Computer simulations of fire behaviour in garrigue in southern France

Applied Geography

(1988), 8, 53-64

Computer simulations southern France

of fire behaviour in garrigue in

George P. Malanson

Department of Geography, University of Iowa, Iowa City, IA 52242, USA and Louis Trabaud CNRS Centre Emberger, BP SOSI, 34033 Montpellier, France Abstract Garrigue is a low shrubland covering extensive areas in southern Europe, in which recurrent fire is both a natural ecological process and hazard. TO analyse some aspects of this dualism, detailed descriptions of fuel types were entered into a computer simulation of fire behaviour. Samples of fuel types were collected for stands of 3,9, and 33 years since last fire in garrigue of dense Quercus coccifera in southern France. To represent spring and autumn conditions, respectively, two models were used: one with herbaceous biomass evenly divided between living and dead categories, and a second with all herbaceous biomass counted as dead. The moisture contents for these models were estimated from prior observations and for relatively dry conditions. To incorporate the impact of a common fire-fighting tactic, a third fuel model was created by calculating the moisture that would be added to the surface areas of standing fuel by an aircraft water drop of 0.5 kgm-* on the second, autumn, fuel type. These three fuel models for each of the three stand ages were entered in a computer simulation that calculated several measures of fire intensity, including fire power, rate of spread, and the temporal pattern of heat release following the passage of the flaming front. The simulations show that the added water extinguishes fire. Without the added water the fire burns relatively slowly, especially if compared to fires observed and simulated in southern California, where water drops are often ineffective. The simulations indicate that prescribed burns could be conducted with low risk at an interval of IO-15 years.

Introduction

In Mediterranean-type vegetation worldwide, fire is considered as both a natural ecological process and a hazard (Cunningham 1984). Both the physiognomy of the vegetation and the Mediterranean climate contribute to a landscape prone to fires. While Kuhnholtz-Lordat (1958) has called this landscape a ‘green screen’ (/‘&ran vert), the title of his earlier work, La terre incindike (1938), may be more appropriate. The effects of fire as a natural ecological process depend on whether or not the fire regime is similar to the regime to which the species of plants and animals, including soil micro-organisms, are adapted. The effects of fire as a natural hazard also depend on the fire regime, which, includes four elements: frequency, intensity, area, and season of the fires. The first goal of fire management is to protect human lives and property; the second goal is to preserve natural ecological functions, such as watershed processes or the maintenance of species diversity. It seems that in some places, such as southern California, the natural fire regime may include severe fires 0143~6228/88/010053-12$03.00 0 1988 Butterworth & Co (Publishers) Ltd

54

Conlplr

fersimularions of fire behaviow in garrigue

and the two goals of fire management in those wildlands, hazard reduction and maintenance of natural vegetation, may be incompatible (Malanson 1985). In Australia frequent prescribed burning has been opposed by conservationists, and the limits they have imposed have in turn been blamed for some of the damage done to property during recent severe fires (Oliver et al. 1984). In the Mediterranean region of France the fire management strategy is to suppress fires at all times; this strategy has until recently been the only one in all Mediterranean-type vegetation except in Australia (Leone 1984). The purpose of this paper is to explore some parameters of the fire regime in garrigue shrublands in southern France. Observations on the resilience of garrigue and intensity (Malanson and have shown it to depend on fire season, interval, Trabaud 1987a). Wrathall (1985) has indicated that fire damage in the region is increasing due to social reasons. Le Houerou (1987) has recently computed the costs of fire in the French Ivlediterranean region in terms of fire prevention, control, and vegetation loss to be USS6.3 x 10’ and for the 1.5Mediterranean countries together to be US$9.8 x 10s. These figures are much higher than what is actually spent because they are extrapolated from the more intensive efforts in France, Spain, and Italy. Because they do not include direct losses to properties, ecological losses of nutrients, sedimentation of reservoirs, or aesthetic and touristic losses, Le Houerou (1987) believes that they may be closer to the actual costs than they would seem. For those countries engaged in expensive efforts at fire prevention and control (France, Spain, Italy), these costs (USSljOOha-t yr-t) are probably within an order of magnitude of actual costs. Of the seven European Mediterranean countries, in 1981 fires burned c. 600000ha of land, of which half were set intentionally (Velez Munoz 1984). The intention here is to illustrate how changes in fire interval and season, and some aspects of suppression, affect fire behaviour and thus the effects of fire as a hazard and as an ecological process. Trabaud (1976, 1979, 1985) has reported observations of flammability and fire behaviour in garrigue and recently calculated fire power (kW m- 1) for a generalized description of garrigue fuels. Several parameters of fire behaviour of interest to fire managers are needed to supplement these observations. A computer simulation of fire behaviour, which relies on a detailed description of fuel to calculate fire behaviour, is used here. Computer simulations have been designed to aid in fire suppression operations and in the planning of prescribed burning (Cohen 1986). Their use has largely been in these direct applications, rather than in scientific investigations. Simulations have, however, been used for Mediterranean-type vegetation in California, Australia, and South Africa. In Californian chaparral Rothermel and Philpot (1973) used simulations to calculate some basic parameters of flammability and fire spread. In Californian coastal sage scrub Westman et al. (1981) used a simulation to calculate fire intensity to analyse fire effects on vegetative resilience, and Malanson and O’Leary (1982, 1985) made similar analyses. In South Africa van Wilgen et al. (1985) used a computer simulation to calculate fire power and rate of spread and they compared their results with those of Rothermel and Philpot (1973) and Westman et al. (1981), as well as with observed values from other vegetation types (Hobbs and Gimingham 1984). Green (1983) and Green et al. (1983) have examined the use of fire simulations for predicting the shapes of fires in Mediterranean vegetation in Australia. Simulations have been used in other types of vegetation; for example, to compare flammability among arctic plant communities (Sylvester and Wein 1981) and to analyse snow avalanche tracks as fuelbreaks in subalpine forests (Malanson and Butler 1984). Although fire simulations are being used more frequently by some fire control agencies (Bradshaw 1980; Cohen 1986), the complexities of actual fires

George P. Malanson and Louis Trabaud

55

make the application of models to specific times and places problematical. Detailed fire models which include a geographic information system as a base (Kessell 1979) have proved too expensive to use daily. Methods

A fire behaviour simulation developed by Albini (1976a) is used here. The model is based on the fire spread equations of Rothermel (1972) for very general fuel conditions. Table 1 shows the equations proposed by Rothermel (1972) and the parameters needed to describe the fuel for this model. The values shown are in English rather than SI units because the coefficients in the equations depend on the units; in practice it is simple to translate input and output from and back to SI units. The mode1 requires input describing: 1. the fuels in terms of: a. biomass by size category based on surface-to-volume ratio b. fuel moisture as a fraction of dry weight c. heat content d. density e. mineral content and effective (silica-free) mineral conent of the wood g. the moisture of extinction 2. site values of: a. slope b. fuel depth (i.e. height of vegetation) c. wind velocity All the parameters needed by the mode1 can be measured in the field. While some values are not easily measured, this essentially empirical basis avoids potential circularity in reliance on theoretical estimates. The major assumption of the model is an even spatial distribution of fuel; litter is handled in a separate subroutine in the simulation. While no vegetation has evenly distributed branch sizes, the shrub physiognomy of garrigue is a close approximation and this model has been shown to correlate well with observed values for shrub vegetation in moderate fire conditions (van Wilgen et al. 1985). No simulations can accurately project fire behaviour for conditions of high wind peed. The model calculates reaction intensity (kWm-*), heat sink in the moisture in the vegetation (kJm-s), propagating flux (kWm-*), fire power (Byram’s intensity, kWm-1 of fireline), and rate of spread (ms- I). It is the last two values that are directly used by fire control agencies. These values indicate difficulty of control and probable location, respectively. A subroutine created by Albini (1976a) called BURNOUT calculates the proportion of fuel consumed, the rate of heat release through the course of burning, and the total heat release for a unit area. These values are of interest to fire ecologists and managers concerned with post-fire recovery. Fuel types

The region studied here is near Montpellier in southern France (Fig. 1) in the village of St Gely du Fesc, about 20 km from the sea, and half-way between Marseilles and Perpignan (3’ 53’E, 43’ 38’N). The vegetation of this area is garrigue, which covers 1 x 1Osha in France and four times this figure in southern Europe. Garrigue is composed of evergreen sclerophyllous shrubs of about 1 m in height. The canopy varies from being completely closed in most natural situations to having openings

56

Computer simulations of fire behaviour in garrigue

Table 1. Fire behaviour

equations presented by Rothermel (1972) and incorporated into a computer simulation by Albini (1976) (many of the coefficients are dependent on non-S1 units)

R=

Rate of spread, ft min - 1

IRE(1++w+@J

QbeQig

1, = I- ’ wnh,Mtls

Reaction intensity, Btuft-2min

where: F’ = F’ ,,(P/flop)Aexp]A(l - P/Pop)1 rImax = a”‘(495 + 0*0594a”q- ’ pop =

Optimum reaction velocity, minMaximum reaction velocity, min-r Optimum packing ratio

3.34&-‘J.s189

A = 1/(4.774#’

- 7.27) + 5.11!$

‘IM = 1-2.5!3;

X 7 = 0.174 S

Moisture damping coefficient

_ 3.52g X

-0.:9

(192+0~e2595cr)-~exp[(0~792+0~681e”~5)(~+O~l)] P -E 4, = cuBp~p [I=

Mineral damping coefficient Propagating flux ratio Wind coefficient

C = 7.47 exp ( - 0.1331~@~~) B = 0.025260@~~ E = 0.715exp(-3.59x10-4u)

Net fuel loading, lb ft - *

w, o, = 5.275/3-“‘3 (tan +)* ob = w,/6 E = exp( - 138/u) Qig = 250+ 1116M, S=eb

Slope factor Oven-dry bulk density, lb ft-’ Effective heating number Heat of pre-ignition, Btulb-’ Packing ratio

eLJ Input parameters for basic equations W*

6 ii ep F S,’ u tan & MX

oven-dry fuel loading, lbfte2 fuel depth, ft fuel particle surface-area-to-volume ratio, ft - 1 fuel particle low heat content, Btulb-t oven-dry particle density, lbfte3 fuel particle moisture content, lb moisture/lb oven-dry wood fuel particle total mineral content, lb minerals/lb oven-dry wood fuel particle effective mineral content, lb silica-free minerals/lb oven-dry wood wind velocity at midflame height, ftmin-’ slope, vertical rise/horizontal distance moisture content of extinction. We are presently using O-30, the fibre saturation point of many dead fuels. For aerial fuels (0 -Z 0.02) with low wind velocity (-=2*2ms-I, <5mph)M,= 0.2 (i.e. two-thirds the fibre saturation point of many dead fuels).

dominated by grasses in cases where combinations of fire and grazing have had a long-term impact (Plate 1). Typical floristic associations found are RosmarinetoLithospermetum and, studied here, Cocciferetum languedocien. These communities are regarded as degraded or successional stages of Quercion ilicis. The individual

George P. Jluianson and Louis Trabaud

.4 Per?

C”arl -_

57

--._-I

Figure 1. The study area on the southern coast of France (near Montpellier)

is at the centre of a broad distribution of garrigue estending from Portugal to Greece.

shrubs are much branched and have generaily hard and spiny leaves. A mature, dense garrigue is virtually impenetrable for the casuaf waiker. Fuel was sampled from 18 50 x 50-cm quadrats in each of three ages, 3, 9, and 33 years, of dense Quercus coccifera garrigue on the Puech de Juge, 1Okm north of Montpeilier in September 1984. This site has been used for experimental fires since 1969 (Trabaud 1974). A11 pfant material was cut at ground level. Herbaceous and dead material were cohected separately; proportions of the dead material were assigned to standing material and litter based on visual estimates for the three age groups. Woody vegetation was divided into five branch diameters: O-2.5, 2.5-5, 5-10, 10-20, 20-30mm, plus foliage, from which surface-to-volume ratios were calculated. The surface-to-volume ratio of the litter is based on the proportions used for dead standing fuel. All material was dried at 80°C for 48 hours and weighed. Two conditions were assumed to represent a difference between spring and autumn fires: the herbaceous material was assumed to be either 50 per cent or 100 per cent dead; these are reasonable values based on field observations of this vegetation. Fuel moisture

Fuet moisture of live material was estimated from samples taken during earlier observations of fire behaviour (Trabaud f 979). Because those samples were primarily

Plate 1. Typical dense garrigue of Qwrc~rs coccifera near St Gely du fesc (above); and view of experimental plots on [he Puech de Juge, IOkm north of ?iIontpellier (belo\s).

George P. ‘~ala~s~~ and Louis Trabaud

59

of new growth it was assumed that older woody vegetation would be drier. The fuet moisture for dead material was chosen to represent two conditions: a dry condition as might be found during a wildfire (cf. Westman et al. 1981; Rothermel 1983; Malanson and Butler 1984), and a condition representing the effects of the addition of water to the fuel by aircraft: water was added at the rate of 0.5 kgm-? to the fuel types and spread evenly on all surface areas, as proposed by Malanson and Butler (1984) in their simulations. Tests of the minimum water drop needed to extinguish fire were not made because the control of the actual distribution of water from an aircraft is rather imprecise. Thus three fuel types are described for each of the three stand ages: a spring condition in which the herbaceous material is 50 per cent live, an autumn condition in which the herbaceous material is ail dead, and an autumn condition to which an aircraft water drop has been added. Standard values, calculated for similar vegetation types, for heat content, density, mineral and effective mineral contents of the wood, and moisture of extinction were used. For site conditions values approximating those in Puech du Juge and wind speeds of 2.2 m set - 1 were used. Results The simulation calculates several measures of interest to fire managers from the perspectives of both hazards and ecology. The basic calculations of fire behaviour most used by fire control agencies are presented in Table 2. Temperature is not calculated by the model and is not a factor regularly used by fire control agencies, although it may be important for the recovery of the vegetation. Trabaud (1979) measured actual values of temperature in fire in garrigue to reach between 750°C and 125O”C, depending on the conditions on the site. The simulation also contains a subroutine called BURNOUT which provides a measure of total heat release and shows the pattern of heat release over time (Fig. 2). These values are critical for an estimation of the effect of fire on the ecosystem. AIbini (I976a) cautioned that these values were tentative estimates because the theory was still untested. The temporal characteristics, at least, are in agreement with observations (Trabaud 1979; Westman et al. 1981). Effecrs of fire suppression The most notable result is that for the condition of added water the simulation stops because the fuel is found to be too wet to sustain a spreading fire. Using the same Table 2. Calculated values of fire intensity and behaviour 3 years

9 years

33 years

Reaction

Spring

Autumn

Spring

Autumn

Spring

Autumn

kWm-* Heat sink (kJms2) Propagating ffux (kWmT2) Byram’s Intensity (kW fireline-m-l) Rate of spread (m s - I)

56.7 4724

72.5 4480

50.5 6151

62.6 5982

57.8 4907

102.4 4619

2.0

l-3

l-7

1.5

2.7

4.2 0.005

6.6 0.006

7.3 0.007

I*_5

12.5 0.010

24.6 0.014

60

Computer simulations of fire behaviour in garrigue

2 F

Burnout time (min)

Figure 2.

Temporal patterns of heat release calculated for stands of 3, 9, and 33 years using the BURNOUT subrouting of FIREMOD (Albini 1976a); the high values given under each curve are the calculated pulses of heat release at the passage of the flaming front, assumed to be two minutes after initial ignition.

approach, a similar result was found for subalpine avalanche track shrub fields (Malanson and Butler 1984). That a water drop of 0.5 kgm-2 is effective in preventing the spread of fire supports its use as the primary fire suppression strategy in France, as opposed to presuppression activities, such as the cutting of fuelbreaks favoured in California. The effectiveness of the tactic in actual fires will, of course, depend on wind conditions and the actual pattern of water applied. Effects

of season

In comparing the values of fire behaviour between spring and autumn burning conditions an expected pattern is found: autumn burns are more intense and faster

61

George P. Malanson and Louis Trabaud spreading than spring ones (Table 2). The simulation is very sensitive of dead fuel, especially in size classes with a high surface-to-volume

to the amount

ratio, such as herbaceous matter. Even with identical weather conditions at the time of fire, the autumn fire will thus be more intense and difficult to control because of fuel conditions following the summer drought.

Of more interest is the pattern of change in fire behaviour through time as represented by the stand ages of 3, 9, and 33 years. Fire intensity does not increase monotonically. Instead the three-year-old stands burn more intensely than do the nine-year-old stands. This difference can be attributed to the larger proportion of standing dead material on the younger stand; three years after the previous fire many dead, charred, but burnable stems remain standing from the previous stand of vegetation. This higher load of dead fuel contributes to the flammability of the younger vegetation. The 33-year-old stands are the most flammable and burn most intensely. Some thinning in the shrub canopy may allow an increase in flammable herbaceous growth in older stands. Ecological

aspects

Albini (1976b) suggested that total heat release would be a useful measure of the effects of fire on vegetation. But the duration of the fire may also be important because over a longer period more heat will be absorbed by the ground surface and transmitted to either the resprouting organs or seeds of plants, while in a faster burning fire a larger proportion of the heat is advected away from the site. Malanson and Trabaud (1987b) have shown that fire intensity, incorporating both total heat release and duration, can affect the vigour of resprouting by Quercus coccifera. The patterns shown by the simulations reveal increasing heat release with plot age and higher rates of burning in autumn than in spring (Table 3, Fig. 2). The greater heat release with age is due to a higher proportion of wood consumed, and this factor is in turn attributed to higher biomass and thus hotter overall fires. The difference between total heat release and rate of release can be seen by comparing the figures for the three-year-old autumn fuel type with those for the nine-year-old spring fuel type.

Table 3. Proportion

of dry fuel load burned and the heat released 3 years

Standing dead Burnout time (minutes) Fraction burned Heat release (kJmT2)

9 years

33 years

Spring

Autumn

Spring

Autumn

Spring

Autumn

31.36 0.15 913

23-26 0.21 1464

58.14 0.28 1464

45.56 0.35 2021

49-67 0.62 2475

26.40 o-70 3621

0.01 1.00 1352

0.01 1.00 1351

0.01 1.00 4688

0.01 1.00 4688

o-01 l-00 11272

0.01 l-00 11272

Litter

Burnout time (minutes) Fraction burned Heat release (kJme2)

62

Computer simulations of fire behaviour in garrigue

Although the total heat release is the same for the two (Table 3) the pattern of heat release is very different. Discussion

The computed values of fire behaviour reinforce the idea that fires can be successfully managed in southern France both to mitigate fire hazards and to maintain the natural vegetation. This result is probably due to the fact that the meaning of ‘natural’ in this region must include the evolutionary effects of human burning on the vegetation. The garrigue is probably adapted as a generalist vegetation type to a wide range of fire regimes, and fires can burn relatively frequently without reducing floristic diversity (Trabaud and Lepart 1980; Malanson and Trabaud 1987a). It is long fire intervals, brought on by vigorous suppression efforts, that perhaps should be avoided. At longer intervals the fires become more difficult to control and their potential for adverse effects on the vegetation and soil is increased. In comparing the projected values with those observed by Trabaud (1979, 1985) the values of rate of spread and fire power are low. Actual rates of fire spread in experimental fires reach 0*08ms-t at wind speeds of about 6ms-1. At the front of the fire Trabaud (1979) calculated the power to range from 485kWm-i to 1456kWm-1, while the rate of propogation was 0*02ms-1 and 0*06ms-1 respectively. Yyet these values of fire power are relatively low in comparison to some reported in the literature-powers of 50000 to lSOOOOkWm-* (Kiil and Grigel 1969, van Wagner 1983). The difference in the calculation of fire power may be due to the more detailed description of fuels in classes of surface-to-volume ratio used here. This mode1 calculates much less than total combustion for the fuel load. The burnout times and patterns, while generalized to a high degree of regularity by the simulation, are in genera1 agreement with the pattern of temperatures recorded by Trabaud (1979). Peak heat release and temperatures at ignition by the flaming front are followed by long periods of smouldering embers. For future fire management one can see that the simulations provide a general outline for planning. For suppression, the application of water is confirmed as an effective tactic. Prescribed burning may be more manageable in spring, and autumn fires may leave behind more standing dead material as fuel for a future fire. Also, frequent fires may promote the dominance of more flammable fuels. In the first years after burning a fire hazard still exists due to a high proportion of standing dead fuel, and in autumn of dried grasses. These fuel elements decline by nine years but begin to re-emerge at 33 years. Fire management programmes that aim toward a fire regime of fires every lo-15 years may be able to achieve both reduced fire hazard and a semblance of natural, though human-modified, vegetation. The simulations do not account for high wind speeds or for the spread of fire by flying brands or embers; experience will have to guide the application of water when these are a factor, and the long burnout times shown by the simulations and observations must be considered in this context. In regard to the effect of fire on the vegetation as a natural community, the simulations show that for the conditions considered here, only at 33 years is the heat release, primarily by the burning litter, likely to affect the potential recovery of the vegetation. This result agrees with experimental observations of resprouting and recovery in garrigue (Malanson and Trabaud 1987a,b). The range of fire intensity considered may have effects on other plant communities in southern France, such as Rosmarinus garrigue or where C&us species are more important. In southern California, Malanson and O’Leary (1985) found the effects of fire intensity to be

George P. Mulanson and Louis Trabaud

63

somewhat greater for more ligneous species in coastal sage scrub. In any case, the effects af fire intensity on resprouting and seed germination wit1 depend in part on the heat transmitted from the burning vegetation to the soil surface. Although computer simulations exist for models of fire behaviour and For the flux of heat in the soil (Aston and Gill 1975f, no model exists that links these two types of simuiation, Steward (1974) presented models which could be used to link the fire behaviour and soil heat flux simulations. He showed that a fireline or flaming front could be modeRed as a wedge with the radiative properties of a grey gas and radiative exchange among volumes and surfaces could be represented by a system of algebraic equations. This model would serve as a first approximation of heat transfer between the flames and the soi surface, assuming that conductive energy transfer is negligible. In practice simulations are limited by the heterogeneity of the soil.

Acknowledgements We wish to thank MM Grandj~~ny, Bastide, Beftran, Serre, and Mme Maistre for help in the field. M. Vilanova drafted the figure. GPM was supported at Centre Emberger by a US-France exchange award from the Centre National de la Recherche Scientifique and the US National Science Foundation.

References Albini, F. A. (1976a) Computer-based

yodels of wjidla~d fire behavior: a user’s ~na~uai. Ogden, Utah: US Forest Service. Afbini, F. A. fl976b) ~sti~~iing w~~d~rebehavior andeffects. Ogden, Utah: US Forest Service General Technical Report, ItNT-30. Aston, A. R. and Gill, A. M. (1976) Coupled soil moisture, heat, and water vapour transfers under simulated fire conditions. A~s~Faf~a~Journal of Soi/ Research 14, 5.5-66. Bradshaw, R. L. (1980) The TKVfire ~havior print programs: a user’s guide. Riverside, Calif.: US Forest Service, CHAP’s Note 1. Cohen, J. D. (1986) Esri~atingf~re behavior with FIRECAST? userSmanuaL Berkeley, CaIif.: US Forest Service General Technical Report PSW-90. Cunningham, C. J. (1984) Recurring natural fire hazards: a case study of the Blue Mountains, New South Wales, Australia. Applied Geography 4, 5-21. Green, D. G. (1983) Shapes of simulated fires in discrete fuels. EcologicalModelling 20,21-32. Green, D. G., Gill, A. M. and Noble, I, R. (1983) Fire shapes and the adequacy of fire-spread models. Ecological Model&g 20, 33-45. Hobbs, R. J. and Gimingham, C. H. (1984) Studies on fire in Scottish heathland communities. 1. Fire characteristics. Journal of Ecology 72. 223-240, Kessell, S. R. f1979) Gradient modeiling. New York: Springer-Verfag. Kiil, A. D. and Grigd, J. E. (1969) The May f968forest con~agra~~o~s in cenrrar’Alberta. Ottawa: Canadian Forest Service, information Report A-X-24. Kuhnholtz-Lordat, G. (1938) La terre incendiPe. Nimes: La Maison Carree. Kuhnholtz-Lordat, G. (19%) L ‘&ran vert. Paris: Musee de I’Histoire NaturaIe, Memoires dela Musee de I’Histoire Naturale, Serie B, No. 9. Le Houerou, H. N. (1987) Vegetation wildfires in the Mediterranean basin: evaluation and trends. In Workshop on the ecofogicaf aspects offorest fires in the Mediterranean basin, Giens, France: European Science Foundation and Forest Ecosystems Research Network. Leone, V. (ed.) (1984) Con vegno i~fe~~azionafe di studi sui problemi degli incendi beschivi in ambienre mediterraneo. Bari: Regione Puglia. Malanson, G. P. (1985) Fire management in coastal sage-scrub, southern California, USA. Environ~e~tai Conservation 12, 141-146.

64

Computer simulations of fire behaviour in garrigue

Malanson, G. P. and Butler, D. R. (1984) Avalanche paths as fuel breaks: implications for fire management. Journal of Environmental Management 19, 229-238. Malanson, G. P. and O’Leary, J. F. (1982) Post-fire regeneration strategies of Californian coastal sage shrubs. Oecologia 53, 355-358. Malanson, G. P. and O’Leary, J. F. (1985) Effects of fire and habitat on post-fire regeneration in Mediterranean-type ecosystems: Ceanothus spinosus chaparral and Californian coastal sage scrub. Oecologia Plantarum 6, 169- 18 1. Malanson, G. P. and Trabaud, L. (1987a) Ordination analysis of components of resilience of Quercus coccirera L. garrigue. Ecology 68, 463-472. Malanson, G. P. and Trabaud, L. (1987b) Vigour of post-fire resprouting by Quercuscocctfera L. Journal of Ecology (in press). Oliver, J., Britton, N. R. and James, M. K. (1984) The Ash Wednesday bushfires in Victoria, I6 February 1983. Townsville, Queensland: Centre for Disaster Studies, Disaster Investigation Report 7. Rothermel, R. C. (1972) A mathematical model for predicting fire spread rate and intensity in wildland fuels. Ogden, Utah: US Forest Service Research Report INT-115. Rothermel, R. C. (1983) How to predict the spread and intensity of forest and range fires. Ogden, Utah: US Forest Service General Technical Report INT-143. Rothermel, R. C. and Philpot, C. W. (1973) Predicting changes in chaparral flammability. Journal of Forestry 71, 640-643.

Steward, F. R. (1974) Radiative heat transfer associated with fire problems. In Heat transfer in fires (P. L. Blackshear, ed.), pp. 273-486. Washington, D.C.: Scripta Book. Sylvester, T. W. and Wein, R. W. (1981) Fuel -haracteristics of arctic plant species and simulated plant community flammability by Rothermel’s model. Canadian Journal of Botany 59, 898-907.

L. (1974) Experimental study on the effects of prescribed burning on a Quercus coccifera L. garrigue. Proceedings of the Annual Tall Timbers Fire Ecology Conference 13, 97-129.

Trabaud,

Trabaud, L. (1976) Inflammabilite et combustibilite des principales especes des garrigues de la region mediterraneenne. Oecologia Plantarum II, 117- 136. Trabaud, L. (1979) Etude du comportement du feu dans la Garrigue de ChCne kermes a partir des temperatures et des vitesses de propagation. Annales des Sciences Forestrieres 36, 13-38.

Trabaud, L. (1985) Quantites d’energie et puissance potentielle de feu de quelques communautes vegetales du Sud de la France. Oecologia Plantarum 6, 387-394. Trabaud, L. and Lepart, J. (1980) Diversity and stability in garrigue ecosystems after fire. Vegetation 43, 49-57.

Van Wagner, C. E. (1983) Fire behaviour in northern conifer forests and shrublands. In The role,of fire in northern circumpolar ecosystems (R. W. Wein and D. A. McLean, eds), pp. 65-80. New York: Wiley. van Wilgen, B. W., Le Maitre, D. C. and Kruger, F. J. (1985) Fire behaviour in South African fynbos (macchia) vegetation and predictions from Rothermel’s fire model. Journal of Applied Ecology 22, 207-216. Velez Munoz, R. (1984) Le probleme des incendies provoques et leurs relations avec les conditions sociales et economiques des zones affectees. In Convegno internazionale di studi sui problemi degli incendi boschivi in ambiente meiditerraneo (V. Leone, ed.), pp. 135-157. Bari, Italy: Regione Puglia. Westman, W. E., O’Leary, J. F. and Malanson, G. P. (1981) The effects of fire intensity, aspect and substrate on post-fire growth of Californian coastal sage scrub. In Components of productivity of Mediterranean-climate regions (N. S. Margaris and H. A. Mooney,

eds), pp. 151-179. The Hague: W. Junk. Wrathall, J. E. (1985) The hazard of forest fires in southern

France.

(Revised manuscript received 8 May 1987)

Disasters 9, 104-l 14.