# HexFire Model Notes

The original version of HexFire was described in the 2022 paper published in Land.

The current version of the HexFire model has been renamed "HexFire Single-Season", and includes the following enhancements:

HexFire Single-Season now works correctly if the Fuel Barriers barrier map is a time series containing multiple images.

The Fuel Breaks hexmap is no longer intended to be binary (0 vs. 1). Previously, all fuels in the Relative Flammability hexmap were removed from any hexagon that had a nonzero value in the Fuel Breaks hexmap. In the latest versions of HexFire, values in the Fuel Breaks hexmap are used as coefficients that modify the Relative Flammability hexmap scores. The coefficients used are actually set to 1 - X, where X is the score of a hexagon in the Fuel Breaks hexmap. This ensures that a value of 0 in the Fuel Breaks hexmap has no impact on fuel availability, while a value of 1 results in 100% of the available fuels being removed.

A new version of HexFire model named "HexFire Multi-Season" is now included in the workspace. This model makes it possible for users to simulate a sequence of wildfires spanning multiple years. HexFire Multi-Season includes features for simulating fire severity and the regrowth of vegetation. Within a season, HexFire Multi-Season is essentially identical to HexFire Single-Season. Thus, the original publication describing HexFire (see above) also captures the principal mechanics built into HexFire Multi-Season.

Features that are unique to HexFire Multi-Season are discussed below:

HexFire Multi-Season assumes that each simulation time step represents one year. A global variable is used to specify the length of a fire season in days. Within each year, the model will simulate wildfire for this specified number of days. In contrast, HexFire Single-Season doesn't explicitly associate any temporal scale with the simulation time steps. In that original model, a time step is typically equated to an hour. Also, HexFire Single-Season includes global variables titled Burn Iterations per Time Step and Iterates to Burn Completely. Those global variables no longer exist in HexFire Multi-Season; they have both essentially been assigned a value of 1.

Wildfires simulated in past seasons should affect the availability of fuels in future seasons. To accomplish this, HexFire Multi-Season continuously updates an internal copy of the Relative Flammability hexmap. This generated hexmap is named Flammability. When wildfire lowers values in the Flammability map, less fuel will be available for future fires.

A hexmap named Relative Burn Severity is used to determine how much a simulated wildfire will lower the values in the Flammability map. The values in the Relative Burn Severity map must range between 0 and 1. Users also supply a global variable named Fire Severity Range [%]. When a hexagon burns, it obtains its mean severity from the Relative Burn Severity hexmap. It then select a random severity value in the range [X - Y, X + Y], where X refers to the mean severity value, and Y is the Fire Severity Range [%] global variable, divided by 100%. Finally, that hexagon's value in the Flammability hexmap is reduced by an amount equal to the product of the random severity value and the corresponding value in the Relative Flammability hexmap. For example:

Suppose a hexagon has a value of 0.9 in the Relative Flammability map. That implies the hexagon has a relatively high fuel load. Assume that the hexagon's score in the Relative Burn Severity map is 0.4, and that the Fire Severity Range [%] parameter has been set to 20%. If this hexagon burns, then it will select a random burn severity value in the range [0.4 - 0.08, 0.4 + 0.08], which equals [0.32, 0.48]. Let's suppose the hexagon selects a random burn severity value of 0.35. Then when it burns, the corresponding hexagon in the dynamic Flammability map will be lowered by an amount equal to 0.9 x 0.35. The first term in this product is the hexagon's value in the static Relative Flammability map, and the second term is the random burn severity. Values in the Flammability map are never reduced below 0.

A hexmap named Yearly Regrowth is used by HexFire Multi-Season to simulate the regeneration of fuels between fire seasons. HexFire simply adds this map to the Flammability hexmap at the beginning of each season. However, the values in the dynamic Flammability map are never allowed to exceed the corresponding values in the static Relative Flammability map. Because the Relative Flammability map values range between 0 and 1, the values in the Yearly Regrowth map must also be fractional, and should vary considerably with land cover type (e.g., fields vs. forests).

HexFire Multi-Season constructs three additional hexmap time series that can be written out to the simulation results. These are titled Flammability, Burn Frequency, and Annual Burn Area. Flammability maps have been discussed extensively above. They track the balance between fuel depletion caused by wildfire and fuel replacement due to regrowth. Values in the Flammability map can never fall below 0, and can never rise above the corresponding value in the static Relative Flammability map. The Burn Frequency hexmaps show how many times each hexagon has burned during a multi-season simulation. Users can turn the generation of these hexmaps on and off via global parameters. The Annual Burn Area maps display the portion of the landscape that burns in any given each year, and indicates the per-hexagon burn severity.