# Escape Route Index: A Spatially-Explicit Measure of Wildland Firefighter Egress Capacity

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## Abstract

**:**

_{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.

## 1. Introduction

_{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.

## 2. Materials and Methods

#### 2.1. Definition

^{−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:

^{−1}, θ is slope in degrees, and a, b, c, d, and e are 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 2 converted into relative, per-slope-class multiplicative factors, rather than absolute travel rates. Those factors can be seen in Table 3.

#### 2.2. Calculation

_{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.

_{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 (${d}_{min}$) divided by the optimal travel distance (${d}_{opt}$) 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 (${d}_{max}$) divided by the optimal travel distance (${d}_{opt}$) 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 [${d}_{1}\dots {d}_{n}$] (${d}_{mean}$) divided by the average distance between the starting point and the edges of the optimal distance octagon [${d}_{opt1}\dots {d}_{optn}$] (${d}_{optmean}$) (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 (${x}_{0},{y}_{0}$) to the furthest boundary point (${x}_{1},{y}_{1}$), 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).

#### 2.3. Analysis

_{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.

## 3. Results

_{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.

_{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.

_{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 R

^{2}values than the 20 and 30 min values.

_{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.

## 4. Discussion

## 5. Conclusions

_{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 cliff or 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 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

_{min}, ERI

_{max}, ERI

_{mean}, and ERI

_{azimuth}.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**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.

**Figure 3.**Study area map showing WFDSS land cover classes derived from the 30m LANDFIRE Existing Vegetation Type (EVT) dataset.

**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.

**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).

**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.

**Figure 7.**Probability densities of ERI metric raster cell values for each of the time frames tested throughout the ANF.

**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 ERI

_{max}and ERI

_{min}.

**Figure 9.**The effects of evacuation time simulation on ERI values (30 vs. 10 min) for (

**a**) ERI

_{max}; (

**b**) ERI

_{min}; and (

**c**) ERI

_{mean}.

**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**) ERI

_{min}, (

**d**) ERI

_{max}, (

**e**) ERI

_{mean}, and (

**f**) ERI

_{azimuth}.

**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 12.**ERI

_{min}, ERI

_{max}, and ERI

_{mean}values modeled from the evacuation starting locations for several recent wildland firefighter entrapment incidents.

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 | --- |

**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 | --- |

**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 |

Time Frame (min) | Optimal Travel Distance (m) |
---|---|

10 | 695.52 |

20 | 1391.03 |

30 | 2086.55 |

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 |

**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 |
---|---|---|---|

ERI_{max} | 10 | 0.54 | 0.22 |

ERI_{max} | 20 | 0.56 | 0.21 |

ERI_{max} | 30 | 0.58 | 0.20 |

ERI_{mean} | 10 | 0.39 | 0.19 |

ERI_{mean} | 20 | 0.41 | 0.18 |

ERI_{mean} | 30 | 0.43 | 0.17 |

ERI_{min} | 10 | 0.20 | 0.15 |

ERI_{min} | 20 | 0.22 | 0.14 |

ERI_{min} | 30 | 0.23 | 0.14 |

**Table 8.**Descriptive statistics of ERI metric raster cell values for each of the time frames tested throughout the ANF.

Metric | Evacuation Time (min) | R^{2} | Slope Importance (%) | Land Cover Importance (%) |
---|---|---|---|---|

ERI_{max} | 10 | 0.64 | 17.94 | 82.06 |

ERI_{max} | 20 | 0.60 | 20.68 | 79.32 |

ERI_{max} | 30 | 0.57 | 21.82 | 78.18 |

ERI_{mean} | 10 | 0.68 | 18.91 | 81.09 |

ERI_{mean} | 20 | 0.64 | 20.01 | 79.99 |

ERI_{mean} | 30 | 0.61 | 20.46 | 79.54 |

ERI_{min} | 10 | 0.60 | 21.26 | 78.74 |

ERI_{min} | 20 | 0.55 | 19.04 | 80.96 |

ERI_{min} | 30 | 0.52 | 18.81 | 81.19 |

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## Share and Cite

**MDPI and ACS Style**

Campbell, M.J.; Page, W.G.; Dennison, P.E.; Butler, B.W.
Escape Route Index: A Spatially-Explicit Measure of Wildland Firefighter Egress Capacity. *Fire* **2019**, *2*, 40.
https://doi.org/10.3390/fire2030040

**AMA Style**

Campbell MJ, Page WG, Dennison PE, Butler BW.
Escape Route Index: A Spatially-Explicit Measure of Wildland Firefighter Egress Capacity. *Fire*. 2019; 2(3):40.
https://doi.org/10.3390/fire2030040

**Chicago/Turabian Style**

Campbell, Michael J., Wesley G. Page, Philip E. Dennison, and Bret W. Butler.
2019. "Escape Route Index: A Spatially-Explicit Measure of Wildland Firefighter Egress Capacity" *Fire* 2, no. 3: 40.
https://doi.org/10.3390/fire2030040