The Physics of Wildfire Spread
A wildfire is not simply burning trees — it is a coupled athermo-chemical system involving turbulent convection, radiant heat transfer, pyrolysis chemistry, and atmospheric interaction. Understanding how it spreads is essential for forecasting it.
1. The Fire Triangle
Fire requires three elements simultaneously. Remove any one and the fire dies:
Dry organic matter: grass, shrubs, trees. Quantity, moisture content, arrangement.
Atmospheric oxygen (21%) sustains combustion. Wind replenishes it continuously.
Temperature above ignition threshold (~250–300 °C for cellulose).
Firefighting targets one of these: water removes heat and moisture, fuel breaks interrupt the fuel supply, firebreaks remove fuel, and aerial retardants coat fuel to deny oxygen.
2. Combustion and Pyrolysis
Wood does not directly burn — it first undergoes pyrolysis: thermal decomposition at 200–300 °C that releases flammable gases (CO, hydrocarbons, H₂) and leaves charcoal. The gases burn, not the solid wood.
Complete: C₆H₁₀O₅ + 6 O₂ → 6 CO₂ + 5 H₂O (ΔH ≈ −2800 kJ/mol)
Typical wood heat of combustion: 18–22 MJ/kg (dry weight)
Moisture content is the single biggest predictor of fire behaviour. Fuel at 30% moisture content barely ignites; fuel at 4% moisture ignites explosively. Each 1% of moisture requires energy to evaporate before combustion can begin.
3. Heat Transfer Mechanisms
Fire spreads because heat is transferred to unburned fuel ahead of the flame front:
- Radiation: Flame emits infrared radiation that heats and dries nearby fuel. Dominates in dense forests and under calm wind conditions. Scales with T⁴ — even small increases in flame temperature dramatically increase radiant flux.
- Convection: Rising hot gases create a convective column that bends forward in wind, pre-heating and drying fuel ahead of the fire. Accounts for ~50–70% of spread rate in most fires.
- Conduction: Slow and minor in wildfire — unimportant compared to radiation and convection.
4. The Rothermel Fire Spread Model
The Rothermel model (1972) is the standard used by fire agencies worldwide (including the US Forest Service's FARSITE tool). It predicts the rate of spread (ROS) as a function of fuel and weather:
I_R — reaction intensity (kW/m²)
ξ — propagating flux ratio
φ_W, φ_S — wind and slope multipliers
ρ_b · ε · Q_ig — volumetric heat of ignition
The model is empirical — fitted to laboratory fire table experiments. It captures the main trends but breaks down in extreme conditions (very high winds, steep terrain).
5. Slope, Wind, and Topography
Wind is the dominant driver of rapid spread. It:
- Bends the flame toward unburned fuel, increasing convective pre-heating.
- Replenishes oxygen to the flame base.
- Dries fuel on the windward side.
- Carries burning embers (firebrands) kilometres ahead — "spotting".
Slope creates exactly the same geometry as wind without actually blowing: fire running uphill has the flame naturally inclined over unburned fuel above. A 20° slope doubles the spread rate compared to flat terrain; 45° slopes can increase it 10-fold.
6. Crown Fires and Spotting
Surface fires burn ground litter and shrubs. More dangerous are crown fires that spread through the tree canopy — moving at 2–10× the surface rate and nearly impossible to suppress directly.
Crown fires require a "ladder" of vegetation connecting the surface to the canopy (young trees, dense shrubs) and sustained high wind. Once the canopy is burning, the fire is self-sustaining.
Spotting occurs when firebrands — burning bark, twigs, cones — are lofted by the convective column and carried by wind to land far ahead of the fire front. Spot fires ignite and merge back with the main fire, creating a chaotic, multi-headed front that overwhelms containment.
7. Fire Weather
Fire weather indices combine temperature, humidity, wind, and drought to predict fire danger:
- Fine Fuel Moisture Code (FFMC): moisture in surface litter — responds within hours to weather changes.
- Duff Moisture Code (DMC): deep organic matter moisture — days-to-weeks timescale.
- Fire Weather Index (FWI): combines wind speed with moisture codes to give overall fire intensity rating.
The most dangerous conditions worldwide share a signature: hot (>35 °C), dry (<20% relative humidity), and windy (>40 km/h). In California, this is the Diablo/Santa Ana wind pattern; in south-eastern Australia, it is the hot northerly ahead of a cold front.
8. Climate Change and Megafires
Climate change expands extreme fire weather in three ways:
- Higher temperatures: Increase vapour pressure deficit (VPD), drying vegetation faster. Each 1 °C warming roughly doubles the area burned in fire-prone regions.
- Longer fire seasons: Earlier snowmelt and later autumn rains extend the window of flammable vegetation by weeks per decade.
- Drought accumulation: Multi-year droughts (amplified by warming) dry deep fuels that normally resist ignition — creating conditions for catastrophic fires on timescales of decades.
The 2019-2020 Australian "Black Summer" burned 24 million hectares — comparable to the entire area of the United Kingdom — and was rendered 30% more likely by anthropogenic climate change (attribution studies).
9. Try the Simulation
The fire & smoke simulation on this site uses a cellular automaton model where each cell can be grass, burning, or burned. Wind is modelled as a directional spread probability multiplier. Watch how slope and wind interact.