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Environmental Modelling & Software 26 (2011) 1028e1040

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Environmental Modelling & Software

journal homepage: www.elsevier .com/locate/envsoft

An integrative model of human-influenced fire regimes and landscape dynamics

Lasse Loepfe*, Jordi Martinez-Vilalta, Josep PiñolCentre for Ecological Research and Forestry Applications (CREAF), Autonomous University of Barcelona, E-08193 Bellaterra, Spain

a r t i c l e i n f o

Article history:Received 18 September 2009Received in revised form21 February 2011Accepted 23 February 2011Available online 21 March 2011

Keywords:Fire regimeLandscape dynamicsModelFire suppressionLand use changeVegetation growthFire weather

* Corresponding author. Tel.: þ34 93 581 3355; faxE-mail addresses: lasse.loepfe@gmail.com (L. Lo

uab.es (J. Martinez-Vilalta), josep.pinol@uab.es (J. Piñ

1364-8152/$ e see front matter � 2011 Elsevier Ltd.doi:10.1016/j.envsoft.2011.02.015

a b s t r a c t

Fire regimes depend on climate, vegetation structure and human influences. Climate determines thewater content in fuel and, in the longer term, the amount of biomass. Humans alter fire regimes throughincreased ignition frequency and by hindering the spread of fire through fire suppression and fuelfragmentation. Here, we present FIRE LADY (FIre REgime and LAndscape DYnamics), a spatially explicitfire regime model that takes into account daily weather data, topography, vegetation growth, firebehaviour, fire suppression and land use changes. In this model, vegetation growth depends on wateravailability, and stem diameter and stand density are the fundamental parameters. Fire behaviour ismodelled using the Rothermel equations and taking into account both crown fire and spotting. Humaninfluences on fire regime, such as ignition frequency, fire suppression and land use changes, are explicitlymodelled. The model was calibrated for three regions in NE Spain and reproduces fire regimes, changesin land cover distribution and tree biomass with promising accuracy. The explicit modelling of humaninfluences makes the model a useful and unique tool for assessing the impacts of climate change andinforming local fire regime management strategies.

� 2011 Elsevier Ltd. All rights reserved.

Software availability

Name of software: FIRE LADYHardware requirements: PC, Pentium IV (or equivalent) and 512 MB

RAM recommendedSoftware requirements: JAVA-JRE 1.5 or higher; platform

independentProgram language: JAVAContact address: Lasse Loepfe, CREAF, Edifici C, Campus de Bella-

terra (UAB), 08193 Cerdanyola del Vallès, Spain. Email:lasse.loepfe@gmail.com

Program size: 481 kBAvailability: Freely available on request for non-commercial uses.

1. Introduction

Fire regimes are determined by climate, vegetation and topog-raphy, and are strongly influenced by the presence of humans(Johnson, 1992). The relative importance of fuel accumulation andweather conditions varies among ecosystems (Meyn et al., 2007;Falk et al., 2007), as does the impact of human activities. Apartfrom extremely wet rainforests, where fire regime is based solely

: þ34 93 581 4151.epfe), jordi.martinez.vilalta@ol).

All rights reserved.

on fuel moisture, and deserts, where the virtual absence of fuelprevents the spread of fire, the fire regime of a region is determinedby a combination of climate, vegetation and human influences.

The modelling of fire regimes can provide information on theirunderlying mechanisms and predict the consequences of forestmanagement strategies and climate change on burn area and firesize distribution. These results can then be employed to assessimpacts on plant composition (Pausas, 1999) or pyrogenic emis-sions (Keane et al., 1997). Because the fire regime of a region is theresult of climatic conditions, vegetation growth, fire managementand (often forgotten) land use, a comprehensive fire regime modelshould incorporate those processes, together with fire behaviour, ina balanced way.

There are many models that calculate ignition probability andthe propagation dynamics of individual fires fairly well, but mostlywithout considering spatially distributed ignition probability. Themost popular model for calculating fire behaviour in a singledimension was developed by Rothermel (1972). Rothermel’sequations have beenwidely used in models predicting fire size andshape, such as FARSITE (Finney, 1998). Comprehensive reviews offire spread models can be found in Weber (1991), Perry (1998),Pastor et al. (2003) and Sullivan (2007). The FIRESCAPE model(Cary, 1997) extends this approach to the landscape level, allowingfor the investigation of, for instance, the impact of climate changeon fire regimes (Cary and Banks, 2000). These models require fuelstructure at the time of burning as a given input. Fuel build-upprocesses are not simulated, as the goal of this type of model is to

Fig. 1. Overview of the model structure. Rectangles represent input data; circlesrepresent model internally calculated variables; and rhomboids represent manage-ment actions.

L. Loepfe et al. / Environmental Modelling & Software 26 (2011) 1028e1040 1029

predict the exact shape of a single fire rather than landscapedynamics over the long term. In contrast, landscape fire successionmodels focus on vegetation dynamics. These models generally usea detailed description of plant growth, whereas fire is typicallysampled only from the perspective of its historical size distributionand then placed on the terrain randomly or following a probabilitydistribution based on landscape characteristics. Such models nor-mally do not present an explicit fire spread module, as the funda-mental interest in fire in these models is its average effect onvegetation at the landscape scale rather than the precise location offire occurrence. For a comprehensive review and classification oflandscape succession models, see Keane et al. (2004) and Schellerand Mladenoff (2007).

A combination of explicit fire-growth modelling with a plantgrowth module is used in the extended version of LANDIS-II(Sturtevant et al., 2009), the SEM-LANDmodel (Li, 2000), LANDSUM(Keane et al., 2006) and the BFOLDS model (Perera, 2008). Thisallows for the analysis of the interaction between fire regime andvegetation structure and the resulting landscape patterns (Pereraet al., 2003). A comparison of these models can be found in Caryet al. (2007).

In most regions of the world, fire regime is highly influenced byhumans, as a consequence of fire management and land coverchanges (Thonicke et al., 2001). Humans have a great impact on fireregimes because they alter ignition frequency and fuel fragmenta-tion and suppress fires (Guyette et al., 2002). However, most of theexisting fire regime models do not include anthropogenicallydriven changes in fire regimes (Mouillot and Field, 2005). Currently,a substantial proportion of fire management budgets goes towardsfire suppression, but the effects of these strategies are controversial.While some authors claim that a reduced number of small andmid-sized fires result in a accumulation of fuel that may lead to cata-strophic fires under extreme weather conditions (Minnich, 1983,2001; Piñol et al., 2005, 2007; Shang et al., 2007), others holdthat, in some ecosystems at least, large fires are not dependent onthe age classes of fuels (Moritz, 2003; Moritz et al., 2004) and thatfire suppression plays a critical role in offsetting the potentialimpacts of increased ignitions (Keeley et al., 1999). A high firefrequency can also induce changes in species composition (Mouillotet al., 2002; Pausas, 1999; Pausas et al., 2006; Syphard et al., 2006,2007c) and hinder vegetation recovery (Díaz-Delgado et al., 2002;Pausas et al., 2008).

An often overlooked fire management opportunity is land usemanagement, i.e., influencing the spatial distribution of crop fieldsthrough subsidies to farmers. Ruralmigration is oftenpointed out asa cause of increased fire occurrence in the Mediterranean region(Bajocco and Ricotta, 2008; Debussche et al., 1999; Terradas et al.,1998; Vega-García and Chuvieco, 2006). The spatial distribution ofstand ages and species composition has an important impact on fireregimes (Turner and Romme, 1994; Miller and Urban, 2000). Theintermixing of woodland and agricultural land is also very likely toinfluence fire regime, as agricultural fields can sometimes act asfirebreaks because of their lower flammability (Lloret et al., 2002;Loepfe et al., 2010), and land use affects the spatial distribution ofhuman-caused ignitions (Syphard et al., 2007b). Since the beginningof the 20th century, economic development has provoked amassiveabandonment of agricultural land in the Mediterranean region(Debussche et al., 1999), leading to an increased homogeneity ofsemi-natural land uses, such as shrublands and forests (Bielsa et al.,2005). Nevertheless,we foundonly twomodels in the literature thatexplicitlydealwithhuman-influenced fuel fragmentation, includinglarge non-flammable areas such as residential areas or croplands(Davis and Burrows, 1994; Syphard et al., 2007a).

Weather conditions, such as temperature, wind speed and fuelmoisture content, affect the probability of fire propagation. In the

Mediterranean region, an increase of CO2 concentrations is expec-ted to translate into warmer and drier summers with increased riskof fire weather (Alcamo et al., 2007; Liu et al., 2010). Many authorsexpect that climate change will translate into increased forest fireactivity (Brown et al., 2004; Carvalho et al., 2010; Flannigan et al.,2000; Mouillot et al., 2002; Williams et al., 2001). Other impor-tant factors for fire regimes, such as vegetation type and abundance,are also influenced by climate (Bachelet et al., 2001; Lenihan, 2003).In Mediterranean climate regions, water availability is the mostlimiting factor for plant growth (Boyer, 1982; Hetherington andWoodward, 2003), and climate change could lead to a decreasedbiomass accumulation rate (Ciais et al., 2005), resulting in a lowerfire activity than predicted by fire weather extrapolations.

Here, we present FIRE LADY (FIre REgime and LAndscapeDYnamics), a fire regime model that includes the influence ofhuman activities on fire regimes, a factor that is frequently notconsidered in other models. The goal of FIRE LADY is not to predictthe exact extent of individual fires, but to promote an under-standing of the human influence on annual burn area and fire sizedistribution. It can therefore be a useful tool for fire managementpolicy developers, as it can be used to assess the effects of differentmanagement strategies e such as fire suppression, land usemanagement and ignition control e on a mid-term time horizon(ca. 50 years). Below, we give a detailed description of the model,calibrate it for three study areas in NE Spain, discuss its strengthsand weaknesses and show some possible applications.

2. Materials and methods

2.1. Overview

FIRE LADY is a spatially explicit landscape fire regime model for forest andshrubland ecosystems. In its present form, it is not a vegetation succession modelbecause species composition is fixed, and no demographic parameters are consid-ered. It is grid based and has a flexible cell size. It uses yearly time-steps for vege-tation growth and land use changes and daily time-steps for fire weather andpropagation. It uses land use maps, daily meteorological data and topography asinput data. Vegetation growth is simulated by taking into account the actualevapotranspiration on each cell. Biomass is divided into a tree and an understorylayer. The fire module includes ignition and propagation. Ignition probabilitydepends on the location of a cell and its fine fuel moisture content. Propagation isa neighbourhood process: fire can spread from a burning cell to its immediateneighbours by surface or crown fire with propagation probabilities based on theRothermel (1972) equations. Fire propagation by wind-transported burningbranches (spotting) is also taken into account. Fire brigades and land use changes areexplicitly modelled. An overview of the model structure can be seen in Fig. 1, anda detailed description of the modules is given in the following paragraphs.

L. Loepfe et al. / Environmental Modelling & Software 26 (2011) 1028e10401030

2.2. Climate and weather

FIRE LADY uses daily data on rainfall, maximum temperature, wind speed anddirection, relative air humidity and potential evapotranspiration as input data. Thesedata might come either from ameteorological station or from aweather generator. Ifthe study area is too large to reasonably assume equal meteorological conditionsthroughout it, grid maps of yearly average values can be used as inputs to theprogram. FIRE LADY then calculates the weather for each cell, using the daily data toestimate temporal fluctuation and the map of yearly averages to describe the spatialvariation across cells. The maximum temperature of a given cell on a given day (Ti,d)is then calculated as

Ti;d ¼ TS;d þ �T i;a � TS;a�

(1)

where TS,d is the maximum temperature of the meteorological station for that day,T i;a is the yearly average maximum temperature of cell i according to the providedmap, and TS;a is the yearly average maximum temperature of the meteorologicalstation. The calculations are analogous for the other weather variables. In the case ofrainfall, multiplication by the map-to-station ratio is used, rather than difference, toavoid negative rainfall amounts.

2.3. Fire weather

To translate daily meteorological data into an index of fire risk, we used theCanadian Forest Fire Weather Index System (FWI) (Van Wagner and Pickett, 1985),which has proven to be a good index of the moisture content of fine live fuels inMediterranean climate regions (Viegas et al., 2001). The FWI follows the dailymoisture content of fuels of different sizes with different drying rates. Each day,a new index value is calculated from the corresponding previous day’s index value,maximum air temperature, minimum air humidity, wind speed and precipitation.The FWI consists of a hierarchical system of indexes, from which we used the FineFuel Moisture Code (FFMC) to establish the probability of ignition and the DroughtCode (DC) to determine the probability of propagation. The FFMC is a numeric ratingof the moisture content of litter and other cured fine fuels, whereas DC indicates thegrade of dryness of medium- and large-sized fuel.

The FWI variables indicate daily maximum risk of fire ignition and propagation.To simulate the drop in these indices at night as a result of lower temperature andhigher air humidity, we introduced an attenuation factor (fN) that is calculated dailyfrom a normal distribution with mean mfn and standard deviation sfn. The minimumvalue of the FWI variables is then calculated by multiplying the maximum value byfN. The maximumwas set to be reached at 4 pm and the minimum at 4 am. At othertimes of the day, the values of FFMC and DC vary linearly between those extremes.

2.4. Vegetation growth

The vegetation in our model consists of two layers: trees and understory. Thisreflects the structure of most Mediterranean forests and is necessary for calculatingthe probability of crown fire occurrence. Each cell has one dominant tree speciesassigned,which determines the allometric relationships of the canopy. Tree growth issimulated by yearly increments of stem diameter at breast height (DBH). From DBH,species-specific allometric equations areused tocalculate thevariablesneeded forfirespread calculations such as stand biomass and canopy base height equivalent. Plantgrowth in Mediterranean climate regions is strongly influenced by water availability(Boyer, 1982; Hetherington and Woodward, 2003). We took this into account bycoupling the annual growth rate to accumulated rainfall, potential evapotranspirationand the topographical situation of each cell. As with trees, understory biomassincrease was determined by water availability and the shading effects of trees.Vegetation growth is simulated to occur at the end of each calendar year.

2.5. Tree growth

2.5.1. DBH incrementThe average yearly increase in stem basal area (BAI, cm2/year) of each cell is

calculated by an annual growth rate parameter (r), the actual evapotranspiration(AET, mmH2O) and the topographic index (Beven and Kirkby, 1979; Quinn, 1991),based on the fact that several studies relate increases in basal area to water avail-ability in theMediterranean (Benson et al., 1992; Mayor and Rodà, 1992; Ogaya et al.,2003). The topographic index qualitatively relates topography to water availabilityusing the upslope catchment area of each cell (a, m2) and the local slope of the cell(b, rad). Basal area increase is calculated as

BAI ¼ r,AET,ln� atan b

�(2)

Actual evapotranspiration is calculated from rainfall and potential evapotranspira-tion (Piñol, 1991) as

AET ¼ PET,

pk

1þ pk

!1=k

(3)

with p being the ratio between annual precipitation (P, mmH2O) and PET (mmH2O)and k is a parameter specific for each catchment, related to the partition of rainfall

into evapotranspiration and streamflow. Annual PET is estimated for each cell by theSamanieHargreaves method (Hargreaves and Samani, 1985). We use the yearlyincrease in basal area (BAI) rather than stem diameter (DBH), as BAI is practicallyindependent of tree age, and therefore its yearly increase is easier to model asa function of external factors such as water availability. For all allometric calcula-tions, we transformed basal area into DBH, as the latter is more commonly used.

2.5.2. Allometric relationsAverage tree height (HT, m) is calculated as a power function of DBH:

HT ¼ aHt,DBHkHt (4)

with aHt and kHt being species-specific scaling parameters. Canopy base height (CBH,m) equivalent is assumed to be proportional to HT, with a species-specific crowncoefficient (kCBH) and subtracting a fuel ladder-mimicking constant (Hl, m). Canopybase height is a vague term in the scientific literature and is not easy to measure, asneither the lowest crown base height in a stand nor the average crown base height islikely to be representative of the stand as a whole (Scott and Reinhardt, 2001); itsuse in our model mimics the lowest height above the ground where sufficient fuelfor crown fire initiation is available, including ladder fuels, according to VanWagner(1993).

The sum of branch and leaf biomass of an average tree (Bt, Mg/tree) is calculatedas

Bt ¼ aBt,DBHkBt (5)

with aBt and kBt being species-specific scaling parameters.We only calculate biomassincrease and accumulation for branches and leaves, excluding trunks of adult trees,as they are never available as fuel (see below). Bt includes both living and deadbiomass. Eqs. (4) and (5) are obtained from the Ecological and Forest Inventory ofCatalonia (IEFC, Burriel et al., 2000e2004).

Each cell of the grid is considered as one stand. Stand density (NT, trees/ha) iscalculated according to the self-thinning equation of Reineke (1933):

lnðNTÞ ¼ minðlnðNT0Þ;12� 1:605,lnðDBHÞÞ (6)

where NT0 corresponds to the stand density when DBH¼ 0 and is obtained for eachcell from a user-introduced map, if available, or from a normal distributionotherwise:

NT0wNðaNt; vNt,aNtÞ: (7)

where aNt is the average stand density of the study area (trees/ha) and vNt is itscoefficient of variation. This implies that at low stand density or DBH, individualtrees can grow freely until they reach the maximum established by the Reinekeequation, when resources become limiting and self-thinning starts. Stand-levelbiomass (BT, Mg/ha) was obtained by multiplying Bt by NT. Finally, leaf area index(LAI) is calculated as:

LAI ¼ aLAI,�DBH2,NT

�kLAI(8)

where aLAI and kLAI are, again, species-specific scaling parameters.

2.6. Understory biomass increase

Understory biomass increase (DBS, Mg/(ha year)) is assumed to be limited bywater availability and by shading from the overstory trees (Saunders andPuettmann, 1999; Zavala and Bravo de la Parra, 2005; Ackerly and Stuart, 2009)using a novel equation:

DBS ¼ra,AET,ln

� atan b

�sa,ð1þ LAIÞ (9)

where ra mimics water-use efficiency and sa mimics shade intolerance, a is theupslope catchment area of each cell (m2) and b is the local slope of the cell (rad).These assumptions imply that in early successional stages, when the overstory treesare small, the understory growth is limited mostly by water availability. At latersuccessional stages, when the canopy closes, i.e., LAI increases, only small incre-ments of understory biomass are possible because of shade cover.

2.7. Land uses

To simplify the modelling and calibration process, we distinguish only betweenthree types of land use/cover types: cultural, forest and shrubland. The culturalcategory includes urban areas, agricultural land, roads, beaches and rocks. Cells inthis category do not accumulate biomass or burn. In contrast, in cells treated asforests or shrublands, biomass can both accumulate and burn. Cells are classified asforest if their LAI is superior to a given minimum (LAImin). Agricultural land aban-donment and creation locations might be read from externally produced maps orsimulated assuming a constant yearly rate. In this case, the relative probability ofabandonment and creation of each cell must be given as an input map.

L. Loepfe et al. / Environmental Modelling & Software 26 (2011) 1028e1040 1031

2.8. Fire ignition and propagation

2.8.1. OverviewThe development of a fire is divided into two sub-processes: ignition and

propagation. Ignition refers to the process of sparking and burning of an initial cell,while propagation is the spreading of fire from one cell to another. Fire spread ismodelled with a stochastic percolation approach, in which propagation probabilitywas obtained from a simplified version of the Rothermel (1972) model, taking intoaccount fuel characteristics and weather conditions. A similar approach has beensuccessfully used to model behaviour of individual fires (Berjak and Hearne, 2002)and fire regimes (Li, 2000; Keane et al., 2006; Perera, 2008; Sturtevant et al., 2009).The occurrence of active and passive crown fires depends on the fuel strata gapheight and the surface fire intensity. In many cases, firebrands (or spotting, burningbranches and leaves that are carried by the wind and start distant fires) are the mainform of propagation. Firebrands also allow fire to cross landscape barriers such asrivers, roads and firebreaks. The number of firebrands is proportional to fireintensity, and the transport distance is modelled as a function of fire intensity, windspeed and topography (see below).

2.8.2. IgnitionEvery day, a given number of “sparks” are sampled from a Poisson distribution

with mean In. Their spatial location is calculated according to a user-introducedignition probability map. This represents the sum of lightning- and human-causedpotential ignitions. These sparks either extinguish or burn the whole cell. Theprobability of burning the first cell (Ip) depends linearly on the fine fuel moisturecode (FFMC), with a constant (ip):

Ip ¼ ipðFMMCÞ (10)

If the first cell is ignited, a starting time for the fire is assigned and the propagationprocess starts.

2.8.3. Propagation2.8.3.1. Surface fire. Following the example of classic percolation models (e.g.,Drossel and Schwabl, 1992), a burning cell can propagate a fire to its four first-order(or Neumann) neighbours (i.e., the cells sharing boundaries). If the fire propagates,the newly burning neighbour cell creates a maximum of three new burning fronts(not four, as rebounding fronts are eliminated in the model). The time when thesenew fronts reach a new cell is calculated based on fire spread velocity and cell size.Propagation is event-driven, with flexible time intervals determined by the rate ofspread. Burning fronts are stored in a list that is sorted by the time when the front isexpected to reach a new cell, allowing the front with lowest time to burn first.

The probability of propagation (Pp) of each burning front is proportional to firespread velocity (Pv, m/s). For computation efficiency reasons, fronts withPv< 0.05 km/h were considered to be extinguished. To calculate Pv, a simplifiedversion of the Rothermel equation (Rothermel, 1972) is used. Fire spread velocitydepends on fire intensity equivalent (Fi, GJ/m), a factor of wind (FW) and slope (FS)(see below) and a constant that summarises the effects of fuel depth, fuel particlearea-to-volume-ratio, fuel particle heat and mineral content (kfv):

Pv ¼ kfvFið1þmaxð0;FW þ FSÞÞ (11)

Fire intensity equivalent (Fi) is calculated as a linear function of biomass available forcombustion in the flaming front (PBa), which is the total shrub biomass (BS) of thecell multiplied by the fraction of biomass available (fB):

Fi ¼ kfiBSfB (12)

Here, kfi is a constant that includes fuel heat content, fuel depth, fuel particle area-to-volume-ratio, fuel particle mineral content and fire front width. The constants kfvand kfi are treated as separate parameters, as fire intensity equivalent (Fi) is neededfor crown fire, spotting and fire fighting calculations (see below). The fraction ofbiomass available for combustion in the flaming front (fB) is a linear function of theDrought Code (DC), which represents the drought state of vegetation. At highmoisture contents, only a small fraction of fuel (like leaves or very small bracheswith a high area-to-volume-ratio) can be burned. As fuel becomes dryer, thickerbranches are considered flammable. During extreme droughts, almost all branchesare considered flammable, i.e., fB approaches one. Trunks of trees are never regardedas available for combustion in the flaming front, following the Rothermel (1972)model, which considers only fuels less than 7.6 cm in diameter, even duringextreme droughts; thus, even when fB equals 1, only branches and leaves areavailable for combustion.

2.8.3.2. Wind and slope. Maximum fire spread velocity depends strongly on windspeed, as the wind tilts the flame towards the fuel. Topography can act either asa physical barrier to fire spread (Kellogg, 2004) or can accelerate it by reducing thecontact angle between flame and fuel.

In FIRE LADY, effective wind speed (vwe, m/s) is calculated for each burning frontbased on actual wind speed (vw, m/s), angle between the cells (ac), wind direction(wd) and a wind attenuation factor (Wa) that depends on the land use of the cor-responding cell (Albini and Baughman, 1979):

vwe ¼ cosðac �wdÞvwWa (13)

Wind direction is obtained from a normal distribution around the daily dominantwind directionwith a standard deviation (sw). Then, the wind and slope coefficients(FW and FS, respectively, as used in Eq. (11)) are computed and vectored as thedimensionless wind and slope coefficients in the Rothermel model according toAlbini’s extended version (Weise and Biging,1997) of the original Rothermel formula(Rothermel, 1972), as this modelling approach performed well when compared towind-channel data (Weise and Biging, 1997).

2.8.3.3. Crown fire. The first condition for starting a crown fire is that there isa sufficient differentiationbetween the tree layerand theunderstory. In theabsenceofa fuel strata gap, asmighthappen in early stagesof succession,when shrubs are higherthan the lowest branches of trees, only surface fires take place, and BT is added to BS. IfCBH> 0, the probability of starting a crown fire (Pcf) is determined by the intensity ofthe surface fire, the height of the fuel strata gap and a scaling constant (kcf). Propertiesof the crown layer (like foliar moisture content or fuel area-to-volume ratio) are notincluded because they hadno significant effect on the likelihood of crown fire ignitionin experimental data nor in detailed modelling (Cruz et al., 2004, 2006). The proba-bility of starting a crown fire (Pcf) is calculated (adapted from VanWagner, 1977) as

Pcf ¼ kcfFð2=3ÞiCBH

(14)

Once the crown fire has started, its propagation process is identical to those ofsurface fires. A cell that is burning with a crown fire automatically also burns witha surface fire, i.e., no independent crown fire is possible. The final rate of fire spreadis computed following Van Wagner (1993) and the Forestry Canada Fire DangerGroup (1992) by summing up the speeds of surface and crown fires, assumingthat within one cell the crown fire is 100% active.

2.8.3.4. Spotting. Spotting can only occur in open fires, i.e., in crown fires or fires inshrublands, assuming that in understory fires the trees would block the ascension ofburning branches. Recent studies have shown that the total mass of firebrands isproportional to the burned biomass (Manzello et al., 2007). In our model, at eachburning cell, the number of firebrands (Sn) is stochastically calculated, taking intoaccount fire intensity Fi, a scaling constant (kSn) and a randomnumber sampled froma uniform distribution (U):

Sn ¼ kSnFilogðUÞ (15)

The transport of firebrands includes the lofting of firebrands by a buoyant plume,horizontal transport by wind and the action of gravity. The distance that a firebrandcan travel depends, therefore, on the intensity of the fire (Fi) e as more intense firesloft firebrands higher up e wind speed and topography (Albini, 1979).

We assumed that firebrands occur mainly in the wind direction but with somedeviations, as wind direction is not constant and turbulence can result in deviationof firebrands. From a very detailedmodel of the 2D distribution of firebrands (Sardoyet al., 2007), we estimated the angle of the distribution fan to be approximately�15� . Thus, for each firebrand, a direction is obtained from a normal distributionwith wind direction as the mean value and a “fan-constant” (dfd) as the standardderivation. This fan-constant is established in order to have 99% of the firebrandswithin the �15� angle.

Firebrands are lifted by a buoyant plume to a height (H0, m) that depends on theintensity of the fire (Albini, 1979). This height is added to the altitude (A, m) of theburning cell:

H0 ¼ kds,Fi þ A (16)

From this point (H0), the brand falls due to gravity, without considering air resis-tance, and it is simultaneously transported laterally with wind speed. The trajectoryof each brand follows the direction obtained as explained above. The brand will fallon cell i as soon as

H0 � 12,g,�divw

�2

� Ai (17)

where Ai is the altitude of cell i, vw is the wind speed, g is the gravitational accel-eration constant, and di is the distance between the focus cell and cell i in meters.

2.8.4. Tree mortality and post-fire recruitmentFires are considered stand replacing within a given pixel. Therefore, all fires in

shrublands and crown fires in a forest would reset DBH, tree biomass and shrubbiomass to zero. Post-fire stand density is assigned from user-introduced densitymaps, if available, or in their absence, from Eq. (7). Undergrowth fires in forestswould reset shrub biomass to zero and retain trees unchanged.

2.9. Fire fighting

Modelling fire brigades in a realistic way is complex, as many factors affect theirbehaviour. In our model, we tried to simulate fire brigade tactics and strategies in

Table 1Comparison of the three study areas. Data sources: climate data fromNinyerola et al.(2000); land uses (1956) from Loepfe et al. (2010); land uses (1993) from DARP(1998); tree biomass from Burriel et al. (2000e2004); fire regime data from Díaz-Delgado (2000) and administration records. Acceptance limits indicate the rangewithin which simulations were considered as behavioural.

Study area Tivissa Els Ports Igualada

Area (ha) 84,605 67,488 71,115Longitude 0�340e0�560 0�90e0�290 1�310e1�480

Latitude 40�540e41�100 40�390e41�00 41�330e41�490

Altitude range (m) 0e929 9e1435 221e1101Max. Temp. in August (�C) 24.5e33.4 22.7e31.9 23.3e30.6Annual Rainfall (mm) 386e796 487e1073 499e828

Proportion of land uses 1956 (%) 1993 (%) 1956 (%) 1993 (%) 1956 (%) 1993 (%)Forest 25.0 20.0 24.4 32.7 52.2 35.0Shrubland 31.1 42.5 33.9 31.9 12.2 26.0Cultural 43.8 37.5 41.7 35.4 35.7 39.0

Cultural land variation (% of total area)Abandoned 11.0% 8.0% 7.7%Created 3.5% 1.3% 8.8%

Branch and leaf biomass in trees (Mg ha�1)Mean 13.8 19 15.3Acceptance limits 13.4e14.2 18.4e19.7 14.8e15.9

Number of fires (year�1 per 100,000 ha)mean 8.0 1.71 4.01Acceptance limits 7.08e8.73 1.55e1.86 3.78e4.42

Annual area burnt (ha year-1 per 100,000 ha)mean 648 70 427Acceptance limits 0.930e0.938 0.837e0.904 0.949e0.957

Gini coefficientMean 531e780 46e97 312-557Acceptance limits 0.934 0.888 0.954

L. Loepfe et al. / Environmental Modelling & Software 26 (2011) 1028e10401032

a simple yet meaningful way according to expert analysis (Marc Castellnou, analystof the Catalan fire brigade, pers. com.).

In our model, fire brigades have two fundamental characteristics: (1) arrivaltime to the fire (ta, in s) and (2) extinction capacity (Ib, in W). Arrival time to the fireincludes the time needed to detect the fire and the travel time to the fire. Fire canburn freely until fire brigades arrive. Fire brigades attack individual burning fronts,trying to avoid the spread of fire from one cell to another. Their extinction capacity(Ib) mimics the effectivewater flowof the fire engine, but can also be regarded as anymeans that reduces fire energy. Extinction energy (Eb, in J) is obtained by multi-plying Ib by the time devoted to extinguish the fire (tc). The maximum energy firebrigades can use on one burning front is determined by multiplying Ib by thedifference between the time when the burning front would reach the next cell andthe time the fire brigades arrive to the front. If this maximum energy is greater thanthe energy of the front (Ef), the front is suppressed, and the time inverted is recal-culated by Ef/Ib. If, however, the maximum energy fire brigades can use is lower thanEf, the fire brigade energy is subtracted from Ef, and fire propagation velocity (Pv) andtime of arrival of the front to the next cell are recalculated.

The basic function of fire brigades is to avoid new expanding fronts, attackingthe fire laterally and advancing at both sides of the fire towards themain front (MarcCastellnou, pers. com.). In our model, the algorithm that mimics this behaviour wasthe following: a unit that arrives to the fire first attacks the fire front that is closest tothe starting point of the fire. If there are various equidistant fronts, fire brigades

Table 2Parameters of the model kept constant throughout the calibration process. When appro

Description V

k Catchment constantvNt Coefficient of variation of stand densityHl Ladder fuel heightkfi Heat content of wood 1kW Wind factor parameterkS Slope factor parameterWa Wind attenuation factor (underwood/shrubland/crown) 0kBf Constant that links available biomass to fire weathermfn Fraction of FWI remaining during night (avg.)sfn Fraction of FWI remaining during night (st. dev.)sw SD of wind direction respect to daily main directiondfd Desviation of wind direction in spottingIb Extinction potential of each fire brigade unitfnB Fire brigades multiplication factorts Time to elapse before new brigade can be sent

attack the one with the lowest propagation speed. Once this front is suppressed,they move to the next closest burning front, and so on. The time needed to movefrom one burning front to another is not modelled explicitly but is implicitlyconsidered in the extinction capacity.

Fire brigade strategy here means the decision to send out more units from thehome base to the fire. At a given time interval (ts), an additional unit is sent to the firewith the most burning fronts until the maximum number of fire brigades available(NB) is reached. Several units can operate at the same front simultaneously,summing their extinction capacities. Note that there might be more than one fireburning simultaneously so that different fires compete for available fire brigades.

2.10. Outputs

The main outputs of FIRE LADY include the following: number of fires greaterthan 1 ha, annual burned area, fire size-frequency distribution (expressed as the Ginicoefficient, Gini, 1912), land cover proportions and tree biomass. Moreover, at anypoint of the simulation, maps of land cover, biomass, fire weather and burned areascan be printed and used in further statistical analyses. Also, many internal results,such as rate of spread, fire intensity, annual biomass increase, energy use of firebrigades, and others, can be retrieved. All fire statistics can be split into crown fireand open and closed surface fires.

2.11. Simulations

2.11.1. Study areasWe calibrated the model for three typical Mediterranean ecosystems in Cata-

lonia (NE Spain; Table 1). Simulations started in 1956, when the first land use mapswere available, and ended in 2005. The first region, “Tivissa”, is situated around themunicipality of Tivissa and has a typical Mediterranean climate with hot and drysummers. The vegetation is mostly composed of shrublands and low-height forestsdominated by Pinus halepensis. The second study area, “Ports”, is situated to thesouthwest of the first study area. Climate is more humid and slightly cooler. Thelower parts are dominated by agricultural land, whereas the mountain areas aremainly covered by open and dense forests. The bases of the mountains are domi-nated by P. halepensis. At higher altitudes, the region is dominated by Pinus sylvestrisand Pinus nigra. The third study area, “Igualada”, is situated north of the town ofIgualada. Vegetation mostly consists of shrublands and low-height forests domi-nated by P. halepensis and, to a lesser extent, P. nigra.

2.11.2. Initialisation and constant parametersCell size was set to 50 m, resulting from a trade-off between data availability and

calculation speed on one side, and spatial accuracy on the other side. Daily weatherdata for each area were obtained from a reconstructed climatic time series based onthe Climatic Research Unit (CRU) monthly dataset (New et al., 1999). Daily dominantwind direction was set randomly. Small-scale spatial variability of weather wastaken into account correcting the daily maximum and minimum temperatures andthe amount of rainfall for each pixel according to the data available from the DigitalClimatic Atlas of Catalonia (Ninyerola et al., 2000), which contains the averagevalues of temperature and precipitation between 1951 and 1991 at a spatial reso-lution of 180 m. Therefore, the temporal variation was the same for the whole studyarea, but mean values were specific for each cell.

The land cover data of 1956 were obtained from Loepfe et al. (2010). A dominantspecies was assigned to each cell with a probability assigned based on the propor-tions of area covered according to a map of land uses of Spain (MAPA, 1980). Theminimum LAI of the forest (LAImin) was set to 0.41, a value that corresponds to the10th percentile of all stations of the Ecological and Forest Inventory of Catalonia(IEFC, Burriel et al., 2000e2004). As no accurate maps of DBH or stand density wereavailable for this period, for each forest cell, DBH was sampled uniformly between

priate, the source is indicated.

alue Units Source

2 e Piñol, 19910.83 e Burriel et al., 2000e20042 m Estimated from field observations

8600 J kg�1 McKendry, 20020.0337 sm�1 Weise and Biging, 1997

22.45 e Weise and Biging, 1997.2/0.4/1 e Albini and Baughman, 1979

0.00059 e 90% of BT available at max DC0.51 e Estimated from air humidity increase0.19 Estimated from air humidity increase1.376 � Estimated from meteorological data0.055 � Sardoy et al., 20075 MW Estimated from technical description1.05 year�1 Estimated from fire brigades budgets1 min Estimated

Table 3Constant species-specific allometric parameters of FIRE LADY to calculate treeheight, tree biomass, leaf area index (LAI) and crown base height equivalent (CBH).Species are Alepo pine (P.h., Pinus halepensis), black pine (P.n., Pinus nigra) and Scotspine (P.s., Pinus sylvestris).

P.h. P.n. P.s. Source

Tree height (m) from DBH (cm)aHt 2.1908 1.3848 1.9285 Burriel et al., 2000e2004kHt 0.5000 0.6687 0.5667 Burriel et al., 2000e2004Biomass branches and leaves (kg) from DBH (cm)aBt 0.1179 0.0504 0.0827 Burriel et al., 2000e2004kBt 1.8945 2.1155 1.9763 Burriel et al., 2000e2004LAI form basal area (m2 ha�1)aLAI 0.0615 0.0688 0.0680 Burriel et al., 2000e2004kLAI 0.9392 0.9634 0.9289 Burriel et al., 2000e2004Proportion of tree height which is CBHkCBH 0.294 0.421 0.553 Álvarez et al., unpublished data;

Fulé et al., 2008; Mäkeläand Vanninen, 1998

Maxim DBH used for initialisation (cm)DBHMAX 41.7 43.4 61.1 Burriel et al., 2000e2004

Table 4Variable parameters used in the calibration of FIRE LADY. Minimum and maximumvalues indicate the initial sampling range used in the calibration process.

Symbol Description Minimum Maximum Units

Vegetation growthr Scaling parameter for area

at breast height increase0.01 0.1 mm2 year�1mm

(H2O)�1

aNt Average stand density 500 1000 # ha�1

ra Underwood growth rateparameter

50 500 g ha�1 year�1mm(H2O)�1

sa Shadowing parameter 1 10 e

IgnitionIn Numbrer of potential

ignitions per dayper 105 ha

1 10 day�1

Fire spread (heat transfer)kfv Constant for calculating

velocity from intensity0.05 0.5 m2 GJ�1

kvp Constant for calculatingprobability to propagatefrom velocity

1 10 sm�1

kcf Scaling parameter forstart of crown fire

0.1 1 m2MW�1

Fire spread (spotting)kSn Scaling parameter for

number of firebrands10 100 mGW�1

kdi Scaling parameter fordistance of firebrands(intensity)

0.1 1 m2 kW�1

Fire fightingta Time for fire brigades to

arrive to fire5 50 min

NB Number fire brigadeunits (total) at simulationstart per 105 ha

1 10 e

L. Loepfe et al. / Environmental Modelling & Software 26 (2011) 1028e1040 1033

the DBH corresponding to LAImin (DBHmin) and 2$(DBHavg�DBHmin), with DBHavg

being the average DBH found in the IEFC for the corresponding study area. Inshrublands, the DBH of trees was sampled uniformly between zero and DBHmin.Stand density was sampled from Eq. (7), bounded by the Reineke equation (Eq. (5))and the stand density necessary to have sufficient LAI in the case of forest. Shrubbiomass was sampled from a uniform distribution within the extremes found in Pla(2002). To avoid excessive fuel heterogeneity from this random generation, basalareas and shrub biomass were blurred; the average value of all cells of the same landcover type within a radius of 150 mwas assigned to each cell. This also implies thatthe initially uniform distributions of basal areas and shrub biomasses resembleda (more realistic) normal distribution.

The area of abandoned and newly created agricultural land was calculated fromthe difference between 1956 land use maps (Loepfe et al., 2010) and the land covermap of Catalonia from 1993 (DARP, 1998) using the GIS-software “MiraMon” (Pons,2000). In our simulations, we assumed a constant yearly change rate. To decidewhich cells were abandoned or created, we used a generalised linearmodel (GLM) topredict the probability of agricultural land being abandoned and another GLM topredict the probability of agricultural land being created from the following cellproperties in 1956: (1) slope, (2) distance to the nearest road, (3) distance to thenearest urban cell, (4) distance to the nearest agricultural border and (5) size of thepatch to which the cell belongs. Cells with highest probabilities were abandoned/created first.

Ignition probability maps, i.e., the probability that a spark falls on a given cell(pi), were established a as a function of the distance to the nearest road (di, m) withan exponent obtained from a histogram of the origins of fires in the three study areasaccording to administration data:

pi ¼ d0:292iPni¼0 d

0:292i

(18)

The values and sources of global constants are shown in Table 2. Fuel ladder heightwas estimated from field observations. We kept this parameter constant, as it iscompensated for by the probability of starting a crown fire (kcf). The average andstandard deviation of the parameter that modulates the variation of decreases in fireweather indices (mfn and sfn) were assumed to be determined by the increasedrelative air humidity at night. We randomly sampled 328 days from meteorologicalstations near the study areas and fitted a Gaussian distribution to the observedfrequencies of minimum/maximum relative humidity ratios. The deviation of winddirection was obtained from the same data source. The constant, kBf, that links thefraction of available biomass (fB) to drought code (DC) was set so that at the highestDC observed for all three study areas, 90% of the biomass was available. Theextinction capacity of each fire brigade was calculated from the water flow ofa typical fire fighting vehicle. The increased rate of the number of fire brigades waslinked to the observed yearly 5% (inflation adjusted) increase of the fire fightingbudget. Species-specific allometric constants and their sources are listed in Table 3.

2.11.3. Sensitivity analysisThe sensitivity of the model towards the parameters was assessed with partial

rank correlation coefficients (PRCCs), using the “sensitivity” package of the R soft-ware (The R project for Statistical Computing). We ran 10,000 simulations for eachstudy area, varying twelve key parameters randomly within the ranges given inTable 4. We have chosen these parameters in order to obtain a balanced number ofthem for each main process. The parameter range corresponds to reasonable esti-mates compared either directly to field measured data (e.g., aNt) or to relatedobservable values (e.g., fire spread velocity, in the case of kfv) We tested sensitivityfor the following outputs: (1) annual number of fires greater than 1 ha, (2) annualarea burned in fires greater than 1 ha, (3) inequity of fire size distribution (Ginicoefficient; Gini, 1912), (4) tree biomass (without stems) and (5) forested area in1993. Ninety-five percent confidence limits were calculated from 1000 bootstrappedsamples. An additional “dummy” parameter, a uniform random number, was used tocontrol significance.

2.11.4. CalibrationWe did not seek a single optimal parameter configuration but looked for 100

acceptable parameter sets for each study area. Simulations were consideredacceptable (or behavioural, following the Generalised Likelihood Uncertainty Esti-mation (GLUE) methodology; Beven and Binley,1992; Beven and Freer, 2001) if theiroutputs laywithin the acceptance limits of each of the five criteria mentioned above,and total biomass of shrublands was between 5 and 25 Mg/ha, according to thevalues from Pla (2002). Acceptance limits were set as the 50% confidence intervalsresulting from 1000 bootstrapped samples of the actual values. This procedureresulted in very narrow acceptance limits, not overlapping across study areas(Table 1). For the forested area in 1993, no bootstrap sampling was possible (n¼ 1),so the acceptance limits were established as the actual value �25%.

Data for the calibration process were obtained from the following sources:annual burned area, number of fires and Gini coefficient were compared with firescars from satellite imagery (Dìaz-Delgado, 2000) for fires greater than 30 ha andthe official database of wildfires available from 1968e2005 for smaller fires. Onlyfires larger than 1 ha were considered, as smaller fires would often escape detection

or accounting, especially in the earlier records. The proportion of forest in 1993 wascompared to the land cover map of Catalunya of 1993 (DARP, 1998). Tree biomasswas compared to data from the Ecological and Forest Inventory of Catalunya (IEFC,Burriel et al., 2000e2004).

2.11.5. Parameter samplingThe main goal of parameter sampling was to find behavioural parameter sets;

a secondary goal was to find them efficiently and comprehensively. Our parametersampling strategy used blocks of 20,000 simulations. For the first block of simula-tions, parameters were sampled randomly within the range given in Table 4, typi-cally comprising one order of magnitude. For each simulation, a likelihood wasassigned to each output according to the percentile it corresponded to on thebootstrap sampling of the measured values. Each parameter range was divided into9 bins; for each bin, a performance index was calculated as the product of theaverage value of all five individual likelihoods. For subsequent sets of 20,000simulations, each parameter bin had a probability to be sampled proportional to thisperformance index.Within the parameter bin, samplingwas random. Additionally, if

L. Loepfe et al. / Environmental Modelling & Software 26 (2011) 1028e10401034

the sum of likelihoods was highest in the lower three bins for a given parameter, theminimum value of this parameter range was decreased by 10%. If, instead, highlikelihood simulations were concentrated in the upper bins, the maximum valuewas increased by 10%. This procedurewas repeated until reaching the target numberof 100 behavioural simulations for each study area.

2.11.6. Additional model testsWe ran 1000 simulations for each study area using the behavioural parameter

sets, but without fixing the stochastic processes within the model. This allowed us toassess the confidence range of the simulations. We also compared the correlationbetween annual burned area and annualmaximumDC in experimental datawith thiscorrelation for both average and individual simulations of the model. Furthermore,we compared the shape of the modelled fires with actual fire scars obtained fromsatellite imagery (Dìaz-Delgado, 2000) using the Fragstat-software (McGarigal andMarks, 1995). For that purpose, we analysed rectangular binary images (burnedand unburned) with the minimum possible extension to encompass the whole fireand calculated the Landscape Shape Index (LSI) of the burned class. The LSI is cal-culated as the edge length of the fire divided by the edge length of a maximallycompacted fire of the same size. This means that a square fire would have an LSI valueof one. We have used LSI rather than Shape Index to account for burned areasresulting from spotting.

Fig. 2. Partial rank correlation coefficient of the 12 varied input parameters for the 5calibration criteria. Abbreviations are as in Table 4. BP is a “dummy” parameter (i.e.,a random number) to test for significance. Error bars indicate the 95% confidenceinterval of 1000 bootstrapped samples.

3. Results

According to the sensitivity analysis (Fig. 2) the number of fires>1 ha and burned areas were positively related to ignitionfrequency (In) and convection spread parameters (kfv, kvp and kcf).This resulted also in a negative relationship between theseparameters and tree biomass and forest area. Spotting parameters(kSn and kdi) had little influence on the number of fires but werepositively related to burned area. High stand density (aNt) resultedin more and larger fires, and a rapid DBH growth (r) reduced theirnumberwhile slightly increasing burned area. This can be explainedby the fact that a rapid DBH increase favours tall trees. This hindersthe occurrence of crown fires but favours its spread due to greaterbiomass. As expected, both vegetation growth parameters posi-tively affected tree biomass and forest area. A higher reaction timeof fire brigades (ta) and a lower number of fire brigades (NB)increased the number of fires �1 ha and, to a lesser extent, burnedarea. Still, the sensitivity of the model towards fire brigades is smallcompared with other parameters. The parameter sensitivity fol-lowed the same qualitative trend in all three study areas.

To obtain 100 behavioural parameter sets, 77,348 simulationswere necessary in Tivissa, 527,440 in Ports and 128,179 in Igualada.Behavioural simulations were not distributed randomly in thesampled parameter space, and differences between study areaswere observed (Fig. 3), most notably for stand density (aNt). ThePorts region required slower understory growth. The behaviouralsimulations had similar values of ignition and propagationparameters (In, kfv and kvp) for all three areas. The Igualada regionshowed higher values for spotting distance (kdi). A late arrival time(ta) and too many or a total absence of fire brigades (NB) resulted infewer behavioural simulations.

We ran 1000 simulations for each study area using the behav-ioural parameter set but without fixing the stochastic processeswithin the model. These simulations gave a scattering of the modeloutcomes that corresponded reasonably well with the observeddata (Fig. 4). The differences between study areas were wellreflected. The average annual burned area of all simulations isassociated with maximum annual drought code (DC r2¼ 0.757,r2¼ 0.262, r2¼ 0.567 for Tivissa, Ports and Igualada), in contrast tothe observed data (r2¼ 0.069, p¼ 0.112; r2¼ 0.123, p¼ 0.031;r2¼ 0.126, p¼ 0.029; for Tivissa, Ports and Igualada, respectively;n¼ 38 in all three cases). This higher correlation for modelledburned area disappears when making the regression withoutaveraging (r2¼ 0.003, r2¼ 0.042, r2¼ 0.177 for Tivissa, Ports andIgualada, respectively). Years with a lowmaximumDC did not showlarge areas burned, either in modelled or in observed data. In years

with higher DC, large burned areas were possible (but did notalways occur) in both observed data and individual simulations. Ingeneral, the model showed fewer years with very low burned areathan the observed data. Also, a map of spatial distribution of firerisk was obtained from these 1000 simulations, expressed as thepercentage of simulations in which each pixel was burned (Fig. 5).The regions of Tivissa and Igualada showed a high coincidencebetween the areas of high fire risk and actual fire occurrence. In thePorts region, the gradient of fire risk differences between fire pronepixels was not as marked, and actual fire location could not bepredicted, likely due to the lower number of observed fires in thisarea. The impression of realistic shapes of individual fires(Supplementary data, Fig. S1) is confirmed by the fact that the LSI of

Fig. 3. Cumulative probability distribution of behavioural (thick lines) and non-behavioural (thin lines) simulations for the 12 varied input parameters in three study areas. SeeTable 4 for description and units of the parameters. A steep increase in cumulative probability indicates a high density of behavioural simulations around that parameter value. Notethat regions of maximum likelihood overlap for the three study areas in the case of fire spread-related parameters, but not for vegetation growth-related parameters.

L. Loepfe et al. / Environmental Modelling & Software 26 (2011) 1028e1040 1035

the simulated fires reproduced well the values of the observed data(Supplementary data, Fig. S2).

4. Discussion

FIRE LADY is a landscape dynamics model that focuses on theinteraction of vegetation growth, fire spread and human influences

involved in the determination of fire regimes and is designed forecosystems with stand-replacing fires and auto-succession, whichis the case in most, but not all, Mediterranean forests (Rodrigo et al.,2004). This model has been shown to reproducemultiple aspects offire regimes, vegetation growth and landscape structure simulta-neously. Many models have treated one or more of the aspects thatdetermine the fire regime of a region, often in a more detailed way

Fig. 4. Box plot of the outcomes of 1000 simulations per study area using thebehavioural parameter sets. Grey crosses represent the actual values, grey lines theacceptance intervals, as indicated in Table 1.

L. Loepfe et al. / Environmental Modelling & Software 26 (2011) 1028e10401036

than FIRE LADY. The goal of our model, however, was not tosimulate each process in great detail but to capture the essentialfeatures of each of those processes and, more importantly, howthey interact with each other. Although other models (Sturtevantet al., 2009; Li, 2000; Keane et al., 2006; Perera, 2008) also allowfor the study of this interaction, the novelty of FIRE LADY is thedetailed inclusion of human impact on fire regimes and theresulting landscape structure.

FIRE LADY is an empirical model, implying that it must becalibrated for each study area. As pointed out by Porté and Bartelink(2002), empirical models aremore accurate in their predictions, butthey are also limited to specific conditions depending on thedataset used for parameter fitting. This implies that the predictivepower of our model is limited by the stability of the factors notcaptured by the model.

4.1. Weather and climate

The incorporation of daily weather data can give insights intothe interaction between climate, vegetation and fire regime. Pre-dicted climate change is likely to increase the length and intensityof the fire season in the Mediterranean (IPCC, Alcamo et al., 2007).This can lead to a decrease in fire return intervals (Cary and Banks2000). Nevertheless, fire extent is also strongly linked to plantproduction (Bowman et al., 2009), and the predicted reduction ofrainfall in the Mediterranean basin presumably will reduce plantproduction (Ciais et al., 2005). In our model, fire spread depends onavailable biomass, which depends on both drought code andaccumulated biomass (Fig. 1). Therefore, FIRE LADY captures boththe fire-promoting and fire-damping sides of climate change,which makes it a useful tool for assessing the net impact of climatechange on fire regimes using external predictions of future climate.

4.2. Vegetation growth

FIRE LADY lacks the details of gap models with fire spreadmodules. Nevertheless, with commonly available data, such as DBHincrease and stand density, FIRE LADY was able to producereasonable estimates simultaneously for fire regime, forestexpansion and biomass in the tree layer at the end of the simulationperiod. Although fuel structure is not explicitly modelled, somebasic influences of vegetation structure on fire behaviour werecaptured. For instance, sites with high stand density and low DBHare more fire prone than sites with the same biomass amountdistributed in a lower number of larger trees, which is realisticcompared to field data (Pollet and Omi, 2002).

The differences in the vegetation growth parameters betweenstudy areas (Fig. 3) suggest that other factors in addition to actualevapotranspiration influence biomass accumulation. These factorsare likely to be related to differences in species compositionbetween study areas and some sort of biomass extraction, either byhumans or by herbivores. A consequence of this is that the modelmay need to be calibrated separately for each study area if accuratepredictions of vegetation growth are required. This limits the val-idity of predictions to scenarios with only moderate changes innon-captured external factors, as is the case with most models thatdeal with complex problems (Guisan and Zimmermann, 2000).Nevertheless, for the desired time horizon of predictions of FIRELADY (approximately 50 years), the assumption of stability of thesefactors seems reasonable.

4.3. Fire behaviour

FIRE LADY satisfactorily reproduced the number of fires, annualburned area and fire size-frequency distribution and evenpredicted

Fig. 5. Maps of the three study areas showing the percentage of simulations in which each pixel (cell) burned. The contours of the actual burned areas (black lines) according toDíaz-Delgado (2000) are also shown. White pixels correspond to land uses treated as non-flammable, such as crop fields, urban areas and water bodies.

L. Loepfe et al. / Environmental Modelling & Software 26 (2011) 1028e1040 1037

realistic spatial patterns of high fire risk (Fig. 5) and fire shapes(Fig. S2). The differentiation between surface and crown fires iscrucial when studying the effects of many fire management strat-egies, such as harvesting the understory (Graham et al., 1999). Therelatively detailed modelling of spotting is important whenassessing the effects of spatial fuel fragmentation. The main limi-tation of our approach is probably the exclusion of bulk density asan explicit parameter, given its importance in fire behaviour(Martins Fernandes, 2001). This reduces the universality of thecalibration parameters, but spatially distributed data on bulkdensity is currently difficult to obtain. The similarity in values of thebehavioural fire spread parameters (Fig. 3) across regions with verydifferent fire regimes (Table 1) shows that our model is able tocapture those differences internally from the input data.

4.4. Land use

An important novelty of FIRE LADY is the inclusion of culturallands and their temporal variation.Most firemodels are designed forvastwilderness areas suchas those found inNorthAmericannationalparks. But theMediterranean basin is characterised by an importantanthropogenic transformationof landscape,whereagriculturalfieldsact as firebreaks (Loepfe et al., 2010). At the same time, landscapestructure is also shaped by the fire regime. Fire scars reduce fuelconnectivity (Turner andRomme,1994) and change land uses (Lloretet al., 2002; Loepfeet al., 2010).Manymodelshavebeenused to studythe impacts of fire regime on landscape structure (e.g., Baker, 1992;He and Mladenoff, 1999; Mouillot et al., 2001; Pausas and Ramos,2006). However, all these models use fixed fire regime data orscenarios (such as fire return intervals), whereas models that simu-late thefire regimeswithin themodel, such as FIRE LADY, can beusedtomake predictions of landscape changeswithout theneed to fix thefire regime scenario (Didion et al., 2007; Sturtevant et al., 2009). Thisis important in a global change context, as fire-induced changes inlandscape structure are likely to interact with fire regimes, creatingfeedbacks that cannot be understood if fire return intervals are fixed.

4.5. Fire fighting

There is a longstanding debate about the origin of very largefiresin Mediterranean climate regions. While some authors (Minnich,

1983, 2001; Minnich and Chou, 1997) state that those very largefires aremainly an artefact of fire suppression, others (Moritz, 1997;Keeley et al., 1999; Keeley and Fotheringham, 2001) consider themthe unavoidable result of extreme weather conditions independentof fire suppression efforts. It is impossible to study the long-termefforts of fire suppression without the use of modelling.

An important contribution of FIRE LADY is its fairly realistic wayof simulating fire suppression, analogous to the approach used by Li(2000). The simple algorithm of fire brigade tactics proved tomimicquite realistically the behaviour of land units during fire fighting(Fig. S1). Realistic values of extinction capacity could be used, whichbrings us closer to understanding the real impact of fire fighting onfire regimes. The difficulties in finding behavioural simulationswithout fire brigades (Fig. 3) are another indicator that the currentMediterranean fire regime cannot be understood without consid-ering the effects of fire suppression. FIRE LADY can therefore bea useful tool for increasing our knowledge about the effects of firesuppression.

4.6. Randomness and model uncertainty

A common problem when studying fire regimes is data avail-ability for a sufficiently large area and time span. Fires are highlyrandom events; the availability of enough fuel under dry conditionsis no guarantee of the occurrence of a fire, as a “spark” is alsoneeded to cause the ignition. This intrinsic stochasticity of fireregimes also impedes the validation of the model because of thelimited length of data series. A deterministic approach of ignitiondistribution and fire spread would greatly reduce the variability ofthe model outcome. However, this would also bring the risk ofaccepting inappropriate parameter sets as a result of incomplete orincorrect inputs and would not work for simulations of futurescenarios, as it is impossible to know the exact times and locationsof future ignitions. Additionally, the ensemble-basedmodelling andcalibration approach allows for the capture of interactions betweenparameters that would go undetected in classical modular process-based approaches (Beven and Binley, 1992). The incorporation ofrandomness and parameter interaction into the model allows us togive reasonable confidence intervals and use the model to answerrelevant questions such as, “How likely is it to have a fire greater

L. Loepfe et al. / Environmental Modelling & Software 26 (2011) 1028e10401038

than a given area during the next 50 years if we reduce ignitionfrequency to half of the actual value?”.

5. Conclusions

FIRE LADY is a fire regimemodel designed for human-influencedlandscapes using simulations of vegetation growth based on wateravailability and individual fire-growth. It can be calibrated tosimultaneously reproduce fire regimes, landscape dynamics andvegetation growth for three study areas in NE Spain. An importantnovelty of the model is the explicit simulation of human influenceson fire regimes, such as ignition frequency, fire suppression andland use changes. FIRE LADY can be a useful tool for studying theinteraction of climate, vegetation and fire under the presence ofhuman activities and the impact of various management strategies.It can be used, for instance, to study the effects of climate change onfire regimes and the extent to which local management optionssuch as fire suppression and land use management can mitigatethose effects. Nevertheless, the intrinsic stochasticity and the needto calibrate for each study area limit the predictive power of themodel in some circumstances, particularly if detailed, quantitativepredictions are required at small spatial scales.

Acknowledgements

We would like to thank Marc Castellnou and the team of theGRAF for their useful discussions on fire behaviour and fire brigadetactics; Trevor Keenan for the weather data and for comments onthe manuscript; and Keith Beven, Wouter Buytaert and five anon-ymous reviewers for their extensive comments on a previousversion of the manuscript. Lasse Loepfe was funded by an FI-stu-dentship of the Generalitat de Catalunya. This study has been partlyfunded by the European Research Projects EUFIRELAB (EVR1-2001-00054), by the INIA project RTA2005-00100 and the SpanishMinistry for Science and Innovation (CGL 2007 e 60120). Compu-tational resources used in this work were provided by the ÒlibaProject of the Universitat Autònoma de Barcelona.

Appendix. Supplementary data

Supplementary data associated with this article can be found inthe online version, at doi:10.1016/j.envsoft.2011.02.015.

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