Canopy Fuels - Wildland Fuel Fundamentals and Applications - page 59

If conditions for active or passive crown fire are not met, then an independent crown
fire is simulated. Linking the van Wagner ( 1977 ); Nabel et al. ( 2014 ); and van Wag-
ner ( 1993 ) crown fire algorithms with Rothermel ( 1972 ) and Rothermel ( 1993 ) sur-
face fire algorithms required many assumptions, modifications, and scaling factors
for operational use (Finney 1998 ).
The final intensity of a crown fire I c (kW m −1 ) is calculated using the combined
loading of both canopy and surface fuel consumed in the flaming front along with
the rate of spread for active crown fires ( R C actual ) or for passive crown fires (surface
fire spread rate R ):

I

+ (

)( ) ( )

(4.7)

I = 300

b

CFBCBD CH CBHR −

c C actual

300 R

where CH is canopy height (m), CFB is canopy fuel burned (kg m −2 ) estimated from
the canopy fuel load ( CFL , kg −2 ) assuming all is consumed, and R is substituted for
R C actual if a passive crown fire.
Several limitations of these algorithms need mention. First, the basic relation-
ships in this model are empirical functions mostly derived from a limited set of
vegetation types (van Wagner 1977 ). There has been little validation of this model
for many fire-prone forested vegetation types of the world because of the difficulty
of experimentation with crown fires (e.g., Stocks et al. 2004 ). Next, the quantita-
tive linkages between surface and crown fire simulation are difficult to implement
because so many assumptions on the scale, behavior, and inertia of the fire had to
be made and these assumptions often introduced additional uncertainty in crown
fire behavior.
It is also important to note that the above crown fire model formulation only
concerns operational fire models. More sophisticated physics-based CFD (com-
putational fluid dynamics) modeling approaches are making improvements in the
simulation of crown fires (Linn 1997 ; Parsons et al. 2010 ), but there are still limita-
tions of this approach (Alexander and Cruz 2013 ; Zhang et al. 2014 ). CFD mod-
els simulate the behavior of a fire in three dimensions so fuels must be described
in three-dimensional volumetric cells called “voxels.” Parsons ( 2006 ) developed a
tool called FUEL3D that maps canopy fuel into voxels using allometric and fractal
relationships of tree biomass to simulate crown fires in CFD models. While CFD
modeling is mostly in the research stage with limited evaluation and most models
haven't yet been implemented for operational use, they illustrate the importance of
describing canopy fuels in a three-dimensional context.
From this thumbnail summary of operational crown fire simulation, it appears
that there are four variables in crown fire simulations that represent canopy fuels:
CBH, CBD, CH, and CFL . Crown fire initiation is dependent on CBH and CBD
(Eq. 5.1), while crown fire spread and intensity are dependent on CBD, CH, and
CFL (Eqs. 5.2, 5.7). One other canopy characteristic, canopy cover ( CC , %), is also
discussed here along with CBD, CH, CBH, and CFL because it is important in fuel
moisture and fire effects simulation.