On the Utility of Shelters in Wildfire Evacuations Kent Steera , Ermyas Abebeb , Mahathir Almashorb , Anton Beloglazovb , Xu Zhongb,∗ a Melbourne
School of Engineering, University of Melbourne, Melbourne, VIC 3010, Australia Research Australia, 204 Lygon St, Carlton, VIC 3053, Australia
b IBM
Abstract The combined challenges of a high fire risk and poor vehicle access in mountainous regions have led planners and emergency management authorities to consider non-traditional alternatives to complete evacuation of a region under threat. Community fire shelters have been put forward as one such alternative; however, their benefits remain contested. In this paper a series of experiments are designed in the Dandenong Ranges in Australia and presented to elucidate the relationship between shelters and community safety in wildfire scenarios. Our approach utilises a multistage simulation workflow to evaluate the outcome of 64 shelter configurations subject to three different fires. When compared to a scenario without shelters, some shelter configurations result in up to 10% reduction in the median exposure count, while some other configurations increase it. It is found that the efficacy of shelters strongly depends on the relative location to the ignition point and the trend of fire progression. The most effective shelters are identified for the specific fires that we simulate. The results demonstrate that sophisticated modelling and simulation is necessary for decision makers to determine a beneficial shelter placement strategy that remains effective across a number of likely wildfire spread scenarios. Keywords: wildfire, evacuation planning, behaviour and risk modelling
1. Introduction Wildfires cause catastrophic consequences on communities around the world resulting in environmental destruction and more importantly loss of life. As populations living within the Wildland Urban Interface [1, 2, 3] increase, more people fall at risk of wildfires that typically ravage these environments. The devastation of recent wildfires in Victoria — Australia in 2009 [4] and South California — United States in 2003 and 2007 [5] have demonstrated the need to better understand why the mitigation plans failed to protect the community in these events and improve community resilience. Community responses to wildfires generally fall into two categories: evacuation and shelter-in-place [6]. In-place shelters can be divided into refuge shelters and in-home shelters [7]. Refuge shelters are often fortified buildings capable of protecting groups of people from an oncoming threat; they typically include shopping centres, warehouses, schools, and sports arenas. Sheltering in-home is usually associated with the ‘prepare, stay and defend’ strategy, where residents stay at their homes and actively defend the property. The ‘prepare, stay and defend’ policy was well implemented in Australia. Well-prepared houses were proved to be able to improve safety and reduce property loss in Australia [8, 9]. Mccaffrey et al. validated the ‘prepare, stay and defend’ policy in four contextual areas in the United States [10]. The validity of the policy can be broken by the contextual differences between Australia and the United States. Careful groundwork is needed to effectively implement the policy in the United States. Evacuations involve migrating a population to an area outside the region at risk. Evacuating populated areas exerts high demand on road networks, often leading to traffic congestion and consequently prolonged evacuation times. Evacuation may not always be optimal or even feasible in this situation, since the efficacy of evacuations is determined by the ability to clear a region before it is impacted by a threat. This is partly highlighted by prior works, which have derived the evacuation risk for a region as a function of the number of exit roads relative to the population ∗ Email:
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Preprint submitted to Fire Safety Journal
October 2, 2017
size. E.g., Church et al. [11, 12] and Cova et al. [13] applied the bulk lane demand analysis to identify high evacuation risk areas within the Western United States. Hence, strategies complementary to evacuation are required to mitigate the risk on populations, especially in areas with flow-restricted access. On the other hand, sheltering-in-place involves evacuees seeking refuges inside safe structures within the area under threat. The use of shelters within at-risk areas has the potential to reduce unnecessary evacuations by providing safe locations within close proximity of residents. Hence the use of such shelters have been proposed as a contingency option for regions where plans such as stay and defend, and leaving early cannot be implemented, e.g., townships in mountainous regions which often have a small number of exit roads [14, 15, 16]. However, while establishing shelters may have an intuitive appeal to both authorities and residents, their use has had mixed results historically [17, 18, 19, 20]. Therefore, the consequences of shelters and other protective strategies should be thoroughly explored before being put to use. In particular, the utility of shelters needs to be thoroughly investigated in situations where a local community is considering establishing a new shelter, or a region consisting of multiple communities is considering establishing multiple shelters. One consideration during such a study is an optimal placement of shelters. To this end, some previous works have looked at modelling the optimal positioning of shelters in flooding scenarios [21, 22, 23, 24]; however, similar work for wildfire evacuations has not been done. While some conclusions have been reached about the effect of the number and capacity of shelters for hurricane and flood evacuations, the questions around the utility of shelters in wildfire disasters remain open. Cova et al. compared evacuation, shelter-in-refuge, and shelter-in-home in wildfires through simulation [7]. The trade-off between the three actions is complex and needs to be considered according to specific scenarios. The core contribution of this paper is to investigate how the placement of refuge shelters changes the risk profile of a wildfire-prone region during a wildfire by leveraging a multi-stage workflow of wildfire/evacuation simulator. Specifically, the following research questions are addressed: • Is it always true that establishing some shelters is better than none? • What is the relationship between the presence of shelters and the risk of personal harm in wildfire evacuations? • What are the factors that influence the utility of shelters, e.g., number of shelters, number of people within range, location relative to fire progression, distance to the fire ignition point? The introduction of a shelter in a region may distort the travel patterns in an evacuation scenario. This paper posits that this distortion can potentially lead to undesirable protective outcomes. During evacuations, the existence of popular destinations, such as shelters within an area at-risk, has the potential to focus traffic. This in turn may elevate the egress time and evacuation risk of residents heading to these shelters. In addition, in the case where a shelter is located near a major access road, any congestion could lead to increased risk for the through-traffic. Our simulation casts new light on understanding the complexity of selecting effective shelter locations in high-fire-risk area across a number of likely wildfire spread scenarios. The remainder of the paper is organised as follows. Following the review of relate work in Section 2, an overview of the models of the simulation workflow, first described in [25], is given in Section 3. Sections 4 and 5 present the experimental design and results, respectively. Section 6 discusses the results and the implications of the discoveries in this paper. Finally, Section 7 provides the final conclusions. 2. Related Work Southworth [26] described evacuation modelling as a five step process involving traffic generation, departure time modelling, destination selection, route selection, and evacuation plan analysis and revision. The destination selection aspect refers to the allocation of safe endpoint locations to evacuees as a part of the modelling process. The selection of such endpoints could be determined in one of four possible ways, based on: (1) the closest exit from the area at risk (in terms of distance and/or expected travel time); (2) the location of relatives and friends; (3) pre-planned evacuation destinations; or (4) the real-time traffic situation (congestions, detours) at the time of the evacuation. The availability of refuge shelters adds another potential destination type, thus requiring additional modelling. 2
The use of refuge shelters (further referred to as shelters) raises a number of interesting questions, including: How does their presence impact the dynamics of traffic flow and consequently, the protective outcomes? How can the assignment of evacuees to shelters be optimised to reduce evacuation times and risk of personal harm? The allocation of evacuees to appropriate shelters has been a focus of prior research, which generally falls into one of three categories: (1) coordinated system-optimal assignments; (2) uncoordinated myopic assignments; and (3) a hybrid strategy. In system optimal assignment models (work by Sherali et al. [21] and ElDessouki [22]) the allocation of evacuees to shelters, as well as the routes to these shelters, are optimised to minimise the overall evacuation time. While such approaches might help establish best case outcomes, they do not account for real-world scenarios where evacuee objectives could notably diverge from the optimal system assignments. On the other hand, uncoordinated or myopic evacuation models allow for scenarios wherein evacuees themselves determine both the shelter to evacuate to, and the specific routes to take. Kongsomsaksakul [23] modelled this approach as a bi-level optimisation problem. At the top-level, the system determines which shelters out of an admissible set should be used, while at the bottom-level, evacuees decide which shelter to go to and which route to take given the locations and capacities of shelters. This bi-level optimisation problem is then solved using a genetic algorithm. While the approach does not yield optimal outcomes, it is more representative of real-world evacuations. Ng [24] proposed a hybrid approach, where the system determines an optimal evacuee-to-shelter assignment and then allows the evacuees to select the routes to shelters. The approach provides closer to optimal protective outcomes compared with uncoordinated approaches while also accounting for unforeseen real-world events (such as road-blocks and detours) that could cause evacuees to take alternative routes. However, such enforcement of destinations for all the evacuees may not be feasible in real world. In this paper, we adopt a similar model to that proposed by Kongsomsaksakul [23], where the locations of shelters are selected by an authority, while the evacuees make their own decisions on the choice of destinations and routes. We believe that this model is a reasonable representation of reality and allows us to conduct realistic analysis on the utility of shelters. Considering this model, a number of interesting questions about refuge shelters emerge. Specifically, does the presence of shelters always offer better protective outcomes? How is the utility of a shelter dependent on the specific progression of the oncoming threat? Are there general location factors that influence the utility of a shelter? What are the impacts of placing shelters, both on the local and global level? For example, could a shelter improve evacuation times for a subregion, but worsen clearance times for the overall region? In general, these questions have not been thoroughly explored. Sherali et al. [21] and ElDessouki [22] studied the effects of shelter placement under system optimal assignments for flood and hurricane scenarios and found that the placement of shelters has an impact on the evacuation times. However more concrete conclusions on what factors influence the utility of shelters have not been discussed. Kongsomsaksakul [23] performed similar studies for uncoordinated evacuation scenarios and found that more shelters improve evacuation times up to a certain point (7 shelters in the specific scenario considered) after which the performance degrades. Their study into the capacity of shelters also identified that low capacity shelters require higher number of shelters which in turn increases the evacuation time. However, as discussed above, a number of open questions on the utility of shelters remain. This study aims to address these questions. Specifically, the paper addresses whether shelters provide a better protective outcome under all scenarios; what spatial factors influence the utility of shelters; and how the utility of a shelter is influenced by the specific threat progression. 3. Wildfire Evacuation Model This paper is based on the wildfire evacuation model proposed in our previous work [25], which can model the impact of dynamic factors on the predicted outcomes of a wildfire evacuation scenario. As shown in Figure 1, the modelling workflow includes models of the following phenomena: wildfire spread, evacuation triggers, resident behaviour, traffic flow, and evacuee risk. The constituting models are described briefly in this section (refer to [25] for more details). 3.1. Wildfire simulation As a threat model, a wildfire simulator is included in the modelling workflow that follows the cellular automata model for forest fire spread prediction proposed and validated by Alexandridis et al. [27]. Cellular automata (CAs) 3
Ignition point and environmental factors
Wildfire simulation
Evacuation trigger modelling
Behaviour categorisation
Departure time modelling
Destination modelling
Traffic simulation
Risk analytics
Risk assessment
Figure 1: The modelling workflow. The model simulates the progression of a wildfire under given environmental conditions and a given ignition point. The propagation of the wildfire triggers evacuation. The selection of evacuation route of individual evacuee is simulated, taking into account human behaviours, distance to evacuation destinations (shelters and exits), and traffic network. The traffic simulator generates the spatiotemporal trajectory of the evacuees, which is used to estimate fire risk in combination with the simulated fire progression.
are discrete, dynamical systems wherein a collection of identical components evolve according to simple, local rules. In our implementation each CA cell is assigned with a label from the set {unaffected, burning, burnt}. The probability of a cell transitioning from unaffected to burning is calculated at each time-step for all cells adjacent to cells in the burning state: pburn = pw · ps · pH · pT · pkveg , (1) where pw , ps , pH , pT , and pkveg are the transition probabilities depending on wind, slope, humidity, temperature, and vegetation, respectively. Detailed formulation of these probabilities can be found in [27]. The effect of ‘spotting’ (airborne burning particles igniting new fires ahead of the main firefront) is also captured in a manner dependent upon wind conditions, as described by Alexandridis et al. [27]. 3.2. Evacuation trigger modelling Evacuation triggers are events that causes the residents to begin evacuation. Several types of events are modelled based on the firefront progression and its projected state. These events trigger the households to evacuate at different points in time during the scenario. Specifically, the modelled events include 24-hour, 6-hour, and 2-hour warnings 4
sent out to residents based on the estimated time until impact. We also account for direct observation as a mechanism through which residents learn of the current location of the fire: the fire visibility event triggers people to evacuate when the firefront is within the visibility range from their initial location. 3.3. Behaviour categorisation The response of residents to the information they receive is modelled through a set of behaviours. Each behaviour determines the evacuation triggers of the residents. We assume 45%, 35%, 15%, and 5% of the residents respond to evacuation triggers ‘fire visible’, ‘2-hour warning’, ‘6-hour warning’, and ‘24-hour warning’, respectively. 3.4. Departure time modelling Once residents receive an evacuation trigger they are responsive to, they get assigned with a departure time, which is calculated as a sum of the decision time delay and preparation time. The random variation in preparation time between evacuees is modelled by the Rayleigh distribution. The Rayleigh distribution covers a variety of departure time, including late departures. Based on our experience, we think the Rayleigh distribution is a good representation of the collective behaviour of the crowd. One can adjust the parameters of the Rayleigh distribution to model desired crowd responses. Moreover, the approach described in this paper is not limited to the Rayleigh distribution. One can assign other distributions to model the collective behaviour of the crowd, which does not affect the effectiveness of the simulation workflow. However, the simulation outcome can be different under different models of departure time. 3.5. Destination selection In the absence of shelters, evacuees are assumed to evacuate to their nearest exit. Exits are defined by intersections of outgoing roads with the boundaries of the at-risk region and are assumed to be thresholds to safety. When shelters are available, shelter destinations are modelled as points accessible from the road network as shown in Figure 2, where origins of the evacuees are denoted by A, B, C, and D. Each shelter is parameterised with a radius of attraction, which defines an area of attraction whose residents may select this shelter as their evacuation destination alternatively to an exit. In the example shown in Figure 2, potential destinations for each evacuee are listed in Table 1.
East exit Shelter 2
Shelter 1
D
C
B A West exit
Figure 2: Schematic of the potential evacuation destinations for evacuees A, B, C, and D. Each evacuee can choose his/her evacuation destination from the nearest exit and the shelters of which the area of attraction (dashed circle) contains the evacuee.
Table 1: Potential shelter and exit destinations of evacuees A, B, C, and D in Figure 2
Evacuee A B C D
West exit X X
Shelter 1 X X
Shelter 2 X X
East exit
X X
Let D s be the set of all possible destinations in a scenario including shelters and exits, and Di ⊆ D s be the set of potential destinations of an evacuee i. Each evacuee i has a probability pi j of selecting a destination j ∈ Di , such that P j∈Di pi j = 1. Shelters are assumed to have unconstrained capacity, which is justified by the fact that the population within the shelter radius is limited, and in reality the capacity of a shelter should be planned based on the population size of 5
the area. Another aspect captured by the model is the fact that evacuees stop choosing the shelter as their destination when the firefront comes to a close proximity to the shelter. In our experiments, the evacuees prefer exit destinations when the firefront is within 2km of the shelter, at which point going to that shelter is perceived of high risk. 3.6. Traffic simulation Microscopic traffic simulation has been applied to evacuation simulation at the neighbourhood scale [12, 28]. In microscopic traffic simulation, the dynamics of each individual vehicle are modelled; and results are derived from the interactions of each agent/vehicle with road conditions and other vehicles. Our approach uses an agent-based microscopic traffic simulator SUMO (Simulation of Urban Mobility) [29] to predict vehicle movements for each scenario. SUMO is chosen due to the granularity of its output, which includes the exact coordinates of each vehicle at any given time during the simulation. The path of each vehicle is computed using Dijkstra’s shortest path algorithm. 3.7. Risk analytics From the spatiotemporal output of the traffic and fire simulators it is possible to derive evacuee-specific risk estimates. Specifically, we approximate the danger to a person by considering their proximity to the threat. This metric provides a more direct estimate of the outcome of a scenario than traditional metrics such as clearance time and egress time. The distance between a point p and a threatened area X is calculated as d(p, X) ≡ inf{d(p, a) : a ∈ X} (see Figure 3). Both the threat and the position of each person varies over time. The person-threat distance (ξit ) of a point pi at time t, relative to the threatened area X at time t is calculated as d(pit , Xt ), where Xt is the perimeter of the area under threat at time t, i.e., the firefront; and pit is the position of the point pi at time t. The exposure count E for a population Q in a given scenario is calculated as the total number of people who were within some distance δ of the threat at some point in time: X 0, x < 0, (2) H(δ − zi ), where H(x) = E= 1, x ≥ 0, i∈Q where zi is the minimum person-threat distance of pi among all time steps. In the experiments conducted in this paper, δ is set to be 0. Xt−1 Xt Xt+1
ξt+1 ξt ξt−1
pt+1
pt pt−1
Figure 3: Person-threat distance (ξ) from a point p to a threatened area X. Xt is the perimeter of the area under threat at time t, i.e., the firefront. pt is the position of the point p at time t. ξt is the person-threat distance from p to X at time t.
4. Experiment Design The aim of the experiments is to investigate the impact of the presence of shelters within the at-risk area on the outcomes of a wildfire evacuation. Multiple evacuation scenarios with a range of shelters placements and wildfire 6
ignitions were simulated to evaluate such impact. The experiments were conducted in a region called the Dandenong Ranges, which is a wildfire-prone part of Victoria, Australia. Figure 4 shows the vegetation density and elevation in the study area. The distribution of address points, the road network, the locations of 6 shelters, and the radius of attraction of the shelters in the study area are illustrated in Figure 5. The shelter placement, fire ignition points, and environmental conditions used in the experiments are described in the following subsections.
(a) Vegetation
(b) Elevation
Figure 4: Vegetation (a) and elevation (b) in the study area (Dandenong Ranges, Victoria, Australia).
4.1. Shelter Placement Due to financial and other constraints, the authorities generally consider establishing refuge shelters based on existing structures within the at-risk area rather than constructing new special-purpose buildings. Typical locations of shelters include schools, sports grounds, and shopping centres [7]. In other words, the set of locations suitable for establishing a shelter is usually highly constrained. For these experiments, based on the prior literature and information from subject matter experts, a set of six potential shelter locations was selected, one for each community within The Dandenong Ranges region. The radius of attraction of each shelter was set to include all members of that community as shown in Figure 5. The fraction of evacuees from within the shelter range choosing that shelter as their destination was set to 50%. The properties of the potential shelters are summarised in Table 2. Table 2: Locations, radius of attraction, and coverage of the six shelters in the experiment.
Shelter ID 1 2 3 4 5 6
Community Miller Park Ferny Creek Mt Dandenong Olinda Sassafras The Basin
Radius (m) 1500 1700 1500 1500 1700 1700
Addresses in range 548 719 540 776 1282 983
All possible combinations of shelter locations are simulated in the experiments, which resulted in a total of 64 shelter placements (also referred to as configurations) including the ‘no shelter’ case. As the evacuees randomly 7
Figure 5: The distribution of address points (dots), the road network (solid lines), the locations of 6 shelter (triangles), and the radius of attraction of the shelters (dashed lines) in the study area (Dandenong Ranges, Victoria, Australia).
8
select their evacuation destinations, each shelter configuration is simulated multiple times. Based on several test simulations, 20 replications are sufficient to make the confidence interval of the exposure count less than 10 units wide. Therefore, the total number of simulations for each fire ignition point across all the shelter placements was 64 × 20 = 1280. 4.2. Ignition Points and Environmental Conditions Three wildfire ignitions were simulated in the experiments. The ignition points were set to simulate distinctively different fire progressions to evaluate shelter configurations under different relative spatial relationships with the fires. The ignition points are referred to by the name of the suburb where they are located, i.e., Tremont, The Basin, and Montrose. The Forest Fire Danger Index (FFDI) and wind conditions for each ignition are set as listed in Table 3. The simulation output for each of the fires relative to the shelter locations is shown in Figure 6. Considering the 3 wildfire ignitions, the total number of simulations conducted was 3840. Table 3: Fire ignition points and environmental conditions
Ignition The Basin Montrose Tremont
FFDI 80 75 75
Wind direction SE SSW NE
Wind speed (km/h) 60 73 40
Figure 6: Spatial intersection between the area of attraction of the six shelters and the final perimeters of the three simulated wildfires ignited at Montrose, the Basin, and Tremont.
4.3. Data Sources Our experiments make use of data sets from several public sources including the road network model from the OpenStreetMap (OSM) project1 licensed under the Open Data Commons Open Database License (ODbL)2 , demo1 OpenStreetMap.
2 OpenStreetMap
http://openstreetmap.org/ License. http://openstreetmap.org/copyright
9
graphic data and regional boundaries from the Australian Bureau of Statistics (ABS)3 , elevation and vegetation data from the Victorian Government Data Directory4 . 4.4. Assumptions The experimental design described above are not necessarily representative of all possible scenarios and care should be taken when attempting to generalise from any findings. Furthermore, the following assumptions need to be taken into account when interpreting the results: • All residents must travel to a shelter or an exit. The case where residents stay if they are already in a shelter is not considered. • The evacuation areas are decided by emergency agents who ensure the safety of the evacuation areas. The evacuees will not be exposed to fire once they successfully evacuate from the study area. • Vehicle numbers are derived from residential data and do not depend on the time of day. However, in reality, the number of people in an area may vary with time. E.g., during the week many people may leave the region during daytime because their workplace is located elsewhere. Conversely, on weekends the number of people in the area can significantly increase as the area is a population tourist destination. • Route selection is static; for each scenario, before beginning their journey, drivers select a route based on their current knowledge of the situation (i.e., the location of the fire, their present location). Once a driver has begun a journey they do not change their route even when encountering delays. • People drive to their nearest exit and obey speed limits. • Residents all receive warnings when they are sent. It is assumed that authorities will use a variety of channels (SMS, radio, television, social media, etc.) to communicate with the public and that this provides sufficient coverage to reach all the relevant people. • Weather conditions are constant throughout the scenario, i.e., FFDI, wind velocity. • There are no car accidents. • Evacuees never select a shelter as their destination if they are outside of the area of attraction of the shelter. 4.5. Computation The model presented here is typically solved in under five minutes on a cluster of mid-tier Virtual Machines (VMs). For our experiments, the instances provisioned were mostly dual-core Linux machines with 4GB of RAM. The only exceptions were the VMs hosting our database (quad-core, 16GB) and traffic-simulator (8-core, 8GB), owing to their more advanced computational requirements. It should also be noted that the architecture we have designed is suited to concurrent execution of scenarios and can scale horizontally by adding more VMs. 5. Results Previous studies have looked at clearance times and egress times as evacuation performance metrics. As discussed in [25] we consider these metrics to be poor predictors in the case of bushfire evacuation due to their independence of the threat. Instead, the global exposure count is used in this paper as the performance metric of shelter placements, where the study region is treated as a whole. Improvement in one area may be cancelled out by deteriorations elsewhere. This is appropriate from an evacuation planning perspective where the value of human lives is assumed equal.
10
5 only
Presence of shelters 5 and 6: 0
1 Shelter
2 Shelters
6 only
Both
Neither
3 Shelters
4 Shelters
5 Shelters
6
600
Exposure count
●
●
● ● ●
● ●
●
●
●
●
550
● ● ●
●
●
500
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●
● ●
●
● ●
●
●
None 1 4 2 3 5 6
3 1 1 1 2 2 2 3 4 4 1 2 1 3 5 4 2 3 4 3 4 5 5 5 6 5 6 6 6 6
1 2 1 1 1 1 2 1 2 2 1 1 3 1 2 3 3 1 2 4 2 3 2 3 3 4 3 2 4 3 3 4 4 2 4 4 5 5 5 5 4 4 3 4 5 5 5 5 5 6 6 6 5 6 6 6 6 6 6 6
1 2 3 4
2 3 4 5
1 2 4 5
1 2 3 5
1 3 4 5
1 3 4 6
1 2 3 6
2 3 4 6
1 2 4 6
1 2 5 6
1 3 5 6
1 4 5 6
2 3 5 6
2 4 5 6
3 4 5 6
1 2 3 4 5
1 2 3 4 6
1 2 3 5 6
1 2 4 5 6
2 3 4 5 6
1 3 4 5 6
All
Combination of shelters
(a) Tremont ignition. Shelters 5 and 6, have a clear beneficial impact.
5 only
Presence of shelters 5 and 6: 0
1 Shelter
2 Shelters
6 only
Both
Neither
3 Shelters
4 Shelters
5 Shelters
6
●
Exposure count
230 ●
220
●
●
●
●
●
210
200
190
●
● ●
● ●
None 1 5 3 6 4 2
4 2 1 2 2 3 5 4 1 1 2 3 1 1 3 5 4 6 3 6 4 6 6 2 5 5 5 4 3 6
●
1 1 2 1 2 3 4 1 1 2 1 2 1 2 1 1 3 1 2 3 2 5 3 2 3 5 5 3 4 3 3 4 2 5 2 3 4 4 4 4 4 6 6 6 5 6 6 6 5 4 4 6 5 6 3 5 5 6 5 6
1 3 4 5
1 2 5 6
2 3 4 5
1 3 5 6
●
●
●
2 3 4 6
1 2 3 4
1 4 5 6
1 3 4 6
2 4 5 6
2 3 5 6
1 2 3 5
1 2 4 5
1 2 4 6
3 4 5 6
1 2 3 6
1 2 3 5 6
1 2 4 5 6
1 3 4 5 6
2 3 4 5 6
1 2 3 4 6
1 2 3 4 5
All
Combination of shelters
(b) Basin ignition. Shelters 5 and 6 no longer show much value.
3 only
Presence of shelters 3 and 4: 0
1 Shelter
2 Shelters
410
4 only
Neither
3 Shelters
4 Shelters
5 Shelters
6
● ●
●
●
Exposure count
Both
●
390
●
● ● ●
●
●
●
● ●
370
●
350
●
● ●
●
●
330 None 1 2 5 6 3 4
2 3 1 2 2 1 1 1 3 5 2 1 4 3 4 3 5 5 5 6 3 6 2 6 6 4 4 6 4 5
1 1 1 1 2 1 3 2 1 2 2 4 3 2 1 2 1 1 1 3 5 3 2 2 3 3 5 3 2 5 4 5 4 4 4 3 3 4 2 4 6 6 3 6 6 5 6 5 5 6 6 6 6 5 5 4 4 6 4 5
1 2 3 6
1 2 3 5
1 2 5 6
2 3 5 6
1 3 5 6
1 2 4 6
1 3 4 6
1 2 3 4
1 4 5 6
2 3 4 6
2 3 4 5
2 4 5 6
1 2 4 5
3 4 5 6
1 3 4 5
1 2 3 5 6
1 2 3 4 5
2 3 4 5 6
1 2 4 5 6
1 2 3 4 6
1 3 4 5 6
All
Combination of shelters
(c) Montrose ignition. Instead of shelters 5 and 6, shelters 3 and 4 are beneficial. Figure 7: Impact of different shelter combinations on exposure counts of the three simulated wildfires. Certain configurations are shaded aid discussion.
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5.1. Efficacy of shelter configurations The experimental results are presented as boxplots in Figure 7, with one for each shelter configuration (recalling that 64 distinct configurations are studied). Each boxplot constitutes a statistical summary of the 20 replications for that configuration. The boxplots are grouped by the total number of shelters available, and within each group ordered by the median. Further, certain configurations that readers should pay more attention to are shaded, with the key presented above each subfigure. The Tremont fire begins in the south-west quadrant, and spreads towards north-east (see Figure 6). The wind speed for this fire is the lowest but the terrain and weather conditions still result in a large fire. Shelter 2 is the first to be impacted, followed by shelters 5, 4 and 6. The boxplots for all configurations exposed to the Tremont fire are depicted in Figure 7(a). Across all configurations the introduction of a single shelter at either site 5 or site 6 noticeably decreases the minimum, median and maximum exposure counts. To highlight the role of these two shelters, the configurations are shaded based on the presence (or absence) of shelters 5 and 6. Those configurations where both shelters 5 and 6 are present are unshaded (white) and tend to have the greatest efficacy. The maximum improvement (10% reduction in median exposure count) is found in the four shelters configurations, specifically with the configuration {3, 4, 5, 6}. More than four shelters shows insignificant difference in the total exposures. It is noted that some configurations increase the median exposure count (e.g., shelter 1 alone, or configuration {1, 2, 4}) with respect to the no shelter situation. Under these configurations, the evacuation routes of some evacuees intersect with the firefront at some point in time, which focuses traffic and increases exposure count. This highlights the importance of detailed modelling and investigation of the effects of establishing a shelter at each potential location. The fire that starts in The Basin begins in the middle of the study region and propagates towards south-west. It quickly engulfs shelters 5 and 6, and later spreads to shelters 4, 3 and 1. Due to the proximity of the ignition point to the shelters, most shelters immediately become unattractive for evacuees. Accordingly, as shown in Figure 7(b), the different shelter configurations do not have a significant effect on the exposure count. No particular shelter is significantly beneficial for this fire. The boxplots are still highlighted according to the presence (or absence) of shelters 5 and 6 to demonstrate the contrast to the Tremont fire. The configuration {1, 2, 3, 4, 5} yields the greatest reduction in the median exposure count, but the improvement is insignificant. Most of the variation can be attributed to the stochasticity of our model. The Montrose fire starts in the north and expands in a south-westerly direction. It first reaches shelter 3, then 4, 5, 6 and finally 2. Figure 7(c) illustrates the boxplots for all shelter configurations. Shelter 4 is the most influential, significantly outperforming the others in the single shelter group, and consistently appearing in the top configurations as the number of shelters increases. Shelter 3 also performs well, especially in combination with shelter 4. The boxplots in Figure 7(c) are shaded by shelters 3 and 4 to highlight their role. The greatest reduction in median exposure count is generated by the 6 shelters together, with an improvement of 10%, closely followed by the three shelters configuration {3, 4, 5}. 5.2. Shelters impacted by fire The results in Section 5.1 demonstrate that some shelters are particularly influential for specific fires. Such shelters share a common feature: in the path of the firefront at some point during the simulation, but not impacted immediately after the ignition. Thus the impact of the presence of impacted shelters on the outcomes of an evacuation is further studied. Specifically, the relationships between average time until impact, the number of vehicles going to the shelters within the burned area, and exposure count are investigated. When considering relative location of a shelter to an ongoing wildfire, several factors come into play, such as the distance from the shelter to the fire ignition point and the fire spread rate towards the shelter. A metric called time until impact is used to capture the integrated effect of these factors. Time until impact is defined as the time interval between the fire ignition and the moment when the fire reaches the shelter. Figure 8(a) shows the relationship between the mean time until impact for each shelter configuration and the number of vehicles going to the impacted shelters, grouped by the number of available shelters and fire ignition locations. A positive correlation (0.6 < r2 < 0.8) can be observed between the mean time until impact and the number 3 Australian 4 Victorian
Bureau of Statistics. http://abs.gov.au/ Government Data Directory. https://www.data.vic.gov.au
12
1 Shelter
2 Shelters
3 Shelters
4 Shelters
5 Shelters
6 Shelters
● ● ● ● ● ● ● ● ● ●
● ●
● ●
●
● ●
●
●
● ● ●
● ● ● ● ●● ● ●
●
● ● ●● ● ● ● ●
● ●
● ● ● ● ●
●
r² = 0.74
●
● ● ●
● ● ● ● ● ●
● ● ● ●
● ●
●
● ●
● ●
● ●
●
●
r² = 0.73
● ●
0
● ● ●● ● ●● ● ●
● ● ●
● ● ● ● ● ●
● ● ●● ● ● ● ● ●
● ● ● ● ● ● ● ●
● ● ●
● ● ●
r² = 0.75
r² = 0.76
● ● ● ● ● ● ● ● ● ●
1000
● ● ●
● ●
500
● ●
● ●
● ●
● ● ●
● ● ●
● ● ●
● ● ● ●
0
● ●
● ●
●
● ●
● ●
● ●
r² = 0.61
● ● ●
●
● ● ●
● ● ● ●
● ●
r² = 0.63
r² = 0.64
● ● ●
● ●
● ● ●
● ● ● ● ● ●
500
●
●
●
● ●
0
●
●
0
2
4
6
●
8
●●
0
2
4
6
● ● ● ● ●
0
● ●
● ● ● ● ●
● ●
●●
r² = 0.8
●
8
r² = NA
● ●● ● ●
●●
r² = 0.8
●
● ●
● ●● ● ● ● ●
●
●
●● ● ●
r² = 0.8
● ●● ● ●
● ●
r² = 0.65
Tremont
1000 ● ●● ●
● ● ● ●
● ● ●
● ●
r² = 0.62
● ●
● ● ● ● ● ●
● ● ● ● ●
● ● ●
● ●● ● ● ● ●●
● ● ●
● ● ●
● ● ● ● ●●
● ●
● ● ●
● ● ●
● ● ● ● ● ●
● ● ●
r² = NA
● ● ● ●
● ● ●
● ● ● ●● ● ●
● ● ● ● ●●
● ●
● ● ●
● ●
● ●
● ● ●
● ●
● ● ●
● ● ●
● ●
● ● ●
● ● ● ●
● ● ●
● ● ●
●
● ● ● ● ●
r² = 0.74
● ●
● ● ● ● ●
● ● ●
● ● ●
● ● ● ● ● ● ● ●
●
Montrose
Vehicles going to shelter
500
Basin
1000
2
4
6
8
r² = 0.8 0
2
4
6
8
r² = 0.8 0
2
4
6
8
r² = NA 0
2
4
6
8
Mean time until impact (hours)
(a) Relationship between the number of shelter users and the time until impact. 1 Shelter
2 Shelters
3 Shelters
4 Shelters
5 Shelters
6 Shelters
●
●
1.1
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ●
● ● ● ●
●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ●
●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ●●
● ● ● ● ● ● ● ●● ●
●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
●
●
●
●
●
● ●● ●● ● ●● ● ● ● ● ●● ●● ● ● ● ●● ● ●● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ●● ● ● ● ●● ●● ● ● ● ●● ● ●
● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ●● ● ●
● ● ●● ● ● ● ●● ●●●● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ●● ● ●● ● ● ●● ●●● ● ● ●● ● ●●● ● ●● ●● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ●● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●
0.9 r² = −0.02
● ●
● ● ● ●● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ●●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ●● ●
r² = −0.05
1.1
● ● ●● ● ● ● ●● ●●● ●● ● ● ●● ● ● ●● ●● ● ● ● ●●● ● ●● ●●● ●● ● ● ● ● ● ● ●● ● ● ● ● ●● ●●● ● ●●● ● ● ● ●● ● ● ● ● ●● ● ●
● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ●● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ●
●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●●● ● ● ●● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ●
● ●
●● ●
● ● ● ● ● ● ●● ●●● ● ● ● ● ● ● ● ●●
r² = −0.05
r² = 0.07
r² = −0.2
r² = −0.16
● ●
● ●
1.0
●
● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
0.9
● ● ● ●
● ● ● ●● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
●
●
● ● ● ● ● ● ● ● ●●● ● ● ● ●● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ●
●●
●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ●● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ●● ● ● ●● ●●● ●● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●●●● ● ●●●●● ● ● ●● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ●● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ●● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ●
● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ●
r² = 0.01
● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ●● ● ● ● ● ●
●
● ● ● ● ● ●● ●● ● ●● ● ● ● ● ●● ● ● ●●●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●●● ●● ● ● ● ●● ● ● ● ● ● ●● ●● ● ● ● ●● ● ● ● ● ●● ●● ● ● ● ● ● ●● ● ● ●●● ● ●● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ●● ● ● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ●●● ● ● ●●●●● ● ● ●● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●
r² = −0.02
● ● ● ●●●●● ●● ● ● ● ● ●●● ● ●●● ● ●● ● ● ●● ● ●● ●● ● ●●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ●
● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
●
r² = −0.1
●● ●
●
● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ●● ● ● ● ● ● ● ● ●● ●● ● ● ●● ● ● ● ●● ● ●● ● ● ● ● ●● ●● ● ●● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ●● ●● ● ● ● ● ●● ● ● ●●● ● ● ● ● ● ● ● ●●● ● ● ●●● ●● ● ● ● ● ● ●● ●● ● ● ● ●● ● ● ●● ● ●●●●● ● ● ●● ● ● ●● ● ●● ● ● ●● ●●●● ● ● ● ● ● ● ● ● ●● ● ●● ●● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ●●●● ● ●● ●● ● ● ● ●
● ● ●
●● ●● ● ●● ● ● ● ● ● ● ●● ● ● ●●
●
●
● ●● ● ●●● ● ● ● ● ● ● ●● ●● ● ● ●● ● ● ● ● ●● ●●●
● ● ●● ● ● ●● ● ●● ● ●● ● ● ● ●● ●
●● ● ● ● ● ● ●● ● ●● ● ● ● ●
r² = −0.02
●● ● ● ●
●
●● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ●●● ● ● ●●● ●
● ●● ● ● ● ●● ● ●● ● ● ● ● ● ● ●●
r² = 0.07
r² = −0.15
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ●● ●● ● ● ●● ● ● ●● ●● ●● ● ●● ● ● ● ●● ●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
●
0.9
● ●
● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ●
● ●
●
0
500
1000
0
● ●
● ● ● ●
r² = −0.45
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ●●● ●●
● ● ● ● ● ● ● ● ● ● ● ● ●
● ●● ●● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ●● ● ● ●● ● ● ● ● ●
● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ●● ●●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ●
● ●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●
r² = −0.5
500
1000
● ●● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
r² = −0.54
●
0
500
● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
1000
0
● ● ●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ●
500
●● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●
r² = −0.58
1000
● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ●
0
500
● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●
r² = −0.5
●●
1000
0
500
Tremont
1.1 1.0
Montrose
Normalised exposure count
●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ●
Basin
1.0
●
● ● ●
r² = −0.17
1000
Vehicles going to shelter
(b) Relationship between the exposure count the number of shelter users. 1 Shelter
2 Shelters
3 Shelters
4 Shelters
5 Shelters
6 Shelters
●
●
1.1
● ● ● ● ●
● ●
● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ●
●
● ●
● ●
● ●● ● ● ● ●● ● ● ● ●● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ●
● ● ● ● ● ● ● ● ● ● ● ● ●
●
●● ● ● ●● ● ●● ● ● ● ●● ● ● ●● ● ●● ● ● ●● ●
●● ● ● ●● ● ● ● ●● ● ● ● ●● ● ●● ● ● ● ● ● ● ●
●● ●
●
●
● ●
● ●●
●
● ●
● ● ●
● ● ● ●
●● ●● ●
●
●● ● ● ● ● ● ●● ● ●● ● ● ●● ● ● ●● ● ● ●● ●● ● ● ● ● ●
● ●
0.9 r² = 0.05
● ● ●● ● ●● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ●● ●● ● ●● ● ● ● ●
●
●
● ● ●● ● ●●● ●● ● ● ● ● ●● ●● ● ● ● ●● ●● ● ● ● ● ●● ● ●● ●●● ●● ● ●
●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ●
● ●
● ● ● ● ●
●● ● ● ●● ●● ●● ●● ● ●● ●● ●● ●● ● ● ● ● ●● ● ●● ● ● ● ● ● ●● ● ● ● ●● ● ● ●● ●● ● ● ●● ●● ● ●
● ● ●● ●● ●● ●● ● ● ●● ● ● ● ●● ● ●● ● ●●● ● ●● ● ●● ● ● ● ● ●●● ●● ●
●
r² = −0.04
1.1
● ● ●● ●● ● ● ●● ● ●● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ●● ● ●● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ● ● ●
● ●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ● ● ●
● ●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ●
r² = −0.04
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
●
● ●
● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ● ● ●
r² = 0.01
r² = −0.08
r² = NA
● ●
● ●
1.0
●●● ● ● ●● ● ●● ● ● ● ●● ● ● ●● ●● ● ● ●● ● ● ● ●●● ● ●● ● ●● ●●
● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ●
● ●● ● ● ● ● ● ●● ● ●● ● ● ●● ●● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ●● ●● ● ● ●● ● ● ● ●● ●● ●● ●
Montrose
● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
●
0.9
● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
●
● ●
●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ● ● ●
●
● ●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
●
● ●
● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
●
● ● ●● ●● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●
●
r² = −0.1
● ● ● ● ●● ● ●● ●● ● ● ● ●●● ● ●● ● ● ●● ● ●● ● ● ●● ●● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ●● ●● ● ● ● ●● ●● ● ● ●●● ● ● ● ● ●● ● ●● ●● ● ● ● ● ●● ● ●● ● ● ● ●● ● ● ● ●● ●● ● ● ●● ● ●● ●● ● ● ●● ●● ● ● ● ●●
●
●
● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ●● ●
r² = −0.15
● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ●● ● ● ● ●● ●● ●●
● ●● ● ●● ● ● ● ●● ● ●● ● ●● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ●● ● ● ● ● ●● ● ● ●● ● ●● ● ● ● ● ● ● ●● ● ●● ●● ● ● ●● ●● ● ●● ●● ● ● ● ● ● ● ●● ● ●● ●●● ● ● ●●
●
r² = −0.21
● ● ● ● ● ● ● ● ●● ●● ● ● ● ●● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ●● ●● ● ● ● ● ● ● ● ●●● ● ● ● ●● ● ●● ● ● ● ●● ●● ● ● ● ● ●● ●● ●● ● ●● ● ● ● ●● ● ● ●● ● ● ● ● ● ●● ●● ●● ● ● ● ● ● ● ●● ● ● ●● ● ● ●● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ● ● ● ●
●
●
● ● ● ● ● ●
● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ●
r² = −0.13
r² = −0.07
r² = NA
1.1
Tremont
Normalised exposure count
● ●
● ●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ●
●
● ●
●
● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ●
● ●● ● ● ● ● ●●● ● ● ●● ● ●● ●● ● ● ●● ●● ● ● ●● ●● ● ●● ● ●●● ● ●●
● ●
Basin
● ● ● ● ● ●
1.0
●
● ● ●
●
1.0
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0.9
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r² = −0.37 0
2
4
6
8
0
2
4
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r² = −0.41 6
8
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r² = −0.48
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0
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4
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6
8
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0
2
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4
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r² = −0.52 6
8
0
2
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r² = −0.5
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4
6
8
0
2
r² = NA 4
6
8
Mean time until impact (hours)
(c) Relationship between the exposure count and the time until impact. Figure 8: Relationship between shelter position relative to fire progression (time until impact), number of shelter users, and exposure count.
13
of vehicles going to the impacted shelters. In our evacuation model evacuees avoid shelters when the wildfire is within 2 km. Thus, the later a shelter is impacted by fire, the longer the shelter stays attractive to the evacuees; and consequently the more people will use the shelter. Figure 8(b) illustrates the relationship between the number of vehicles going to impacted shelters and the exposure count normalised by the median exposure count of the ‘no shelter’ configuration. No significant correlation can be observed between these two factors for the Basin and Montrose fires (−0.2 < r2 < 0.2). For the Basin fire, the ignition point is close to shelters 1, 4, 5, and 6. These four shelters become unattractive to evacuees in a short period of time after the ignition. Few people uses these four shelters in the Basin fire, hence the shelters have little impact upon the outcome of the evacuation. For the Montrose fire, the ignition point is so distant from the evacuees that most evacuees have adequate time to leave through an exit. Hence the effect of shelters vanishes. In contrast, the Tremont fire yields a negative correlation between the number of vehicles going to impacted shelters and the normalised exposure count(r2 ≈ −0.5). The ignition point of the Tremont fire is in moderate distance from shelters 1, 4, 5, and 6. These four shelters have adequate time to attract evacuees before the impact. The ignition point is also close to the populous areas, leaving the evacuees insufficient time to evacuate through an exit. In this situation, going to the shelters is a wise action. Thus, the more vehicles go to shelters in the Tremont fire, the lower the exposure count (reaching up to 10% reduction). Figure 8(c) shows the effect of the mean time until impact on the normalised exposure counts. As can be anticipated from the results in Figures 8(a) and (b), there is no correlation observed for the Basin and Montrose fires (−0.21 < r2 < 0.05) and a negative correlation in the case of the Tremont fire (−0.52 < r2 < −0.37). The results in Figure 8 highlight that having shelters within the threat area can be beneficial if the locations of shelters are carefully selected. More specifically, shelters have the highest positive effect when they are located around high population areas, and are neither too close to nor too distant from the ignitions. 6. Discussion This paper casts new light on the problem of shelter placement in wildfire-prone regions. Different from existing research, we focused on how the relative location of shelters to ignitions can dramatically change the outcome of evacuation. Our simulation framework integrates fire simulator, human behaviour models, traffic simulator, and fire exposure estimator, which enables comprehensive simulation of different evacuation scenarios in a close-to-real-life setup. The experimental results show that it is possible to improve the protective outcomes by establishing shelters within the threat area. However, the results also made it clear that the locations of shelters play a crucial role and may increase the risk of personal harm when selected poorly. The effect of shelters is also highly dependent on how the wildfire spreads in the region (based on the ignition point, environmental conditions, etc.); in some scenarios shelters make a big difference, while in others the effect is negligible. Our results demonstrate that shelter placement is already considerably complex and difficult. However, there is more complexity that we did not consider in the simulation. One important assumption of our experiment is that all residents must travel to a shelter or an exit. We did not take into account the ‘stay and defend’ strategy. In places where the ‘stay and defend’ policy is well implemented (e.g., Australia), a proportion of residents may stay and defend in a real-life wildfire event. This can affect the volume of traffic and the efficacy of shelters. Property-level information needs to be collected to properly model if the residents are well prepared and can survive if they stay and defend. The number vehicles is static and derived from residential data in our experiment. Diurnal, weekday-weekend, or seasonal changes of population in the study area are not considered. In addition, the behaviour of evacuees is also modelled as static functions. In reality, the decisions and responses of evacuees can change at different time of the day, day of the week, and day of the year. To more accurately model and evaluate the efficacy of shelters, the dynamics of population and human behaviour need to be taken into account. The dynamics can be learned from historical traffic data during wildfire events or empirically modelled by expert experience if such historical data is unavailable. Route selection is also static and made by the driver before beginning the journey. Hence the route is deterministic depending on the instantaneous situation when the driver decides to travel to a shelter or an exit. In reality, one may reroute according to update information about the fire. The capacity of predicting fire exposure counts from an ignition point and a shelter placement has significant practical implications for decision making under unexpected emergencies. Emergency agents can send out more 14
informative warnings to guide the resident to evacuate or to seek the best protection. They can also decide to close certain shelters to avoid focusing traffic and placing people at a higher risk. 7. Conclusion The utility of shelters in wildfire evacuations is investigated in this paper through simulation. All possible configurations of shelters at the 6 pre-selected sites across 3 wildfires are evaluated in the Dandenong Ranges region. The analysis of the threat exposure counts across the simulated scenarios allow us to address the research questions stated in the introduction. The results demonstrate that protective outcomes strongly depend on shelter configurations. This study made it apparent that there is considerable complexity in the problem of shelter placement for wildfire evacuations, and this complexity hinders the search for simple rules. In our experiment the most significant improvements to the protective outcomes are delivered by the shelters that are located near highly populated areas in the path of the fire. The location needs to be at a sufficient distance from the fire ignition point, such that the shelter remains an attractive destination for a reasonable period of time. It also should not be too far away from the ignition point, so that choosing the shelter as a destination remains beneficial to the evacuees in terms of traveling distance and time compared with exiting from the threatened area. We also find that adding a destination point in the path of a wildfire has the potential to focus traffic and thereby place people at a higher risk. There are some future works that are meaningful to explore. When considering establishing shelters, the efficacy of the shelters can be statistically evaluated using Monte Carlo simulation. A large number of ignitions that obey a distribution learned from historical data can be simulated efficiently using our simulation system. Such simulation enables statistical evaluation of the efficacy of shelter configurations and mapping of the risk of ignitions for a certain shelter configuration. In addition, this paper focuses on the effect of ignition locations while fixing other factors constant. Similar simulation framework can be used to investigate the effect of other factors such as departure time, route selection, and ignition time. These insights can have significant practical implications on real-life decision making. References [1] R. B. Hammer, V. C. Radeloff, J. S. Fried, S. I. Stewart, Wildland–urban interface housing growth during the 1990s in california, oregon, and washington, International Journal of Wildland Fire 16 (3) (2007) 255–265. [2] A. D. Syphard, J. E. 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