Dead Fuel Moisture and the Wildfire Extinction Threshold

Fuel & Weather

Dead fuel moisture M_f 8%

Wind speed 15 km/h

Slope 10°

Fire Behavior

Unignited

Head-fire ROS

0.0 m/min

Damping η_M

100%

Area burned

M_f / M_x

0.27

How it works

Rothermel's (1972) fire-spread model scales a fuel bed's baseline spread rate by a moisture damping coefficient η_M, which measures how much of the fuel's heat content is wasted evaporating water before combustion can proceed:

η_M = 1 − 2.59·r + 5.11·r² − 3.52·r³,   r = M_f / M_x
η_M = 0  once r ≥ 1  (fire cannot sustain itself)

M_f is the dead fuel's moisture content (% of dry weight) and M_x is the moisture of extinction — about 30% for fine dead fuels like grass and litter, the value used here. Below that threshold, drier fuel burns faster; at or above it, evaporative losses exceed the heat the fire can deliver ahead of itself and the front stalls.

Each grid cell's local moisture is your slider value perturbed by a fixed spatial pattern (drier ridgelines, damper hollows), so the fire can gut a moist pocket independently. Wind and slope are combined into simplified directional multipliers φ_w and φ_s that speed the front only along the downwind / upslope directions — real headfires. The per-cell ignition rate each frame is:

R(dir) = R₀ · [1 + max(0, dir·ŵ)(φ_w−1) + max(0, dir·ŝ)(φ_s−1)] · η_M(cell)

M_f slider — raise it toward and past 30% to watch head-fire ROS collapse to zero as η_M hits 0.
Wind / Slope — both bias spread toward downwind and upslope cells, the two dominant real-world accelerants of head-fire rate of spread.
Ignite — starts a single spot fire at the upwind, downslope edge; Reset Fuel Bed reseeds the moisture pattern and clears the burn.

This is a simplified, qualitatively faithful adaptation for teaching purposes — real fire behavior analysts use the full Rothermel equations (fuel load, surface-area-to-volume ratio, packing ratio, heat content) inside tools like BehavePlus and FARSITE.

Unburned fuel (moist → dry) Burning Burned out

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