Traffic Performance Indicators for Evacuation: The Case Study of the 2020 Silverado Wildfire
- Open Access
- 03-10-2025
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Abstract
1 Introduction
Millions of people are affected by wildfires across the globe, making it a great challenge that requires extensive preparation. Considering several physical and environmental factors, wildfire threats are becoming more frequent, extensive, and intense [1]. The worldwide expansion of the wildland-urban interface (WUI) poses serious life safety challenges [2]. In this context, effective emergency management, including evacuation strategies, may be used to mitigate the negative consequences of wildfires.
Evacuation planning is a critical and challenging issue as it should encourage timely and effective protective actions by the affected population. Evacuating residents too early or too late not only causes negative economic and social impacts but also wastes resources [3]. The understanding of traffic evacuation dynamics during wildfires can play an important role in designing and evaluating evacuation plans and aiding real-time decision-making. In particular, the definition of dedicated traffic evacuation performance indicators can provide a standardized framework for assessing evacuation efficiency and facilitate communication with stakeholders and in turn possibly improve life safety. A key strength of some of these indicators is their focus on relative performance— comparing traffic conditions during evacuations to those under routine scenarios.
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Evacuation traffic present unique complexities, distinguishing itself from routine traffic in two ways: different driver behavior [4‐6] and changes in traffic demand patterns [7]. On the behavioral side, evacuees often drive more cautiously, resulting in changes in the reduced speed-density relationship and therefore a lower road capacity. At the same time, traffic volumes can spike suddenly and become highly directional, leading to congestion not only due to behavioral effects but also due to surges in total vehicle numbers. These combined effects highlight the need for indicators that capture both shifts in traffic flow parameters and the impact of sudden, directional demand, as addressed in this study.
In addition, traffic evacuation datasets are useful for the development, calibration, and validation of wildfire evacuation models. Multi-layer evacuation simulation models represent different layers (i.e., fire and smoke spread, pedestrian movement, and traffic) of an evacuation condition [8]. In this context, previous work [9‐16] has adopted several approaches such as trigger modelling, or pedestrian/traffic simulation to couple fire spread and community evacuation.
Since current wildfire evacuation model accuracy is affected by the scarcity of real world data, researchers [17] have highlighted the need for more datasets. Previous studies have utilized survey or interview data [18‐25] to study evacuation decisions during wildfires. In most recent work, Ma and Lee [26] used survey data to investigate evacuee responses to varying levels of wildfire evacuation orders, and identified factors that affected evacuation timing. Furthermore, they examined the destinations of evacuees and the use of GPS navigation by evacuees during evacuations. Emerging data sources and big data (e.g., GPS data from mobile phone devices, cellular data) have also been used in wildfire evacuation. Zhao et al. [27] and Cova et al. [28] used GPS data and inferring algorithms to discover residents’ evacuation decisions, departure times, and destinations during the 2019 Kincade fire. Melendez et al. (2021) used cellular data and traffic data from California’s Performance Measurement System (PeMS) to estimate traffic densities in evacuation routes during wildfires. In a recent work by Ahmad et al. [29], connected vehicle (CV) data along with PeMS data was used to estimate travel time during a historical wildfire event in U.S. Hou et al. [30] used three historical datasets from 2010 to 2020 wildfires in California, including PeMS data, wildfire data, and meteorological data to create a traffic performance prediction model using machine learning. Among all these studies, it is apparent that traffic data has a key role in understanding wildfire evacuation behavior.
In wildfire evacuation modelling, macroscopic, mesoscopic or microscopic traffic models can be used [31]. Dixit and Wolshon [6] investigated the importance of traffic data for a Hurricane case study, in which the road capacity was reduced by 16% during evacuation. Rohaert et al. [4] studied traffic dynamic during 2019 Kincade fire. They found that evacuees drive 3.5 km/h slower compared to drivers in routine traffic and that, in turn, the road capacity was reduced by 5% during the fire event. Furthermore, a similar trend has been observed in another study by Rohaert et al. [5] for the 2020 Glass fire in which the speed and capacity were reduced by 1.1% and 1.9%, respectively, during evacuation. These studies focused mostly on investigating these differences using traffic variables such as speed, flow and density.
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While research on wildfire evacuation has progressed in recent years, significant gaps remain in understanding traffic dynamics during such events. The differences between evacuation and routine traffic are not just behavioral but they are also observed in traffic parameters. Evacuations may indeed alter traffic flow parameters, such as reducing free-flow speed, increasing jam density, and lowering road capacity. Such changes have been observed in previous studies [4, 32] and are quantified in our work, strengthening the case for evacuation-specific indicators.
Many studies have focused on estimating evacuation behavior via surveys [18, 20, 25], interviews [33], simulation-based models [14, 34], and recently GPS data [27]. Despite these efforts, most existing work emphasizes traffic performance indicators related to general traffic dynamics rather than evacuation. To address this gap, our study introduces a set of traffic performance indicators specifically designed for wildfire evacuation scenarios. The present work aims to define traffic performance indicators beyond speed, flow, and density, which could facilitate the understanding of the differences between routine and evacuation conditions. By doing so, this work bridges the gap between the estimation of traffic performance and wildfire evacuation dynamics, thereby enhancing evacuation modelling and decision-making strategies.
The objectives of this paper are, therefore: (1) to compile and define a set of traffic performance indicators (including speed-density and flow-density relationships) to understand traffic dynamics in evacuation conditions in comparison with routine conditions and (2) to demonstrate the use of such traffic performance indicators through the case study of the 2020 Silverado wildfire (USA), making it possible to compare our findings with other case studies. To stimulate further uses of the new dataset presented here, this has been made available in open access to any interested party [33].
2 The Proposed Traffic Performance Indicators for Wildfire Evacuation Scenarios
2.1 Speed, Flow, Density Relationships
Three quantities are typically used to describe traffic dynamics in macroscopic models: (1) the average vehicle speed v (km/h), (2) the traffic density k (veh/km/lane), and (3) the traffic flow q (veh/h/lane). Macroscopic traffic models are used to demonstrate the relationships between these quantities. The first one was developed by Greenshields [35]. It was followed by many well-known models, such as the models developed by Underwood [36], Drake et al. [37], Daganzo [38], Van Aerde and Rakha [39, 40], Del Castillo and Benítez [41] and Cheng et al. [42].
Since traffic detection stations measure speed, flow, and density, it is possible to calibrate macroscopic models’ parameters by fitting them to traffic data. This allows for the comparison of the obtained values for routine conditions with those for evacuation conditions. In this study, two well-known traffic macroscopic models, v = f(k) are considered: the model by Daganzo [38] (Eq. 1), and the model by Van Aerde and Rakha [39, 40] (Eq. 2). The reasons for selecting these models are: (1) the data fits best to these models, (2) these models can be derived from behavioral rules (used in microscopic simulations) and the model and parameters have physical interpretations, (3) these relationships are used in wildfire evacuation simulation models [13, 43]. Their superior fit to the data was achieved by minimizing the weighted least-square function (Eq. 3) developed by [44] and previously applied in studies [4, 5, 45, 46]. The model by Van Aerde has more parameters, allowing it more flexibility on fitting data. Also, the model by Daganzo showed good fit in prior study [4]. In addition, both models are multi-regime models that generally provide a better fit to traffic data. These models can then be utilized to compare different conditions (evacuation and routine).
In addition, polynomial regression trendlines based on the routine and evacuation data can be used to further observe overall differences between these conditions.
$$\:v=\left\{\begin{array}{c}{v}_{f},\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:0\le\:k\le\:{k}_{c}\\\:\frac{{q}_{c}}{k}\left(\frac{{k}_{j}-k}{{k}_{j}-{k}_{c}}\right),\:\:\:\:\:\:\:\:\:\:\:\:\:{k}_{c}\le\:k\le\:{k}_{j}\end{array}\right.$$
(1)
$$\:k=\frac{1}{a+\frac{b}{{v}_{f}-v}+c\:v}\:with\:\left\{\begin{array}{c}a=\frac{{v}_{f}\left(2{v}_{c}-{v}_{f}\right)}{{k}_{j}{v}_{c}^{2}}\:\\\:b=\frac{{v}_{f}{\left({v}_{c}-{v}_{f}\right)}^{2}}{{k}_{j}{v}_{c}^{2}}\:\\\:c=\frac{1}{{v}_{c}{k}_{c}}-\frac{{v}_{f}}{{k}_{j}{v}_{c}^{2}}\end{array}\right\}$$
(2)
$$\:{min}S={\sum\:}_{i}^{m}{w}_{i}{\left({v}_{i,observed}-{v}_{i,predicted}\right)}^{2}$$
(3)
Where \(\:{w}_{i}=\left\{\begin{array}{c}{k}_{2}-{k}_{1},\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:i=1\\\:\frac{{k}_{i+1}-{k}_{i-1}}{2},\:\:\:\:\:\:\:\:\:\:\:\:\:i=2,\:3,\:\dots\:,\:m-1\\\:{k}_{m}-{k}_{m-1},\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:i=m\end{array}\right.\).
2.2 Traffic Performance Indicators
While macroscopic traffic models provide valuable insights into the relationships between traffic variables (speed-density and flow-density), traffic performance indicators can be extremely helpful in understanding traffic dynamics during fire evacuation in comparison to routine conditions. This section defines a set of traffic performance indicators that are recommended for use in the evaluation of traffic evacuation during wildfire scenarios. Some of those indicators are well known in traffic analysis for routine conditions, while others are newly defined specifically for evacuation scenarios.
(1) System efficiency (e): This ratio is defined as the productivity or measure of the efficiency of the transportation system for a road segment over time [47‐50]. It is also known as the space mean speed (vehicle-kilometer-weighted speed), e, which is calculated as presented in Eq. 4.
$$\:e=VDT/VHT$$
(4)
Where VDT is Vehicle Distance (e.g., kilometers) Travelled, and VHT is by Vehicle Hours Travelled. In a road segment, VDT represents the total distance driven by all vehicles over a time period, and VHT represents the total time spent by all vehicles over the same segment. Since system efficiency (e) is derived from the ratio of vehicle distance traveled (VDT) to vehicle hours traveled (VHT), it inherently represents the space mean speed, rather than the time mean speed reported by individual loop detectors. This ensures that the traffic performance indicators used in this study are based on SMS, as required for macroscopic traffic modeling. Indicator e can be compared across different time periods to observe how road performance has changed during evacuation (or to compare routine and evacuation). This indicator can be calculated using the selected detectors’ data points considering averages in the whole segments for a specific time period. It is also possible to calculate a system Efficiency Ratio (ER) using the following Equation:
$$\:ER={e}_{evac}/{e}_{ref}$$
(5)
The parameter eevac represents the hourly system efficiency for a specific segment during an evacuation period, while eref represents the hourly system efficiency under reference conditions (e.g., routine conditions) for that segment.
(2) Travel Time Ratio (TTR): This indicator is defined as a ratio considering the equivalent time that the same number of vehicles would take if they would travel at a reference speed (e.g., free flow speed). A free-flow travel time is the time required to travel at a free-flow speed across the road segment distance [47] and a reference travel time indicates the average time needed to cross that road segment when no evacuation takes place in a given reference time interval. In other words, the TTR represents the time required for a trip during evacuation compared with that trip duration in free-flow speed or in reference speed. This indicator can be used to compare the delays in a particular segment during evacuation and routine conditions (see Eq. 6). The closer TTR is to 1, the more similar are the travel times in the evacuation conditions and reference conditions (e.g., routine conditions).
$$\:TTR={t}_{evac}/{t}_{ref}$$
(6)
The parameter tevac represents the actual travel time for a specific segment during an evacuation period, while tref signifies the travel time under reference conditions for that segment. When tref corresponds to travel time in conditions of free-flow speed, a TTR value greater than 1 indicates that the travel time during evacuation exceeds the time taken when vehicles move at free-flow speed. Conversely, a TTR value of smaller than 1 suggests that the travel time during evacuation is less than the travel time under free-flow speed conditions.
Similarly, if tref reflects travel time under reference conditions (such as considering average speed in routine traffic), a TTR value greater than 1 implies that the travel time during evacuation is greater than the reference travel time. On the other hand, a TTR value of smaller than 1 indicates that the travel time during evacuation is less than the travel time under reference conditions.
While both system efficiency (e) and TTR offer valuable insights into traffic conditions during evacuation, they serve distinct purposes and capture different aspects of traffic performance. System efficiency provides a macroscopic, aggregate measure of the overall speed and functionality of the transportation network, reflecting its ability to sustain vehicular movement under varying conditions. However, it does not account for the user experience or the variability in travel times across different segments or time periods. In contrast, TTR directly quantifies the relative increase in travel time experienced by evacuees compared to reference conditions, normalizing delays to provide a clearer understanding of their severity. Importantly, TTR captures travel time variability, which is a critical factor influencing evacuee decision-making and route choice.
(3) Level of Service (LOS); This indicator is calculated using either the volume-to-capacity (\(\:q/{q}_{c}\)) ratio or the density of vehicles on the freeway. PeMS determines the quantity of vehicles encountering a specific density by multiplying the segment’s density by its length. This calculation yields the number of vehicles associated with each Level of Service (LOS). PeMS employs the derived density and vehicle count to generate distributions. Consequently, if the percentage of vehicles for LOS (A) is 10%, it signifies that 10% of the vehicles within the freeway segment are operating at LOS (A) during that particular time [47]. The relationship between LOS (level A to F) and the density of vehicles on a freeway is defined in the Highway Capacity Manual (HCM) [51]. For example, LOS (A) occurs when traffic is light and unimpeded, and LOS (F) occurs when the traffic flow is broken down and the roadway is completely congested. This indicator provides insights into evacuation similar to Fruin’s level of service for pedestrian evacuation [52].
4) Jam time (tj): This indicator is defined as the time that total congestion occurs in a given segment of the road over a given time period. Total congestion occurs when the density of vehicles within a specific segment exceeds the road’s capacity, leading to a slowdown or halt in the movement of vehicles. For example, this can be defined as the density greater than 30 veh/km/lane. It is also possible to calculate Jam time during evacuation conditions and routine conditions to evaluate the difference between them.
Previous studies observed that evacuees have chosen to drive longer vehicles (i.e., boat trailers, caravans, campers) during wildfire and hurricane evacuations to save their property from fire [4, 53, 54]. Detectors in Vehicle Detection Stations (VDS) also measure the occupancy, which is given by the amount of time taken by a vehicle to pass over the detector’s location. At a given speed, longer vehicles occupy the detector for a longer time, and vice versa. As a result, it can be used to understand vehicle types (and eventually compare them in evacuation and routine traffic conditions). Based on the assumption that a vehicle’s length and speed are independent within the time interval, the average vehicle length can be calculated as follows [4]:
$$\:l=vo/q$$
(7)
There are four variables in this equation: l is the average length (m/veh) of all vehicles passing by the detector, v is the average speed (m/s), o is the detector occupancy (-), and q is the flow (veh/s) passing by the detector (all during the 5-minute interval). The following equation can be used to calculate the Vehicle Length Ratio (VLR):
$$\:VLR={l}_{evac}/{l}_{ref}$$
(8)
Where levac is the average vehicle length during evacuation and lref is the average vehicle length under reference conditions.
3 Methods
To demonstrate the benefits of using traffic performance indicators, we applied them to the 2020 Silverado fire in California, US. This fire was chosen as a case study because of its large number of evacuees, vicinity of the fire to the urban area, the availability of traffic data on impacted roads, and the ability to compare it with previous case studies in California. Traffic data were obtained from the PeMS database using the Traffic Dynamics Analyzer [4, 5]. We also used information from the media, news, and related reports to obtain context for this evacuation event. Figure 1 shows the steps performed for the analysis of the case study. After selecting the case study, the information related to the fire was collected and investigated based on existing reliable reports and media releases. Then, traffic data were obtained from a traffic vehicle detector database. The PeMS, used in the current case study, was chosen because of its public availability and reported traffic data. The PeMS website (https://pems.dot.ca.gov/) provides real-time and historical traffic data recorded by VDSs, covering highways and ramps. By accessing the database, traffic dynamics variables such as vehicle speed, road occupancy, and traffic flow can be sourced for each lane at five-minute intervals (or longer intervals). It should be noted that PeMS provides data from a variety of detector types. In this case study, only data from dual-loop detectors has been used, as this is the only type of detector on roadways close to fire that is able to measure vehicle speeds.
Traffic data were obtained after selecting VDSs through a specific process involving a set of inclusion/exclusion criteria. The criteria and related process were based on Rohaert et al. [4, 5] and included detector’s location, speed measurement, detector’s health status, and distance between selected detectors. The variables calculated from the PeMS database for data analysis were speed, occupancy, and traffic flow along with a set of newly defined traffic performance indicators. To extract and analyze the data and create traffic fundamental diagrams during the fire event, the Traffic Dynamic Analyzer (TDA) [5] was used. Ultimately, a traffic analysis was carried out by fitting the well-known macroscopic traffic models to the data such as speed, flow, and density and analyzing traffic performance indicators. This allowed a deeper understanding of traffic evacuation dynamics during the evacuation (also in comparison to routine conditions and previous fires).
Fig. 1
Methodological framework for extracting and analysing traffic data during a wildfire evacuation
3.1 Overview of the Fire Event
A wildfire known as the 2020 Silverado Fire burned in southern Orange County, California northeast of Irvine, in October and November 2020. The fire started at 6:50 am on 26 October 2020. Strong Santa Ana winds up to 130 km/h combined with low humidity fueled the fire. Three structures were destroyed, and nine were damaged. The fire was contained on 7 November 2020, burned approximately 50.5 km2 of land, and nearly 100,000 people were ordered to evacuate.
Orange County Fire Authority and CalFire (California Department of Forestry and Fire Protection) issued mandatory evacuation orders to manage the incident. Since no official evacuation timetable has been made available for this fire, media reports were consulted to reconstruct the warning timeline [55]. Figure 2 illustrates the Silverado fire’s location, perimeter, and evacuation warnings/orders zones during this fire. The first round of mandatory evacuations was ordered affecting approximately 60,000 residents east of Irvine on 26 October (Monday, 9:00 am). The second round of mandatory evacuation was ordered five hours later, just before 2 p.m. and spread to the City of Lake Forest, northern communities in the afternoon.
Fig. 2
Map (obtained by Google maps) with the location of the selected VDSs (detectors, coordinates source from PeMS), the 2020 Silverado wildfire perimeter (red color) and the evacuation zones (yellow color) at the time of fire (Orange County, City of Irvine, and City of Lake Forest). Road closures are presented by dark lines for the SR241, SR133, SR261. Blue markers show northbound detectors, and red markers show Southbound detectors by the authors
3.2 Highways and Routes during Fire Event
Santiago Canyon Road, SR241, SR133, SR261, and Freeways I-5 and I-405 are the major routes in the Cities of Irvine and Lake Forest. VDSs are installed on all routes except Santiago Canyon, and traffic data is recorded in the PeMS. Parts of highways SR133, SR241 and SR261 were closed by the California Highway Patrol as soon as the fire spread on 26 October 2020 [56]. All road closures were lifted by 5:00 am on 2 November 2020. During this event, I-5 remained open, while most of the closures were in the City of Irvine. Therefore, only traffic data from Freeway I-5 was available during the evacuation.
To extract PeMS traffic data, Freeway I-5 was chosen since it is the closest to the evacuated areas, equipped with several detectors, and allowed access across the evacuation zones. Freeway I-5 has 4 to 7 lanes in each direction, including HOV (High Occupancy Vehicle) lanes, depending on the segment location along the freeway. The speed limit of I-5 in urban settings is 65 mi/h (≈ 105 km/h) with 4 to 6 lanes; and in rural settings, the speed limit is 70 mi/h (≈ 113 km/h) with a maximum of 7 lanes.
3.3 Data Selection and Extraction for the Fire Event
The process of detectors’ selection has been visualized for the case study in Fig. 3. There are 704 VDS along Freeway I-5 in Orange County, 201 of which use double loop detectors (and therefore measure vehicle speeds). The selection process (see Fig. 3) resulted in selecting 18 VDSs, 9 for each direction (Northbound and Southbound). However, recognizing that the PeMS health-score system alone may not capture all anomalies, we supplemented this process with extensive manual checking. Specifically, we conducted a detailed visual inspection of time-series data and speed-density relationships for all detectors (per lane). This visual examination allowed us to identify and exclude detectors that exhibited unrealistic patterns, such as fixed values over extended periods (e.g., half a day) or implausible speed-density curves, which were not flagged by the PeMS health-score system. By combining automated health inspection with visual examination, we ensured that only high-quality data were included in our analysis. Among 18 VDS, 11 were 100% healthy and the remaining 7 had health above 89% during the times before and during the fire event. This process has been briefly discussed in the WUI-NITY3 report [57] and further details on this methodology can be found in the WUI-NITY2 report [58].
Regarding the traffic data, first, data was extracted for the nine weeks before the fire (week 35, which started on 24 August and ended on 25 October) to compare changes in traffic flow. Then, the measurement periods (as shown in Table 1) were used for all further analysis. To ensure a fair comparison, we selected routine data from specific weekdays (matching the day of the week of the evacuation) thereby controlling for typical weekday traffic patterns and excluding their influence on the results. The three different time intervals include evacuation time periods for all lanes along with comparable routine time periods. This allowed for fitting the traffic speed-density, and flow-density relationships. Since all evacuation orders were issued on Monday 26 October, it was decided to consider one day (26 October) for the evacuation period (Week 44). We also extracted routine data one week earlier (Week 43), and two weeks earlier (Week 42). The choice of time intervals for the analysis of routine and evacuation traffic was done to ensure a meaningful comparison. Traffic data from the evacuation day and the corresponding weekday two weeks earlier were chosen to represent typical routine traffic conditions. The inclusion of additional data would “dilute” the change in traffic dynamics possibly underestimating the drop in capacity observed during the evacuation.
The data has been extracted, processed and released in open access [59]. The longitude and latitude of each detector were derived from PeMS and overlayed onto a map of the Silverado fire location and evacuation zones (as shown in Fig. 2).
Table 1
Measurement periods of data extraction and average traffic flow
Conditions | Start | End | Week | Average traffic flow (veh/day) |
|---|---|---|---|---|
(October 2020) | ||||
Routine (two weeks before) | the 12th 00:00 | the 12th 23:59 | 42 | 109,669 |
Routine (one week before) | the 19th 00:00 | the 19th 23:59 | 43 | 110,771 |
Evacuation | the 26th 00:00 | the 26th 23:59 | 44 | 104,521 |
4 Analysis of the Traffic Dynamics during the 2020 Silverado Fire
In this section, the data are first presented in terms of the traffic volume, the relationship between speed, flow, and density. Figure 4 shows the traffic flows on Freeway I-5 before and during the fire event. A comparison is made between the traffic flows during the fire event (week 44) and the nine weeks before the fire (week 35, which started on 24 August). The entire period falls within the school season (which began on 18 August). Thus, the school summer breaks were not considered as a factor affecting traffic patterns. Labor Day (Monday 7 September), a national holiday in the United States, is excluded from this calculation due to its significantly lower traffic volume (visible in Fig. 4). Additionally, Table 1 shows the average daily traffic flow over the period of data extraction.
According to Fig. 4, traffic volumes on Monday and Tuesday (26 and 27 of October, i.e., week 44) were lower than the nine weeks before the fire. This pattern is also evident in the average daily traffic flow with a volume decrease of at least 5% during evacuation compared with routine conditions (see Table 1). All evacuation warnings and orders were lifted in Irvine and Lake Forest on Wednesday and Thursday (28 and 29 October). As shown in Fig. 4, traffic flow on I-5 was higher on Wednesday (28 October, week 44) until Friday (30 October, week 44) than the nine-weeks traffic flow (before the fire started). On Saturday and Sunday (31 October and 1 November) at the end of week 44, normal traffic conditions were observed.
Fig. 4
Average traffic flow before, during the 2020 Silverado fire
To find speed-density and flow-density relationships before and during the fire evacuation, the TDA tool was used to extract and fit the models to the data based on the measurement periods in Table 1. In this study, the model by Daganzo and the model by Van Aerde and Rakha were fitted to the data, and second-order polynomial regression lines were employed to present the data trends. The speed-density graphs for the selected models are shown in Fig. 5. The fitted curves were optimized to the weighted sum of squares. The values of the model parameters are presented in Table 2. This table provides the optimal values, confidence margins, and ratios φ, which illustrate the value of each parameter during an evacuation condition, relative to its value during a routine condition. Based on the fitted curves illustrated in these figures for all models, compared with routine conditions, traffic speed is slightly lower during evacuation.
Based on the obtained fitted curves, all three models show a good fit. Considering the weighted root-mean-square error (WRMSE) presented in Table 2, the model by Van Aerde and Rakha demonstrates a better fit since the low value indicates a better fit [4]. Specifically, according to the Van Aerde and Rakha model, there was an average absolute reduction in speed of 7.5 km/h across densities ranging from 0 to 27 veh/km/lane. The corresponding average relative reduction was 8.6%. Notably, the highest absolute reduction occurred at a density of 18.7 veh/km/lane, amounting to 14.2 km/h. Also, the highest relative reduction was observed at a density of 21 veh/km/lane, reaching 16.5%. When comparing the flows (speed*densities), the maximum values for road capacity dropped from 1704 to 1462 veh/h/lane, a decrease of 14.2%.
In Table 2, the fitted macroscopic traffic models show that absolute differences between routine and evacuation conditions exist. Note that the confidence intervals for the routine data parameters are generally narrower than those for the evacuation data. This is expected because the routine dataset (two days) is approximately twice as large as the evacuation dataset (one day), providing greater confidence in the accuracy of the average parameter estimates for routine conditions. However, confidence intervals reflect our certainty in the best estimates, not the variability in the underlying data. Both routine and evacuation scenarios exhibit similar levels of variability in traffic measurements (speed, density, and headway) as individual driving behavior shows a comparable degree of fluctuation in both conditions. This similarity in variability might be less apparent in Fig. 5 due to the red (evacuation) data occluding blue (routine) data.
There is a difference between traffic dynamics and traffic performance metrics changes. While the traffic dynamics (speed, flow, and density) may change during the evacuation caused by behavioral changes in driving, for example, different headways or vehicles, the performance indicators may be affected by the traffic demand, which leads to different speeds during evacuation. With that said, this paper also suggests measuring performance indicators for the case study.
Fig. 5
Speed-density diagrams for the evacuation and routine data and best-fit curves. The evacuation data points (red) correspond to 26 October 2020, the routine data points (blue) correspond to 12 and 19 October 2020
Table 2
Fitted macroscopic traffic models to the 2020 Silverado fire evacuation traffic data (Freeway I-5), related parameters and best fit value
Model | Parameters and WRMSE | Best fit value ± 95% Confidence interval | Best fit value ± 95% Confidence interval | φ (%) | ||
|---|---|---|---|---|---|---|
(Routine) | (Evacuation) | |||||
Daganzo, [39] | WRMSE | 5.94 | 7.58 | |||
vf (km/h) | 109.4 | ± 0.15 | 107.8 | ± 0.31 | 98.5 | |
kc (v/km/l) | 15.2 | ± 0.05 | 12.9 | ± 0.08 | 84.9 | |
Van Aerde and Rakha, [40] | WRMSE | 5.15 | 7.00 | |||
vf (km/h) | 113.6 | ± 0.23 | 111.6 | ± 0.47 | 98.2 | |
a | 6.1E-03 | ± 0.001 | – 1.7E-03 | ± 0.001 | – 27.8 | |
b | 0.22 | ± 0.017 | 0.19 | ± 0.032 | 86.4 | |
c | 4.3E-04 | ± 1.89E-05 | 6.7E-04 | ± 2.88E-05 | 155.8 | |
Second order polynomial regression | WRMSE | 5.31 | 8.00 | |||
a | – 0.09 | ± 1.83E-03 | – 0.04 | ± 3.33E-03 | 44.4 | |
b | 0.42 | ± 5.19E-02 | – 1.31 | ± 1.02E-01 | – 311.9 | |
c | 113.0 | ± 3.09E-01 | 117.7 | ± 6.57E-01 | 104.1 | |
5 Analysis of the Traffic Performance
As explained in the methodology section, different traffic performance indicators including \(\:e\) (efficiency), TTR (Travel Time Ratio), LOS (Level of Service), Jam time and a traffic dynamic indicator \(\:l\) (vehicle length) are proposed for the analysis of the routine and evacuation conditions associated with this fire event. The indicator Jam time is equal to 0 for this road since there was no overall congestion during the time periods and segments. Figures 6 and 7 show the hourly value of indicator \(\:e\) over time for Monday (26 October) in the two time periods of data extraction (evacuation and the routine time period) for the selected detectors. These figures indicate that on Freeway I-5 during the evacuation time period, \(\:e\) decreased by a maximum of 18% for northbound and 19% for southbound, compared with the average of routine conditions (two weeks before the fire). Also on average, \(\:e\) decreased by 5.4% during evacuation compared with the average of two weeks before the fire, and the average ER (Efficiency Ratio) was calculated as 0.944. In addition, Fig. 8 shows the variation of indicator ER in both directions.
Fig. 6
The hourly value of e in different time periods of data extraction on I-5-Northbound
Fig. 7
The hourly value of e in different time periods of data extraction on I-5-Southbound
Fig. 8
The hourly quantity of ER on I-5
The indicator TTR (Travel Time Ratio) was investigated for the selected detectors within the fire-impacted areas considering free flow speed of 70 mi/h (≈ 113 km/h) as the reference. Figures 9 and 10 show hourly quantities of TTR before and during fire evacuation. As shown, TTR increased in both directions with a maximum of 20% on the morning of the fire day (when evacuation orders have been issued) and the day after the fire compared with the two weeks before the fire (i.e., the routine condition). On average, TTR increased by 6.2% during evacuation compared with the average of two weeks before the fire. Results from the indicator TTR confirm the information obtained by the indicator \(\:e\). The average quantities for both indicators are presented in Table 3.
Fig. 9
The hourly value of TTR in different time periods of data extraction on I-5-Northbound
Fig. 10
The hourly value of TTR in different time periods of data extraction on I-5-Southbound
Table 3
Average quantities for performance indicators e and TTR
Performance indicator | Average Quantity | |
|---|---|---|
Evacuation | Routine | |
e (km/h) | 101.9 | 107.7 |
TTR | 1.12 | 1.05 |
Level of Service (LOS) was obtained through the time series report from PeMS for the postmile 84 to 105 segment (see Fig. 11). The graphs show the distribution percentage of vehicles from all detectors on a specified segment of freeway I-5 over a specified time period (evacuation and routine). The distribution illustrates the average percentage of vehicles in the system operating at each LOS, including morning and afternoon peak hours from 6:00 am to 8:00 pm. As shown in these figures, on I-5 Northbound and Southbound, the average percentage of vehicles at both LOS (B) and LOS (C) decreased by 16% in Northbound and 18% in Southbound during evacuation. In contrast, the percentage of vehicles at LOS (D), LOS (E) and LOS (F) increased by 14% in Northbound and 16% in Southbound (including a 9% increase for LOS (E)) during evacuation. Figure 11 also indicates that Freeway I-5 mainly operated at LOS (B), LOS (C), and LOS (D) in routine (94% of vehicles) and evacuation conditions (81%~84% of vehicles) in both directions and only in evacuation conditions, did it operate at the LOS (F); for 5.5% of vehicles in Northbound and 2.5% of vehicles in Southbound.
Fig. 11
Average percentage of vehicles at each LOS for Freeway I-5-Northbound (left) and Southbound (right)
Figure 12 shows the distribution of average vehicle length for evacuation and routine conditions. The histogram and the cumulative probability curve show that the vehicle length patterns across the routine and evacuation conditions overlap in most intervals and the indicator VLR was calculated as 1.003.
Fig. 12
The histogram and the cumulative probability curve for average vehicle length
6 Discussion
In this study, a set of traffic performance indicators were presented to analyze evacuation data in case of wildfires, capturing both changes in driving behavior and traffic demand. This approach was demonstrated through the extraction and analysis of traffic data of Freeway I-5, before and during the 2020 Silverado Fire. However, these relationships do not account for how changes in traffic demand (such as sudden, directional surges) influence system performance. For example, even if individual driving behavior remains unchanged, an increase in demand can lead to longer travel times. To capture these combined effects, we use traffic performance indicators that offer a broader view of evacuation efficiency. These indicators could facilitate the use of evacuation simulation tools. Some of the proposed indicators are relative to the routine traffic and therefore highlight deviations from normal operations, meaning that it is easier for stakeholders to understand the impact of wildfires on traffic dynamics. The indicators can support authorities and emergency planners in recognizing operational challenges and more effectively assess mitigation strategies.
As shown in Fig. 4, the traffic volume was lower during the evacuation (Monday and Tuesday) compared with the average routine traffic conditions. The smaller volumes observed during the evacuation period can be attributed to multiple factors, including the direct impact of evacuation-induced traffic, the influence of driver’s travel behavior (i.e., driving more carefully and using larger headways [32]), , and the reduction in non-essential trips due to public awareness and official alerts. While it is true that some regular travelers may have altered their routes or postponed trips, the overall reduction in system efficiency and the increase in travel time ratio (TTR) confirm that evacuation traffic significantly influenced road performance. This reduction in volume has been observed in recent studies by Rohaert et al. [5] and [4] for the 2019 Kincade fire and the 2020 Glass fire, respectively, where, for both fires, mandatory evacuations were ordered. Shadow evacuation, where people decide to leave the affected areas before mandatory evacuation orders are given, could be a reason for this reduction.
From Wednesday (two days after the fire started) until Friday, there was an increase in traffic volume. Since evacuation orders were mandatory for people who live in the evacuation zones, and previous studies showed high evacuation compliance rates in California [18, 21], this unusual traffic volume increase compared with the average nine weeks before can likely be attributed to the lifting of evacuation orders (on Wednesday, 28 October) and people returning to their homes. It could also be related to nearby road closures during these periods. As a result of these road closures, traffic volume could have temporarily increased on route I-5.
The mean speed calculated using the TDA data based on the speed-density relationship shows an average reduction of 7.5 km/h during evacuation compared with the routine condition. This reduction is larger than the findings from Rohaert et al. [4], and [5] for the 2019 Kincade fire and the 2020 Glass fire (in which traffic data was analyzed for Highway US101). The same findings were observed for the road capacity. During the 2020 Silverado fire, the capacity of freeway I-5 was reduced by 14.2% during evacuation compared with routine condition, showing a larger reduction than previous studies. The difference identified between the 2020 Silverado Fire and previous works for the Kincade and Glass Fires likely relates to the locations of the fire, evacuation zones, and the capacity of evacuation routes. While the evacuation zones surrounded both sides of the US101 during the Kincade Fire, in the 2020 Silverado Fire, the Freeway I-5 was located nearby the affected areas. Thus, the impact of evacuation on traffic performance was reduced, as the share of evacuation traffic was lower during the Silverado Fire considering the additional lanes on I-5 and higher levels of background traffic along this route.
The analysis of indicator e (system efficiency) shows that during the time of evacuation on 26 October, compared with the routine condition, e reduced by a maximum of 18% in the northbound direction (at 10:00 am and 3:00 pm, reduced by 17.2 km/hr) and 19% Southbound (at 9:00 am, reduced by 19.3 km/hr). This is reasonable since the first and second evacuation orders were issued around 9:00 am and 2:00 pm on 26 October. A similar pattern was also observed for the indicator TTR, showing a maximum increase of 20% during the hours of evacuation compared with routine conditions. These indicators show that the evacuation orders caused more congestion.
The analysis for indicator LOS reveals that at the LOS (D), LOS (E) and LOS (F), the percentage of the vehicles increased by 14% in the Northbound direction and 16% Southbound during evacuation compared with routine conditions. This is aligned with the results from the other indicators (e and TTR), showing more congestion during evacuation. Vehicle length is the other indicator considered in this study, but no difference was observed in the frequency of larger vehicles during evacuation when compared with routine conditions.
Freeway I-5 is a high-capacity route that rarely experienced the high-density traffic that was observed in other fires (e.g., during the 2019 Kincade fire in US101) as 99.9% of densities in the I-5 were less than 30 veh/km/lane. Nevertheless, the fire evacuation still impacted on the traffic performance since the evacuation zones were close to this freeway. This is also consistent with the recent findings by Hou et al. [30] who reported that when the fire distance increases from evacuation routes, the impact on traffic performance decreases and vice versa.
The findings from this study confirm the results from previous case studies in California [4, 5] that the traffic performance is different during wildfire evacuations than routine conditions, indicating a clear need to not assume that traffic parameters in models developed for routine conditions can be directly applicable to wildfire evacuation. Therefore, conservative assumptions should be made when employing models from routine traffic.
While the traffic performance indicators in this study are specifically introduced for wildfire evacuation, additional performance measures have been identified as potentially useful, either as supplemental measures or for screening purposes depending on the type of study [60]. Further, performance indicators, such as system efficiency, travel time ratio and LOS, provide a deeper understanding of evacuation traffic during wildfires since they can address the needs and objectives of this study and provide comprehensive insights into evacuation traffic.
While our findings provide important insight into traffic behavior during wildfire evacuations, they can also be used to improve evacuation planning and management. Traffic performance indicators enhance the ability to assess evacuation effectiveness and support evidence-based strategies for emergency traffic management and planning. The results from these indicators confirm that wildfire evacuations lead to measurable reductions in traffic performance, indicating the need for evacuation simulation and planning that consider real-world traffic dynamics rather than relying solely on assumptions from routine conditions. These findings can assist emergency planners in optimizing evacuation routes, adjusting traffic control measures (such as ramp-metering), manual traffic management and developing dynamic and staged evacuation plans to decrease delays and improve road network performance during wildfires. Moreover, this study provides a newly developed dataset related to traffic evacuation dynamics, which offers valuable empirical evidence for understanding traffic conditions during wildfire evacuations. The availability of real-world traffic data is essential for validating evacuation models, improving traffic forecasting under emergency scenarios, and supporting the calibration of simulation tools. By making this dataset accessible in open access, future research can focus on refining and improving evacuation modeling approaches, enhancing evacuation planning, and developing more resilient evacuation strategies.
Future studies should investigate traffic evacuation dynamics in arterial roads since most studies so far (including the present one) refer to data from highways and freeways. Other complementary datasets and data sources, if sufficiently representative of all vehicles on the road, such as GPS data [61], connected vehicle data [29], and evacuation drills [62] may be used for this purpose.
This study has some limitations and areas for improvement that should be addressed in future research. First, the traffic dynamics and performance indicators analysis were based on the data from Freeway I-5; the only route for which data regarding the fire under consideration was available in the PeMS database. Therefore, our analysis is limited to the closest monitored roadway to the evacuation zones. This limitation prevents us from explicitly distinguishing evacuation traffic from other behavioral changes, such as rerouting or reduced travel demand. As a result, our study refers to “evacuation conditions” as the overall traffic state observed on Freeway I-5 during the fire event, recognizing that these conditions may result from a combination of evacuation-induced travel demand, background traffic fluctuations, and avoidance behaviors of drivers. Future studies should explicitly account for changes in route choice and travel demand to enhance the comprehensiveness of evacuation traffic analysis.
Second, while PeMS provides high-resolution traffic data, it is generally limited to freeway and highway segments and does not capture evacuation dynamics on smaller arterial roads or local streets, which may also experience significant traffic congestion during evacuations. This restriction means that the dataset primarily reflects freeway conditions rather than a complete representation of evacuation traffic across the entire road network. Moreover, PeMS data aggregates vehicle counts and speeds at fixed locations, which may introduce spatial sampling biases, particularly in areas with widely spaced detectors. The combination of PeMS data with alternative data sources, such as GPS-based vehicle trajectories, connected vehicle data, or crowdsourced mobility data (e.g., mobile phone location data) can address these biases in future studies and provide a more comprehensive analysis of evacuation traffic and improve the accuracy of evacuation traffic modeling.
7 Conclusions
This paper presents an approach relying on the study of speed-density and flow-density relationships along with traffic performance indicators for the analysis of traffic data during wildfire evacuations. This approach is deemed useful to compare routine traffic and evacuation conditions. It is designed to help interpret traffic evacuation dynamics and in turn facilitate communication with stakeholders interested in understanding the wildfire evacuation process. The approach was demonstrated through a case study of the 2020 Silverado fire. Results show the differences in routine and evacuation traffic performance, thus highlighting the need for dedicated calibration and validation efforts of traffic models for evacuation applications.
Acknowledgements
This work has been funded under award 60NANB21D118 from the National Institute of Standards and Technology (NIST), U.S. Department of Commerce. This work was also supported by National Research Council Canada (Contract #: 975228, Resilience and Adaptation to Climatic Extreme Wildfires [RACE wildfires]) and an ARC Future Fellowship by the Australian Government through the Australian Research Council (Grant No. FT220100618). The authors would like to thank the WUI-NITY team (Jonathan Wahlqvist, Guillermo Rein, Harry Mitchell, Nikolaos Kalogeropoulos, Steve Gwynne, Hui Xie, Peter Thompson, Max Kinateder, Hamed Mozaffari Maaref, Maxine Berthiaume, and Amanda Kimball). We also acknowledge the technical panel of the project for their support and guidance: Carole Adam, Amy Christianson, Tom Cova, Lauren Folk, Abishek Gaur, Paolo Intini, Justice Jones, Bryan Klein, Chris Lautenberger, Ruggiero Lovreglio, Jerry McAdams, Ruddy Mell, Elise Miller-Hooks, Cathy Stephens, Steve Taylor, Sandra Vaiciulyte, Xilei Zhao, Rita Fahy, Lucian Deaton, and Michele Steinberg.
Declarations
Competing Interests
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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