A review of wildland fire spread modelling, 1990-present 2: Empirical and quasi-empirical models
aa r X i v : . [ phy s i c s . g e o - ph ] J un A review of wildland fire spread modelling,1990-present2: Empirical and quasi-empirical models
A.L. SullivanFebruary 17, 2013
Ensis Bushfire Research PO Box E4008, Kingston, ACT 2604, Australiaemail: [email protected] or [email protected]: +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 andbehaviour of wildland fires across the landscape. This series of review papers endeav-ours to critically and comprehensively review all types of surface fire spread modelsdeveloped since 1990. This paper reviews models of an empirical or quasi-empiricalnature. These models are based solely on the statistical analysis of experimentallyobtained data with or without some physical framework for the basis of the re-lations. Other papers in the series review models of a physical or quasi-physicalnature, and mathematical analogues and simulation models. The main relationsof empirical models are that of wind speed and fuel moisture content with rateof forward spread. Comparisons are made of the different functional relationshipsselected by various authors for these variables.
Introduction
History
An empirical model is one that is based upon observation and experiment and not ontheory. Empiricism has formed the basis for much of the scientific and technologicaladvances in recent centuries and generally provides the benchmark against which theory A CSIRO/Scion Joint Venture current address: Department of Theoretical Physics,Research School of Physical Sciences and EngineeringThe Australian National University, Canberra 0200, Australia.
1s tested. The study of fire and combustion in general was mainly an empirical endeavour,directed primarily toward application of combustion to industrial processes (for example,the industrial revolution of the late 1700s-1800s), until early in the previous century whenthe physical or theoretical approach had matured to the point of providing significantadvances in understanding and prediction. The development of physical understanding ofother forms of combustion (i.e. unintentional or uncontrolled fire) in general and wildlandfires in particular, did not occur, however, until only very recently (in the last few decades)(Sullivan, 2007).While there had always been a great general interest in unintentional fire in urban settings(Williams, 1982), for instance, the Great Fire of London in 1666, or the Chicago Fireon October 1871–prevention, control, prediction–unintentional fire in wildlands receivedmuch less attention, mainly due to the relatively little impact such fires have on the generalpopulace. The study of the behaviour of fires in wildland regions has traditionally beendriven by the needs of those practitioners involved in wildland resource management–foresters for the most part–for whom understanding this natural phenomenon was criticalto the success of their work.Despite the fact that practically no region of the world (except for Antarctica) is free fromsuch fires, much of the work in this field was galvanised in the United States following thedevastating 1910 fires in the mid-west (Pyne, 2001), where workers such as Hawley (1926)and Gisborne (1927, 1929) pioneered the notion that understanding of the phenomenonof wildland fire and the prediction of the danger posed by a fire could be gained throughmeasurement and observation and theoretical considerations of the factors that mightinfluence such fires. Curry and Fons (1938, 1940), and Fons (1946) brought a rigorousphysical approach to the measurement and modelling of the behaviour of wildland firesthat set the benchmark for wildland fire research for decades following.In addition to the work conducted in the US, through the Federal US Forest Service andState agencies, other countries became increasingly involved in wildland fire research,primarily through their forest services–the Canadian Forest Service, the CommonwealthForestry and Timber Bureau (later absorbed into the Commonwealth Scientific and In-dustrial Research Organisation (CSIRO) in conjunction with various state authorities inAustralia–although many other countries such as South Africa, Spain, Russia, France,Portugal to name a few, have also had significant impact on wildland fire research.Since the early 1990s, European Union countries have committed significant funds towardswildland fire research, resulting in a boom period for this research in mainly Mediterraneancountries and a major shift in focus away from the pioneering three (US, Canada andAustralia).During the past two decades, the direction of much of the wildland fire research has beentoward the use of fire as a resource management tool in the form of hazard reduction burn-ing or the study of ecological effects of fire (e.g. Gill et al. (1981); Goldammer and Jenkins(1990); Abbot and Burrows (2003).
Empirical modelling
The focus of empirical modelling of wildland fire in the past has been on the determinationof the key characteristics used to describe the behaviour of the fire. These generally have2een the rate of forward spread (ROS) of the head fire (that portion of the fire perimeterbeing blown downwind and normally of much greater intensity that the rest of the fireperimeter), the height of the flames, the angle of the flames, and the depth of flames atthe head, although other characteristics such as rate of perimeter or area increase mayalso be of some interest.While observations of wildfires or fires lit intentionally for other purposes (such as hazardreduction or prescribed fires) have been used in the development of empirical models offire behaviour, the predominant method has been the lighting of ‘experimental’ fires–fires whose only purpose is that of an experimental nature. This method can be dividedinto four parts. Firstly, the characterisation and quantification of the fuel and terrainin which the fire will lit (the slowly varying variables, which has included fuel load, fuelheight, moisture content, bulk density, combustion characteristics, slope, etc.). Secondly,the observation and measurement of the atmospheric environment (the quickly varyingvariables, wind speed and direction, air temperature, relative humidity, etc.). Thirdly, thelighting, observation and measurement of the fire itself (its speed, spread, flame geometry,combustion rate, combustion residues, smoke, etc.). Fourthly, the statistical correlationbetween any and all of the measured quantities in order to produce the model of firebehaviour. Many workers have chosen to limit or control the possible natural variation inmany quantities by conducting experimental fires in laboratory conditions which aids inthe analysis of such fires.The primary use of such models has been to estimate the likely spread in the direction ofthe wind (and potential for danger to firefighter safety) for suppression planning purposes,much of which has traditionally been conducted in the form of simple ‘back of the envelope’calculations for plotting on a wall map. Due to this simple need, empirical fire spreadmodels have traditionally been one dimensional models in which the independent variablethat is predicted is the rate of forward spread of the head of the fire in the direction ofthe wind. The rather pragmatic nature of these models, their relatively straightforwardimplementation, their direct relation to the behaviour of real fires, and, perhaps mostimportantly, their development by for the most part by forestry agencies for their ownimmediate use, have meant that empirical fire spread models have gained acceptance withwildland fire authorities around the world and to varying degrees form the basis for alloperational fire behaviour models in use today.
Operational models
In the United States, the quasi-empirical model of Rothermel (1972) forms the basis of theNational Fire Danger Rating System (Deeming et al., 1977; Burgan, 1988) and the firebehaviour prediction tool BEHAVE (Andrews, 1986). This model is based on a heat bal-ance model first proposed by Fransden (1971) and utilised data obtained from wind tunnelexperiments in artificial fuel beds of varying characteristics and from Australian field ex-periments of grassfires in a range of wind speed conditions to correlate fire behaviour withmeasured input variables. The model of Rothermel (1972) and associated systems havebeen introduced to a number of countries, particularly Mediterranean Europe.In Australia, the predominant operational fire spread prediction systems have been theMcArthur Grassland (McArthur, 1965, 1966) and Forest (McArthur, 1967) Fire DangerRating Systems (FDRS), and the Forest Fire Behaviour Tables for Western Australia3commonly called the Red Book) (Sneeuwjagt and Peet, 1985), based on the work of Peet(1965). Both McArthur’s systems and the Red Book are purely empirical correlations ofobserved fire behaviour and measured fuel and environmental variables from mainly fieldexperimental fires augmented by well-documented wildfires . More recently, the CSIROGrassland Fire Spread Meter (GSFM) (CSIRO, 1997; Cheney and Sullivan, 1997) basedon the empirical modelling of Cheney et al. (1998) has replaced the McArthur GrasslandFDRS as the preferred tool for predicting fire behaviour in grasslands. This, too, is basedon field experimentation and documented wildfire observations.In Canada, the quasi-empirical Fire Behaviour Prediction (FBP) System (Forestry Canada Fire Danger Group1992) forms part of the Canadian Forest Fire Danger Rating System (CFFDRS) and is theculmination of 60 years of research effort in fuel moisture and fire behaviour (Van Wagner,1998; Taylor and Alexander, 2006). Almost 500 fires were used in the construction of theFBP system, of which approximately 400 were field experiments, the remainder well-documented observations of prescribed and wild fires. The CFFDRS has been introducedand implemented in a number of countries, including New Zealand, Mexico and severalcountries of south-east Asia.The main characteristic of all but the CSIRO GSFM is that these systems were basedprimarily on small ( < . The series of experiments upon which the CSIRO GFSM was based(Cheney et al., 1993) was the first to use experimental burning plots of which the smallestwas 1 ha (See review of this model below). 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 rangeof methods that have been undertaken over the years represents a continuous spectrumof possible modelling (Karplus, 1977), ranging from the purely physical (those that arebased on fundamental understanding of the physics and chemistry involved in the be-haviour of a wildland fire) through to the purely empirical (those that have been based onphenomenological description or statistical regression of fire behaviour). In between is acontinuous meld of approaches from one end of the spectrum or the other. Weber (1991),in his comprehensive review of physical wildland fire modelling, proposed a system bywhich models were described as physical, empirical or statistical, depending on whetherthey accounted for different modes of heat transfer, made no distinction between differentheat transfer modes, or involved no physics at all. Pastor et al. (2003) proposed modeldescriptions of theoretical, empirical and semi-empirical, again depending on whether themodel was based on purely physical understanding, of a statistical nature with no physicalunderstanding, or a combination. Grishin (1997) divided models into two classes, deter-ministic or stochastic-statistical. However, these schemes are rather limited given thecombination of possible approaches, and, given that describing a model as semi-empiricalor semi-physical is a ‘glass half-full or half-empty’ subjective issue, a more comprehensiveand complete convention was required. Another interesting characteristic is that the CSIRO GFSM model was the only one published in apeer-reviewed journal; all the others were published as technical reports by the associated organisations.
Previous reviews
Many of the reviews that have been published in recent years have been for audiences otherthan wildland fire researchers and conducted by people without an established backgroundin the field. Indeed, many of the reviews read like purchase notes by people shoppingaround for the best fire spread model to implement in their part of the world for theirparticular purpose. Recent reviews (e.g. Perry (1998); Pastor et al. (2003); etc), whileendeavouring to be comprehensive, have offered only superficial and cursory inspectionsof the models presented. Morvan et al. (2004) take a different line by analysing a muchbroader spectrum of models in some detail and conclude that no single approach is goingto be suitable for all purposes.While the recent reviews provide an overview of the models and approaches that have beenundertaken around the world, mention must be made of significant reviews published muchearlier that discussed the processes in wildland fire propagation themselves. Foremost isthe work of Williams (1982) which comprehensively covers the phenomenology of bothwildland and urban fire, the physics and chemistry of combustion, and is recommendedreading 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 era. Grishin(1997) provides an extensive review of the work conducted in Russia in the 1970s, 80sand 90s. Chandler et al. (1983) and Pyne et al. (1996) provide a useful review of theforestry approach to wildland fire research, understanding and practice.The first paper in this series discussed those models based upon the fundamental principlesof the physics and chemistry of wildland fire behaviour. This particular paper will discussthose models based directly upon only statistical analysis of fire behaviour observationsor models that utilise some form of physical framework upon which the statistical analysisof observations have been based. In this paper, particular distinction is made betweenobservations of the behaviour of fires in the strictly controlled and artificial conditions ofthe laboratory and those observed in the field under more naturally occurring conditions.5he last paper in the series will focus upon models concerned only with the simulation offire spread over the landscape and models that utilise mathematical conceits analogousto fire spread but which have no real-world connection to fire.
Empirical models
The following sections identify and discuss those empirical and quasi-empirical surface-only fire spread models that appeared in the literature since 1990. It is interesting tonote the observation of Catchpole (2000) that the majority of new models that have beendeveloped in recent years have been the result of efforts to initially develop and validatelocal fuel models required for the implementation of the BEHAVE (based on Rothermel)fire behaviour prediction system. Many researchers obviously felt that it was far easier tostart from scratch with a purpose built model than to try to retrofit their local conditionsinto an existing model. Table 1 summarises the empirical models discussed in this review.Due to the varied nature of the empirical models presented here, including the fuelsand weather conditions under which the data for the construction of the models werecollected, the size and number of experimental fires and purposes for which the modelswere developed, it is difficult to compare them side by side. One possible method isthe relationship between rate of forward spread (ROS) and wind speed. Wind speed iswidely accepted as being the dominant variable determining the forward speed of a firefront. The reasons for this are cause for significant debate, ranging from the reduction inangle of separation of flame to unburnt fuel to increased turbulent mixing of combustants.Regardless of the mechanics of the process, the empirical approach to modelling fire spreadmust cater for this process and is manifested in the functional form chosen to representit. Fuel moisture content (FMC) is also a key variable in determining rate of spread andthis is also discussed. Fire spread models for fuel layers other than surface fuels, such ascrown fires or ground fires, are not covered.
Canadian Forest Service (CFS) - Acceleration (1991)
While the Canadian Forest Service (CFS-accel) work (McAlpine and Wakimoto, 1991)is not a model of fire spread as such, it does address a major concern of fire spread,namely the acceleration in rate of fire spread from initiation. The assumption is that afire will attain an equilibrium rate of spread for the prevailing conditions (the predictionof which is the primary aim of all fire spread prediction systems discussed here). Theform of the function for the time to reach this equilibrium ROS is assumed to be expo-nential based on models proposed by Cheney (1981) and Van Wagner (1985) (as cited byMcAlpine and Wakimoto (1991)).29 experimental fires were conducted in a wind tunnel with a fuel bed 6.15 m long by 0.915m wide consisting of
Pinus ponderosa needles or excelsior of varying fuel load and bulkdensity. Four wind speeds (0, 0.44, 1.33 and 2.22 m s − ) measured at mid-flame heightwere used. Temperature and relative humidity were held constant at 26.7 ◦ C and 80%. Excelsior is wood shavings cut into long thin strands
CALM Spinifex (1991)
The Western Australia Department of Conservation and Land Management (CALM)Spinifex model (Burrows et al., 1991) was developed from 41 experimental fires conductedin predominantly spinifex (
Triodia basedowii and
Plectrachne schinzii ) fuels on relativelyflat sand plains. These fires were lit using drip torches to create lines of fire up to 200 mlong perpendicular to the wind direction. Fuel particle dimension and arrangement weremeasured for individual clumps; fuel distribution, quantity and moisture content weremeasured using line transect methods. Bare ground between clumps was also measured.Wind speed and direction, air temperature and relative humidity were measured at 10-min intervals. Wind speed ranged over 1.11 - 10 m s − and FMC over 12-31%. Fire spreadwas measured using metal markers placed near the flame front at intervals of 1-4 minsand later surveyed. Fires were allowed to spread until they self-extinguished. The rangeof ROS was 0-1.53 m s − . Data gathered were analysed using multiple linear regressiontechniques.Burrows et al. (1991) found that above a threshold wind speed zone (3.33-4.72 m s − ), inwhich flames are tilted sufficiently to bridge the gap between hummocks (Bradstock and Gill,1993; Gill et al., 1995), the ROS varied with the square of the wind speed (R = 0.85).Below the threshold wind speed zone, which depends on the percent cover of fuel (ratio ofpercentage of area covered by hummocks to bare ground), the fire does not spread. Thehigher the percent cover, the lower the threshold wind speed required. A lesser, negative,linear correlation was determined with FMC. Percent cover and air temperature were alsofound to influence the ROS but much less than either wind or FMC. Fuel load and otherfuel characteristics were found not to be important. Canadian Forest Fire Behaviour Prediction (CFBP) System (1992)
The Canadian Forest Fire Behaviour Prediction (CFBP) System is a component of theCanadian Forest Fire Danger Rating System (CFFDRS) (Stocks et al., 1991), which alsoincorporates the Canadian Forest Fire Weather Index (CFWI) System. The CFFDRS isthe result of continuing research into forest fire behaviour since the mid-1920s and hasundergone several incarnations in that time. The current CFFDRS system came into beingin the late 1960s in the form of a modular structure. The first major component to becompleted was the CFWI in 1971, which provided a relative measure of fuel moisture andfire behaviour potential for a standard fuel type, and has been revised several times since7ts introduction (Van Wagner, 1987). While there have been several interim editions of theCFBP, the first of which appeared in 1984 (Lawson et al., 1985), it was not until 1992 thata final version of the prediction system was released (Forestry Canada Fire Danger Group,1992; Taylor and Alexander, 2006) and thus is covered in this review.The CFBP system, following on from the long-established Canadian approach to studyingwildland fire, is based on the combined observations of nearly 500 experimental, prescribedand wild fires in 16 discrete fuel types covering 5 major groups: coniferous, deciduous,mixed wood, slash and grass fuels. The experimental work on which the system is basedwas conducted by individual researchers working in specific fuel types and locales acrossthe country using a variety of methods and published in a variety of places (initiallyincluding the 1966 work of McArthur in Australian grasslands, later replaced by the dataof Cheney et al. (1993) (Forestry Canada Fire Danger Group, 1992)). Alexander et al.(1991) provides an overview of the methods used since the 1960s to obtain the datasetfrom the CFBP was derived, but which, due to a number of factors (including technologicalimprovements) evolved over the years. The result is a system constructed by a small groupof dedicated researchers over a period of 20 years that has broad applicability to a widerange of fuels and climates.Experimental burn plots varied in size from 0.1 ha up to 3 ha (Alexander et al., 1991),with the majority being less than 1 ha. Ignition methods included both point ignitionsas well as line-ignitions. Wind speed unaffected by the fire was measured at 10-m in theopen (or converted a 10-m in the open equivalent). Experiments were usually conductedin the late afternoon in order to attain maximum burning conditions for the day. ROS wasnormally measured by visual observations of fire passage over predetermined distances.For point ignition experiments, metal tags were placed at the head and flanks of the fireand surveyed afterwards.The final version of the CFBP system works in conjunction with the CFWI system todetermine an Initial Spread Index (ISI) for the standard fuel type (pine forest) and basedsolely on fine FMC and wind speed. The functions chosen for the effect of wind speedand fine FMC on the ISI are exponential (exponent 0.05039) for wind, and a complicatedmix of exponential and power law (exponents -0.1386 and 5.31 respectively) for FMC(Van Wagner, 1987). No quantification of performance of these functions is given.To predict ROS, the ISI is modified by a Build-up Index (BUI), which is a fuel-specificfuel consumption factor that includes fuel moisture. Predicted ROS is the headfire ROSon level terrain under equilibrium conditions, thereby implicitly including effects of ac-celeration and crowning (Forestry Canada Fire Danger Group, 1992). The effect of slope(Van Wagner, 1977b) and crown fire transition effects (Van Wagner, 1977a) then mod-ify the basic ROS. Recent work of the International Crown Fire Modelling Experiment(Stocks et al., 2004) has investigated the behaviour of fully-developed crown fires (whichis not covered in this review as it is outside the scope of surface fire spread).
Button (1995)
Marsden-Smedley and Catchpole (1995b) presented a model for the prediction of ROSand flame height of fires in Tasmanian buttongrass moorlands, described as largely tree-less communities dominated by sedges and low heaths (Marsden-Smedley and Catchpole,8995a). The behaviour of 64 fires (of which 44 were experimental fires, 4 test fires, 11fuel reduction fires and 5 wildfires) at 12 sites was measured. Experimental burns wereconducted on blocks of either 0.25 or 1.0 ha with ignition line lengths of 50 or 100 mrespectively under a limited range of weather conditions. ROS was measured by eitherusing metal tags thrown at different times or by timing the passage of flames past pre-measured locations. For experimental fires, wind speed and direction, temperature andrelative humidity were measured at 10 m, and wind speed only at 1.7 m above groundlevel, all averaged over 1-3 min periods. Meteorological data for non-experimental fireswere collected using handheld sensors at 1.7 m. Data ranged from 0.19 - 10 m s − forwind speed and 8.2-96% for FMC, and 0 - 0.92 m s − for ROS.Marsden-Smedley and Catchpole (1995b) found surface wind speed, dead FMC and fuelage (time since last fire) to be the key variables affecting ROS, with wind being the domi-nant factor. Age and FMC each accounted for 15 to 20% of the observed variation in ROS.A power law with an exponent of 1.312 was used to describe the effect of wind, whereasboth the FMC and fuel age were modelled as exponential functions (FMC decreasing, ageincreasing to a maximum at about 40 years). Rates of spread of the back and flank ofthe fires were found to be approximately 10% and 40% of the head ROS, respectively. CALM Mallee (1997)
McCaw (1997) conducted a large-scale field experiment in
Eucalyptus tetragona mallee-heath community in south-west Western Australia. Shrubs < ×
200 m were established in 20-year-old fuel in flat terrain. A semi-permanent meteorological site was set up 500 m fromthe experimental plots recording 30 min averages of temperature and relative humidity at1.5 m and wind speed and direction at 2 m. During each experiment, mean wind speedand direction at a location up to 250 m upwind of the plot were measured at heights of 2m and 10 m at 30 s intervals. FMC was measured using 5 samples of four fuel components(3 dead and 1 live) collected post-fire within 30 min of ignition. Wind speed at 10 m inopen ranged from 1.5-6.9 m s − , FMC 4-32%. Experimental fires were ignited using avehicle-mounted flame thrower to establish a line perpendicular to the prevailing windup to 200 m long. Fire spread was measured using buried electronic timers (placed ona 24-point grid) equipped with a fusible link that melted on exposure to flames. ROSranged 0.13-0.68 m s − .Isopleths representing the position of the fire front at successive time intervals were fittedto the grid of timer data for each plot using a contouring routine based on a distance-weighted least squares algorithm. ROS up to 0.67 m/s and fireline intensities up to 14MW/m were recorded. Fires were found to spread freely when the FMC of the deadshallow litter layer beneath the low shrubs was < SIRO Grass (1997)
The CSIRO Grassland Fire Spread Meter (CSIRO, 1997) is a cardboard circular sliderule that encapsulates the algorithms developed by Cheney et al. (1998) for fire spread innatural, grazed and eaten-out grassland pastures. These algorithms are based primarilyon the results of experiments conducted in annual grasses of the Northern Territory withthe aim of determining the relative importance of fuel characteristics on rate of forwardspread of large unconstrained fires, particularly fuel load (Cheney et al., 1993), augmentedby large experimental fires conducted in open woodland (Cheney and Gould, 1995) anddetailed observations of 20 wildfires. 121 experimental fires were carried out on a floodplain in a range of fuel treatments under a variety of weather conditions (Cheney et al.,1993; Cheney and Gould, 1995) in prepared blocks ranging in size from 100 ×
100 m to200 ×
300 m. These fires were predominantly lit from lines ranging in length from 30to 175 m, although there were also a number of point ignitions, and allowed to burnfreely. The range of fuel treatments included mowing and removing cuttings, mowing andretaining cuttings, or leaving the grass in its natural state. Two distinct grass species(
Eriachne burkittii and
Themeda australis ), of different height, bulk density and finenesswere present.Fuel characteristics (height, load, bulk density, etc.) were measured on four transectsthrough each plot approximately every 25 m. In addition to remote standard 10 m and2 m meteorological stations, the wind speed at 2 m was measured at the corner of eachplot and averaged for each ROS interval. FMC samples were taken before and after eachfire. ROS and flame depth were measured from a series of rectified time-stamped obliqueaerial photographs of each fire. Wind speed ranged from 2.9 - 7.1 m s − , FMC 2.7-12.1%,and ROS 0.29-2.07 m s − .Cheney and Gould (1995) found the growth of the fires to be related to wind speed andthe width of the head fire normal to the wind direction. They found that the width ofthe fire required to achieve the potential quasi-steady ROS for the prevailing conditionsincreased with increasing wind speed, and the time to reach this quasi-steady ROS washighly variable. ROS was found to depend on the initial growth of the fire, the pasture type(natural, grazed or eaten-out), wind speed and live and dead FMC. Utilising the notion ofpotential quasi-steady ROS and a minimum threshold wind speed for continuous forwardspread, Cheney et al. (1998) developed a model of fire spread assuming a width necessaryto reach the potential ROS. This model uses wind speed, dead FMC and degree of curingto predict the potential (i.e. unrestricted) ROS for the prevailing conditions. Above athreshold of 5 km h − the ROS is assumed to have a power function (with an exponentless than 1 (0.844)) relation with the wind speed. This wind speed function is similar tothat proposed by Thomas and Pickard (1961), in which a power function with exponentof just less than 1 was found. Less than the threshold, the ROS is linear with wind speedand dominated by dead FMC. Heath (1998)
A cooperative research effort from a number of Australasian organisations, Heath (Catchpole et al.,1998a) utilises observations of 133 fires (comprising a mix of experimental (95), prescribed1022) and wild (16) fires) conducted in mixed heathland (heath and shrub) fuels. This in-cludes 48 experiments conducted by Marsden-Smedley and Catchpole (1995b) in button-grass. Only experimental and prescribed fires were used in model development; wildfireobservations were used for validation.In mixed heathland (comprising heath, scrub and gorse in New Zealand and mixed speciesincluding Banksia, Hakea and Allocasuarina in Australia), fuel age ranged from 5-25 years.Fires were lit as lines of unstated length on slopes < ◦ . Due to the disparate natureof the researchers involved, methods for measuring variables varied from experiment toexperiment. Wind speed was generally measured by handheld anemometry at 2 m at20 s intervals and averaged over the life of the fire. Wind speed ranged from 0.11-10.1m s − and ROS 0.01-1.00 m s − . Fuel load does not appear to have been measuredbut fuel height was. FMC was measured in some cases and modelled in others usingpre-established functions based on air temperature and relative humidity.Wind speed was found to account for 53% of the variation in ROS. Aerial dead fuel (i.e.those fuels not in contact with the ground) FMC was found not to be significant. Fuelheight was highly significant and with wind accounted for 70% of the variation in ROS.A power function of wind speed (exponent 1.21) was used to describe this variation. Apower function was also used for fuel height (exponent 0.54).The model was found to perform reasonably well for the selection of wildfires, consideringthe paucity of available data and necessary assumptions about the involved fuel charac-teristics (fuel height, moisture etc.) but could be improved with more variables. Thewind power function does fail for zero wind but was found to better fit the data than anexponential growth function. PortShrub (2001)
Fernandes (2001, 1998) presented a model developed from field experiments and obser-vations of prescribed burns conducted in four different types of shrub in flat terrain ofPortugal. He found that Rothermel (1972) did not predict observed ROS well. 29 fireswere conducted on flat ( < ◦ slope) in gorse, low heath, tall heath and tall heath/tree mix.Fine aerial live and dead FMC was sampled prior to each burn. Meteorological variables(wind speed, air temperature, relative humidity) were measured at 2 m in the open us-ing either a fixed weather station placed near the burn plot or upwind with handheldinstruments. Fires were lit as lines of length 10 m in experimental fires and 100 m inprescribed burns. ROS was measured by recording time of arrival of the head fire atreference locations. Wind speed ranged 0.28-7.5 m s − , FMC 10-40% and ROS 0.01-0.33m s − .ROS was significantly correlated with wind speed (1% level) and less so with RH, temper-ature, and aerial dead FMC (5%). Other fuel characteristics were also found to affect ROSbut were strongly intercorrelated and thus could not be separated, however, preferencewas given to fuel height. The initial model found a power law (exponent 1.034) for windspeed. However, as the model predicted no ROS in zero wind, an exponential function(coefficient 0.092) was subsequently incorporated. The final model, with an exponentialdecay function for dead FMC (coefficient -0.067) and power function (exponent 0.932) forfuel height, improved the overall performance of the model (R = 0.91). The model was11lso found to predict well the data sets of other authors and be in close agreement withother field studies (e.g. Marsden-Smedley and Catchpole (1995b); Cheney et al. (1998);Catchpole et al. (1998a)). CALM Jarrah I (1999)
Burrows (1999a, 1994) conducted a series of 144 laboratory experiments (54 wind-driven,6 no wind, 13 backing, 34 with slope, 15 point ignition) using fallen leaves and twigs ( < − with mean 1.06 m s − . ROS ranged 0.002-0.075 m s − .In wind-driven fires, no relationship between fuel load and forward ROS was found. Mostvariation in ROS was due to wind speed (correlation coefficient 0.94). ROS was negativelyrelated to FMC (correlation coefficient -0.31). Backing ROS was found to be directlyrelated to fuel load.At wind speeds < − , ROS was relatively insensitive to wind. Above this value,ROS was found to vary linearly with wind speed. However, a power function (exponent2.22) was used to model wind speed effect on ROS. An inverse linear function was usedfor FMC. This model was found to underspecify ROS > − with an error variancethat increased with ROS. CALM Jarrah II (1999)
Burrows (1999b, 1994) studied four series of fire behaviour data obtained from field ex-periments and fuel reduction burns on flat to gently sloping terrain in Jarrah (
Eucalyptusmarginata ) forest in south-west Western Australia to test Jarrah I and other models forforest fire spread. Fuel was characterised by a layer of dead leaves, twigs, bark and floralparts on the forest floor with low ( < ×
200 m long. 56 of 66 total plots were lit from linesof 50-100 m length, the remainder being point ignitions.Historical (pre-fire) weather data (including rainfall, temperature, relative humidity, windspeed and direction at 2 hourly intervals) were obtained from nearby permanent weatherstations. During each experiment a portable weather station approximately 50 m fromthe fire recorded wind speed at 1.5 m and 10 m and temperature and relative humidityat 1.5 m at 5 minute averages. FMC was measured at the time of ignition. Wind speedat 10 m in the open ranged 0.72-3.33 m s − and FMC 3-18.6%.ROS was measured by recording the time of arrival at a grid of predetermined locations,along with other fire characteristics, after first allowing the fire to spread 20 - 40 m ( ≃
15 min) in order for it to attain a quasi-steady ROS for the prevailing conditions. The12osition of the flames in relation to the grid was mapped at 5 min intervals. ROS ranged0.003-0.28 m s − .Unlike the laboratory findings (Burrows, 1999a), Burrows here found a non-linear relationbetween wind speed and ROS. A power function (exponent 2.674) was selected. FMC wasdetermined to also be a power function (exponent -1.495). Like the laboratory findings,fuel load was not found to correlate with ROS. The model was found to underpredictROS of large wildfires burning under severe conditions. Gorse (2002)
Baeza et al. (2002) conducted field experiments during spring and autumn in gorse shrub-lands of eastern Spain with the aim of developing a prescribed burning guide. Fuels were3, 9 and 12 years old and were replicated 3 times resulting in a total of 9 fires. Plots were33 m ×
33 m and were burnt under low ( < − at 2 m) wind, utilising headfirespread for the 3-year-old fuel and backing fires for the other two age classes. Meteoro-logical data was recorded at 2 m at 15 min intervals. Fuel characteristics were recordedalong 5 parallel transects 5 m in length. FMC was measured from 10 samples of the mostabundant species collected prior to ignition and ranged from 22-85%, presumably includ-ing both live and dead fuels . Ignition technique is not specified. ROS was measured byrecording the time to travel a fixed distance within the plot and ranged 0.004-0.039 ms − .It was found that FMC was the dominant factor affecting ROS in a linear manner (coeffi-cient 0.487). The combination of heading and backing propagation negated any consistenteffect of wind speed on ROS. PortPinas (2002)
Fernandes et al. (2002) developed a model for the behaviour of fires in maritime pine(
Pinus pinaster stands in northern Portugal under a range of fire weather conditionsthat occur outside the wildfire season for the purpose of improving the understanding ofprescribed fire for hazard reduction. Six study sites in mountainous terrain with forestsfounded by plantation or regeneration following fire events and aged 14 to 41 years wereestablished. Fuel complexes were dominated by litter, shrubs or non-woody understorey(e.g. grass) types. Extensive destructive and non-destructive sampling to quantify thefuels was undertaken along transects in each experimental plot. Four strata of fine fuellayers were defined: shrubs, herbs and ferns, surface litter and upper duff. Experimentalplots were square, 10-15 m wide, and defined by 0.3 to 1.2 wide control strips assisted bya hose line during burning.Wind speed was measured continuous at 1.7 m above ground approximately 10 m fromeach experimental plot. Three composite fuel moisture samples (one litter, one duff andone live) were sampled at random locations prior to ignition. It should be noted that the authors dried their fuels at 80 ◦ for 24 hours which is much less than thegenerally accepted 104 ◦ C for 24 hours (e.g. Cheney et al. (1993)), perhaps resulting in lower than actualFMC values–see discussion on Measurement issues.
134 experimental fires for fire behaviour studies were conducted when slope and winddirection were aligned within 20 ◦ . Line ignition occurred 2 m from the windward edge toallow both forward and backing spread observations. Fire behaviour measurements used1.5-m-high poles located at regular distances along the plot axis as reference points. ROSwas determined by recording the time at which the base of the fire front reached eachpole. Flame height and flame angle were estimated visually and used to calculate flamelength. Wind speed ranged from 0.3 - 6.4 m s − , surface dead FMC ranged 8 - 56%, airtemperature 2 - 22 ◦ C and relative humidity 26 -96%. ROS ranged 0.004 - 0.231 m s − .Fernandes et al. (2002) found that three existing models underestimated ROS with sig-nificant differences between predicted and observed values, as much as 8-fold in one case.Undertaken non-linear least=squares analysis, they found that slope and wind speed werethe most significant variables with dead FMC in a less significant role. A power law func-tion with wind speed only (exponent 0.803) explained 45% of the variation in ROS. Ifwind speeds less than 0.83 m s − were excluded, the correlation coefficient increased to0.996. Slope alone explained 30% of the variation. The final model selected for litter-shrub fuels (the general case for maritime pine stands) involved wind speed (power law,exponent 0.868) dead surface FMC (exponential, coefficient -0.035), slope and understoreyfuel height. Fuel height was selected as could be considered a surrogate for the overallfuel complex structure effect on ROS. The model was then adapted through changes inconstants to predict ROS in litter and non-woody understorey complexes. No assessmentof the performance of this model was reported. Maquis (2003)
Bilgili and Saglam (2003) conducted a series of 25 field experiments in open, level shrub-land of maquis fuel in southwestern Turkey. Average height of the fuel was 0.53 m andfires were conducted under a range of wind and fuel conditions. Each fire plot was 20 mwide by 30 m long. A meteorological station recorded air temperature, relative humidity,wind speed and precipitation at 1.8 m daily. Fuel characteristics were measured fromrandom destructive sampling prior to the experiment series. Live and dead FMC wassampled immediately prior to ignition. During each fire, wind speed, temperature andrelative humidity at 1.8 m were recorded at 1 min intervals using the automatic meteo-rological station. These were averaged over the period of fire spread. Wind speed ranged0.02-0.25 m s − , FMC 15.3-27.7%.Fires were lit with a drip torch along the upwind (20 m long) edge to quickly establish a linefire and were allowed to propagate with the wind across the plot. ROS was measured byrecording time of arrival at a series of predetermined locations and ranged 0.01-0.15 m s − .ROS was strongly correlated with wind speed; a linear function explained 71% of observedvariation. FMC was found not to have any significant effect on ROS, attributed to thenarrow range studied. The final model used a linear function of wind speed (coefficient0.495) and total fuel load, with an R = 0.845.14 uasi-empirical models Where the data gathered from experimental observation is analysed using a physicalframework for the functional relationships between dependent and independent variables,a quasi-empirical model results. The degree to which the physical framework controls thestructure of the model can vary but the nature of the model is essentially based upon theobserved data (which differentiates it from quasi-physical models which use data solelyfor parameterisation). Table 2 summarises the quasi-empirical models discussed below.
TRW (1991)
Wolff et al. (1991) presented the results of laboratory experiments conducted in a purpose-built wind tunnel 1.1 m wide by 7 m long with a moveable ceiling. The fuel layer wasvertical match splints (1.3-4.4 mm in diameter) set in a ceramic substrate. Wind speedvaried from 0-4.7 m s − , ROS ranged from 0-0.007 m s − . The results confirmed thetheoretical treatment conducted by Carrier et al. (1991), in which it was hypothesisedthat the dominant heat transfer mechanism in such a set-up would be a mix of convectionand diffusion (i.e. ‘confusion’) heating that would result in a relationship in which the ROSwould vary as the square root of the wind speed normalised by the fuel load. If radiationwas the predominant preheating mechanism, it was hypothesised that the variation wouldbe as the power of 1.5 rather than 0.5.Wolff et al. found that not only did the width of the fuel bed play an important part indetermining the ROS but also the total width of the wind tunnel itself. The narrowerthe fuel bed, and the facility, the slower the ROS. It was suggested that a narrower fuelbed forced air away from the fuel bed due to drag considerations in the fuel. A series ofexperiments with tapering fuel beds and working section confirmed this. If the fuel bedand working section was too narrow, ROS ceased. NBRU (1993)
Beer (1993b, 1991) investigated the interaction of wind and fire spread utilising a seriesof 18 small-scale wind tunnel (length 40 cm, height 16 cm) experiments using a singlerow of match splints in wind ranging from 0.0 to 9 m s − . ROS ranged from 0.004-0.38 ms − . Rather than a single continuous function to describe the relationship between windspeed and ROS, Beer put forward the hypothesis that there exists a critical characteristic(threshold) wind speed that affects ROS with different wind speed functions above andbelow this value. Below the threshold Beer found a normalised (by the threshold windspeed) power function (exponent 0.5). Above the threshold, Beer found a normalisedpower function (exponent 3.0). Beer postulates that the choice of the value is related tothe wind speed at which the wind shear is strong enough to generate flame billows andthat this value corresponds to a mid-flame wind speed of 2.5 m s − . Above this value it isthought that the flames remain within the fuel bed rather than above it. Beer attemptedto fit this model to observations of grassfire behaviour but could not.Beer (1993a) further explored the effects of wind on fire spread through simplified (matchsplints) fuel. His extension of a simple geometric model of fire spread in no wind to include15ind (based on geometry of wind-tilted flame and distance between fuel elements), inwhich the ROS-wind function is a complicated solution to a set of equations to determinethe critical time for flame immersion of adjacent fuel elements, did not perform well.This was attributed to assumptions about the characteristics of the flame and a constantignition temperature. Beer concludes that a single simple power law or exponential isunlikely to be a correct mathematical description for the ROS-wind speed relation. USFS (1998)
Catchpole et al. (1998b) conducted an extensive series of environmentally-controlled windtunnel experiments and used the results, in conjunction with energy transfer considera-tions, to develop a spread model, USFS (United States Forest Service). 357 experimentalfires were carried out on a fuel bed 8 m long by 1 m wide in a 12-m long wind tunnelof 3 m square cross section. Four fuels with different surface-area-to-volume ratios (twosizes of poplar excelsior, ponderosa pine needles and ponderosa pine sticks) were chosen tobe reasonable approximations to natural fuel layers. Temperature and relative humiditywere controlled to produce a range of FMC, 2% to 33% (although the majority of fireswere carried out at ambient values of 27 ◦ C and 20% RH giving an FMC range of 5-9%).Wind speed above the tunnel’s boundary layer ranged from 0.0 to 3.1 m s − . Rate ofspread was measured at 0.5 m intervals using photovoltaic diodes placed 25 mm abovethe fuel bed to record the time of arrival of the flame front.Utilising the conservation of energy model of Fransden (1971), Fransden’s (1973) effectiveheating number, a propagating flux model that is linear in packing ratio, and an expo-nential decay function for FMC, the authors built a model of fire spread very similar inits construction to that of Rothermel (1972) except that they used the heat of ignition ofa unit mass of fuel (which comprises the heat of pyrolysis and heat of dessication) ratherthan the heat of pre-ignition as used by Rothermel. A power function for wind was thenfitted to the data and an exponent of 0.91 determined. Although a cubic polynomialfunction was found to better fit the data, the authors chose the power function as it wasmore consistent with data from wildfire observations. Coimbra (2002)
Viegas (2002) presents a quasi-empirical model of fire spread that utilises the geometry ofthe fire perimeter to determine the forward spread rate. The main conceit of this notion,previously proposed in Viegas (1998) and Viegas et al. (1998), is that a line fire lit atan angle to a slope or wind gradient undergoes a translation and rotation of the firelinein order to spread with the maximum rate in the direction of the gradient. Extensivelaboratory experimentation utilising a double-axis tiltable fuel bed (1.6 m × Pinus pinaster needles with an FMC determined by ambient conditions (ranging10% - 15%). 23 experimental fires were conducted, with 10 fires of varying slope and13 fires of varying inclination. Viegas (2002) found a maximal rotation velocity at aninclination angle of 60 ◦ but was unable to convert this to a forward ROS. However,Viegas does develop a fire perimeter propagation algorithm in which the perimeter istreated as a continuous entity that will endeavor to align itself with the gradient, through16his proposed rotation mechanism, to an angle of approximately 60 ◦ . The translationand rotation hypothesis, however, ignores a basic observation of the evolution of flankingspread and instead assumes that spread at non-parallel angles to the slope or wind gradientmust be driven by a headfire.Viegas (2005) attempts to extend these ideas to describe the phenomenon of ‘fire blow-up’based on the concepts of fire ‘feedback effects’. Viegas proposes the existence of a positivedynamic feedback between the ROS of a fire and the flow velocity driving the fire suchthat the fire accelerates exponentially. He uses some of the results of experimental firesburnt in a “canyon”, a doubly-sloped tray, in no wind and a range of canyon slopes andinclinations to parameterise his model and the remainder to test it. Viegas treats all datafor all slope and inclination combinations as independent and continuous. As a result,his model increases ROS exponentially, resulting in extremely rapid acceleration–what hedescribes as blow-up. However, categorised by slope, rather than treated continuously,the ROS data actually asymptotes to a reasonable number in each case, which in mostcases confirms the long-held rule of thumb of doubling the flat ground ROS for every 10degrees increase in slope (McArthur, 1967; Van Wagner, 1988). Viegas (2006) conductsa parameteric study of this model and determines that fires in light and porous fuels aremore likely to exhibit ‘eruptive’ behaviour than fires in heavy and compacted fuels.Viegas’s extrapolation of this model to fatal wildfire incidents is tenuous at best andreally only proves the widely accepted acceleration up a slope. Other, more robust,theories of unexpected fire behaviour resulting in fatalities are probably more applicable(e.g. Cheney et al. (2001)). Nelson (2002)
Nelson (2002) extended the quasi-empirical work of Nelson and Adkins (1988) utilisingthe laboratory data of Weise and Biging (1997) to build a trigonometric model of firespread that combines wind and slope effects into a single combined ‘effective’ wind speed.The Nelson and Adkins (1988) model utilised the dimensional analysis of fire behaviourof Byram (1966), where three dimensionally homogeneous (i.e. dimensionless) relationswere derived: 1) the square root of the Froude number, 2) a buoyancy number relatingconvective heat output to rate of buoyancy production, and 3) the ratio of combustiontime to time characteristic of flame dynamics. Nelson and Adkins (1988) then used spreadobservations from 59 experimental fires (a total of 44 lab and 21 field, some deleted) andmixed and matched the dimensionless relations until they found a combination that gavea reasonable correlation. They derived a dimensionless form of ROS and wind speed,which, when fitted to the data and converted back to dimensions, gave a power lawrelation between wind speed and ROS (exponential 1.51). As the maximum wind speedused to obtain the data was 3.66 m s − and maximum observed ROS was 0.271 m s − ,Nelson and Adkins (1988) acknowledged the need for higher wind speed experiments.ROS was also found to be a function of fuel load (power function, exponent 0.25) andresidence time (inversely proportional). FMC was considered to be accounted for in theestimate of fuel load and residence time.Rather than the traditional approach used by McAlpine et al. (1991) where the equivalentwind speed for a slope-only ROS was determined, Nelson (2002) used the concept of17ertical buoyant velocity and the slope angle component of this wind to construct aslope-induced wind which was then added vectorally to the ambient wind across slope.Nelson extended the dimensional analysis of Nelson and Adkins (1988) to then determineROS. The resultant equations, which do not apply to flanking or backing fires due to theassumption about convective heating through the Froude number, were then comparedagainst the data of Weise and Biging (1997), gathered from 65 experiments in a portabletilting wind tunnel using vertical paper birch sticks as the fuel bed in a variety of windand slope configurations, ranging from 0.0 to 1.1 m s − and -30 ◦ to +30 ◦ . The effectivewind speed was found to correlate linearly with ROS. Discussion
Wind speed function
As stated earlier, one method of comparing the structure of each of the above models isto examine the form of the functional relationship between ROS and wind speed chosenby the authors. Table 3 summarises the models discussed and the form of the wind speedfunction chosen. Also listed are the experimental bounds of the wind speed and ROS.Only three of the models for which the wind function is given are not power functions,PortShrub and CFBP are exponential and Maquis is linear. Of the remaining models,3 models have exponents less than one: TRW, CSIRO Grass and USFS. The remainingwind functions all result in non-linear increases (Figure 1) in the ROS that will result ina speed greater than the wind speed driving it, which is unphysical (Beer, 1991). (Whilethis is also the case also for CFBP as illustrated here for wind speeds >
15 m s − , the ROSfunction is further modified in the CFFDRS system by fuel-specific functions which canreduce the predicted ROS below the wind speed.) The reason for this choice of functionappears to be the desire by the modellers to fit data at low wind speeds (including zero).Many of the models had ranges of wind speed that were fairly low ( < − ).The few models that were based on large ranges of wind speed in field experiments (withthe exception of CALM Jarrah II) tended to result in power functions with exponents lessthan one. CSIRO Grass is the highest power function less than one and is very similar inform to the linear function of Maquis over the given range. Fendell and Wolff (2001), intheir brief review of the topic including a number of older models, found that the windpower function exponents ranged from 0.42 (Thomas, 1967) to 2.67 (Burrows, 1999b).There seem to be two key factors in the choice of functional relationship used to describefire spread and wind speed. The first is the need to fit the function through the origin. Inmany cases, particularly laboratory experiments, zero wind speed is taken as the defaultstate and thus any continuous function must not only fit the data of non-zero wind, butalso of zero wind. This is discussed in greater detail below. The second is that for themost part, the range of wind speeds studied (again particularly in the laboratory) is verysmall. As can be seen in Figure 1, any function, be it cubic or very shallowly linear,performs rather similarly at low wind speeds ( < − ).It is interesting to note that in the full range of functions presented here, the nearlymedian wind function in Figure 1 (i.e. Heath) is the result of the combination of multiple18atasets, experimental methods and authors, perhaps resulting in a middle ground ofapproaches. Many physical models of fire spread (e.g. Grishin (1984); Linn (1997)) haveobserved linear functional relationships between wind speed and ROS, suggesting thatpower law functions with exponents close to unity may have a more fundamental basis.In their validation of the performance in Mediterranean shrub fuels of seven wildland firespread models, including the CFBP and Rothermel, Sauvagnargues-Lesage et al. (2001)found that a model’s performance is not related to the model’s complexity and that eventhe most simple model (in this particular case a local fire officer’s rule of thumb based ona linear discount of the wind speed) performed as well as more complicated models suchas CFBP. Threshold wind speed
One important aspect differentiating the various choices of wind function, is the idealof a continuous function that includes zero wind speed. It has been noted previously(Burrows et al., 1991) that fires in discontinuous fuels such as spinifex have a minimumwind speed required before forward spread is achieved. This notion was extended furtherby Cheney et al. (1998) to define a threshold wind speed at which fires spread forward consistently . The argument is that fires burning in low winds in the open respond toeddy fluctuations in the wind flow (resulting in near circular perimeter spread after a longperiod) and do not spread in a continuous consistent manner until the wind speed exceedsa certain threshold. Above this threshold, the fire spreads forward in a manner directlyrelated to the wind speed.The choice of threshold value is dependent then upon the method of measuring the windspeed (location, height, period, etc) and the fuel type in which the fire is burning (tallerfuels reduce the wind speed reaching the fire). Cheney et al. (1998) chose a 1.39 m s − open wind speed threshold for open grasslands. Fernandes et al. (2002) found that windspeed explained more variation in ROS when wind speeds below 0.83 m s − (at 1.7 m)were excluded, suggesting that at low wind speeds factors other than wind play a moresignificant role in determining ROS. Fuel moisture content function
Another method of comparing the various empirical and quasi-empirical models is thatof fuel moisture content function. Not all the models discussed here addressed the rela-tion between fuel moisture content and rate of spread, and so the discussion here is notcomprehensive. Figure 2 shows the various functions for those models that include fuelmoisture content.As with the wind function, there is a wide spread of functional forms used to describedthe influence of FMC on ROS, perhaps reflecting modelling approaches, methods or per-sonal choice. There appear to be three types of functions representing the fuel moisturecontent/ROS function: weakly linear (e.g. Gorse (normalised) or CALM Spinifex (nor-malised)) in which the FMC plays a minor role in determining the ROS, strongly expo-nential (e.g. CALM Jarrah II and USFS) in which FMC plays a strong role until very low19MC values, and strongly linear or weakly exponential (which might be approximated tolinear) in which the role of FMC is spread over a large range of values. The majority ofmodels discussed here fall into the latter group.The weakest of the linear models (Gorse (normalised) is characterised by few experimentswith a limited range of FMC values, which raises the issue of how many sample points areneeded to properly inform functional choice and model validation–one could argue that 9fires is simply not enough given the range of the uncontrolled variables.The weakly exponential group of models, which includes strictly linear models (e.g.CALM-Spinifex), appears to be the most robust in terms of range of FMC values and ex-perimentation. It is interesting to note the similarity between the CALM Mallee and theCSIRO Grass models. The large difference in functionality between the strongly exponen-tial and weakly exponential is interesting and may reflect differences in functionality as aresult of wind function modelling, as all modelling identified wind speed as the primaryvariable and FMC as the secondary.
Measurement issues
All empirical science is limited by the ability to measure necessary quantities, to quantifythe errors in those measurements, and then relate those measurements to the phenomenonunder investigation and wildland fire science is no different. Sullivan and Knight (2001)discussed the determination of the errors in measuring wind speed under a forest canopysome distance from an experimental fire and relating that measurement to measurementsof fire spread. The issues of where to measure (location, height, in the open, under thecanopy, etc.), how long to measure (instantaneous, period sampling, average, period ofaverage, etc.), and how to correlate measurements with observations are complex andnecessarily require approximations and simplification in order to be undertaken.Similarly, destructive sample of FMC has issues that complicate a seemingly simple quan-tity. The time of sampling (morning, afternoon, wetting period, drying period), the gen-eral location (in the open or under the canopy, in the sun, in the shade, in between, etc.),the specific location (surface litter fuels, profile litter fuels, mid-layer fuels), the speciesof fuel (predominant fuels, non-predominant fuel, live, dead, etc.). Also once the sampleshave been taken there then is the issue of best drying methods for the particular samplesto ensure a water-free weight, the best method of determining an average value for a plot,variance, error, etc.Quantifying other factors such as fuel, again seemingly simple quantities rely upon aknowledge of the mode of combustion of the fire and which aspects of the fuel mostinfluence that combustion and therefore the behaviour of the fire. These include definitionof fuel strata (which itself depends on the intensity of the fire and which parts of the fuelcomplex will be burning during the fire and thus contribute to the energy released by thefire), the structure of the fuel and the size of fuel particles important to fire behaviourof the front, flanks and behind the flame zone, the amount of fuel available, the amountconsumed, the chronology of the consumption of the fuel, the mode of consumption,transport of burning fuel (i.e. firebrands), spatial and temporal variation of these fuel andfire characteristics, determination of averages and methods of averaging, determination oferrors, etc. The list could continue. Other factors, such as air temperature and relative20umidity, insolation, atmospheric stability, slope, soil type and moisture, have their ownrange of measurement difficulties, and are by no means the only quantities involved inquantifying the behaviour of wildland fires.Laboratory-based experiments may aim to reduce the variation and control the errorsin measurement of many of these quantities but are not immune to the difficulties ofmeasurement.
Field versus laboratory experimentation
Empirical or quasi-empirical modelling of fire behaviour has resulted in significant ad-vances in the state of wildfire science and produced effective operational guides for de-termining the likely behaviour of wildfires for suppression planning purposes. Unlikephysical or quasi-physical models of fire behaviour, these systems are simple, utilise read-ily available fuel and weather input data, and can be calculated rapidly. However, thereis a significant difference between those models developed from field experimentation andthose developed from laboratory experimentation.Large-scale field experiments are costly, difficult to organise, and inherently have many ofthe difficulties associated with wildfire observations (e.g. spatial and temporal variation ofenvironmental variables, uncontrolled variations, changing frames of reference and bound-ary conditions, etc.). Laboratory experiments can be cheap and safe, provide relativelyrepeatable conditions, and can limit the type and range of variations within variablesand thus simplify analysis. Van Wagner (1971) raises the issue of laboratory versus fieldexperimentation but avoids any categorical conclusions (perhaps because there are none),simply stating some features of wildland fire behaviour are better suited to studying in thecontrolled environment of the laboratory or could not be attempted in the field, and otherfeatures cannot be suitably replicated anywhere but in large-scale outdoor experiments.Correct scaling of laboratory experiments (and field experiments for that matter) is vitalto replicating the conditions expected during a wildfire. Byram (1966) and Williams(1969) conducted dimensional analysis of (stationary) mass fires in order to develop scalinglaws to conduct scaled model experiments. Both found that scaling across all variablespresents considerable difficulty and necessitates approximations, particularly in regard toatmospheric variables, which result in impractical lower limits (e.g. model forest fires ≃ ≃
10 g (Williams, 1969)). As aresult, it is clear that any scaled experiments must take great care in drawing conclusionsthat are expected to be applicable at scales different from that of the experiments; notonly may physical and chemical processes behave differently at different scales but thephenomena as a whole may behave differently.The key difference between field-based and laboratory-based experimentation, in thisauthor’s opinion, is the assumptions about the nature of combustion (including heattransfer) that are required in order to design a useful small-scale laboratory experiment.That is, there is the presumption implicit in any laboratory experiment that there issufficient understanding about the nature of fire such that key variables can be isolatedand measured without regard to the fire itself.One such aspect identified by Cheney et al. (1993) is the importance of the size and shapeof the fire in determining resultant fire behaviour. Prior to this work, it was thought that21he size of the fire played little part in determining the behaviour of a fire and thus theresults of small experimental fires could be extrapolated to larger fires burning underless mild conditions. Other factors such as the physical structure of the fuel or moisturecontent of live fuels, or other hitherto unconsidered factors, may play less significant butimportant roles in explaining the unaccounted variation in ROS.Field experiments on the other hand, by their very nature, are real fires and thus in-corporate all the interactions that define wildland fire. This aspect holds considerableweight with end users who endow such systems with a confidence that purely theoreticalor laboratory-only-based models do not receive. As Morvan et al. (2004) concluded, nosingle approach to studying the behaviour of wildland fire will provide a complete solutionand thus it is important that researchers maintain open and broad paradigm
Acknowledgements
I would like to acknowledge Ensis Bushfire Research and the CSIRO Centre for ComplexSystems Science for supporting this project; Jim Gould and Rowena Ball for commentson the draft manuscript; and the members of Ensis Bushfire Research who ably assistedin the refereeing process, namely Stuart Anderson, Miguel Cruz, and Juanita Myers.
References
Abbot, I. and Burrows, N., editors (2003).
Fire in Ecosystems of South-West WesternAustralia: Impacts and Management . Backhuys, Leiden, The Netherlands.Alexander, M., Stocks, B., and Lawson, B. (1991). Fire behaviour in Black Spruce-lichenwoodland: The Porter Lake project. Information Report NOR-X-310, Forestry Canada,Northwest Region, Northern Forestry Centre, Edmonton, Alberta.Andrews, P. (1986). Behave: fire behaviour prediction and fuel modellings system - burnsubsystem, part 1. Technical Report General Technical Report INT-194, 130 pp., USDAForest Service, Intermountain Forest and Range Experiment Station, Ogden, UT.Baeza, M., De Lu´ıs, M., Ravent´os, J., and Escarr´e, A. (2002). Factors influencing firebehaviour in shrublands of different stand ages and the implications for using prescribedburning to reduce wildfire risk.
Journal of Environmental Management , 65(2):199–208.Beer, T. (1991). The interaction of wind and fire.
Boundary-Layer Meteorology , 54(2):287–308.Beer, T. (1993a). Fire propagation in vertical stick arrays: The effects of wind.
Interna-tional Journal of Wildland Fire , 5(1):43–49.Beer, T. (1993b). The speed of a fire front and its dependence on wind speed.
InternationalJournal of Wildland Fire , 3(4):193–202.Bilgili, E. and Saglam, B. (2003). Fire behavior in maquis fuels in Turkey.
Forest Ecologyand Management , 184(1-3):201–207. 22radstock, R. and Gill, A. (1993). Fire in semiarid, mallee shrublands - size of flamesfrom discrete fuel arrays and their role in the spread of fire.
International Journal ofWildland Fire , 3(1):3–12.Burgan, R. (1988). 1988 revisions to the 1978 National Fire-Danger Rating System.Research Paper SE-273, USDA Forest Service, Southeastern Forest Experiment Station,Asheville, North Carolina.Burrows, N. (1994).
Experimental development of a fire management model for jarrah(
Eucalyptus marginata
Donn ex Sm) forest . PhD thesis, Dept of Forestry, AustralianNational University, Canberra.Burrows, N. (1999a). Fire behaviour in jarrah forest fuels: 1. Laboratory experiments.
CALMScience , 3(1):31–56.Burrows, N. (1999b). Fire behaviour in jarrah forest fuels: 2. Field experiments.
CALM-Science , 3(1):57–84.Burrows, N., Ward, B., and Robinson, A. (1991). Fire behaviour in spinifex fuels onthe Gibson Desert Nature Reserve, Western Australia.
Journal of Arid Environments ,20:189–204.Byram, G. (1966). Scaling laws for modeling mass fires.
Pyrodynamics , 4:271–284.Carrier, G., Fendell, F., and Wolff, M. (1991). Wind-aided firespread across arrays ofdiscrete fuel elements. I. Theory.
Combustion Science and Technology , 75:31–51.Catchpole, W. (2000).
FIRE! The Australian Experience. Proceedings of the 1999 Sem-inar , chapter The International Scene and Its Impact on Australia, pages 137–148.National Academies Forum.Catchpole, W., Bradstock, R., Choate, J., Fogarty, L., Gellie, N., McArthy, G., McCaw,L., Marsden-Smedley, J., and Pearce, G. (1998a). Co-operative development of equa-tions for heathland fire behaviour. In
Proceedings of III International Conference onForest Fire Research, 14th Conference on Fire and Forest Meteorology, Luso, Portugal,16-20 November 1998, Vol 1 , pages 631–645.Catchpole, W., Catchpole, E., Butler, B., Rothermel, R., Morris, G., and Latham, D.(1998b). Rate of spread of free-burning fires in woody fuels in a wind tunnel.
CombustionScience and Technology , 131:1–37.Chandler, C., Cheney, P., Thomas, P., Trabaud, L., and Williams, D. (1983).
Fire inForestry 1: Forest Fire Behaviour and Effects . John Wiley & Sons, New York.Cheney, N. (1981). Fire behaviour. In Gill, A., Groves, R., and Noble, I., editors,
Fireand the Australian Biota , chapter 5, pages 151–175. Australian Academy of Science,Canberra.Cheney, N. and Gould, J. (1995). Fire growth in grassland fuels.
International Journalof Wildland Fire , 5:237–247.Cheney, N., Gould, J., and Catchpole, W. (1993). The influence of fuel, weather and fireshape variables on fire-spread in grasslands.
International Journal of Wildland Fire ,3(1):31–44. 23heney, N., Gould, J., and Catchpole, W. (1998). Prediction of fire spread in grasslands.
International Journal of Wildland Fire , 8(1):1–13.Cheney, P., Gould, J., and McCaw, L. (2001). The dead-man zone-a neglected area offirefighter safety.
Australian Forestry , 64(1):45–50.Cheney, P. and Sullivan, A. (1997).
Grassfires: Fuel, Weather and Fire Behaviour . CSIROPublishing, Collingwood, Australia.CSIRO (1997). CSIRO Grassland Fire Spread Meter. Cardboard meter.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 pinetype of california.
Journal of Agricultural Research , 57(4):239–267.Deeming, J., Burgan, R., and Cohen, J. (1977). The National Fire-Danger Rating System- 1978. Technical Report General Technical Report INT-39, USDA Forest Service,Intermountain Forest and Range Experiment Station, Ogden, UT.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.Fendell, F. and Wolff, M. (2001).
Wildland Fire Spread Models , chapter 6: Wind-AidedFire Spread, pages 171–223. Academic Press, San Diego, CA, 1st edition.Fernandes, P. (1998). Fire spread modelling in Portuguese shrubland. In
Proceedings of IIIInternational Conference on Forest Fire Research, 14th Conference on Fire and ForestMeteorology, Luso, Portugal, 16-20 November 1998, Vol 1 , volume 1, pages 611–628.Fernandes, P. (2001). Fire spread prediction in shrub fuels in Portugal.
Forest Ecologyand Management , 144(1-3):67–74.Fernandes, P., Botelho, H., and Loureiro, C. (2002). Models for the sustained ignitionand behaviour of low-to-moderately intense fires in maritime pine stands. page 98,Rotterdam, Netherlands. Millpress. Proceedings of the IV International Conference onForest Fire Research, Luso, Coimbra, Portugal 18-23 November 2002.Fons, W. L. (1946). Analysis of fire spread in light forest fuels.
Journal of AgriculturalResearch , 72(3):93–121.Forestry Canada Fire Danger Group (1992). Development and structure of the CanadianForest Fire Behavior Prediction System. Information Report ST-X-3, Forestry CanadaScience and Sustainable Development Directorate, Ottawa, ON.Fransden, W. (1971). Fire spread through porous fuels from the conservation of energy.
Combustion and Flame , 16:9–16.Fransden, W. H. (1973). Using the effective heating number as a weighting factor inRothermel’s fire spread model. General Technical Report INT-10, USDA Forest Service,Intermountain Forest and Range Experiment Station, Ogden UT.24ill, A., Burrows, N., and Bradstock, R. (1995). Fire modelling and fire weather in anAustralian desert.
CALMScience Supplement , 4:29–34.Gill, A., Groves, R., and Noble, I., editors (1981).
Fire and the Australian Biota . Aus-tralian Academy of Science, Canberra.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.Goldammer, J. and Jenkins, M., editors (1990).
Fire in Ecosystem Dynamics . SPBAcademic Publishing bv, The Hague, The Netherlands.Grishin, A. (1984). Steady-state propagation of the front of a high-level forest fire.
SovietPhysics Doklady , 29(11):917–919.Grishin, A. (1997).
Mathematical modeling of forest fires and new methods of fightingthem . Publishing House of Tomsk State University, Tomsk, Russia, english translationedition. Translated from Russian by Marek Czuma, L Chikina and L Smokotina.Hawley, L. (1926). Theoretical considerations regarding factors which influence forestfires.
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.Lawson, B., Stocks, B., Alexander, M., and Van Wagner, C. (1985). A system for pre-dicting fire behaviour in Canadian forests. In
Eighth Conference on Fire and ForestMeteororology , pages 6–16.Lee, S. (1972). Fire research.
Applied Mechanical Reviews , 25(3):503–509.Linn, R. R. (1997). A transport model for prediction of wildfire behaviour. PhD ThesisLA-13334-T, Los Alamos National Laboratory. Reissue of PhD Thesis accepted byDepartment of Mechanical Engineering, New Mexico State University.Marsden-Smedley, J. and Catchpole, W. (1995a). Fire behaviour modelling in Tasmanianbuttongrass moorlands I. Fuel characteristics.
International Journal of Wildland Fire ,5(4):202–214.Marsden-Smedley, J. and Catchpole, W. (1995b). Fire behaviour modelling in Tasmanianbuttongrass moorlands II. Fire behaviour.
International Journal of Wildland Fire ,5(4):215–228.McAlpine, R., Lawson, B., and Taylor, E. (1991). Fire spread across a slope. In
Proceedingsof the 11th Conference on Fire and Forest Meteorology , pages 218–225, Missoula, MT.Society of American Foresters.McAlpine, R. and Wakimoto, R. (1991). The acceleration of fire from point source toequilibrium spread.
Forest Science , 37(5):1314–1337.25cArthur, A. (1965). Weather and grassland fire behaviour. Country Fire Authority andVictorian Rural Brigades Association Group Officers Study Period, 13th - 15th August1965.McArthur, A. (1966). Weather and grassland fire behaviour. Technical Report Leaflet100, Commonwealth Forestry and Timber Bureau, Canberra.McArthur, A. (1967). Fire behaviour in eucalypt forests. Technical Report Leaflet 107,Commonwealth Forestry and Timber Bureau, Canberra.McCaw, L. (1997).
Predicting fire spread in Western Australian mallee-heath shrubland .PhD thesis, School of Mathematics and Statistics, University of New South Wales,Canberra, ACT, Australia.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 wildlandfires: a state of the art. Deliverable D-03-01, EUFIRELAB. 33 p.Nelson, Jr., R. (2002). An effective wind speed for models of fire spread.
InternationalJournal of Wildland Fire , 11(2):153–161.Nelson, Jr., R. M. and Adkins, C. W. (1988). A dimensionless correlation for the spreadof wind-driven fires.
Canadian Journal of Forest Research , 18:391–397.Pastor, E., Zarate, L., Planas, E., and Arnaldos, J. (2003). Mathematical models andcalculation systems for the study of wildland fire behaviour.
Progress in Energy andCombustion Science , 29(2):139–153.Peet, G. (1965). A fire danger rating and controlled burning guide for the northern jarrah(euc. marginata sm.) forest of western australia. Technical Report Bulletin No 74,Forests Department, Perth, Western Australia.Perry, G. (1998). Current approaches to modelling the spread of wildland fire: a review.
Progress in Physical Geography , 22(2):222–245.Pyne, S., Andrews, P., and Laven, R. (1996).
Introduction to Wildland Fire, 2nd Edition .John Wiley and Sons, New York.Pyne, S. J. (2001).
Year of the Fires : The Story of the Great Fires of 1910 . Viking, NewYork.Rothermel, R. (1972). A mathematical model for predicting fire spread in wildland fuels.Research Paper INT-115, USDA Forest Service.Sauvagnargues-Lesage, S., Dusserre, G., Robert, F., Dray, G., and Pearson, D. (2001).Experimental validation in mediterranean shrub fuels of seven wildland fire rate ofspread models.
International Journal of Wildland Fire , 10(1):15–22.Sneeuwjagt, R. and Peet, G. (1985). Forest fire behaviour tables for Western Australia(3rd Ed.). Department of Conservation and Land Management, Perth, WA.Stocks, B., Lawson, B., Alexander, M., Van Wagner, C., McAlpine, R., Lynham, T., andDub´e, D. (1991). The Canadian system of forest fire danger rating. In Cheney, N. andGill, A., editors,
Conference on Bushfire Modelling and Fire Danger Rating Systems ,pages 9–18, Canberra. CSIRO. 26tocks, B. J., Alexander, M. E., and Lanoville, R. A. (2004). Overview of the InternationalCrown Fire Modelling Experiment (ICFME).
Canadian Journal of Forest Research ,34(8):1543–1547.Sullivan, A. (2007). A review of wildland fire spread modelling, 1990-present, 1: Physicaland quasi-physical models. arXiv:0706.3074v1[physics.geo-ph], 46 pp.Sullivan, A. and Knight, I. (2001). Estimating error in wind speed measurements forexperimental fires.
Canadian Journal of Forest Research , 31(3):401–409.Taylor, S. and Alexander, M. (2006). Science, technology, and human factors in fire dangerrating: the canadian experience.
International Journal of Wildland Fire , 15(1):121–135.Thomas, P. (1967). Some aspects of the growth and spread of fire in the open.
Journalof Forestry , 40:139–164.Thomas, P. and Pickard, R. (1961). Fire spread in forest and heathland materials. Reporton forest research, Fire Research Station, Boreham Wood, Hertfordshire.Van Wagner, C. (1971). Two solitudes in forest fire research. Information Report PS-X-29, Canadian Forestry Service, Petawawa Forest Experiment Station, Chalk River,ON.Van Wagner, C. (1977a). Conditions for the start and spread of crown fire.
CanadianJournal of Forest Research , 7(1):23–24.Van Wagner, C. (1977b). Effect of slope on fire spread rate.
Canadian Forestry ServiceBi-Monthly Research Notes , 33:7–8.Van Wagner, C. (1985). Fire spread from a point source. Memo PI-4-20 dated January 14,1985 to P. Kourtz (unpublished), Canadian Forest Service, Petawawa National ForestInstitute, Chalk River, Ontario.Van Wagner, C. (1987). Development and structure of the canadian forest fire weatherindex system. Forestry Technical Report 35, Canadian Forestry Service, PetawawaNational.Van Wagner, C. (1988). Effect of slope on fires spreading downhill.
Canadian Journal ofForest Research , 18:818–820.Van Wagner, C. (1998). Modelling logic and the Canadian Forest Fire Behavior PredictionSystem.
The Forestry Chronicle , 74(1):50–52.Viegas, D. (2002). Fire line rotation as a mechanism for fire spread on a uniform slope.
International Journal of Wildland Fire , 11(1):11–23.Viegas, D. (2006). Parametric study of an eruptive fire behaviour model.
InternationalJournal of Wildland Fire , 15(2):169–177.Viegas, D., Ribeiro, P., and Maricato, L. (1998). An empirical model for the spread of afireline inclined in relation to the slope gradient or to wind direction. In
III InternationalConference on Forest Fire Research. 14th Conference on Fire and Forest MeteorologyLuso, Portugal, 16-20 November 1998. Vol 1. , pages 325–342.27iegas, D. X. (1998). Forest fire propagation.
Philosophical Transmissions of the RoyalSociety of London A , 356:2907–2928.Viegas, D. X. (2005). A mathematical model for forest fires blowup.
Combustion Scienceand Technology , 177(1):27–51.Weber, R. (1991). Modelling fire spread through fuel beds.
Progress in Energy CombustionScience , 17(1):67–82.Weise, D. R. and Biging, G. S. (1997). A qualitative comparison of fire spread modelsincorporating wind and slope effects.
Forest Science , 43(2):170–180.Williams, F. (1969). Scaling mass fires.
Fire Research Abstracts and Reviews , 11(1):1–23.Williams, F. (1982). Urban and wildland fire phenomenology.
Progress in Energy Com-bustion Science , 8:317–354.Wolff, M., Carrier, G., and Fendell, F. (1991). Wind-aided firespread across arrays ofdiscrete fuel elements. II. Experiment.
Combustion Science and Technology , 77:261–289. 28able 1: Summary of empirical models discussed in this paper
Model Author Year Country Field/Lab Fuel type No. fires Size (w × l)(m) CFS-accel McAlpine 1991 Canada Lab needles/Excel. 29 0.915 × × × × × × × × Table 2: Summary of quasi-empirical models discussed in this paper
Model Author Year Country Field/Lab Fuel type No. fires Size (w × l)(m)TRW Wolff 1991 USA Lab match splints ? 1.1 × × × × Where only one dimension is given by the authors, this is assumed to be both width and length ofthe fire or plot
Model Field/Lab Fuel type FMC Fn FMC Wind Fn Wind Range ROS RangeRange (%) (m s − ) (m s − ) Empirical
CFS-accel Lab. Pond./Excel - - - 0-2.22* ?-?CALM-Spinifex Field Spinifex − . M U − . M (1 + M . ) ? e . U ? ?PWS-Tas Field Buttongrass e − . M U . − . M ld U . − . M U . U . − . M . U . . M U . M − . U . − . M U . < . U U . U exp − . M (700+2260 M ) U . U . <30