www.publish.csiro.au/journals/ijwf International Journal of Wildland Fire, 2004, 13, 253–274
Fire spread in canyons
Domingos Xavier ViegasA,B and Luis Paulo PitaA
ACentro de Estudos sobre Incêndios Florestais–Associação para o Desenvolvimentoda Aerodinâmica Industrial, Universidade de Coimbra, Apartado 10131, 3031-601 Coimbra, Portugal.
Abstract. Canyons or ridges are associated with a large number of fatal accidents produced during forest fires allover the world. A contribution to the understanding of fire behaviour in these terrain conditions is given in this paper.The basic geometrical parameters of the canyon configuration are described.An analytical model assuming ellipticalgrowth of point ignition fires and constant values of rate of spread is proposed. A non-dimensional formulationto transfer results from analytical, numerical, laboratory or field simulations to other situations is proposed. Anexperimental study at laboratory scale on a special test rig is described. A wide set of canyon configurations werecovered in the experimental program. In spite of the relatively small scale of the experiments they were able to putin evidence some of the main features found in fires spreading in this type of terrain. They show that in practicallyall cases the rate of spread of the fire front is non-constant. On the contrary, the fire has a dynamic behaviour and itsproperties depend not only on the canyon geometry but on the history of fire development as well. The convectioninduced by the fire is enhanced by terrain curvature and the fire accelerates causing the well-known blow-up thatis associated with canyon fires. The rate of spread of the head fire increases continuously even in the absence ofwind or any other special feature or change of boundary conditions that are sometimes invoked to justify suchfire behaviour. The results of the present study confirm the predictions of a previous numerical study of the flowand fire spread in canyons that showed the important feedback effect of the fire on the atmospheric flow and howthis affects fire behaviour in canyons. Results from a field experiment carried out in a canyon-shaped plot coveredby tall shrubs were used to validate the laboratory scale experiments. Case studies related to fatal accidents thatoccurred in canyon-shaped configurations are analysed and recommendations to deal with this problem are made.It is shown that these accidents may occur even in the absence of special fuel or atmospheric conditions as they areintrinsically related to terrain configuration.
Additional keywords: blow-up; chimney effect; convection effect; fire behaviour; fire dynamics.
Introduction
Canyons or ridges are associated with a great percentage offatal accidents produced during forest fires all over the world.The chimney effect created by this topographic configurationinduces a sudden and very fast propagation of the fire thathas surprised even some very experienced fire fighters andcaused much loss of life.
In spite of the relevance of this terrain configuration inpractical terms, namely in the very important fire safety area,there have been very few systematic studies on this topic.There are many references to fires in canyons in the literaturebut these authors did not find any detailed and quantifiedanalysis of fire spread in this terrain feature. Most referencesgive only qualitative but otherwise very useful descriptionsand insight into the extreme fire behaviour that occurs incanyons. An overview of some well-known basic texts on
forest fires is given below in order to present the state of theart as it is expressed in the literature known to these authors.
Brown and Davis (1973) give a very good qualitativedescription of fire behaviour in general. They mention theimportant role of wind and topography and describe thebehaviour of a fire in a steep slope or a ridge. They make avery interesting and important distinction between the rolesof slope and wind that is sometimes overlooked. In the sectionon high-energy fires they define the phenomenon of blow-upand the transition from a low-energy to a high-energy fire.According to these authors this transition is seldom a gradualprocess and it is usually the result of a conjunction of fac-tors like a pick-up in wind speed, start of crowning or a rapidgrowth of numerous spot fires.
Pyne (1984) also gives a very good description of for-est fire phenomena, namely of the factors affecting fire
behaviour. He mentions that deep narrow canyons are likely toburn like a unit due to radiation and fire-brand emission fromone side to the other. Pyne says that deep canyons encouragethe formation of convective columns that act as chimneys,channelling heat into narrow funnels. As a result the convec-tion velocity increases and, with it, the rate of combustion.Pyne also mentions that several fire casualties have occurredfrom fire behaviour dominated by topographic factors suchas steep slopes and ridges. In the chapter on fire suppressionPyne presents some selected cases of fire fatalities, amongthem the Loop Fire, 1966, and the Battlement Creek Fire,1976, that occurred in canyons.
In their chapter on fire behaviour, Chandler et al. (1983)describe the development of a fire from a point source andrefer to two acceleration phases, the second one correspond-ing to the transition to large fire behaviour. According tothese authors this transition can be caused either by pseudo-flame front formation by spot fires or due to topography.The latter possibility is illustrated by the case of a fire enter-ing the mouth of a drainage basin with a strong up-canyonwind. The fire runs up-canyon pushed by the wind but slopeeffects causes the fire to burn rapidly to the ridge crests onboth sides. The result is very rapid involvement of the entiredrainage.
Pyne et al. (1996) in part one of their book, dealing withfire environment, mention that narrow canyons or ravinescan affect fire behaviour in several ways. Radiation from oneslope to another and sparks or embers may cause a wholeslope to ignite in a matter of a few minutes. The existenceof a thermal inversion is also mentioned as a factor that mayincrease fire activity.
Velez (2000) in chapter 8.2 dealing with the influence oftopography on fire behaviour indicate that terrain slope is amost important factor in fire behaviour. These authors con-sider that canyons or ridges with closely spanned faces createadequate conditions for fast fire spread due to pre-heating offuels ahead of the flames.
It is easy to recognise that the common idea behind quickfire growth in canyons is related essentially to secondaryeffects like preheating of fuel well ahead of the fire front, theprojection of fire embers and even on the existence of thermaleffects on the atmosphere, like a thermal inversion. The cen-tral role of terrain slope and configuration is not presented inevidence.
The only previous work known to the authors dedicatedto the study of canyon fires is Lopes (1994) who carriedout a numerical study about fire spread in canyons usingcomplete physical equations to model turbulent air flow andits interaction with the heat source created by the fire. Twodifferent fuels and various geometrical configurations wereanalysed. The flow acceleration created by canyon configura-tion and the radical increase in rate of spread and general firebehaviour resulting from wind–fire interaction were demon-strated for the first time. These results were also reported in
PbPa
Z0 Y1�YA
X0�X1
XAO
Y0
Smax
�2
�1
�2
�1�1
�1
�
Fig. 1. Definition of the geometry of a non-symmetrical canyon.
Lopes et al. (1995). This work is analysed more in detail laterin this paper.
In forest fire behaviour studies, quite often much attentionis devoted to radiation from the flame front as the dominatingprocess in fire spread. The role of convection induced bythe fire, eventually enhanced by terrain configuration andits interaction with the combustion process and the fire frontshape, is sometimes overlooked, making it difficult to explainsome features that are observed in forest fire propagation incomplex terrain, like in the case of a canyon.
The basic geometrical parameters of the canyon config-uration are described. The effects of slope and wind on firespread are revised, putting in evidence the role of fire-inducedconvection.
Comparison with the results of a numerical study of theflow and fire spread in canyons that show the important feed-back effect of the fire on the atmospheric flow and how thisaffects fire behaviour will be presented.
Canyon geometry
Canyons are a relatively common topographical feature incomplex terrain. Without great loss of generality we willassume that the terrain surfaces are plane surfaces, i.e.without any curvature. Therefore we consider a canyon asthe space above three planes intersecting at given angles. Thebase of the canyon is a horizontal datum plane P0 and thefaces of the canyon are two other planes Pa and Pb that areinclined in relation to the horizontal. In analogy to what hap-pens frequently in nature, the intersection line of the two facesof the canyon will be designated as the water line. The gen-eral form of a canyon is a non-symmetrical canyon that isrepresented schematically in Fig. 1.
It is easy to see that the canyon can be generated in twosteps:
(1) First we consider two planes Pa and Pb that intersectalong axis OY0 and initially make an angle δ1 and δ2
with the reference horizontal plane OX0Y0.
Fire spread in canyons 255
Table 1. Nomenclature of canyon geometry
Designation Definition
OX0Y0Z0 Orthogonal basic referenceOX0Y0 Reference horizontal plane (Plane P0)OX1Y1 Inclined reference plane (Plane P1)OXAYA Right face of the canyon (Plane Pa)OXBYB Left face of the canyon (Plane Pb) (Axis OXB is not
marked in the figure)Smax Line of maximum slope in face OXAYA
δ1 Angle between axis OX0 and OXA
δ2 Angle between axis OX0 and OXB (δ1 = δ2 = δ
for symmetrical canyon)α Angle between axis OY0 and OY1θ Slope of canyon faces (angle between Smax and the
horizontal plane)φ Angle between OX0 and the intersection of each face
with horizontal plane OX0Y0ψ Angle between OY1 and the maximum slope direction
of each face
(2) Second, if the dihedral formed by both planes is inclineduntil their intersection line—the water line—makes anangle α with the horizontal plane, the non-symmetricalcanyon that is presented in Fig. 1 is formed.
In this figure the water line is the OY1 axis of a new ref-erence frame that is obtained from the basic OX0Y0Z0 by arotation of the angle α around axis OX0. As these two move-ments, defined by angles α, δ1 and δ2 are sufficient to generateand characterise the canyon geometry, we will use these threeangles as basic canyon geometry parameters in the presentstudy.
For practical purposes it is important to identify a set ofadditional angles that can be used in complement to α, δ1 andδ2. These angles are θ, φ and ψ that are shown in Fig. 1 forplane Pa and are defined in Table 1.
As the symmetrical canyon is the main situation that willbe considered in the present work the following descriptionand definitions pertain only to this case.
With some mathematical manipulation it can be demon-strated that the following relationships (equation 1, equation 2and equation 3) exist between angles θ, φ and ψ and the twobasic angles α and δ. The graphical form of those functionsis presented in Figs 2–4.
tan θ =√
sin2 α + tan2 δ
cos α(1)
tan φ = − tan δ
sin α(2)
tan ψ =cos δ + cos α · sin α · cos δ
+ sin α · tan δ − sin2 α · cos δ
sin αtan δ
+ sin2 αtan δ
+ sin2 αcos α·cos δ
(3)
0
15
30
45
60
75
90
0 15 30 45 60 75 90
0°5°10°20°30°40°45°
α
δ
θ
Fig. 2. Slope θ of each face of the canyon as a function of α and δ.
0
15
30
45
60
75
90
0 15 30 45 60 75 90
0°5°10°20°30°40°45°
α
δ
φ
Fig. 3. Modulus of angle φ between axis OX0 and the trace of eachface of the canyon on the horizontal plane, as a function of α and δ.
0
15
30
45
60
75
90
0 15 30 45 60 75 90
0°5°10°20°30°40°45°
α
δ
ψ
Fig. 4. Angle ψ between axis OY1 and the direction of maximumslope of each face of the canyon, as a function of α and δ.
As can be observed in Figs 2–4 for each pair of values of α
and δ, there is a single value of each other angle, φ, θ and ψ,but the reciprocal is not true. For example there are differentpairs of values of α and δ that correspond to the same valueof θ or ψ.
A non-symmetrical canyon can be obtained makingδ1 �= δ2. The equations to determine the geometry in this caseare the same as the ones presented here although they have tobe applied to each face of the canyon using the appropriate
256 D. X. Viegas and L. P. Pita
value of δ. As this case is not dealt with in this paper we donot give the corresponding equations here.
Our experimental program did not cover the case of thenon-symmetrical canyon yet but it is anticipated that this sit-uation is not just the addition of two cases as fire spread inboth faces of the canyon are not independent of each other.
Fire spread modelling
Fire spread parameters
The fire spread properties will be dependent on the followingparameters:
In this paper we are looking in particular to the effect ofcanyon geometry on fire spread, therefore only very sim-ple situations related to all the other parameters will beconsidered.
Fuel cover will be assumed to be uniform and withhomogeneous properties in the entire canyon.
We will consider mainly the case of no wind although areference will be made to a model that includes wind flowas well.
Ignition will be assumed to be at a single point in the line ofsymmetry of the canyon and near its base, i.e. slightly abovethe origin of the reference axis.
In this paper we will deal mainly with the local rate ofspread and with the overall shape of the fire. Therefore onlykinematical parameters like the ones described below shallbe dealt with. It is obvious that other related properties likeflame length or fire line intensity may be derived from theseones for given fuel cover conditions.
Analytical model
A simple analytical model to estimate the shape and size ofthe fire in symmetrical canyons is presented here. This modelis not proposed as a fire behaviour predictor in a canyon. Itspurpose is only to serve as a reference and to put in evidencethe limitations of present state-of-the-art fire behaviour mod-els based on the concepts of elliptical fire growth and constantrate of spread. Comparing the results of this model with theexperimental measurements, we will see the importance offire dynamics induced by convective flow around the firefront and its interaction with the reactive fire front.As a corol-lary we will conclude that fire behaviour prediction using aconstant rate of spread is not at all correct in the present case.
As the driving force of the fire is the terrain slope we haveto determine its maximum gradient angle θ (equation 1) andestimate the rate of spread of the head fire along this direction.In the presence of a slope of inclination θ, the upslope anddown-slope rate of spread of the fire line, parallel to the slope
plane, is given, respectively, by equation (4) and equation (5):
R1 = f1 · R0 (4)
R2 = f2 · R0 (5)
In these equations R0 is the basic rate of spread of a linearfire front on a horizontal fuel bed in the absence of wind.R0 depends on several properties of the fuel, namely on itssurface to volume ratio σ, its moisture content mf , and itspacking ratio β (as defined in Rothermel 1972). We assumethat the value of R0 is well defined for the fuel bed and that itis known. Rothermel’s (1972) mathematical model providesan algorithm to estimate the basic rate of spread R0 for a widerange of fuel beds with reasonable accuracy. The value of R0
can also be obtained empirically by direct measurement aswill be the case in the present study.
In principle both f1 and f2 are a function of θ, but wecan assume that, for down-slope propagation, f2 ≈ 1 as anapproximation.
For convenience in this study we will use an empirical lawobtained in this work for one of the fuel beds (Pinus pinasterneedles) that was more extensively used (cf. Fig. 17b):
f1 = 1 + a1 · θ + a2 · θ2 + a3 · θ3 + a4 · θ4 (6)
The values of the constants are a1 = −0.0175; a2 = 0.0039;a3 = −0.0001; and a4 = 3 × 10−6. Equation (6) is valid for0 < θ < 55◦.
In the absence of wind the only factor affecting the rate ofspread will be the local slope θ of the fuel bed. For point igni-tion fires, according to some authors like Bilgili and Methven(1990), the fire will evolve like a simple or double ellipse withits major axis aligned with the slope gradient direction of theterrain.
We will use a double ellipse model shown in Fig. 5.The equations of the double ellipse in the OXsYs plane
depicted in Fig. 5 are:
a = f2 · R0 · t (7)
b = f1 · R0 · t (8)
ys > 0 ⇒ ys = b
a
√(a2 − x2
s ) (9)
ys < 0 ⇒ ys = a
a
√(a2 − x2
s ) (10)
If the line of maximum slope has an inclination ψ in rela-tion to axis OY1, we have the following transformation ofcoordinates between both systems OX1Y1 and OXsYs:
y′1 = ys cos ψ − xs sin ψ (11)
x1 = xs cos ψ + ys sin ψ (12)
In this equation y′1 = y1 −yig, yig, being the distance between
the ignition point and the origin of the coordinate system O0.In the present experiments yig = 0.50 m.
Fire spread in canyons 257
Xs
Ys
a
b
a
Fig. 5. Double ellipse propagation model.
Knowing the reference angles α and δ, the values of ψ
and θ can be easily determined. Knowing the value of R0 andof f1(θ) and f2(θ), using the system of equations given aboveit is possible to determine the shape of the fire at a given timestep t. It is easy to demonstrate that the shape of the fire frontat a given time step depends only on ψ and on f1/f2. It willthen be possible to determine universal shapes of the fire linefor pairs of values of ψ and f1/f2 that could then be appliedto all cases of canyon fires.
This model does not take into account the interactionof neighbouring sections of the fire front. In particular itassumes that both main sections of the fire when it bifur-cates do not interact in the region of the water line. As will beseen later, this is a very crude assumption that is not respectedin reality due to the very strong convection in that region ofthe fire front.
The shapes of the fire fronts given by this model for someof the 20 geometrical configurations studied in the presentexperimental program (see chapter 5) are given in Figs 12–14.
It is easy to derive explicit expressions to evaluate thedistance from the fire origin Oig to some particular points ofthe fire line that are illustrated in Fig. 6. The definitions of thesymbols used in the following equations are given in Table 2.
s1 = ab
cos ψ√
a2 − b2 tan2 ψ
= f1f2R0t
cos ψ
√f 2
2 − f 21 tan2 ψ
(13)
s2 = a = f2R0t (14)
s3 = b = f1R0t (15)
P1
P3
P4P2
Oig
s3
s1
s2s4
�
X
Y
1
O
Fig. 6. Schematic presentation of fire shape given by the analyticalmodel for a point ignition fire in a symmetrical canyon.
Table 2. Definition of relevant points and distances for firespread analysis
Symbol Definition Distance from fire origin Oig to:
s1 OigP1 The most advanced point P1 in axis OY1s2 OigP2 The least advanced point P2 in axis OY1s3 OigP3 The most advanced point P3 along the major
axis of the ellipse (axis OYs)s4 OigP4 The point P4 with ys = yig on the fire line
s4 = ab tan ψ
cos ψ√
a2 tan2 ψ + b2
= f1f2 tan ψR0t
cos ψ
√f 2
2 tan2 ψ + f 21
(16)
The perimeter P of the fire line is given by:
P = π(a + b) − ψb = [π(f2 + f1) − ψf1]R0t (17)
and the area A is given by:
A = (π − ψ)ab + ψa2 = [(π − ψ)f1f2 + ψf 2
2
]R2
0t2. (18)
It is found that all the above parameters, with the exceptionof the area, are linear functions of time. The area grows withthe second power of time.
As a consequence, according to this model the time deriva-tive of the distances si and of the perimeter P are in principleequal to constant values.
The rate of area growth dA/dt is a linear function of timeand it is easy to see that it is proportional to the square rootof the area itself.
dA
dt=
√A
2[(π − ψ)f1f2 + ψf 2
2
] (19)
The authors observed that in canyon fires the spread of thefire along axis OY1 tends to reach and even to overcome theadvance along the maximum slope direction. This is due tothe strong convection effects that occur in these fires espe-cially near the water line. The present analytical model does
258 D. X. Viegas and L. P. Pita
not predict this effect as it does not take into account thefeed back from the fire convection to the reaction zone. Inorder to assess the difference between model prediction andobservations we introduce the following parameter:
σ3 = s3 cos ψ
s1(20)
This function is the ratio between the y component of thedistance s3 from the origin to the fire front along the maxi-mum slope direction and the distance s1. If σ3 < 1 then thefire front advance along the OY1 axis is greater than the OY1
component of the fire advance along the maximum slopedirection. It is easy to see that:
σ3 = cos2 ψ
√
1 + b2 tan2 ψ
a2= cos2 ψ
√
1 + f 21 tan2 ψ
f 22
(21)This function is shown in Fig. 7a for different values of
the ratio f1/f2. As can be seen in this figure the present ana-lytical model predicts that, in the majority of cases, the firewill bifurcate and the separate heads will advance ahead ofpoint P1 (σ3 > 1). The experimental results shown in Fig. 7bconfirm the trend given by equation (21) as is illustrated bythe curves for three different values of the ratio f = f1/f2,although in general the values of σ3 are always lower than 2.In many cases they are very close to or even lower than 1,showing that the head of the fire tends to propagate as a hor-izontal line forming a wide and devastating fire front as hasbeen observed in some real cases. Only three experimentalpoints are close to the line corresponding to f = 3; accord-ing to the present experimental conditions (cf. Fig. 15a) thenormal values of f are larger than 3.
Non-dimensional parameters
We now address the problem of deriving non-dimensionalparameters related to the fire behaviour descriptors in orderto be able to compare results obtained or derived in differentbut similar conditions or to apply results from one case toanother. This question is part of a more general problem ofphysical modelling and physical similarity.We will only makereference to the required concepts here.
A prerequisite of physical similarity is that there is geo-metrical similarity; therefore this analysis can be applied onlyto cases for which the canyon geometry is the same. Accord-ing to the present study this requires that the values of α andδ be the same for both cases.
A second requisite is that pairs of non-dimensional param-eters describing the relevant phenomena in the process areequal in both cases. The choice of these parameters has tobe made with great care. As we are dealing with a thermalprocess and with the description of time evolution of fireposition, we require reference values for at least the follow-ing fundamental parameters: space and time. To characterisespace we need at least a reference length or distance L0 and
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 10 20 30 40 50 60 70 80 90
11°20°30°40°f� � 1f� � 2f� � 3
0
1
2
3
4
5
6
0 10 20 30 40 50 60 70 80 90
f � 1f � 2f � 3f � 5f � 8f � 10
σ 3σ 3
�
(a)
(b)δ
Fig. 7. Analysis of ratio of fire advance along maximum slope angleand the water line of the canyon (axis OY1). (a) Analytical model;(b) experimental results.
the same for time t0. The definition of a parameter character-ising thermal processes in fire spread may be included in oneof the above parameters, considering that the heat transfer isthe main process driving the fire line in this physical process.This is a simplified or reduced version of non-dimensionalanalysis that we follow here.A more complete analysis wouldinvolve the definition of at least a third parameter character-ising heat transfer processes for each particular fuel type butthis is not attempted in this paper.
As was described above the canyon configuration isdefined entirely by a set of two angles (α, δ). All the otherfeatures of the canyon geometry can be derived from these.Therefore if we are situated far from the borders of the facesof the canyon there is not a relevant length that can be used asa reference or scale for length dimension. The same happenswith a time scale that cannot be found naturally from geo-metrical considerations. We have then to consider propertiesof the fire itself to define our reference scales.
Fire spread in canyons 259
One logical parameter is the basic rate of spread R0 thatis characteristic of the fuel bed. R0 is by definition the rateof spread of a linear fire front of infinite length in that samefuel bed in the absence of slope and wind.
A length scale could be defined from R0 and consider-ing some characteristic time, like the residence time of theflames. We prefer to take the length of the flames L0 (no slopeand no wind propagation) as a length scale. A characteristictime t0 = L0/R0 can be easily derived from the other twoparameters. Non-dimensional time is defined by t′ = t/t0.
From these reference values the following non-dimensional parameters can be derived:
Area A′ = A
L20
(22)
Area growth A′′ = dA
dt· 1
L0R0(23)
Perimeter P ′ = P
L0(24)
Perimeter growth P ′′ = dP
dt· 1
R0(25)
Using the present analytical model it is easy to demonstratethat we have:
A′ =[(π
2− ψ
)f1f2 + ψf2
]t′2 (26)
P ′ =[π
2(f1 + f2) − ψf1
]t′ (27)
and also that:
A′′ = 2[(π
2− ψ
)f1f2 + ψf2
]t′ (28)
P ′′ =[π
2(f1 + f2) − ψf1
](29)
Numerical model
General description
Lopes (1994) developed a numerical model for the analy-sis of fire spread in a canyon. A brief revision of this paper isgiven here. For more details one should consult the given ref-erence of the original thesis Lopes (1994) and also Lopeset al. (1995). The full Navier-Stokes equations for turbu-lent flow including thermal effects were solved in order tosimulate the wind over a canyon terrain with different geo-metric configurations. A full-size symmetrical canyon withdifferent geometrical configurations (defined by α and δ) wasconsidered in the study. The overall size of the computationdomain was of the order of 200 m. Wind flow simulationconsidering an incoming flow of the boundary layer typeshowed a marked influence of the canyon shape on the flowpattern even in the absence of fire. It was found that a stag-nation zone existed at the base of the canyon and that the
0500
1000
1500
2000
2500
3000
3500
4000
4500
5000
0 1000 2000 3000 4000
39°/60°30°/90°22°/180°22°/180°
Time (s)
Are
a (m
2 ) δ α
Fig. 8. Area growth in a canyon fire using static and dynamic sim-ulations for four geometric configurations. The corresponding valuesof δ and α for each configuration are given in the legend. Dotted linescorrespond to static model while full lines correspond to dynamic firesimulation.
flow accelerated upslope reaching higher velocities for moreclosed canyons in comparison with a simple plane slope withthe same inclination.
Numerical simulation of a non-reactive heat source placedat the bottom of the canyon demonstrated a strong interactionbetween the wind flow and the buoyancy induced by the heatsource. The wind flow was markedly modified by the heatsource.
Fire spread simulation was performed using fuel cells anda Dijsktra spread algorithm. It was assumed that the angularvariation of the rate of spread was such that the resulting fireshape was a double ellipse with axis defined as in Fig. 5.
Two different fuels were used in that work. Fuel a typical ofherbaceous vegetation and fuel b similar to slash. Rothermel’smodel was used to determine the local rate of spread. The rateof spread at each fire line element was computed taking intoaccount the local wind velocity and direction and the slopeeffect. A modified Rothermel algorithm (cf. Viegas 2004)was used to take into account the correspondent slope andwind effects.
Static and dynamic models
In the simulation of fire spread, a boundary layer turbulentwind flow with a velocity of 5 m/s at 10 m height was usedand two basic situations were considered:
(1) Static model—so called because in this it was assumedthat the wind flow was not disturbed by the fire.
(2) Dynamic model—in this case it was considered that thepresence of fire and the heat that it released affected thewind flow and therefore modified fire spread.
It was found that the results of both simulations were quitedifferent for practically all configurations: the dynamic modelshowed a much higher rate of fire growth than the static one,as could be expected. A typical result of that simulation isshown in Fig. 8. In this figure the dotted lines correspond to
260 D. X. Viegas and L. P. Pita
Table 3. Reference values for fire simulation in a canyon(cf. Lopes 1994)
Fuel R0 (cm/s) L0 (m) t0 (s)
U = 0 m/s U = 5 m/s U = 5 m/s U = 5 m/s
a 2 110 5 4.55b 0.29 5.9 3 50.8
L0, flame length for the conditions defined for R0; R0, rate of spread ofa linear fire front in horizontal fuel bed with wind velocity equal to U; t0,characteristic residence time for the flaming combustion in the conditionsdefined for R0; U, mid-flame wind velocity.
0
20
40
60
80
100
120
140
160
0 10 20 30 40 50 60 70
ab
0
100
200
300
400
500
600
0 10 20 30 40 50 60 70
ba
(a)
(b)
Time/t0
Per
imet
er/L
0A
rea/
L 02
Fig. 9. Non-dimensional evolution of perimeter (a) and area growth(b) for fuels a and b, for a simple slope: α = 22◦ and δ = 0◦.
the static model and the full lines correspond to the resultsof the dynamic model. Although the results of the dynamicmodel seemed more plausible than those of the other model,at that stage there were no data to prove this.
Test of non-dimensional parameters
In order to test the formulation of non-dimensional param-eters proposed above, we used the results from Lopes (1994).The reference values that were adopted are shown in Table 3for the two fuels used. As the simulation was made with asuperimposed wind flow, it was considered that the reference
0
100
200
300
400
500
600
0 5 10 15 20 25 30 35
0 5 10 15 20 25 30 350
50
100
150
200
250
300
(a)
(b)
Time/t0
Per
imet
er/L
0A
rea/
L 02
ab
ab
Fig. 10. Non-dimensional evolution of area (a) and perimeter growth(b) for fuels a and b, for a canyon: α = 22◦ and δ = 21◦.
rate of spread value should not be the basic rate of spread R0
(without slope and without wind). Instead we considered analternative value (designated also as R0 here) for the samefuel bed on a horizontal surface but with the same wind flowas considered in the simulation.
The results are shown in Figs 9 and 10 for the simple planeand for a canyon with α = 22◦ and δ = 21◦, respectively. Ascan be seen the non-dimensional formulation works quitewell, as both curves in the non-dimensional representationare practically coincident, for the simple plane slope and alsoat the initial stage of the canyon case for both parameters.
The configuration considered in Fig. 9 corresponds toa simple slope without ‘canyon effect’. For this configu-ration the non-dimensional parameters work very well andthe fire spread curves practically coalesce into a single oneindependently of the fuel bed.
The case considered in Fig. 10 is a canyon with a valueδ = 21◦ and it is observed that the non-dimensional param-eters do not provide a single curve for both fuel cases aswould be expected. The fact that the non-dimensional curvesdo not coincide in the final stage of fire development indicatesthat most certainly a single set of reference values—namely
Fire spread in canyons 261
(a)
(b)
(c)
Fig. 11. Laboratory test rigs. (a) DE 1; (b) DE 2; (c) DE 3.
R0 and L0 corresponding to the no-slope case—may not besufficient to represent the fire conditions during all stages,namely during the ‘blow-up’ that occurs at the final stageof a canyon fire as will be described below. The authors feelthat the simplified non-dimensional modelling using only twoparameters is not sufficient to describe fire spread in canyons
Table 4. Geometrical properties of the basic set ofexperiments in DE 2
when there is a blow-up. More research is required in orderto clarify this point.
Laboratory experiments
Test rigs
In the experimental program three different test rigs wereused.
The first one DE 1 (Fig. 11a) was a preliminary rig adaptedfrom the Combustion Table MC 3 of our Industrial Aero-dynamics Laboratory. It had two faces inclined at a fixedvalue of δ = 30◦ attached to a structure that could be inclined(0◦ < α < 40◦). A series of tests was performed on this tablein order to assess the feasibility of analysing at a laboratoryscale the main features of canyon fires. In spite of the smalldimensions of the faces of this table (1.6 m × 0.8 m each), theresults were satisfactory so a larger device DE 2 was built.
The structure DE 2 (Fig. 11b) was built purposely for thisresearch program and it is installed at the Forest Fire ResearchLaboratory of ADAI, in Lousã (Portugal). It has two faces(2.9 m × 1.45 m each) that are hinged to a base allowing thesetting of δ values for each face (0◦ < δ < 40◦) independently.The base is fixed to a structure and can be inclined manually(0◦ < α < 40◦). Practically all tests reported in this articlewere made in this test rig.
The structure DE 3 (Fig. 11c) is basically the same as DE 2but its supporting structure was built on purpose allowingthe setting of the desired values of α using hydraulic jacks toperform the movements.
A series of 20 experiments was carried out with differentconfigurations in DE 2 with the reference parameters given inTable 4. This set of experiments covers a large majority of the
262 D. X. Viegas and L. P. Pita
situations of canyons that are found in practice. Most resultsreported here refer to this set that is designated as the basicset of experiments from now on. In Appendix 1 a schematicrepresentation of the 20 configurations studied in the basicset of experiments is given.
Methodology
In the basic set of experiments the fuel bed was composed ofdead needles of Pinus pinaster with a load of 0.6 kg/m2 (dry
δ � 11°
δ � 20°
δ � 40°
(a) (b)
Fig. 12. Fire spread contours obtained in tests with α = 0◦ for three values of δ. Time stepbetween bold lines is 60 s. (a) Analytical model; (b) experimental results.
basis). In order to characterise the fuel bed in each session,at least two tests of the basic rate of spread were made witha fuel bed created in the same conditions as in the mainexperiments. Fuel moisture content was monitored frequentlyduring the experiments.
Tests were made also with other fuels, particularly withstraw. This fuel has a much higher value of R0 for similarmoisture content conditions (typically 0.6 cm/s in compari-son to 0.2 cm/s).
Fire spread in canyons 263
Fire ignition was produced at a single point in the OY1 axisat a point 50 cm above the base of the canyon (yig = 50 cm).
During all experiments video and infrared images of theevolution of the fire front were recorded.
Images were analysed using standard image processingsystems. The algorithm for image correction due to non-orthogonality of the optical axis of the cameras to the fuelbed surface developed by André et al. (2002) was used exten-sively.The analysis of fire spread was then carried out on these
δ � 11°
δ � 20°
δ � 40°
(a) (b)
Fig. 13. Fire spread contours obtained in tests with α = 20◦ for three values of δ. Time stepbetween bold lines is 60 s. (a) Analytical model; (b) experimental results.
corrected images in order to retrieve various properties of thefire front advance at given time steps.
Results and discussion
Fire shape
Shapes of the fire fronts computed using the analytical modelfor some of the canyon configurations studied are shown inFigs 12–14. In each figure combinations of the following
264 D. X. Viegas and L. P. Pita
δ � 11°
δ � 20°
δ � 40°
(a) (b)
Fig. 14. Fire spread contours obtained in tests with α = 40◦ for three values of δ. Time step betweenbold lines is 60 s. (a) Analytical model; (b) experimental results.
values of the geometrical parameters are shown: α = 0◦, 20◦and 40◦; δ = 11◦, 20◦ and 40◦. For each case the resultsfrom the experiments are shown for comparison for the sameconfigurations and for the same time steps.
As can be seen the analytical model results are only a verycrude approximation of the experiments. The bifurcation of
the fire front with two distinct heads is observed only for lowvalues of α and for high values of δ. Otherwise the fire front atthe water line (axis OY1) tends to catch the other two headsmerging in a single and wide fire front in most cases. It isalso observed that the rate of spread of the head fire does notremain constant as is assumed in the analytical model.
Fire spread in canyons 265
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0 5 10 15 20 25 30 35 40 45
11º20º32º40º
0
1
2
3
4
5
6
7
8
0 5 10 15 20 25 30 35 40 45
11º20º32º40º
δ
δ
α
(a)
(b)
R2/R
0R
1/R
0
Fig. 15. Average value of the rate of spread of R′1 along the waterline
for up-slope propagation (a) and R′2 for down-slope propagation (b).
Rate of advance
Average values
In order to characterise the evolution of the fire front,namely to estimate a rate of spread at representative pointsof the fire front, we considered the following four points P1,P2, P3 and P4, which were already considered above and areshown in Fig. 6. The distance si (i = 1, 4) was measured fromthe plots obtained in each test. It must be noted that the evo-lution along direction s4 does not correspond to a real rate ofspread as this line is not perpendicular to the fire perimeterin the general case.
In a first step we estimate the average value of the rate ofincrease of si(t) assuming that this is a linear function of timeof the type:
si = Ri · t + s0 (30)
As will be seen later these average values of Ri are repre-sentative of the true rate of spread only in some cases of lowvalues of α and/or δ. The results obtained for Ri are shownin Figs 15 and 16. Given the dynamic character of canyonfire behaviour, these average values of the rate of spread arevery low when compared with instantaneous values. They aregiven here as they were used to estimate the average rate of
0
2
4
6
8
10
12
0 5 10 15 20 25 30 35 40 45
11º20º32º40º
0
1
2
3
4
5
6
0 5 10 15 20 25 30 35 40 45
11º20º32º40º
δ
δ
α
(a)
(b)
R3/R
0R
4/R
0
Fig. 16. Average value of the rate of spread of R′3 along the maximum
slope direction (a) and R′4 along a horizontal line at the level of fire
origin (b).
spread for the analytical model presented in the subsectionFire shape in Results and discussion.
As can be seen in Fig. 15a, the average rate R′1 of up-
slope spread along axis OY1 increases with both α and δ.There is nevertheless a discrepancy for α = 40◦ and for bothδ = 20◦ and 32◦ that may be due to experimental errors. Theaverage rate R′
2 of down-slope spread along axis OY1 remainspractically constant and close to one in the range of values ofboth α and δ that were tested, as can be seen in Fig. 15b.
The average rate R′3 of up-slope spread along the maxi-
mum slope axis that is shown in Fig. 16a increases with bothα and δ. It must be remarked that the relative increase of therate of spread with α is not so large as for the case of Fig. 15a.The average rate R′
4 of horizontal spread at the level of theorigin point remains practically constant with α for low val-ues of δ and decreases for high values of δ due to geometricalconditions.
Comparison with the measured value of the angle of max-imum spread (defined by the head fire) and the maximumslope angle ψ for each case is made in Fig. 17a. The full linesin this figure correspond to the geometrical model describedin the section Canyon geometry (equation 3); these lines can
266 D. X. Viegas and L. P. Pita
0
10
20
30
40
50
60
70
80
90
100
0 5 10 15 20 25 30 35 40
11°20°32°40°
0
2
4
6
8
10
12
14
16
0 5 10 15 20 25 30 35 40 45 50 55 60
11º20º32º40º
δ
δ
α
(a)
(b)
R� 3 R �4
θ
�
Fig. 17. (a) Direction of maximum spread compared with maximumslope direction ψ. The lines correspond to equation (3). (b) Non-dimensional rate of spread of R′
3 as a function of the slope angle θ.The dotted line corresponds to equation (6).
be compared with those of Fig. 4. As can be seen the mea-sured angle tends to be lower than the theoretical value. Thismeans that the head of the fire is closer to the water line direc-tion of the canyon, indicating that there is a convective effect‘pushing’ the fire head towards the centre line of the canyon.
The average rate of spread R3/R0 as a function of slopeangle θ is shown in Fig. 17b. The dotted line that is shownin this figure is an extrapolation of the function given byequation (6) obtained for point ignitions in a slope withoutcanyon effect (α = 0◦ or δ = 0◦). As can be seen both sets ofresults of average values collapse quite well in a single curve.
Dynamic analysis
As was said above the increase of the distance si from pointPi to the fire origin was not always a linear function of time. Itwas observed that, on the contrary, the rate of distance growthincreased steadily with time in most cases. As an example thevariation of s1 as a function of time for the set of tests with
0
50
100
150
200
250
0 100 200 300 400 500 600 700 800
s 1 (
cm)
0°10°20°30°40°
t (s)
α
Fig. 18. Time evolution of distance s1 of fire line to fire origin up-slopealong the water line for δ = 20◦.
δ = 20◦ for each value of α is shown in Fig. 18.As can be seenin this figure the variation of s1 with time can be consideredapproximately linear only for α = 0◦ and for α = 10◦. Forgreater values of α the increment of distance increases at eachtime step, corresponding to a non-constant rate of spread. Inthese cases one observes that there is a relatively low value ofthe rate of spread at the beginning and then the rate of spreadincreases very rapidly. This is an effect of fire dynamics dueto the feedback from the reactive fuel bed to the convectioninduced by the fire in the concave shape of the canyon.
The derivative dsi/dt corresponding to an instantaneousvalue of the rate of spread in each case is presented in non-dimensional form:
f ′1 = dsi/dt
R0. (31)
The values of f ′1 for all the cases that were studied are
shown in Fig. 19. In this figure it is clearly shown that, inmany cases, the local rate of spread is not constant duringfire growth and this feature is common to all values of δ.Our tests show that for α > 30◦ the fire growth is dynamic inall cases and the rate of spread increases exponentially withtime. For α = 20◦ it has dynamic features for δ > 20◦. It isinteresting to note that the larger values of f ′
1 are found forδ = 32◦ while one would expect that they should be larger forδ = 40◦. This is probably due to the fact that the fire has notdeveloped sufficiently in the limited space of the CombustionTable for this geometry.
Perimeter and area growth
Perimeter and area of the fire front during the period inwhich the fire front did not reach the border of the table wereanalysed using the image analysis methods mentioned above.
As was shown above, the fire growth in canyons has adynamic character for the majority of cases. Therefore it isnot relevant to analyse the average values of perimeter and
Fire spread in canyons 267
0
1
2
3
4
5
6
0 100 200 300 400 500 600 700t (s)
0°10°20°30°40°
0
1
2
3
4
5
6
0 100 200 300 400 500 600 700
0°10°20°30°40°
0
1
1
2
2
3
3
4
4
0 100 200 300 400 500 600 700
0°10°20°30°40°
0
1
2
3
4
5
0 50 100 150 200 250 300 350 400 450 500
0°10°20°30°40°
t (s)
f� 1f� 1
(a)
(c)
(b)
(d )
α
α
α
α
Fig. 19. Instantaneous non-dimensional velocity f ′1 of fire evolution along the water line for all cases that were studied. (a) δ = 11◦; (b) δ = 20◦;
(c) δ = 32◦; and (d) δ = 40◦.
area growth, so only results for dynamic or time-dependentgrowth are presented.
In Fig. 20 the temporal variation of fire perimeter in eachcase is shown. In this figure it is again clear that the rate ofgrowth of the perimeter is not constant as predicted by clas-sical fire behaviour models, namely by the present analyticalmodel. Interestingly it is found that, in the range of our exper-iments, the configuration δ = 40◦ is the one that presents alinear growth of the perimeter for practically all values of α
that were tested.Area growth is shown in Fig. 21 for all the cases tested.
The dynamic character of fire growth is also apparent in thisfigure.
Test with two different fuels
In order to test the proposed methodology by using non-dimensional parameters to transpose results from one exper-iment to another situation, two experiments were made withthe same canyon geometry (δ = 40◦ and α = 40◦) but withtwo different fuels.
In test DE 521 the normal bed of pine needles was usedwhile in test DE 522 a fuel bed composed of straw was used
instead.A sequence of photographs of both tests taken at prac-tically the same time steps from ignition is shown in Fig. 22.As can be seen in this figure there is a marked differencebetween both fuels. The basic rate of spread and the flamelength L0 were measured directly in both cases and the resultsare given in Table 5.
The evolution of fire perimeter and fire area in both testsis shown in Fig. 23. Using the non-dimensional formulationproposed above, the same properties are shown in non-dimensional form in Fig. 24. As can be seen in these figures,the two sets of curves for P ′ and for A′ in many cases are prac-tically coincident at the first phase of the fire development(t′ < 0.7) but afterwards the agreement is not so good. Thisresult is an indication that the basic fire spread properties—namely R0 and L0—obtained for flat terrain conditions in theabsence of wind are good similarity factors only for the ini-tial stages of the fire. Once blow-up starts, fire is dominatedby its own convection and its spread properties do not retainsimilarity to those basic parameters. Probably if we had usedsome other similarity parameters related to wind-spread firea better agreement would be obtained. The analysis of thisassertion is left to future work.
268 D. X. Viegas and L. P. Pita
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
0 20 40 60 80 100 120 140
0°10°20°30°40°
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
0 20 40 60 80 100 120 140 160 180 200
0°10°20°30°40°
0.0
1.0
2.0
3.0
4.0
5.0
6.0
0 50 100 150 200 250
0°10°20°30°40°
0.0
1.0
2.0
3.0
4.0
5.0
6.0
0 50 100 150 200 250
0°10°20°30°40°
t (s) t (s)
(a)
(c)
(b)
(d )
α
α α
α
P (
m)
P (
m)
Fig. 20. Perimeter growth in each of the basic cases: (a–d) δ = 11◦, 20◦, 32◦ and 40◦ respectively.
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
0 50 100 150 200 250
0°10°20°30°40°
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0 50 100 150 200 250
0°10°20°30°40°
0.0
0.5
1.0
1.5
2.0
2.5
0 20 40 60 80 100 120 140 160 180 200
0°10°20°30°40°
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 20 40 60 80 100 120 140
0°10°20°30°40°
t (s) t (s)
(a)
(c)
(b)
(d )
α
α
α
α
A (
m2 )
A (
m2 )
Fig. 21. Area growth in each of the basic cases: (a–d) δ = 11◦, 20◦, 32◦ and 40◦ respectively.
Fire spread in canyons 269
DE 521 9�
DE 521 23�
DE 522 8�
DE 522 24�
DE 521 33�
DE 521 43�
DE 522 34�
DE 522 42�
Fig. 22. Fire growth during tests DE 521 and DE 522 with two different fuels. Time since fire origin in seconds is indicated below each picture.
Table 5. Properties of the fuel beds with two different fuels
Ref. Material Load FMC R0 L0 T0
(kg/m2) (%) (cm/s) (cm) (s)
DE 521 Pine needles 0.6 13 0.151 13.3 88.1DE 522 Straw 0.6 9.7 0.577 21.7 37.9
The non-dimensional rate of perimeter and area growth,P ′ and A′ respectively, are shown in Fig. 25. The agree-ment between both sets of curves is not so good as beforebut it is considered to be sufficient to validate the pro-posed methodology of using the similarity laws defined byequations (22) to (25).
Convection inhibition
In order to put in evidence the role of convection induced bythe fire in the dynamics of fire growth, an experiment wascarried out in which this convection was inhibited by a plateplaced across the base of the canyon. A sequence of photosof tests DE 520 and DE 521 performed with the same fuelbed conditions and for δ = 40◦ and α = 40◦ with and withoutthe plate is shown in Fig. 26. The time steps of each pairof photographs are not the same in all cases but they aresufficiently close to illustrate the large differences betweenboth experiments.
These results are put in evidence in the comparative anal-ysis of perimeter and area growth for these two cases as isshown in Fig. 27. The difference between both sets of data isquite clear showing the importance of air entrainment inducedby natural convection.
Field cases
Field experiment
In the scope of the Gestosa field experiments in CentralPortugal (cf. Viegas et al. 2002), a test of fire propagation
in a canyon was performed in June 2001 in a plot designatedG 63. Vegetation cover of this plot was shrubland with anaverage height of 0.87 m and a fuel load of 3.7 kg/m2. Thegeneral dimensions of the canyon and a general view of theexperiment are shown in Fig. 28. The canyon configurationcorresponded approximately to the following values α = 25◦and δ = 31◦.
Extreme precaution was taken during this test to avoid fireescaping to surrounding vegetation. Ignition was performedat two points near the water line at the base of the canyon.The total duration of the experiment was 32 min. Character-istically more than 30% of the area was burned during thelast 4 min of the experiment.
Using the following reference values for the field case,the perimeter and area growth in non-dimensional form wereplotted: R0 = 0.06 m/s; t0 = 400 s; (L0 = 12 m) in Fig. 29. Inthe same figure the corresponding results for laboratory testsfor δ = 30◦ and α = 20◦ and α = 25◦ are shown for compar-ison. Assuming that the reference values are taken correctlyit appears that the laboratory tests show the same trend asthose observed in the field although the range of variation ofthe parameters, namely non-dimensional time, was not suf-ficient in the small-scale experiments to allow a definitiveconclusion.
Real fires
There are many examples in the literature of fire-related fatal-ities that occurred in canyon or similarly shaped terrain. Justa few that are well known in the literature are the Mann GulchFire (cf. MacLean 1992; Rothermel 1993); the Storm KingFire (cf. Butler et al. 1998); the Thirtymile Fire (cf. Furnishet al. 2001); the Loop Fire, 1966, and the Battlement CreekFire, 1976 (cf. Pyne 1984); theAlajar Fire (cf. Silva 1997); theAlvão Fire (cf. Viegas et al. 2000). In the description of theseaccidents it is frequently mentioned that a ‘blow-up’of the fire
270 D. X. Viegas and L. P. Pita
0.0
0.5
1.0
1.5
0 20 40 60 80 100 120
StrawPinus
StrawPinus
0.0
1.0
2.0
3.0
4.0
5.0
0 20 40 60 80 100 120t (s) t (s)
(a) (b)
A (
m2 )
P (
m)
Fig. 23. Area (a) and perimeter (b) growth during tests DE 521 and DE 522 with two different fuels.
0
0.1
0.2
0.3
0.4
0.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2
521522
521522
0
10
20
30
40
50
60
70
80
90
0.0 0.2 0.4 0.6 0.8 1.0 1.2
(a) (b)
P�
A�
t � t �
Fig. 24. Non-dimensional perimeter P ′ (a) and area A′ (b) growth during tests DE 521 and DE 522with two different fuels.
00.10.20.30.40.50.60.70.80.9
1
0.0 0.2 0.4 0.6 0.8 1.0 1.2
521 (Pinus)522 (Straw)
521 (Pinus)522 (Straw)
0
50
100
150
200
250
300
0.0 0.2 0.4 0.6 0.8 1.0 1.2
(a) (b)
P�
A�
t � t �
Fig. 25. Non-dimensional rate of perimeter P ′ (a) and area A′ (b) growth during tests DE 521 and DE 522with two different fuels.
or a ‘sudden explosion’ occurred. It is always mentioned thatthe fire behaviour changed suddenly and in an unexpectedway so as to surprise all involved. It is also reported that thefire consumed in very few minutes an area larger than thatburned during the previous hours or even days in the samearea and type of fuel. Witnesses and survivors have reported
strong to very strong winds in the area of the fire, even whenthe overall winds in the region were weak. The report on theStorm King Mountain accident in particular is very detailedand informative in this aspect.
In order to explain the sudden change of fire behavioursome analysts assume the existence of special phenomena
Fire spread in canyons 271
DE 521 69�
DE 521 78�
DE 520 64�
DE 520 84�
DE 521 107�
DE 521 124�
DE 520 103�
DE 520 124�
Fig. 26. Fire growth during tests DE 521 and DE 520 with open and closed canyon. Time since fire origin in seconds is indicated below each picture.
0.0
1.0
2.0
3.0
4.0
5.0
0 50 100 150
ClosedOpen
ClosedOpen
0.0
0.5
1.0
1.5
0 50 100 150
(a) (b)
t �(s) t �(s)
P (
m)
A (
m2 )
Fig. 27. Perimeter (a) and area growth (b) during tests with open and closed canyon.
(a) (b)
Fig. 28. Canyon field experiment G 63 of Gestosa 2001. (a) Contour map. (b) View of the test site during the final stagesof the experiment.
that contribute to the observed and apparently unexplainedfire behaviour. For example Butler et al. (1998) mention a‘Venturi effect’ of the wind around the Storm King Mountainto justify the sudden acceleration of the fire. These authors
also hypothesise about the interaction between general windand up-canyon flow to justify the extreme fire behaviourobserved. They also look at the possible occurrence of severespotting ahead of the fire line as a mechanism to induce fire
272 D. X. Viegas and L. P. Pita
0
20
40
60
80
100
120
140
0 1 2 3 4 5 6
� � 30º � � 20º� � 30º � � 30ºGestosa 2001
� � 30º � � 20º� � 30º � � 30ºGestosa 2001
0
20
40
60
80
100
120
140
160
180
200
0 1 2 3 4 5 6
(a) (b)
t't'
P�
A�
Fig. 29. Non-dimensional perimeter (a) and area growth (b) in the field experiment compared withlaboratory tests for two different configurations.
acceleration. Silva considers that a thermal belt at mid-slopeprovoked fire acceleration in the Alajar Fire. The report onthe Thirtymile accident makes only a very short reference totopography in its analysis of factors contributing to the rapidfire spread during the final stages of the fire although, in ouropinion, this was certainly one of the major factors in the veryrapid fire development.
Our experiments show that these special effects are not atall necessary to produce a blow-up in a canyon. The terrainitself and the concave shape of the canyon are enough to gen-erate the dynamic behaviour of the fire as was observed evenat the relatively small scale of our laboratory experiments.There was no wind at all inside the laboratory and even lessstratification effects or fuel bed heterogeneities that couldprovoke the observed behaviour.
Therefore in our opinion some of the analysis that was pro-duced in past accidents involving canyons can be misleadingand even dangerous. As some of them invoke the conjugationof a set of special circumstances that one might expect to berare or with a very low probability, people may be inducedto take a chance and put their lives in danger in a canyonfire. Our results show that a blow-up will always occur in acanyon even if it is quite shallow. It is not necessary to haveany wind flow blowing over the fire and even less any suddenburst of wind. The only things that are needed are space andtime for the fire to accelerate and to create its own wind. Ifthese conditions are available, no one should ever be placedin the way of such a powerful fire front.
Conclusion
This study is a first approach to the analysis of fire spreadin canyons based on analytical and on experimental work.The simple case of symmetrical canyons with plane faces,uniform vegetation and single and symmetrical point ignitionwithout wind was considered. It was shown that two angles
are sufficient to characterise the geometry of the canyon inthis case.
An analytical model to estimate fire growth based on theconcepts of semi-elliptical growth and assuming a constantrate of spread for the head fire showed that fire shape dependsonly on the maximum slope angle θ of the canyon face andon the angle ψ between the maximum slope direction and thewater line of the canyon. This model is very limited as theassumption of a constant rate of spread is not valid and alsobecause it is observed that in some cases the strong convectioninduced by the fire masks the bifurcation effect predicted bythe model in all cases.
Non-dimensional parameters are proposed to comparedata from numerical or physical experiments performed atdifferent scales or with different fuels. The present resultscan be considered a preliminary and limited validation of theproposed method of transferring and comparing data.
The results of the numerical model developed by Lopeset al. (1995), for the simulation of the behaviour of fire ina canyon were recalled. The predicted but not yet validateddynamic behaviour of fire in this terrain configuration wasdemonstrated in the present study.
A laboratory experimental program carried out in an orig-inal test bench was described. A wide range of geometricalconfigurations was covered in the present study. All testswere recorded using video and infrared cameras. An originalalgorithm was used to correct the images due to oblique inci-dence of the cameras, and fire spread analysis was performedusing a very large number of images collected during theexperiments.
The dynamic behaviour of the fire was clearly observed inthe sense that for the majority of cases the spread of the fireis governed by a time-dependent rate of spread. This effectis not predicted in classical models, which assume that a firein a homogeneous fuel bed in a uniform slope will propagatewith a constant rate of spread. This is not at all the case.
Fire spread in canyons 273
It was observed that the fire growth is relatively slow at thebeginning but suddenly the rate of fire growth increases veryrapidly. The time lag for transition must depend on geometryand on fuel properties. Our results show this dependence butare not sufficient to allow for more definitive or quantitativeconclusions at this stage.
The fire behaviour mentioned above can be misleading infire suppression activities.The fire appears to be well behavedwhen it is at its initial stages near the bottom of the canyon.When sufficient convection is generated by the fire it feedsthe combustion reaction with fresh oxygen, then the pro-cess enters in an unstable equilibrium with the rate of spreadincreasing probably exponentially and reaching values thatare not commonly observed for the same type of vegetation.Our study showed that there are no additional conditions likefuel changes, strong winds or stratification effects requiredto provoke fire acceleration in this terrain configuration.
A laboratory experiment performed with a plate to inhibitair entrainment at the base of the canyon demonstrated thevery important role played by natural convection in this typeof fire.A well-monitored field experiment in a canyon showedthe same fire behaviour as was observed in the small-scaleexperiment. The non-dimensional parameters that were usedshowed a similar trend for both sets of data.
Past cases of fires in canyons can be explained in light ofthe present study. In particular the phenomena described inaccidents involving fatalities that occurred in canyons can beexplained based only on terrain features. Although the exis-tence of some other special circumstances in some of themcannot be ruled out, it was demonstrated that such conditionsare not at all necessary for a blow-up to occur. This conclu-sion has very important practical implications in terms of firesafety as it implies that fires in canyons are always potentiallyvery dangerous. Exposure to fire spread above the fire lineshould be eliminated by all means in order to avoid loss oflives. If there is no absolute certainty that a fire at the bottomof a canyon—or a very steep slope—can be extinguished ina very short time with the existing fire fighting force, oneshould never attempt to encircle the fire or to put resources atany place in the slope above the fire as the high rate of spreadregime can be attained suddenly. According to our study thisis only a matter of time for a given terrain configuration andit does not depend very much on other ambient conditions.
Acknowledgements
The authors thank their colleagues A. Lopes, G. Vaz andR. Figueiredo for a critical review of this manuscript.The experimental program in the laboratory was performedwith the help of Mr Nuno Luis, Mr A. Cardoso andMr P. Palheiro; their support is gratefully acknowledged.The present research is included in the program of ProjectsWinslope (Contract POCTI/34128/EME/2000) and Spread
http://www.publish.csiro.au/journals/ijwf
(Contract EVG1-CT2001–00043) supported, respectively, byFundação para a Ciência e Tecnologia and by the EuropeanCommission under the Program Environment. This supportis also gratefully acknowledged.
References
André JCS, Martinez Dios JR, Gonçalves JC, Arrue B, Ollero A (2002)‘Fire spread analysis using visual and infrared images.’ SpreadTechnical Report. (ADAI: Coimbra, Portugal)
Bilgili E, Methven IR (1990) The simple ellipse: a basic growth model.In ‘Proceedings of the 1st international conference on forest fireresearch, 19–22 November 1990, Coimbra, Portugal’. B.18.
Brown AA, Davis KP (1973) ‘Forest fire. Control and use.’ 2nd edn.(McGraw-Hill: New York)
Butler BW, Bartlette RA, Bradshaw LS, Cohen JD, Andrews PL,Putnam T, Mangan RJ (1998) ‘Fire behaviour associated with the1994 South Canyon Fire on Storm King Mountain, Colorado.’USDA Forest Service, Rocky Mountain Research Station ReportRMRS-RP-9. (Ogden, UT)
Chandler C, Cheney P, Thomas P, Trabaud L, Williams D (1983) ‘Firein forestry.’ Vol. 1. (John Wiley & Sons: New York)
Furnish J, Chockie A, Anderson L, Connaughton K, Das D, Duran J,Graham B, Jackson G, Kern T, Lasko R, Prange J, Pincha-Tulley J,Withlock C (2001) ‘Thirtymile Fire Investigation.’ Factual reportand management evaluation report. USDA, Forest Service, October2001.
Lopes AG (1994) ‘Modelação numérica e experimental do escoa-mento turbulento tridimensional em topografia complexa:Aplicaçãoao caso de um desfiladeiro.’ PhD thesis, University of Coimbra,Portugal. [In Portuguese]
Lopes AG, Sousa CM, Viegas DX (1995) Numerical simulation of tur-bulent flow and fire propagation in complex topography. NumericalHeat Transfer Journal 27, 229–253.
MacLean N (1992) ‘Young men and fire.’ (University of Chicago Press:Chicago)
Pyne SJ (1984) ‘Introduction to wildland fire—Fire management in theUnited States.’ (John Wiley & Sons: New York)
Pyne SJ, Andrews P, Laven RD (1996) ‘Introduction to wildland fire.’2nd edn. (John Wiley & Sons: New York)
Rothermel RC (1972) ‘A mathematical model for predicting fire spreadin wildland fuels.’ USDA Forest Service, Intermountain Forest andRange Experiment Station Research Paper INT-115. (Ogden, UT)
Rothermel RC (1993) ‘Mann Gulch Fire: a race that couldn’t be won.’USDA Forest Service, Intermountain Research Station GeneralTechnical Report INT-299.
Silva FR (1997) ‘El accidente de Alajar.’ Report of INFOCA, Spain.[In Spanish]
Velez R (2000) ‘La defensa contra incendios forestales—Fundamentosy experiencias.’ (McGraw Hill/Interamericana de España: Madrid,Spain) [In Spanish]
Viegas DX (2004) Slope and wind effects on fire propagation. Interna-tional Journal of Wildland Fire 13, 143–156. doi:10.1071/WF03046
Viegas DX, SilvaAJM, Cruz MG (2000)Analysis of three fatal accidentsinvolving Portuguese firefighters. In ‘Proceedings of 2000 Interna-tional Wildfire Safety Summit, 10–12 October 2000, Edmonton,Canada’. pp. 190–199.
Viegas DX, Cruz MG, Ribeiro LM, Silva AJ, Ollero A, et al. (2002)Gestosa fire spread experiments. In ‘Proceedings of the IV Interna-tional Conference on Forest Fire Research and Wildland Fire Safety,Luso, Portugal, 18–23 November 2002’. (Ed. DX Viegas) (MillpressScience Publishers: Rotterdam, The Netherlands)
