Fundamentals - Wildland Fuel Fundamentals and Applications - page 32

the area of consideration. Fuelbed depth is an important parameter in fire behav-
ior systems that use the Rothermel ( 1972 ) model (Andrews 1986 ; Andrews 2014 )
(Table 2.2 ), and, because of this, it is a parameter that is commonly adjusted to
match observed with simulated fire behaviors in creating fire behavior fuel models
(Chap. 7; Burgan 1987 ). Burgan ( 1987 ), for example, mentions that a fire behavior
fuel model can be made more sensitive to wind by increasing fuelbed depth. Fu-
elbed depth is often used to describe only the depth of the surface fuel layer and it is
mostly used to derive fuel bulk densities in US fire models (Eq. 2.10).
Fuelbed depth has little ecological value since it is so highly variable across
space and time scales. Its greatest use is as input into point-level fire behavior mod-
els that simulate fire in one dimension, such as BEHAVE (Andrews 2014 ). Because
of its scale problems and high variability, it is often difficult to obtain an accurate
measurement of fuelbed depth. Initial attempts to accurately measure depth were to
envision a virtual sheet over the top of the surface fuel layer and visually estimat-
ing the average height of that sheet (Jensen et al. 1993 ). Moreover, it is difficult to
evaluate if widely spaced and distinctive fuel particles constitute part of the fuelbed.
For example, should widely scattered shrubs or occasional large logs be included
in the depth estimation (Fig. 2.4d ). Fruiting stalks on grass and forbs, as another
example, are widely scattered and are easily blown by wind because they are often
taller than the plant's foliage, making it quite difficult to determine if fruiting stalks
contribute to fire spread and are therefore used to estimate depth.

2.3.3.2 Packing Ratio ( β )

The packing ratio is an index used to represent the compactness of the fuelbed (Ro-
thermel 1972 ). It is easily quantified as the ratio ρ b : ρ p (fuelbed bulk density divided
by particle density). This variable was invented to simulate the important damping
effect of fuelbed looseness or compression on combustion using an index that is the
fraction of fuelbed volume occupied by fuel. In fact, Catchpole et al. ( 1998 ) found
that rate of spread decreased with the square root of the packing ratio. It had been
observed that fire intensity and rate of spread occur at two extremes of compact-
ness. Lack of fuel contagion causes loss of heat transfer in loose fuelbeds, while
low air-to-fuel ratios and poor heat penetration result in lower spread rates and
intensities in dense fuelbeds (Rothermel 1972 ). Between these two extremes is an
optimum range of fuelbed packing where there is the best balance of air, fuel, and
heat transfer, and this optimum packing ratio ( β op in Table 2.2 ) is greatly dependent
on the fuel particles and how they are arranged in the fuelbed. Sandberg et al. ( 2007 )
modified Rothermel's ( 1972 ) equations to include a damping coefficient represent-
ing fuel compactness based on a new variable called relative packing ratio, which is
the fuelbed packing ratio divided by the optimum packing ratio.
The main problem with packing ratio is that fuelbeds are often composed of
many kinds of fuel particles from grass blades to woody twigs and logs; therefore,
particle densities can be highly variable at very fine scales, resulting in highly vari-
able packing ratios. Moreover, optimum packing ratios can vary across the year