canopy bulk density and canopy base height equations for assessing crown fire hazard in ...

Canopy bulk density and canopy base heightequations for assessing crown fire hazard inPinus radiata plantations

Ana Daría Ruiz-González and Juan Gabriel Álvarez-González

Abstract: Crown fires combine high rates of spread, flame lengths, and intensities, making it virtually impossible to controlthem by direct action and having significant impact on soils, vegetation, and wildlife habitat. For these reasons, fire manag-ers have great interest in preventive silviculture of forested landscapes to avoid the initiation and propagation of crown fires.The minimum conditions necessary to initiate and propagate crown fires are assumed to be strongly influenced by the standstructural variables canopy bulk density (CBD) and canopy base height (CBH). However, there is a lack of quantitative in-formation on these variables and how to estimate them. To characterize the aerial fuel layers of Pinus radiata D. Don, thevertical profiles of canopy fuel in 180 sample plots of pure and even-aged P. radiata plantations were analysed. EffectiveCBD and CBH were obtained from the vertical profiles, and equations relating these variables to common stand variableswere fitted simultaneously. Inclusion of the fitted equations in existing dynamic growth models, together with the use of cur-rent fire behaviour and hazard prediction tools, will provide a decision support system for assessing the crown fire potentialof different silvicultural alternatives for this species.

Résumé : Parce que les feux de cime ont à la fois des taux de propagation ainsi que des intensités et des longueurs de flam-mes élevés, ils sont pratiquement impossibles à maîtriser par une intervention directe et ils ont un impact important sur lessols, la végétation et l’habitat faunique. Pour ces raisons, les gestionnaires du feu s’intéressent beaucoup à la sylviculturepréventive des paysages forestiers pour éviter l’initiation et la propagation des feux de cime. On pense que les conditionsminimales pour l’initiation et la propagation des feux de cime sont fortement influencées par les variables structurales dupeuplement, la densité apparente du couvert (DAC) et la hauteur de la base du couvert (HBC). Cependant, il y a un manqued’information quantitative au sujet de ces variables et de la façon de les mesurer. Pour caractériser les couches aériennes decombustibles de Pinus radiata D. Don, le profil vertical des combustibles dans le couvert a été analysé dans 180 placetteséchantillons établies dans des peuplements purs et équiennes de P. radiata en plantation. Des valeurs réelles de DAC etHBC ont été obtenues à partir des profils verticaux et des équations reliant ces variables aux variables courantes de peuple-ment ont été ajustées simultanément. L’inclusion de ces équations dans des modèles dynamiques de croissance existants,combinée à l’utilisation des outils courants de prédiction des risques d’incendie et de leur comportement, procureront unsystème d’aide à la décision pour évaluer les risques de feu de cime associés à différentes approches sylvicoles adaptées àcette essence.

[Traduit par la Rédaction]

IntroductionCrown fire is an undesirable phenomenon from different

points of view: the high rate of spread, the intensity, andspotting activity make such fires difficult to extinguish andthe risk to human safety is greater than with a surface fire.In addition, the effects of crown fire are more severe andlong-lasting than with surface fire, tree mortality is total, andmore smoke is produced (Scott and Reinhardt 2001). The un-fortunate implications of this type of fire therefore justify thecurrent great interest in assessing crown fire potential.Van Wagner (1977) developed some semi-physical criteria

for crown fire initiation and spread in coniferous forests or

plantations that are accepted worldwide. This author definedthree limiting factors (surface fire intensity, horizontal heatflux, and spread rate) and two stages in the process (initiationand propagation) and also established three different classesof crown fire (passive, active, and independent). The possi-bility of crown fire initiation can be estimated by use of themodels developed by Xanthopoulos (1990), Alexander(1998), Cruz (1999), and Cruz et al. (2002, 2003a, 2004,2006), and the rate of spread of a crown fire can be estimatedby use of the equations proposed by Rothermel (1991), For-estry Canada Fire Danger Group (1992), Cruz (1999), andCruz et al. (2002, 2005). The Van Wagner criteria and crown

Received 26 February 2010. Accepted 2 December 2010. Published at www.nrcresearchpress.com/cjfr on 8 April 2011.

A.D. Ruiz-González and J.G. Álvarez-González. Unidad de Gestión Forestal Sostenible, Departamento de Ingeniería Agroforestal,Universidad de Santiago de Compostela, Escuela Politécnica Superior, Campus Universitario s/n 27002, Lugo, Spain.

Corresponding author: A.D. Ruiz-González (e-mail: [email protected]).

839

Can. J. For. Res. 41: 839–850 (2011) doi:10.1139/X10-237 Published by NRC Research Press

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fire classification, together with the above-cited empirical orsemi-physical initiation and spread models, have been usedregularly and implemented in well-known fire-behaviour pre-diction systems (Forestry Canada Fire Danger Group 1992;Finney 1998; Scott 1999; Reinhardt and Crookston 2003;Alexander et al. 2006; Andrews 2008).The models cited and derived methodologies for assessing

crown fire potential such as the torching and crowning indi-ces proposed by Scott and Reinhardt (2001) require quantifi-cation of the lack of continuity from surface to canopystratum and also the available fuel for combustion in the aer-ial layer, i.e., the fuel that would be consumed in the flamingfront of a fully active crown fire. Two stand structural varia-bles are usually used for this purpose: the canopy base height(CBH) and the canopy bulk density (CBD). However, thesestand variables are relatively difficult to quantify and alsodifficult to define accurately (Carey and Schumann 2003;Cruz et al. 2003b; Reinhardt et al. 2006a). Existing crownfire behaviour and hazard management tools are therefore oflimited use.Sando and Wick (1972) suggested considering CBH as the

lowest height above ground level at which there is sufficientcanopy fuel to propagate fire vertically through the canopy,i.e., the height above ground level at which the canopy bulkdensity reaches a specified minimum value. These authorsfixed CBH as the lower vertical 0.3 m section with a fuelmass greater than 112.4 kg/ha, equivalent to 0.037 kg/m3,and Reinhardt et al. (2006a, 2006b) considered CBH as thelowest point at which CBD exceeds 0.012 (rather than0.037) kg/m3. However Van Wagner (1977), Mcalpine andHobbs (1994), and Cruz et al. (2003b) indicated that CBHis the vertical distance between the surface and the live can-opy fuel layer.Scott and Reinhardt (2001) defined CBD in a general way

as the mass of available canopy fuel per unit of canopy vol-ume. However, there is no full consensus about what is con-sidered available fuel, and studies are clearly needed toresolve this question (Reinhardt et al. 2006b). Some modeldevelopers and users only take live canopy foliage into ac-count (Fernandes et al. 2004). Van Wagner (1977) consideredthat live foliage is the principal crown fuel consumed andthat little else burns except in unusually intense fires, butthat when there is considerable dead material within the livecrowns, this must be taken into account to determine theCBD. Other authors indicated that foliage and crown finelive and dead twigs, as well as ladder fuels, must be in-cluded, and for example, Brown and Reinhardt (1991),Brown and Bradshaw (1994), and Reinhardt et al. (1997)considered than lichen, moss, and some portion of live anddead branch wood less than 6 mm should be considered asavailable fuel. Call and Albini (1997) suggested considering65% of canopy fuel of diameter 0–6 mm at 100% moisturecontent as available fuel. Reinhardt et al. (2006a) consideredall of the foliage and half of the 0–6 mm branch material inthe stand as the available canopy fuel load. However, the lackof complete fuel quantitative information often prevents con-sideration of all of the fine live and dead twigs, lichens, andbark flakes (Cruz et al. 2003b).Nonetheless, both CBH and CBD must be estimated from

instrument-based optical techniques (Keane et al. 2005) orinventory-based techniques (Mcalpine and Hobbs 1994; Cruz

et al. 2003b; Reinhardt et al. 2006b), as direct measurementis impractical for operative use (Scott and Reinhardt 2001;Cruz et al. 2003b; Reinhardt et al. 2006b). One procedurefor estimating CBD, only applicable to uniform stands andassuming a uniform vertical distribution of canopy fuel, is todivide the available canopy fuel load by canopy depth. Thisapproach, cited by Reinhardt et al. (2006b) as the “load overdepth method”, was used first by Van Wagner (1977) andlater by other authors (i.e., Fernandes et al. 2004; Harrington2005; Crecente-Campo et al. 2009). Sando and Wick (1972)proposed a more complex method that accounts for a non-uniform vertical distribution of aerial biomass at stand leveland that also enables determination of CBH as definedabove. Based on this method, the Fire and Fuel Extension tothe Forest Vegetation Simulator (Beukema et al. 1997; Rein-hardt and Crookston 2003) defined “effective” CBD as themaximum 4.5 m running mean of canopy bulk density forlayers 0.3 m thick and CBH as the lowest height above whichat least 0.011 kg/m3 of canopy fuel is present. However, allthese methods require estimation of the available canopy fuelload, and therefore, equations relating CBD and CBH toeasy-to-measure stand variables may simplify the estimationwhile preserving the necessary accuracy.In Spain, few studies have been made of relevant aspects

of crown fire modelling or crown fire hazard evaluation,although some partial information about prediction of canopybiomass or crown profile models is available (Balboa-Muriaset al. 2006; Crecente-Campo 2008). Reliable tools are re-quired for assessing the crown fire potential in coniferousstands, and new research challenges have been addressed: de-velopment of allometric equations for CBH and CBD predic-tion; study of the temporal foliar moisture content variationfor pine species; review of the current knowledge about thecharacteristics of the pine surface fuel complexes that affectfire intensity (Fernandes and Rego 1998; Vega et al. 2002;Fernandes et al. 2002, 2004, 2008; Fernandes and Rigolot2007; Vega et al. 2008); and finally, evaluation of the per-formance of existing initiation and spread models when ap-plied to specific coniferous stands in the region.Wildfires are a serious ecological, economic, and social

problem in Spain, especially in Galicia (northwestern Spain),where about 10 000 fires take place every year during the dryseason (MIMAM 2008). In this area, radiata pine (Pinus ra-diata D. Don) is the most commonly used exotic conifer inreforestation, covering an area of approximately 60 000 ha(Xunta de Galica 2001) as the dominant species. Pinus radi-ata stands are highly productive because of the mild climatein the area, but understory fuel accumulation is also high,and loads of 30–50 tonnes (t)/ha are frequent (Vega 1985;Vega et al. 1987). This situation, together with the low littermoisture content that may be reached in dry summer periods(Ruiz-González and Vega-Hidalgo 2005; Ruiz-González2007), makes possible the occurrence of high-intensity sur-face fires, which may result in torching or crowning. The ob-jectives of the present study include (i) quantification of therange of variation in CBH and the effective CBD of P. radi-ata stands in northwestern Spain, (ii) analysis of the verticalprofile of available canopy fuel for the species, and (iii) de-velopment of allometric equations for predicting these varia-bles from easily measurable stand descriptors.

840 Can. J. For. Res. Vol. 41, 2011

Published by NRC Research Press

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Material and methods

DataThe data used were obtained from a network of 180 sam-

ple plots established in the winter of 1995 by the SustainableForest Management Unit of the University of Santiago deCompostela in pure and even-aged P. radiata plantations inGalicia.The plots were located throughout the area of distribution

of this species in the study region and were subjectively se-lected to represent the existing range of ages, stand densities,and site indexes. The size of the plots ranged from 625 to1200 m2, depending on stand density, to obtain a minimumof 30 trees per plot.After examination of the data for evidence of plots in-

stalled in extremely poor site conditions and taking into ac-count that some plots had disappeared because of forest firesor clear-cutting, a subset of 154 of the initially establishedplots was re-measured in the winter of 1998. Following sim-ilar criteria, a subset of 67 of the twice-measured plots weremeasured again in the winter of 2004. The data thereforecomprise a total of 401 inventories carried out in 1995,1998, and 2004.The diameter at breast height (1.3 m above ground level)

of each tree was measured twice (measurements at right an-gles to each other) with callipers to the nearest 0.1 cm, andthe arithmetic mean of the two measurements was calculated.Total height was measured to the nearest 0.1 m with a digitalhypsometer in a randomized sample of 30 trees and in an ad-ditional sample including the dominant trees (the proportionof the 100 thickest trees per hectare, depending on plot size).The height of the remaining trees was estimated using thestochastic generalized height–diameter relationship developedby Castedo-Dorado et al. (2006) for this species. The follow-ing stand variables were also calculated for each inventory:stand age (t), stand basal area (BA, m2/ha), quadratic meandiameter (dg, cm), number of trees per hectare (N), dominantheight (H0, m) (defined as the mean height of the 100 thick-est trees per hectare), dominant diameter (D0, cm) (defined asthe mean diameter of the 100 thickest trees per hectare), andsite index (S, defined as the dominant height of the stand, inmetres, at a reference age of 20 years), which was obtainedfrom the site quality system developed by Diéguez-Aranda etal. (2005). Summary statistics, including the mean, mini-mum, maximum, and standard deviation of these stand varia-bles, are given in Table 1.

Estimation of canopy bulk density (CBD) and canopybase height (CBH)CBD and CBH were estimated following the approach

used by the Fire and Fuels Extension to the Forest VegetationSimulator (Beukema et al. 1997) and based on the methodreported by Sando and Wick (1972), but assuming that crownbiomass is not equally distributed throughout the entirelength of the tree crown. According to Keyser and Smith(2010), the manner of fuel distribution within the crown ofan individual tree may have a significant impact on estima-tions of effective CBD and CBH as defined by Sando andWick (1972) and, therefore, the crown architecture should beconsidered.“Effective” CBD has been defined as the maximum 4.5 m Tab

le1.

Summarized

data

correspondingto

thesampleof

plotsused

inthisstudy.

1stinventory(180

plots)

2ndinventory(154

plots)

3rdinventory(67plots)

Variable

Mean

Max.

Min.

SDMean

Max.

Min.

SDMean

Max.

Min.

SDt(years)

22.58

388

8.48

25.34

4111

8.31

29.28

4720

6.66

N(stems/ha)

991

3120

200

529.8

887

3856

192

512.3

722

1488

280

282.8

d g(cm)

23.22

50.91

6.93

9.85

26.06

53.56

8.66

9.60

28.35

45.90

19.67

5.92

BA

(m2 /ha)

32.57

87.11

5.16

12.31

36.72

69.84

10.83

9.98

41.96

64.00

17.75

9.79

H0(m

)19.19

32.47

6.78

5.74

21.56

34.02

11.34

5.05

26.27

35.17

18.10

4.22

D0(cm)

32.70

61.71

10.43

11.32

35.95

63.79

14.65

10.30

38.40

57.70

28.10

6.81

S(m

)18.66

26.06

11.32

3.17

19.04

26.06

11.32

3.15

20.72

26.06

13.82

3.05

Note:

Min.,minim

um;m

ax.,maxim

um;S

D,standarddeviation;

t,standage;

N,n

umberof

stem

sperhectare;

d g,q

uadratic

meandiam

eter;B

A,stand

basala

rea;

H0,dominanth

eight;D

0,dominantd

iameter;

S,site

indexdefinedas

themeandiam

eter

ofthe100thickesttreesperhectareat

areferenceheight

of20

years.

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running mean of canopy bulk density for layers 0.3 m thick,and CBH has been defined as the lowest height above whichat least 0.037 kg/m3 of canopy fuel is present. This thresholdis a compromise between the minimum value of 0.011 kg/m3

proposed by Beukema et al. (1997) and the maximum of0.067 kg/m3 proposed by Williams (1978) until completestudies of crown fire activity are developed for this speciesin northwestern Spain. The values of canopy bulk densityfor layers 0.3 m thick were calculated for each sample plotand inventory by combining the estimates from an individualtree crown profile model with a system of biomass equations.The crown architecture of each tree was estimated using

the crown profile model developed by Crecente-Campo(2008) for P. radiata in Galicia. This model includes two el-liptical equations, one for the upper crown (above the maxi-mum crown radius) and another for the lower crown (belowthe maximum crown radius). The model requires measure-ments of d, h, t, BA, H0, and S as input variables and wasused to estimate the upper and lower crown radii (CR) ofeach tree for 0.3 m thick layers above ground level. Theequations of the crown profile model are as follows:

½1� Upper crown CRi ¼ MCR �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� ðhi � HMCRÞ2

ðh� HMCRÞ2r

½2� Lower crown CRi ¼ MCR �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� ðhi � HMCRÞ2

ðHMCR� HBLCÞ2r

½3� MCR ¼ 0:06185 � d1:185 � e�0:009319�BA�0:009502�t

½4� HBLC ¼ �3:265� 0:1415 � d þ 0:5117 � hþ 0:1430 � t þ 0:1691 � H0

½5� HMCR ¼ �4:7570� 0:08092 � d þ 0:6408 � hþ 0:1881 � t þ 0:1998 � S

where CRi is the crown radius (m) at height above groundlevel (hi), MCR is the maximum crown radius (m), HBLC isthe height to the base of the live crown (m) defined as thepoint on the stem of the lowest live branch above which therewere at least two consecutive live branches, HMCR is theheight at which maximum crown radius occurs (m), and theother variables are as previously defined.Once the upper and the lower crown radii of any 0.3 m

thick layer were estimated for each tree of the sample plot,the volume of the crown section was calculated as

½6� Crown volumek ¼ p � ðCRup2k þ CRlow2kÞ

2� 0:3

where CRupk and CRlowk are the upper and lower crown ra-dii (m), respectively, of the 0.3 m thick layer k.The available fuel load of each crown section was esti-

mated by assuming that the fine biomass is distributed verti-cally according to the vertical distribution of the crownvolume. This approach is more realistic than assuming a uni-form distribution over the length of the crown but provides apossible source of error that could be reduced by developingequations for predicting biomass to any upper diameter or

height limit. Further development of this approach is clearlyneeded.The compatible system of tree biomass equations devel-

oped by Balboa-Murias et al. (2006) for this species in Gali-cia was used to estimate the dry mass of the fineaboveground tree fractions. The original equation for thinbranches included all the dry mass from 0.5 to 2 cm, andthe equation was therefore refitted using the original databaseto take into account only the interval from 0.5 to 0.6 cm, asno author includes particles thicker than 0.6 cm as availablefuel. The system requires measurements of d and h as inputvariables.

½7� Thin branches ðd from 0:5 to 0:6 cmÞ:w ¼ 0:00944 � d2:6091 � h�0:9417

½8� Twigs ðd < 0:5 cm at the insertionÞ:w ¼ 0:0078 � d1:9606

½9� Needles: w ¼ 0:0423 � d1:7141

where w is the dry mass of the different tree components(kg), d the diameter at breast height (cm), and h the tree totalheight (m).The vertical profile of available canopy fuel for each plot

and inventory was obtained by summing available fuel massin thin (0.3 m) vertical layers across all trees and dividing bythe volume of the layer (plot area × layer depth). The effec-tive value of CBD was computed as the maximum 4.5 mrunning mean of this vertical distribution, and CBH was de-fined as the lowest height above which at least 0.037 kg/m3

of canopy fuel is present.To analyse the mean location of effective CBD in the can-

opy for all sample plots, the relative CBD was plotted againstthe relative crown length and the relative height. The firstvariable was obtained for each 0.3 m thick layer as the ratioof CBD to the maximum CBD; the relative crown length wascalculated as the quotient between the height of each 0.3 mthick layer from the base of the crown and crown length,and the relative height was calculated as the quotient betweenthe height of each 0.3 m thick layer and total height. A non-parametric mean profile was fitted by local regression, withthe LOESS procedure of SAS/STAT (SAS Institute 2004b),which involves local quadratic fitting with optimization ofthe smoothing parameter to reduce the root mean square er-ror (RMSE).As effective CBD and CBH values estimated using the

above approach should not be used with models integratingthe crown fire spread theories proposed by Van Wagner(1977) (Cruz and Alexander 2010), the average CBD andthe mean live CBH were also estimated. Average CBD wasconsidered as the quotient between the available canopy fuelload (kg/m2) and the mean live crown length (m).

Relationship between effective CBD and CBH andcommon stand descriptorsAllometric models relating the values of effective CBD

and CBH to the measured stand variables were analysed. Se-lection of the best set of independent variables was carriedout by use of a logarithmic transformation of the original

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models and applying the stepwise variable selection method(Draper and Smith 1998), combined with the values of theTukey’s multiple comparison test and an understanding ofthe fitting process.There are several problems associated with this type of

model that violate the fundamental least squares assumptionof independence and equal distribution of errors with zeromean and constant variance: multicollinearity, cross-correlatederrors, and heteroscedasticity.The presence of multicollinearity among variables in the

models analysed was evaluated by the condition number,which is defined as the square root of the ratio of the largestto the smallest eigenvalue of the correlation matrix. Accord-ing to Belsey (1991), if the condition number ranges from 5to 10, collinearity is not a major problem; if it is in the rangeof 30–100, then there are problems associated with collinear-ity; and if it is in the range of 1000–3000, there will be se-vere problems associated with collinearity.As the values of effective CBD and CBH were obtained

for each plot and inventory from the same vertical profilesof available canopy fuel, it would be unrealistic to expectthat the equation errors would be uncorrelated. To improvethe efficiency of the estimation, the equations were fitted si-multaneously by the iterative seemingly unrelated regression(ITSUR) method, which takes into account the cross-equationcorrelations, in the MODEL procedure of SAS/ETS (SAS In-stitute 2004a). An estimation of the cross-equation error co-variance matrix to initiate the iterative procedure wasobtained by first using ordinary least squares.To avoid the problem of heterocedasticity, each observa-

tion should be weighted by the inverse of its variance (s2i ).

Although this variance is unknown, it is often assumed thatthe variance of the error of the ith individual can be modelledas a power function of the independent variables (Cailliez1980), i.e., s2

i ¼ ðXiÞk. To optimize the value of the exponen-tial term k to provide the most homogeneous studentized re-sidual plot, the method suggested by Harvey (1976) wasused. This method consists of using the estimated errors ofthe unweighted model (bei) as the dependent variable in theerror variance model:

½10� be2i ¼ gðXiÞk

or taking the natural logarithm (ln) of the function:

½11� lnbe2i ¼ ln g þ k ln ðXiÞThe k parameter of eq. 11 was estimated by linear regression.The weighting factor for heteroscedasticity 1/(Xi)k was multi-plied and programmed in the MODEL procedure of SAS/ETS (SAS Institute 2004a) for each dependent variable (V)by specifying that the residual V (resid. V) =resid: V=

ffiffiffiffiffiffiffiffiffiffiðXiÞk

p(note that resid. V is multiplied by 1=

ffiffiffiffiffiffiffiffiffiffiðXiÞk

pbecause the latter is acting on the residual before it is squared(SAS Institute 2004a)).Evaluation of the performance of the models was based on

graphical analysis by plotting the observed values against thepredicted values of the dependent variable and the studen-tized residuals against the estimated value residuals and twostatistical indices: the RMSE and the model efficiency(MEF). The expressions of these statistics are as follows:

½12� RMSE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXni¼1

ðyi � byiÞ2n� p

vuuuut

½13� MEF ¼ 1�ðn� 1Þ

Xni¼1

ðyi � byiÞ2ðn� pÞ

Xni¼1

ðyi � yÞ2

where yi, byi, and y are the observed, predicted, and mean va-lues of the dependent variable, respectively, n is the totalnumber of observations, and p is the number of parametersin the model.

Results and discussion

Vertical profiles of CBDIn general, the vertical profiles of available canopy fuel of

each inventory were smooth, as expected because of the un-complicated structure of even-aged stands linked to the use ofmodels to estimate the crown architecture and the fuel load.However, differences in the shape of the vertical profileswere found in the different inventories of the same sampleplots. The plots were grouped into 10-year age classes to an-alyse the effect of age on the vertical available canopy fuelprofile. The pooled vertical available canopy fuel profiles(all the data of the same age class together) are shown inFig. 1.As stand age increases, the distribution of the canopy fuel

Fig. 1. Available canopy fuel profile for the pooled data for 10-yearage classes.



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moves up and the profile become more irregular because ofdifferentiation among height strata within the stand. However,the mean value of effective CBD is similar for all age classes(approximately 0.22 kg/m3) except for the younger plots(0.14 kg/m3). The FARSITE Fire Area Simulator (Finney1998) uses 0.2 kg/m3 as a default value for CBD (Reinhardtet al. 2006b), which is only slightly lower than the meanvalue found in this study for most of the age classes.Figure 2 illustrates the plots of the relative CBD against

the relative crown length (Fig. 2a) and the relative height(Fig. 2b) and the non-parametric mean profile fitted by localregression.The relative height at which effective CBD is reached

ranged from 0.40 to 0.74, with a mean value of 0.63 (63%of the canopy total height), and the relative crown height atwhich the effective CBD is reached ranged from 0.24 to0.61, with a mean value of 0.41 (41% of the canopy crownlength measure from the base of the canopy crown).

Estimations of effective CBD and CBHThe mean, maximum, and minimum values and standard

deviations of effective CBD and CBH obtained for each sam-ple plot and inventory are given in Table 2.The effective CBD ranged from 0.067 to 0.376, with mean

values of 0.207, 0.217, and 0.216 kg/m3 for the first, second,and third inventories, respectively (total mean 0.212 kg/m3).The distribution of effective CBD was symmetrical, and theresults of the Shapiro–Wilk test indicate that it correspondsto a normal probability density function (a = 0.05). Scott

and Reinhardt (2002) indicate that CBD may reach as highas 0.4 kg/m3 in very dense stands, similar to the upper limitreached in this study.The mean values of effective CBD obtained were higher

than the value of 0.10 kg/m3 empirically deduced by Agee(1996) and accepted by Alexander (1998) and Cruz et al.(2005) as the CBD below which the likelihood of activecrown fire propagation is considerably reduced. Johnson(1992) indicated that a CBD of 0.2 kg/m3 is common in bor-eal forests that burn with crown fire. The potential for crownfire spread in the P. radiata stands in the study region istherefore remarkably high.The CBD values obtained in the present study were similar

to those obtained by Cruz et al. (2003b) for Pseudotsugamenziesii (Mirbel) Franco and Pinus ponderosa P.&C. Law-son stands in western North America (0.18 kg/m3), for even-aged Pinus halepensis P. Mill. forests in Greece (Mitsopoulosand Dimitrakopoulos 2007), and for mixed unthinned P. men-ziesii and Pinus contorta Dougl. ex Loud. stands in Idaho(Reinhardt et al. 2006b).Higher CBD values were found for mixed conifer stands in

western North America because of the multilayered canopystructure of this type of forest (Cruz et al. 2003b) and for Pi-nus sylvestris L. in northern Spain (Crecente-Campo et al.2009). However, such comparisons are inconclusive becauseof the differences in the approaches used to obtain canopyfuel characteristics (foliage biomass equations with differentestimation errors; considerations about the available fuel con-cept; assumption of a uniform rather than non-uniform distri-

Fig. 2. (a) Relative crown length calculated as the quotient between the height of each 0.3 m thick layer from the base of the crown andcrown length and (b) relative height, calculated as the quotient between the height of each 0.3 m thick layer and total height plotted againstrelative canopy bulk density (the quotient between available canopy bulk density to each 0.3 m thick layer and maximum canopy bulk den-sity) for the 401 inventories used. The continuous line corresponds to a local regression loess smoothing curve (the smoothing parameter isindicated in the graph).

Table 2. General statistics obtained for effective canopy bulk density (CBD) and canopy base height (CBH) correspondingto the sample of plots used in this study.

1st inventory (180 plots) 2nd inventory (154 plots) 3rd inventory (67 plots)

Variable Mean Max. Min. SD Mean Max. Min. SD Mean Max. Min. SDCBD (kg/m3) 0.207 0.352 0.067 0.054 0.217 0.376 0.104 0.049 0.216 0.350 0.114 0.051CBH (m) 8.23 18.00 0.60 3.67 9.74 19.20 2.70 3.36 13.29 19.80 7.50 2.76

Note: Min., minimum; max., maximum; SD, standard deviation.

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bution of available fuel at the tree and (or) stand level; as-sumption of a particular tree crown structure to distribute thefoliage biomass, etc.).The values of average CBD, estimated as the quotient be-

tween the available canopy fuel load (kg/m2) and the meanlive crown length (m), ranged from 0.049 to 0.338 kg/m3,with a mean value of 0.162 kg/m3. As expected, the averagevalues are lower than the effective CBD, which is the maxi-mum of the 4.5 m running mean of the vertical available fueldistribution (Fig. 3). Therefore, as pointed out by Cruz andAlexander (2010), the use of effective CBD with systems in-tegrating the crown fire theories proposed by Van Wagner(1977) leads to lower values of critical minimum spread ratefor active crown fire propagation and should not be used.The values of CBH ranged from 0.6 to 19.8 m, with mean

values of 8.23, 9.74, and 13.29 m for the first, second, andthird inventories, respectively (total mean 9.66 m). As oc-curred with the effective CBD, the distribution of CBH wassymmetrical, and the distribution corresponds to a normalprobability density function (a = 0.05).In this study, the value of CBH is defined as the lowest

height above which at least 0.037 kg/m3 of canopy fuel ispresent. However, there is no standard accepted definitionfor this variable, which limits comparison of estimations. Foreven-aged stands, some authors have defined the CBH as themean value of the crown base height of all the trees in thestand, considering the crown base height as the lower inser-tion point of live branches in the tree (e.g., Cruz et al.2003b; Crecente-Campo et al. 2009). To evaluate the ap-proach used to calculate the CBH, the values of CBH ob-tained were compared graphically with the mean value of thelive crown base height observed in the sample plots (Fig. 4).The scatterplot reveals a linear relationship between CBH

and the mean live crown base height, with a very high coef-ficient of determination for the linear model fitted. Therefore,for this species in Galicia, the mean crown base height or theCBH estimated as suggested by Sando and Wick (1972) but

taking into account the crown architecture may be used inter-changeably in assessing the possibility of crown fire initia-tion.

Relationship between effective CBD and CBH andcommon stand descriptorsThe first step in this part of the study was to analyse the

influence of the common stand variables (age, dominantheight, number of stems per hectare, basal area, and site in-dex) on effective CBD and CBH. The values of these canopyvariables were grouped by classes of each of the commonstand variables, and Tukey’s multiple comparison test wasused to compare the mean values of the classes. The boxplots of effective CBD and CBH against age, dominantheight, site index, number of stems per hectare, and basalarea classes and the results of the multiple comparison testare shown in Fig. 5.For CBH, the results of the multiple comparison tests re-

vealed significant differences for all stand variables analysed(at P < 0.05 level), especially for age, dominant height, andbasal area classes. The effect of age, site index, dominantheight, and basal area was positive, and therefore, an increasein these stand variables reflects an increase in the CBHvalue; the effect of density (stems per hectare) was negativebecause denser classes are associated with younger stands. Ina study of different conifer forests in western North America,Cruz et al. (2003b) also found that CBH was significantlycorrelated with basal area and mean height but was not corre-lated with density and age (based only on dominant and co-dominant trees). These different results are probably due tothe differences between the structure and composition of thiskind of forest and the pure and even-aged P. radiata planta-tions analysed in the study.The results for effective CBD only showed differences for

basal area and density classes (at a 0.05 level) and for the

Fig. 3. Average canopy bulk density (CBD), estimated as the quoti-ent between the available canopy fuel load (kg/m2) and the meanlive crown length (m), plotted against effective CBD. The brokenline corresponds to the diagonal.

Fig. 4. Mean live crown base height plotted against canopy baseheight (CBH) obtained as the lowest height above which at least0.037 kg/m3 of canopy fuel is present. The continuous line corre-sponds to the linear model fitted, and the broken line corresponds tothe diagonal.



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Fig. 5. Box-and-whisker plots of CBH (left) and effective CBD (right) for age (1st row), dominant height (2nd row), site index (3rd row),number of stems per hectare (4th row), and basal area (5th row) classes. Open circles represent the means, boxes represent the interquartilerange, and maximum and minimum of effective CBD and CBH are represented by upper and lower whiskers, respectively. Different lettersindicate differences between mean values (a = 0.05).

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lowest dominant height class. Similar results were obtainedby Cruz et al. (2003b) with average CBD for different typesof conifer fuel in western North America.The second step was to linearize the allometric models by

logarithm transformation and to fit each equation separately.The stepwise variable selection method, together with the re-sults of the multiple comparison test, were used along withan understanding of the process modelled to select the bestset of independent variables. The values of the conditionnumber were analysed to prevent multicollinearity, and themethod proposed by Harvey (1976) was used to estimate theweighting factor for heteroscedasticity.Basal area and dominant height were the best set of inde-

pendent variables for modelling effective CBD, whereasdominant height was the only significant variable for model-ling CBH. Both independent variables are easy to measure ina forest inventory, are estimated in the Spanish National For-est Inventory, and are also included in the usual stand growthmodels existing for this species in Galicia (Castedo-Doradoet al. 2007; Sánchez Rodríguez 2008). Although other standvariables influenced the values of CBD and particularlyCBH, inclusion of those variables in the models did not sig-nificantly reduce the RMSE because of the correlation be-tween the different stand variables. The allometricexpressions used to estimate effective CBD and CBH aretherefore as follows:

½14� CBDeffective ¼ b0 � BAb1 � Hb20

½15� CBH ¼ b3 � Hb40

where BA is the stand basal area (m2/ha) and H0 is the domi-nant height (m). To take into account the cross-equation cor-relations, both equations were fitted simultaneously by usingthe ITSUR method and including the previously estimatedweighting factors.Finally, because of the observed difference between the

values of effective and average CBD, a new equation relatingthe average CBD with stand variables was fitted using thesame approach as described in Material and methods, butwith ordinary least squares. The allometric expression of therelationship is as follows:

½16� CBDaverage ¼ b5 � BAb6 � Hb70 � Nb8

where N is the number of stems per hectare. The values ofthe parameter estimates, the associated standard error, andthe goodness-of-fit statistics obtained from the simulta-neously fitted eqs. 14 and 15 and ordinary least square fittedeq. 16 are shown in Table 3.All parameters were significant at P < 0.05, with biologi-

cally consistent values and signs. The effective CBD modelaccounted for approximately 87% of the total variability, theaverage CBD model accounted for 76% of the total variabil-ity, and the CBH model accounted for more than 97% of thetotal variability, and the three equations provided a randompattern of studentized residuals around zero, with homogene-ous variance and no detectable significant trends. The valuesof the condition numbers did not indicate problems of multi-collinearity.The equations obtained in this study are static models be-

cause they do not predict rates of change of effective CBD,average CBD, and CBH with age or with natural or humandisturbance. For example, silvicultural treatments such asthinning or pruning cause instantaneous changes in these var-iables that cannot be reflected with the equations proposed.Data from thinning and pruning trials should be used to esti-mate the values of CBD and CBH after disturbance (see, forexample, Reinhardt et al. 2006b). However, inclusion of thesestatic equations in the dynamic model developed for this spe-cies in Galicia (Castedo-Dorado et al. 2007) enables estima-tion of projections of basal area and dominant height startingfrom the new state after treatments and then use of the staticmodels to estimate future values of effective CBD, averageCBD, and CBH.

ConclusionsComparison between the distribution of effective CBD cor-

responding to the representative sample of stands analysedand the threshold proposed by Agee (1996) for crown firespread indicate the high potential for this undesirable phe-nomenon in P. radiata plantations in Galicia. However, thehigh value of CBH that stands may reach around the age of20 years indicates a reduction in the likelihood of crown fireinitiation after that age.

Table 3. Parameter estimates and statistics obtained by simultaneous fitting of effective CBD and CBH models and ordinary least squarefitting of average CBD.

Variable Parameter Estimate SEWeightingfactor Condition number RMSE MEF

CBDeffective (kg/m3) (eq. 14) b0 0.0948 0.0040 1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðBA�H0Þ0:3539

p 26.5582 0.0188 0.8682

b1 1.0385 0.0161b2 –0.9515 0.0202

CBH (m) (eq. 15) b3 0.1012 0.0044 1ffiffiffiffiffiffiffiffiffiffiH0:6383

0

p 33.1092 0.6557 0.9708

b4 1.4822 0.0135CBDaverage (kg/m3) (eq. 16) b5 0.0056 0.0011 1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðBA�H0Þ0:3705p 29.7707 0.0236 0.7606

b6 0.8121 0.0353b7 –0.4725 0.0487b8 0.2757 0.0170

Note: SE, standard error; RMSE, root mean square error; MEF, model efficiency; BA, stand basal area (m2/ha); H0, dominant height (m).



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There is need for a clear definition of the canopy fuel thatactually burns in the flaming zone of a crown fire in P. radi-ata plantations under the environmental conditions in Galicia.The canopy bulk density threshold that permits surface fire topropagate vertically into the tree crowns must also be accu-rately defined. Meanwhile, the effective CBD, average CBD,and CBH prediction equations presented are a suitable ap-proach for assessing the possibility of initiate crowning andthe type of crown fire when combined with the current firebehaviour models and simulation systems.The link between the dynamic model (Castedo-Dorado et

al. 2007) and the static equations obtained in this study ena-ble simulation of different silvicultural alternatives and con-stitute a suitable decision support system that will enableforest managers to generate optimal management strategiestaking into account the mid- and long-term crown fire hazardpotential following treatment.

AcknowledgementsThis document has been elaborated in the context of the

Xunta de Galicia 08MRU019291PR project. We are sincerelygrateful to the two anonymous referees for their useful sug-gestions and comments that improved an earlier version ofthe manuscript.

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