United States Department of Agriculture

DEPAR TMENT OF AGRICULT URE

Forest 

Service

Pacific Southwest 

Research Station

Research Paper

PSW-RP-269

March

2017

Physical Characteristics 

of Shrub and Conifer Fuels for 

Fire Behavior Models

Jonathan R. Gallacher, Thomas H. Fletcher, Victoria Lansinger, 

Sydney Hansen, Taylor Ellsworth, and David R. Weise
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Authors 

Jonathan R. Gallacher is a former graduate student and Thomas H. Fletcher

is a professor, Department of Chemical Engineering, Brigham Young University, 

Provo, UT 84602; Victoria Lansinger, Sydney Hansen, and Taylor Ellsworth

were students, Brigham Young University, Provo, UT 84602; David R. Weise is a 

research forester, U.S. Department of Agriculture, Forest Service, Pacific Southwest 

Research Station, 4955 Canyon Crest Drive, Riverside, CA 92507.

Cover photo: Horseshoe Meadows Hotshot firefighter (see back cover) takes a short 

breather at the Rim Fire on the Stanislaus National Forest in California, which 

began on August 17, 2013. U.S. Forest Service photo by Mike McMillan.
Abstract

Gallacher, Jonathan R.; Fletcher, Thomas H.; Lansinger, Victoria; Hansen, 

Sydney; Ellsworth, Taylor; Weise, David R. 2017. Physical characteristics 

of shrub and conifer fuels for fire behavior models. Res. Pap. PSW-RP-269. 

Albany, CA: U.S. Department of Agriculture, Forest Service, Pacific Southwest 

Research Station. 43 p.

The physical properties and dimensions of foliage are necessary inputs for some fire 

spread models. Currently, almost no data exist on these plant characteristics to fill 

this need. In this report, we measured the physical properties and dimensions of the 

foliage from 10 live shrub and conifer fuels throughout a 1-year period. We developed models to predict relative moisture content, apparent density, length, width, 

needle length, thickness, stem diameter, and surface area. Seasonal variability of 

the response variables was found to be adequately explained with a single model, 

so season-specific models or models with a seasonal parameter were unnecessary.

Keywords: Fuel element properties, live fuels, growth patterns, wildland 

fire, wildfire, Adenostoma fasciculatum, Arctostaphylos glandulosa, Artemisia 

tridentata, Ceanothus crassifolius, Ilex glabra, Lyonia lucida, Pinus clausa, Pinus 

contorta, Pseudotsuga menziesii, Quercus gambelii.
Summary

Fuels, weather, and topography influence wildland fire behavior. Thousands of vascular plant species in North America produce wildland fuels; however, the physical 

characteristics of only a small fraction of these species have been determined. As 

living organisms, vascular plants change dynamically over time on daily, monthly, 

seasonal, annual, and longer cycles. The physical characteristics of the living and 

dead plant components also change over time. The amount of water in a wildland 

fuel (moisture content) is perhaps the most widely measured and studied physical 

characteristic because of its importance for fire behavior and fire danger. Fire and 

fuel models typically assume that other physical characteristics remain constant. 

As part of a larger study of ignition of live foliage samples by radiant and convective heating, we measured the physical properties of foliage from 10 live shrub 

and conifer fuels throughout a 1-year period. A single model captured the effect of 

season on many of the physical characteristics. Linear regression produced a series 

of equations to predict relative moisture content, apparent density, length, width, 

needle length, thickness, stem diameter, and surface area of the foliage particles. 

The Weibull distribution modelled the dry mass of foliage particles enabling Monte 

Carlo simulation of the foliage component of the 10 shrub and conifer species for 

fire behavior simulation. This report presents the methodology and equations; the 

data reside in the Forest Service Research Data Archive (http://dx.doi.org/10.2737/

RDS-2016-0023).

Contents

1 Introduction

2 Allometric Models

2 Fuel Placement Models

3 Fuel Element Property Models

5 Methods

6 Measurements

8 Model Development

9 Model Use

10 Results and Discussion

10 Water Content

16 Mass Distribution

16 Prediction Models

22 Conclusions

22 English Equivalents

23 Literature Cited

32 Appendix: Two-Parameter Weibull Distribution for Mass Data
1

Physical Characteristics of Shrub and Conifer Fuels for Fire Behavior Models

Introduction

Knowledge of the role of wildland fire in shaping the landscapes in North America 

has dramatically increased over the past 60 years. With this knowledge, federal 

wildland fire policy in the United States has evolved. The focus a century ago 

was on fire suppression. Current policy holds firefighter safety paramount while 

recognizing fire’s important ecological functions as well as the economic impact 

that fire management has on the federal budget (Bunsenberg 2004, Fire Executive 

Council 2009, Stephens and Ruth 2005). A key component of the current policy is 

the emphasis on risk management and decision support, providing an impetus for 

the improvement of the current suite of operational fire models.

Models of wildland fire spread are of particular interest because they often form 

the basis of tactical and strategic responses to wildland fire events. Many fire spread 

models have been developed, each with various strengths and limitations. Fire models can be categorized in many ways. Two types of fire models, physics-based and 

empirical, following the definitions proposed by Weber (1991) and Sullivan (2009a, 

2009b, 2009c), are described briefly herein. Examples of current physics-based models 

include FIRETEC and FDS along with its wildland-urban interface extension WFDS 

and WRF-Fire/CAWFE (Coen and Riggan 2014; Coen et al. 2013; Linn 1997; Linn and 

Cunningham 2005; Linn et al. 2005; McGrattan and Forney 2004; Mell et al. 2007, 

2009). These models are based on fundamental physics and chemistry principles and 

solve the governing conservation equations in three-dimensional (3D) space. Although 

these models can provide useful insight into fire behavior, they are hampered by the 

lack of experimental data needed to validate the models and the resolution needed to 

model the fine-scale features of shrub and tree combustion (Clark et al. 2010, Sullivan 

2009a). Examples of current empirical models used in the United States based on 

the Rothermel fire spread model (Albini 1976, Rothermel 1972) include BehavePlus, 

FIRECAST, FARSITE, and HFIRE (Cohen 1986, Finney 1998, Heinsch and Andrews 

2010, Peterson et al. 2009). The Rothermel model was based heavily on experimentally derived fire behavior correlations to describe the underlying physics and 

chemistry of fire. Consequently, its predictions can be very accurate in some cases but 

inaccurate in others. The limitations of the Rothermel model as applied to live fuels 

are well-documented (Albini 1976, Cohen and Bradshaw 1986, Rothermel 1972) and 

have been demonstrated in chaparral fuel beds (Weise et al. 2016). Characterization of 

wildland fuels needed in current physics-based and empirical models is very limited 

(Weise and Wright 2014); a majority of the information has been incorporated into the 

Fuel Characteristics Classification System (Riccardi et al. 2007, USDA FS 2012). Solid 

fuel (i.e., grasses, shrubs, and trees) properties are modelled, and these models fall into 

three categories: allometric, 3D fuel placement, and fuel element property.
2

RESEARCH PAPER PSW-RP-269

Allometric Models

Allometric models are single-stem models that can predict general fuel properties, such as fuel loading, canopy height, relative amounts of live and dead fuel, 

and biomass by size class. These models can be used in conjunction with remote 

sensing or ground cover data to describe general fuel properties over large areas. 

Considerable work has been done in this area. Most techniques are destructive and 

time-intensive (e.g., Brown 1976, 1978; Frandsen 1983; Helgerson et al. 1988; Ludwig 

et al. 1975; Riccardi et al. 2007; Schlecht and Affleck 2014; Williams 1989). The 

main drawback of these models, beyond the labor necessary to develop them, is their 

limited applicability—the regression equations are specific to both the fuel type 

and location. Efforts to improve these models and reduce the required labor through 

the use of remote sensing have received increased attention in recent years. Remote 

sensing data have been used to measure detailed information about individual plants 

and general information about large areas. Seielstad et al. (2011) found that remote 

sensing can be used to distinguish foliage and small branches from large branches 

in Douglas-fir.1 Skowronski et al. (2007, 2011) and Barbier et al. (2012) discussed 

remote sensing models that predict properties such as canopy bulk density for 

large areas of land with a high degree of accuracy. A different approach is to use 

plant growth theory to predict bulk properties. One such model was developed by 

Bartelink (1998) and allows growth predictions to be adjusted based on simulated 

growing conditions. Although these models provide some necessary information to 

describe solid fuels, they do not provide all the necessary information. This is seen in 

the work by Wright (2013), in which prescribed burn plots with similar fuel loading 

and fuel type experienced widely different total burn areas even after accounting for 

weather variations.

Fuel Placement Models

Fuel placement models seek to capture the natural structure of plants and the resulting local fuel-density fluctuations. Research has shown fuel bulk density to be an 

important variable in fire propagation (Marino et al. 2012, Rothermel 1972, White 

and Zipperer 2010). Work by Parsons et al. (2011) illustrated the need for accurate 3D 

fuel characterization. Using a stochastic fuel placement technique called FUEL3D, 

they showed that, for the same mass and volume, fire spread behaves very differently 

between fuel beds with homogeneous fuel density and those with variable fuel density. 

Schwilk (2003) found that cutting dead fuel from the shrub canopy and placing it 

1 Spelling of scientific names of plants follows the PLANTS database (USDA NRCS 2016). 

With the exception of wax myrtle (Morella cerifera (L.) Small), scientific names mentioned 

in this report are listed in the tabulation on p. 6).
3

Physical Characteristics of Shrub and Conifer Fuels for Fire Behavior Models

on the ground significantly reduced fire intensity, and thus concluded that canopy 

structure, not just fuel load, affects fire behavior. Weise and Wright (2014) cited several 

studies indicating the importance of fuel arrangement. Prince et al. (2014) developed 

a fuel placement model for chamise and juniper based on fractal theory (L-systems). 

They used bulk descriptors (Countryman and Philpot 1970) to provide guidance for the 

overall shrub properties, then built the shrub using the natural repeating patterns found 

in those species. Although these models provide the location in 3D space of the shrub’s 

trunk, branches, and foliage, they do not provide a physical description of the various 

shrub parts that affect burning behavior (e.g., Loudermilk et al. 2009).

Fuel Element Property Models

Fuel element property models describe the physical, chemical, and shape properties 

of individual leaves or small branch segments. Chemical properties have received 

considerable attention (e.g., Behm et al. 2004, Hough 1969), but this work focuses on 

physical and shape properties, so chemical properties are not discussed further. Size, 

shape, and orientation of fine fuels could affect burning behavior (Lyons and Weber 

1993). Fons (1946) found that properties like surface area, fuel volume, and foliage 

density are important in fire behavior predictions. More recent work (Engstrom et 

al. 2004, Fletcher et al. 2007, Shen 2013) showed fuel orientation and thickness can 

drastically influence ignition of shrub foliage. Despite the established effect of these 

physical properties and dimensions, there is a startling lack of data in the literature 

(Riccardi et al. 2007) on these characteristics. Countryman (1982) and Countryman 

and Philpot (1970) provided excellent descriptions of some common California shrub 

fuels, including fuel properties such as ash content, percentage of extractives, extractive heat content, density, surface area, and volume, but did not report other geometrical properties for the woody branches and foliage. Fahnestock and Key (1971) 

provided leaf measurements of wax myrtle. McNab et al. (1978) sampled a large 

number of southern pine stands with a palmetto-gallberry understory and developed 

regression equations to predict loading of different fuel bed components including 

live fuels <0.64 cm, but did not present other characteristics of the fuel particles. 

Hough and Albini (1978) presented other characteristics of the fuel particles; however, 

the basic dimensional measurements from this early work are no longer available.

Diameter, specific gravity, and surface-area-to-volume ratio for downed woody 

fuels from the branches of 19 western conifer species based on size class and age are 

available; foliage properties for these species were not determined (van Wagtendonk 

et al. 1996). Tree- and stand-level characteristics of crown fuels of western conifers 

including spatial variability and loading are available (Cruz et al. 2003, Keane et al. 

2012, Reinhardt et al. 2006); no fuel particle properties were presented. Shen and 

Fletcher (2015) provided correlations for the geometrical properties of the foliage of four 
4

RESEARCH PAPER PSW-RP-269

species to be used in fire spread models but did not measure surface area or density, two 

properties known to affect fire behavior. Pickett (2008) measured physical dimensions 

of several fuels but did not report any prediction models for these properties, although 

Prince (2014) reported correlations for manzanita leaves. We are aware of no other 

work that has been done to measure or model the physical properties and dimensions of 

individual fuel elements for live wildland fuels in the United States. This lack of data 

for individual live fuel particles also occurs elsewhere in shrub-dominated systems (e.g., 

Papió and Trabaud 1990, Pereira et al. 1995) and highlights the need to develop predictive models for other fuel types so that solid fuels can be characterized completely. This 

report presents measured dimensions and physical properties of foliage samples for 10 

common plant species found in important fuel types in the United States (fig. 1) and the 

models developed from the measurements to predict these properties.

Douglas-fir

Lodgepole pine Sagebrush

Gambel oak

Fetterbush

Galberry

Sand pine

Chamise Manzanita

Ceanothus

Figure 1—Sample collection locations and illustrations of 10 common plants found in important wildland fuel types in the conterminous 

United States. Images from Britton and Brown (1913), Conrad (1987), and Powell (2013).
5

Physical Characteristics of Shrub and Conifer Fuels for Fire Behavior Models

Methods

As part of a project to determine the effects of radiant versus convective heating and 

live fuel moisture content on ignition of live fuels (Gallacher 2016; McAllister and 

Weise 2017; Weise et al. 2015; Yashwanth et al. 2015, 2016), physical properties of 10 

plants common to important wildland fuel types were determined by measurement 

(see tabulation below and figure 1.) These data are available (Gallacher et al. 2016) 

for use. Various models were fit to the data to develop predictive models to be used in 

conjunction with 3D fuel placement models and allometric models to fully describe a 

shrub and provide the detail necessary for shrub combustion models (fig. 2). 

Dry mass from

Weibull distribution

Moisture content 

specified by user

Fresh mass and 

water mass

Relative moisture 

content using 

stepwise regression

Predictor variables: M, R, md

, mf, mw

Response variables: L, W, t, D, N

Response variable (RV) 

with best model saved and 

that RV added to predictor variables

Response variable 

with best model saved and 

that RV added to predictor variables

Repeat until all response 

variables have a model saved

Surface area and foliage density 

using stepwise regression

Figure 2—Flow chart for fuel element 

property model development. M = moisture 

content, R = relative moisture content, L = 

length, W = width, N = needle length, t = 

thickness, D = stem diameter, mf = fresh 

mass, mw = water mass, and md = dry mass.
6

RESEARCH PAPER PSW-RP-269

Common name Scientific name Foliage

Chamise Adenostoma fasciculatum Hook & Arn. Needle

Douglas-fir Pseudotsuga menziesii (Mirb.) Franco var. 

glauca (Beissn.) Franco

Needle

Big sagebrush Artemisia tridentata Nutt. Needle-like

Lodgepole pine Pinus contorta Douglas ex Loudon var. 

latifolia Engelm. ex S. Watson

Needle

Sand pine Pinus clausa (Chapm. ex Engelm.) 

Vasey ex Sarg.

Needle

Eastwood’s manzanita Arctostaphylos glandulosa Eastw. Broadleaf

Hoaryleaf ceanothus Ceanothus crassifolius Torr. Broadleaf

Gambel oak Quercus gambelii Nutt. var. gambelii Broadleaf

Gallberry Ilex glabra (L.) A. Gray Broadleaf

Fetterbush Lyonia lucida (Lam.) K. Koch Broadleaf

Measurements

Physical dimensions, moisture content (MC), relative moisture content (RMC), and 

apparent density (ρ) were measured at the Brigham Young University Wildfire Lab 

in Provo, Utah, each month for 1 year. Typically, 25 replicates of each species were 

measured each month. All measurements were made within 48 hours of sample 

collection—nonlocal species were sealed in plastic bags and shipped overnight to 

Provo. The plastic bags were kept sealed and out of direct sunlight until measurements could be made. The 10 species were categorized as broadleaf or needle based 

on the shape of the foliage. Broadleaf samples consisted of whole, undamaged 

leaves while needle samples consisted of 2- to 6-cm branch tips with the foliage 

attached. Foliage samples were also categorized as new (current year) growth or old 

(prior year) growth:

Property Definition

Length Broadleaf: Distance from leaf base to leaf tip

Needle, needle-like: Length of stem

Width Broadleaf: Largest distance in direction perpendicular to length

Needle, needle-like: Largest distance between needle tips normal to 

length

Thickness Broadleaf: Distance from leaf top surface to bottom surface. Measured 

using calipers without crossing the main leaf vein

Needle length Needle: Average length of sample

Stem diameter Needle, needle-like: Diameter of stem holding needles

Mass Mass of sample
7

Physical Characteristics of Shrub and Conifer Fuels for Fire Behavior Models

Moisture content (dry basis, eq. 1) was estimated with a Computrac Max10002

moisture analyzer using a drying temperature of 95 °C; MC for live fuels ranges 

from 0 to 2.5 for many shrub species. Relative MC (Weatherley 1950) (eq. 2) was 

determined after soaking a sample in water for 24 to 48 hours before weighing to 

achieve full turgidity; RMC ranges from 0 to 1. Note that a calculation method 

using full turgid mass was proposed as an alternative method to determine specific 

gravity of small wood samples that eliminated the need to measure volume (Smith 

1954). In the present study, several leaves or branch sections were necessary to 

reach the required minimum mass (1 g) so the reported MC and RMC are averages 

of several fuel particles.

f d

d

m m

MC

m

− = (1)

f d

t d

m m

RMC

m m

− = − , (2)

where the mass subscripts f, d, and t denote fresh, dry, and turgid, respectively. 

Density was measured using Archimedes’ principle that the force exerted on a submerged object is equal to the mass of the displaced fluid (Fernandes and Rego 1998, 

Ryan and Pickford 1978, Sackett 1980). Each sample was submerged in silicone oil 

(Dow Corning® 704 Diffusion Pump Fluid) and the weight of the displaced fluid 

was recorded. Using the density of the oil (1.07 g cm-3), the volume of the sample 

was obtained. The presubmerged mass of the sample was used with the displaced 

volume to get the sample density. Oil was used instead of water to prevent the plant 

sample from absorbing the liquid into pores on the sample surface and to prevent 

fluid evaporation during mass measurements. Only whole leaves or needles were 

used, and three replicates were performed for each species each month. Aluminum 

6061 rectangular blanks were used to verify the procedure. The density of aluminum 6061 is 2.72 g cm-3 (Narender et al. 2013). The estimated density of aluminum 

based on 10 samples with a 95-percent confidence interval was 2.72 ± 0.008 g cm-3, 

indicating the validity of this approach to estimate density. Density was estimated 

for all species except chamise, big sagebrush, and lodgepole pine. Leaf external 

surface area for broadleaf species was obtained from images of each sample as 

has been done elsewhere (e.g., Weise et al. 2005). The surface area of one side of 

2 The use of trade or firm names in this publication is for reader information and does not 

imply endorsement by the U.S. Department of Agriculture of any product or service.
8

RESEARCH PAPER PSW-RP-269

each leaf and the leaf perimeter were measured using in-house computer vision 

algorithms written in MATLAB (Gallacher 2016). The total surface area was then 

calculated (eq. 3), where As is the total external surface area, Ai is the area of the 

image, and P is the leaf perimeter.

A = 2A + PT. s i (3)

Model Development

Before developing the property models, we determined if there were seasonal 

changes (Burgan and Susott 1991, Jolly et al. 2014, Philpot 1969, Weise et al. 2005) 

in the data using nonlinear mixed-effects models (Pinheiro and Bates 2000). Several functions of month were considered to model seasonal trends: no transformation, square, absolute value, power, sine and cosine. The significance of the seasonal 

term was determined by the F-statistic at a 99 percent significance level. 

MC and md were the initial variables used to develop the prediction models (fig. 

2). Dry mass was an input parameter for all the prediction models reported herein. 

We considered three two-parameter functions (beta, gamma, Weibull) to model 

dry mass frequency distribution. Forest growth and yield modelers frequently use 

the Weibull distribution to simulate distributions of biomass variables including 

the vertical distribution of foliage mass (e.g., Bailey and Dell 1973, Fleming 2001, 

Keyser and Smith 2010, Schreuder and Swank 1974). Other modelers prefer the beta 

distribution (Maguire and Bennett 1996). In the present study, the beta distribution could not be fit to three species when dry mass fell outside the interval [0, 1] 

even after scaling by the maximum observed value for the species. The gamma 

distribution generally performed slightly better than the Weibull distribution based 

on goodness of fit measures. However, the gamma parameter estimates were highly 

correlated (greater than 0.9) for all 10 species, and the Weibull estimates were not, 

so the Weibull distribution was selected to model dry mass of the fuel particles (eq. 

4). In this report, we chose the fitdist routine of the fitdistrplus package (R Core 

Team 2013) because it is open-source software. The parameter estimates presented 

here differ from those reported in Gallacher (2016), which were estimated using the 

wblfit routine in Matlab®. Goodness of fit of the Weibull distribution was evaluated 

with three statistics—the Kolmogorov-Smirnov, Anderson-Darling, and Cramervon Mises statistics and plots of the empirical and theoretical probability and cumulative distribution functions, quantile (Q-Q), and probability (P-P) plots. Because 

no single goodness of fit statistic captures characteristics of the entire function, 

visual assessment of the plots was favored (Delignette-Muller and Dutang 2015):
9

Physical Characteristics of Shrub and Conifer Fuels for Fire Behavior Models

= −

( )

( ) ( )

( ) ( ( )

(

) /

1

1

; , 1

; , l 1

,

n

;

b

b

d

md

a

a

d

m

d

b

b

d

F

b m

m a b

f m a b e

e

a

Q p

a

a b a p

− −

−

=

= − −

(4)

where f, F, and Q are the probability density, cumulative distribution, and inverse 

cumulative distribution functions, respectively (Rinne 2008).

Predictive models were developed using the procedure shown in figure 2, which 

includes an iterative step. For each of the 10 species, several models were fit for 

each physical property using forward and backward stepwise regression. The best 

model for each property was selected using the adjusted R2 value (Ezekiel 1930, 

Mason et al. 1989) and the Bayesian Information Criterion (BIC), (Burnham and 

Anderson 2004). From known MC and md, we calculated mf and water mass 

mH20 = mf – md by rearranging eq. 1. RMC was regressed against MC, mf, md, and 

mH20; equations for the physical properties were developed simultaneously using 

RMC, MC, mf , md, and mH20. The physical property response variable with the best 

fit was then added to the set of predictor variables, and the equations for the remaining physical properties were refit with the augmented set of predictor variables. This 

iterative process was repeated until equations for each of the physical properties 

were developed. Equations for As and ρ were fit via stepwise regression using all 

previously defined variables as predictor variables.

Model Use

In addition to providing basic physical properties of the fuel particles used to interpret the results of the radiant/convective heating study, the equations we developed 

can be used in a predictive framework to simulate shrubs as in Parson et al. (2011) 

and Prince et al. (2014). The process to accomplish this is similar to the framework in figure 2. First, a value for desired MC is specified. The desired number 

Property Unit

MC, RMC proportion

L, W, N cm

T, D mm

mf, md, mw g

As cm2
10

RESEARCH PAPER PSW-RP-269

of random values for the probability p is then generated (often generated from a 

uniform [0, 1] distribution), and the inverted cumulative distribution function (Q, 

eq. 4) generates the dry mass (md) using p and the estimated Weibull parameters (â, 

b

ˆ) (Fishman 1997); mf

 and mw are then calculated using equation 1. The physical 

properties and RMC then follow from the several equations developed above.

Results and Discussion

Over the 2-year period of the study, 2,743 foliage and branch samples were measured (Gallacher et al. 2016). The number of fuel particles measured ranged from 

150 for Gambel oak to 333 for chamise. Gambel oak is deciduous so its foliage was 

available for collection for only part of the year; similarly, access to the Douglas-fir 

and lodgepole pine sites was affected by snow.

Water Content

Seasonal MC and RMC curves from the same region of the country exhibited 

similar but not identical behavior (fig. 3). California species had the lowest MC on 

average. Coniferous species (Douglas-fir, lodgepole pine, and sand pine) had consistently higher MC than other species from the same region. California and Rocky 

Mountain species had the lowest MC during the summer and fall months, and 

southern species experienced a maximum in MC during late summer. The lone 

deciduous species, Gambel oak, showed a strong relationship between MC and 

the growing season. Local fire seasons are nominally March through December 

in southern California (all year during drought years), May/June through October 

for the northern Rocky Mountains, and March through November for the southern 

coastal plain (Hull et al. 1966; Werth 2015a, 2015b). Moisture content is usually 

Species Count

Chamise 333

Douglas-fir 275

Big sagebrush 300

Lodgepole pine 220

Sand pine 290

Eastwood’s manzanita 300

Hoaryleaf ceanothus 275

Gambel oak 150

Gallberry 300

Fetterbush 300
11

Physical Characteristics of Shrub and Conifer Fuels for Fire Behavior Models

Month

Apr

May

Jun

Jul

AugSep

Oct

NovDec

Jan

Feb

Mar

Apr

r = 0.55

Fetterbush

r = 0.43

Chamise

r = 0.35

Gallberry

r = 0.76

Ceanothus

r = 0.50

Sand pine

r = 0.69

Manzanita

r = 0.59

Lodgepole pine

r = 0.51

Gambel oak

r = 0.87

Douglas−fir

AprMayJunJulAugSepOctNovDecJanFebMarApr

r = 0.71

Sagebrush

MC

RMC

Moisture content and relative moisture content

2.0

1.5

1.0

0.5

0

2.0

1.5

1.0

0.5

0

2.0

1.5

1.0

0.5

0

2.0

1.5

1.0

0.5

0

2.0

1.5

1.0

0.5

0

Figure 3—Yearly patterns for foliage moisture content (MC) and relative moisture content (RMC) for 10 live fuels from three regions of 

the United States.
12

RESEARCH PAPER PSW-RP-269

lowest during the local fire season, although the agreement is far from perfect. The 

correlation between monthly mean MC and RMC was generally low (fig. 3); this 

is due in part to the small number of months. However, as in Jolly et al. (2014), we 

also found a statistically significant (probability of greater F-statistic <1 × 10-12)

relationship between the water mass and the RMC (fig. 4). While our fitted model 

accounted for less of the variation (43 percent) in relative MC than Jolly’s (2014) 

model (59 percent), the range of RMC in the present study (10 species) was greater 

(0.25 to 0.85 vs. 0.69 to 0.89) (1 species).

Only 13 percent of the nonmoisture sample characteristics exhibited 

seasonal changes. Summary statistics for the species characteristics that did 

not exhibit seasonal trends are in tables 1 and 2. If a particular characteristic 

exhibited a seasonal trend (such as the density of manzanita leaves), the figure 

illustrating the trend is identified in the table. Significant monthly trends for 

density (manzanita and Gambel oak), surface area (gallberry), thickness (fetterbush, Gambel oak, and manzanita), and width (gallberry) were observed (figs. 

5 through 7). Surface area and width for gallberry both followed a similar trend 

and were correlated (fig. 5); large leaves were observed in April, small leaves 

in July, and relatively large leaves from August to the next April. The relatively 

high correlation between surface area and width is not surprising if the assumed 

leaf shape is elliptical; the surface area of an ellipse is a function of its major 

(length) and minor (width) axes (AS = πLW). Density of manzanita was high in 

April, decreased rapidly to a low in August, and then increased slowly through 

March (fig. 6). Density for Gambel oak showed the opposite trend, with lows 

in May and October and a high in August. Thickness for fetterbush, Gambel 

oak, and manzanita all showed the same pattern: high in the spring, low in the 

summer, then increasing slowly through the rest of the sample period (fig. 7). 

Changes in density and thickness for manzanita compared to Gambel oak show 

some interesting relationships. Thickness and density for manzanita seemed to 

be correlated fairly well with each other (R2 = 0.76), but the observed seasonal 

changes in thickness and density did not correlate solely to changes in MC 

(R2

density = 0.25, R2thickness = 0.12). The trends for Gambel oak thickness and 

density were not well correlated (R2 = 0.10). The trend for Gambel oak thickness 

is at least partly due to MC (R2 = 0.40), while that for density had no relationship to MC (R2

 = 0.00).
13

Physical Characteristics of Shrub and Conifer Fuels for Fire Behavior Models

0 0.2 0.4 0.6 0.8 1.0

0.3

0.4

0.5

0.6

mf − md

mf

= 0.24 + 0.33

mf − md

mt− md

mf

mf

−

md

mf − md

mt − md

F1,90 = 68.94, p < 0.001

R2

 = 0.43

Figure 4—Relationship between water mass and relative moisture content for combined data from 10 different live fuels.
14

RESEARCH PAPER PSW-RP-269

Table 1—Yearly mean and standard deviation for measured foliage characteristics—broadleaf species

Species Density Length Width Thickness Surface area Fresh mass

Grams per cubic 

centimeter - - - - - - - Centimeters- - - - - - - - - Millimeters - -

Square

- - centimeters - - - - - Grams - - -

Manzanita a 3.77 0.56 2.14 0.46 b 13.0 4.30 0.33 0.13

Ceanothus 0.99 0.03 1.60 0.28 1.23 0.23 0.57 0.11 3.2 0.97 0.09 0.04

Gambel oak a 6.51 1.63 4.33 1.36 b 29.8 15.08 0.23 0.13

Fetterbush 0.89 0.04 5.25 1.06 2.51 0.63 b 19.2 8.01 0.28 0.12

Gallberry 0.89 0.03 3.89 0.73 c 0.32 0.06 c 0.12 0.05

Note: If the characteristic exhibited a significant seasonal trend, the figure that illustrates the trend is listed.

a See figure 6.

b

 See figure 7.

c See figure 5.

Table 2—Yearly mean and standard deviation for measured foliage characteristics—needle species

Species Density Length Width Needle length Stem diameter Fresh mass

Grams per cubic

- - centimeter - - - - - - - - - - - - - - - Centimeters - - - - - - - - - - - - - - - Millimeters - - - - - Grams - - -

Douglas-fir 0.95 0.03 3.00 0.97 4.28 0.70 2.01 0.50 1.44 0.45 0.60 0.26

Lodgepole pine 2.24 0.45 8.57 2.45 5.44 0.97 3.14 1.00 1.33 0.47

Sand pine 0.98 0.03 2.47 0.92 7.02 2.35 5.60 1.09 1.35 0.41 0.67 0.25

Big sagebrush 4.42 0.47 1.22 0.39 0.22 0.13

Chamise 3.93 0.59 1.05 0.30 0.14 0.07

Month

Apr

Mar

Jun

Jul

AugSep

Oct

NovDec

Jan

Feb

Mar

Apr

2.0

1.5

1.0

0.5

0

20

15

10

5

0

Width

Surface area r = 0.88

Surface area (cm2

)

Width (mm)

Figure 5—Monthly leaf surface area and width values for gallberry. Vertical lines indicate range of the mean ± the standard 

deviation. The month value is dithered to separate width and surface area data.
15

Physical Characteristics of Shrub and Conifer Fuels for Fire Behavior Models

Month

Apr

May

Jun

Jul

AugSep

Oct

NovDec

Jan

Feb

Mar

Apr

1.10

1.05

1.00

0.95

0.90

0.85

Gambel oak

Manzanita

Density (g cm−3)

Figure 6—Monthly foliage density values for manzanita and Gambel oak. Vertical lines indicate range of the mean ± the standard 

deviation. The month value is dithered to separate species data.

Month

Thickness (mm)

Apr

Mar

Jun

Jul

AugSep

Oct

NovDec

Jan

Feb

Mar

Apr

0

0.2

0.4

0.6

0.8

1.0

Manzanita

Gambel oak

Fetterbush

Figure 7—Monthly leaf thickness values for manzanita, Gambel oak, and fetterbush. Vertical lines indicate range of the mean ± the 

standard deviation. The month value is dithered to separate species data.
16

RESEARCH PAPER PSW-RP-269

Mass Distribution

As can be seen in figure 8 and the appendix, the 2-parameter Weibull distribution 

fit a variety of empirical distributions of fuel particle mass. We separated the 10 

species by the scale parameter (â) into three groups. Estimates for the Weibull 

scale and shape parameters and the standard error of the estimates are contained in 

table 5 in the appendix. With the exception of lodgepole pine, the scale estimates 

were similar (appendix). There were no distinct seasonal trends in the mass data 

so the fitted distributions can be used throughout the year to simulate foliage mass. 

Although the data represent a random sample of the foliage within each species, 

caution should be used when applying these distributions. We assumed that the 

foliage/fuel particles did not change appreciably throughout the shrub or tree crown 

vertically. This assumption is valid for some species and not for others that have 

different leaf types in response to light. These are the first such measurements for 

some of these species.

Prediction Models

Regression models to predict four to six physical characteristics were developed. 

These prediction models for the various fuel element characteristics are shown 

in tables 3 and 4 for the broadleaf and needle species, respectively. The order of 

presentation in the table indicates the order in which they were developed and 

should be applied as they are interdependent per figure 2. The strength of each 

model is shown by the amount of data variation accounted for by the model as 

measured by R2. For the overall collection of models, 36 percent have R2 values 

greater than 0.7, and 72 percent have an R2 value greater than 0.5. When broken 

out by species type, 50 percent of the broadleaf species models have an R2 value 

greater than 0.7, and 90 percent have values greater than 0.5. Models for the 

needle species accounted for less of the data variation, with 17 and 48 percent of 

the models having an R2 value greater than 0.7 and 0.5, respectively. The difference between needle and broadleaf species models in the amount of variation 

explained likely could have been reduced if the number of needles per sample 

was measured for the needle species. This was not practical. Many of the models 

suffer from severe multicollinearity. This issue is inherent in any dataset comparable to the one presented here owing to plant growth patterns and therefore 

cannot be avoided when trying to develop prediction models for foliage characteristics. However, the models can still be useful for prediction purposes as long 

as the relationships between measured characteristics in the model-development 

dataset are the same as the relationships between characteristics in the model-use 

dataset (Gujarati 2003). 
17

Physical Characteristics of Shrub and Conifer Fuels for Fire Behavior Models

0 0.5 1.0 1.5 2.0

0

2

4

6

8

10

Leaf mass (g)

PDF

0

2

4

6

8

10

Ceanothus

Gallberry

Chamise

0

2

4

6

8

10

Gambel oak

Manzanita

Leaf mass (g)

0 0.5 1.0 1.5 2.0

0 0.5 1.0 1.5 2.0

0 0.5 1.0 1.5 2.0

0

2

4

6

8

10

Sand pine

Lodgepole pine

Douglas-fir

Sagebrush

Fetterbush

Figure 8—Fitted Weibull distributions for mass of foliage particles for 10 species of live fuels from the United States. All species are 

plotted on left graph; right graphs group species with similar scale (â) parameters. PDF = probability density function.
18

RESEARCH PAPER PSW-RP-269

Table 3—Regression equations developed to predict physical properties of foliage for several broadleaf 

species in the United States

Species and 

physical property R2

adj Regression equation

Ceanothus:

RMC 0.676

Length 0.615

Width 0.523

Thickness 0.508

Density 0.523

SA 0.873

Fetterbush:

RMC 0.411

Length 0.841

Width 0.809

Thickness 0.662

Density 0.737

SA 0.948

Gallberry:

RMC 0.214

Width 0.740

Length 0.714

Thickness 0.597

Density 0.599

SA 0.905

Gambel oak:

RMC 0.443

Length 0.912

Width 0.838

Thickness 0.720

Density 0.879

SA 0.937
19

Physical Characteristics of Shrub and Conifer Fuels for Fire Behavior Models

Species and 

physical property R2

adj Regression equation

Manzanita:

RMC 0.600

Length 0.758

Width 0.631

Thickness 0.619

Density 0.633

SA 0.918

Note: R2

adj is the adjusted R2

 value. The variables are relative moisture content (RMC), surface area (SA), moisture content (M), length (L), width 

(W), thickness (t), fresh mass (mf), dry mass (md), and water mass (mw).

Table 3—Regression equations developed to predict physical properties of foliage for several broadleaf 

species in the United States (continued)

Table 4—Regression equations developed to predict physical properties of foliage for several needle species 

in the United States

Species and physical 

property R2adj Regression equation

Chamise:

RMC 0.631

Diameter 0.576

Length 0.392

Douglas-fir:

RMC 0.846

Length 0.723

NL 0.421

Width 0.524

Diameter 0.418

Density 0.303

Lodgepole pine:

RMC 0.773

Diameter 0.614

Length 0.524
20

RESEARCH PAPER PSW-RP-269

Species and physical 

property R2adj Regression equation

NL 0.45

Width 0.31

Sagebrush:

RMC 0.821

Diameter 0.493

Length 0.493

Sand pine:

RMC 0.24

Length 0.634

Width 0.355

NL 0.481

Diameter 0.224

Density 0.571

Note: R2

adj is the adjusted R2

 value. The variables are relative moisture content (RMC), needle length (NL), moisture content (M), length (L), width (W), 

diameter of stem (D), fresh mass (mf), dry mass (md), and water mass (mw).

Table 4—Regression equations developed to predict physical properties of foliage for several needle species 

in the United States (continued)

None of the models developed here contain a seasonal parameter. Although this 

lack of a seasonal parameter is not typical for plant growth models, the constancy of 

the measured data throughout the year made the inclusion of a seasonal parameter 

unnecessary. The measured characteristics that did change with season changed in 

concert with other characteristics (usually MC) so that the single prediction model 

is valid for the whole year. Although some of the needle species, particularly sand 

pine, exhibited visual seasonal variation in the shape and size of individual fuel 

samples, the statistical test for seasonal trends did not detect this. The variability in 

the sand pine data rendered differences based on growing season indistinguishable 

from the general trends. To illustrate the range of variability associated with the 

fitted models, three plots illustrating high (0.95), moderate (0.49), and low (0.24) R2

values are shown in figure 9.
21

Physical Characteristics of Shrub and Conifer Fuels for Fire Behavior Models

0 10 20 30 40 50

0

10

20

30

40

50

Predicted (cm2

)

Measured (cm2)

Fetterbush surface area

R2 = 0.95

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Sagebrush stem diameter

Predicted (mm)

Measured (mm)

R2 = 0.49

0.0 0.2 0.4 0.6 0.8 1.0

Predicted (mm)

0.0

0.2

0.4

0.6

0.8

1.0

Measured (mm)

R2 = 0.24

Sand pine relative moisture content

Figure 9—Representative plots for prediction models showing fetterbush surface area (top, R2 = 0.95), sagebrush diameter 

(middle, R2 = 0.49), and sand pine relative moisture content (bottom, R2 = 0.24).
22

RESEARCH PAPER PSW-RP-269

Conclusions

Physical properties and dimensions for 10 live fuels in the United States were measured throughout a 1-year period to determine if the properties and flammability 

changed over the year. Broadleaf samples consisted of whole leaves; needle samples 

consisted of a small length of branch with the foliage attached. Although sagebrush 

foliage comprises leaves rather than needles, the sagebrush samples were characterized as needle samples because the leaves are so small. Measurements included 

MC, RMC, apparent density, length, width, needle length, stem diameter, leaf 

thickness, leaf surface area, fresh mass, volatiles content, fixed-carbon content, ash 

content, and lipid content. We developed and used an alternate method for measuring foliage apparent density that used oil instead of water. Whole-leaf surface 

area measurements not requiring an assumed idealized shape were reported. The 

two-parameter Weibull distribution modeled foliage dry mass distributions to allow 

a user to calculate the dry mass for a single leaf or branch tip. Prediction equations 

based on sample dry mass and MC were developed for each measured property. 

Most measured sample characteristics did not change throughout the year, making 

the use of a seasonal parameter unnecessary. Sample characteristics that did change 

throughout the year were associated with changes in the other characteristics 

(usually MC) so that the models developed here are accurate for the entire year. It is 

anticipated that these models can be used in conjunction with bulk fuel description 

models and fuel placement models such as L-systems to describe the fuel matrix in 

detail for comprehensive fire spread models.

English Equivalents

When you know: Multiply by: To find:

Centimeters (cm) 0.394 Inches

Millimeters (mm) 0.0394 Inches

Square centimeters (cm2) 0.155 Square inches

Cubic centimeters (cm3) 0.061 Cubic inches

Cubic meters (m3) 35.3 Cubic feet

Grams (g) 0.0352 Ounces

Kilograms (kg) 2.205 Pounds

Grams per cubic cm (g/cm3) 0.0000624 Pounds per cubic foot
23

Physical Characteristics of Shrub and Conifer Fuels for Fire Behavior Models

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Appendix: Two-Parameter Weibull Distribution for 

Mass Data

The empirical and fitted probability density (PDF) functions, empirical and fitted 

cumulative distribution functions (CDF), empirical and fitted quantiles (Q-Q plot), 

and empirical and fitted probabilities (P-P plot) for each species are presented here. 

A summary of the fitted distribution including correlation of the scale (a) and shape 

(b) parameters as well as details of the goodness of fit statistics (KolmogorovSmirnov, Anderson-Darling, and Cramer-von Mises) are also presented. A 95thpercentile confidence interval for the fitted CDF, represented by the grey band, 

was estimated using parametric bootstrapping with the bootdist function in the 

fitdistrplus package (Delignette-Muller and Dutang 2015).

The species plots are arranged in the order of appearance in the table above in 

figure 10. For each species, the upper left graph is of the fitted PDF and a histogram of 

the data. The lower left graph illustrates the empirical CDF and the 95 percent confidence interval for the fitted CDF. The upper right graph plots the empirical and fitted 

quantiles while the lower right graph shows the fitted and empirical probabilities.
33

Physical Characteristics of Shrub and Conifer Fuels for Fire Behavior Models

Table 5—Parameter estimates (â,bˆ) and goodness of fit measures of the 

2-parameter Weibull distribution for fuel particle oven-dry mass

Species Scale Shape ρâ,bˆ AIC

â Sâ bˆ Sb

ˆ

Ceanothus 0.100 0.003 2.508 0.107 0.337 -1055

Gallberry 0.134 0.003 2.685 0.120 0.321 -984

Chamise 0.157 0.004 2.128 0.082 0.333 -890

Gambel oak 0.261 0.012 1.929 0.123 0.323 -215

Big sagebrush 0.258 0.009 1.796 0.076 0.330 -421

Fetterbush 0.316 0.008 2.474 0.105 0.331 -442

Manzanita 0.373 0.009 2.621 0.107 0.333 -379

Douglas-fir 0.677 0.018 2.447 0.108 0.330 18

Sand pine 0.753 0.016 2.890 0.131 0.313 21

Lodgepole pine 1.489 0.036 2.941 0.142 0.332 292

Goodness of fit

Kolmogorov-Smirnov Anderson-Darling Cramér-von Mises

Ceanothus 0.114 R 5.442 R 0.904 R

Gallberry 0.050 NR 0.933 R 0.158 R

chamise 0.077 R 3.954 R 0.552 R

Gambel oak 0.068 NR 0.834 R 0.119 NR

Big sagebrush 0.061 NR 2.192 R 0.245 NR

Fetterbush 0.088 R 3.388 R 0.539 R

Manzanita 0.073 NR 3.749 R 0.529 R

Douglas-fir 0.077 NR 2.590 R 0.428 R

Sand pine 0.041 NR 0.509 NR 0.066 NR

Lodgepole pine 0.068 NR 2.389 R 0.329 R

Note: Sâ, Sb

ˆ, ρâ,bˆ are the standard errors for the parameters estimates and the correlation

of the estimates, respectively. AIC is the Akaike Information Criterion. For each

measure of goodness of fit, the statistic and its significance are reported. R indicates

rejection of the null hypothesis at α = 0.05, NR indicates the null hypothesis was not rejected.
34

RESEARCH PAPER PSW-RP-269

Ceanothus

PDF

0.05 0.10 0.15 0.20 0.25

0

2

4

6

8

10

12

14

0.05 0.10 0.15 0.20

0.05

0.10

0.15

0.20

0.25

Fitted quantiles

Empirical quantiles

0.05 0.10 0.15 0.20 0.25

Leaf mass (g)

CDF

0.05 0.10 0.15 0.20 0.25

0

0.2

0.4

0.6

0.8

1.0

0.2 0.4 0.6 0.8 1.0

0

0.2

0.4

0.6

0.8

1.0

Fitted probabilities

Empirical probabilities

Figure 10—Graphical measures of goodness of fit of Weibull distribution for foliage mass for 10 live fuels in the United States. 

PDF = fitted probability density, CDF = cumulative distribution functions. 
35

Physical Characteristics of Shrub and Conifer Fuels for Fire Behavior Models

Gallberry

PDF

0.05 0.10 0.15 0.20 0.25 0.30

0

2

4

6

8

0.05 0.10 0.15 0.20 0.25

0.05

0.10

0.15

0.20

0.25

0.30

Fitted quantiles

Empirical quantiles

0.05 0.10 0.15 0.20 0.25 0.30

0.0 0.2 0.4 0.6 0.8 1.0

Leaf mass (g)

CDF

0.05 0.10 0.15 0.20 0.25 0.30

0

0.2

0.4

0.6

0.8

1.0

0 0.2 0.4 0.6 0.8 1.0

0

0.2

0.4

0.6

0.8

1.0

Fitted probabilities

Empirical probabilities

Figure 10—Continued. 
36

RESEARCH PAPER PSW-RP-269

Chamise

PDF

0.1 0.2 0.3 0.4 0.5

0

1

2

3

4

5

6

0 0.1 0.2 0.3

0.1

0.2

0.3

0.4

0.5

Fitted quantiles

Empirical quantiles

0.1 0.2 0.3 0.4 0.5

0.0 0.2 0.4 0.6 0.8 1 .0

Leaf mass (g)

CDF

0.1 0.2 0.3 0.4 0.5

0

0.2

0.4

0.6

0.8

1.0

0 0.2 0.4 0.6 0.8 1.0

0

0.2

0.4

0.6

0.8

1.0

Fitted probabilities

Empirical probabilities

Figure 10—Continued. 
37

Physical Characteristics of Shrub and Conifer Fuels for Fire Behavior Models

Gambel oak

PDF

0.1 0.2 0.3 0.4 0.5

1

2

3

4

0.1 0.2 0.3 0.4 0.5 0.6

0.1

0.2

0.3

0.4

0.5

Fitted quantiles

Empirical quantiles

0.1 0 .2 0.3 0 .4 0.5

0.0 0 .2 0.4 0 .6 0.8 1 .0

CDF

0.1 0.2 0.3 0.4 0.5

0.2

0.4

0.6

0.8

1.0

0.2 0.4 0.6 0.8 1.0

0.2

0.4

0.6

0.8

1.0

Fitted probabilities

Empirical probabilities

Leaf mass (g)

0

0

0

0

0

0

Figure 10—Continued. 
38

RESEARCH PAPER PSW-RP-269

Sagebrush

PDF

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Fitted quantiles

Empirical quantiles

0.0 0 .1 0.2 0 .3 0.4 0 .5 0.6 0 .7

0.0 0 .2 0.4 0 .6 0.8 1 .0

CDF

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0

0.2

0.4

0.6

0.8

1.0

0 0.2 0.4 0.6 0.8 1.0

0

0.2

0.4

0.6

0.8

1.0

Fitted probabilities

Empirical probabilities

Leaf mass (g)

Figure 10—Continued. 
39

Physical Characteristics of Shrub and Conifer Fuels for Fire Behavior Models

Fetterbush

PDF

0.1 0.2 0.3 0.4 0.5 0.6 0.7

0

1

2

3

0 0.1 0.2 0.3 0.4 0.5 0.6

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Fitted quantiles

Empirical quantiles

0.1 0 .2 0.3 0 .4 0.5 0 .6 0.7

0.0 0 .2 0.4 0 .6 0.8 1 .0

CDF

0.1 0.2 0.3 0.4 0.5 0.6 0.7

0

0.2

0.4

0.6

0.8

1.0

0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Fitted probabilities

Empirical probabilities

Leaf mass (g)

Figure 10—Continued. 
40

RESEARCH PAPER PSW-RP-269

Manzanita

PDF

0.2 0.4 0.6 0.8

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.2 0.4 0.6

0.2

0.4

0.6

0.8

Fitted quantiles

Empirical quantiles

0.2 0 .4 0.6 0 .8

0.0 0 .2 0.4 0 .6 0.8 1 .0

CDF

0.2 0.4 0.6 0.8

0.2

0.4

0.6

0.8

1.0

0 0.2 0.4 0.6 0.8 1.0

0.2

0.4

0.6

0.8

1.0

Fitted probabilities

Empirical probabilities

Leaf mass (g)

0

0 0

Figure 10—Continued. 
41

Physical Characteristics of Shrub and Conifer Fuels for Fire Behavior Models

Douglas−fir

PDF

0.5 1.0 1.5

0.5

1.0

1.5

0.2 0.4 0.6 0.8 1.0 1.2 1.4

0.5

1.0

1.5

Fitted quantiles

Empirical quantiles

0.5 1 .0 1.5

0.0 0 .2 0.4 0 .6 0.8 1 .0

CDF

0.5 1.0 1.5

0.2

0.4

0.6

0.8

1.0

0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Fitted probabilities

Empirical probabilities

Leaf mass (g)

0

0

0

0

Figure 10—Continued. 
42

RESEARCH PAPER PSW-RP-269

Sand pine

PDF

0.2 0.4 0.6 0.8 1.0 1.2 1.4

0.5

1.0

1.5

0.2 0.4 0.6 0.8 1.0 1.2 1.4

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Fitted quantiles

Empirical quantiles

0.2 0 .4 0.6 0 .8 1.0 1 .2 1.4

0.0 0 .2 0.4 0 .6 0.8 1 .0

CDF

0.2 0.4 0.6 0.8 1.0 1.2 1.4

0.2

0.4

0.6

0.8

1.0

0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Fitted probabilities

Empirical probabilities

Leaf mass (g)

0

0

Figure 10—Continued. 
43

Physical Characteristics of Shrub and Conifer Fuels for Fire Behavior Models

Lodgepole pine

PDF

0.5 1.0 1.5 2.0 2.5 3.0

0

0.2

0.4

0.6

0.8

0.5 1.0 1.5 2.0 2.5

0.5

1.0

1.5

2.0

2.5

3.0

Fitted quantiles

Empirical quantiles

0.5 1 .0 1.5 2 .0 2.5 3 .0

0.0 0 .2 0.4 0 .6 0.8 1 .0

CDF

0.5 1.0 1.5 2.0 2.5 3.0

0

0.2

0.4

0.6

0.8

1.0

0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Fitted probabilities

Empirical probabilities

Leaf mass (g)

Figure 10—Continued. 

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