Wind and Slope Multiply the No-Wind Rothermel Spread Rate
Rothermel does not put wind and slope inside the energy balance. It computes the no-wind, no-slope spread rate first, then multiplies it by two dimensionless factors: \( R = R_0 (1 + \phi_w + \phi_s) \). The wind factor \( \phi_w \) rises with midflame wind speed raised to a power that itself depends on how packed the fuel bed is, so the same wind speeds up a grass fire far more than a dense litter bed. The slope factor \( \phi_s \) depends on the square of the slope steepness, which is why a fire crossing a 30 percent slope roughly doubles and a 60 percent slope is a different fire entirely. Two things trip people up. First, the wind that matters is midflame wind, not the wind at 10 metres in the forecast, so a wind-reduction factor for the canopy has to be applied before the equation is used. Second, the factors are additive multipliers on \( R_0 \), so a fire in fuel that will barely burn stays slow no matter how hard the wind blows, because anything times a near-zero \( R_0 \) is still near zero. After this Concept you can predict the direction and rough size of a spread-rate change from a wind or slope change.
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Rothermel does not put wind and slope inside the energy balance. It computes the no-wind, no-slope spread rate first, then multiplies it by two dimensionless factors: \( R = R_0 (1 + \phi_w + \phi_s) \). The wind factor \( \phi_w \) rises with midflame wind speed raised to a power that itself depends on how packed the fuel bed is, so the same wind speeds up a grass fire far more than a dense litter bed. The slope factor \( \phi_s \) depends on the square of the slope steepness, which is why a fire crossing a 30 percent slope roughly doubles and a 60 percent slope is a different fire entirely. Two things trip people up. First, the wind that matters is midflame wind, not the wind at 10 metres in the forecast, so a wind-reduction factor for the canopy has to be applied before the equation is used. Second, the factors are additive multipliers on \( R_0 \), so a fire in fuel that will barely burn stays slow no matter how hard the wind blows, because anything times a near-zero \( R_0 \) is still near zero. After this Concept you can predict the direction and rough size of a spread-rate change from a wind or slope change.
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