# HexFire: A Flexible and Accessible Wildfire Simulator

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Model Overview

_{contagion}= P

_{proximity}× P

_{flammability},

_{proximity}and P

_{flammability}are hexagon-specific values derived in part from HexFire model state (proximity) and input maps (flammability). For every unburned cell that has at least one neighbor presently on fire, we compute the value of P

_{contagion}, draw a uniformly distributed random number R between 0 and 1, and initiate a new fire if P

_{contagion}> R. To accomplish this, we define

_{proximity}= 1 − (1 − N / 6)

^{α},

_{flammability}= 1 − (1 − F)

^{β},

_{proximity}and P

_{flammability}will generate families of nontrivial probability curves (Figure 1).

_{contagion}is the product of P

_{proximity}and P

_{flammability}, HexFire’s local fire spread dynamics can vary widely (Figure 2). Through judicious choice of the proximity and flammability exponents, users can make contagious fire spread more or less sensitive to a cell’s relative flammability, or its number of burning neighbors. Alternatively, users may simply replace our functions governing contagious fire spread with their own (see Supplemental Materials).

**ε**.

**ε**is a parameter we refer to as the Ember Creation Rate, and F (discussed above) represents a cell’s relative flammability. The Ember Creation Rate sets the maximum number of embers that can be created per iterate, for each burning cell. The number of embers actually created in a cell (within a single iterate) will range between zero and this maximum value. E is always rounded to an integer. Each ember will then move a distance D (in hexagons) defined by

**δ**,

**δ**, our Ember Max Distance parameter, sets the maximum distance in hexagons that embers are allowed to travel before settling into a distant cell. The distance that any given ember actually travels will range between zero and this maximum value. D is always rounded to an integer. As embers move, they take successive steps along the wind gradient, and then in a random direction, until they reach their assigned movement distance. The lengths of these gradient-following and random steps are controlled by the Ember Step Length—Wind and Ember Step Length—Random parameters. The addition of random steps keeps the ember’s movements from becoming overly deterministic. When embers land, they initiate new fires at a rate specified by P

_{flammability}, as defined above. The mechanisms that HexFire uses to simulate fire spotting may be easily modified (see Supplemental Materials).

#### 2.2. Example 1—Model Parameters

#### 2.3. Example 2—Fire Suppression

#### 2.4. Example 3—Coupled Models

## 3. Results

#### 3.1. Example 1—Model Parameters

#### 3.2. Example 2—Fire Suppression

#### 3.3. Example 3—Coupled Models

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Shapes of the probability curves derived from specific values of N (neighbors on fire) or F (relative flammability), and α or β (the proximity and flammability exponents). Exponent values are superimposed on the curves they produce.

**Figure 2.**Six examples of how the probability of contagious fire spread changes as a function of a cell’s relative flammability, and its number of burning neighbors (N).

**Figure 3.**Example 2 spatial inputs, including relative flammability (

**left**), wind gradient (

**center**) and relative wind speed (

**right**). The emergent simulated burn perimeter (see Results) is shown as a black outline. The arrow at the top-center indicates the location at which the fire was initiated.

**Figure 4.**Example 3 spatial inputs, including (

**A**) relative flammability, (

**B**) wind gradient, and (

**C**) marten habitat quality.

**Figure 5.**Mean burn frequencies produced by 100 replicates of six model variants: (

**A**) the baseline model, (

**B**) increased influence of proximity to fire, (

**C**) increased influence of fuel flammability, (

**D**) longer ember distances, (

**E**) enhanced wind influence, (

**F**) diminished wind influence. The checkerboard patterns derive from the model’s flammability map, which was made up from alternating blocks of low and high flammability fuels.

**Figure 6.**Mean burn frequencies (

**A**) without and (

**B**) including fuel breaks. Fuel breaks, shown in white, indicate areas where the fuel flammability was set to zero. Black arrows show the location at which the fires were initiated. These results were assembled from 100 replicate simulations.

**Figure 7.**The emergent distribution of burn areas observed from 1000 fire simulations. Replicates that generated a fire size of less than 100 hexagons (of 119 K hexagons total) were replaced with the results from an additional simulation.

**Figure 8.**Mean burn frequency generated from 1000 fire simulations (

**left**), and nine illustrative non-overlapping fires selected from this collection (

**right**). Mean burn frequency is displayed using the color ramp of Figure 4, and the black outline indicates the extent of marten habitat. Burn sizes indicate the proportion of the landscape consumed by a single fire. The color assigned to individual fires (black vs. blue) has no significance.

**Figure 9.**Estimates of population size from marten life history simulator, without ((

**left**), 100 replicates) and including ((

**right**), 1000 replicates) impacts from wildfire. The dark blue and red lines at the plot centers indicate mean population size, while the pairs of light blue and orange lines bracket the range of observed values.

Parameter Name | Parameter Interpretation |
---|---|

Burn Iterations per Time Step | The number of times that the contagious and ember-driven fire spread algorithms are run per time step. |

Iterates to Burn Completely | The number of burn iterations during which an ignited cell will continue to burn. |

Flammability Exponent | The exponent that influences how fuel flammability affects contagious wildfire spread. |

Proximity Exponent | The exponent that influences how the number of burning neighbors affects contagious wildfire spread. |

Ember Creation Rate | The maximum number of embers that can be created, per iterate, within each burning cell. |

Ember Max Distance | The maximum distance, in hexagons, that an individual ember may travel. |

Ember Step Length—Wind | The step length, in hexagons, assigned to embers moving along a wind gradient. |

Ember Step Length—Random | The step length, in hexagons, assigned to embers moving in a random direction. |

**Table 2.**Input maps used by the HexFire model. Variable suggests that map construction effort will range from minimal to significant, depending on study design. Automatic implies that a method or utility is available to construct the map. Optional indicates that a map may be left blank.

Map Name | Level of Effort | Map Function |
---|---|---|

Relative Flammability | Variable | Provides the relative flammability of each cell in the landscape. Values must range between 0 and 1. |

Ignition Sites | Variable | Controls the time and location at which fires are initiated, including back burns. |

Hexagon ID | Automatic | Contains the individual ID of each cell. This map is trivial to create in HexSim. |

Patch Maps (A-D) | Automatic | A collection of four patch maps for which the union of all patches is space-filling, and each patch slightly overlaps its neighbors. We provide a utility for constructing these patch maps, which are used to improve model performance. |

Relative Wind Speed | Variable | Provides the wind speed for each cell in the landscape. Values must range between 0 and 1. |

Wind Gradient | Variable | Indicates the directions that embers will travel. We provide a utility that builds wind gradient maps from maps of wind direction. |

Fuel Breaks | Optional | Indicates where and when fuels should be removed from the flammability map. |

Fuel Barriers | Optional | Specifies the location of fuel barriers, which can block the movement of embers. |

**Table 3.**Example 1 input parameters. Labels used to distinguish the six experiments are shown in parentheses. Experiments B–F were conducted using the baseline model (experiment A) parameters, except where indicated.

Baseline | Model Variants | |||||
---|---|---|---|---|---|---|

(A) | (B) | (C) | (D) | (E) | (F) | |

Burn Iterations per Time Step | 2 | |||||

Iterates to Burn Completely | 3 | |||||

Flammability Exponent | 2 | 5 | 0.2 | |||

Proximity Exponent | 0.5 | 0.2 | 5 | |||

Ember Creation Rate | 5 | |||||

Ember Max Distance | 10 | 50 | ||||

Ember Step Length—Wind | 1 | 10 | ||||

Ember Step Length—Random | 1 | 10 |

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**MDPI and ACS Style**

Schumaker, N.H.; Watkins, S.M.; Heinrichs, J.A. HexFire: A Flexible and Accessible Wildfire Simulator. *Land* **2022**, *11*, 1288.
https://doi.org/10.3390/land11081288

**AMA Style**

Schumaker NH, Watkins SM, Heinrichs JA. HexFire: A Flexible and Accessible Wildfire Simulator. *Land*. 2022; 11(8):1288.
https://doi.org/10.3390/land11081288

**Chicago/Turabian Style**

Schumaker, Nathan H., Sydney M. Watkins, and Julie A. Heinrichs. 2022. "HexFire: A Flexible and Accessible Wildfire Simulator" *Land* 11, no. 8: 1288.
https://doi.org/10.3390/land11081288