Fundamentals - Wildland Fuel Fundamentals and Applications - page 21

In the Rothermel ( 1972 ) algorithms, reaction intensity ( I r ) is computed from
another equation (see Table 2.2 ):

I =Γ′ Wh ηη

(2.11)

r n ms

where W n is fuel loading (kg m −2 ) adjusted for the mineral content, Γ′ is the reac-
tion velocity (a dynamic variable that represents the rate and completeness of fuel
consumption), and η m and η s are damping functions to account for the effect of fuel
moisture and mineral content, respectively, on combustion (equations for all vari-
ables in Table 2.2 ). Two fuel properties have a major effect on reaction intensity.
Increasing fuel moisture and mineral content decreases I r using the damping coef-
ficients η m and η s that are represented by empirical relationships. The coefficient
η m is calculated using an empirical polynomial regression equation where the only
variable is the ratio of the fuel moisture content (FMC; %) to the moisture of extinc-
tion ( M x ; %; Eq. 29 in Rothermel ( 1972 ); see Table 2.2 ). These two fuel moisture
variables are the seventh and eighth important fuel property. The mineral content
damping coefficient ( η s ) is calculated using the following empirical equation devel-
oped by Philpot ( 1970 ):

− 0.19

η = 0.174 S

(2.12)

s e

where S e is the effective mineral content calculated as the amount of silica in the
fuel component minus the mineral content ( S T ). Mineral content ( S e and S T ) is the
ninth important fuel property. Fuelbed compactness is another important fuelbed
property affecting I r and it is often represented by the packing ratio ( β ) defined by:

β ρ

=

b

(2.13)

p

where ρ p is the average particle density of the particles that comprise the fuel com-
ponent (kg m −3 ), the eleventh important fuel property (Table 2.1 ).

2.2.2 Fire Behavior Assumptions

To simplify the spatial complexity of the combustion process, early fire scientists
had to make the assumption that fire spread can be represented by the movement
of a flame across a semipermeable surface using a one-dimensional point model
(Fig. 2.3 ; Rothermel 1972 ). This would have been a good assumption if (1) fuels
were homogeneously distributed over the scale of a burning, (2) fires act at only one
scale, and (3) the scale of the fire matched the scale of the fuels. But unfortunately,
the distribution, condition, characteristics, and consumption of burnable biomass
are highly complex over space and time (Frandsen and Andrews 1979 ; Chap. 6).
Therefore, the scale mismatch between fire modeling and fuel properties may bias
the simulation of fire in a one-dimensional approach. For example, an input fuel