![The concept of the Margin of Safety adapted from Beighley [5]. T1 represents the time required for the fire to reach a safety zone and T2 is the time required for firefighter(s) (FF) to reach the same safety zone. In order to create a Margin of Safety T1 should exceed T2.](https://www.researchgate.net/profile/Michael-Campbell-72/publication/334303881/figure/fig1/AS:778372711997444@1562589924895/The-concept-of-the-Margin-of-Safety-adapted-from-Beighley-5-T1-represents-the-time_Q320.jpg)
![Relative energetic cost of pedestrian movement through various land cover types, adapted from [15,16].](https://www.researchgate.net/profile/Michael-Campbell-72/publication/334303881/figure/tbl1/AS:778372720390147@1562589926962/Relative-energetic-cost-of-pedestrian-movement-through-various-land-cover-types-adapted_Q320.jpg)
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fire
Article
Escape Route Index: A Spatially-Explicit Measure of
Wildland Firefighter Egress Capacity
Michael J. Campbell 1, * , Wesley G. Page 2, Philip E. Dennison 3and Bret W. Butler 2
1Department of Geosciences, Fort Lewis College, Durango, CO 81301, USA
2Rocky Mountain Research Station, USDA Forest Service, Missoula, MT 59808, USA
3Department of Geography, University of Utah, Salt Lake City, UT 84112, USA
*Correspondence: mcampbell@fortlewis.edu; Tel.: +1-970-247-6565
Received: 20 June 2019; Accepted: 5 July 2019; Published: 8 July 2019
Abstract:
For wildland firefighters, the ability to efficiently evacuate the fireline is limited by terrain,
vegetation, and fire conditions. The impacts of terrain and vegetation on evacuation time to a safety
zone may not be apparent when considering potential control locations either at the time of a wildfire
or during pre-suppression planning. To address the need for a spatially-explicit measure of egress
capacity, this paper introduces the Escape Route Index (ERI). Ranging from 0 to 1, ERI is a normalized
ratio of the distance traveled within a time frame, accounting for impedance by slope and vegetation,
to the optimal distance traveled in the absence of these impediments. An ERI approaching 1 indicates
that terrain and vegetation conditions should have little impact on firefighter mobility while an ERI
approaching 0 is representative of limited cross-country travel mobility. The directional nature of
evacuation allows for the computation of four ERI metrics: (1) ERI
mean
(average ERI in all travel
directions); (2) ERI
min
(ERI in direction of lowest egress); (3) ERI
max
(ERI in direction of highest
egress); and (4) ERI
azimuth
(azimuth of ERI
max
direction). We demonstrate the implementation of ERI
for three different evacuation time frames (10, 20, and 30 min) on the Angeles National Forest in
California, USA. A previously published, crowd-sourced relationship between slope and travel rate
was used to account for terrain, while vegetation was accounted for by using land cover to adjust
travel rates based on factors from the Wildland Fire Decision Support System (WFDSS). Land cover
was found to have a stronger impact on ERI values than slope. We also modeled ERI values for
several recent wildland firefighter entrapments to assess the degree to which landscape conditions
may have contributed to these events, finding that ERI values were generally low from the crews’
evacuation starting points. We conclude that mapping ERI prior to engaging a fire could help inform
overall firefighter risk for a given location and aid in identifying locations with greater egress capacity
in which to focus wildland fire suppression, thus potentially reducing risk of entrapment. Continued
improvements in accuracy of vegetation density mapping and increased availability of light detection
and ranging (lidar) will greatly benefit future implementations of ERI.
Keywords:
firefighter safety; escape routes; evacuation; egress; travel rates; wildland fire decision
support system; LANDFIRE; GIS; least-cost path modeling
1. Introduction
Escape routes are some of the most important safety measures available to wildland firefighters,
acting as pre-defined pathways for firefighters to access a safety zone or other low-risk area from their
current position [
1
]. They are an integral component of the Lookouts, Communications, Escape routes,
and Safety zones (LCES) safety protocol and are imbedded throughout the 10 Standard Firefighting
Orders and the 18 Situations that Shout Watch Out [
2
,
3
]. The Incident Response Pocket Guide,
which is used by all US wildland firefighters, describes some ideal characteristics of escape routes,
Fire 2019,2, 40; doi:10.3390/fire2030040 www.mdpi.com/journal/fire
Fire 2019,2, 40 2 of 19
including having more than one, avoiding steep uphill routes, and timing them considering the slowest
crewmember given current levels of fatigue [
4
]. In order to be maximally-effective, escape routes
should provide fire crews with a positive Margin of Safety (MOS) [
5
]. MOS is defined as the difference
between the time it takes a fire to reach a given location, such as a safety zone (T1) and the time it takes
a fire crew to reach that same location (T2) (Figure 1). If T1 is greater than T2 (positive MOS), the crew
should reach the safety zone without harm; however, if T2 is greater than T1 (negative MOS), the crew
is at risk of becoming entrapped and suffering a burnover.
Fire 2019, 2, x FOR PEER REVIEW 2 of 20
routes, including having more than one, avoiding steep uphill routes, and timing them considering
the slowest crewmember given current levels of fatigue [4]. In order to be maximally-effective, escape
routes should provide fire crews with a positive Margin of Safety (MOS) [5]. MOS is defined as the
difference between the time it takes a fire to reach a given location, such as a safety zone (T1) and the
time it takes a fire crew to reach that same location (T2) (Figure 1). If T1 is greater than T2 (positive
MOS), the crew should reach the safety zone without ha rm; ho wever, i f T2 is gr eater th an T1 (ne gativ e
MOS), the crew is at risk of becoming entrapped and suffering a burnover.
Figure 1. The concept of the Margin of Safety adapted from Beighley [5]. T1 represents the time
required for the fire to reach a safety zone and T2 is the time required for firefighter(s) (FF) to reach
the same safety zone. In order to create a Margin of Safety T1 should exceed T2.
Both T1 and T2 are difficult to predict accurately in the field. T1 is controlled by fire behavior,
the drivers of which are fuel, weather, and topography [6]. Due to both the complexity of modeling
fire behavior and the importance of being able to understand how fire moves through and affects a
landscape, there is an extensive body of literature and several operational products aimed at
predicting fire behavior (for a review of fire behavior modeling systems, please refer to [7]).
Considerably less attention has been devoted to predicting T2, which is controlled by a combination
of internal factors (e.g., height, weight, fitness and endurance levels, and load carriage) and external
factors (e.g., landscape and environmental conditions). Internal factors are highly variable within a
population, but if a fire crew moves as a unit, then they are only as fast as the slowest individual in
the group. This makes modeling population-level differences as a function of external factors more
important than modeling individual differences. An additional benefit to focusing on external factors
is that most external factors can be mapped on a broad spatial scale using a combination of remote
sensing and geographic information systems (GIS).
The most important external factors that affect one’s ability to efficiently move through a given
landscape include terrain slope, ground surface condition (e.g., roughness, firmness, and stability),
Figure 1.
The concept of the Margin of Safety adapted from Beighley [
5
]. T1 represents the time
required for the fire to reach a safety zone and T2 is the time required for firefighter(s) (FF) to reach the
same safety zone. In order to create a Margin of Safety T1 should exceed T2.
Both T1 and T2 are difficult to predict accurately in the field. T1 is controlled by fire behavior,
the drivers of which are fuel, weather, and topography [
6
]. Due to both the complexity of modeling
fire behavior and the importance of being able to understand how fire moves through and affects a
landscape, there is an extensive body of literature and several operational products aimed at predicting
fire behavior (for a review of fire behavior modeling systems, please refer to [
7
]). Considerably
less attention has been devoted to predicting T2, which is controlled by a combination of internal
factors (e.g., height, weight, fitness and endurance levels, and load carriage) and external factors
(e.g., landscape and environmental conditions). Internal factors are highly variable within a population,
but if a fire crew moves as a unit, then they are only as fast as the slowest individual in the group.
This makes modeling population-level differences as a function of external factors more important
than modeling individual differences. An additional benefit to focusing on external factors is that most
Fire 2019,2, 40 3 of 19
external factors can be mapped on a broad spatial scale using a combination of remote sensing and
geographic information systems (GIS).
The most important external factors that affect one’s ability to efficiently move through a given
landscape include terrain slope, ground surface condition (e.g., roughness, firmness, and stability), and
the presence, abundance, and arrangement of vegetation [
8
]. The effects of slope on travel rates have
been studied since the nineteenth century, and several models for predicting travel rates based on slope
have been developed, including the widely-used Naismith’s Rule and Tobler’s Hiking Function [
9
,
10
].
Though widely-cited, these travel rate functions lack the scientific rigor inherent to large sample
sizes, GPS-driven instantaneous travel rates, and modern statistical modeling techniques. A recent
study by Campbell et al. [
11
] overcame previous limitations, producing an improved slope-travel
rate predictive model based on a very large database of GPS tracks harvested from the widely-used
mobile fitness tracking application Strava, and light detection and ranging (lidar)-derived terrain slope
data. At present, their resulting model represents the most accurate understanding of the relationship
between slope and travel rates, and as such, will be used as the basis of simulating slope impedance in
this study. Given the fact that digital elevation models (DEM) are available on a nationwide basis in
the US as a part of the United States Geological Survey (USGS) 3D Elevation Program (3DEP) [
12
],
a slope-based, spatially-explicit model for predicting optimal, or “least-cost” escape routes could be
realized (e.g., [
8
,
13
]). However, to more accurately simulate movement in a wildland environment, the
effects of land cover on travel rates also need to be taken into account.
The effects of ground surface condition and vegetation are both less well-understood and more
difficult to map. In a review of the energetic costs associated with traversing a diversity of landscape
conditions, Richmond et al. [
14
] identify four parameters that affect the efficiency of pedestrian
movement in a wildland environment: (1) sinkage (how deep a foot will sink into the ground surface);
(2) slipperiness (the relative friction of the ground surface); (3) roughness (the microtopography that
controls foot placement on the ground surface); and (4) vegetation (the presence, abundance, and
arrangement of physical impediments on top of the ground surface). The first three parameters can
be categorized broadly as ground surface conditions, controlled primarily by a combination of soil
type (e.g., clay vs. sand), soil condition (e.g., dry vs. wet), underlying geology (e.g., sedimentary vs.
igneous), history of geomorphological activity (e.g., erosion vs. deposition), history of human activity
(e.g., paved vs. natural) and presence and depth of snow or ice on the ground surface. The fourth
parameter—vegetation—impedes movement in a variety of ways, including obstacle avoidance
(avoiding dense patches of vegetation altogether, thus increasing travel distance and decreasing net
travel rate), obstacle navigation (stepping over debris, crouching under branches, squeezing through
gaps), friction (woody and/or foliar biomass resisting forward movement), and bushwhacking (physical
alteration of the desired path requiring additional time and energy). Much of the research aimed
at understanding how these different landscape conditions affect pedestrian movement stems from
the field of applied physiology, where human experimentation dating back to the 1970s has yielded
estimates for the energetic costs associated with traversing diverse landscape conditions. However, due
to the complex and interacting nature of the effects of these four parameters, rather than quantifying
the effects individually, they are typically described in terms of broadly-defined “terrain coefficients”,
which represent the relative energetic costs associated with traversing a variety of general land cover
types, as seen in Table 1[15,16].
Campbell et al. [
8
] used airborne lidar remote sensing to derive continuous measures of slope,
vegetation density, and ground surface roughness as the basis of travel impedance analysis. Absent
direct quantification of ground surface condition and vegetation, land cover or fuel type can serve as
a proxy, assuming that land cover classes or fuel types represent typical or average vegetation and
ground surface conditions within each class. Alexander et al. [
17
] tested the combined effects of load
carriage, terrain slope, and fuel type on wildland firefighter travel rates. They did not present specific
multiplicative factors, such as those in Table 1and travel rates were measured, rather than metabolic
costs. The results show that open fuel types, such as grasslands and logging slash tend to promote
Fire 2019,2, 40 4 of 19
the fastest travel, whereas lodgepole pine stands with an open understory increase travel time by
a factor of about 1.3, and dense spruce and fir forests increased travel time by a factor of about 1.8.
The Wildland Fire Decision Support System (WFDSS) uses land cover factors to adjust travel rates for
its Ground Medevac Time dataset (Table 2). This is a US nationwide GIS dataset representing transport
time to the nearest hospital [18].
Table 1.
Relative energetic cost of pedestrian movement through various land cover types, adapted
from [15,16].
Land Cover Relative Energy Cost
Blacktop surface 1.0
Dirt road 1.1
Light brush 1.2
Hard-packed snow 1.3
Heavy brush 1.5
Swampy bog 1.8
Loose sand 2.1
Soft snow (15 cm) 2.5
Soft snow (25 cm) 3.3
Soft snow (35 cm) 4.1
Table 2.
Wildland Fire Decision Support System (WFDSS) travel rates based on slope and land cover,
in miles per hour.
Land Cover
Slope Grass/Non-Burnable Brush Timber Water
Flat (≤10◦) 3.00 1.50 0.75 0.01
Moderate (10
◦
–30
◦
)
1.50 0.75 0.25 —
Steep (≥30◦) 1.00 0.50 0.10 —
By combining the slope-travel rate function defined by Campbell et al. [
11
], and the land
cover-travel rate effects defined by WFDSS [
18
], spatially-explicit escape route mapping could become
a reality. However, as the National Wildfire Coordinating Group (NWCG) points out, escape routes
are “probably the most elusive component of LCES” [
19
], as their effectiveness changes continuously
throughout a day. Thus, to be useful for wildland firefighters, escape route mapping has to be done in
real-time or near-real-time, which requires three things: (1) the location of the crew; (2) the location
of the designated safety zone; and (3) the extent and predicted spread of the fire. In the absence
of a widely-adopted, GPS-driven, mobile platform to implement such a real-time mapping effort,
operational escape route mapping may not be currently feasible. However, even without knowing (1),
(2), or (3) described above, one can still use pre-mapped terrain and land cover information to help
wildland firefighters determine what areas have generally better or worse egress capacity.
The goal of this paper is to introduce the Escape Route Index (ERI), which is a spatially-explicit
measure of relative egress capacity based on the effects of terrain slope and land cover on pedestrian
travel rates. ERI is a suite of four spatial metrics aimed at capturing the directionally-specific effects of
the landscape on travel rates: (1) ERI
mean
(average ERI in all travel directions from a given starting
location); (2) ERI
min
(ERI in the direction of lowest/worst egress); (3) ERI
max
(ERI in the direction of
highest/best egress); and (4) ERI
azimuth
(azimuth of the direction of highest/best egress). When mapped
in advance of a wildland fire, the ERI can help wildland firefighters identify potential control locations
in areas with favorable conditions for evacuation. We first describe the conceptual basis of ERI, followed
by a detailed description of how it is implemented in a geospatial environment. To demonstrate
utility on a broad spatial scale, ERI is mapped throughout the entire Angeles National Forest (ANF) in
southern California. Lastly, ERI is used to look back in time at previous wildland firefighter entrapment
events to assess how slope and land cover may have contributed to the events.
Fire 2019,2, 40 5 of 19
2. Materials and Methods
2.1. Definition
ERI is a relative measure of egress capacity based on existing terrain and land cover conditions.
It is measured as a ratio between the actual distance one can travel within a given time frame, and
the optimal distance one can travel within that same time frame. Optimal distance is defined as the
distance traveled from a given starting point in the absence of any landscape impediments. Actual
distance is defined as the distance one can travel from a given starting point, as modeled in a geospatial
environment, factoring in the decrease in travel rate caused by slope and land cover. Accordingly, ERI
ranges from 0 to 1, where 0 indicates extremely poor egress, such that landscape conditions prevent
any kind of movement from a given location, and 1 represents ideal egress. An ERI value of 0.5 would
indicate that, under a given set of landscape impediments, one can travel 50% of the distance that
could be covered in the absence of those impediments. Alternatively, it can be conceptualized in terms
of a travel rate, such that an ERI of 0.5 means one could only evacuate a given location at 50% of the
travel rate under optimal conditions.
To calculate ERI, you first need to establish the relative travel cost (a.k.a. impedance, resistance,
friction), or inversely, the conductance associated with the landscape conditions of interest. A high
travel cost (low travel conductance) means that one would move more slowly, whereas a low travel
cost (high travel conductance) means that one would move more quickly. The choice of whether
to use cost or conductance when simulating movement depends on the geospatial software being
used. In this study, ERI is modeled entirely in R [
20
] using the gdistance library [
21
], which relies on
conductance values, so the methods will be discussed under the conductance framework henceforth.
Travel conductance can be an absolute measure, such as the rate of travel (in m s
−1
) through a given
environment. For example, on flat ground one may travel at 1 m s
−1
, whereas on a steep slope one
may travel at 0.5 m s
−1
. Travel conductance can also be a relative measure, such as a multiplicative
factor that modifies an absolute measure of conductance. For example, one may travel at 0.5x the travel
rate through dense vegetation as compared to sparse vegetation. In this study, the absolute travel
conductance values associated with terrain slope are derived from Campbell et al.’s [
11
] slope-travel
rate function recommended for simulating an average hiking pace (Lorentz 5
th
percentile), as follows:
v=c
1
πb1+θ−a
b2
+d+eθ, (1)
where vis the absolute conductance measured as velocity in m s
−1
,
θ
is slope in degrees, and a,b,c,d,
and eare constants with the values
−
1.53, 14.04, 36.81, 0.32, and
−
0.0027, respectively. The relative
travel conductance values associated with land cover are derived from WFDSS, with values taken from
Table 2converted into relative, per-slope-class multiplicative factors, rather than absolute travel rates.
Those factors can be seen in Table 3.
Table 3.
Adaptation of the WFDSS estimated travel rates, where absolute travel rates are converted to
per-slope-class travel rate conductance relative to traversing grass/non-burnable land cover.
Land Cover
Slope Grass/Non-Burnable Brush Timber Water
Flat (≤10◦) 1.000 0.500 0.250 0.003
Moderate (10
◦
–30
◦
)
1.000 0.500 0.167 —
Steep (≥30◦) 1.000 0.500 0.100 —
When combined, the slope and land cover conductance values can be seen in Figure 2. For the
purpose of this study, to avoid extrapolation of the Campbell et al. [
11
] travel rate function and to
Fire 2019,2, 40 6 of 19
avoid modeling travel up or down very steep slopes, travel was restricted to directionally-specific
slopes within
±
30
◦
. The operative term here is “directionally-specific”, because although it is extremely
inefficient to travel directly up and down slopes of greater than 30
◦
, such slopes are not entirely
impassable, as one can travel up or down said slopes at an angle, such as in a switchback fashion.
However, above a certain slope threshold, travel is entirely impassable (e.g., you can’t switchback up a
cliff). For the purpose of this study, that completely impassable threshold was set to ±45◦.
Fire 2019, 2, x FOR PEER REVIEW 6 of 20
Figure 2. The effects of terrain slope on pedestrian travel rates by WFDSS land cover class.
2.2. Calculation
To implement the ERI model spatially, we selected ANF in southern California as a test study area
(Figure 3). ANF was chosen for three reasons: (1) to demonstrate model implementation on a practical
spatial scale; (2) it features a high diversity of both terrain and land cover conditions; and (3) it is a very
fire-prone area, with a history of wildland firefighter entrapments [22]. The model requires three spatial
datasets as inputs: (1) a DEM; (2) a Landscape Fire and Resource Management Planning Tools
(LANDFIRE) Existing Vegetation Type (EVT) dataset, both in raster format and at 30 m spatial
resolution for consistency; and (3) a roads and trails dataset, in vector format. The DEM and LANDFIRE
data were acquired within the extent of ANF, re-projected into the same coordinate system (NAD 1983
UTM Zone 11N), and co-registered spatially so that cells aligned perfectly within the same grid. At the
time of writing, 2014 was the most recent year that LANDFIRE data were available for ANF.
LANDFIRE data were reclassified into the WFDSS land cover classes based primarily on the National
Vegetation Classification Standard (NVCS) order attribute, as shown in Table 4.
Because LANDFIRE data are generated at a spatial resolution of 30m, only roads that are roughly
at least 30m wide are captured in the dataset. Thus, many smaller roads and trails are not represented.
However, given their relative low slope, ground surface stability, and lack of vegetation impedance,
roads and trails tend to promote maximally efficient travel, where available [8,10,16,17]. Accordingly,
roads and trails data were acquired from two sources: (1) FSTopo, which is the USDA Forest Service’s
primary base map series and contains detailed roads and trails data throughout Forest Service lands
in the US; and (2) The USGS National Map, which contains roads and trails data throughout the entire
US. These roads and trails were converted to raster format with the same resolution as, and co-
registered to, the elevation and land cover data. Roads and trails were merged with the land cover,
and classified as “Grass/Non-Burnable”, representing the class of highest travel conductance.
Calculation of ERI requires that a time frame be chosen to facilitate actual vs. optimal travel
distance calculation from a given starting point. For the purpose of this study, to compare the effects of
different time frames on the resulting ERI values, three times were chosen: 10 minutes, 20 minutes, and
30 minutes. These times were chosen to reflect reasonable travel times from the fireline to a safety zone,
according to historical, well-documented wildland firefighter entrapments [23], while balancing the
computational cost associated with processing longer travel times. Thus, the ERI10 indicates, for
example, how far or fast one can travel in 10 minutes from a starting point with existing landscape
Figure 2. The effects of terrain slope on pedestrian travel rates by WFDSS land cover class.
2.2. Calculation
To implement the ERI model spatially, we selected ANF in southern California as a test study
area (Figure 3). ANF was chosen for three reasons: (1) to demonstrate model implementation on a
practical spatial scale; (2) it features a high diversity of both terrain and land cover conditions; and
(3) it is a very fire-prone area, with a history of wildland firefighter entrapments [
22
]. The model
requires three spatial datasets as inputs: (1) a DEM; (2) a Landscape Fire and Resource Management
Planning Tools (LANDFIRE) Existing Vegetation Type (EVT) dataset, both in raster format and at 30 m
spatial resolution for consistency; and (3) a roads and trails dataset, in vector format. The DEM and
LANDFIRE data were acquired within the extent of ANF, re-projected into the same coordinate system
(NAD 1983 UTM Zone 11N), and co-registered spatially so that cells aligned perfectly within the same
grid. At the time of writing, 2014 was the most recent year that LANDFIRE data were available for
ANF. LANDFIRE data were reclassified into the WFDSS land cover classes based primarily on the
National Vegetation Classification Standard (NVCS) order attribute, as shown in Table 4.
Because LANDFIRE data are generated at a spatial resolution of 30 m, only roads that are roughly
at least 30 m wide are captured in the dataset. Thus, many smaller roads and trails are not represented.
However, given their relative low slope, ground surface stability, and lack of vegetation impedance,
roads and trails tend to promote maximally efficient travel, where available [
8
,
10
,
16
,
17
]. Accordingly,
roads and trails data were acquired from two sources: (1) FSTopo, which is the USDA Forest Service’s
primary base map series and contains detailed roads and trails data throughout Forest Service lands in
the US; and (2) The USGS National Map, which contains roads and trails data throughout the entire US.
These roads and trails were converted to raster format with the same resolution as, and co-registered
to, the elevation and land cover data. Roads and trails were merged with the land cover, and classified
as “Grass/Non-Burnable”, representing the class of highest travel conductance.
Fire 2019,2, 40 7 of 19
Fire 2019, 2, x FOR PEER REVIEW 7 of 20
impediments relative to how far or fast one could travel within that same time frame in the absence of
any impediments.
Figure 3. Study area map showing WFDSS land cover classes derived from the 30m LANDFIRE
Existing Vegetation Type (EVT) dataset.
Table 4. Lookup table for converting LANDFIRE EVT National Vegetation Classification Standard
(NVCS) orders to WFDSS land cover types.
EVT NVCS Order WFDSS Land Cover
Herbaceous/Nonvascular-Dominated Grass/Non-Burnable
No Dominant Lifeform Grass/Non-Burnable
Non-Vegetated (not EVT “Open Water”) Grass/Non-Burnable
Non-Vegetated (EVT “Open Water”) Water
Shrub-Dominated Brush
Tree-Dominated Timber
ERI modeling was performed on a cell-by-cell basis throughout ANF as follows (Figure 4). It is
worth noting that while Figure 4 depicts the process for modeling ERI for a single starting location
(Figure 4a) within ANF at a single time frame (30 minutes), this same procedure was performed on
every raster cell within the study area for each of the three time frames. The two input variables, a DEM
and the reclassified LANDFIRE EVT dataset with the roads and trails modification, can be seen in
Figure 4b. From the starting point, total travel time on a cell-by-cell basis was calculated using Dijkstra’s
algorithm [24], as implemented in the accCost function within the gdistance library [21] in R (Figure 4c).
A travel time threshold was then applied to the accumulative cost raster for the time frame of interest
(in the example figure, 30 minutes) and converted to a vector polygon (Figure 4d). This polygon
represents the actual travel distance one can traverse from the starting point. However, as can clearly
be seen, not all travel directions provide the same egress capacity. Thus, to calculate directionally-
specific travel distances, 100 evenly-spaced points were generated along the polygon boundary and
distances were calculated from the starting point to those edge points (Figure 4d). Optimal travel
conductance conditions were calculated based on the fastest combination of slope and land cover
conditions seen in Figure 2. The land cover of highest conductance was grass/non-burnable, and the
slope of highest conductance was -1.85°, which was determined by performing an optimization of
Figure 3.
Study area map showing WFDSS land cover classes derived from the 30m LANDFIRE
Existing Vegetation Type (EVT) dataset.
Table 4.
Lookup table for converting LANDFIRE EVT National Vegetation Classification Standard
(NVCS) orders to WFDSS land cover types.
EVT NVCS Order WFDSS Land Cover
Herbaceous/Nonvascular-Dominated Grass/Non-Burnable
No Dominant Lifeform Grass/Non-Burnable
Non-Vegetated (not EVT “Open Water”) Grass/Non-Burnable
Non-Vegetated (EVT “Open Water”) Water
Shrub-Dominated Brush
Tree-Dominated Timber
Calculation of ERI requires that a time frame be chosen to facilitate actual vs. optimal travel
distance calculation from a given starting point. For the purpose of this study, to compare the effects of
different time frames on the resulting ERI values, three times were chosen: 10 min, 20 min, and 30 min.
These times were chosen to reflect reasonable travel times from the fireline to a safety zone, according to
historical, well-documented wildland firefighter entrapments [
23
], while balancing the computational
cost associated with processing longer travel times. Thus, the ERI
10
indicates, for example, how far or
fast one can travel in 10 min from a starting point with existing landscape impediments relative to how
far or fast one could travel within that same time frame in the absence of any impediments.
ERI modeling was performed on a cell-by-cell basis throughout ANF as follows (Figure 4). It is
worth noting that while Figure 4depicts the process for modeling ERI for a single starting location
(Figure 4a) within ANF at a single time frame (30 min), this same procedure was performed on every
raster cell within the study area for each of the three time frames. The two input variables, a DEM
and the reclassified LANDFIRE EVT dataset with the roads and trails modification, can be seen in
Figure 4b. From the starting point, total travel time on a cell-by-cell basis was calculated using Dijkstra’s
algorithm [
24
], as implemented in the accCost function within the gdistance library [
21
] in R (Figure 4c).
A travel time threshold was then applied to the accumulative cost raster for the time frame of interest
(in the example figure, 30 min) and converted to a vector polygon (Figure 4d). This polygon represents
Fire 2019,2, 40 8 of 19
the actual travel distance one can traverse from the starting point. However, as can clearly be seen,
not all travel directions provide the same egress capacity. Thus, to calculate directionally-specific
travel distances, 100 evenly-spaced points were generated along the polygon boundary and distances
were calculated from the starting point to those edge points (Figure 4d). Optimal travel conductance
conditions were calculated based on the fastest combination of slope and land cover conditions
seen in Figure 2. The land cover of highest conductance was grass/non-burnable, and the slope of
highest conductance was -1.85
◦
, which was determined by performing an optimization of Equation (1).
Accordingly, for each of the three time frames, an optimal travel distance was calculated, the results of
which can be seen in Table 5.
Fire 2019, 2, x FOR PEER REVIEW 8 of 20
Equation (1). Accordingly, for each of the three time frames, an optimal travel distance was calculated,
the results of which can be seen in Table 5.
Figure 4. Spatial depiction of Escape Route Index (ERI) modeling technique: (a) sample starting point
within the Angeles National Forest (ANF); (b) input spatial datasets for ERI calculation, including
elevation and LANDFIRE-derived land cover; (c) accumulated travel time modeled from the starting
point with a 30-minute threshold applied; and (d) comparison of actual 30-minute travel distance to
optimal 30-minute travel distance, with distance calculations.
Table 5. Optimal travel distances for the three time frames.
Time Frame (min) Optimal Travel Distance (m)
10 695.52
20 1391.03
30 2086.55
Figure 4.
Spatial depiction of Escape Route Index (ERI) modeling technique: (
a
) sample starting point
within the Angeles National Forest (ANF); (
b
) input spatial datasets for ERI calculation, including
elevation and LANDFIRE-derived land cover; (
c
) accumulated travel time modeled from the starting
point with a 30-min threshold applied; and (
d
) comparison of actual 30-min travel distance to optimal
30-min travel distance, with distance calculations.
Fire 2019,2, 40 9 of 19
Table 5. Optimal travel distances for the three time frames.
Time Frame (min) Optimal Travel Distance (m)
10 695.52
20 1391.03
30 2086.55
In reality, optimal travel distance from a given starting point would be represented as a circle
with a radius of that distance. However, in raster GIS, movement is typically limited to four directions
(a.k.a. the “king’s case”), eight directions (a.k.a. the “queen’s case”), or sometimes 16 directions (a.k.a.
the “knight’s case”) (Figure 5). As a result, the optimal travel distance polygons from these three
cases are not perfectly circular. For the purpose of this study, eight directions were chosen to balance
realistic travel movement patterns (i.e., four directions is too restrictive) with computer processing
power (i.e., 16 directions is more processing-intensive).
Fire 2019, 2, x FOR PEER REVIEW 9 of 20
In reality, optimal travel distance from a given starting point would be represented as a circle
with a radius of that distance. However, in raster GIS, movement is typically limited to four directions
(a.k.a. the “king’s case”), eight directions (a.k.a. the “queen’s case”), or sometimes 16 directions (a.k.a.
the “knight’s case”) (Figure 5). As a result, the optimal travel distance polygons from these three cases
are not perfectly circular. For the purpose of this study, eight directions were chosen to balance
realistic travel movement patterns (i.e., four directions is too restrictive) with computer processing
power (i.e., 16 directions is more processing-intensive).
Figure 5. Raster geographic information systems (GIS) simulated travel directions (gray arrows) from
a starting point (white circle) in (a) four directions, (b) eight directions, and (c) 16 directions, and the
resulting polygon shapes representing the optimal travel distance (black lines).
Four different ERI metrics were calculated to condense directional information (e.g., Figure 4)
into single values for each raster cell: (1) minimum ERI (ERImin); (2) maximum ERI (ERImax); (3) mean
ERI (ERImean); and (4) ERI azimuth (ERIazimuth). ERImin was calculated as the distance between the
starting point and the closest boundary point (𝑑) divided by the optimal travel distance (𝑑)
within a given time frame (Equation 2). ERImin represents the “worst-case” scenario, meaning that if
all other travel directions are limited due to, for example, surrounding flames, then you will only be
able to evacuate at a proportional travel rate of ERImin. If ERImin is high for a given location, that means
that, even in the worst-case scenario, evacuation travel rates should be relatively high, irrespective of
travel direction. ERImax was calculated as the distance between the starting point and the furthest
boundary point (𝑑) divided by the optimal travel distance (𝑑) within a given time frame
(Equation 3). ERImax represents the “best-case” scenario, meaning that if there are no travel direction
limitations, one could evacuate a given location at a proportional travel rate of ERImax. ERImean was
calculated as the average distance between the starting point and all of the boundary points [𝑑…𝑑]
(𝑑) divided by the average distance between the starting point and the edges of the optimal
distance octagon [𝑑 …𝑑 ] (𝑑 ) (Equations (4–6)). ERImean represents the average egress
capacity from a given starting point in all directions within a given time frame. Lastly ERIazimuth was
calculated as the azimuthal direction from the starting point (𝑥,𝑦) to the furthest boundary point
(𝑥,𝑦), representing the best evacuation direction from a given starting location within a given time
frame (Equation (7)). The R code for implementation of the ERI algorithms is contained within the
Supplementary Materials (S1).
𝐸𝑅𝐼 =𝑑
𝑑, (2)
𝐸𝑅𝐼 =𝑑
𝑑 , (3)
𝐸𝑅𝐼 =𝑑
𝑑 , (4)
Figure 5.
Raster geographic information systems (GIS) simulated travel directions (gray arrows) from
a starting point (white circle) in (
a
) four directions, (
b
) eight directions, and (
c
) 16 directions, and the
resulting polygon shapes representing the optimal travel distance (black lines).
Four different ERI metrics were calculated to condense directional information (e.g., Figure 4) into
single values for each raster cell: (1) minimum ERI (ERI
min
); (2) maximum ERI (ERI
max
); (3) mean ERI
(ERI
mean
); and (4) ERI azimuth (ERI
azimuth
). ERI
min
was calculated as the distance between the starting
point and the closest boundary point (
dmin
) divided by the optimal travel distance (
dopt
) within a given
time frame (Equation (2)). ERI
min
represents the “worst-case” scenario, meaning that if all other travel
directions are limited due to, for example, surrounding flames, then you will only be able to evacuate at
a proportional travel rate of ERI
min
. If ERI
min
is high for a given location, that means that, even in the
worst-case scenario, evacuation travel rates should be relatively high, irrespective of travel direction.
ERI
max
was calculated as the distance between the starting point and the furthest boundary point (
dmax
)
divided by the optimal travel distance (
dopt
) within a given time frame (Equation (3)). ERI
max
represents
the “best-case” scenario, meaning that if there are no travel direction limitations, one could evacuate a
given location at a proportional travel rate of ERI
max
. ERI
mean
was calculated as the average distance
between the starting point and all of the boundary points [
d1. . . dn
] (
dmean
) divided by the average
distance between the starting point and the edges of the optimal distance octagon [
dopt 1. . . dopt n
]
(
dopt mean
) (Equations (4)–(6)). ERI
mean
represents the average egress capacity from a given starting
point in all directions within a given time frame. Lastly ERI
azimuth
was calculated as the azimuthal
direction from the starting point (
x0
,
y0
) to the furthest boundary point (
x1
,
y1
), representing the best
evacuation direction from a given starting location within a given time frame (Equation (7)). The R
code for implementation of the ERI algorithms is contained within the Supplementary Materials (S1).
ERImin =dmin
dopt , (2)
Fire 2019,2, 40 10 of 19
ERImax =dmax
dopt , (3)
ERImean =dmean
dopt mean , (4)
dmean =Pn
i=1di
n, (5)
dopt mean =Pn
i=1dopt i
n, (6)
dazimuth = 450 −180 ×atan2(y1−y0,x1−x0)
π!mod 360. (7)
2.3. Analysis
All four metrics were calculated on a cell-by-cell basis for every 30-m raster cell throughout the
entirety of the ANF to demonstrate applicability on a useful, operational scale. Because ERI is based
on travel simulation from a given raster cell to the surrounding cells, it is not simply a reflection
of the landscape conditions at that cell—it is an amalgamation of the broader landscape conditions.
The longer the simulated evacuation time, the broader the spatial scale of impact and vice versa.
Accordingly, it is valuable to understand the relative effects of the input variables (slope and land
cover) on the output variables (ERI values for each evacuation time). To do this, we performed a series
of Analysis of Variance (ANOVA) analyses using 10,000 randomly-generated points within ANF. For
each, the dependent variable was the ERI metric (limited to max, mean, and min), and the independent
variables were slope and land cover. Then, to determine relative variable importance, the calc.relimp
function in the relaimpo library in R [
25
], which parses the relative variance explained by independent
variables in a linear model, was used. Those same random points were used to perform two additional
regression analyses: (1) ERI
max
vs. ERI
min
, aimed at describing how the relationship between these
two metrics can illuminate spatial characteristics of the egress capacity and (2) 30-min evacuation time
vs. 10-min evacuation time for ERI
max
, ERI
min
, and ERI
mean
, aimed at understanding the sensitivity of
ERI values to evacuation time simulation.
Lastly, to assess the degree to which landscape conditions may have limited efficient movement
in real-life situations, ERI was modeled for 11 recent wildland firefighter entrapment events involving
pedestrian travel (non-equipment) that have occurred since 2001 (Table 6). The year 2001 was chosen
since the first LANDFIRE EVT dataset was produced for the year 2001, thus allowing for pre-fire
land cover conditions to be factored into the analysis. For each incident, the location of the crew’s
evacuation starting point was used as the starting point for ERI modeling. Those starting points were
used to acquire a subset of DEM, LANDFIRE, and roads and trails data, all of which were re-projected
into the local UTM projection and co-registered to align pixels.
Table 6. Recent wildland firefighter entrapments used as a basis for ERI evaluation.
Year Incident Name State Type Fatality
2003 Cramer Idaho Burnover Yes
2006 Little Venus Wyoming Burnover No
2008 Panther California Burnover Yes
2011 Horseshoe 2 Arizona Burnover No
2012 Holloway Oregon Burnover No
2013 Yarnell Arizona Burnover Yes
2014 King California
Near Miss
No
2017 Liberty Montana
Near Miss
No
2017 Preacher Nevada
Near Miss
No
2018 Horse Park Colorado
Near Miss
No
2018 Ranch California
Near Miss
No
Fire 2019,2, 40 11 of 19
3. Results
The results of the study area-wide ERI modeling effort can be seen in Figures 6and 7, and Table 7.
By virtue of their formulations, ERI
max
values are higher than ERI
mean
values which are higher than
ERI
min
values. Spatially, ERI
min
, ERI
max
, and ERI
mean
all follow similar geographic patterns—areas
of high ERI in one metric tended to produce high ERI in another and vice versa. This is because
areas that had high travel impedance (e.g., steep slopes, and tree-dominated land cover) tended to
reduce the egress capacity, regardless of travel direction. However, the directionality of egress had a
definite effect. ERI
max
, representing the best-case scenario for evacuation, and ERI
min
, representing the
worst-case scenario, although correlated, have a high degree of variability between them (Figure 8).
The magnitude of difference between ERI
max
and ERI
min
can yield valuable information about the
spatial characteristics of the egress in a given area. For example, a high ERI
max
:ERI
min
ratio suggests a
high degree of escape route directionality—that is, there is at least one direction by which evacuation
would be relatively more efficient and at least one direction where evacuation would be relatively less
so. Conversely, an ERI
max
:ERI
min
ratio that approaches 1 would suggest directional independence of
evacuation, as the worst-case and the best-case evacuation direction have similar travel impedance.
Fire 2019, 2, x FOR PEER REVIEW 11 of 20
3. Results
The results of the study area-wide ERI modeling effort can be seen in Figures 6 and 7, and Table
7. By virtue of their formulations, ERImax values are higher than ERImean values which are higher than
ERImin values. Spatially, ERImin, ERImax, and ERImean all follow similar geographic patterns—areas of
high ERI in one metric tended to produce high ERI in another and vice versa. This is because areas
that had high travel impedance (e.g., steep slopes, and tree-dominated land cover) tended to reduce
the egress capacity, regardless of travel direction. However, the directionality of egress had a definite
effect. ERImax, representing the best-case scenario for evacuation, and ERImin, representing the worst-
case scenario, although correlated, have a high degree of variability between them (Figure 8). The
magnitude of difference between ERImax and ERImin can yield valuable information about the spatial
characteristics of the egress in a given area. For example, a high ERImax:ERImin ratio suggests a high
degree of escape route directionality—that is, there is at least one direction by which evacuation
would be relatively more efficient and at least one direction where evacuation would be relatively
less so. Conversely, an ERImax:ERImin ratio that approaches 1 would suggest directional independence
of evacuation, as the worst-case and the best-case evacuation direction have similar travel impedance.
Figure 6. Results of ERI modeling for ERImin, ERImax, ERImean, and ERIazimuth, for each of the three time
frames tested (10, 20, and 30 minutes) throughout the entirety of the ANF.
Figure 6.
Results of ERI modeling for ERI
min
, ERI
max
, ERI
mean
, and ERI
azimuth
, for each of the three
time frames tested (10, 20, and 30 min) throughout the entirety of the ANF.
Fire 2019,2, 40 12 of 19
Fire 2019, 2, x FOR PEER REVIEW 12 of 20
Figure 7. Probability densities of ERI metric raster cell values for each of the time frames tested
throughout the ANF.
Table 7. Descriptive statistics of ERI metric raster cell values for each of the time frames tested
throughout the ANF. SD is the standard deviation.
Metric Evacuation Time (min) Mean SD
ERImax 10 0.54 0.22
ERImax 20 0.56 0.21
ERImax 30 0.58 0.20
ERImean 10 0.39 0.19
ERImean 20 0.41 0.18
ERImean 30 0.43 0.17
ERImin 10 0.20 0.15
ERImin 20 0.22 0.14
ERImin 30 0.23 0.14
Figure 8. The relationship between ERImax and ERImin for a 30-minute evacuation time frame, where
the red line represents a log-linear regression model, and the black dotted line represents a 1:1
relationship between ERImax and ERImin.
Figure 7.
Probability densities of ERI metric raster cell values for each of the time frames tested
throughout the ANF.
Table 7.
Descriptive statistics of ERI metric raster cell values for each of the time frames tested
throughout the ANF. SD is the standard deviation.
Metric Evacuation Time (min) Mean SD
ERImax 10 0.54 0.22
ERImax 20 0.56 0.21
ERImax 30 0.58 0.20
ERImean 10 0.39 0.19
ERImean 20 0.41 0.18
ERImean 30 0.43 0.17
ERImin 10 0.20 0.15
ERImin 20 0.22 0.14
ERImin 30 0.23 0.14
Fire 2019, 2, x FOR PEER REVIEW 12 of 20
Figure 7. Probability densities of ERI metric raster cell values for each of the time frames tested
throughout the ANF.
Table 7. Descriptive statistics of ERI metric raster cell values for each of the time frames tested
throughout the ANF. SD is the standard deviation.
Metric Evacuation Time (min) Mean SD
ERImax 10 0.54 0.22
ERImax 20 0.56 0.21
ERImax 30 0.58 0.20
ERImean 10 0.39 0.19
ERImean 20 0.41 0.18
ERImean 30 0.43 0.17
ERImin 10 0.20 0.15
ERImin 20 0.22 0.14
ERImin 30 0.23 0.14
Figure 8. The relationship between ERImax and ERImin for a 30-minute evacuation time frame, where
the red line represents a log-linear regression model, and the black dotted line represents a 1:1
relationship between ERImax and ERImin.
Figure 8.
The relationship between ERI
max
and ERI
min
for a 30-min evacuation time frame, where the
red line represents a log-linear regression model, and the black dotted line represents a 1:1 relationship
between ERImax and ERImin.
Figure 6also highlights the effects of evacuation time frame on ERI values, best illustrated in the
larger-scale inset maps. Across all ERI metrics, as travel time increases, the ERI values “smooth out”
Fire 2019,2, 40 13 of 19
over space. This is because, for a short evacuation (e.g., 10 min), a small, spatially-isolated impeding
feature, such as a cliffor a dense patch of forest, can have a large relative effect on the distance one
could travel. For longer evacuations, smaller travel impediments do not have as significant of an effect
on the relative distance one can travel. This smoothing effect is evident across ERI
max
, ERI
min
, and
ERI
mean
in Figure 9, as the slope of the regression line is less than 1. The smoothing is also particularly
clear in the ERI
azimuth
values, such that longer travel times tend to produce larger patches of area with
similar evacuation direction. From an operational standpoint, having these larger patches may be
more useful for escape route planning.
Fire 2019, 2, x FOR PEER REVIEW 13 of 20
Figure 6 also highlights the effects of evacuation time frame on ERI values, best illustrated in the
larger-scale inset maps. Across all ERI metrics, as travel time increases, the ERI values “smooth out”
over space. This is because, for a short evacuation (e.g., 10 minutes), a small, spatially-isolated
impeding feature, such as a cliff or a dense patch of forest, can have a large relative effect on the
distance one could travel. For longer evacuations, smaller travel impediments do not have as
significant of an effect on the relative distance one can travel. This smoothing effect is evident across
ERImax, ERImin, and ERImean in Figure 9, as the slope of the regression line is less than 1. The smoothing
is also particularly clear in the ERIazimuth values, such that longer travel times tend to produce larger
patches of area with similar evacuation direction. From an operational standpoint, having these
larger patches may be more useful for escape route planning.
Figure 9. The effects of evacuation time simulation on ERI values (30 vs. 10 minutes) for (a) ERImax; (b)
ERImin; and (c) ERImean.
When comparing the spatial characteristics of the input datasets seen in the study area map
(Figures 3) and those of the ERImax, ERImin, and ERImean results (Figure 6), it becomes apparent that
land cover has a dominant effect on egress capacity. Figure 10 contains a larger-scale depiction of the
model inputs and outputs to highlight this effect. As can be seen, the forested areas demonstrate a
strong influence on the ERI model results, particularly ERImax and ERImean (Figure 10d and 10e,
respectively). Land cover has 3–4x the influence of slope based on multiple regression-based variable
importance analysis (Table 8). This is predictable, given the fact that the maximum relative effects of
the input conductance values differ significantly between slope and land cover. However, it is also
important to note that, due to the fact that ERI is not simply calculated on a cell-by-cell basis by
performing raster map algebra on input cells, the R2 values for the regression analyses are not very
high. ERI values are calculated based not just on local conditions, but broader surrounding
conditions. In the case of 30 minute travel time simulations, conditions as far away as 2 km can affect
ERI values at a given location. Accordingly, as discussed earlier, shorter travel time simulations are
more affected by local conditions. This is also evident in the fact that the 10 minute ERI values have
higher R2 values than the 20 and 30 minute values.
Figure 9.
The effects of evacuation time simulation on ERI values (30 vs. 10 min) for (
a
) ERI
max
;
(b) ERImin; and (c) ERImean .
When comparing the spatial characteristics of the input datasets seen in the study area map
(Figure 3) and those of the ERI
max
, ERI
min
, and ERI
mean
results (Figure 6), it becomes apparent that land
cover has a dominant effect on egress capacity. Figure 10 contains a larger-scale depiction of the model
inputs and outputs to highlight this effect. As can be seen, the forested areas demonstrate a strong
influence on the ERI model results, particularly ERI
max
and ERI
mean
(Figure 10d,e, respectively). Land
cover has 3–4x the influence of slope based on multiple regression-based variable importance analysis
(Table 8). This is predictable, given the fact that the maximum relative effects of the input conductance
values differ significantly between slope and land cover. However, it is also important to note that, due
to the fact that ERI is not simply calculated on a cell-by-cell basis by performing raster map algebra
on input cells, the R
2
values for the regression analyses are not very high. ERI values are calculated
based not just on local conditions, but broader surrounding conditions. In the case of 30 min travel
time simulations, conditions as far away as 2 km can affect ERI values at a given location. Accordingly,
as discussed earlier, shorter travel time simulations are more affected by local conditions. This is also
evident in the fact that the 10 min ERI values have higher R2values than the 20 and 30 min values.
Mapped travel times for wildland firefighter entrapments can be seen in Figure 11. The results
highlight a diversity of landscape conditions faced by firefighters among these events, with some
featuring comparably favorable landscape conditions (e.g., Holloway (Figure 11e), Yarnell (Figure 11f),
King (Figure 11g), and Preacher (Figure 11i)), and others featuring comparably unfavorable conditions
(e.g., Cramer (Figure 11a), Little Venus (Figure 11b), Horseshoe 2 (Figure 11d), and Horse Park
(Figure 11j)). However, these results should be interpreted with caution for a few important reasons:
(1) the mapped land cover conditions represent pre-fire conditions, and do not reflect the degree to
which the fires had altered the cover (i.e., travel in the “black” can be substantially faster); (2) it is
impossible to determine on a case-by-case scenario the temporal accuracy of the roads and trails—some
may have existed pre-fire, but some may have been developed during or after the fire; (3) the ERI
does not include any information on the spatial extent of the fire at the time of evacuation, which
Fire 2019,2, 40 14 of 19
has perhaps the most important effect on evacuation direction; and (4) although some of the travel
distances mapped are larger than others, and as such suggest greater egress capacity, the ERI values
across the board are still quite low (Figure 12). For example, for the 30-min evacuation simulations, the
mean ERI
min
across all incidents was 0.21, the mean ERI
max
across all incidents was 0.64, and the mean
ERI
mean
across all incidents was 0.43. The mean ERI values for burnovers with fatalities tended to be
lower than the near misses and the burnovers without fatalities.
Fire 2019, 2, x FOR PEER REVIEW 14 of 20
Figure 10. Large-scale maps containing the two model input datasets (a) elevation, roads/trails, and
(b) land cover as well as model output datasets (c) ERImin, (d) ERImax, (e) ERImean, and (f) ERIazimuth.
Table 8. Descriptive statistics of ERI metric raster cell values for each of the time frames tested
throughout the ANF.
Metric Evacuation Time (min) R2 Slope Importance (%) Land Cover Importance (%)
ERImax 10 0.64 17.94 82.06
ERImax 20 0.60 20.68 79.32
ERImax 30 0.57 21.82 78.18
ERImean 10 0.68 18.91 81.09
ERImean 20 0.64 20.01 79.99
ERImean 30 0.61 20.46 79.54
ERImin 10 0.60 21.26 78.74
ERImin 20 0.55 19.04 80.96
ERImin 30 0.52 18.81 81.19
Mapped travel times for wildland firefighter entrapments can be seen in Figure 11. The results
highlight a diversity of landscape conditions faced by firefighters among these events, with some
featuring comparably favorable landscape conditions (e.g., Holloway (Figure 11e), Yarnell (Figure
11f), King (Figure 11g), and Preacher (Figure 11i)), and others featuring comparably unfavorable
conditions (e.g., Cramer (Figure 11a), Little Venus (Figure 11b), Horseshoe 2 (Figure 11d), and Horse
Park (Figure 11j)). However, these results should be interpreted with caution for a few important
reasons: (1) the mapped land cover conditions represent pre-fire conditions, and do not reflect the
degree to which the fires had altered the cover (i.e., travel in the “black” can be substantially faster);
(2) it is impossible to determine on a case-by-case scenario the temporal accuracy of the roads and
trails—some may have existed pre-fire, but some may have been developed during or after the fire;
(3) the ERI does not include any information on the spatial extent of the fire at the time of evacuation,
Figure 10.
Large-scale maps containing the two model input datasets (
a
) elevation, roads/trails, and (
b
) land
cover as well as model output datasets (c) ERImin, (d) ERImax, (e) ERImean, and (f) ERIazimuth.
Table 8.
Descriptive statistics of ERI metric raster cell values for each of the time frames tested
throughout the ANF.
Metric Evacuation Time (min) R2Slope Importance (%) Land Cover Importance (%)
ERImax 10 0.64 17.94 82.06
ERImax 20 0.60 20.68 79.32
ERImax 30 0.57 21.82 78.18
ERImean 10 0.68 18.91 81.09
ERImean 20 0.64 20.01 79.99
ERImean 30 0.61 20.46 79.54
ERImin 10 0.60 21.26 78.74
ERImin 20 0.55 19.04 80.96
ERImin 30 0.52 18.81 81.19
Fire 2019,2, 40 15 of 19
Fire 2019, 2, x FOR PEER REVIEW 15 of 20
which has perhaps the most important effect on evacuation direction; and (4) although some of the
travel distances mapped are larger than others, and as such suggest greater egress capacity, the ERI
values across the board are still quite low (Figure 12). For example, for the 30-minute evacuation
simulations, the mean ERImin across all incidents was 0.21, the mean ERImax across all incidents was
0.64, and the mean ERImean across all incidents was 0.43. The mean ERI values for burnovers with
fatalities tended to be lower than the near misses and the burnovers without fatalities.
Figure 11. Simulated travel time results from several recent wildland firefighter entrapment incidents
used as the basis for ERI evaluation: (a) Cramer (2003); (b) Little Venus (2006); (c) Panther (2008); (d)
Horseshoe 2 (2011); (e) Holloway (2012); (f) Yarnell (2013); (g) King (2014); (h) Liberty (2017); (i)
Preacher (2017); (j) Horse Park (2018); and (k) Ranch (2018).
Figure 11.
Simulated travel time results from several recent wildland firefighter entrapment incidents
used as the basis for ERI evaluation: (
a
) Cramer (2003); (
b
) Little Venus (2006); (
c
) Panther (2008);
(
d
) Horseshoe 2 (2011); (
e
) Holloway (2012); (
f
) Yarnell (2013); (
g
) King (2014); (
h
) Liberty (2017);
(i) Preacher (2017); (j) Horse Park (2018); and (k) Ranch (2018).
Fire 2019, 2, x FOR PEER REVIEW 16 of 20
Figure 12. ERImin, ERImax, and ERImean values modeled from the evacuation starting locations for
several recent wildland firefighter entrapment incidents.
4. Discussion
ERI is focused on pre-fire terrain and land cover conditions. Accordingly, it does not account for
a number of critical variables that can affect a fire crew’s safety planning decision making processes.
Perhaps the most important variable not considered by ERI is the fire extent and growth trajectory.
ERI makes the naïve assumption that travel is not restricted in any direction by any factors other than
slope and land cover. In reality, fire crews may have 50% or more of potential evacuation directions
cut off by the fire itself. Thus, ERI is not a real-time product, as it does not reflect real-time conditions
making it a pre-fire decision support tool.
Another important consideration not included in the ERI modeling process is the presence of
safety zones. LCES is not a sequence of four disparate safety measures, it is an integrated system of
four inherently interdependent safety measures. If no suitable safety zone is accessible from the
fireline, then no escape route, regardless of how efficient, is going to be of value. This could be
remedied in the future by incorporating ERI maps with maps of existing safety zones, such as those
mapped using lidar [26,27]. However, safety zones are often designated “in the black”—in areas that
have already burned [28]. As in the case of the fire extent, the dynamism of the fire environment and
the associated evolving presence of safety zones is not accounted for in ERI.
Other important safety factors not directly incorporated into ERI are: (1) situational awareness;
and (2) potential for snag hazard. Regarding the first exclusion, one could potentially model
situational awareness, at least in terms of the ability to perceive surrounding conditions through a
GIS-driven viewshed analysis. It is likely that ERI and a terrain-driven viewshed analysis would be
highly correlated, since, for example a narrow canyon with limited visibility would also have low
egress capacity and vice versa. Regarding the second exclusion, snags act as a significant hazard to
Figure 12.
ERI
min
, ERI
max
, and ERI
mean
values modeled from the evacuation starting locations for
several recent wildland firefighter entrapment incidents.
Fire 2019,2, 40 16 of 19
4. Discussion
ERI is focused on pre-fire terrain and land cover conditions. Accordingly, it does not account for a
number of critical variables that can affect a fire crew’s safety planning decision making processes.
Perhaps the most important variable not considered by ERI is the fire extent and growth trajectory.
ERI makes the naïve assumption that travel is not restricted in any direction by any factors other than
slope and land cover. In reality, fire crews may have 50% or more of potential evacuation directions cut
offby the fire itself. Thus, ERI is not a real-time product, as it does not reflect real-time conditions
making it a pre-fire decision support tool.
Another important consideration not included in the ERI modeling process is the presence of
safety zones. LCES is not a sequence of four disparate safety measures, it is an integrated system of
four inherently interdependent safety measures. If no suitable safety zone is accessible from the fireline,
then no escape route, regardless of how efficient, is going to be of value. This could be remedied in the
future by incorporating ERI maps with maps of existing safety zones, such as those mapped using
lidar [
26
,
27
]. However, safety zones are often designated “in the black”—in areas that have already
burned [
28
]. As in the case of the fire extent, the dynamism of the fire environment and the associated
evolving presence of safety zones is not accounted for in ERI.
Other important safety factors not directly incorporated into ERI are: (1) situational awareness;
and (2) potential for snag hazard. Regarding the first exclusion, one could potentially model situational
awareness, at least in terms of the ability to perceive surrounding conditions through a GIS-driven
viewshed analysis. It is likely that ERI and a terrain-driven viewshed analysis would be highly
correlated, since, for example a narrow canyon with limited visibility would also have low egress
capacity and vice versa. Regarding the second exclusion, snags act as a significant hazard to wildland
firefighters, and thus it is suggested that ERI be used in conjunction with a snag hazard map [29].
Although critical, safety is but one component of the complex, multifaceted wildland fire decision
making process [
30
]. For example, fire crews should also consider the relative potential for suppression
effectiveness, incorporating the suppression difficulty index into control location establishment [
31
].
Accordingly, we are suggesting that ERI become integrated into existing decision support systems,
such as WFDSS—particularly since WFDSS data play such a critical role in the formulation of ERI [
32
].
It is important to distinguish between the existing WFDSS ground evacuation map product and ERI.
Although the same land cover travel impedance coefficients are used in both, the end goals of the two
products are distinct. WFDSS evacuation maps provide fire managers with a map of the estimated time
it would take someone to evacuate to the nearest hospital, and as such, necessarily takes into account
the distance to hospitals and automotive travel along a road network. In addition, relatively coarse
slope categories are used to model travel impedance. The resulting product is a map of absolute travel
time. ERI maps, on the other hand, provide fire managers with a map of relative egress capacity from
anywhere in a wildland environment, regardless of proximity to a hospital, and are thusly focused
more on evacuation from the fireline to a safety zone than to a health care facility. Additionally, a
more precise slope-travel rate function is used as a basis of travel impedance. The output maps either
provide a relative safety index, ranging from 0 to 1, or a suggested travel direction.
In its current formulation, based on its current input parameters and datasets, ERI clearly
demonstrates a strong influence from land cover—a much greater influence than that of slope. While a
previous study has likewise concluded that land cover (in particular, the density of vegetation) can
have a stronger effect than slope on travel rates [
8
], the magnitude of the relative land cover effects
derived from WFDSS in this study are very dominant (Figure 10; Table 8). When compared to the few
previous studies who have tested the effects of land cover on travel rates, the WFDSS-based effects
are the strongest. Given the sparseness of experimental data on the effects of land cover on travel
rates, it is unclear which among the few studies, have produced the most reliable results. WFDSS was
chosen in this study due to its reliance on existing nationwide data and its wide use in the wildland
fire community, but future research may reveal different, more accurate land cover conductance values
that should be incorporated into future iterations of ERI.
Fire 2019,2, 40 17 of 19
Another limitation of the WFDSS-driven approach is the fact that, in reality, tree-dominated land
cover types are not universally more difficult to traverse than shrub-dominated land cover types.
For example, one can move through a mature ponderosa pine parkland environment with a sparse
understory, even though it is technically “tree-dominated”, much more readily than one can move
through a “shrub-dominated” chaparral environment, such as is present in ANF. This may explain
some of the surprising results of the comparison to recent firefighter entrapment events. For example,
our evaluation highlighted the fact that the starting point of the escape route that the Granite Mountain
Hotshots took possessed a relatively high ERI value, even though their evacuation resulted in one the
most significant fatality events in the history of wildland firefighting. This may be due, in part, to the fact
that the LANDFIRE EVT data classified the pre-fire land cover for that area as being “shrub-dominated”,
thus having a much higher travel conductance than other events. However, according to the Yarnell
Hill Serious Accident Investigation Report, “the dominant vegetation type, chaparral brush, ranged in
height from one to ten feet and, in some places, was nearly impenetrable” [33].
To overcome the limitations imposed by using categorical land cover types as the basis of travel
conductance, we recommend that future research attempt to refine our understanding of how travel
rates are affected by more objective, continuous measures of landscape conditions. Because land cover
datasets are predominantly derived from passive remote sensing instruments that record reflected
solar radiation from the uppermost portions of the Earth’s surface, such as Landsat, they lack the
ability to precisely model vertical structure of the landscape. However, active instruments, such as
lidar, are capable of making precise x,y, and zmeasurements, and exploiting small gaps in a vegetated
canopy to make measurements of understory vegetation density, which is thought to be a much better
predictor of travel conductance [
8
,
34
]. With the ever-increasing availability of lidar data in the US,
future research should aim to enhance ERI with more precise measures of structurally-based, rather
than categorically-based, pedestrian travel conductance.
5. Conclusions
In this paper, we have introduced a new metric for assessing and mapping egress capacity, or the
degree to which one can evacuate from a given location, on a broad, spatial scale based on existing
landscape conditions. ERI is not a single metric, but a suite of four spatially-explicit metrics that define
the relative travel impedance caused by terrain and land cover faced by a fire crew, should that fire
crew need to evacuate. The intent is that this modeling technique will be employed to aid in wildland
firefighter safety operations prior to engaging a fire, acting as a decision support tool. Given that
the metric relies on US nationwide, publicly-available datasets, the goal is that ERI metrics would be
mapped in advance of fire suppression and used to direct fire crews toward potential control locations
with higher capacity for evacuation, thus reducing the potential for injurious or even fatal entrapments.
ERI does not map escape routes, per se, it highlights areas that have a greater or lesser capacity
for providing efficient escape routes. Areas with high ERI values will likely have an abundance of
open, easily-traversable terrain, through which many potential escape routes may exist requiring
little alteration of the land cover. Conversely, areas with low ERI values possess some combination of
rugged terrain and dense vegetation, thus making the designation of suitable escape routes difficult or
even impossible.
We suggest that the four metrics be used as follows. If a single metric is to be used, then ERI
mean
should be that metric. It is the best representation of the overall egress capacity for a given location.
High ERI
mean
values are likely to produce desirable evacuation conditions. However, means are simply
a measure of central tendency, and do not reflect the directionally-specific evacuation conditions. Thus,
if a more nuanced planning process is feasible, it is advisable to use the remaining three metrics in
conjunction with ERI
mean
. ERI
min
provides fire personnel with a sense of the worst-case evacuation
scenario based on existing landscape conditions. For example, even with a relatively high ERI
mean
, if
a crew is backed up against a cliffor other impassable feature ERI
min
will be very low. In wildland
firefighting, where risk levels are high and threats abound, conservative safety planning, such as is
Fire 2019,2, 40 18 of 19
offered by ERI
min
may be advisable. ERI
mean
and ERI
min
being equal, a crew might want to know what
areas to target for suppression based on the best-case evacuation scenario. This is where ERI
max
and
ERI
azimuth
come into play. A high ERI
max
value tells a fire crew that there is at least one direction by
which pedestrian evacuation travel efficiency will be very high. ERI
azimuth
tells that same fire crew
which direction, generally, to take.
Supplementary Materials:
The following are available online at http://www.mdpi.com/2571-6255/2/3/40/s1, S1: R
code for calculating four ERI metrics: ERImin, ERImax , ERImean, and ERIazimuth .
Author Contributions:
Conceptualization, M.J.C., W.G.P., P.E.D. and B.W.B.; Methodology, M.J.C., W.G.P.
and P.E.D.; Software, M.J.C.; Validation, M.J.C. and W.G.P.; Formal Analysis, M.J.C.; Data Curation, M.J.C.;
Writing—Original Draft Preparation, M.J.C.; Writing—Review and Editing, M.J.C., W.G.P., P.E.D. and B.W.B.;
Visualization, M.J.C. and W.G.P.; Funding Acquisition, B.W.B.
Funding:
This research was funded by the USDA Forest Service National Fire Plan through the Washington Office
of the Forest Service Deputy Chief for Research, and the National Wildfire Coordinating Group Fire Behavior
Subcommittee, Cooperative Agreement 18JV11221637154.
Conflicts of Interest: The authors declare no conflict of interest.
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2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access
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