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A review of wildland fire spread modelling,
1990-present
1: Physical and quasi-physical models
A.L. Sullivan
February 1, 2008
Ensis1 Bushfire Research 2
PO Box E4008, Kingston, ACT 2604, Australia
email: Andrew.Sullivan@ensisjv.com or als105@rsphysse.anu.edu.au
phone: +61 2 6125 1693, fax: +61 2 6125 4676
version 3.0
Abstract
In recent years, advances in computational power and spatial data analysis (GIS,
remote sensing, etc) have led to an increase in attempts to model the spread and
behaviour of wildland fires across the landscape. This series of review papers endeav-
ours to critically and comprehensively review all types of surface fire spread models
developed since 1990. This paper reviews models of a physical or quasi-physical
nature. These models are based on the fundamental chemistry and/or physics of
combustion and fire spread. Other papers in the series review models of an empiri-
cal or quasi-empirical nature, and mathematical analogues and simulation models.
Many models are extensions or refinements of models developed before 1990. Where
this is the case, these models are also discussed but much less comprehensively.
Introduction
History
The field of wildland fire behaviour modelling has been active since the 1920s. The work
of Hawley (1926) and Gisborne (1927, 1929) pioneered the notion that understanding of
the phenomenon of wildland fire and the prediction of the danger posed by a fire could be
gained through measurement and observation and theoretical considerations of the factors
that might influence such fires. Despite the fact that the field has suffered from a lack of
1A CSIRO/Scion Joint Venture
2current address: Department of Theoretical Physics,
Research School of Physical Sciences and Engineering,
The Australian National University, Canberra 0200, Australia.
1

readily achievable goals and consistent funding (Williams, 1982), the pioneering work by
those most closely affected by wildland fire–the foresters and other land managers–has led
to a broad framework of understanding of wildland fire behaviour that has enabled the
construction of operational models of fire behaviour and spread that, while not perfect
for every situation, at least get the job done.
In the late 1930s and early 1940s, Curry and Fons (1938, 1940), and Fons (1946) brought
a rigorous physical approach to the measurement and modelling of the behaviour of wild-
land fires. In the early 1950s, formal research initiatives by Federal and State Government
forestry agencies commenced concerted efforts to build fire danger rating systems that em-
bodied a fire behaviour prediction component in order to better prepare for fire events.
In the US this was through the Federal US Forest Service and through State agencies; in
Canada this was the Canadian Forest Service; in Australia this was through the Com-
monwealth Forestry and Timber Bureau in conjunction with various state authorities.
In the 1950s and 60s, spurred on by incentives from defense budgets, considerable effort
was expended exploring the effects of mass bombing (such as occurred in Dresden or
Hamburg, Germany, during World War Two) and the collateral incendiary effects of
nuclear weapons (Lawson, 1954; Rogers and Miller, 1963). This research effort was closely
related to large forest or conflagration fires and had the spin-off of bringing additional
research capacity into the field (Chandler et al., 1963). This resulted in an unprecedented
boom in the research of wildland fires. The late 1960s saw a veritable explosion of research
publications connected to wildland fire that dominated the fields of combustion and flame
research for some years.
The 1970s saw a dwindling of research interest from defense organisations and by the
1980s, research into the behaviour of wildland fires returned to those that had direct
interest in the understanding and control of such phenomena. By the 1980s, it was of
occasional interest to journeyman mathematicians and physicists on their way to bigger,
and more achievable, goals.
An increase in the capabilities of remote sensing, geographical information systems and
computing power during the 1990s resulted in a revival in the interest of fire behaviour
modelling, this time applied to the prediction of fire spread across the landscape.
Background
This series of review papers endeavours to comprehensively and critically review the ex-
tensive range of modelling work that has been conducted in recent years. The range of
methods that have been undertaken over the years represents a continuous spectrum of
possible modelling (Karplus, 1977), ranging from the purely physical (those that are based
on fundamental understanding of the physics and chemistry involved in the combustion of
biomass fuel and behaviour of a wildland fire) through to the purely empirical (those that
have been based on phenomenological description or statistical regression of observed fire
behaviour). In between is a continuous meld of approaches from one end of the spectrum or
the other. Weber (1991a) in his comprehensive review of physical wildland fire modelling
proposed a system by which models were described as physical, empirical or statistical,
depending on whether they account for different modes of heat transfer, make no dis-
tinction between different heat transfer modes, or involve no physics at all. Pastor et al.
2

(2003) proposed descriptions of theoretical, empirical and semi-empirical, again depend-
ing on whether the model was based on purely physical understanding, of a statistical
nature with no physical understanding, or a combination of both. Grishin (1997) divided
models into two classes, deterministic or stochastic-statistical. However, these schemes
are rather limited given the combination of possible approaches and, given that describing
a model as semi-empirical or semi-physical is a ‘glass half-full or half-empty’ subjective
issue, a more comprehensive and complete convention was required.
Thus, this review series is divided into three broad categories: physical and quasi-physical
models; empirical and quasi-empirical models; and simulation and mathematical analogue
models. In this context, a physical model is one that attempts to represent both the
physics and chemistry of fire spread; a quasi-physical model attempts to represent only
the physics. An empirical model is one that contains no physical basis at all (generally
only statistical in nature), a quasi-empirical model is one that uses some form of physical
framework upon which to base the statistical modelling chosen. Empirical and quasi-
empirical models are further subdivided into field-based and laboratory-based. Simulation
models are those that implement the preceding types of models in a simulation rather than
modelling context. Mathematical analogue models are those that utilise a mathematical
precept rather than a physical one for the modelling of the spread of wildland fire.
Since 1990, there has been rapid development in the field of spatial data analysis, e.g.
geographic information systems and remote sensing. Following this, and the fact that
there has not been a comprehensive critical review of fire behaviour modelling since Weber
(1991a), I have limited this review to works published since 1990. However, as much of
the work that will be discussed derives or continues from work carried out prior to 1990,
such work will be included much less comprehensively in order to provide context.
Previous reviews
Many of the reviews that have been published in recent years have been for audiences other
than wildland fire researchers and conducted by people without an established background
in the field. Indeed, many of the reviews read like purchase notes by people shopping
around for the best fire spread model to implement in their part of the world for their
particular purpose. Recent reviews (e.g. Perry (1998); Pastor et al. (2003); etc), while
endeavouring to be comprehensive, have offered only superficial and cursory inspections
of the models presented. Morvan et al. (2004) takes a different line by analysing a much
broader spectrum of models in some detail and concludes that no single approach is going
to be suitable for all uses.
While the recent reviews provide an overview of the models and approaches that have
been undertaken around the world, mention must be made of significant reviews pub-
lished much earlier that discussed the processes in wildland fire propagation themselves.
Foremost is the work of Williams (1982), which comprehensively covers the phenomenol-
ogy of both wildland and urban fire, the physics and chemistry of combustion, and is
recommended reading for the beginner. The earlier work of Emmons (1963, 1966) and
Lee (1972) provides a sound background on the advances made during the post-war boom
era. Grishin (1997) provides an extensive review of the work conducted in Russia in the
1970s, 80s and 90s.
3

This particular paper will discuss those models based upon the fundamental principles
of the physics and chemistry of wildland fire behaviour. Later papers in the series will
discuss those models based upon observation of fire behaviour and upon mathematical
analogies to fire spread. As the laws of physics are the same no matter the origin of
the modeller, or the location of the model, physical models are essentially based on the
same rules and it is only the implementation of those rules that differs in each model.
A brief discussion of the fundamentals of wildland fire behaviour covering the chemistry
and physics is given, followed by discussions of how these are applied in physical models
themselves. This is then followed by a discussion of the quasi-physical models.
Fundamentals of fire and combustion
Wildland fire is the complicated combination of energy released (in the form of heat)
due to chemical reactions (broadly categorised as an oxidation reaction) in the process
of combustion and the transport of that energy to surrounding unburnt fuel and the
subsequent ignition of said fuel. The former is the domain of chemistry (more specifically,
chemical kinetics) and occurs on the scale of molecules, and the latter is the domain of
physics (more specifically, heat transfer and fluid mechanics) and occurs on scales ranging
from millimetres up to kilometres (Table 1). It is the interaction of these processes over
the wide range of temporal and spatial scales that makes the modelling of wildland fire
behaviour a not inconsiderable problem.
Grishin (1997, pg. 81) proposed five relative independent stages in the development of a
deterministic physical model of wildland fire behaviour:
1. Physical analysis of the phenomenon of wildland fire spread; isolation of the mech-
anism governing the transfer of energy from the fire front into the environment;
definition of the medium type, and creation of a physical model of the phenomenon.
2. Determination of the reaction and thermophysical properties of the medium, the
transfer coefficients and structural parameters of the medium, and deduction of
the basic system of equations with corresponding additional (boundary and initial)
conditions.
3. Selection of a method of numerical solution of the problem, and derivation of dif-
ferential equations approximating the basic system of equations.
4. Programming; test check of the program; evaluation of the accuracy of the difference
scheme; numerical solution of the system of equations.
5. Testing to see how well the derived results comply with the real system; their phys-
ical interpretation; development of new technical suggestions for ways of fighting
wildland fire.
Clearly, stages one and two represent considerable hurdles and sources of contention for
the best method in which to represent the phenomenon of wildland fire. This section aims
to provide a background understanding of the chemistry and physics involved in wildland
fire. However, it must be noted that even though these fields have made great advances
in the understanding of what is going on in these processes, research is still very active
and sometimes cause for contention (di Blasi, 1998).
4

Chemistry of combustion
The chemistry of combustion involved in wildland fire is necessarily a complex and com-
plicated matter. This is in part due to the complicated nature of the fuel itself but also
in the range of conditions over which combustion can occur which dictates the evolution
of the combustion process.
Fuel chemistry
Wildland fuel is composed of live and dead plant material consisting primarily of leaf lit-
ter, twigs, bark, wood, grasses, and shrubs. (Beall and Eickner, 1970), with a considerable
range of physical structures, chemical components, age and level of biological decompo-
sition. The primary chemical constituent of biomass fuel is cellulose (of chemical form
(C6O5H10)n), which is a polymer of a glucosan (variant of glucose) monomer, C6O6H12
(Shafizadeh, 1982; Williams, 1982). Cellulose is a linear, unbranched polysaccharide of ≃
10,000 D-glucose units in β(1, 4) linkage3. The parallel chains are held together by hy-
drogen bonds, a non-covalent linage in which surplus electron density on hydroxyl group
oxygens is distributed to hydrogens with partial positive charge on hydroxyl groups of
adjacent residues (Ball et al., 1999).
Other major chemical components of wildland fuel include hemicelluloses (copolymers of
glucosan and a variety of other possibly monomers) and lignin (a phenolic compound)
in varying amounts, depending upon the species, cell type and plant part (See Table 2).
Minerals, water, salts and other extractives and inorganics also exist in these fuels. The
cellulose is the same in all types of biomass, except for the degree of polymerisation (i.e.
the number of monomer units per polymer). Solid fuel is often referred to as a condensed
phase fuel in the combustion literature.
Cellulose is an extraordinarily stable polysaccharide due to its structure: insoluble, rel-
atively resistant to acid and base hydrolysis, and inaccessible to all hydrolytic enzymes
except those from a few biological sources. Cellulose is the most widely studied sub-
stance in the field of wood and biomass combustion; by comparison, few studies have
been carried out on the combustion of hemicelluloses or lignin (di Blasi, 1998), due per-
haps to the relative thermal instability of these compounds. The degradation of biomass
is generally considered as the sum of the contribution of its main components (cellulose,
hemicelluloses and lignin) but the extrapolation of the thermal behaviour of the main
biomass components to describe the kinetics of complex fuels is only a rough approxima-
tion (di Blasi, 1998). The presence of inorganic matter in the biomass structure can act
as a catalyst or an inhibitor for the degradation of cellulose; differences in the purity and
physical properties of cellulose and hemicelluloses and lignin also play an important role
in the degradation process (di Blasi, 1998).
3The D- prefix refers to one of two configurations around the chiral centre of carbon-5. The β(1, 4)
refers to the configuration of the covalent link between adjacent glucose units, often called a glycosidic
bond. There are two possible geometries around C-1 of the pyranose (or 5-membered) ring: in the β
anomer the hydrogen on C-1 sits on the opposite side of the ring to that on C-2; in the α anomer it is
on the same side. The glycosidic bond in cellulose is between C-1 of one β D-glucose residue and the
hydroxyl group on C-4 of the next unit (see Figure 1).
5

Combustion reactions
Chemical reactions can be characterised by the amount of energy required to initiate
a reaction, called the activation energy, Ea. This energy controls the rate of reaction
through an exponential relation, which can be derived from first principles, known as the
Arrhenius law:
k = A(−EaRT ) (1)
where k is the reaction rate constant, A is a pre-exponential factor related to collision
rate in Eyring theory, R is the gas constant and T is the absolute temperature of the
reactants. Thus, the rate constant, k, is a function of the temperature of the reactants;
generally the higher the temperature, the faster the reaction will occur.
Solid phase reactions–competing processes
When heat is applied to cellulose, the cellulose undergoes a reaction called thermal degra-
dation. In the absence of oxygen, this degradation is called pyrolysis, even though in
the literature the term pyrolysis is often used incorrectly to describe any form of thermal
degradation (Babrauskas, 2003). Cellulose can undergo two forms of competing degrada-
tion reaction: volatilisation and char formation (Figure 2). While each of these reactions
involves the depolymerisation of the cellulose (described as the ‘unzipping’ of the polymer
into shorter strands (Williams, 1982, 1985)), each has a different activation energy and
promoting conditions, and result in different products and heat release.
Volatilisation generally occurs in conditions of low or nil moisture and involves thermoly-
sis of glycosidic linkages, cyclisation and the release of free levoglucosan via thermolysis at
the next linkage in the chain (Ball et al., 2004). This reaction is endothermic (requiring
about 300 J g−1 (Ball et al., 1999)) and has a relatively high activation energy (about
240 kJ mol−1(di Blasi, 1998)). The product, levoglucosan (sometimes described as ‘tar’
(Williams, 1982)), is highly unstable and forms the basis of a wide range of subsequent
species following further thermal degradation that readily oxidise in the process of com-
bustion, resulting in a multitude of intermediate and final, gas and solid phase, products
and heat.
Char formation, on the other hand, occurs when thermal degradation happens in the
presence of moisture or low rates of heating. In this competing reaction pathway, the
nucleophile that bonds to the thermolysed carbo-cation at C-1 is a water molecule. The
initial product is a reducing end which has ‘lost the opportunity’ to volatilise. Instead,
further heating of such fragments dehydrates, polyunsaturates, decarboxylates, and cross-
links the carbon skeleton of the structure, ultimately producing char. This reaction has
a relatively low activation energy (about 150 kJ mol−1(di Blasi, 1998)) and is exothermic
(releasing about 1 kJ g−1).
Thus, the thermal degradation of cellulose results in two competing pathways controlled
by thermal and chemical feedbacks such that if heating rates are low and/or moisture
is present, the charring pathway is promoted. If sufficient energy is released in this
6

process (or additional heat is added) or moisture evaporated, then cyclisation and the
release of free levoglucosan from thermolysed, positively charged chain fragments, becomes
statistically favoured over nucleophilic addition of water and char production. If the
subsequent combustion of the levoglucosan and products releases enough energy then this
process becomes self-supporting. However, if the heat released is convected away from
the reactants or moisture is trapped, then the char-formation path becomes statistically
favoured. These two competing pathways will oscillate until conditions become totally
self-supporting or thermal degradation stops.
Gas phase reactions
Gas phase combustion of levoglucosan and its derivative products is highly complex and
chaotic. The basic chemical reaction is assumed to be:
C6O5H10 + 6O2 → 6CO2 + 5H2O, (2)
however, this assumes that all intermediate reactions, consisting of oxidisation reactions of
derivative products mostly, are complete. But the number of pathways that such reactions
can take is quite large, and not all paths will result in completion to water and carbon
dioxide.
As an example of a gas-phase hydrocarbon reaction, Williams (1982) gives a non-exhaustive
list of 14 possible pathways for the combustion of CH4, one of the possible intermediates of
the thermal degradation of levoglucosan, to H2O and CO2. Intermediate species include
CH3, H2CO, HCO, CO, OH and H2.
At any stage in the reaction process, any pathway may stop (through loss of energy or
reactants) and its products be advected away to take no further part in combustion. It is
these partially combusted components that form smoke. The faster and more turbulent
the reaction, the more likely that reaction components will be removed prior to complete
combustion, hence the darker and thicker the smoke from a headfire, as opposed to the
lighter, thinner smoke from a backing fire (Cheney and Sullivan, 1997).
Because the main source of heat into the combustion process comes from the exothermic
reaction of the gas-phase products of levoglucosan and these products are buoyant and
generally convected away from the solid fuel, the transport of the heat generated from
these reactions is extremely complex and brings us to the physics of combustion.
Physics of combustion
The physics involved in the combustion of wildland fuel and the behaviour of wildland
fires is, like the chemistry, complicated and highly dependent on the conditions in which
a fire is burning. The primary physical process in a wildland fire is that of heat transfer.
Williams (1982) gives nine possible mechanisms for the transfer of heat from a fire:
1. Diffusion of radicals
7

2. Heat conduction through a gas
3. Heat conduction through condensed materials
4. Convection through a gas
5. Liquid convection
6. Fuel deformation
7. Radiation from flames
8. Radiation from burning fuel surfaces
9. Firebrand transport.
1, 2 and 3 could be classed as diffusion at the molecular level. 4 and 5 are convection
(although the presence of liquid phase fuel is extremely rare) but can be generalised
to advection to include any transfer of heat through the motion of gases. 7 and 8 are
radiation. 6 and 9 could be classed as solid fuel transport. This roughly translates to the
three generally accepted forms of heat transfer (conduction, convection and radiation) plus
solid fuel transport, which, as Emmons (1966) points out, is not trivial or unimportant
in wildland fires.
The primary physical processes driving the transfer of heat in a wildland fire are that
of advection and radiation. In low wind conditions, the dominating process is that of
radiation (Weber, 1989). In conditions where wind is not insignificant, it is advection
that dominates (Grishin et al., 1984). However, it is not reasonable to assume one works
without the other and thus both mechanisms must be considered.
In attempting to represent the role of advection in wildland fire spread, the application of
fluid dynamics is of prime importance. This assumes that the gas flow can be considered
as a continuous medium or fluid.
Advection or Fluid transport
Fluid dynamics is a large area of active research and the basic outlines of the principles
are given here. The interested reader is directed to a considerable number of texts on the
subject for more in-depth discussion (e.g. Batchelor (1967); Turner (1973)).
The key aspect of fluid dynamics and its application to understanding the motion of
gases is the notion of continuity. Here, the molecules or particles of a gas are considered
to be continuous and thus behave as a fluid rather than a collection of particles. Another
key aspect of fluid mechanics (and physics in general) is the fundamental notion of the
conservation of quantities which is encompassed in the fluidised equations of motion.
A description of the rate of change of the density of particles in relation to the velocity of
the particles and distribution of particles provides a method of describing the continuity
of the particles. By taking the zeroth velocity moment of the density distribution (multi-
plying by uk (where k = 0, in this case) and integrating with respect to u), the equation
8

of continuity is obtained. If the particles are considered to have mass, then the continuity
equation also describes the conservation of mass:
∂ρ
∂t +∇.(ρu) = 0, (3)
where ρ is density, t is time, and u is the fluid velocity (with vector components u, v, and
w) and ∇. is the Laplacian or gradient operator (i.e. in three dimensions i ∂∂x + j
∂
∂y +k
∂
∂z ).
This is called the fluidised form of the continuity equation and is presented in the form
of Euler’s equations as a partial differential equation.
However, in order to solve this equation, the evolution of u is needed. This incompleteness
is known as the closure problem and is a characteristic of all the fluid equations of motion.
The next order velocity moment (k = 1) can be taken and the evolution of the velocity
field determined. This results in an equation for the force balance of the fluid or the
conservation of momentum equation:
∂ρu
∂t +∇.(ρu)u+∇p = 0, (4)
where p is pressure. However, the evolution of p is then needed to solve this equation.
This can be determined by taking the second velocity moment (k=2) which provides an
equation for the conservation of energy, but it itself needs a further, incomplete, equation
to provide a solution. One can either continue determining higher order moments ad
nauseum in order to provide a suitably approximate solution (as the series of equations
can never be truly closed) or, as is more frequently done, utilise an equation of state to
provide the closure mechanism. In fluid dynamics, the equation of state is generally that
of the ideal gas law (e.g. pV = nRT ). The above equations are in the form of the Euler
equations and represent a simplified (inviscid) form of the Navier-Stokes equations.
Buoyancy, convection and turbulence
The action of heat release from the chemical reaction within the combustion zone results
in heated gases, both in the form of combustion products as well ambient air heated by, or
entrained into, the combustion products. The reduction in density caused by the heating
of the gas increases the buoyancy of the gas and results in the gas rising as convection
which can then lead to turbulence in the flow. Turbulence acts over the entire range of
scales in the atmosphere, from the fine scale of flame to the atmospheric boundary layer,
and acts to mix heated gases with ambient air and to mix the heated gases with unburnt
solid phase fuels. It also acts to increase flame immersion of fuel. The action of turbulence
also affects the transport of solid phase combustion, such as that of firebrands, resulting
in spotfires downwind of the main burning front.
Suitably formulated Navier-Stokes equations can be used to incorporate the effects of
buoyancy, convection and turbulence. However, these components of the flow can be
investigated individually utilising particular approximations, such as Boussinesq’s concept
of eddy viscosity for the modelling of turbulence, or buoyancy as a renormalised variable
9

for modelling the effects of buoyancy. Specific methods for numerically solving turbulence
within the realm of fluid dynamics, including renormalisation group theory (RNG) and
large eddy simulation (LES), have been developed. Convective flows are generally solved
within the broader context of the advection flow with a prescribed heat source.
Radiant heat transfer
Radiant heat is a form of electromagnetic radiation emitted from a hot source and is in
the infra-red wavelength band. In flame, the primary source of the radiation is thermal
emission from carbon particles, generally in the form of soot (Gaydon and Wolfhard,
1960), although band emission from electronic transitions in molecules also contributes
to the overall radiation from a fire.
The general method of modelling radiant heat transfer is through the use of a radiant
transfer equation (RTE) of which the simplest is that of the Stefan-Boltzmann equation:
q = σT 4, (5)
where σ is the Stefan-Boltzmann constant (5.67 × 10−8JK−4 m−2 s−1 and T is the ra-
diating temperature of the surface (K). While it is possible to approximate the radiant
heat flux from a fire as a surface emission from the flame face, this does not fully capture
the volumetric emission nature of the flame (Sullivan et al., 2003) and can lead to inac-
curacies in flux estimations if precise flame geometry (i.e. view factor), temperature and
emmissivity equivalents are not known.
More complex solutions of the RTE, such as treating the flame as a volume of radiation
emitting, scattering and absorbing media, can improve the prediction of radiant heat
but are necessarily more computationally intensive; varying levels of approximation (both
physical and numerical) are frequently employed to improve the computational efficiency.
The Discrete Transfer Radiation Model (DTRM) solves the radiative transfer equation
throughout a domain by a method of ray tracing from surface elements on its boundaries
and thus does not require information about the radiating volume itself. Discrete Ordinate
Method (DOM) divides the volume into discrete volumes for which the full RTE is solved
at each instance and the sum of radiation along all paths from an observer calculated. The
Differential Approximation (or P1 method) solves the RTE as a diffusion equation which
includes the effect of scattering but assumes the media is optically thick. Knowledge about
the media’s absorption, scattering, refractive index, path length and local temperature
are required for many of these solutions. Descriptions of methods for solving these forms
of the RTE are given in texts on radiant heat transfer (e.g. Drysdale (1985)). Sacadura
(2005) and Goldstein et al. (2006) review the use of radiative heat transfer models in a
wide range of applications.
Transmission of thermal radiation can be affected by smoke or band absorption by certain
components of the atmosphere (e.g CO2, H2O).
10

Firebrands (solid fuel transport)
Determination of the transport of solid fuel (i.e. firebrands), which leads to the initiation
of spotfires downwind of the main fire front is highly probabilistic (Ellis, 2000) and not
readily amenable to a purely deterministic description. This is due in part to the wide
variation in firebrand sources and ignitions and the particular flight paths any firebrand
might take. Maximum distance that a firebrand may be carried is determined by the
intensity of the fire and the updraught velocity of the convection, the height at which the
firebrand was sourced and the wind profile aloft (Albini, 1979; Ellis, 2000). Whether or
not the firebrand lands alight and starts a spotfire is dependent upon the nature of the
firebrand, how it was ignited, its combustion properties (including flaming lifetime) and
the ignition properties of the fuel in which it lands (e.g. moisture content, bulk density,
etc) (Plucinski, 2003).
Atmospheric interactions
The transport of the gas phase of the combustion products interacts with the atmosphere
around it, transferring heat and energy, through convection and turbulence. The condition
of the atmosphere, particularly the lapse rate, or the ease with which heated parcels of
air rise within the atmosphere, controls the impact that buoyancy of the heated air from
the combustion zone has on the atmosphere and the fire.
Changes in the ambient meteorological conditions, such as changes in wind speed and
direction, moisture, temperature, lapse rates, etc, both at the surface and higher in the
atmosphere, can have a significant impact on the state of the fuel (moisture content),
the behaviour of a fire, its growth, and, in turn, the impact that fire can have on the
atmosphere itself.
Topographic interactions
The topography in which a fire is burning also plays a part in the way in which energy is
transferred to unburnt fuel and the ambient atmosphere. It has long been recognised that
fires burn faster upslope than they do down, even with a downslope wind. This is thought
to be due to increased transfer of radiant heat due to the change in the geometry between
the fuel on the slope and the flame, however recent work (Wu et al., 2000) suggests that
there is also increased advection in these cases.
Physical Models
This section briefly describes each of the physical models that were developed since 1990
(Table 3). Many are based on the same basic principles and differ only in the methodology
of implementation or the purpose of use. They are presented in chronological order of
first publication. Some have continued development, some have been implemented and
tested against observations, others have not. Many are implemented in only one or two
11

dimensions in order to improve computational or analytical feasibility. Where information
about the performance of the model on available computing hardware is available, this is
given.
Weber (1991)
Weber’s (1991b) model was an attempt to provide the framework necessary to build a
physical model of fire spread through wildland fuel, rather than an attempt to actually
build one. To that end, Weber highlights several possible approaches but does not give
any definitive answer.
Weber begins with a reaction-transport formulation of the conservation of energy equa-
tion, which states that the rate of change of enthalpy per unit time is equal to the spatial
variation of the flux of energy plus heat generation. He then formulates several com-
ponents that contribute to the overall flux of energy, including radiation from flames,
radiation transfer to fuel through the fuel, advection and diffusion of turbulent eddies.
Heat is generated through a chemical reaction that is modelled by an Arrhenius law which
includes heat of combustion.
This results in a first cut model that is one dimensional in x plus time. Advection,
radiation and reaction components allow the evolution of the fluid velocity to be followed.
Solid phase and gas phase fuel are treated separately due to different energy absorption
characteristics.
In a more realistic version of this model, Weber treats the phase differences more explicitly,
producing two coupled equations for the conservation of energy. The coupling comes
from the fact that when the solid volatilises it releases flammable gas that then combusts,
returning a portion of the released energy back to the solid for further volatilisation.
Weber determines that in two dimensions, the solution for the simple model is a two-
dimensional travelling wave that produces two parametric equations for spatial x and y
that yields an ellipse whose centre has been shifted. Weber favourably compares this
result with that of Anderson et al. (1982), who first formalised the spread of a wildland
fire perimeter as that of an expanding ellipse. No performance data are given.
AIOLOS-F (CINAR S.A., Greece)
AIOLOS-F was developed by CINAR S.A., Greece, as a decision support tool for wildland
fire behaviour prediction. It is a computational fluid dynamics model that utilises the
3-dimensional form of the conservation laws to couple the combustion of a fuel layer
with the atmosphere to model forest fire spread (Croba et al., 1994). It consists of two
components, AIOLOS-T which predicts the local wind field and wind-fire interaction, and
AILOS-F which models the fuel combustion.
The gas-phase conservation of mass equation is used to calculate the local wind perturba-
tion potential, the gas-phase conservation of momentum is used to determine the vertical
component of viscous flow, and a state equation to predict the air density and pressure
change with air temperature (Lymberopoulos et al., 1998).
12

The combustion model is a 3D model of the evolution of enthalpy from which change in
solid-phase temperature is determined. A thermal radiation heat transfer equation pro-
vides the radiant heat source term. Fuel combustion is modelled through a 3-dimensional
fuel mixture-fraction evolution that is tied to a single Arrhenius Law for the consumption
of solid phase fuel. The quantity of fuel consumed by the fire within a time interval is an
exponential function of the mixture fraction.
The equations are solved iteratively and in precise order such that the wind field is solved
first, the enthalpy, mixture-fraction, and temperature second. These are then used to
determine the change in air density which is then fed back into the wind field equations
taking into account the change in buoyancy due to the fire. The enthalpy, mixture-fraction
and temperature are then updated with the new wind field. This is repeated until a
solution converges, then the amount of fuel consumed for that time step is determined
and the process continues for the next time step.
Fuel is assumed to be a single layer beneath the lowest atmosphere grid. Fuel is specified
from satellite imagery on grids with a resolution in the order of 80 m. No data on cal-
culation time is given, although it is described (Croba et al., 1994; Lymberopoulos et al.,
1998) as being faster than real time.
FIRETEC (Los Alamos National Laboratory, USA)
FIRETEC (Linn, 1997), developed at the Los Alamos National Laboratory, USA, is a
coupled multiphase transport/wildland fire model based on the principles of conservation
of mass, momentum and energy. It is fully 3-dimensional and in combination with a hy-
drodynamics model called HIGRAD (Reisner et al., 1998, 2000a,b), which is used to solve
equations of high gradient flow such as the motions of the local atmosphere, it employs
a fully compressible gas transport formulation to represent the coupled interactions of
the combustion, heat transfer and fluid mechanics involved in wildland fire (Linn et al.,
2002b).
FIRETEC is described by the author as self-determining, by which it is meant that
the model does not use prescribed or empirical relations in order to predict the spread
and behaviour of wildland fires, relying solely on the formulations of the physics and
chemistry to model the fire behaviour. The model utilises the finite volume method
and the notion of a resolved volume to solve numerically its system of equations. It
attempts to represent the average behaviour of the gases and solid fuels in the presence
of a wildland fire. Many small-scale processes such as convective heat transfer between
solids and gases are represented without each process actually being resolved in detail
(Linn, 1997; Linn and Harlow, 1998a; Linn et al., 2002a). Fine scale wind patterns around
structures smaller than the resolved scale of the model, including individual flames, are
not represented explicitly.
The complex combustion reactions of a wildland fire are represented in FIRETEC using a
few simplified models, including models for pyrolysis, char burning, hydrocarbon combus-
tion and soot combustion in the presence of oxygen (Linn, 1997). Three idealised limiting
cases were used as a basis for the original FIRETEC formulation:
1. gas-gas, with two reactants forming a single final product and no intermediate
species.
13

2. gas-solid, being the burning of char in oxygen.
3. single reactant, being pyrolysis of wood.
However, Linn et al. (2002a) further refined this to a much simplified chemistry model
that reduced the combustion to a single solid-gas phase reaction:
Nf +NO2 → products+ heat (6)
where Nf,O2 are the stoichiometric coefficients for fuel and oxygen. The equations for the
evolution of the solid phase express the conservation of fuel, moisture and energy:
∂ρf
∂t = −NfFf (7)
∂ρw
∂t = −Fw (8)
(cpfρf + cpwρw)
∂Ts
∂t = Qrad,s + hav(Tg − Ts)− Fw(Hw + cpwTvap) +
F (ΘHf + cpfTpyrNf) (9)
where Ff,W are the reaction rates for solid fuel and liquid water depletion (i.e. the evapo-
ration rate), ρf,w are the solid phase (i.e. fuel and liquid water) density, Θ is the fraction
of heat released from the solid-gas reaction and deposited back to the solid, cpf ,w are the
specific heats at constant pressure of the fuel and water, Ts,g is the temperature of the
solid or gas phase, Tpyr is the temperature at which the solid fuel begins to pyrolyse, Qrad,g
is the net thermal radiation flux to the gas, h is the convective heat transfer coefficient,
av is the ratio of solid fuel surface area to resolved volume, Hw,f is the heat energy per
unit mass associated with liquid water evaporation or solid-gas reaction (Eq. 6). It is
assumed that the rates of exothermic reaction in areas of active burning are limited by the
rate at which reactants can be brought together in their correct proportions (i.e. mixing
limited). In a later work (Colman and Linn, 2003) a procedure to improve the combus-
tion chemistry used in FIRETEC by utilising a non-local chemistry model in which the
formation of char and tar are competing processes (as in for example, Fig. 2) is outlined.
No results have been presented yet.
The gas phase equations utilise the forms of the conservation of mass, momentum, energy
and species equations (Linn and Cunningham, 2005), similar to those of eqs (3 & 4),
except that the conservation of mass is tied to the creation and consumption of solid and
gas phase fuel, a turbulent Reynolds stress tensor and coefficient of drag for the solid fuel
is included in the momentum equation, and a turbulent diffusion coefficient is included
in the energy equation.
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A unique aspect of the FIRETEC model is that the variables that occur in the relevant
solid and gas phase conservation equations are divided into mean and fluctuating com-
ponents and ensemble averages of the equations taken. This approach is similar to that
used for the modelling of turbulence in flows.
The concept of a critical temperature within the resolved volume is used to initiate com-
bustion and a probability distribution function based on the mean and fluctuating com-
ponents of quantities in the resolved volume used to determine the mean temperature of
the volume. Once the mean temperature exceeds the critical temperature, combustion
commences and the evolution equations are used to track the solid and gas phase species.
The critical temperature is chosen to be 500 K (Linn, 1997).
Turbulence in the flow around the combusting fuel is taken into account as the sum of
three separate turbulence spectra corresponding to three cascading spatial scales, viz.:
scale A, the scale of the largest fuel structure (i.e. a tree); scale B, the scale of the
distance between fuel elements (i.e. branches); and scale C, the scale of the smallest fuel
element (i.e. leaves, needles, etc) (Linn, 1997). In the original work modelling fire spread
through a forest type, the characteristic scale lengths, s, for each scale were sA = 4.0 m,
sB = 2.0 m and sC = 0.05 m. By representing turbulence explicitly like this, the effect of
diffusivity in the transfer of heat can be included.
The original version of FIRETEC did not explicitly include the effects of radiation, from
either flame or fuel bed, or the absorption of radiation into unburnt fuel–primarily be-
cause flames and flame effects were at an unresolved scale within the model. As a result
fires failed to propagate in zero wind situations or down slopes. Later revised versions
(Bossert et al., 2000; Linn et al., 2001, 2002a) include some form of radiant transfer, how-
ever, this has not been formally presented anywhere and Linn et al. (2003) admits to the
radiant heat transfer model being ‘very crude’.
Because FIRETEC models the conservation of mass, momentum and energy for both
the gas and solid phases, it does have the potential, via the probability density function
of temperature within a resolved volume, to track the probability fraction of mass in a
debris-laden plume above the critical temperature (Linn and Harlow, 1998b) and thus
provide a method of determining the occurrence of ‘spotting’ downwind of the main fire.
Running on a 128-node SGI computer with R10000 processors, a simplified FIRETEC
simulation is described as running at ‘one to two orders of magnitude slower than realtime’
for a reasonable domain size (Hanson et al., 2000).
Forbes (1997)
Forbes (1997) developed a two dimensional model of fire spread utilising radiative heat
transfer, species consumption and flammable gas production to explain why most fires
don’t become major problems and why, when they do, they behave erratically. The
basis for his model is observations of eucalypt forest fires which appeared either to burn
quiescently or as raging infernos.
The main conceit behind the model is a two-path combustion model in which the solid fuel
of eucalypt trees either thermally degrades directly and rapidly in an endothermic reac-
tion, creating flammable fuel that then combusts exothermically, or produces flammable
‘eucalypt vapours’ endothermically which then combust exothermically.
15

Forbes developed a set of differential equations to describe this process and, because the
reaction rates are temperature dependent, a temperature evolution for both the solid and
gas phases, which are the sum of radiation, conduction (only included in the solid phase),
convective heat loss, and the endothermic reaction losses in the production of the two
competing flammable gases. Wind is included in the reaction equations.
Forbes concludes from his analysis of the one-dimensional form of the equations that a
travelling wave solution is only sustainable if one of the two reaction schemes is endother-
mic overall and, since this won’t be the case in a large, intense bushfire, that bushfires
are unlikely to propagate as simple travelling waves. He determines a solution of a one-
dimensional line fire but found that for most parameter values, the fire does not sustain
itself. He found that the activation energies for each reaction, rate constants and heat
release coefficients govern the propagation of the fire. Low activation energies and tem-
peratures and high heat release rates are most likely to lead to growth of large fires.
Forbes then develops a two-dimensional solution for his equations, making the assumption
that the height of the processes involved in the vertical direction (i.e. the flames) is small
when compared to the area of the fire (i.e. by some orders of magnitude). This solution
produces an elliptical fire shape stretched in the direction of the wind. He suggests
improving the model by including fuel moisture. No performance data are given.
Grishin (Tomsk State University, Russia)
The work of AM Grishin has long been recognised for its comprehensive and innovative
approach to the problem of developing physical models of forest fire behaviour (Weber,
1991b). While most of this work was conducted and published in Russia in the late
1970s and early 1980s, Grishin published a major monograph in 1992 that collected the
considerable research he had conducted in one place, albeit in Russian. In 1997, this
monograph was translated into English (Grishin, 1997) (edited by Frank Albini) and, for
the first time, all of Grishin’s work was available for English readers and is the main
reason for the inclusion of his work in this review.
Grishin’s model, as described in a number of papers (Grishin et al., 1983; Grishin, 1984;
Grishin et al., 1984; Grishin and Shipulina, 2002), was based on analysis of experimental
data and developed using the concepts and methods of reactive media mechanics. In
this formulation, the wildland fuel (in this case, primarily forest canopy) and combustion
products represent a non-deformable porous-dispersed medium (Grishin, 1997). Turbulent
heat and mass transfer in the forest, as well as heat and mass exchange between the near-
ground layer of the atmosphere and the forest canopy, are incorporated. The forest is
considered as a multi-phase, multi-storied, spatially heterogeneous medium outside the
fire zone. Inside the fire zone, the forest is considered to be a porous-dispersed, seven-
phase, two-temperature, single-velocity, reactive medium. The six phases within the
combustion zone are: dry organic matter, water in liquid state, solid products of fuel
pyrolysis (char), ash, gas (composed of air, flying pyrolytic products and water vapour),
and particles in the dispersed phase.
The model takes into account the basic physicochemical processes (heating, drying, pyrol-
ysis of combustible forest material) and utilises the conservation of mass, momentum and
energy in both the solid and gas phases. Other equations, in conjunction with initial and
16

boundary conditions, are used to determine the concentrations of gas phase components,
radiation flux, convective heat transfer, and mass loss rates through Arrhenius rate laws
using experimentally-determined activation energy and reaction rates. Grishin uses an
effective reaction whose mass rate is close to that of CO to describe the combustion of
‘flying’ pyrolytic materials, because he determined that CO is the most common pyrolytic
product (Grishin et al., 1983). Numerical analysis then enables the structure of the fire
front and its development from initiation to be predicted. Versions of the full formulation
of the multi-phase model are given in each of the works of Grishin (e.g. Grishin et al.
(1983); Grishin (1997); Grishin and Shipulina (2002)).
While the model is formulated for three spatial dimensions plus time, the system of
equations is generally reduced to a simpler form in which the vertical dimension is averaged
over the height of the forest and the fire is assumed to be infinite in the y-direction,
resulting in a one-dimensional plus time system of equations in which x is the direction
of spread. The original formulation was intended only for the acceleration phase from
ignition until steady state spread is achieved (Grishin et al., 1983). This was extended
using a moving frame of reference and a steady-state rate of spread (ROS) to produce
an analytical solution for the ROS which was found to vary linearly with wind speed
(Grishin, 1984).
The speed of the fire front is taken to be the speed of the 700 K isotherm. The domain
used for numerical analysis is in the order of 100-200 m long. Rate of spread is found to
be dependent on initial moisture content of the fuel. No performance data are given.
IUSTI (Institut Universitaire des Syste´mes Thermiqes Indus-
triels, France)
IUSTI (Larini et al., 1998; Porterie et al., 1998a,b, 2000) is based on macroscopic conser-
vation equations obtained from local instantaneous forms (Larini et al., 1998) using an
averaging method first introduced by Anderson and Jackson (1967). It aims to extend the
modelling approach of Grishin et al. (1983) to thermal non-equilibrium flows. IUSTI con-
siders wildland fire to be a multi-phase reactive and radiative flow through a heterogeneous
combustible medium, utilising coupling through exchange terms of mass, momentum and
energy between a single gas phase and any number of solid phases. The physico-chemical
processes of fuel drying and pyrolysis due to thermal decomposition are modelled explic-
itly. Whereas FIRETEC was intended to be used to model wildland fire spread across
large spatial scales, IUSTI concentrates on resolving the chemical and conservation equa-
tions at a much smaller spatial scale at the expense of 3-dimensional solutions. Thus, in
its current formulation, IUSTI is 2-dimensional in the x and z directions.
Having derived the set of equations describing the general analysis of the reactive, radia-
tive and multi-phase medium (Larini et al., 1998; Porterie et al., 1998a), the authors of
IUSTI then reduced the system of equations to that of a much simplified version (called
a zeroth order model) in which the effects of phenomena were dissociated from those of
transfers. This was done by undertaking a series of simplifying assumptions. The first
assumption was that solid particles are fixed in space, implying that solid phase momen-
tum is nil; there is no surface regression and no char contribution in the conservation
equations; and that the only combustion process is that of pyrolysis in the gaseous phase.
17

Mass loss rates are deduced from Arrhenius-type laws following on from the values used
by Grishin et al. (1983) and Grishin (1997) and thermogravitic analysis (Porterie et al.,
2000). Mass rate equations for the conversion of solid fuel (gaseous production and solid
fuel mass reduction) assume an independent reaction path between char formation and
pyrolysis such that the rate of particle mass reduction relative to thermal decomposition
of the solid phase and gas production rate is the sum of the all solid fuel mass loss rates
due to water vaporisation, pyrolysis, char combustion (as a consequence of pyrolysis),
and ash formation (as a consequence of char oxidation from the idealised reaction, C +
O2 → CO2). The model also includes a set of equations governed by the transition from
the solid phase to a gas phase called the ‘jump’ condition because IUSTI considers such
relatively small volumes. The pyrolysis products are assumed to be removed out of the
solid instantaneously upon release. Mass diffusion of any chemical species is neglected
and no chemical reactions occur in the solid phase. A single one-step reaction model in
which fuel reacts with oxidant to produce product is implemented.
A later version of IUSTI (Porterie et al., 2000) utilises the density-weighted or Favre
average form of the conservation equations due to the density variations caused by the
heat release. The time-averaged, density-weighted (Favre) fluctuation of turbulent flux is
approximated from Boussinesq’s eddy viscosity concept and the turbulent kinetic energy,
κ, and dissipation rate, ǫ, are obtained from the renormalisation group theory (RNG).
The formation of soot is modelled as the soot volume fraction which forms mostly as a
result of the pyrolysis process and so is assumed to be a percentage of the mass loss rate
due to pyrolysis. The radiative transfer equation is based upon the mole fraction of the
combustion products and the average soot volume fraction, treating the gas as gray.
Drag is included through the drag coefficient which is a function of the Reynolds number
of the solid phase. Solid phase particles are treated as spheres. The conductive/convective
heat transfer coefficient is expressed using the Reynolds number for flow around cylinders.
The governing equations of conservation in both gas and solid phases are discretised on
a non-uniform grid using a finite-volume scheme. The domain over which the equations
are solved is in the order of 1-2 m long by 0.1 m with an average resolution of ≃ 0.01 m.
A one-dimensional version of this model was constructed in an attempt to simplify the
model (Morvan and Larini, 2001). A numerical experiment replicating fire spread through
a tube containing pine needles (in order to replicate one-dimensional spread experimen-
tally) was conducted. Results showed a linear increase in ROS with increasing wind speed
up to a value of 16 cm s−1. Beyond this value, ROS dropped off dramatically and pyrol-
ysis flow rate reduced. Analysis of the species composition mass fractions showed that
below 16 cm s−1, the combustion is oxygen limited and is akin to smouldering combustion.
Above 16 cm s−1, the combustion became fuel-limited as the increased air flow increased
convective cooling and slowed pyrolysis and hence ROS.
No performance data are given.
PIF97
The detailed work of Larini et al. (1998), Porterie et al. (1998a) and Porterie et al. (2000)
provided the framework for the development of a related model, named PIF97 by its
18

authors (Dupuy and Larini, 1999; Morvan and Dupuy, 2001). The aim of this work was
to simplify the multi-phase IUSTI model of Larini et al. (1998) and Porterie et al. (1998a)
in order to develop a more operationally-feasible model of wildland fire spread. The full 2D
IUSTI was reduced to a quasi-two-dimensional version in which the fuel bed is considered
to be one-dimensional and the gas interactions (including radiation and convective mixing
above the bed) are two dimensional (x and z). In a manner similar to IUSTU, two
phases of media are considered–gas and solid. However, PIF97 assumes that the solid is
homogeneous, unlike IUSTI which considers multiple solid phases.
PIF97 comes in two parts. The first is a combustion zone model that considers the
radiative and convective heat transferred to the fuel bed in front of the flaming zone. The
radiative component considers radiation flux from adjacent fuels, the ignition interface,
flame and the ambient media surrounding the fuel. Radiation from solids is assumed
to be blackbody at a temperature of 1123K. This value was selected so that the model
could predict the spread of a single experimental fire in pinaster needles. Convective heat
exchange depends on the Nusselt number which is approximated through a relation with
the Reynolds number for the type of flow the authors envisage. This in turn relies on
the assumption of flow around a cylinder of infinite length. Mass transfer and drag forces
are similarly derived using approximations to published models and empirical correlations
(i.e. assuming cylindrical particles). An ignition temperature for solid fuel of 600 K is
used.
The second part of the model is the fire-induced flow in the flaming combustion zone
behind the ignition interface. This depends on the ROS of the interface derived from the
combustion part of the model. The temperature of this gas is assumed to be fixed at 900K.
Other values between 750K and 1050K were investigated but no significant difference in
results was found.
The numerical solution of PIF97 is based on a domain that is 25 cm long and uses a
spatial resolution of 1 mm. Results of the model are compared to experimental results
presented by Dupuy (2000) in which two radiation-only models, that of de Mestre et al.
(1989) and a one-dimensional version of Albini (1985, 1986) were compared to laboratory
experiments conducted with Pinus pinaster and P. halipensis needles. PIF97 was found
to be comparable to the Albini model, except in P.halipensis needles where it performed
markedly better. However, no model was found to ‘perform well’ in conditions of wind
and slope.
A later version of PIF97 (Morvan and Dupuy, 2004) was extended to multiple solid phases
in order to simulate Mediterranean fuel complexes comprising live and dead components
of shrub and grass species, including twigs and foliage. An empirical correlation is used
for the drag coefficient based on regular shapes (i.e. cylinder, sphere, etc.) A RNG κ− ǫ
turbulence model using turbulent diffusion coefficients is incorporated and a pressure
correction algorithm used to couple the pressure with the velocity.
The revised model was implemented as a 2D vertical slice through the fire front as a
compromise between the computational time and need to study the main physical mech-
anisms of the fire propagation. 80 × 45 control volumes, each 10 cm × 3 cm were used,
defining a domain 8 m by 1.35 m. ROS was defined as the movement of the 500K isotherm
inside the pyrolysis front. ROS was compared to other models and observations of shrub
fires (Fernandes, 2001) and did not perform well. The authors summarise their model
19

as producing a ROS relationship for wind < 3 m s−1 as ‘an increasing function of wind
speed’ and then say the ROS reaches a limiting value at a wind speed of about 5 m
s−1. The other models and observations showed either linear or power law (exp < 1.0)
relationships.
Dupuy and Morvan (2005) added a crown layer to this model resulting in six families of
solid phase fuel: three for shrubs (leaves and two size classes of twigs (0-2, 2-6 mm), one
for grass, and two for the overstorey P. halepensis canopy (needles and twigs 2-6 mm).
This version implemented a combustion model based on Arrenhius-type laws after Grishin
(1997). Soot production (for the radiation transfer) was assumed at 5% of the rate of
solid fuel pyrolysis.
The domain was 200 m × 50 m high with, at its finest scale, cells 0.25 m × 0.025 m,
average of 0.25 × 0.25 and largest 1.0 × 0.25 m. 200 s of simulation took 48 hours on an
Intel Pentium P4 2GHz machine.
LEMTA (Laboratoire d’E´nerge´tique et de Me´canique The´orique
et Applique´e, France)
This comprehensive model, developed by Sero-Guillaume and Margerit (2002) of Lab-
oratoire d’E´nergtique et de Me´canique The´orique et Applique´e in France, considers a
two-phase model, gas and solid, in three regions of a forest–above the forest, in the forest
and below the ground–at three scales: microscopic (plant cell solid/gas level), mesoscopic
(branch and leaf level) and macroscopic (forest canopy/atmosphere level). They identify
but do not investigate a fourth scale, that of the ‘gigascopic’ or landscape level.
The combustion chemistry is simplified in that only gas-phase combustion is allowed.
Solid phase chemistry only considers pyrolysis to gas-phase volatile fuel, char and tar.
Soot production is not considered, nor is char combustion. Gas phases include O2, water,
N2, fuel and inert residue. Solid to gas phase transitions are handled by interface jump
relations.
Conservation of species mass, momentum and energy are derived for mesoscopic gas and
solid phase interactions. These are then averaged over the larger macroscopic scale by us-
ing distribution theory and convoluting the equations to macroscopic quantities. Extended
irreversible thermodynamics is then used to close the system of equations. Arguments
about thermal equilibrium are used to further reduce the non-equilibrium equations for
temperature and pressure.
The system of equations are then further simplified using assumptions about the nature of
the fuel (at rest) and the size and interaction of the fuel particles with the gas phase (i.e.
no advection, pressure or porosity variations in the solid phase). Drag is not included.
Gas phase equations in the region above the forest do not include solid phase particles
and, since soot is not modeled, cannot suitably describe radiant heat from flames.
Margerit and Sero-Guillaume (2002) and Chetehouna et al. (2004) reduced Sero-Guillaume and Margerit
(2002) to two dimensions in order to produce a more operationally-feasible fire spread
model. Margerit and Sero-Guillaume (2002) achieved this through assumptions that the
scale of the fuel to the fire was such that the fuel could be considered a boundary layer and
20

the fire a one-dimensional interface between burning and unburnt fuel on the surface. (i.e.
the fuel is thin relative to the width of the fire). A few assumptions are then made: there
is no vertical component in the wind, the solid and gas phases are in thermal equilibrium,
and the non-local external radiative heat flux is blackbody. The resulting two-dimensional
model is a reaction-diffusion model similar in form to Weber (1991b). Assumptions about
the speed of chemical reactions are made to get the pyrolysis occurring at an ignition
temperature.
Chetehouna et al. (2004) further reduced the two-dimensional reaction-diffusion equations
of Margerit and Sero-Guillaume (2002) by making some simplifying assumptions about
the evaporation and ignition of the solid phase fuel. Here, fixed temperatures are used,
100 and 300◦C respectively. Five distinct heating stages are used, each separated by the
temperature of the fuel: 1) fuel heating to 100◦C; 2) moisture evaporation at 100◦C; 3)
fuel heating to ignition temperature; 4) combustion at 300◦C; and 5) mass loss due to
chemical reactions and heat loss at flame extinction.
Separate equations with different boundary conditions are used for each stage but only
stages 1-3 are important for fire spread. The equations for these stages are then non-
dimensionalised and a limiting parameter, the thermal conductivity in the solid phase, is
used as a parameter for variation. The equations are then solved as an eigenvalue problem
in order to determine the ROS for each stage. Two flame radiation models are used to
incorporate long distance radiant heat flux from flames: de Mestre et al. (1989) and the
version given by Margerit and Sero-Guillaume (2002). Rates of spread are similar for both
flame models and reduce with increasing thermal conductivity. However, despite the fact
that the authors say the models compare well with experimental results, no results or
comparisons are given.
The model is then simulated on a computer. It provides a circular shape in no wind/no
slope, and an elongated shape under wind. An example burning in real terrain is shown
but no discussion of its performance against real fires is given. Mention is made of it
operating in real-time on a PC.
UoS (University of Salamanca, Spain)
Asensio and Ferragut (2002) constructed a 2D model of fire spread that used radiation as
the primary mode of heat transfer but also incorporated advection of hot gas and convec-
tive cooling of fuels. The model, described here as UoS, employed a simplified combustion
chemistry model (only two phases: gas and solid, and two species: fuel and oxygen) and
utilised only conservation of energy and species mass. It is assumed combustion is fuel
limited and thus only one species is conserved. Arrhenius laws for fuel consumption are
used. Turbulence is not accounted for directly or explicitly, but a term for advection with
a wind velocity vector is included.
The model is of a form that explicitly includes convective heating, radiation, chemical
energy release and natural convection. Non-dimensionalised forms of the system of equa-
tions are then discretised into a finite element form for numerical computation. The
model is considered to be a first step and the authors aim to link it to the Navier-Stokes
equations for better incorporation of turbulence.
21

Asensio et al. (2005) attempted to provide a link from the 2D surface fire spread of UoS
to a model of convection above the fire. The model starts with the conservation of
momentum equation and then makes hydrostatic assumptions about the atmosphere.
It then decomposes this 3D model into a 2D model with height that is averaged over
a layer of fixed thickness. An asymptotic model is then formed and solved producing
2D streamfunctions and an equation for the velocity on the surface (which can then be
inserted directly into the original spread model for the advection of heat around the fire).
No performance data are given.
WFDS (National Institute of Safety Technology, USA)
The Wildland Fire Dynamic Simulator (WFDS), developed by the US National Institute
of Safety Technology (Mell et al., 2006), is an extension of the model developed to pre-
dict the spread of fire within structures, Fire Dynamic Simulator (FDS). This model is
fully 3D, is based upon a unique formulation of the equations of motion for buoyant flow
(Rehm and Baum, 1978) and is intended for use in predicting the behaviour of fires burn-
ing through peri-urban/wildlands (what the authors call ‘Community-scale fire spread’
(Rehm et al., 2003; Evans et al., 2003)). The main objective of this model is to predict
the progress of fire through predominantly wildland fuel augmented by the presence of
combustible structures.
WFDS utilises a varying computational grid to resolve volumes as low as 1.6 m (x) × 1.6
m (y) × 1.4 m (z) within a simulation domain in the order of 1.5 km2 in area and 200 m
high. Outside regions of interest, the grid resolution is decreased to improve computation
efficiency.
Mell et al. (2006) give a detailed description of the WFDS formulated for the specific
initial case of grassland fuels, in which vegetation is not resolved in the gas-phase (atmo-
sphere) grid but in a separate solid fuel (surface) grid (which the authors admit is not
suitable for fuels in which there is significant vertical flame spread and air flow through
the fuel). In the case presented, the model includes features such as momentum drag
caused by the presence of the grass fuel (modelled as cylinders) which changes over time
as the fuel is consumed. Mechanical turbulence, through the dynamic viscosity of the
flow through the fuel, is modelled as a subgrid parameter via a variant of the Large Eddy
Simulation (LES) method.
The WFDS assumes a two-stage endothermic thermal decomposition (water evaporation
and then solid fuel ‘pyrolysis’). It uses the temperature dependent mass loss rate ex-
pression of Morvan and Dupuy (2004) to model the solid fuel degradation and assumes
that pyrolysis occurs at 127◦C. Solid fuel is represented as a series of layers which are
consumed from the top down until the solid mass reaches a predetermined char fraction
at which point the fuel is considered consumed.
WFDS assumes combustion occurs solely as the result of fuel gas and oxygen mixing in
stoichiometric proportion (and thus is independent of temperature). Char oxidation is not
accounted for. The gas phase combustion is modelled using the following stoichiometric
relation:
C3.4H6.2O2.5 + 3.7(O2 + 3.76N2)→ 3.4CO2 + 3.1H2O+ 13.91N2 (10)
22

Due to the relatively coarse scale of the resolved computation grids within WFDS, detailed
chemical kinetics are not modelled. Instead, the concept of a mixture fraction within a
resolved volume is used to represent the mass ratio of gas-phase fuel to oxygen using a fast
chemistry or flame sheet model which then provides the mass loss flux for each species.
The energy release associated with chemical reactions is not explicitly presented but is
accounted for by an enthalpy variable as a function of species. The model assumes that
the time scale of the chemical reactions is much shorter than that of mixing.
Thermal radiation transport assumes a gray gas absorber-emitter using the P1 radiation
model for which the absorption coefficient is a function of the mixture fraction and tem-
perature for a given mixture of species. A soot production model is not used; instead it
is an assumed fraction of the mass of fuel gas consumed.
Mell et al. (2006) provides simulation information for two experimental grassfires. In the
first case, a high intensity fire in a plot 200 m × 200 m within a domain of 1.5 km ×
1.5 km and vertical height of 200 m for a total 16 million grid cells, the model, running
on 11 processors, took 44 cpu hours for 100 s of simulated time. Another lower intensity
experiment over a similiar domain took 25 cpu hours for 100 s of simulated time.
Quasi-physical models
This section briefly describes quasi-physical models that have appeared in the literature
since 1990 (de Mestre et al. (1989) is included because it was missed by previous reviews
and provides the basis for a subsequent model).
The main feature of this form of model is the lack of combustion chemistry and reliance
upon the transfer of a prescribed heat release (i.e. flame geometry and temperature are
generally assumed). They are presented in chronological order of publication (Table 4).
Australian Defence Force Academy (ADFA) I, Australia
de Mestre et al. (1989) of the Australian Defence Force Academy, University of New South
Wales, developed a physical model of fire spread based initially only on radiative effects, in
much the same manner as that of Albini (1985, 1986) (see below) but in a much simplified
manner.
The authors utilise a conservation of heat approach to model the spread of a planar fire
of infinite width across the surface of a semi-transparent fuel bed in a no wind, no slope
situation. However, unlike Albini, who modelled the fuel bed in two dimensions (i.e., x
and z), de Mestre et al. (1989) chose to model only the top of the fuel bed, arguing that
it is this component of the fuel bed that burns first before burning down into the bed;
thus this model is one dimensional plus time.
Assumptions include vertical flames that radiate as an opaque surface of fixed temperature
and emissivity, a fixed fuel ignition temperature, and radiation from the combustion zone
as an opaque surface of fixed temperature and emissivity. Here they also assume that the
23

ignition interface in the fuel bed is a linear surface, as opposed to Albini’s curved one, in
order to simplify the computations.
Two approaches to the vaporisation of the fuel moisture are modelled–one in which it all
boils off at 373 K (i.e. 3 phase model (<373 K, 373 K, >373 K) and one in which it boils
off gradually below 373 K (2 phase model (≤ 373 K, > 373 K).
The final model includes terms for radiation from flame, radiation from combustion zone,
radiative cooling from solid fuel, and convective cooling from solid fuel. Without the
cooling terms, the model was found to over-predict ROS by a factor of 13. A radiative
cooling factor brought the over-prediction down to a factor of 9. Including a convective
cooling term to the ambient air apparently brought the prediction down to the observed
ROS but this was not detailed.
No performance data are given.
TRW, USA
Carrier et al. (1991) introduced an analytical model of fire spread through an array of
sticks in a wind tunnel (called here TRW). Unlike many preceding fire modelling attempts,
they did not assume that the dominant preheating mechanism is radiation, but a mixture
of convective/diffusive (what they called ‘confusive’) heating.
Predominately concerned with deriving a formula for the forward spread of the fire in-
terface in the wind tunnel (based on a series of experiments conducted and reported by
Wolff et al. (1991)), Carrier et al. (1991) assumed that the fire achieves a ‘quasi-steady’
ROS in conditions of constant wind speed and fuel conditions. They make the point that,
at the scale they are looking at, the spread can be viewed as continuous and can thus
involve a catch-all heat transfer mechanism (gas-phase diffusion flame) in which radiation
plays no part and it is the advection of hot gas from the burned area that preheats the
fuel (assuming all of it is burnt).
The model is two-dimensional in the plane XY in which it is assumed there is no lateral
difference in the spread of the fire (which is different to assuming an infinite width fire).
Indeed, their formulation actually needs the width of the fuel bed and the width of the
wind tunnel. The fluctuating scale of the turbulence within the tunnel is incorporated in
a scale length parameter. Air flow within the fuel bed is ignored.
Using a first-principles competing argument, they say that if radiation was to be the
source of preheating, the estimate of radiant energy (2.9 J/g) ahead of the fire falls
well short of the 250 J/g required for pyrolysis. A square root relation between wind
speed normalised by fuel load consumed and rate of forward spread was determined and
supported by experimental observation (Wolff et al., 1991). Carrier et al. (1991) suggest
that only when fuel loading is very high (on the order of 2 kg m−2) will radiative preheating
play a role comparable to that of convective/diffusive preheating.
No performance data are given.
24

Albini, USA
Albini (1985, 1986) developed a two-dimensional (XZ) quasi-physical radiative model of
fire spread through a single homogeneous fuel layer. The latter paper improved upon
the former by including a fuel convective cooling term. Both models required that flame
geometry and radiative properties (temperature and emissive power) be prescribed a priori
in order for the model to then determine, in an iterative process, the steady-state speed
of the fire front. The fire front is considered to be the isothermal flame ignition interface
between unburnt and burnt fuel expressed as an eigenvalue problem, utilising a 3-stage
fuel heating model (<373 K, 373 K, 373 K ≤ Ti), where Ti is the ignition temperature
of 700 K.
A modified version of this spread model, in which a thermally-inert zone that allowed the
passage of a planar flame front but did not influence the spread process was placed beneath
the homogeneous fuel layer to simulate propagation of a fire through the tree crowns, was
tested against a series of field-based experimental crown fires conducted in immature
Jack Pine (Albini and Stocks, 1986). The results from one experimental fire were used
to parameterise the model (flame radiometric temperature and free flame radiation) and
obtain flame geometry and radiative properties for the remaining fires. The model was
found to perform reasonably well, with a maximum absolute percent error of 14%.
Albini (1996) extended the representation of the fuel to multiple levels, where surface fuel,
sub-canopy fuel and the canopy fuel are incorporated into the spread model. Albini also
introduced a closure mechanism for removing the requirement for flame geometry and
radiative properties to be given a priori. The former transcribed the fuel complex into
a vertical series of equivalent single-component (homogeneous) surrogate layers based on
weighted contributions from different fuel components (e.g. surface-volume ratio, packing
ratio, etc.) within a layer.
The closure method involves the positing of a ‘trial’ rate of spread, along with free flame
geometry and ignition interface shape, that are then used to predict a temperature dis-
tribution within the fuel. This distribution is then subsequently used in a sub-model to
refine the fire intensity, rate of spread, flame geometry, etc. This continues iteratively
until a convergence of results is achieved. A quasi-steady ROS is assumed and the tem-
perature distribution is assumed stationary in time. A conservation of energy argument,
that the ROS will yield a fire intensity that results in a flame structure that will cause
that ROS, is then used to check the validity of the final solution.
Butler et al. (2004) used the heat transfer model of Albini (1996) in conjunction with
models for fuel consumption, wind velocity profile and flame structure, to develop a
numerical model for the prediction of spread rate and fireline intensity of high intensity
crown fires. The model was found to accurately predict the relative response of fire spread
rate to fuel and environment variables but significantly over-predicted the magnitude of
the speed, in one case by a factor of 3.5. No performance data are given.
University of Corsica (UC), France
The University of Corsica undertook a concerted effort to develop a physical model of
fire spread (called here UC) that would be suitable for faster than real-time operational
25

use. The initial approach (Santoni and Balbi, 1998a,b; Balbi et al., 1999) was a quasi-
physical model in which the main heat transfer mechanisms were combined into a so-called
‘reactive diffusion’ model, the parameters of which were determined experimentally.
The main components of UC are a thermal balance model that incorporates the combined
diffusion of heat from the three mechanisms and a diffusion flame model for determination
of radiant heat from flames. The heat balance considers: heat exchanged with the air
around a fuel cell, heat exchanged with the cell’s neighbours, and heat released by the
cell during combustion. It is assumed that the rate of energy release is proportional
to the fuel consumed and that the fuel is consumed exponentially. The model is two-
dimensional in the fuel layer (the plane XY). No convection, apart from convective cooling
to neighbouring cells is taken into account, nor is turbulence. The model assumes that
all combustion follows one path. Model parameters were determined from laboratory
experiments.
Initially, radiation from the flame was assumed to occur as surface emission from a flame
of height, angle and length computed from the model and an isothermal of 500K. Flame
emissivity and fuel absorptivity were determined from laboratory experiments in a com-
bined parameter. The early version of the model was one dimensional for the fuel bed and
two dimensional (x and z) for flame. Forms of the conservation of mass and momentum
equations are used to control variables such as gas velocity, enthalpy, pressure and mass
fractions.
Santoni et al. (1999) presented a 2D version of the model in which the radiative heat
transfer component was reformulated such that the view factor, emissivity and absorp-
tivity were parameterised with a single value for each fuel and slope combination that
was derived from laboratory experiments. This version was compared to experimental
observations (Dupuy, 1995) and the radiation-only models of Albini (1985, 1986) and
de Mestre et al. (1989) (Morandini et al., 2000). It was found to predict the experimen-
tal increase in ROS with increasing fuel load much better than the other models. The
UC model also outperformed the other models on slopes but this is not surprising as it
had to be parameterised for each particular slope case.
Simeoni et al. (2001a) acknowledged the inadequacies of the initial ‘reaction-diffusion’
model and Simeoni et al. (2001a,b, 2002, 2003) undertook to improve the advection com-
ponent of the UC model by reducing the physical modelling of the advection component
of the work of Larini et al. (1998) and Porterie et al. (1998a,b) to two dimensions to link
it to the UC model. It occurred in two parts: one as a conservation of momentum com-
ponent that is included in the thermal balance equations (temperature evolution), and
one as a velocity profile through the flaming zone. They assumed that buoyancy, drag
and vertical variation are equivalent to a force proportional to the quantity of gas in the
multi-phase volume and that all the forces are constant whatever the gas velocity. The
net effect is that the horizontal velocity decreases through the flame to zero at the ignition
interface and does not change with time. Again, the quasi-physical model was param-
eterised using a temperature-time curve from a laboratory experiment with no wind or
slope. The modified model improves the performance only marginally, particularly in the
no slope case but still underpredicts ROS.
The original UCmodel included only the thermal balance with a diffusion term encompass-
ing convection, conduction and radiation. The inclusion of only short distance radiation
26

interaction failed to properly model the pre-heating of fuel due to radiation prior to the
arrival of the fire front. Morandini et al. (2001a,b, 2002) attempted to address this issue
by improving the radiant heat transfer mechanism of the model. Surface emission from a
vertical flame under no wind conditions is assumed and a flame tilt factor is included when
under the influence of wind. The radiation transfer is based on the Stefan-Boltzmann ra-
diation transfer equation where the view factor from the flame is simplified to the sum
of vertical panels of given width. The length of each panel is assumed to be equal to the
flame depth, mainly because flame height is not modelled.
In cases of combined slope and wind, it was assumed that the effects on flame angle are
independent of slope. Morandini et al. (2002) approximate the effects of wind speed by an
increase in flame angle in a manner similar to terrain slope by taking the inverse tangent
of the flame angle of a series of experiments divided into the mid-flame wind speed. This
is then considered a constant for a range of wind speeds and slopes. Again, the model is
parameterised using a laboratory experiment in no-wind, no slope conditions.
Results are given for a range of slopes (-15 to +15◦) and wind speeds (1,2,3 m s−1). The
prediction in no wind and slope is good, as are the predictions for wind and no slope.
The model breaks down when slope is added to high wind (i.e. 3 m s−1). Here, however,
they determine that their model only works for equivalent flame tilt angles (i.e. slope and
wind angles) up to 40 degrees.
The model is computed on a fine-scale non-uniform grid using the same methods as
Larini et al. (1998). In this case the smallest resolution is 1 cm3 and 0.1 seconds. On a
Sun Ultra II, the model took 114 s to compute 144 s of simulation. When the domain is
reduced to just the fire itself, the time reduced to 18 s.
ADFA II, Aust/USA
Catchpole et al. (2002) introduced a much refined and developed version of ADFA (de Mestre et al.,
1989), here called ADFA II. Like ADFA I, it is a heat balance model of a fuel element
located at the top of the fuel bed. The overall structure of the model is the same, with
radiative heating and cooling of the fuel (from both the flames and the combustion zone),
and convective heating and cooling. It is assumed that the flame emits as a surface and
they use laboratory experiments to determine the emissive energy flux based on a Gaus-
sian vertical flame profile and a maximum flame radiant intensity. It assumes infinite
width for the radiative emissions.
Combustion zone radiation is treated similarly. Byram’s convective number (Byram,
1959b) and fireline intensity (Byram, 1959a) are used to determine flame characteristics
(angle, height, length, etc). Empirical models are used to determine gas temperature
profile above and within the fuel as well as maximum gas temperature, etc. ADFA II
utilises an iterative method to determine ROS, similar to that of Albini (1996), assuming
that the fire is at a steady-state rate of spread.
No performance data are given.
27

Coimbra (2004)
The aim of Vaz et al. (2004) was not to develop a new model of fire spread as such, but to
combine the wide range of existing models in such a way as to create a seamless modular
quasi-physical model of fire spread that can be tailor-made for particular situations by
picking and choosing appropriate sub-models. The ‘library’ of models from which the
authors pick and choose their sub-models are classified as: heat sink models (including
Rothermel (1972); Albini (1985, 1986); de Mestre et al. (1989)), which consider the con-
servation of energy aspects of fuel heating and moisture loss and ignition criteria; heat
flux models (including Albini (1985, 1986); Van Wagner (1967)), which consider the net
exchange of radiative energy between fuel particles; and heat source models (including
Thomas (1967, 1971)), that consider the generation of energy within the combustion zone
and provide closure for the other two types of models.
The authors compared a fixed selection of sub-models against data gathered from a labo-
ratory experiment conducted on a fuel bed 2 m wide by 0.8 m long under conditions of no
wind and no slope. The set of models was found to underpredict ROS by 46%. This was
improved to 6% when observed flame height was used in the prediction. Predicted flame
height, upon which several of the sub-models depend directly, did not correspond with ob-
servations, regardless of the combination of sub-models selected. Rather than producing
a fire behaviour prediction system that utilises the best aspects of its component models,
the result appears to compound the inadequacies of each of the sub-models. None of the
three classes of sub-models consider advection of hot gases in the heat transfer.
Discussion and summary
The most distinguishing feature of a fully physical model of fire spread in comparison with
one that is described as being quasi-physical is the presence of some form of combustion
chemistry. These models determine the energy released from the fuel, and thus the amount
of energy to be subsequently transferred to surrounding unburnt fuel and the atmosphere,
etc., from a model of the fundamental chemistry of the fuel and its combustion. Quasi-
physical models, on the other hand, rely upon a higher level model to determine the
magnitude of energy to be transferred and generally require flame characteristics to be
known a priori.
Physical models themselves can be divided primarily into two streams; those that are
intended for operational or experimental use (or at least field validation) and those that
are purely academic exercises. The latter are characterised by the lack of follow-up work
(e.g. Weber, Forbes, UoS), although it is possible that components of such models may
later find their way into models intended for operational or experimental use. Sometimes
the nature of the model itself dictates its uses, rather than the authors’ intention. Grishin,
IUSTI, and LEMTA were all formulated with the intention of being useful models of
fire spread but either due to the complex nature of the models, the reduced physical
dimensionality of the model or the restricted domain over which the model can operate
feasibly, the model has not and most probably will not be used operationally.
The remaining physical models, AIOLOS-F, FIRETEC, PIF97 and WFDS have all had
extended and ongoing development and each are capable of modelling the behaviour of
28

a wildland fire of landscape scale (i.e. computational domains in excess of ≃ 100 m.
However, in the effort to make this computationally feasible, each model significantly
reduces both the resolution of the computational domain and the precision of the physical
models implemented.
Each of these remaining physical models is also different from the others in that efforts
to conduct validation of their performance against large scale wildland fires have been
attempted. Difficulties abound in this endeavour. As is the case with any field experiment,
it is very difficult to measure all required quantities to the degree of precision and accuracy
required by the models. In the case of wildland fires, this difficulty is increased by two or
three orders of magnitude. Boundary conditions are rarely known and other quantities
are almost never measured at the site of the fire itself. Mapping of the spread of wildland
fires is haphazard and highly subjective.
IUSTI and PIF97 undertook validation utilising laboratory experiments of suitable spa-
tial scales in which the number and type of variables were strictly controlled. In many
laboratory experiments, the standard condition is one of no wind and no slope. While
wildland fires in flat terrain do occur, it is very rare (if not impossible) for these fires to
occur in no wind. The ability to correctly model the behaviour of a fire in such conditions
is only one step in the testing of the model. Both IUSTI and PIF97 (as well as a number
of the quasi-physical models discussed here) were found wanting in conditions of wind
and/or slope.
Morvan et al. (2004) argues that purely theoretical modelling with no regard for field ob-
servations is of less use than a field-based model for one particular set of circumstances.
Validation against fire behaviour observed in artificial fuel beds under artificial conditions
is only half the test of the worth of a model. The importance of comparison against
field observation is not to be understated. For regardless of the conditions under which
a field experiment (i.e. an experimental fire carried out in naturally occurring, albeit
modified, conditions) is conducted, it is the real deal in terms of wildland fire behaviour
and thus provides the complete set of interactions between fire, fuel, atmosphere and to-
pography. Both Linn and Cunningham (2005) and Mell et al. (2006) identified significant
deficiencies within their models (FIRETEC and WFDS, respectively) that only compari-
son against field observations could have revealed.
Both FIRETEC and WFDS attempted validation against large scale experimental grass-
land fires (Cheney et al., 1993) and thus avoided many of the issues of validation against
wildfire observations. However, the issue of identifying the source of discrepancy in such
complex models is just as difficult as obtaining suitable data against which to test the
model.
Computationally feasible models can be either constructed from simple models or reduced
from complete models (Sero-Guillaume and Margerit, 2002) and each of the preceding
physical models are very much in the latter category. Quasi-physical models are very
much of the former but suffer from the same difficulties in validation against large scale
fires. Of the quasi-physical models discussed here, only those of Albini have been tested
against wildland fires, the others against laboratory experimental fires.
However, being constructed from simple models may make the quasi-physical models less
complex but does not necessarily make them any more computationally feasible. Table 5
shows a summary of the scope, resolution and computation time available in the literature
29

for each of the models. Not all models have such information, concentrating primarily on
the underlying basis of the models rather than their computational feasibility. But for
those models whose raison de tre is to be used actively for fire management purposes,
computational feasibility is of prime concern. Here models such as AIOLOS-F, FIRETEC,
WFDS and UC standout from the others because of their stated aim to be a useful tool
in fire management.
PIF97, WFDS and UC all give nominal computation times for a given period of simulation.
Only UC, being a quasi-physical model reduced from a more fundamental model is better
than realtime. PIF97 and WFDS, using the current level of hardware, are all much
greater than realtime (in the order of 450 times realtime for WFDS on 11 processors
(Mell et al., 2006). FIRETEC is described as being ‘several orders of magnitude slower
than realtime’. FIRETEC, WFDS and UoS are significantly different from the other
physical models (and most of the quasi-physical models for that matter) in that their
resolutions are significantly larger (in some cases by two orders of magnitude). However,
the time step used by FIRETEC (0.002 s) in the example given, means that the gains
to be made by averaging the computations over a larger volume are lost in using a very
short time interval.
The authors of FIRETEC are resolved to not being able to predict the behaviour of land-
scape wildland fires and suggest that the primary use of purely physical models of fire
behaviour is the study of fires under a variety of conditions in a range of fuels and to-
pographies in scenarios that are not amenable to field experimentation. This is a laudable
aim, and in an increasingly litigious social and political environment, may be the only
way to study large scale fire behaviour in the future, but this assumes that the physical
model is complete, correct, validated and verified. Hanson et al. (2000) suggest that the
operational fire behaviour models of the future will be reduced versions of the purely
physical models being developed today.
It is obvious from the performance data volunteered in the literature, that the current
approaches to modelling fire behaviour on the hardware available today are not going to
provide fire managers with the tools to enable them to conduct fire suppression planning
based on the resultant predicted fire behaviour. The level of detail of data (type and
resolution of parameters and variables) required for input into these models will not be
generally available for some time and will necessarily have a high degree of imprecision.
The basis for fire behaviour models of operational use is unlikely to be one of purely
physical origin, simply because of the computational requirements to solve the equations
of motion at the resolutions necessary to ensure model stability. Approximations do and
will abound in order to improve computational feasibility and it is these approximations
that lessen the confidence users will have in the final results. Such approximations span
the gamut of the chemical and physical processes involved in the spread of fire across the
landscape; from the physical structure of the fuel itself, the combustion chemistry of the
fuel, the fractions of species within a given volume, turbulence over the range of scales
being considered, to the chemical and thermal feedbacks within the atmosphere.
It is most likely that for the foreseeable future operational models will continue to be of
empirical origin. However, there may be a trend towards hybrid models of a more physical
nature as the physical and quasi-physical models are further developed and refined.
30

Acknowledgements
I would like to acknowledge Ensis Bushfire Research and the CSIRO Centre for Complex
Systems Science for supporting this project; Jim Gould and Rowena Ball for comments
on the draft manuscript; and the members of Ensis Bushfire Research who ably assisted
in the refereeing process, namely Miguel Cruz, Stuart Matthews and Grant Pearce.
31

References
Albini, F. (1979). Spot fire distance from burning trees–a predictive model. General
Technical Report INT-56, USDA Forest Service, Intermountain Forest and Range Ex-
perimental Station, Odgen UT.
Albini, F. (1985). A model for fire spread in wildland fuels by radiation. Combustion
Science and Technology, 42:229–258.
Albini, F. (1986). Wildland fire spread by radiation–a model including fuel cooling by
natural convection. Combustion Science and Technology, 45:101–112.
Albini, F. (1996). Iterative solution of the radiation transport equations governing spread
of fire in wildland fuel. Combustion, Explosion and Shock Waves, 32(5):534–543.
Albini, F. and Stocks, B. (1986). Predicted and observed rates of spread of crown fires in
immature jack pine. Combustion Science and Technology, 48:65–76.
Anderson, D., Catchpole, E., de Mestre, N., and Parkes, T. (1982). Modelling the spread
of grass fires. Journal of Australian Mathematics Society, Series B, 23:451–466.
Anderson, T. B. and Jackson, R. (1967). Fluid mechanical description of fluidized beds:
Equations of motion. Industrial & Engineering Chemistry. Fundamentals, 6(4):527–539.
Asensio, M. and Ferragut, L. (2002). On a wildland fire model with radiation. Interna-
tional Journal for Numerical Methods in Engineering, 54(1):137–157.
Asensio, M., Ferragut, L., and Simon, J. (2005). A convection model for fire spread
simulation. Applied Mathematics Letters, 18:673–677.
Babrauskas, V. (2003). Ignition Handbook. Fire Science Publishers, Issaquah, WA.
Balbi, J., Santoni, P., and Dupuy, J. (1999). Dynamic modelling of fire spread across a
fuel bed. International Journal of Wildland Fire, 9(4):275–284.
Ball, R., McIntosh, A., and Brindley, J. (1999). The role of char-forming processes in the
thermal decomposition of cellulose. Physical Chemistry Chemical Physics, 1:5035–5043.
Ball, R., McIntosh, A. C., and Brindley, J. (2004). Feedback processes in cellulose thermal
decomposition: implications for fire-retarding strategies and treatments. Combustion
Theory and Modelling, 8(2):281–291.
Batchelor, G. (1967). An Introduction to Fluid Mechanics. Cambridge University Press,
London, 1970 edition.
Beall, F. and Eickner, H. (1970). Thermal degradation of wood components: A review of
the literature. Research Paper FPL 130, USDA Forest Service, Madison, Wisconsin.
Bossert, J. E., Linn, R., Reisner, J., Winterkamp, J., Dennison, P., and Roberts, D. (2000).
Coupled atmosphere-fire behaviour model sensitivity to spatial fuels characterisation.
In Third Symposium on Fire and Forest Meteorology, 9-14 January 2000, Long Beach,
California., pages 21–26. American Meteorological Society.
Butler, B., Finney, M., Andrews, P., and Albini, F. (2004). A radiation-driven model for
crown fire spread. Canadian Journal of Forest Research, 34(8):1588–1599.
32

Byram, G. (1959a). Combustion of forest fuels. In Davis, K., editor, Forest Fire Control
and Use, chapter 3, pages 61–89 pp. McGraw-Hill, New York.
Byram, G. (1959b). Forest fire behaviour. In Davis, K., editor, Forest Fire Control and
Use, chapter 4, pages 90–123. McGraw-Hill, New York.
Carrier, G., Fendell, F., and Wolff, M. (1991). Wind-aided firespread across arrays of
discrete fuel elements. I. Theory. Combustion Science and Technology, 75:31–51.
Catchpole, W., Catchpole, E., Tate, A., Butler, B., and Rothermel, R. (2002). A model
for the steady spread of fire through a homogeneous fuel bed. In Viegas (2002), page
106. Proceedings of the IV International Conference on Forest Fire Research, Luso,
Coimbra, Portugal 18-23 November 2002.
Chandler, C. C., Storey, T. G., and Tangren, C. D. (1963). Prediction of fire spread
following nuclear explosions. Technical Report Research Paper PSW-5, USDA Forest
Service, Berkeley, Calif.
Cheney, N., Gould, J., and Catchpole, W. (1993). The influence of fuel, weather and fire
shape variables on fire-spread in grasslands. International Journal of Wildland Fire,
3(1):31–44.
Cheney, P. and Sullivan, A. (1997). Grassfires: Fuel, Weather and Fire Behaviour. CSIRO
Publishing, Collingwood, Australia.
Chetehouna, K., Er-Riani, M., and Sero-Guillaume, O. (2004). On the rate of spread
for some reaction-diffusion models of forest fire propagation. Numerical Heat Transfer
Part A-Applications, 46(8):765–784.
Colman, J. J. and Linn, R. R. (2003). Non-local chemistry implementation in HI-
GRAD/FIRETEC. In Fifth Symposium on Fire and Forest Meteorology, 16-20 Novem-
ber 2003, Orlando, Florida. American Meteorological Society.
Croba, D., Lalas, D., Papadopoulos, C., and Tryfonopoulos, D. (1994). Numerical sim-
ulation of forest fire propagation in complex terrain. In Proceedings of the 2nd Inter-
national Conference on Forest Fire Research, Coimbra, Portugal, Nov. 1994. Vol 1.,
pages 491–500.
Curry, J. and Fons, W. (1940). Forest-fire behaviour studies. Mechanical Engineering,
62:219–225.
Curry, J. R. and Fons, W. L. (1938). Rate of spread of surface fires in the ponderosa pine
type of california. Journal of Agricultural Research, 57(4):239–267.
de Mestre, N., Catchpole, E., Anderson, D., and Rothermel, R. (1989). Uniform propaga-
tion of a planar fire front without wind. Combustion Science and Technology, 65:231–
244.
di Blasi, C. (1998). Comparison of semi-global mechanisms for primary pyrolysis of lig-
nocellulosic fuels. Journal of Analytical and Applied Pyrolysis, 47(1):43–64.
Drysdale, D. (1985). An Introduction to Fire Dynamics. John Wiley and Sons, Chichester.
Dupuy, J. (1995). Slope and fuel load effects on fire behaviour: Laboratory experiments
in pine needle fuel beds. International Journal of Wildland Fire, 5(3):153–164.
33

Dupuy, J. (2000). Testing two radiative physical models for fire spread through porous
forest fuel beds. Combustion Science and Technology, 155:149–180.
Dupuy, J. and Larini, M. (1999). Fire spread through a porous forest fuel bed: a radia-
tive and convective model including fire-induced flow effects. International Journal of
Wildland Fire, 9(3):155–172.
Dupuy, J. L. and Morvan, D. (2005). Numerical study of a crown fire spreading toward a
fuel break using a multiphase physical model. International Journal of Wildland Fire,
14(2):141–151.
Ellis, P. (2000). The aerodynamic and combustion characteristics of eucalypt bark: A
firebrand study. PhD thesis, The Australian National University School of Forestry,
Canberra.
Emmons, H. (1963). Fire in the forest. Fire Research Abstracts and Reviews, 5(3):163–178.
Emmons, H. (1966). Fundamental problems of the free burning fire. Fire Research Ab-
stracts and Reviews, 8(1):1–17.
Evans, D., Rehm, R., and McPherson, E. (2003). Physics-based modelling of wildland-
urban intermix fires. In Proceedings of the 3rd International Wildland Fire Conference,
3-6 October 2003, Sydney.
Fernandes, P. (2001). Fire spread prediction in shrub fuels in Portugal. Forest Ecology
and Management, 144(1-3):67–74.
Fons, W. L. (1946). Analysis of fire spread in light forest fuels. Journal of Agricultural
Research, 72(3):93–121.
Forbes, L. K. (1997). A two-dimensional model for large-scale bushfire spread. Journal of
the Australian Mathematical Society, Series B (Applied Mathematics), 39(2):171–194.
Gaydon, A. and Wolfhard, H. (1960). Flames: Their Structure, Radiation and Tempera-
ture. Chapman and Hall Ltd, London, 2nd edition.
Gisborne, H. (1927). The objectives of forest fire-weather research. Journal of Forestry,
25(4):452–456.
Gisborne, H. (1929). The complicated controls of fire behaviour. Journal of Forestry,
27(3):311–312.
Goldstein, R. J., Ibele, W. E., Patankar, S. V., Simon, T. W., Kuehn, T. H., Strykowski,
P. J., Tamma, K. K., Heberlein, J. V. R., Davidson, J. H., Bischof, J., Kulacki, F. A.,
Kortshagen, U., Garrick, S., and Srinivasan, V. (2006). Heat transfer: A review of 2003
literature. International Journal of Heat and Mass Transfer, 49(3-4):451–534.
Grishin, A. (1984). Steady-state propagation of the front of a high-level forest fire. Soviet
Physics Doklady, 29(11):917–919.
Grishin, A. (1997). Mathematical modeling of forest fires and new methods of fighting
them. Publishing House of Tomsk State University, Tomsk, Russia, english translation
edition. Translated from Russian by Marek Czuma, L Chikina and L Smokotina.
34

Grishin, A., Gruzin, A., and Gruzina, E. (1984). Aerodynamics and heat exchange be-
tween the front of a forest fire and the surface layer of the atmosphere. Journal of
Applied Mechanics and Technical Physics, 25(6):889–894.
Grishin, A., Gruzin, A., and Zverev, V. (1983). Mathematical modeling of the spreading
of high-level forest fires. Soviet Physics Doklady, 28(4):328–330.
Grishin, A. and Shipulina, O. (2002). Mathematical model for spread of crown fires in
homogeneous forests and along openings. Combustion, Explosion, and Shock Waves,
38(6):622–632.
Hanson, H., Bradley, M., Bossert, J., Linn, R., and Younker, L. (2000). The potential
and promise of physics-based wildfire simulation. Environmental Science & Policy,
3(4):161–172.
Hawley, L. (1926). Theoretical considerations regarding factors which influence forest
fires. Journal of Forestry, 24(7):7.
Karplus, W. J. (1977). The spectrum of mathematical modeling and systems simulation.
Mathematics and Computers in Simulation, 19(1):3–10.
Larini, M., Giroud, F., Porterie, B., and Loraud, J. (1998). A multiphase formulation
for fire propagation in heterogeneous combustible media. International Journal of Heat
and Mass Transfer, 41(6-7):881–897.
Lawson, D. (1954). Fire and the atomic bomb. Fire Research Bulletin No. 1, Department
of Scientific and Industrial Research and Fire Offices’ Committee, London.
Lee, S. (1972). Fire research. Applied Mechanical Reviews, 25(3):503–509.
Linn, R. and Cunningham, P. (2005). Numerical simulations of grass fires using a coupled
atmosphere-fire model: Basic fire behavior and dependence on wind speed. Journal of
Geophysical Research, 110(D13107):19 pp.
Linn, R. and Harlow, F. (1998a). Use of transport models for wildfire behaviour simula-
tions. In III International Conference on Forest Fire Research, 14th Conference on Fire
and Forest Meteorology, Luso, Portugal, 16-20 November 1998. Vol 1, pages 363–372.
Linn, R., Reisner, J., Colman, J., and Smith, S. (2001). Studying wildfire behaviour using
FIRETEC. In Fourth Symposium on Fire and Forest Meteorology, 13-15 November
2001, Reno, Nevada., pages 51–55. American Meteorological Society.
Linn, R., Reisner, J., Colman, J. J., and Winterkamp, J. (2002a). Studying wildfire
behavior using FIRETEC. International Journal of Wildland Fire, 11(3-4):233–246.
Linn, R., Winterkamp, J., Edminster, C., Colman, J., and Steinzig, M. (2003). Model-
ing interactions between fire and atmosphere in discrete element fuel beds. In Fifth
Symposium on Fire and Forest Meteorology, 16-20 November 2003, Orlando, Florida.
American Meteorological Society.
Linn, R. R. (1997). A transport model for prediction of wildfire behaviour. PhD Thesis
LA-13334-T, Los Alamos National Laboratory. Reissue of PhD Thesis accepted by
Department of Mechanical Engineering, New Mexico State University.
35

Linn, R. R. and Harlow, F. H. (1998b). FIRETEC: A transport description of wildfire
behaviour. In Second Symposium on Fire and Forest Meteorology, 11-16 January 1998,
Pheonix, Arizona, pages 14–19. American Meteorological Society.
Linn, R. R., Reisner, J. M., Winterkamp, J. L., and Edminster, C. (2002b). Utility
of a physics-based wildfire model such as FIRETEC. In Viegas (2002), page 101.
Proceedings of the IV International Conference on Forest Fire Research, Luso, Coimbra,
Portugal 18-23 November 2002.
Lymberopoulos, N., Tryfonopoulos, T., and Lockwood, F. (1998). The study of small
and meso-scale wind field-forest fire interaction and buoyancy effects using the aiolos-f
simulator. In III International Conference on Forest Fire Research, 14th Conference
on Fire and Forest Meteorology, Luso, Portugal, 16-20 November 1998. Vol 1., pages
405–418.
Margerit, J. and Sero-Guillaume, O. (2002). Modelling forest fires. Part II: Reduction to
two-dimensional models and simulation of propagation. International Journal of Heat
and Mass Transfer, 45(8):1723–1737.
Mell, W., Jenkins, M., Gould, J., and Cheney, P. (2006). A physics based approach to
modeling grassland fires. International Journal of Wildland Fire, 15(4):in press.
Morandini, F., Santoni, P., and Balbi, J. (2000). Validation study of a two-dimensional
model of fire spread across a fuel bed. Combustion Science and Technology, 157:141 –
165.
Morandini, F., Santoni, P., and Balbi, J. (2001a). The contribution of radiant heat
transfer to laboratory-scale fire spread under the influences of wind and slope. Fire
Safety Journal, 36(6):519–543.
Morandini, F., Santoni, P., and Balbi, J. (2001b). Fire front width effects on fire spread
across a laboratory scale sloping fuel bed. Combustion Science and Technology, 166:67–
90.
Morandini, F., Santoni, P., Balbi, J., Ventura, J., and Mendes-Lopes, J. (2002). A two-
dimensional model of fire spread across a fuel bed including wind combined with slope
conditions. International Journal of Wildland Fire, 11(1):53–63.
Morvan, D. and Dupuy, J. (2001). Modeling of fire spread through a forest fuel bed using
a multiphase formulation. Combustion and Flame, 127(1-2):1981–1994.
Morvan, D. and Dupuy, J. (2004). Modeling the propagation of a wildfire through
a mediterranean shrub using a multiphase formulation. Combustion and Flame,
138(3):199–210.
Morvan, D. and Larini, M. (2001). Modeling of one dimensional fire spread in pine needles
with opposing air flow. Combustion Science and Technology, 164(1):37–64.
Morvan, D., Larini, M., Dupuy, J., Fernandes, P., Miranda, A., Andre, J., Sero-Guillaume,
O., Calogine, D., and Cuinas, P. (2004). Eufirelab: Behaviour modelling of wildland
fires: a state of the art. Deliverable D-03-01, EUFIRELAB. 33 p.
36

Pastor, E., Zarate, L., Planas, E., and Arnaldos, J. (2003). Mathematical models and
calculation systems for the study of wildland fire behaviour. Progress in Energy and
Combustion Science, 29(2):139–153.
Perry, G. (1998). Current approaches to modelling the spread of wildland fire: a review.
Progress in Physical Geography, 22(2):222–245.
Plucinski, M. P. (2003). The investigation of factors governing ignition and development
of fires in heathland vegetation. PhD thesis, School of Mathematics and Statistics
University of New South Wales, Australian Defence Force Academy, Canberra, ACT,
Australia.
Porterie, B., Morvan, D., Larini, M., and Loraud, J. (1998a). Wildfire propagation:
A two-dimensional multiphase approach. Combustion Explosion and Shock Waves,
34(2):139–150.
Porterie, B., Morvan, D., Loraud, J., and Larini, M. (1998b). A multiphase model for
predicting line fire propagation. In III International Conference on Forest Fire Research,
14th Conference on Fire and Forest Meteorology, Luso, Portugal, 16-20 November 1998.
Vol 1., pages 343–360.
Porterie, B., Morvan, D., Loraud, J., and Larini, M. (2000). Firespread through fuel
beds: Modeling of wind-aided fires and induced hydrodynamics. Physics of Fluids,
12(7):1762–1782.
Rehm, R., Evans, D., Mell, W., Hostikka, S., McGrattan, K., Forney, G., Boulding, C.,
and Baker, E. (2003). Neighborhood-scale fire spread. In Fifth Symposium on Fire
and Forest Meteorology, 16-20 November 2003, Orlando, Florida. paper J6E.7 8pp,
unpaginated.
Rehm, R. G. and Baum, H. R. (1978). The equations of motion for thermally driven,
buoyant flows. Journal of Research of the National Bureau of Standards, 83(3):297–308.
Reisner, J., Knoll, D., Mousseau, V., and Linn, R. (2000a). New numerical approaches for
coupled atmosphere-fire models. In Third Symposium on Fire and Forest Meteorology,
9-14 January 2000, Long Beach, California., pages 11–14. American Meteorological
Society.
Reisner, J., Wynne, S., Margolin, L., and Linn, R. (2000b). Coupled atmospheric-fire
modeling employing the method of averages. Monthly Weather Review, 128(10):3683–
3691.
Reisner, J. M., Bossert, J. E., and Winterkamp, J. L. (1998). Numerical simulations of
two wildfire events using a combined modeling system (HIGRAD/BEHAVE). In Second
Symposium on Fire and Forest Meteorology, 11-16 January 1998, Pheonix, Arizona,
pages 6–13. American Meteorological Society.
Rogers, J. C. and Miller, T. (1963). Survey of the thermal threat of nuclear weapons.
Technical Report SRI Project No. IMU-4201, Standford Research Institute, California.
Unclassified version, Contract No. OCD-OS-62-135(111).
Rothermel, R. (1972). A mathematical model for predicting fire spread in wildland fuels.
Research Paper INT-115, USDA Forest Service.
37

Sacadura, J. (2005). Radiative heat transfer in fire safety science. Journal of Quantitative
Spectroscopy & Radiative Transfer, 93:5–24.
Santoni, P. and Balbi, J. (1998a). Modelling of two-dimensional flame spread across a
sloping fuel bed. Fire Safety Journal, 31(3):201–225.
Santoni, P. and Balbi, J. (1998b). Numerical simulation of a fire spread model. In III
International Conference on Forest Fire Research, 14th Conference on Fire and Forest
Meteorology, Luso, Portugal, 16-20 November 1998. Vol 1., pages 295–310.
Santoni, P., Balbi, J., and Dupuy, J. (1999). Dynamic modelling of upslope fire growth.
International Journal of Wildland Fire, 9(4):285–292.
Sero-Guillaume, O. and Margerit, J. (2002). Modelling forest fires. Part I: A complete set
of equations derived by extended irreversible thermodynamics. International Journal
of Heat and Mass Transfer, 45(8):1705–1722.
Shafizadeh, F. (1982). Introduction to pyrolysis of biomass. Journal of Analytical and
Applied Pyrolysis, 3(4):283–305.
Simeoni, A., Larini, M., Santoni, P., and Balbi, J. (2002). Coupling of a simplified flow
with a phenomenological fire spread model. Comptes Rendus Mecanique, 330(11):783–
790.
Simeoni, A., Santoni, P., Larini, M., and Balbi, J. (2001a). On the wind advection
influence on the fire spread across a fuel bed: modelling by a semi-physical approach
and testing with experiments. Fire Safety Journal, 36(5):491–513.
Simeoni, A., Santoni, P., Larini, M., and Balbi, J. (2001b). Proposal for theoretical im-
provement of semi-physical forest fire spread models thanks to a multiphase approach:
Application to a fire spread model across a fuel bed. Combustion Science and Technol-
ogy, 162(1):59–83.
Simeoni, A., Santoni, P., Larini, M., and Balbi, J. (2003). Reduction of a multiphase
formulation to include a simplified flow in a semi-physical model of fire spread across a
fuel bed. International Journal of Thermal Sciences, 42(1):95–105.
Sullivan, A., Ellis, P., and Knight, I. (2003). A review of the use of radiant heat flux
models in bushfire applications. International Journal of Wildland Fire, 12(1):101–110.
Thomas, P. (1967). Some aspects of the growth and spread of fire in the open. Journal
of Forestry, 40:139–164.
Thomas, P. (1971). Rates of spread of some wind driven fires. Journal of Forestry,
44:155–175.
Turner, J. (1973). Buoyancy effects in fluids. Cambridge University Press, Cambridge.
Paperback edition 1979.
Van Wagner, C. (1967). Calculation on forest fire spread by flame radiation. Technical
Report Departmental Publication No. 1185, Canadian Department of Forestry and
Rural Development Forestry Branch.
38

Vaz, G., Andre, J., and Viegas, D. (2004). Fire spread model for a linear front in a hori-
zontal solid porous fuel bed in still air. Combustion Science and Technology, 176(2):135–
182.
Viegas, D., editor (2002). Forest Fire Research & Wildland Fire Safety, Rotterdam,
Netherlands. Millpress. Proceedings of the IV International Conference on Forest Fire
Research, Luso, Coimbra, Portugal 18-23 November 2002.
Weber, R. (1989). Analytical models of fire spread due to radiation. Combustion and
Flame, 78:398–408.
Weber, R. (1991a). Modelling fire spread through fuel beds. Progress in Energy Combus-
tion Science, 17(1):67–82.
Weber, R. (1991b). Toward a comprehensive wildfire spread model. International Journal
of Wildland Fire, 1(4):245–248.
Williams, F. (1982). Urban and wildland fire phenomenology. Progress in Energy Com-
bustion Science, 8:317–354.
Williams, F. A. (1985). Combustion Theory: The Fundamental Theory of Chemically
Reacting Flow Systems. Addison-Wesley Publishing Company, Massachusetts, 2nd edi-
tion, 1994 edition.
Wolff, M., Carrier, G., and Fendell, F. (1991). Wind-aided firespread across arrays of
discrete fuel elements. II. Experiment. Combustion Science and Technology, 77:261–
289.
Wu, Y., Xing, H. J., and Atkinson, G. (2000). Interaction of fire plume with inclined
surface. Fire Safety Journal, 35(4):391–403.
39

Table 1: Outline of the major biological, physical and chemical components and processes
occurring in a wildland fire and the temporal and spatial (vertical and horizontal) scales
over which they operate.
Type Time scale (s) Vertical scale (m) Horizontal scale (m)
Combustion reactions 0.0001 - 0.01 0.0001 - 0.01 0.0001 - 0.01
Fuel particles - 0.001 - 0.01 0.001 - 0.01
Fuel complex - 1 - 20 1 - 100
Flames 0.1 - 30 0.1 - 10 0.1 - 2
Radiation 0.1 - 30 0.1 - 10 0.1-50
Conduction 0.01 - 10 0.01 - 0.1 0.01 - 0.1
Convection 1 - 100 0.1 - 100 0.1 - 10
Turbulence 0.1 - 1000 1 - 1000 1 - 1000
Spotting 1 - 100 1 - 3000 1 - 10000
Plume 1 - 10000 1 - 10000 1 - 100
Table 2: Approximate analysis of some biomass species (Shafizadeh, 1982).
Species Cellulose (%) Hemicellulose (%) Lignin (%) Other (%)
Softwood 41.0 24.0 27.8 7.2
Hardwood 39.0 35.0 19.5 6.5
Wheat straw 39.9 28.2 16.7 15.2
Rice straw 30.2 24.5 11.9 33.4
Bagasse 38.1 38.5 20.2 3.2
Table 3: Summary of physical models (1990-present) discussed here.
Model Author Year Country Dimensions Plane
Weber Weber 1991 Australia 2 XY
AIOLOS-F Croba et al. 1994 Greece 3 -
FIRETEC Linn 1997 USA 3 -
Forbes Forbes 1997 Australia 1 X
Grishin Grishin et al. 1997 Russia 2 XZ
IUSTI Larini et al. 1998 France 2 XZ
PIF97 Dupuy et al. 1999 France 2 XZ
LEMTA Sero-Guillaume et al. 2002 France 2(3) XY
UoS Asensio et al. 2002 Spain 2 XY
WFDS Mell et al. 2006 USA 3 -
Table 4: Summary of quasi-physical models (1990-present) discussed here.
Model Author Year Country Dimensions Plane
ADFA I de Mestre 1989 Australia 1 X
TRW Carrier 1991 USA 2 XY
Albini Albini 1996 USA 2 XZ
UC Santoni 1998 France 2 XY
ADFA II Catchpole 1998 Aust/USA 2 XZ
Coimbra Vaz 2004 Portugal 2 XY
40

Table 5: Summary of all models
Model No. Domain Size Resolution (m) CPU Simulation Computation Comment
Dimensions (x × y × z) ∆x ∆y ∆z ∆t No. & Type Time(s) Time (s)
Physical
Weber 2 ? ? - - ? ? ? ?
AIOLOS-F 3 10 × 10 × ? km ? ? ? ? ? ? ? < real time
FIRETEC 3 320 × 160 × 615 m 2 m 2 m 1.5 m 0.002 s 128 nodes ? ? >> real time
Forbes 2 ? ? ? - ? ? ? ?
Grishin 2 50 × - × 12 m ? - ? ? ? ? 700 K isotherm
IUSTI 2 2.2 × - × 0.9 m 0.02 - 0.09 ? ? ? ? 500 K isotherm
PIF97 2 200 × - × 50 m 0.25 0.25 1 s P4 2GHz 200 s 48 h 500 K isotherm
LEMTA 2 ? ? ? - ? ‘PC’ ? ? ≃ real time
UoS 2 ? 1.875 m 1.875 m - 0.25µs ? ? ?
WFDS 3 1.5 × 1.5 × 0.2 km 1.5 m 1.5 m 1.4 m - 11 nodes 100 s 25 h
Quasi-physical
ADFA I 1 ? ? - - ? ? ?
TRW 2 ? ? ? - ? ? ? ?
Albini 2 ? ? - ? ? ? ? ?
UC 1 1 × 1 × - m 0.01 m 0.01 0.01 0.01 s Sun Ultra II 144 s 114 s 500 K isotherm
ADFA II 2 ? ? - ? ? ? ? ?
Coimbra 2 ? ? ? ? ? ? ? ?
41

Figure 1: Schematic of chemical structure of portion of neighbouring cellulose chains,
indicating some of the hydrogen bonds (dashed lines) that may stabilise the crystalline
form of cellulose (Source: Ball et al. (1999)
S
V
C + D + H2O
k1
k2
D
O2
H2O
O2
Products + D
Products + D
k3
k4
Figure 2: Schematic of the competing paths possible in the thermal degradation of cellulose
substrate (S). Volatilisation into levoglucosan (V) in the absence of moisture is endothermic.
Subsequent oxidisation of levoglucosan into products is exothermic. Char formation (C) occurs
at a lower activation energy in the presence of moisture. This path is exothermic and forms
water. Chemical and thermal feedback paths (dashed lines) can encourage either volatilisation
or charring. (After di Blasi (1998); Ball et al. (1999))
42