.1, 1.5] to simulate T₁ and T₂ , respectively.

These intervals are estimated based on the given values of the parameters that are used to determine the road width occupied by the pedestrian or car in Sect. 4.2.1. For the decision on the shelter selection, we consider the closest shelter as the evacuation desti- nation in terms of the shortest distance, which is identified for all evacuees using the A*

algorithm (Anguelov 2011).

Fig. 3 Population distribution

Fig. 4 The relationship between walking speed and pedestrian density ahead

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In the modeling of the multi-modal evacuation, we consider the speed variability for the pedestrian, and speed adjustment for both the pedestrian and car. The preferred walking speed is assumed to follow a truncated within (0.75, 3.83) (unit: m/s) normal distribution with mean 𝜇_p and SD 𝜎_p (Wang et al. 2016; Goto et al 2012). The lower and upper bound of v_p corresponds to the slow walk and fast run, respectively. Due to the limited knowledge about 𝜇_p and 𝜎_p , we assume that 𝜇_p and 𝜎_p follow uniform distribution within [1.4, 2] (unit: m/s) and [0.1, 0.6], respectively. Based on the speed-density relationship in Goto et al (2012), we introduce a walking speed adjustment model which is shown in Fig. 4. In the model, v_p

0 represents the preferred walking speed; 𝜌_p denotes the pedestrian density 4m ahead along the shortest path. According to the model, the walking speed will reduce as 𝜌_p increases.

To model the evacuation by car more realistically, instead of directly modeling the evacuees as car agents, the evacuation on foot (i.e., before the evacuees reach their cars) is also explicitly modeled. Essentially, the evacuees first walk to their cars at the assigned wak- ing speeds and then, the evacuation is modeled by the cars’ movements once they arrive at their cars. Car speed v_c is adjusted according to the car density 𝜌_c within the free run- length ahead of it. Here, we use the well-known Greenshields’ model of speed and density (Greenshields et al. 1935) to approximate the car speed adjustment

where v_cm is the maximum speed limit and 𝜌_cm is the maximum density (i.e., jam density).

Based on the cross section of roads, it is assumed that v_cm = 40 km/h. According to the study in Mostafizi et al. (2019, 2017), 𝜌_cm=160 veh/km is considered for the links without traffic capacity reduction. For links with reduced traffic capacity due to the seismic damage, the jam density is reduced correspondingly based on the residual traffic capacity rate defined in Sect. 4.2.1, e.g., 𝜌_cm=120 veh/km for roads with extensive/complete damage.

4.2.3 Evacuation performance

A fixed critical depth h_c is usually used to approximate the casualty in previous research, e.g., h_c=0.5 m (Sugimoto et al. 2003), h_c=1 m (Goto et al 2012), or h_c=2 m (Yeh 2014). To model the uncertainty in h_c for evacuation performance evaluation (i.e., casualty estimation), we consider h_c follows a uniform distribution in [0.5, 3] (unit: m), which is applicable to both evacuation on foot and by car.

4.3 Stochastic simulation

The tsunami evacuation simulation using the proposed agent-based model is implemented in NetLogo (run from R using the package “RNetLogo” Thiele 2014, 2017). Since the computational time increases with the number of agents (or population size) and the number of simulations, to speed up the simulation, parallel computing is implemented on the Summit High-Performance Computing (HPC) system, a joint activity of Colorado State University (CSU) and the University of Colorado Boulder (CU). This allows us to run evacuation models with a large number of agents and also to run a large number of simulations for uncertainty propagation.

(6) v_c=v_cm

( 1− 𝜌_c

𝜌_cm )

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In this example, the uncertain model parameter vector consists of the evacuation environment model parameters 𝜽_eem= [𝜃_di,i=1,…,n] with n=896 , the evacuation decision and behavior model parameters 𝜽_ebm= [t₀,𝜏,𝜎_t,𝜇_c,T₁,T₂,𝜇_p,𝜎_p] , and the evacuation performance model parameters 𝜽

epm= [h_c] . The distributions of these model parameters are summarized in Table 1, in which U(a, b) represents the uniform distribution in the interval between a and b.

To illustrate the tsunami evacuation simulation and risk assessment using the proposed agent-based tsunami evacuation model, different cases are considered (e.g., by switching some of the proposed features/improvements on or off). These cases are classified based on whether the model considers (1) the seismic damage to the transportation network, (2) pedestrian–vehicle interaction, and (3) speed adjustment. Besides the baseline case C0, four other cases are considered. The cases are listed in Table 2. In particular, when there is no pedestrian–vehicle interaction, the traffic stage corresponding to T₁<V_p∕V_v≤ T₂ in Eq. (5) is used; when the interaction is considered, the traffic stage transition expressed by Eq. (5) is used. When there is speed adjustment, the speeds of both the pedestrian and the car will be adjusted according to the traffic density ahead. C4 corresponds to the proposed agent-based tsunami evacuation model while other cases (i.e., C0-C3) are less realistic.

All the five cases are implemented under three population sizes (i.e., n_e = 5000, 10,000, 15,000). In the model, we simulate the evacuation for 1 hour, starting from the earthquake occurrence time.

5 Results and discussions

5.1 Overview of tsunami evacuation simulation using the agent‑based model The general behavior of the agent-based tsunami evacuation model is shown in Fig. 5 by running one single simulation with 5000 evacuees under case 4 considering that it Table 1 Distributions of

evacuation model parameters 𝜽 Distribution 𝜽 Distribution

t0 U(3, 10) 𝜇_p U(1.4, 2)

𝜏 U(0, 10) 𝜎_p U(0.1, 0.6)

𝜎_t U(1, 5) h_c U(0.5, 3)

T1 U(0.3, 0.7) 𝜇_c U(0, 1)

T2 U(1.1, 1.5)

Table 2 Definition of simulation

cases Cases Seismic damage Pedestrian–vehicle

interaction Speed adjustment

C0 No No No

C1 No No Yes

C2 No Yes Yes

C3 Yes No Yes

C4 Yes Yes Yes

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corresponds to the more realistic simulation. In this particular simulation, the mean value of each uncertain parameter is selected. At the end of the initial strike of the earthquake (i.e., t = 0 min) shown in Fig. 5a, the evacuees including pedestrians and cars represented by the orange and violet points, respectively, are distributed throughout the community. Figure 5b shows most of the evacuees have started evacuation after 10 Fig. 5 The general behavior of the agent-based tsunami evacuation model at a t = 0 min, b t = 10 min, c t = 28 min, d t = 38 min, e t = 45 min, and f t = 55 min

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min. Around t = 28 min, shown in Fig. 5c, the tsunami inundation almost goes across the beach. Most of the evacuees are on the way to their destinations, while some of the evacuees have arrived at the shelters, and these evacuees are represented by green points. Figure 5d shows the tsunami starts to inundate the city after 38 min. The casualties represented by red points occur when the inundation depth exceeds the critical depth. Figure 5e shows that the tsunami inundation crosses the Necanicum River and is moving further inland after 45 min when more evacuees become casualties. By t = 55 min shown in Fig. 5f, the tsunami inundation has reached the run-up limit and most of the evacuees have reached the shelters.

5.2 Evacuation risk assessment for simulation with 5000 evacuees

To assess the evacuation risk, Eq. (2) is used and N=4000 tsunami evacuation simulations are used for each case presented in Sect. 4.3. The use of N=4000 results in high accuracy estimates for the expected TCR at the end of the tsunami inundation simulation (i.e., 60 min), with 𝛿_CoV below 1% for all cases.

Fig. 6 Variation of evacuation risk in terms of danger rate, safety rate, casualty rate for different cases, where a shows the expected pedestrian rate, b shows the expected car rate, and c shows the expected total rate

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5.2.1 Overall evacuation risk

This section investigates the overall probabilistic evacuation performance over time. The mean predictions of three important risk performance measures (i.e., the total danger rate (TDR), total safety rate (TSR), and the total casualty rate (TCR)) and their variation over time are shown in Fig. 6c. The total rate includes contributions from pedestrians and cars;

accordingly, we can define danger rate, safety rate, and casualty rate for pedestrians and cars. Their variations are shown in Fig. 6a, b, respectively.

From Fig. 6c, we can see that overall the changes of the three rates over time for all five cases are consistent with the general behavior of the agent-based tsunami evacuation model discussed in Sect. 5.1. At t = 0 min, TDR is 100%, while TSR and TCR are zero due to the definition that all evacuees are in danger facing the coming tsunami inundation. As time goes by, as expected TDR decreases while TSR and TCR increase. On average, after around 10 min, some of the evacuees will reach the shelters (i.e., reach safety), from which point on TSR is not zero anymore and starts increasing. On the other hand, on average, before around 28 min, TCR is still zero; afterward, casualty starts occurring and TCR starts increasing over time and reaches around 30% at around 50 min. Note that the TCR might reach the peak at some point before the end of evacuation simulation and stop increasing;

for the current simulations, on average, it reaches the largest value (around 30%) at around 50 min, which might correspond to the time when the tsunami inundation reaches the run- up limit. However, there might be evacuees still traveling towards the shelters through the transportation network between the run-up limit points and the shelters. Therefore, TDR will keep decreasing with the increase of TSR until the end of the simulation.

From Fig. 6a, b, we can see that overall the variation of the mean values of the three rates for the pedestrian and car show similar trends to the total rate. When comparing the results for the pedestrian and car, the following interesting observations are made. First, although the evacuation on foot and by car is almost half by half (based on the selection of the distribution for p_c in this example), the safety rates for the pedestrian and car show different variations over time. Around 10 min after the earthquake, both the pedestrian safety rate (PSR) and car safety rate (CSR) are not zero due to successful evacuation for both on foot and by car; however, the increase of the PSR is much slower than that of the CSR for the following 10min, i.e., the mean PSR is only about 3% while the CSR is about 12%

when t = 20 min. Between t = 20 min and t = 30 min, the mean PSR increases from around 3% to around 17%, which shows a much faster increase than the CSR that increases from around 12% to around 16%. With the increase of time, the PSR keeps increasing although the increase becomes slower while the CSR increases very slowly. The above differences between the changes of the PSR and CSR should attribute to different characteristics of evacuation on foot and by car. Compared to evacuation on foot, evacuation by car is more likely to cause severe traffic congestion as more cars are driving on the same link with the increase of time, which will reduce the car speed significantly and thus delay the evacuation. Therefore, the CSR will increase very fast when the cars can travel at free-flow speed before the occurrence of traffic congestion and will increase very slowly once there is traffic congestion.

Second, due to the reasons that cause the difference in variation of the PSR and CSR, the variation of casualty rates for the pedestrian and car over time is also different. The variations will be discussed in detail in the next section.

Third, due to the differences in variations of the safety rate and casualty rate for the pedestrian and car, the pedestrian danger rate (PDR) and car danger rate (CDR) also show

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different variations over time. For example, between 10 min and 20 min, the decrease of the PDR is much smaller than that of the CDR, while the opposite trend shows between 20 min and 30 min. Also, the PDR keeps decreasing till the end of the evacuation simulation, while the CDR stops decreasing about 10 min before the end once both the safety rate and casualty rate stop increasing.

5.2.2 Evacuation risk in terms of casualty rate

The expected casualty rates for the pedestrian, the car, and the total for all the five cases are shown in Fig. 7a–c, respectively.

Pedestrian casualty rates (PCRs) Comparing the variation of PCRs among different cases shown in Fig. 7a, we can see the following differences.

(1) Overall, C0 gives the smallest PCR at the end of the evacuation, i.e., 2.7%, while C3 gives the largest PCR, i..e, 5.2%. This can be explained by the differences in the models. As defined in Table 2, C0 neglects the seismic damage to the transportation network, pedestrian–vehicle interaction, and pedestrian speed adjustment, while C3 considers the seismic damage but neglects pedestrian–vehicle interaction. Consid- Fig. 7 Variation of evacuation risk in term of casualty rate for a pedestrian, b car, and c total for different cases

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eration of the seismic damage will lead to a reduction in the traffic capacity of the damaged link, which could slow down the evacuation and increase the casualty rate.

Based on Eq. (5), neglecting the pedestrian–vehicle interaction means the pedestrian cannot take advantage of more road space if the pedestrian dominates the road when the pedestrian congestion is more likely to occur. Due to the above reasons, typically C3 has the largest casualty rate. On the contrary, the evacuation on foot in C0 would not be delayed because no traffic capacity reduction is considered. Also, C0 neglects pedestrian speed adjustment and pedestrians can evacuate at their preferred speed by neglecting the potential speed reduction due to pedestrian congestion. Combining the above considerations, C0 is more likely to have the smallest PCR.

(2) Based on the above discussions about the impacts of the seismic damage, pedestrian–

vehicle interaction, and speed adjustment on the pedestrian evacuation, the PCRs for other cases fall between that of C0 and that of C3.

(3) Comparison between PCRs for C1 (i.e., 4.8%) and C3 (i.e., 5.2%), where the difference is that C3 considers the seismic damage while C1 neglects it, further confirms that consideration of the seismic damage to the transportation network leads to increase in the PCR. A similar observation holds for comparison between C2 and C4, with PCRs of 2.8% and 3.1%, respectively.

(4) Comparison between PCRs for C1 (i.e., 4.8%) and C2 (i.e., 2.8%), where the difference is that C2 considers the pedestrian–vehicle interaction while C1 neglects it, further confirms that neglecting pedestrian–vehicle interaction leads to an increase in the PCR.

A similar observation holds for comparison between C3 and C4, with PCRs of 5.2%

and 3.1%, respectively.

(5) Comparing the impacts of seismic damage and pedestrian–vehicle interaction on the PCR, we can see that the pedestrian–vehicle interaction has a larger impact on the PCR in this example. For example, the difference in the PCR is around 2% between C1 and C2 as well as between C3 and C4, while the difference is only about 0.4% between C1 and C3, and around 0.3% between C2 and C4.

Car casualty rates (CCRs) Comparing the variation of CCRs among different cases shown in Fig. 7b, we can make the following observations.

(1) The CCRs for C0, C1, and C2 are the same for any given time after earthquake. This can be explained by the way that pedestrian–vehicle interaction is modeled. Based on Eq. (5), pedestrian–vehicle interaction is considered by changing the road width that can be used by the car according to the traffic stage transition. However, based on the car speed-density model in Sect. 4.2.2, the change of road width will not affect the car speed. This is because the car speed is adjusted according to the car density some distance ahead on the same lane where the car density per lane is measured by the average number of cars that occupy some distance (usually one mile or one kilometer) on the lane and is not affected by the road width. Therefore, considering pedestrian–vehicle interaction or not does not affect the evacuation by car. Similarly, C3 and C4 have the same CCR for any time.

(2) Comparing the cases with and without considering the seismic damage to the transportation network, i.e., comparing C0 or C1 or C2 with C3 or C4, it can be seen that the cases considering seismic damage have larger CCR than the cases that neglect the

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seismic damage under any given time once casualty occurs. Ultimately, the CCR is around 27.4% for C3 and C4, and 26.1% for C0, C1, and C2.

Comparison between PCRs and CCRs Comparing the PCR and CCR, we can see that the CCR is much higher than the PCR for all cases. The largest PCR corresponding to C3 is only around 5.2% while the corresponding CCR for C3 is about 27.4%. These observations are based on the particular distributions of 𝜇_c and p_c which are defined in Sect. 4.2.2.

For the current selection, the average proportion of evacuation on foot or by car is around 50%, which can be seen in Fig. 6a, b. The comparison indicates that evacuation by car might lead to a larger evacuation risk than evacuation on foot.

Total casualty rates (TCRs) From Fig. 7c, we can make the following observations regard- ing the TCRs.

(1) The variations of the mean of the TCRs show a similar trend to CCRs between around 28 min and around 45 min while the similar trend to PCRs between around 45 min and the end of evacuation (i.e., 60 min).

(2) Out of all cases, C0 has the smallest TCR (i.e., 28.7%), while C3 has the largest TCR (i.e., 32.6%). This is because C0 and C3, respectively, have the smallest and largest casualty rate for both pedestrians and cars. Based on the above observation as well as the definitions of C0 and C3, we know that neglecting the seismic damage to the transportation network and pedestrian speed adjustment might lead to underestimation of the evacuation risk while neglecting the pedestrian–vehicle interaction might lead to overestimation of the evacuation risk.

(3) According to the discussions in Sect. 4.3, C4 corresponds to the proposed agent-based tsunami evacuation model and is expected to be more realistic than the other four cases for tsunami evacuation simulation due to the consideration of seismic damage to the transportation network, pedestrian–vehicle interaction, and speed adjustment. The TCR for C4 is around 30.5%. Treating C4 as the reference value, the smallest and largest underestimation is 1.7% and 1.8%, corresponding to C2 and C0, respectively, while the smallest and largest overestimation is 0.4% and 2.1%, corresponding to C1 and C3,

Fig. 8 a Sample realizations for the total casualty rates over time (plotted for 200 realizations), and b the mean and the 95% confidence interval of the total casualty rates

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respectively. The smallest difference in the estimation of casualties still corresponds to around 20 casualties ( 0.4% ×5000 ), while the largest difference corresponds to around 105 casualties ( 2.1% ×5000 ). Note that the results will also depend on the population size, whose impact will be investigated and discussed in Sect. 5.3.

To show the impact of uncertainties in the parameters on the variability of the casualty rate, as an illustration, Fig. 8a plots some of the sample realizations for the variation of the total casualty rate over time where each realization corresponds to the evacuation under particular realizations/values for the parameters and Fig. 8b plots the mean prediction of the total casualty rate as well as the 95% confidence interval of the total casualty rate. All the results correspond to C4. From the sample realizations and their large variability, it can be seen that the uncertainties in the parameters have large impact on the casualty rate. However, note that the variability of the casualty rate shown in the figure stems from the impact of all the parameters (i.e., not from an individual parameter). To fully investigate the impact of each parameter and its associated uncertainty on the casualty rate and the evacuation risk (i.e., the expected casualty rate), full probabilistic sensitivity analysis would be needed (Jia and Taflanidis 2016; Wang and Jia 2020a), which is beyond the scope of this study. The focus here is to develop a novel agent-based model by incorporating the typically neglected or simplified but important

Fig. 9 Impacts of population size on the evacuation risk in terms of casualty rate for a pedestrian, b car, and c total

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factors and/or mechanisms in tsunami evacuation for evacuation simulation and risk assessment.

5.3 Comparison of evacuation risks under different populations

This section investigates the impacts of population size on the evacuation risk in terms of the casualty rates. The expected casualty rates for the pedestrian, the car, and the total for all the five cases under the three selected population sizes are shown in Fig. 9.

Pedestrian casualty rates (PCRs) Overall, the variations of the PCRs over time for n_e

= 10,000 and n_e = 15,000 show similar trends to that for n_e = 5000, i.e., initially the rate has a slow increase that lasts for a while (around 20 min), and then, the rate has steep increase that only lasts for several minutes, after which the PCR almost does not increase anymore. One important observation from Fig. 9a is that for n_e = 10,000 and n_e

= 15,000 the estimated PCRs in C1-C4 are much higher than that of n_e = 5000. These differences can be explained by the fact that a larger population is more likely to cause more severe pedestrian congestion, which causes more casualties under the same tsunami inundation. For C0, the PCRs for different populations are very close due to the assumption of constant walking speeds. The results verify the nonlinear nature of the evacuation. The comparisons highlight that simulations using smaller than actual population size may significantly underestimate the casualty rate.

Car casualty rates (CCRs) Overall, the variations of the CCRs over time for n_e = 10,000 and n_e = 15,000 show similar trends to that for n_e = 5000. In terms of the values of the CCRs, similar to the PCRs, for n_e = 10,000 and n_e = 15,000 the estimated CCRs are higher than that of n_e = 5000. This is because more car casualties occur for larger n_e due to more severe traffic congestion.

Comparison between PCRs and CCRs Comparing the casualty rates for the pedestrian and car, we can see that as the population size increases the PCR has a much larger relative increase than the CCR. Take C4 for example, the CCR is 27.4%, 31.6%, and 33.5% for n_e = 5000, 10,000, and 15,000, respectively, while the corresponding PCR is 3.1%, 10.1%, and 15.6%, respectively. This may be attributed to the fact that there might already be severe traffic congestion for n_e=5000 and further increasing the population might not significantly increase the severity of traffic congestion. On the other hand, with a larger population, pedestrians might face more severe pedestrian congestion.

Total casualty rates (TCRs) The following observations are made.

(1) As population size increases, the TCRs increases significantly, stemming from increases in both PCRs and CCRs.

(2) Population size also affects the differences between TCRs estimated by different models (i.e., C0-C4). For example, C0 and C2 have very close TCRs for n_e=5000 ; as population size increases, the corresponding TCRs for C0 and C2 become 33.1% and 40.4%

for n_e=10, 000 , and 35.1% and 47.9% for n_e=15, 000.

(3) Compared to C4 (which is the more realistic case in evacuation simulation), the underestimation or overestimation of the TCR by other cases becomes larger as the population size increases. For example, when n_e=5000 , the TCR is 30.5% for C4 and 28.7%

for C0, which means the underestimation is 1.8%. However, when n_e=10, 000 and n_e=15, 000 , the underestimation by C0 becomes 8.6% (with TCR 41.7% for C4 and 33.1% for C0) and 14% (with TCR 49.1% for C4 and 35.1% for C0), respectively.