United States

Department

of Agriculture

Forest Service

Rocky Mountain

Research Station

Research Paper 

RMRS-RP-98

September 2012

Spatial Variability of Wildland Fuel 

Characteristics in Northern 

Rocky Mountain Ecosystems

Robert E. Keane, Kathy Gray, Valentina Bacciu

Silver Mountain

Big Hole

Tenderfoot

Lubrecht

Ninemile

Dry Lake

Helena

Boise

Salt

Lake

City

Las

Vegas

FuelVar Study Sites

October 2012
Keane, Robert E.; Gray, Kathy; Bacciu, Valentina. 2012. Spatial variability of 

wildland fuel characteristics in northern Rocky Mountain ecosystems. Res. Pap. 

RMRS-RP-98. Fort Collins, CO: U.S. Department of Agriculture, Forest Service, 

Rocky Mountain Research Station. 56 p.

Abstract

We investigated the spatial variability of a number of wildland fuel characteristics 

for the major fuel components found in six common northern Rocky Mountain 

ecosystems. Surface fuel characteristics of loading, particle density, bulk density, and 

mineral content were measured for eight fuel components—four downed dead woody 

fuel size classes (1, 10, 100, 1000 hr), duff, litter, shrub, and herb—on nested plots 

located within sampling grids to describe their variability across spatial scales. We also 

sampled canopy bulk density, biomass, and cover for each plot in the grid. The spatial 

distribution and variability of surface and canopy fuel characteristics are described 

using the variance, spatial autocorrelation, semi-variograms, and Moran’s I. We found 

that all fuels had high variability in loading (two to three times the mean), and this 

variability increased with the size of fuel particle. We also found that fuel components 

varied at different scales, with fine fuels varying at scales of 1 to 5 m, coarse fuels at 

10 to 150 m, and canopy fuels at 100 to 500 m. Findings and data from this study 

can be used to sample, describe, and map fuel characteristics, such as loading, at 

the appropriate spatial scales to accommodate the next generation of fire behavior 

prediction models.

Keywords: wildland fire, biomass, landscape ecology, woody debris, spatial scale, 

mineral content, particle density, bulk density, loading

Authors

Robert E. Keane is a Research Ecologist with the U.S. Department of Agriculture, Forest 

Service, Rocky Mountain Research Station at the Missoula Fire Sciences Laboratory in 

Montana. Since 1985, Keane has developed various ecological computer models for 

research and management applications. His recent research includes (1) developing 

ecological computer models for exploring landscape, fire, and climate dynamics; 

(2) describing, classifying, and mapping fuel characteristics; (3) investigating the 

ecology and restoration of whitebark pine; and (4) conducting fundamental wildland 

fuel science. He received his B.S. degree in Forest Engineering from the University 

of Maine, his M.S. degree in Forest Ecology from the University of Montana, and his 

Ph.D. degree in Forest Ecology from the University of Idaho.

Kathy Gray is an Assistant Professor at California State University, Chico. She received 

her Ph.D in Mathematics from the University of Montana in Missoula. Her research 

interests are (1) hierarchical modeling, (2) quantitative ecology, (3) sustainability, and 

(4) climate change.

Valentina Bacciu is a Scientist with the Euro-Mediterranean Center for Climate 

Change, IAFENT Division, Department of Economic and Woody Plant Ecosystems, 

University of Sassari. Her research includes (1) the analysis of the relationship between 

weather/climate and fire, (2) the description and mapping of fuel characteristics from 

extrinsic and intrinsic point of view, and (3) the investigation of first order fire effect 

modeling approaches. She received her Ph.D. in Agrometeorology and Ecophysiology 

of Agricultural and Natural Ecosystems from the University of Sassari, Italy.
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Acknowledgments

We acknowledge Aaron Sparks, Christy Lowney, Signe Leirfallom, Violet Holley, Brian 

Izbicki, and Greg Cohn, Rocky Mountain Research Station, for countless hours spent 

sampling, collecting, measuring, and analyzing fuels; and Duncan Lutes and Signe 

Leirfallom, Rocky Mountain Research Station, for technical reviews.

This work was funded by the National Fire Plan, Rocky Mountain Research 

Station Fire, Fuels, and Smoke Program, and U.S. Forest Service Fire and Aviation 

Management.

Research Summary

Wildland fuel is the one factor that can be directly manipulated to achieve 

management goals, such as restoring ecosystems, lowering fire intensity, minimizing 

plant mortality, and reducing erosion. However, many fire managers find it difficult 

to measure, describe, and map wildland fuels because the great variability of the 

characteristics of the fuelbed components over space and time makes it difficult to 

accurately predict fire behavior and effects. Few researchers have quantified this 

variability over space to understand its effect on fire spread, burning intensity, and 

ecological effects. In this study, we investigated the spatial variability of a number of 

fuel characteristics of the major surface and canopy fuel components that comprise 

northern Rocky Mountain forest and range fuelbeds. Surface fuel characteristics 

of (1) loading, (2) particle density, (3) bulk density, and (4) mineral content were 

measured for eight surface fuel components—four downed dead woody fuel size 

classes (1, 10, 100, 1000 hr), duff plus litter, shrub, and herb—on sampling grids at 

nested sampling intensities. Canopy bulk density, fuel load, and cover were estimated 

from measured tree population data to describe canopy fuel variability. We describe 

the spatial distribution of fuel characteristics along with their variance using spatial 

autocorrelation, semi-variograms, and Moran’s I. We found that most fuel components 

have high variability (greater than 100 percent of the mean), and this variability 

increases with the size of fuel particles. We also found that fuel components vary at 

different scales with smaller fuel particles varying over 1 m scales, large logs varying 

over 100 m, and canopy fuel attributes varying over 400 m. Findings and data from 

this study can be used to map fuel characteristics, such as loading, at finer scales to 

accommodate the next generation of fire behavior prediction models.
Contents

Introduction...........................................................................1

Background.....................................................................3

Objectives..............................................................................7

Methods.................................................................................8

Sampled Fuel Properties..................................................8

Study Sites.......................................................................8

Field Methods ...............................................................12

Laboratory Measurements .............................................17

Analysis.........................................................................18

Results..................................................................................21

Fuel Variability ..............................................................22

Spatial Variability ..........................................................32

Discussion............................................................................41

Study Findings...............................................................42

Study Limitations...........................................................44

Research and Management Implications .......................46

Summary and Conclusions...................................................47

References ...........................................................................49
USDA Forest Service RMRS-RP-98. 2012. 1

Introduction

Wildland fuel is important to fire managers because, unlike weather, topography, and wind, it is the one factor that can be directly manipulated to achieve 

management goals, such as restoring ecosystems, lowering fire intensity, reducing 

fire spread, minimizing plant mortality, and reducing erosion (Graham and others 

2004; Ingalsbee 2005; Reinhardt and others 2008). Fuel characteristics are critical 

inputs into the fire behavior and effects models that are used to plan, prioritize, design, and implement important fuel treatments that could to save lives and property 

(Andrews 2008; Reinhardt and Keane 1998). Fuelbed information is also used to 

predict smoke emissions (Ottmar 1983; Hardy and others 1999), quantify carbon 

pools (Reinhardt and Holsinger 2010), describe wildlife habitat (Bate and others 

2004), and evaluate site productivity (Brais and others 2005; Hagan and Grove 

1999; Woodall and Nagel 2006). A comprehensive description of surface and 

canopy fuels is needed for nearly all phases of fire management, including fighting wildfires (Chen and others 2006; Graham and others 2004; Ohlson and others 

2006), implementing prescribed burns (Agee and Skinner 2005), describing fire 

danger (Deeming and others 1977), and predicting fire effects (Ottmar and others 

1993; DeBano and others 1998). In summary, effective fire management depends 

on comprehensive, consistent, and accurate descriptions of the characteristics of 

wildland fuel that dictate fire behavior and effects.

Many fire managers find it difficult to measure, describe, and map wildland 

fuels for a number of reasons. Surface fuelbeds consist of a diverse number of 

components that are often differentiated by the fire behavior and effects modeling 

objectives (Table 1). A description of fuels for fire behavior prediction, for example, would require the downed dead woody surface fuel loadings to be stratified by 

particle size classes based on their rate of drying (Fosberg 1970). Fuel components 

can be specified by size (particle diameter ranges), condition (dead or alive; dry 

or moist), and material (woody or non-woody; shrub or herbaceous; sound or rotten). And each of these diverse components has different properties that influence 

fire behavior (Nadler and others 1999; Van Wagtendonk and others 1996). It is 

this diversity of components and their highly variable properties across space and 

time that is the main reason fuels are so difficult to describe, measure, and map. 

The patchy distribution of fuels across a stand or landscape often confounds development of effective measurement protocols, fuel classifications, and spatial fuel 

data layers suitable for fire management applications at all scales. Fuel loadings, 

for example, are so highly variable that they often can’t be correlated to vegetation characteristics, topographic variables, or climate parameters (Brown and See 

1981; Rollins and others 2004; Cary and others 2006).

In natural resource management, the mean or average of an ecosystem characteristic, such as fuel loadings or basal area, is often used to represent that 

characteristic for large areas such as stands, polygons, or pixels (Keane and others 1998). However, many climatic, biological, and environmental variables are 

so highly variable across time and space that their mean doesn’t fully capture the 

influence and importance of that variable in the ecosystem. Daily precipitation, 

for example, is meaningless if it is represented by an average across a year because every day would have light rain. It is both the magnitude and variability of 

that characteristic that governs impacts on ecosystems, and nowhere is that more 

evident than in wildland fuels. Fuel properties, such as loading (Brown and See 

1981), heat content (Van Wagtendonk and others 1998), specific gravity (Harmon 

and others 2008), size (Van Wagtendonk and others 1996), and moisture (Agee and 
2 USDA Forest Service RMRS-RP-98. 2012.

others 2002), are astonishingly variable in time and in space, and this variability 

ultimately influences wildland fire effects and behavior. Fire spread, for example, 

is greatly influenced by the spatial distribution of fuels (Rocca 2009; Parsons and 

others 2010); fine-scale patches without fuels can dictate the direction, speed, and 

intensity of fire spread (Finney 1998b; Agee and others 2000; King and others 

2008; Thaxton and Platt 2006). To assign an average of fuel values across large areas, as is frequently done with fire behavior fuel models (Keane and others 2001), 

ignores the extraordinary influence that fuel variability can have on wildland fire 

processes. In fire ecology, for example, it is the uneven distribution of fuels across 

a landscape that primarily dictates post-fire plant mortality, growth, and colonization dynamics (DeBano and others 1998), yet this complex fuel patchwork is often 

overlooked when managers assume uniform fire behavior. 

This research is a comprehensive effort to describe the variability of major 

fuel properties across eight fuel components on six common forest and rangeland 

ecosystem types in the northern Rocky Mountains of the United States. We measured these characteristics at staggered sampling points within a large sampling 

grid to describe their variability across several spatial scales using geostatistical 

Table 1. Descriptions of the three canopy fuel characteristics and the eight surface fuel components sampled or estimated in 

this study. We combined the duff and litter layer together in this study because it was difficult to distinguish between the 

two layers.

General Fuel Fuel Common

 Type Component Name Size Description

Canopy Fuels

Canopy Aerial fuels Canopy load All dead and live All burnable biomass that is higher than 2 m

>2 m above (CL) biomass less than above ground and small enough to burn in a crown

ground surface 3 mm in diameter fire (<3 mm diameter) summarized to a per area 

basis (kg m-2)

Aerial fuels Canopy Bulk All dead and live The maximum bulk density (kg m-3) of burnable

>2 m above Density (CBD) biomass less than canopy biomass across all 1 m layers higher than

ground surface 3 mm in diameter 2 m

All material Canopy Cover All canopy biomass Vertically projected canopy cover estimated in

>2 m above (CC) 10 percent classes

ground

Surface Fuels

Downed Dead 1 hour woody Twigs <1 cm (0.25 inch) Detached small woody fuel particles on the ground

Woody diameter

10 hour woody Branches 1-2.5 cm (0.25-1.0 Detached small woody fuel particles on the ground

inch) diameter

100 hour Large 2.5-7 cm (1-3 inch) Detached small woody fuel particles on the ground

woody Branches diameter

1000 hour Logs 7+ cm (3+ inch) Detached small woody fuel particles on the ground

woody diameter

Shrubs Shrub Shrubby All shrubby All burnable shrubby biomass with branch

material less diameters less than 5 cm

than 5 cm 

 diameter

Herbaceous Herb Herbs All sizes All live and dead grass, forb, and fern biomass

Duff Duff Duff All sizes Partially decomposed biomass whose origins 

cannot be determined

Litter Litter Litter All sizes, Freshly fallen, non-woody material that includes

excluding leaves, cones, pollen, and cones

 woody
USDA Forest Service RMRS-RP-98. 2012. 3

techniques. We also describe the spatial distribution and autocorrelation of these 

fuel variables. Results from this study may illustrate that many conventional fuel 

products and analyses ignore scale-dependent variability that may make them inappropriate for future mechanistic fire behavior simulations (Parsons and others 

2010).

Background

Wildland fuels

In this paper, wildland fuel comprises all the organic matter available to permit 

fire ignition and sustain combustion (Albini 1976; Sandberg and others 2001). 

Specifically, fuel is the live and dead surface and canopy biomass that fosters the 

spread of wildland fire. Several terms that describe fuel characteristics need to 

be defined for this paper. Surface fuel is the biomass within 2 m vertical of the 

mineral soil surface, and it is often divided into the fuel components of duff and 

litter, downed and dead woody biomass in a range of diameter classes, and live 

and dead vegetation (Table 1). It is often difficult to estimate duff and litter loadings separately because it is challenging to assess where the litter (freshly fallen 

biomass whose origins can be easily determined) ends and the duff (litter that has 

decomposed so origins cannot be determined) starts. In this study, we grouped both 

duff and litter together as one fuel component (litter+duff). Downed dead woody 

fuels are often separated into four diameter size classes based on the drying time 

of the woody fuel particle (Fosberg 1970) for predicting fire behavior and effects 

(Table 1), and these size classes are employed in this study. Canopy fuel is live 

and dead aerial biomass that is greater than 2 m above ground and is primarily 

composed of branches and foliage but also includes arboreal mosses, lichens, dead 

ladder fuels, and other hanging dead material such as needles and dead branches 

(Reinhardt and others 2006).

Surface fuels are described by a unique set of characteristics when they are used 

by fire management to predict fire behavior and effects, and we measured four 

common characteristics in this study. Fuel loading is defined as the mass of a fuel 

component per unit area, expressed in this study as kg m-2. The density of woody 

fuel particles (particle density, kg m-3) is the mass per unit volume of fuel particles 

and is a function of the species, particle size, and degree of decay. It is a major 

factor determining fuel loadings (Brown 1974). Bulk density is the amount of fuel 

per unit volume (Figure 1) and is measured as the mass of a fuel component(s) in 

the volume of space that defines it in the fuelbed (Brown 1981). This volume is 

usually estimated as a unit area times the height of the fuelbed or fuel component. 

Bulk densities of the litter+duff, shrub, and herb fuelbed components are important 

for estimating fuel loadings (Figure 1) (Lutes and others 2006). Mineral content

is the amount of fuel component biomass that is inorganic, usually expressed as a 

proportion, and is important in the prediction of surface fire behavior because high 

mineral contents dampen fire spread and combustion processes (Rothermel 1972; 

Hartford 1990).

Canopy fuels are treated differently from surface fuels in wildland fire science 

(Cruz and others 2003; Burgan and Rothermel 1984). Surface fuels usually accumulate until the decomposition rate equals or becomes greater than the deposition 

rate (Keane 2008b); while canopy fuels tend to increase as shade-tolerant tree species become established in the understory and then in the overstory (Agee and Huff 

1987). Many fire behavior prediction systems do not differentiate among canopy 

fuel components because of the low resolution of crown fire models (Rothermel 
4 USDA Forest Service RMRS-RP-98. 2012.

1991) and the minor influence that large canopy fuels have on crown fire behavior 

(van Wagner 1977; Albini 1999). Therefore, canopy fuels are often described by 

the biomass that is burned in a crown fire, defined in this study as all canopy material less than 3 mm in diameter (Call and Albini 1997). This amount of material 

summed over a unit area is called the canopy fuel loading (CFL, kg m-2). Since 

remaining canopy material (particles greater than 3 mm diameter) rarely burns 

in a wildfire or prescribed fire, it is often ignored in fire management models, yet 

this material is fundamentally important in carbon dynamics (Finkral and Evans 

2008; Reinhardt and Holsinger 2010). Canopy cover (CC, percent) is the vertically 

projected cover of all canopy fuels, including the particles greater than 3 mm diameter. CC is important for describing and modeling the contagion and connectedness 

of canopy fuels and for the attenuation of solar radiation that drives dead and live 

fuel moisture dynamics (Anderson 1990).

Another canopy fuel characteristic important in simulating crown fire propagation is canopy bulk density (CBD, kg m-3), defined as the mass per unit volume 

of canopy biomass that would burn in a crown fire (again, foliage and twigs less 

than 3 mm in diameter; Figure 2) (Alexander 1988; van Wagner 1977). A number 

of fire behavior and effects models require estimates of CBD and several other 

canopy fuel characteristics (namely canopy base height, stand height, and canopy 

cover) to accurately simulate crown fires using models such as FIRETEC (Linn 

1997), NEXUS (Scott 1999), and FARSITE (Finney 1998a). Like the other canopy 

characteristics mentioned above, standardized indirect field methods do not exist 

for directly sampling and estimating CBD because its measurement requires detailed knowledge of the vertical distribution of crown biomass (Alexander 1988) 

(Figure 2). Direct methods of destructively sampling tree biomass by vertical canopy layers are prohibitively expensive and time consuming (Gary 1976; Reinhardt 

and others 2006). The most popular indirect method for estimating CBD involves 

using measurements of tree diameter, height, and crown base height for all trees 

in a plot to calculate crown biomass distribution from allometric crown biomass 

equations (Reinhardt and others 2006). Reinhardt and Crookston (2003) used the 

Sando and Wick (1972) approach in combination with the Brown (1978) crown 

equations to estimate CBD from stand inventory data (tree density, species, diameter, tree height, crown base height) in the Forest Vegetation Simulator growth 

and yield model. Because the vertical distribution of CBD is highly variable in a 

Figure 1. Illustration of the use of 

bulk density in the description and 

quantification of wildland surface 

fuels. The volume of the fuelbed or 

fuel component, such as shrubs, 

herbs, or litter, is multiplied by bulk 

density to estimate fuel loading.
USDA Forest Service RMRS-RP-98. 2012. 5

stand, average values across the canopy profile may not adequately represent the 

fuel conditions required for crown fire propagation (Figure 2). Crown fire spread 

may depend only on a few dense canopy layers with high CBD. Vertical canopy 

fuel characteristics are associated with species composition and stand structure 

where shade-tolerant species tend to occupy the lower canopy and tend to have 

higher proportions of flammable foliage and fine fuel than shade-intolerant, early 

seral species (Brown 1978; Roberts and Long 1992). Therefore, any estimate of 

CBD must describe those canopy layers that account for the majority of crown fire 

spread.

Fuel Variability

As mentioned, the most notable factor that confounds describing and quantifying fuel is the high variability of fuel characteristics across time and space (Brown 

and Bevins 1986; Agee and Huff 1987; Keane 2008a). A fuelbed can consist of 

many fuel components, such as litter, duff, logs, and cones, and the properties of 

each component, such as loading, mineral content, and moisture, can be highly 

variable, even within a single fuel particle, such as a needle, twig, and log. And 

since each component is composed of different sized fuel particles, these properties can vary at different spatial scales (Habeeb and others 2005). The variability of 

fuel loading, for example, can be as high within a stand as it is across a landscape, 

and this variability can be different for each component, each fuel size, and each 

landscape setting (Brown and Bevins 1986; Keane 2008a). It is the distribution and 

variability of fuel across space that confounds many fire management applications 

such as fuel classification, mapping, description, and fire behavior prediction.

Assessments of spatial variability have been made for ecophysiological 

(Rodeghiero and Cescatti 2008), soils (Grunwald and others 2007), weather 

(Augustine 2010), hydrology (Russo and Bouton 1992), and vegetation (Powell 

and Hansen 2007) characteristics across landscapes of various extents. However, 

few studies have assessed spatial variability of wildland fuels. Reich and others 

(2004) evaluated the coarse-scale (30 m) spatial variability of several fuel components over a large landscape in the Black Hills, United States, by modeling fuel 

properties from remote sensing products and found that variability was correlated 

Figure 2. Visual depiction of canopy bulk density and its distribution throughout the canopy profile.
6 USDA Forest Service RMRS-RP-98. 2012.

to topography and vegetation. But, they did not evaluate the inherent scale of this 

variability, or spatial variability at fine scales (<5 m). Hiers and others (2009) 

measured small-scale variations in surface fuel that were quantified using LIDAR 

heights and found that heights become spatially independent after small lag distances (0.5 m2

). Parsons and others (2010) simulated fine scale variations in fuel 

characteristics in a small area using a computer model called FUEL3D, and then 

input the simulated fuel distributions into highly mechanistic computational fluid 

dynamics models to simulate fire behavior. Spatial variations of grasslands have 

been described in the context of population dynamics and restoration potential 

(Peters and others 2006; Thorhallsdottir 1990). Fuel loadings have been manipulated at fine scales (1 to 5 m) to investigate the influence of fine fuel mosaics on 

fire intensity and effects (Rocca 2009; Thaxton and Platt 2006). Several studies 

have described the patterns of fuel distributions across the landscape, but few have 

actually quantified the variability of fuel properties across space (Jia and others 

2006; King and others 2008; Kennedy and others 2008; Miller and Urban 2000). 

To our knowledge, there have been no studies that assessed the spatial variabilities 

of multiple fuel properties using field sampling and empirical techniques.

Spatial Analysis

Several statistical techniques and tools were used to describe the variability 

of wildland fuels in this project. We used the common descriptive statistics of 

mean, range, and standard deviation to provide context for interpreting the variability of fuel characteristics across a sample site (Sokal and Rohlf 1981; Reich 

and others 2004). However, the variability is often related to the amount of fuel, 

so we also included the coefficient of variation defined as the ratio of the standard 

deviation to the mean converted to a percent (multiplied by 100). We also report 

IQR (InterQuartile Range or the distance between the 75th percentile and 25th percentile) and skewness (a measure of asymmetry of a probability distribution). The 

skewness for the normal distribution is zero; negative values for the skewness 

indicate that the data are skewed left (many small values, fewer large values), and 

positive skewness indicates that the data are skewed right (many large values) 

(Sokal and Rohlf 1981).

Spatial variability is described primarily using semivariograms (Bellehumeur 

and Legendre 1998; Townsend and Fuhlendorf 2010). The variogram is a descriptive technique that graphically represents the spatial continuity of a data set. The 

semivariogram depicts the spatial autocorrelation of the measured sample points 

and involves calculating the variance for a pair of observations of a variable as 

a function of their separation distance (Isaaks and Srivastava 1989). Once each 

pair of locations is plotted, a model is fit through them. There are certain graphical characteristics that are commonly used to describe these models (Figure 3). 

Theoretically, the semivariogram value is zero at zero distances, but at small distances, the semivariogram can often exhibit a nugget effect, which is a value greater 

than zero that is often attributed to both measurement errors and spatial sources 

of variation at distances smaller than the sampling interval (Fortin 1999). Natural 

phenomena, such as fuel characteristics, can vary spatially over a wide range of 

scales and variation at distances smaller than the smallest sampling distances will 

appear as part of the nugget effect. The distance where the model first flattens is 

known as the range (Figure 3). Sample locations separated by distances smaller 

than the range are spatially autocorrelated, whereas locations farther apart than the 

range are not. Semivariogram range is important in ecology because it represents 

the scale at which the entity is best described in space (inherent patch size). The 

value of the semivariogram model at the range is called the sill or the maximum 
USDA Forest Service RMRS-RP-98. 2012. 7

level of variation in the spatial data (Townsend and Fuhlendorf 2010). This spatial 

variation can be directionally dependent (anisotrophic) or it can be equal in all 

directions (isotrophic).

We also used several statistical indices to describe spatial distribution 

(Bellehumeur and Legendre 1998). Moran’s I is a weighted correlation coefficient 

ranging from -1 to 1 that is used to detect departures from spatial randomness 

(Moran 1950). Departures from randomness indicate spatial patterns such as clusters. The statistic may identify other kinds of pattern such as geographic trend. 

Moran’s I tests for spatial autocorrelation in geographic data. Positive spatial autocorrelation means that nearby areas have similar values, indicating global spatial 

clustering, and Moran’s I will be large and positive. When rates are dissimilar, 

Moran’s I will be negative. Geary’s C is another measure of spatial autocorrelation 

that is similar but not identical to Moran’s I; while Moran’s I is a measure of global 

spatial autocorrelation, Geary’s C is more sensitive to local spatial autocorrelation 

(Cliff and Ord 1970). The value of Geary’s C lies between 0 and 2, where values 

near 1 indicate no spatial autocorrelation.

Objectives

The primary objective of this study was to describe the spatial variability of 

surface and canopy fuel characteristics for forest and range ecosystems of the 

northern Rocky Mountains.

Fire managers, carbon scientists, fuel managers, and fire scientists interested 

in describing and sampling fuels for fire behavior and effects prediction will find 

this project valuable. This research may lead to new methods of simplifying fuels 

characteristics to aid fuel quantification efforts, such as fuel sampling, mapping, 

and classification.

Figure 3. Important characteristics of a semivariogram. The nugget, sill, and range are commonly used to 

describe the spatial variability of an ecological characteristic.
8 USDA Forest Service RMRS-RP-98. 2012.

Methods

Sampled Fuel Properties

Even though fuelbeds are incredibly diverse, we only had the time and funding to sample those conventional fuel components described in Table 1, which we 

considered most important to fire management at this time. Other fuel components, 

such as needle drape, stumps, squirrel middens, and animal scat (Ottmar and others 

2007), were not included because they were (1) rare on the landscape; (2) complicated to measure in a sampling unit compatible to this study; (3) difficult to sample 

because there were few standardized methods to measure their properties; and (4) 

unimportant inputs to the fire effects and behavior models. We included most of 

these special fine fuel components as part of the litter and duff but ignored stumps. 

In this study, the fuel variables are the four properties for each of the surface fuel 

components.

Canopy and surface fuels were sampled and calculated differently in this study 

because of methodological, modeling, logistical, and scale concerns (Reinhardt 

and others 2006). For canopy fuels, we calculated the biomass of all burnable 

canopy fuels (dry weight mass in kg of all fuels less than 3 mm diameter) from allometric tree structural relationships summarized into two measurements–canopy 

fuel loading (CFL, kg m-2) and canopy bulk density (CBD, kg m-3) (Table 1). The 

third canopy fuel variable, canopy cover (CC, percent), was visually estimated in 

the field at the plot level. In contrast, surface fuelbeds with their diverse fuel components have many characteristics that are required by fire models, so we sampled 

the following characteristics for all or some of the eight fuel components in Table 

1 or for the entire fuelbed (unless otherwise stated):

•  Loading (kg m-2). The dry weight biomass per unit area. This was measured for 

all eight components.

•  Particle Density (kg m-3). The mass per unit volume of woody fuel particles. 

We only measured particle densities for the four downed dead woody fuel 

components.

•  Mineral Content (proportion). Proportion of biomass that is inorganic. This 

was only measured for the four downed woody components and the litter+duff.

•  Bulk Density (kg m-3). The mass of fuel in a unit volume of fuelbed. This was 

measured for only the litter+depth, shrub, and herb components.

Loading was the only characteristic that was measured at all of the sampling 

points. The other characteristics were only measured on 20 percent of all sampling 

points (see next section).

Study Sites

Six study sites were selected for sampling after extensive GIS analysis and field 

reconnaissance (Figure 4; Table 2). We targeted the most common mature forested 

and rangeland vegetation types in the northern Rocky Mountains, but these areas 

had to be (1) homogeneous with respect to vegetation and topography; (2) large 

with at least 2 km2 in area to accommodate the large sampling grid; (3) flat with 

less than 10 percent slope to minimize the influence of slope and topography on 

woody fuel alignment; and (4) accessible (within 1 km of a road). Few contiguous, 

homogeneous areas met our criteria, especially in the remote and topographically 
USDA Forest Service RMRS-RP-98. 2012. 9

Figure 4. The geographic locations of the six study sites in the northern Rocky Mountains, 

USA. “Dry Lake” is the Colville Forest site.
10 USDA Forest Service RMRS-RP-98. 2012.

complex high-elevation forests. As a result, we ended up sampling mostly lowelevation, semi-arid ecosystems.

The first site that we sampled was on the University of Montana’s Lubrecht 

State Forest (Lubrecht Forest, LF) in west-central Montana (Figure 5c; Table 2). 

This site was a second-growth dry mixed conifer stand of ponderosa pine (Pinus 

ponderosa), Douglas-fir (Pseudotsuga menziesii), and western larch (Larix occidentalis). Overstory trees ranged from 25 to 50 cm DBH and 10 to 25 m tall with 

the undergrowth primarily pinegrass (Calamagrostis rubescens), Oregon grape 

(Mahonia repens), and several species of huckleberry (Vaccinum spp.). This site 

had been thinned approximately nine years prior to sampling, so some residual 

down woody fuels were still present on the site. Many of our sampling methods 

were prototyped on this site. The second site was a ponderosa pine-Douglas-fir 

stand on the Ninemile Ranger District of the Lolo National Forest (Ninemile, NM) 

(Figure 5d). This site was on a gentle (<10 percent), south-east facing slope in the 

Douglas-fir/ninebark habitat type (Pfister and others 1977). It consisted of 20 to 

50 cm DBH ponderosa pine trees with scattered mature Douglas-fir and sparse 

Douglas-fir understory. This site had a prescribed burn implemented approximately eight years prior to sampling.

The Tenderfoot Forest (TF) site was on the Tenderfoot Creek Experimental 

Forest in the Lewis and Clark National Forest in central Montana and is composed 

of an open, mature lodgepole pine (Pinus contorta) overstory (10 to 40 cm DBH 

trees) in a subalpine fir/grouse whortleberry habitat type with a history of nonlethal surface fires. The fuelbed was primarily low grouse whortleberry (Vaccinum 

scoparium) shrubs with scattered downed woody fuels (Figure 5f). The Silver 

Mountain (SM) site was an open pinyon pine (Pinus edulis) and juniper (Juniperus 

Table 2. General description of the selected study sites.

 Habitat Structural Primary Dominant Past

Site Name Code Typea Cover Type Stage Fuels Undergrowthb Activities

Lubrecht Forest LF PSME/ Ponderosa pine/ Mature Partially Pinegrass, snowberry, Recent thinning nine

VACA, Douglas-fir/ decomposed spirea, and elk sedge years prior to sampling

PSME/ western larch light thinning

VAGL slash

Tenderfoot Forest TF ABLA/ Lodgepole pine Pole- Low live Grouse whortleberry, Low intensity surface fire

VASC mature shrub, elk sedge, arnica approximately 64 years

 scattered prior to sampling

 woody

Ninemile NM PSME/ Ponderosa pine- Mature Grass, widely Pinegrass, elk sedge, Thinning and prescribed

PHMA, Douglas-fir scattered snowberry, burn approximately 

PSME/ thinning slash kinnikinnick 8 years prior to sampling

SYAL

Bighole Valley BV NA Sagebrush Mature Sagebrush, Mountain sagebrush, History of cattle grazing

 grasslands grass bluebunch wheatgrass, 

Silver Mountain SM NA Pinyon pine/ Mature Patchy, light Sagebrush, ephedra, History of cattle grazing;

juniper herbaceous poa wildland fire excluded

 fuels from these landscapes

Colville Forest CF PSME/ Ponderosa pine Mature Grass, Rough fescue, History of frequent

SYAL savanna scattered pinegrass, burning and grazing

PSME/ woody snowberry recent thinning 4 years

VACA ago prior to sampling

a

Habitat types were keyed from Pfister and others (1977), and the codes are: PSME—Douglas-fir (Pseudotsuga menziesii), ABLA—subalpine fir 

(Abies lasiocarpa), PHMA—ninebark (Physocarpus malvaceus), VASC—grouse whortleberry (Vaccinium scoparium), VAGL—blue huckleberry 

(Vaccinium globulare), VACA—dwarf huckleberry (Vaccinium caespitosum), and SYAL—snowberry (Symphoricarpus alba).

bScientific names are: pinegrass (Calamgrostis rubescens), rough fescue (Festuca scabrella), kinnikinnick (Arctostaphylos uva-ursi), elk sedge 

(Carex geyerii), spirea (Spirea betulafolia), mountain sagebrush (Artemisia tridentata vaseyana), arnica (Arnica latifolia), sagebrush (Artemisia 

tridentate), poa (Poa secunda and bulbosa), and ephedra (Ephedra viridis).
USDA Forest Service RMRS-RP-98. 2012. 11

Figure 5. The six sites selected for this study: (a) Bighole Valley, (b) Colville Forest, (c) Lubrecht Forest, (d) Ninemile, 

(e) Silver Mountain, and (f) Tenderfoot Forest.

(a)

(c)

(e)

(b)

(d)

(f)
12 USDA Forest Service RMRS-RP-98. 2012.

occidentis) woodland with woody scattered fuels, sparse sagebrush shrubs, and 

frequent depauperate patches dominated by bare soil and gravel (Figure 5c). 

The Colville Forest (CF) site was a ponderosa pine savanna with a rough fescue 

(Festuca scabrella) undergrowth. Thickets of Douglas-fir trees were scattered in 

a matrix of widely spaced ponderosa pine trees with DBHs ranging from 25 to 60 

cm DBH around 25 m tall (Figure 5b). This site had been thinned in a fuel treatment approximately four years ago to reduce crown fuels by removing Douglas-fir 

and ponderosa pine sapling and pole thickets. The Bighole Valley (BV) site is a 

non-forested stand of 30-50% canopy cover of sagebrush (Artemisia tridentata 

vaseyana) with a diverse mixture of grass species (Figure 5a). Because of the lack 

of trees, no canopy fuels are present on the site.

Field Methods

Sampling Grid Design

We installed a nested grid design within a square 1 km2 (1000 m by 1000 m) 

area in the center of each selected study site (Figure 6) (Bellehumeur and Legendre 

Figure 6. The sample grid installed 

in the center of each study area 

with the four areas that received 

additional sampling to intensify 

the grid. A set of nested plots 

were installed at each of the 

sample points shown in the grid.
USDA Forest Service RMRS-RP-98. 2012. 13

1998; McCollum 2005). Corners of this “sampling grid” were monumented using 

1-m rebar and georeferenced using a global positioning system (GPS). Sides of the 

sampling grid were oriented along the four cardinal directions. Transects were established across each corner and at 100-m intervals along each grid side. Transects 

that were oriented west-to-east were numbered from 00 (NW corner to NE corner), 

01 (100 m south of NW corner to 100 m south NE corner), and so on until 10 (SW 

corner to SE corner). North-south transects had the same naming convention in 

that 00 was the NW corner to SW corner, 01 was 100 m east of NW corner to 100 

m east of NE corner, and so on until 10 (NE corner to SE corner) (Figure 6).

Starting in the NW corner of the sampling grid, we established sampling points 

at 200-m distances along each of the west-east running transects but staggered the 

start of the 200-m distance by 100 m on every other transect (Figure 6). Plots along 

the even transects (00, 02, and so on), for example, had sampling points established 

every 200 m while plots along the odd transects have plots established at 100-, 

300-, 500-, 700-, and 900-m distances. This design provided additional distances 

between sampling points. Each sampling point was labeled as to its coordinate distance, in hundreds of meters, from the NW corner of the sample grid; sample point 

0103, for example, was 100 m south and 300 m east of the NW corner.

We intensified sampling around four grid points to increase the number of distances between sample points. At grid sampling points 0303, 0307, 0703, and 0707 

(Figure 6), we installed a nested sampling grid of 16 additional sampling points 

around a 100-m square (eight sampling points) and 50-m square (another eight 

points) centered around each of the four grid sampling points. These additional 

sampling points were placed at the corners and side mid-points for the two nested 

squares. This intensive grid provided the additional distances, including 25, 35, 50, 

and 100 m. All intensified grid sample points were again georeferenced with a GPS 

and temporarily monumented using wooden stakes.

Plot Sampling Design

We established a set of nested plots at each sampling point using the sample grid 

point as plot center (Table 3; Figure 7). A 400-m2 circular macroplot was established at each sample point for sampling trees greater than 10 cm DBH (diameter 

breast height) and canopy cover. Using the same sample point as plot center, we 

installed a 100-m2 circular subplot on which we sampled logs (woody fuel particles greater than 8 cm diameter) and sapling trees (trees greater than 1.37 m tall 

and less than 10 cm DBH). We then centered a 1-m2 square microplot over the grid 

sampling point, within which we measured shrub, herb, and fine woody (wood fuel 

particles less than 8 cm diameter; twigs and branches) fuel characteristics. Last, we 

installed a 0.25-m2 (50 by 50 cm) square nanoplot in the NW corner of the microplot to measure duff and litter fuels (Figure 7). 

Macroplot Measurements 

We sampled general site characteristics and canopy fuels on each macroplot 

(Figure 7) using FIREMON sampling protocols (Lutes and others 2006). First, 

we estimated general site characteristics, such as slope, elevation, and aspect, using FIREMON Plot Description methods and plot forms (Lutes and others 2006). 

These general site characteristics provided context and categories for data stratification and pooling. Other important visually estimated data were tree, shrub, and 

herbaceous canopy cover; ground cover; fire behavior fuel model; and most importantly, CC (percent). We also took several photos of each sample point to visually 

describe the biological conditions (Figure 5).
14 USDA Forest Service RMRS-RP-98. 2012.

Table 3. Summary of the wildland fuel components sampled in this study and the scale and method at which they are sampled.

Fuel Component Sample Unit and Size Sub-Sampled? Sub-Sampling Frequencya Sampling Methodb

Surface Fuels

1 hour woody Microplot 1 m2 Yes Every 5 micro Photoload; collection; length 

 measurements

10 hour woody Microplot 1 m2 Yes Every 5 micro Photoload; collection; length 

 measurements

100 hour woody Microplot 1 m2 Yes Every 5 micro Photoload; collection; length 

 measurements

1000 hour woody Subplot 100 m2 No Not needed Diameters-length, rot class

Shrub Microplot 1 m2 Yes Every 5 micro Photoload; collection; cover-height

Herb Microplot 1 m2 Yes Every 5 micro Photoload; collection; cover-height

Litter+Duff Nanoplot 0.25 m2 Yes Every 5 micro FIREMON depth

Canopy Fuels

Canopy fuel via Macroplot 400 m2 No Not needed Tree DBH, height, crown base

tree population height

allometric 

relationships

a

Sub-sampling was used to destructively collected all fuel within the microplot and bring to the laboratory to dry and weigh. These subsampled weights were correlated to photoload estimates to correct photoload estimates.

b

Methods used in this study include the FIREMON Tree Data (TD) survey as detailed in Lutes and others (2006), Photoload fuel loading visual 

estimates detailed in Keane and Dickenson (2007), the length method involves measuring the total length of the fuel particles in the 

sampling unit as detailed by Sikkink and Keane (2008), and the FIREMON depth method where depth is multiplied by a bulk density to 

estimate loading (Lutes and others 2006).

Figure 7. The nested plots that 

were established at each of the 

sampling points. The circular 

macroplot was a 400 m2, the 

circular subplot was 100 m2, 

the square microplot was 

1 m2, and the square nanoplot 

was 0.25 m2. All plots but the 

nanoplot used the grid sampling 

point as plot center.
USDA Forest Service RMRS-RP-98. 2012. 15

We then recorded tree population data using the FIREMON Tree Data method 

for all trees larger than saplings within the macroplot (Table 3). Tree population 

data were used as input to allometric biomass equations to calculate the CBD and 

CFL canopy fuels variables (Reinhardt and others 2006). We recorded species and 

health class for all trees above 10 cm DBH and then measured their DBH (cm), 

tree height (m), canopy fuel base height (m), crown class, crown position, and live 

crown ratio. Tree crown height and base were measured using a hypsometer or 

clinometer. We measured the trees in order from the north progressing clockwise 

around the plot.

Subplot Measurements

We measured all saplings (trees less than 10 cm DBH and greater than 1.37 m 

in height) within a circular 100-m2 subplot (Figure 7) again using the FIREMON 

methods. Saplings were individually measured for species, DBH class (2 cm), 

height, and crown base height (Table 3). These sapling measurements were augmented with the larger tree measurements to compute canopy fuel variables. 

Three dimensions of all downed dead woody fuel particles greater than 8 cm diameter (logs) were also measured within the 100-m2

 subplot using cloth tapes and 

rulers. We measured the small and large end log diameters and the length of each 

log within subplot boundaries and then assessed the log’s decay class using the five 

rot classes described in the FIREMON Fuel Loading method. A log’s length was 

measured along the longitudinal axis and terminated at the boundary of the circular 

plot. Only logs whose central longitudinal axis was above the litter-duff surface 

were measured. From a 10 percent sample of measured logs, we took at least three 

cross-sectional areas from selected logs within the subplot to measure log particle 

densities. Sub-sampled logs were selected for species and rot class. Log crosssections were placed in labeled paper bags and transported back to the lab where 

they were dried and weighed to determine particle density.

Microplot Measurements

Seedlings (trees less than 1.37 m in height) were counted by species and height 

classes on square 1-m2 microplots (Figure 7) using the FIREMON Tree Data methods. We then estimated vertically projected canopy cover (percent) and average 

height (m) of each vascular plant species within the microplot using the Cover 

Frequency method in FIREMON. Fuel loadings for each of the 1 hr, 10 hr, 100 hr, 

shrub, and herb fuel components were visually estimated using the photoload 

technique (Keane and Dickinson 2007b). We also visually estimated the ground 

cover of rock, soil, wood, litter+duff, and moss. Last, we inserted a ruler downward through the duff and litter layers until we hit mineral soil, then read the total 

litter+duff depth directly from the ruler at 13 points within the microplot (Figure 8) 

using FIREMON Fuel Loading methods. Microplot measurements were always 

the first conducted on the sample point so the fragile fuelbed wouldn’t be disturbed 

from trampling.

An intensive microplot grid was installed at the four sampling points that were 

used to intensify the microplot sampling grid to increase the number of fine scale 

distances (Figure 9). At the plot centers of points 0303, 0307, 0703, and 0707, we 

installed a 5-m by 5-m grid containing 25 microplots. The center of the microplot 

grid was the sampling grid point and macroplot center. All four corners of the 5-m 

grid area were located using a 20-cm nail. Cloth tapes were tightly attached to each 

corner nail to guide the sampling of the 25 microplots. All 25 microplots in the 

intensive microplot grid were measured exactly the same as the other microplots 

on the 1-km2 sampling grid.
16 USDA Forest Service RMRS-RP-98. 2012.

Figure 8. Duff and litter depth 

measurement points on the 

microplot and nanoplot.

Figure 9. The intensive 5-m by 

5-m microplot grid installed 

at the four sampling points 

shown in Figure 6.
USDA Forest Service RMRS-RP-98. 2012. 17

We randomly selected 20 percent of the microplots, including those on the intensive microplot grid, to destructively sample all fuel for the measurement of 

actual fuel loading to calibrate and adjust the photoload visual estimates (Table 3). 

Once the photoload estimates were taken, the total lengths of all woody particles 

within each of the three fine woody components were measured using a cloth tape 

on these randomly selected microplots. Length was used to calculate volume, and 

volume multiplied by wood density provided a more accurate estimate of loading 

(Sikkink and Keane 2008). We then collected all the fuel in 1, 10, 100, shrub, and 

herb components and sorted them on site into separate paper bags. These bags 

were labeled and placed in a burlap bag for transport to the lab where they were 

dried and weighed to determine loading.

Nanoplot Measurements

One nanoplot (50 cm by 50 cm; Figure 7) was established in the NW corner of 

each microplot to estimate duff-litter loadings. We measured litter+duff depths for 

seven points at each corner of the nanoplot and directly in the middle (Figure 8). 

Duff and litter depths were taken using FIREMON procedures where depth of 

the entire duff-litter profile was taken (we did not estimate duff and liter depth 

separately). Litter+duff depth was measured from the top of the mineral soil to the 

top of the litter material at each point of measurement. This did not include grass, 

forbs, and shrub height—only the height to the top of the downed dead woody 

fuels on the forest floor. The five microplot litter+duff measurements, plus an additional two depth measurements (NE and SW corners of the nanoplot), were used 

to compute litter+duff volume (see next section).

We collected all duff and litter material from the nanoplots on the 20 percent 

randomly selected, destructively sampled microplots using a flat shovel, trowel, 

and soil knife. The extracted profile was then stored in a labeled burlap or paper 

bag (Snell 1979; Stephens and others 2004) and brought to the laboratory where 

profile was dried and weighed to determine loading. This loading was then converted to litter+duff bulk density using the depth measurements, and the calculated 

bulk densities were used to calculate duff and litter loading for all the remaining 

microplots. Only the nanoplot on the center microplot within the intensive 5 by 

5-m microplot grid was sampled for litter+duff bulk density.

Laboratory Measurements

All collected fuels that were brought to the laboratory for additional measurements were first measured for dry weight by weighing the fuel after it had been 

dried in an oven for three days at 80 oC . Dry weights were measured for all collected fuel particles, log cross sections, and litter+duff profiles.

All collected fine woody fuel particles were measured to determine particle volume. We measured the end diameter of the particle, then moved over the particle to 

determine when the diameter changed by more than 2 mm. The distance from the 

end to this point was measured to the nearest mm, and both the distance and second 

diameter were recorded. This process was repeated until the end of the particle was 

encountered; at that point, we measured the distance and other end point diameter. 

We calculated the interval particle volume using the particle’s length and small and 

large diameter measurements assuming a truncated frustum shape. Results from 

this sampling and measurement are not discussed in this report but were used to 

estimate volume of fuel particles.

Particle densities for downed woody fuel were then calculated from the dry 

weights and volume of each woody particle gathered from the sub-sampled 
18 USDA Forest Service RMRS-RP-98. 2012.

microplots (fine woody fuel components) and the sawn log cross-sections (coarse 

woody fuel component). We estimated a volume by immersing the particle in water 

and recording its displacement (Fasth and others 2010). We coated the smaller particles with wax or paraffin to reduce water absorption into the wood. We randomly 

selected at most three particles for each fuel component from each microplot. For 

unsampled woody species, we used density values from the literature (Green and 

others 1999; Harmon and others 2008; Nalder and others 1999) to estimate loading. 

An assessment of mineral content of the fuelbed is important because high mineral concentrations can influence fire behavior by dampen fire spread and intensity 

(Rothermel 1972). We measured mineral content by grinding a pre-weighed portion 

of the collected dried fuel from each fuel component in the microplot subsample 

and burning that ground portion in a muffle furnace for 24 hours and then weighing the ash.

Analysis

We calculated the variability of a total of 22 fuel variables—19 surface fuel 

variables that describe the four major characteristics of the eight surface components, and 3 canopy fuel variables (CC, CBD, CFL) estimated from the tree 

population data that describe the major canopy fuel characteristics (Table 4). The 

values of these 22 fuel variables were either estimated from direct measurements 

Table 4. List of fuel variables that are used to describe the variability of major fuel characteristics in the northern Rocky 

Mountains. Note that some characteristics are only for specific fuel components.

Fuel Variable 

Fuel Characteristic Fuel Component Name Description

Surface Fuels

Loading 1 hour woody L1 Biomass per unit area of downed dead woody twigs

(kg m-2) 10 hour woody L10 Biomass per unit area of downed dead woody branches

100 hour woody L100 Biomass per unit area of downed dead woody large branches

1000 hour woody L1000 Biomass per unit area of downed dead woody logs

Shrub LSHRUB Live and dead biomass per unit area of shrubs

Herb LHERB Live and dead biomass per unit area of shrubs

Litter+Duff LDUFF Biomass per unit area of duff and litter

Particle density 1 hour woody PD1 Density of downed dead woody twigs

(kg m-3) 10 hour woody PD10 Density of downed dead woody branches

100 hour woody PD100 Density of downed dead woody large branches

1000 hour woody PD1000 Density of downed dead woody logs

Bulk density (kg m-3) Shrub BDSHRUB Bulk density of live and dead shrub layer

Herb BDHERB Bulk density of live and dead herb layer

Duff+Litter BDLDUFF Bulk density of the litter and duff layer

Mineral content 1 hour woody MC1 Mineral content of downed dead woody twigs

(%) 10 hour woody MC10 Mineral content of downed dead woody branches

100 hour woody MC100 Mineral content of downed dead woody large branches

1000 hour woody MC1000 Mineral content of downed dead woody logs

Duff+Litter MCDUFFLIT Mineral content of downed dead woody duff and litter

Canopy Fuels

Canopy fuel loading Canopy fuels CFL Biomass per unit area of the burnable crown fuel

(kg m-2)

Canopy bulk density Canopy fuels CBD Maximum bulk density of the canopy for the burnable crown fuel

(kg m-3)

Canopy cover (%) Canopy fuels CC Vertically projected canopy cover of the canopy fuels
USDA Forest Service RMRS-RP-98. 2012. 19

made in the field or computed from the field sampled measurements. This section 

describes the computations used to calculate those fuel variable values not directly 

measured in the field.

Calculating Surface Fuel Loading Variables

As mentioned, we measured fuel loading from all microplots using two methods 

in a double sampling technique (Okafor and Lee 2000). Fine fuel loadings (1, 10, 

100 hr size classes) were estimated on all microplots using the visual photoload 

sampling technique because it was easy, fast, and somewhat accurate (Sikkink 

and Keane 2008). However, photoload loading estimates are based on visual assessments, which may be of sufficient resolution for management applications but 

probably should be further refined for research measurements. Therefore, we used 

a regression approach to correlate the destructively collected and measured fine 

fuel loadings to the photoload fuel estimates to improve microplot loading estimations. We regressed photoload visual estimates for the fine woody, shrub, and herb 

fuels to the destructively sampled loading estimates for the 20 percent sub-sample 

of the microplots. The regression equation was applied to the photoload estimates 

to “correct” the loading estimates for all microplots. The coefficients of determination (R2

) and correction factors for the fine fuel loadings are shown in Table 5.

Log loadings on the subplot were calculated by summing the mass of all measured logs on the subplot and dividing by 100 (area of subplot, m2

) to convert to 

kg m-2 units. Biomass of individual logs (m, g) was calculated by multiplying log 

volume by the measured wood density using the following equation:

M=VD (1)

where V is the volume of the particle (m3), and D is the wood density (kg m-3) 

quantified from laboratory analysis of the collected woody fuel (see previous section). Particle volume (V, M3

) was calculated using the following equation:

v ( ) ( ) l a a a a 3 = +s l + s l 6 @ (2)

Table 5. Statistics for the photoload-actual fuel regression equations that were used to adjust visual fuel loading estimates to 

calculate the fuel loading values at each sampling point used in the study.

Fuel Component Lubrecht (LF) Tenderfoot (TF) Ninemile (NM) Bighole (BV) Silver (SM) Colville (CF)

Coefficient of Determination (R2)

1 hour 0.825 0.677 0.765 0.424 0.518 0.494

10 hour 0.573 0.595 0.661 0.420 0.735 0.509

100 hour * *** 0.777 *** *** *

Shrub **0.761 0.757 0.510 0.262 0.706 0.415

Herb 0.287 * 0.265 * * 0.471

Correction Factor (intercept, slope)

1 hour -0.0007, 0.500 -0.009, 0.843 0.001, 0.431 0.002, 0.127 -3.03, 0.578** 0.009, 0.167

10 hour -0.012, 5.480 -0.012, 3.528 0.462, 0.991** 0.003, 0.702 -0.002, 0.936 0.029, 0.614

100 hour * *** 0.173, 0.881 *** *** *

Shrub -0.100, 0.926** 0.100, 1.20**** 0.016, 1.46 0.169, 0.364 0.000, 0.401 0.019, 1.150

Herb 0.017, 0.289 * 0.020, 0.501 * * 0.025, 0.693

*Model Insignificant and did not improve visual estimates

**Natural log transformation on both visual and measured observations

***Too few values to build a model; visual estimates were used

 Log base 10 transformation on both visual and measured observations 
20 USDA Forest Service RMRS-RP-98. 2012.

where as and al are the areas (m2) of the small and large end of the fuel particle 

(a = �d2/4, where d is the log diameter, m), respectively, and l is the length of 

the particle (m). We assumed particle shape approximated a truncated frustum. 

Wood density (kg m-3) was directly calculated from all samples taken by species 

and rot class from the site for all sizes of woody fuel particles (see previous section). If a species or rot class density was un-sampled, we used values taken from 

the literature. To determine densities, we divided the total mass of the collected 

fuel particles for a size class by the total volume as calculated from equation (2).

Loading (L, kg m-2) for the litter+duff was calculated by multiplying the volume of the litter+duff layer (V, m3

) by bulk density using a variation of equation 

(1):

	 L = 

( )( )

A

V BD (3)

where BD is the litter+duff bulk density (kg m-3) (Snell 1979; Stephens and 

others 2004; Woodard and Martin 1980) and A is the area (m2) of the microplot 

sampling frame (1 m2). The volume was calculated using the following equation:

V=dA (4)

where d is the average depth (m) of all 13 litter+duff depth measurements taken 

on the microplot and A is the area of the microplot (1 m2). The BD for litter+duff 

is an average of all bulk densities calculated from the destructively collected 

nanoplot samples removed from the 20 percent microplot subsample. To compute field-sampled duff and litter bulk densities, we first computed the loading 

by dividing the dry weight of the litter and duff profile by the nanoplot area 

(0.25 m2). We then divided this loading by the measured volume of the nanoplot 

duff-litter profile. The volume was computed using equation (4) where d was the 

average of the five nanoplot depth measurements, and A was the nanoplot area.

Calculating Canopy Fuel Variables

CFL and CBD were computed using the FUELCALC program. FUELCALC 

was initially developed for the LANDFIRE program (Keane and others 2006) 

and was refined by Scott and others (2011). FUELCALC computes several canopy fuel characteristics based on allometric equations relating individual tree size, 

canopy, and species characteristics to crown biomass. The canopy characteristics 

for a stand are computed from a tree list that specifies the tree species, density 

(trees per unit area), DBH, height, crown base height, and crown class. CFL is 

computed by dividing the sum of all burnable canopy biomass (particles less 

than 3 mm diameter) by the area of the plot within which the trees were sampled 

(400 m2 for this study). FUELCALC was then used to compute vertical canopy 

fuel distribution using the Reinhardt and others (2006) algorithms that evenly 

distribute crown biomass over the live crown for each tree and divide the canopy 

fuel summed across all trees into horizontal layers of a user-specified width and 

reports the CBD value of the layer with the greatest CBD (see Figure 2).

CC (percent) was visually estimated in the field using the FIREMON methods 

where percent vertically projected canopy cover for all trees greater than 2 m tall 

was recorded on the Plot Description form using the FIREMON cover classes (0, 

1, 3 = 1-5 percent, 10 = 5-15 percent, and so on).
USDA Forest Service RMRS-RP-98. 2012. 21

Calculating Fuel Variability

We first calculated the descriptive statistics of mean, standard deviation, 

range, coefficient of variation, skewness, and IQR for all 22 fuel variables. We 

then compared and contrasted these variables across ecosystem types (study 

sites) using standard statistical tests. Relationships of the variance across fuel 

components and particle size were then explored using graphical and regression 

techniques, and tests for equal variance were conducted (Levene’s test). Next, 

we used correlation analysis to evaluate if any of the commonly used stand variables shown in Table 6 explained any of the variance in fuel variables, and also 

if the surface and canopy fuel components were related.

The spatial variation of surface fuel variables was described using the spatial 

statistical analysis techniques described in the Introduction. First, we used spatial autocorrelation analysis to construct semivariograms for each fuel variable 

to determine the scale at which that variable is best measured and described. We 

compared these scales by fuel variable and then by sample site to evaluate if fuel 

properties are constant across study sites. We also evaluated whether the spatial 

variation in fuel variables is isotropic (same in all directions) or anisotropic (directional) (Maglione and Diblasi 2004), and we addressed whether the variation 

is stationary (homogeneous in space). Two spatial statistics were computed to 

describe the spatial structure of fuel variables: Moran’s I and Geary’s C. Spatial 

analysis was performed using the geoR spatial package (Ribeiro and Diggle 

2001) in R statistical computing software. Because of the skewed distribution 

of the canopy fuel variables, a log transformation was performed, after adding a 

small constant. The best fitting theoretical model was performed through the use 

of authorized models (spherical, exponential, linear, and pure nugget), and the 

weighted least squares method was used as a fitting procedure in cases in which 

two or more theoretical variograms were found. The weight applied to each of 

the semi-variance estimates was proportional to the number of couples of data 

involved in that estimate (Cressie 1985; McBratney and Webster 1986). We used 

spatial dependence and variation analysis to determine the relationship of the 

ecosystem variables in Table 6 to the fuel variables.

Results

Results from this study are stratified by the sampled variability across the entire grid (Fuel Variability) and then by the spatial variability analyzed within the 

grid (Spatial Variability). Surface and canopy fuels are then summarized within 

these two broad variability categories. Because this study generated abundant 

data that created many diverse results, we mostly present general summary tables 

Table 6. Site variables used to correlate with the surface and canopy fuel variables to 

explain the sources of variation in fuel distributions.

Variable Name Description Source Units

AVEDBH Average DBH (quadratic mean) FIREMON Tree Data cm

AVEHT Average tree height FIREMON Tree Data m 

BAREA Overstory basal area FIREMON Tree Data m2 ha-1

TDENSITY Trees per hectare FIREMON Tree Data m2 ha-1
22 USDA Forest Service RMRS-RP-98. 2012.

for the majority of the complex analysis in this study. To describe the important 

intermediate findings used to create these summary tables, we use detailed results from the Tenderfoot Forest (TF) study site to illustrate the how the statistics 

in the summary tables were derived.

Fuel Variability

Surface Fuels

Loading. Surface fuel characteristics were highly variable both within and 

across study sites (Table 7; Figure 10). For loading, it appears that the sampled 

variability was high across nearly all of the down woody fuel components with 

the larger fuel having the highest variabilities. One hour fuel loadings were low 

ranging from 0.005 (BV; see Table 1 for site acronyms) to 0.066 kg m-2 (TF) with 

high standard errors (0.005 at BV to 0.057 at TF) and high coefficients of variation 

(80 percent at CF to 187 percent at NM) (see Table 2 for sample site descriptions 

and codes). Loadings for 10 hr woody fuels were highest (0.009 kg m-2 for BV 

to 0.458 kg m-2 for LF) across all four downed woody fuel components for four 

sites (LF, TF, BV, and SM), probably as a result of management activities; as a 

consequence, the variability was also the highest with standard deviations ranging 

from 0.022 (BV) to 1.169 (LF) corresponding to ranges of 0.214 (BV) to 9.859 kg 

m-2 (LF), and IQR (25 to 75 percentile) from 0.01 (BV) to 0.264 (LF) kg m-2. 

Interestingly, the highest coefficient of variations for 10 hr fuels did not occur on 

the sites with the highest fuel loadings and variance (range was from 132 percent 

for TF to 329 percent for SM). The larger 100 hr fuel loadings were similar in 

loading and variability across all sites except the sagebrush grassland BV site; 

excluding BV, 100 hr loadings ranged from 0.025 kg m-2 (SM) to 0.219 (NM) kg 

m-2, deviations ranged from 0.11 (TF, SM) to 0.50 (NM) kg m-2, IQR ranged from 

zero to 0.261 (NM) kg m-2, and the similar coefficient of variation was around 

250 percent (185 to 444 percent). The sagebrush grassland BV loadings were low 

and variable because sagebrush shrubs rarely produce woody material greater than 

2.5 cm in diameter. Logs (1000 hr fuels) were rare across all sites but had some of 

the highest fuel loads (zero at BV to 0.57 kg m-2 in lodgepole pine forests at the 

TF), high deviations (zero to 0.707 kg m-2), and the highest ranges (zero to 7.4 kg 

m-2 at SM), yet the coefficients of variations were approximately the same as the 

other woody fuel components (101 percent at NM to 603 percent at SM).

One important result is that the Levene test for equal variances showed strong 

evidence of differences between the population variance at each site for all fuel 

components except the herb, indicating that the variation of these surface fuels is 

quite different across sites and across components. Moreover, this variance across 

all downed woody classes is not normally distributed with skewness statistics well 

over 1.0 for most sites and components. Skewness statistics ranged from 2.0 for 

1 hr loadings in the lodgepole (TF) forest to over 7.0 for 1000 hr fuels in the pinefir-larch (LF) forest and 10 hr fuels in pine savanna (CF). Skewness was over 9.7 

for logs on the pinyon-juniper (SM) site, indicating that there were many plots 

with small loading estimates and few plots with high loading estimates.

The live and dead shrub and herbaceous loads were perhaps the least variable 

of all surface fuels (Table 7; Figure 10). Shrub loadings ranged from 0.05 kg m-2

(sites LF, TF, CF) to 0.225 kg m-2 (sagebrush BV) with low deviations (0.042 kg 

m-2 in lodgepole TF to 0.187 kg m-2 in SM pinyon-juniper) and low ranges 

(0.194 kg m-2 in TF to 1.28 kg m-2 in SM; IQR ranged from 0.038 kg m-2 to 0.164 

kg m-2), and the variance was a small proportion of the mean (0.5 in BV to 2.0 at 
USDA Forest Service RMRS-RP-98. 2012. 23

Table 7. General statistics describing the variability of the surface fuel components across the six study sites. Number in 

parentheses under fuel component is the number of observations.

Fuel

Attribute Fuel Component Mean

Standard 

Deviation Range

Coefficient 

of Variation 

(CV) Skewness IQR

Lubrecht Forest (LF)

1 hour woody (125) 0.027 0.037 0.273 134.922 3.626 0.030

10 hour woody (125) 0.458 1.169 9.859 255.345 5.728 0.264

100 hour woody (125) 0.103 0.292 2.500 284.212 5.621 0.085

1000 hour woody (125) 0.276 0.597 6.00 216.131 7.355 0.260

Shrub (125) 0.056 0.064 0.409 113.626 3.115 0.045

Herb (125) 0.032 0.019 0.146 59.039 3.486 0.014

Litter+Duff (125) 11.379 6.654 35.616 58.473 1.393 7.518

Loading 

(kg m-2

)

Entire fuelbed (125) 12.058 7.343 43.989 60.895 1.639 8.030

1 hour woody (22) 629.228 174.487 798.755 27.730 -0.566 181.180

10 hour woody (28) 509.909 209.232 865.870 41.033 1.638 189.066

100 hour woody (13) 326.899 226.709 702.471 69.351 0.322 433.896

Particle 

density 

(kg m-3

) 1000 hour woody (35) 195.884 60.443 261.975 30.857 0.178 85.650

Shrub (185) 0.388 0.439 2.646 113.194 2.775 0.368

Herb (218) 0.257 0.172 1.242 67.142 2.213 0.152

Bulk 

density 

(kg m-3

) Litter+Duff (24) 416.400 321.028 1088.208 77.096 0.982 437.342

1 hour woody (25) 3.613 5.794 30.314 160.369 4.421 1.430

10 hour woody (29) 1.048 0.678 2.859 64.696 1.683 0.692

100 hour woody (9) 0.730 0.240 0.755 32.921 1.143 0.320

1000 hour woody (10) 0.778 0.507 1.333 65.163 1.422 0.649

Mineral 

content 

(%)

Litter+Duff (34) 47.470 21.348 71.626 44.971 -0.442 38.953

Tenderfoot Forest (TF)

1 hour woody (124) 0.066 0.057 0.328 85.857 2.021 0.042

10 hour woody (124) 0.136 0.179 1.293 131.747 3.792 0.141

100 hour woody (124) 0.046 0.115 0.600 252.185 3.514 0.040

1000 hour woody (123) 0.568 0.707 3.800 124.490 2.356 0.600

Shrub (124) 0.053 0.042 0.194 78.628 1.312 0.051

Herb (124) 0.027 0.020 0.150 73.383 2.482 0.030

Litter+Duff (124) 4.704 3.046 18.551 64.743 1.795 3.417

Loading 

(kg m-2

)

Entire fuelbed (124) 5.037 3.106 19.001 61.664 1.755 3.297

1 hour woody (27) 567.025 162.651 949.998 28.685 0.880 72.521

10 hour woody (25) 498.520 90.985 366.413 18.251 0.117 103.074

100 hour woody (7) 453.666 132.549 396.242 29.217 0.281 222.792

Particle 

density 

(kg m-3

) 1000 hour woody (38) 190.299 25.869 110.337 13.594 -0.241 39.659

Shrub (212) 0.382 0.290 1.505 75.794 1.216 0.364

Herb (213) 0.241 0.148 0.783 61.646 0.977 0.213

Bulk 

density 

(kg m-3

) Litter+Duff (30) 191.102 169.148 846.763 88.512 2.863 142.766

1 hour woody (27) 1.583 1.189 5.341 75.117 2.527 0.792

10 hour woody (23) 3.591 13.222 63.865 368.152 4.788 0.541

100 hour woody (4) 0.758 0.316 0.674 41.611 0.054 0.600

1000 hour woody (7) 0.510 0.165 0.463 32.419 1.548 0.181

Mineral 

content 

(%)

Litter+Duff (30) 28.441 19.161 63.324 67.370 0.902 27.328

Ninemile (NM)

1 hour woody (120) 0.023 0.044 0.389 187.886 5.609 0.017

10 hour woody (120) 0.198 0.410 3.155 207.272 4.699 0.113

100 hour woody (120) 0.219 0.501 4.578 228.263 6.173 0.261

1000 hour woody (120) 0.377 0.386 2.600 101.328 2.183 0.500

Shrub (120) 0.076 0.081 0.454 105.949 2.904 0.058

Herb (120) 0.041 0.020 0.104 48.796 0.812 0.020

Litter+Duff (120) 4.459 2.988 18.815 67.006 2.128 2.757

Loading 

(kg m-2

)

Entire fuelbed (120) 5.016 3.430 20.415 68.374 2.278 2.867

-2)

-3)

-2)

-2)

-3)

-3)

-3)
24 USDA Forest Service RMRS-RP-98. 2012.

1 hour woody (21) 606.059 125.187 548.027 20.656 -0.897 104.759

10 hour woody (22) 553.432 200.092 1027.321 36.155 3.019 98.373

100 hour woody (14) 519.869 88.084 275.055 16.944 -0.405 153.463

Particle 

density 

(kg m-3

) 1000 hour woody (19) 178.130 55.634 203.496 31.232 0.333 89.744

Shrub (203) 0.633 1.099 14.748 173.661 10.75 0.450

Herb (215) 0.629 5.628 82.713 894.363 14.65 0.153

Bulk 

density 

(kg m-3

) Litter+Duff (25) 148.696 120.347 598.811 80.935 2.838 98.197

1 hour woody (21) 2.043 0.668 2.303 32.701 -0.363 1.058

10 hour woody (23) 1.540 0.550 1.810 35.694 -0.396 1.015

100 hour woody (6) 0.552 0.198 0.515 35.804 -1.486 0.316

1000 hour woody (5) 0.672 0.242 0.534 36.001 -0.001 0.476

Duff (25) 14.640 9.136 29.136 62.402 0.453 15.187

Mineral 

content 

(%)

Litter (25) 33.499 16.087 51.247 48.022 0.220 29.622

Bighole Valley (BV)

1 hour woody (124) 0.005 0.005 0.027 100.616 2.555 0.003

10 hour woody (124) 0.009 0.022 0.214 240.723 6.529 0.010

100 hour woody (124) 0.004 0.029 0.300 776.240 9.396 0.000

1000 hour woody No logs were found on any plots

Shrub (124) 0.225 0.110 0.686 49.054 1.280 0.087

Herb (124) 0.044 0.112 0.978 251.382 6.867 0.024

Litter+Duff (124) 0.210 0.221 1.045 105.549 1.851 0.201

Loading 

(kg m-2

)

Entire fuelbed (124) 0.497 0.323 1.801 64.982 1.633 0.262

1 hour woody (21) 595.585 111.023 515.873 18.641 2.709 64.699

10 hour woody (2) 597.330 107.264 151.694 17.957 Not enough data

100 hour woody No fuel particles were found on any plots

Particle 

density 

(kg m-3

) 1000 hour woody No logs were found on any plots

Shrub (216) 1.833 1.790 19.454 97.630 5.186 1.260

Herb (223) 0.331 0.723 7.752 218.699 8.484 0.211

Bulk 

density 

(kg m-3

) Litter+Duff (30) 153.426 214.647 1097.277 139.903 3.209 200.613

1 hour woody (29) 8.311 3.303 13.172 39.742 0.741 4.356

10 hour woody (22) 7.999 2.817 12.747 35.214 1.004 3.552

100 hour woody No fuel particles were found on any plots

1000 hour woody No logs were found on any plots

Mineral 

content 

(%)

Litter+Duff (30) 46.931 17.401 54.870 37.079 -0.469 29.916

Silver Mountain (SM)

1 hour woody (123) 0.008 0.009 0.061 109.691 3.037 0.006

10 hour woody (123) 0.025 0.082 0.654 328.719 6.279 0.026

100 hour woody (123) 0.025 0.110 1.000 444.586 6.729 0.000

1000 hour woody (123) 0.113 0.685 7.400 603.667 9.751 0.018

Shrub (123) 0.092 0.187 1.283 202.769 3.785 0.164

Herb (123) 0.011 0.089 1.000 846.729 11.155 0.001

Litter+Duff (123) 1.431 2.141 16.603 149.595 3.470 2.037

Loading 

(kg m-2

)

Entire fuelbed (123) 1.556 2.190 16.668 140.741 3.230 2.201

1 hour woody (26) 657.414 119.498 466.667 18.177 0.689 182.13

10 hour woody (5) 632.553 31.303 74.297 4.949 -2.144 40.891

100 hour woody (0) No fuel particles were found on any plots

Particle 

density 

(kg m-3

) 1000 hour woody (30) 521.628 75.295 360.330 14.435 -0.147 94.512

Shrub (48) 1.105 0.894 5.053 80.833 2.566 0.928

Herb (122) 1.782 12.734 99.996 714.626 7.708 0.073

Bulk 

density 

(kg m-3

) Litter+Duff (22) 339.816 976.524 4784.88 287.368 4.693 188.08

1 hour woody (29) 3.262 2.732 16.553 83.759 -0.509 2.259

10 hour woody (10) 4.249 2.918 9.433 68.671 1.837 3.196

100 hour woody (0) 2.168 No fuel particles were found on any plots

1000 hour woody (10) 1.097 0.371 1.038 33.832 0.709 0.618

Mineral 

content 

(%)

Litter+Duff (27) 41.190 23.509 93.519 57.075 0.375 41.697

Colville Forest (CV)

Table 7. General statistics describing the variability of the surface fuel components across the six study sites. Number in 

parentheses under fuel component is the number of observations.

Fuel

Attribute Fuel Component Mean

Standard 

Deviation Range

Coefficient 

of Variation 

(CV) Skewness IQR

Lubrecht Forest (LF)

1 hour woody (125) 0.027 0.037 0.273 134.922 3.626 0.030

10 hour woody (125) 0.458 1.169 9.859 255.345 5.728 0.264

100 hour woody (125) 0.103 0.292 2.500 284.212 5.621 0.085

1000 hour woody (125) 0.276 0.597 6.00 216.131 7.355 0.260

Shrub (125) 0.056 0.064 0.409 113.626 3.115 0.045

Herb (125) 0.032 0.019 0.146 59.039 3.486 0.014

Litter+Duff (125) 11.379 6.654 35.616 58.473 1.393 7.518

Loading 

(kg m-2)

Entire fuelbed (125) 12.058 7.343 43.989 60.895 1.639 8.030

1 hour woody (22) 629.228 174.487 798.755 27.730 -0.566 181.180

10 hour woody (28) 509.909 209.232 865.870 41.033 1.638 189.066

100 hour woody (13) 326.899 226.709 702.471 69.351 0.322 433.896

Particle 

density 

(kg m-3) 1000 hour woody (35) 195.884 60.443 261.975 30.857 0.178 85.650

Shrub (185) 0.388 0.439 2.646 113.194 2.775 0.368

Herb (218) 0.257 0.172 1.242 67.142 2.213 0.152

Bulk 

density 

(kg m-3) Litter+Duff (24) 416.400 321.028 1088.208 77.096 0.982 437.342

1 hour woody (25) 3.613 5.794 30.314 160.369 4.421 1.430

10 hour woody (29) 1.048 0.678 2.859 64.696 1.683 0.692

100 hour woody (9) 0.730 0.240 0.755 32.921 1.143 0.320

1000 hour woody (10) 0.778 0.507 1.333 65.163 1.422 0.649

Mineral 

content 

(%)

Litter+Duff (34) 47.470 21.348 71.626 44.971 -0.442 38.953

Tenderfoot Forest (TF)

1 hour woody (124) 0.066 0.057 0.328 85.857 2.021 0.042

10 hour woody (124) 0.136 0.179 1.293 131.747 3.792 0.141

100 hour woody (124) 0.046 0.115 0.600 252.185 3.514 0.040

1000 hour woody (123) 0.568 0.707 3.800 124.490 2.356 0.600

Shrub (124) 0.053 0.042 0.194 78.628 1.312 0.051

Herb (124) 0.027 0.020 0.150 73.383 2.482 0.030

Litter+Duff (124) 4.704 3.046 18.551 64.743 1.795 3.417

Loading 

(kg m-2)

Entire fuelbed (124) 5.037 3.106 19.001 61.664 1.755 3.297

1 hour woody (27) 567.025 162.651 949.998 28.685 0.880 72.521

10 hour woody (25) 498.520 90.985 366.413 18.251 0.117 103.074

100 hour woody (7) 453.666 132.549 396.242 29.217 0.281 222.792

Particle 

density 

(kg m-3) 1000 hour woody (38) 190.299 25.869 110.337 13.594 -0.241 39.659

Shrub (212) 0.382 0.290 1.505 75.794 1.216 0.364

Herb (213) 0.241 0.148 0.783 61.646 0.977 0.213

Bulk 

density 

(kg m-3) Litter+Duff (30) 191.102 169.148 846.763 88.512 2.863 142.766

1 hour woody (27) 1.583 1.189 5.341 75.117 2.527 0.792

10 hour woody (23) 3.591 13.222 63.865 368.152 4.788 0.541

100 hour woody (4) 0.758 0.316 0.674 41.611 0.054 0.600

1000 hour woody (7) 0.510 0.165 0.463 32.419 1.548 0.181

Mineral 

content 

(%)

Litter+Duff (30) 28.441 19.161 63.324 67.370 0.902 27.328

Ninemile (NM)

1 hour woody (120) 0.023 0.044 0.389 187.886 5.609 0.017

10 hour woody (120) 0.198 0.410 3.155 207.272 4.699 0.113

100 hour woody (120) 0.219 0.501 4.578 228.263 6.173 0.261

1000 hour woody (120) 0.377 0.386 2.600 101.328 2.183 0.500

Shrub (120) 0.076 0.081 0.454 105.949 2.904 0.058

Herb (120) 0.041 0.020 0.104 48.796 0.812 0.020

Litter+Duff (120) 4.459 2.988 18.815 67.006 2.128 2.757

Loading 

(kg m-2)

Entire fuelbed (120) 5.016 3.430 20.415 68.374 2.278 2.867

(kg m

3

) 1000 hour woody (38) 190.299 25.869 110.337 13.594 -0.241 39.659

Shrub (212) 0.382 0.290 1.505 75.794 1.216 0.364

Herb (213) 0.241 0.148 0.783 61.646 0.977 0.213

Bulk 

density 

(kg m-3) Litter+Duff (30) 191.102 169.148 846.763 88.512 2.863 142.766

1 hour woody (27) 1.583 1.189 5.341 75.117 2.527 0.792

10 hour woody (23) 3.591 13.222 63.865 368.152 4.788 0.541

100 hour woody (4) 0.758 0.316 0.674 41.611 0.054 0.600

1000 hour woody (7) 0.510 0.165 0.463 32.419 1.548 0.181

Mineral 

content 

(%)

Litter+Duff (30) 28.441 19.161 63.324 67.370 0.902 27.328

Ninemile (NM)

1 hour woody (120) 0.023 0.044 0.389 187.886 5.609 0.017

10 hour woody (120) 0.198 0.410 3.155 207.272 4.699 0.113

100 hour woody (120) 0.219 0.501 4.578 228.263 6.173 0.261

1000 hour woody (120) 0.377 0.386 2.600 101.328 2.183 0.500

Shrub (120) 0.076 0.081 0.454 105.949 2.904 0.058

Herb (120) 0.041 0.020 0.104 48.796 0.812 0.020

Litter+Duff (120) 4.459 2.988 18.815 67.006 2.128 2.757

Loading 

(kg m-2)

Entire fuelbed (120) 5.016 3.430 20.415 68.374 2.278 2.867

Table 7. Continued.

-3)

-3)

-2)

-2)

-3)

-3)

-3)

-3)

100 hour wood No fuel particles were found on subsampled microplots

No fuel particles were found on subsampled microplots

No fuel particles were found on subsampled microplots

No fuel particles were found on subsampled microplots
USDA Forest Service RMRS-RP-98. 2012. 25

SM). The sagebrush-grassland site (BV) had the highest shrub and herb loadings 

and variance, but for shrubs, variance was only half the mean, yet the variance 

of the herb loading was 2.5 times the mean. Herb loadings were low for all sites 

(0.011 kg m-2 at SM to 0.056 kg m-2 at CF) with correspondingly low standard 

deviations and ranges (0.019 to 0.112 kg m-2 and IQR of 0.001 to 0.035 kg m-2). 

Coefficient of variation values were below 100 percent for all but two sites; the 

sagebrush grassland (BV) was 251 percent and the pinyon juniper (SM) woodland 

was 850 percent. Similar to down woody fuels, loadings of shrub and herbs were 

positively skewed toward plots with high fuel loadings (skewness statistic ranged 

from 0.8 to 11.0 for herbs and 1.3 to 7.0 for shrubs). Herb loadings were the most 

skewed, while shrubs tended to have skewness statistics around 3.0 for many sites.

The highest loads were typically found in the litter+duff fuel component ranging from 0.2 kg m-2 (BV) to 11.3 kg m-2 (LF), and these loads usually comprised 

over 90 percent of the total fuelbed load. These loads had a high standard error 

(0.22 to 6.6 kg m-2), but they also had a low coefficient of variation (58 to 149 percent) with respect to the other fuel components. The high loads at LF were due to 

the high bulk density values (average of 416 kg m-3) measured for this site, which 

was probably a result of the harvest residues containing many woody particles embedded in the litter+duff profile. Duff and litter loading was the least skewed with 

statistics ranging from 0.2 to 3.5, indicating that this is the only fuel component 

where loadings may be normally distributed.

Overall, it appears that fuel component loadings were rarely correlated with 

each other (Table 8). While most correlation coefficients were significant (p<0.05), 

the highest correlation was 0.41 between 10 and 100 hr fine woody fuels. All others were well below 0.3 and were both positive and negative, indicating a general 

lack of correlation across surface fuel components. Interestingly, log loadings were 

especially unrelated to all other fuel loadings with coefficients ranging from -0.07 

for logs to shrub correlations to 0.23 for logs to 10 hr woody fuel.

Table 7. General statistics describing the variability of the surface fuel components across the six study sites. Number in 

parentheses under fuel component is the number of observations.

Fuel

Attribute Fuel Component Mean

Standard 

Deviation Range

Coefficient 

of Variation 

(CV) Skewness IQR

Lubrecht Forest (LF)

1 hour woody (125) 0.027 0.037 0.273 134.922 3.626 0.030

10 hour woody (125) 0.458 1.169 9.859 255.345 5.728 0.264

100 hour woody (125) 0.103 0.292 2.500 284.212 5.621 0.085

1000 hour woody (125) 0.276 0.597 6.00 216.131 7.355 0.260

Shrub (125) 0.056 0.064 0.409 113.626 3.115 0.045

Herb (125) 0.032 0.019 0.146 59.039 3.486 0.014

Litter+Duff (125) 11.379 6.654 35.616 58.473 1.393 7.518

Loading 

(kg m-2)

Entire fuelbed (125) 12.058 7.343 43.989 60.895 1.639 8.030

1 hour woody (22) 629.228 174.487 798.755 27.730 -0.566 181.180

10 hour woody (28) 509.909 209.232 865.870 41.033 1.638 189.066

100 hour woody (13) 326.899 226.709 702.471 69.351 0.322 433.896

Particle 

density 

(kg m-3) 1000 hour woody (35) 195.884 60.443 261.975 30.857 0.178 85.650

Shrub (185) 0.388 0.439 2.646 113.194 2.775 0.368

Herb (218) 0.257 0.172 1.242 67.142 2.213 0.152

Bulk 

density 

(kg m-3) Litter+Duff (24) 416.400 321.028 1088.208 77.096 0.982 437.342

1 hour woody (25) 3.613 5.794 30.314 160.369 4.421 1.430

10 hour woody (29) 1.048 0.678 2.859 64.696 1.683 0.692

100 hour woody (9) 0.730 0.240 0.755 32.921 1.143 0.320

1000 hour woody (10) 0.778 0.507 1.333 65.163 1.422 0.649

Mineral 

content 

(%)

Litter+Duff (34) 47.470 21.348 71.626 44.971 -0.442 38.953

Tenderfoot Forest (TF)

1 hour woody (124) 0.066 0.057 0.328 85.857 2.021 0.042

10 hour woody (124) 0.136 0.179 1.293 131.747 3.792 0.141

100 hour woody (124) 0.046 0.115 0.600 252.185 3.514 0.040

1000 hour woody (123) 0.568 0.707 3.800 124.490 2.356 0.600

Shrub (124) 0.053 0.042 0.194 78.628 1.312 0.051

Herb (124) 0.027 0.020 0.150 73.383 2.482 0.030

Litter+Duff (124) 4.704 3.046 18.551 64.743 1.795 3.417

Loading 

(kg m-2)

Entire fuelbed (124) 5.037 3.106 19.001 61.664 1.755 3.297

1 hour woody (27) 567.025 162.651 949.998 28.685 0.880 72.521

10 hour woody (25) 498.520 90.985 366.413 18.251 0.117 103.074

100 hour woody (7) 453.666 132.549 396.242 29.217 0.281 222.792

Particle 

density 

(kg m-3) 1000 hour woody (38) 190.299 25.869 110.337 13.594 -0.241 39.659

Shrub (212) 0.382 0.290 1.505 75.794 1.216 0.364

Herb (213) 0.241 0.148 0.783 61.646 0.977 0.213

Bulk 

density 

(kg m-3) Litter+Duff (30) 191.102 169.148 846.763 88.512 2.863 142.766

1 hour woody (27) 1.583 1.189 5.341 75.117 2.527 0.792

10 hour woody (23) 3.591 13.222 63.865 368.152 4.788 0.541

100 hour woody (4) 0.758 0.316 0.674 41.611 0.054 0.600

1000 hour woody (7) 0.510 0.165 0.463 32.419 1.548 0.181

Mineral 

content 

(%)

Litter+Duff (30) 28.441 19.161 63.324 67.370 0.902 27.328

Ninemile (NM)

1 hour woody (120) 0.023 0.044 0.389 187.886 5.609 0.017

10 hour woody (120) 0.198 0.410 3.155 207.272 4.699 0.113

100 hour woody (120) 0.219 0.501 4.578 228.263 6.173 0.261

1000 hour woody (120) 0.377 0.386 2.600 101.328 2.183 0.500

Shrub (120) 0.076 0.081 0.454 105.949 2.904 0.058

Herb (120) 0.041 0.020 0.104 48.796 0.812 0.020

Litter+Duff (120) 4.459 2.988 18.815 67.006 2.128 2.757

Loading 

(kg m-2)

Entire fuelbed (120) 5.016 3.430 20.415 68.374 2.278 2.867

Table 7. Continued.

1 hour woody (111) 0.017 0.014 0.076 80.049 2.250 0.010

10 hour woody (111) 0.078 0.150 1.440 193.649 7.039 0.037

100 hour woody (111) 0.082 0.152 0.800 185.399 2.480 0.100

1000 hour woody (111) 0.657 0.685 4.200 105.532 2.117 0.777

Shrub (111) 0.055 0.097 0.951 176.966 7.073 0.038

Herb (111) 0.056 0.025 0.164 44.417 0.948 0.035

Litter+Duff (111) 2.546 1.322 7.124 51.930 0.239 1.614

Loading 

(kg m-2

)

Entire fuelbed (111) 2.745 1.491 7.540 54.310 0.243 1.691

1 hour woody (19) 493.475 45.402 132.103 9.201 -0.101 87.505

10 hour woody (11) 482.016 76.071 281.294 15.782 0.151 98.342

100 hour woody No Data

Particle 

density 

(kg m-3

) 1000 hour woody (40) 348.273 102.038 399.177 29.298 0.220 162.637

Shrub (159) 0.671 0.545 3.460 81.155 1.574 0.730

Herb (207) 0.210 0.157 1.068 74.575 2.328 0.161

Bulk 

density 

(kg m-3

) Litter+Duff (30) 66.132 41.798 168.133 63.203 0.789 61.326

1 hour woody (24) 1.239 0.968 5.263 78.112 3.288 0.652

10 hour woody (23) 0.889 0.382 1.401 42.933 0.641 0.626

100 hour woody (6) 0.604 0.126 0.365 20.846 -0.661 0.202

1000 hour woody (10) 0.609 0.189 0.576 31.055 -0.103 0.362

Mineral 

content 

(%)

Litter+Duff (30) 22.152 12.485 51.851 56.361 0.924 21.064

100 hour woody (0) No fuel particles were found on any plots

(kg m-3) 1000 hour woody (30) 521.628 75.295 360.330 14.435 -0.147 94.512

Shrub (48) 1.105 0.894 5.053 80.833 2.566 0.928

Herb (122) 1.782 12.734 99.996 714.626 7.708 0.073

Bulk 

density 

(kg m-3) Litter+Duff (22) 339.816 976.524 4784.88 287.368 4.693 188.08

1 hour woody (29) 3.262 2.732 16.553 83.759 -0.509 2.259

10 hour woody (10) 4.249 2.918 9.433 68.671 1.837 3.196

100 hour woody (0) 2.168 No fuel particles were found on any plots

1000 hour woody (10) 1.097 0.371 1.038 33.832 0.709 0.618

Mineral 

content 

(%)

Litter+Duff (27) 41.190 23.509 93.519 57.075 0.375 41.697

Colville Forest (CV)

-2)

-3)

-3)

(CF)
26 USDA Forest Service RMRS-RP-98. 2012.

Figure 10. Box and whisker plots of the loadings (kg m-2) of each surface fuel component across all sampled sites: 

(a) Lubrecht Forest, (b) Tenderfoot Forest, (c) Ninemile, (d) Colville Forest, (e) Bighole Valley, and (f) Silver Mountain.

Ninemile

Fuel Component

Duff/Litter Herbs Shrubs 1 hour 10 hour 100 hour 1000 hour

Loading (kg m-2)

0

2

4

6

8

10

Lubrecht

Fuel Component

Duff/Litter Herbs Shrubs 1 hour 10 hour 100 hour 1000 hour

Loading (kg m-2)

0

5

10

15

20

25

30

Big Hole

Fuel Component

Duff/Litter Herbs Shrubs 1 hour 10 hour 100 hour

Loading (kg m-2) 0.0

0.2

0.4

0.6

0.8

Colville

Fuel component

Duff/Litter Herbs Shrubs 1 hour 10 hour 100 hour 1000 hour

Loading (kg m-2) 0

1

2

3

4

5

Tenderfoot

Fuel Component

Duff/Litter Herbs Shrubs 1 hour 10 hour 100 hour 1000 hour

Loading (kg m-2)

0

2

4

6

8

10

12

Silver Mountain

Fuel Component

Duff/Litter Herbs Shrubs 1 hour 10 hour 100 hour 1000 hour

Loading (kg m-2) 0

1

2

3

4

5

6

(a) (b)

(c) (d)

(e) (f)
USDA Forest Service RMRS-RP-98. 2012. 27

Particle Density. While not as variable as loadings, the density of wood particles was different by fuel component and sample site (Table 7). In general, wood 

particle densities usually decreased as particle diameter increased, and, as expected, wood particle density was more variable across sites than fuel components. 

Densities of 1 hr particles ranged from 493 kg m-3 (CF) to 657 kg m-3 (SM) with 

standard deviations that were from 9 percent to 28 percent of the mean (45 kg m-3

at CF to 163 kg m-3 at TF). The ranges and IQR were also small (65 to 182 kg m-3), 

and particle densities for this fuel component were also the most highly skewed 

(skewness ranging from -0.1 to 2.7). Particle densities were quite high for these 

fine woody fuels and probably reflect the difficulty of measuring volume on these 

small twigs.

The 10 and 100 hr fuels showed the highest variation across sites with means 

that were the closest to documented densities of sound wood. Particle densities of 

10 hr fuels ranged from 482 kg m-3 at the CF pine savanna to over 632 kg m-3 at 

the pinyon-juniper SM site (Table 7) with corresponding deviations of 31 kg m-3

(SM) to 209 kg m-3 (LF), ranges of 74 kg m-3 (SM) to over 1000 kg m-3 (NM), and 

IQRs of 41 (SM) to over 189 (LF). However, this variation was not a significant 

portion of the mean with coefficients of variation ranging from 5 (SM) to 41 percent (LF). Only three sites had 100 hr fuel particles, but these sites had the highest 

variabilities with means ranging from 326 kg m-3 (LF) to 519 kg m-3 (NM), standard deviations from 88 to 226 kg m-3, and ranges from 275 to 702 kg m-3. And like 

other fuel components, this variability in 100 hr fuels was not a significant portion 

of the mean (16 percent at NM to 69 at LF). The 100 hr fuel particle densities were 

the one fuel characteristic that was mostly normally distributed with skewness 

statistics between -1.0 and 1.0.

Logs had the lowest particle densities (178 kg m-3 at NM to 523 kg m-3 for SM) 

with the lowest deviations (25 kg m-3 for TF to 102 kg m-3 for CF) that were around 

4 to 30 percent of the mean. Log densities also seemed to be somewhat normally 

distributed (skewness between -0.2 to 0.2) in a narrow range of sampled values. 

Most sites had log densities below 200 kg m-3 (LF, TF, NM), reflecting the high 

proportion of rotten logs in the sample.

Table 8. Pearson’s correlation table for surface fuel loadings for all plots across all sites.

Surface Fuel Component

Surface Fuel

Component 1 hour 10 hour 100 hour Shrubs Herbs Litter+Duff

10 hour 0.197** *

(n = 1321)

100 hour 0.150*** 0.408***

(n = 1322) (n = 1321)

Shrubs -0.088*** -0.074*** -0.048*

(n = 1321) (n = 1323) (n = 1322)

Herbs -0.001 -0.009 0.075*** 0.246***

(n = 1322) (n = 1320) (n = 1321) (n = 1321)

Litter+Duff 0.174*** 0.334*** 0.265*** -0.193*** 0.007

(n = 1322) (n = 1321) (n = 1322) (n = 1322) (n = 1321)

Logs 0.074* 0.231*** 0.088** -0.066 0.128*** 0.081**

(n = 599) (n = 600) (n = 599) (n = 600) (n = 599) (n = 600)

*significant at .10

**significant at .05

***significant at .01
28 USDA Forest Service RMRS-RP-98. 2012.

Bulk Density. Shrub layer bulk densities were surprisingly low in variability 

across sites when compared with woody fuel particle densities (Table 7). Shrub 

layer bulk densities ranged from 0.67 kg m-3 at the CF pine grassland savanna 

to over 1.8 kg m-3 for the sagebrush grassland BV site. Variability statistics were 

somewhat low with low deviations (0.29 kg m-3 for grouse whortleberry at TF 

to 1.7 kg m-3 at the sagebrush BV site), high ranges (1.5 kg m-3 at TF to over 

14 kgm-3 at NM), and low IQR (0.36 kg m-3 at LF to 1.3 kg m-3 at BV), indicat-

ing a few plots containing high abundance of shrubs at each site. This variability 

was around 90 percent of the mean (coefficient of variation ranged from 75 per-

cent for TF to 113 percent for LF) and highly skewed from normal (skewness 

from 1.2 to 10.7).

Herb layer bulk densities were similar in magnitude to shrubs ranging from 

0.21 kg m-3 in the pine savanna of CF to 1.78 kg m-3 in the SM pinyon-juniper, 

and they were also as variable across sites (Table 7). Standard deviations and 

ranges were lowest (0.15 kg m-3 and 0.78 kg m-3, respectively) on the grouse 

whortleberry understory of TF and the pine-grass savanna of CF and highest on 

the SM pinyon-juniper site (12.7 kg m-3 and 99.99 kg m-3, respectively). This 

variation was around 70 percent of the mean for three sites (LF, TF, and CF), but 

was over 200 percent for the other three (BV was at 219 percent, NM was at 894 

percent, and SM was over 700 percent). Herb bulk densities were more skewed 

than shrubs with ranges from 0.98 to 14.65 and 1.20 to 10.75, respectively.

The litter+duff bulk densities were much higher than shrub and herb layer 

bulk densities, but their variabilities were quite similar. Duff and litter bulk den-

sities were high, ranging from 66 kg m-3 in the pine needle-grass layer of CF to 

416 kg m-3 in the logging residue pine-fir-larch stand of LF. The litter+duff layer 

bulk density deviations were quite variable from 42 kg m-3 in the homogeneous 

pine-grass of CF to 976 kg m-3 at the highly discontinuous pinyon-juniper SM 

site, and the span of bulk densities were only 168 at CF to over 1000 kg m-3 at 

three sites with discontinuous litter+duff layers (LF, BV, and SM where the range 

was over 4000 kg m-3). While this range is somewhat large, the deviation was 

mostly less than 100 percent of the mean (coefficient of variations ranged from 

63 in the pine savanna of CF to over 287 at the SM pinyon-juniper). Skewness 

statistics were well above 0.5, indicating a high number of dense litter+duff layer 

measurements.

Mineral Content. Of all the fuel characteristics, the percent mineral content 

was the least variable within a site but it did tend to vary across fuel components 

and across sites (Table 7). One hour fuel particles had the highest mineral con-

tents for the downed woody fuels, ranging from 1.2 percent at CF to 8.3 percent 

at BV, while the 10 hr woody fuels were the most variable (over 300 percent 

coefficient of variation on TF). Logs had the lowest mineral contents (less than 

1 percent), but their coefficients of variation were comparable to the fine woody 

fuels (31 percent to 65 percent at LF). The BV sagebrush grassland easily had the 

highest mineral contents of all woody fuel components (greater than 8 percent), 

while the CF pine savanna had the lowest contents (less than 1.2 percent). The 

three Montana forest sites (LF, TF, NM) had comparable mineral contents across 

all woody fuel components (approximately 1 to 4 percent for 1 hr, 1 to 3 percent 

for 100 hr, 0.5 to 0.8 percent for 100 hr, and 0.6 to 0.7 for 1000 hr). Overall, 

woody fuel mineral contents were moderately variable, having coefficient of 

variations that hovered around 50 percent of the mean with small ranges (IQR 

values from 0.1 to 1.0 percent).

Litter+duff mineral contents were often an order of magnitude higher than 

woody fuel mineral contents, ranging from 22 percent for the CF pine savanna 
USDA Forest Service RMRS-RP-98. 2012. 29

Table 9. Description of canopy fuel variability for canopy loading, canopy bulk density, and canopy cover for general 

variability descriptions for all sites with a tree layer (Bighole Valley site was sagebrush grassland with no canopy fuels).

Measure of Variability Canopy Loading Canopy Bulk) Canopy Cover 

Units (kg m-3) (kg m-2) (percent)

Silver Mountain (SM) Pinyon Juniper

Mean 0.83 0.28 29.84

Range 2.17 0.74 57.38

Standard Deviation 0.51 0.18 15.04

Coefficient of Variation 0.61 0.65 0.50

Skewness 0.62 0.71 0.23

IQR 0.77 0.27 22.90

Number Observations (n) 124 124 124

Colville Forest (CF) Ponderosa Pine Savanna

Mean 0.15 0.02 15.75

Range 0.45 0.06 24.41

Standard Deviation 0.08 0.01 5.34

Coefficient of Variation 0.52 0.53 0.34

Skewness 1.06 2.15 0.69

IQR 0.12 0.01 5.09

Number Observations (n) 69 69 69

Ninemile (NM) Ponderosa Pine-Douglas-Fir

Mean 0.70 0.08 35.82

Range 1.77 0.21 51.64

Standard Deviation 0.34 0.05 11.70

Coefficient of Variation 0.49 0.57 0.33

Skewness 1.00 1.02 0.11

IQR 0.46 0.06 18.24

Number Observations (n) 120 120 120

Lubrecht Forest (LF) Ponderosa Pine-Douglas-Fir-Larch

Mean 0.58 0.06 34.20

Range 1.75 0.19 55.17

Standard Deviation 0.29 0.04 11.30

Coefficient of Variation 0.49 0.59 0.33

Skewness 1.33 1.65 0.27

IQR 0.34 0.04 13.62

Number Observations (n) 123 123 123

Tenderfoot Forest (TF) Lodgepole Pine

Mean 0.83 0.13 43.85

Range 1.11 0.34 49.98

Standard Deviation 0.21 0.06 8.89

Coefficient of Variation 0.26 0.48 0.20

Skewness -0.15 1.03 -0.35

IQR 0.28 0.08 11.56

Number Observations (n) 123 123 123

Canopy Bulk Density
30 USDA Forest Service RMRS-RP-98. 2012.

a. Canopy fuel load CFL b. Canopy bulk density CBD

c. Canopy cover CC

to over 47 percent in the LF pine-fir-larch thinning unit (Table 7). These duff 

and litter layers also had the greatest variation in range (51 to 93 percent), IQR 

(21 percent at CF to 42 percent at SM), and coefficient of variation (37 percent 

at BV to 67 percent at TF). Sites that had thinning and grazing activity seemed 

to have the highest mineral contents (SM, BV, LF).

Canopy Fuels

Canopy fuel characteristics were quite similar across sites and across all three 

variables (Table 9; Figure 11). Perhaps the most important canopy characteristic to 

fire management, CBD, ranged from 0.02 to 0.28 kg m-3 with standard deviations 

from 0.01 to 0.18, but coefficients of variation ranged from only 48 to 65 percent. The range of the data, as measured by IQR, was also quite similar (0.01 to 

0.08 kg m-3), except for the SM site, which had a high IQR of 0.271 because of 

the discontinuous canopy of the pinyon-juniper forest type. The BV sagebrushgrassland site had no canopy fuels on any of the plots within that grid.

It appears canopy fuels are highly correlated to some stand characteristics 

(Table 10), but they have little relationship with surface fuels (Table 11). Most 

canopy fuel characteristics were correlated to basal area and tree density and less 

correlated to average tree diameter and height with most of correlation coefficients 

Figure 11. Box and whisker plots of the three 

canopy fuel characteristics (a) canopy fuel 

loading (CFL, kg m-2); (b) canopy bulk 

density (CBD, kg m-3); and (c) canopy cover 

(CC, %) across all sites: Lubrecht Forest 

(LF), Tenderfoot Forest (TF), Ninemile (NM), 

Silver Mountain (SM), and Colville Forest 

(CF). Bighole Valley (BV) site was sagebrush 

grassland with no canopy fuels.
USDA Forest Service RMRS-RP-98. 2012. 31

 Table 10. Pearson’s correlation results for the three canopy fuel characteristics across all plots in all sites for the stand level 

 variables.

Average DBH 

(cm)

Average Tree Height 

(m)

Overstory Basal 

Area (m2 ha-1)

Trees Density 

(trees ha-1)

Lubrecht Forest (LF) Ponderosa Pine-Douglas-Fir-Larch

Canopy loading (kg m-2) -0.207* -0.260** 0.663*** 0.530***

Canopy bulk density (kg m-3) -0.307** -0.322** 0.595*** 0.583***

Canopy cover (%) -0.437*** -0.316** 0.854*** 0.830***

Tenderfoot Forest (TF) Lodgepole Pine

Canopy loading (kg m-2) -0.229* 0.173 0.822*** 0.853***

Canopy bulk density (kg m-3) -0.210* 0.238** 0.714*** 0.819***

Canopy cover (%) -0.286** 0.121 0.842*** 0.905***

Ninemile (NM) Ponderosa Pine-Douglas-Fir

Canopy loading (kg m-2) 0.131 0.020 0.773*** 0.709***

Canopy bulk density (kg m-3) 0.054 0.003 0.638*** 0.620***

Canopy cover (%) 0.078 -0.041 0.906*** 0.861***

Silver Mountain (SM) Pinyon Juniper

Canopy loading (kg m-2) 0.590*** 0.068 0.982*** 0.894***

Canopy bulk density (kg m-3) 0.497*** -0.095 0.928*** 0.921***

Canopy cover (%) 0.545*** 0.037 0.946*** 0.930***

Colville Forest (CF) Ponderosa Pine Savanna

Canopy loading (kg m-2) 0.061 0.051 0.199 0.110

Canopy bulk density (kg m-3) -0.165 -0.116 0.480*** 0.664***

Canopy cover (%) -0.045 0.100 0.805*** 0.795***

 *p value<0.1, **p value<0.05, ***p value<0.01

 Table 11. Pearson’s correlation table showing relationships between surface fuel loading and canopy fuel and stand 

 characteristics using values for all plots across all sites (n = 167).

Fuel

Component

Canopy 

Loading 

(kg m-2)

Canopy Bulk 

Density 

(kg m-3) 

Canopy 

Cover (%)

Average DBH 

(cm)

Average Tree 

Height (m)

Overstory 

Basal Area 

(m2 ha-1)

Trees per 

Hectare 

(m2 ha-1)

Surface fuel components (n = 320)

1 hour 0.109** -0.069 0.259*** -0.16*** 0.243*** 0.383*** 0.346***

10 hour -0.034 -0.105** 0.044 0.003 0.116*** 0.041 -0.021

100 hour -0.001 -0.079* 0.039 0.123*** 0.141*** 0.042 -0.07*

1000 hour -0.037 -0.111*** 0.051 -0.158*** 0.155*** 0.098** 0.103**

Herbs -0.021 -0.06 -0.007 0.103** 0.19*** 0.042 -0.087**

Shrubs -0.124*** -0.087** -0.177*** 0.019 -0.09** -0.157*** -0.132**

Litter+Duff -0.05 -0.245*** 0.15*** 0.102** 0.376*** 0.203*** 0.004

Canopy fuel characteristics (n = 559)

CFL, Fuel 

loading 1.000 0.791*** 0.875*** 0.069 0.010 0.688*** 0.619***

CBD, Bulk 

density 0.791*** 1.000 0.521*** -0.026 -0.058 0.671*** 0.721***

CC, Cover 0.875*** 0.521*** 1.000 -0.029 -0.020 0.871*** 0.864***

 *p value<0.1, **p value<0.05, ***p value<0.01
32 USDA Forest Service RMRS-RP-98. 2012.

significant, but these correlations were quite different across sites (Tables 10, 11). 

The highest correlations were for canopy cover to basal area across all sites, which 

ranged from 0.84 to 0.95, while the lowest coefficients were for tree height to all 

three canopy variables, which ranged from -0.32 to 0.24 across all sites. The SM 

pinyon juniper site had the highest correlations overall, ranging from 0.50 to 0.95 

excluding the tree height variable. Correlations of all canopy fuel and stand variables to the surface fuel loadings were low (<0.38), especially for coarse woody 

debris, shrubs, herbs, and litter+duff (Table 11). The highest correlations (>0.2) 

were relationships of 1 hr fuel loadings to canopy cover and all three stand characteristics. Canopy fuel characteristics were highly correlated with each other with 

coefficients ranging from 0.7 to 0.99 (Table 11).

Spatial Variability

Surface Fuel Loadings

Semivariograms of loading (kg m-2) for the seven surface fuel components 

sampled at the TF study site are shown to illustrate the complexity of fitting semivariograms for each fuel component across different sites (Figure 12). Semivariance 

values are highly variable across each of the distances in the study (Figure 12), as 

shown by the scatter of the points used to build the model. Most sites had excellent 

fits (NM, LF, TF) while the CF pine savanna site had a poor fit with widely scattered semivariances. Exponential models were used for the three Montana sites, 

but the lack of distance-semivariance relationships for CF and SM required the use 

of a Gaussian or pure nugget model.

Statistics from the semivariograms arranged across the six sites showed some 

interesting relationships (Table 12). In general, all spatial statistics (range, sill, and 

nugget) seemed to increase with fuel particle diameter (Figure 13). The litter+duff, 

shrub, and herb are the components with the smallest particle diameters, and their 

spatial statistics are quite different across sites. Litter+duff had both the lowest 

(0.058) and the highest values for the sill, indicating a great disparity of spatial 

variance across sites for this component. Shrub fuels show similar behavior in that 

low values (less than 0.7 value) were present on all but the shrubby pinyon-juniper 

SM site where sill value exceeded 2.0. In contrast, herb fuels had some of the lowest spatial variance with sills ranging from 0.08 to 0.67 in semivariance. Downed 

woody fuels showed somewhat predictable behavior in that the semivariance was 

usually positively correlated with the size of the woody particle (1hr  10 hr 

100 hr), except for 1000 hr fuels, for which the semivariance generally decreased. 

Sill values for 1 hr fuels (0.03 to 0.52) were generally lower than 10 hr fuels (0.35 

to 2.18) which were generally lower than 100 hr fuels (0.74 to 3.59), but values 

for the 1000 hr fuels (0.05 to 2.13) were more similar to 10 hr fuels and did not 

increase over 100 hr fuels. This is in direct contrast to the general variability where 

1000 hr fuels had the highest standard deviations, but those deviations were less 

than 50 percent of the mean (Table 7).

Nugget values were confusing and did not provide any additional information 

about spatial fuel variability because it was difficult to fit semivariograms with the 

data collected in this project. Nugget values usually indicate the amount of error 

involved in the measurement of the response variable, in this case fuel loading. 

However, many sites and components had nugget values at or near zero (Table 12). 

Loading measurements of fine woody debris (1, 10, 100 hr) were the most variable 

because they were quantified by corrected visual estimates, yet nugget values were 

the lowest for these components. The highest nugget values (1.1 and 1.7) were for 
USDA Forest Service RMRS-RP-98. 2012. 33 Figure 12. Semivariograms for the surface fuel characteristics measured on the Tenderfoot (TF) site: (a) duff+litter, (b) herbs, (c) shrubs, (d) 1 hr, (e) 10 hr, (f) 100 hr, and (g) 1000 hr. distance

semivariance

0.0010.0020.0030.0040.0050.006

20 40 60 80

distance

semivariance

0.51.0

20 40 60 80

distance

semivariance

0.51.0

20 40 60 80

distance

semivariance

0.10.20.30.40.5

20 40 60 80

distance

semivariance

0.050.100.150.20

20 40 60 80

distance

semivariance

0.10.20.30.40.50.6

100 200 300 400

c. Shrubs b. Herbs

distance

semivariance

0.050.100.150.200.250.30

20 40 60 80

a. Duff+litter

d. 1 hr e. 10 hr f. 100 hr g. 1000 hr
34 USDA Forest Service RMRS-RP-98. 2012.

 Table 12. Semivariogram statistics for all surface fuel components across the six sites. 

Fuel 

Component

Bighole Valley 

(BV)

Sagebrush

Grassland

Silver 

Mountain

(SM)

Pinyon

Juniper

Colville Forest 

(CF)

Pine Savannah

Ninemile

(NM)

Pine-Fir

Lubrecht Forest

(LF)

PineFir-Larch

Tenderfoot 

Forest

(TF)

Lodgepole

Pine

Sill (kg m-2)

2

1 hour 0.128 0.174 0.282 0.051 0.029 0.524

10 hour 0.350 0.917 0.744 2.188 1.825 1.274

100 hour No 100 hr 0.736 3.590 3.510 2.689 1.018

1000 hour No Logs 2.129 1.967 0.055 1.825 1.778

Shrub 0.657 2.040 0.302 0.634 0.390 0.426

Herb 0.175 0.480 0.140 0.671 0.080 0.200

Litter+Duff 0.058 2.770 3.590 0.268 0.445 0.249

Nugget (kg m-2)

2

1 hour 0.072 0.019 0.052 0.007 0.008 0.085

10 hour 0.121 0.000 0.000 1.500 0.575 0.478

100 hour No 100 hr 0.053 2.260 1.430 0.449 0.190

1000 hour No Logs 1.142 0.377 0.000 1.700 0.000

Shrub 0.389 0.000 0.000 0.000 0.050 0.000

Herb 0.000 0.000 0.000 0.103 0.000 0.073

Litter+Duff 0.059 0.000 2.260 0.115 0.000 0.016

Range (m)

1 hour 4.67 2.50 2.83 16.30 8.90 6.02

10 hour 6.60 2.46 0.88 4.95 2.23 11.10

100 hour No 100 hr 2.46 2.54 4.56 2.41 4.14

1000 hour No Logs No Logs 84.01 22.01 87.30 157.01

Shrub 2.44 15.10 0.85 1.79 3.61 2.66

Herb 0.72 1.11 0.80 3.50 0.52 1.83

Litter+Duff 0.45 1.41 2.54 1.29 0.48 0.85

Moran’s I (p value)

1 hour *0.217 *0.157 0.060 *0.184 *0.242 *0.333

10 hour *0.087 *0.109 0.021 -0.010 0.066 0.068 

100 hour No 100 hr 0.048 0.084 0.050 0.030 0.069 

1000 hour No Logs -0.004 *0.045 *0.041 -0.007 *0.024 

Shrub 0.022 *0.400 *0.074 0.018 *0.262 *0.138

Herb 0.023 0.014 *0.160 -0.012 *0.122 *0.130 

Litter+Duff 0.064 *0.130 0.117 *0.124 *0.146 *0.219 

Geary’s C (p value)

1 hour *0.90 *0.94 *0.95 *0.76 *0.79 *0.942

10 hour *0.93 *0.86 0.96 0.97 *0.88 *0.91

100 hour No 100 hr 0.99 1.03 *0.91 0.97 *0.93

1000 hour No Logs *0.88 *0.87 *0.82 1.01 0.93

Shrub 0.99 *0.73 *0.81 *0.89 *0.53 *0.93

Herb *0.95 0.99 0.95 0.96 1.01 *0.94 

Litter+Duff 0.96 *0.92 0.98 *0.84 0.99 *0.81

 *p value<0.1
USDA Forest Service RMRS-RP-98. 2012. 35

logs, which were the easiest to measure but were rarer in occurrence within the 

sampling grid. Litter+duff had both the highest (2.26) and the lowest (0.0) nugget 

values.

The range statistics provided the most important information on the spatial dynamics of surface and canopy fuels because range values indicate the inherent 

patch size of the measured entity (Table 12; Figure 13). Overall, it appears that the 

range generally increased with fuel size. Litter+duff ranges were the lowest and 

scaled from 0.5 m at LF pine-fir-larch to 2.5 m at CF pine savanna. Herbs had the 

next lowest patch size with ranges from 0.5 m (LF) to 3.5 m (NM), both pine-fir 

sites. Shrub fuels appeared to vary at the next highest scale with ranges from 0.9 m 

(CF) to 3.5 m (LF) and a large range of 15 m at SM indicating higher discontinuity 

in shrub-dominated pinyon-juniper. Fine woody fuels varied at about the same or 

greater patch sizes with 1 hr fuel ranges from 2.5 m (SM) to 16.3 m at LF, 10 hr 

ranges from 0.9 at CF to 11 m at TF, and 100 hr ranges from 2.4 m to 4.5 m (patch 

sizes are more variable with smaller particle diameters). Logs (1000 hr) fuels had 

the highest patch sizes ranging from 22 m at NM to 157 m at SM. We performed 

extensive statistical analysis relating the semivariogram range of each surface fuel 

component to the four measures of variance (standard deviation, range, IQR, and 

coefficient of variation) and found no significant relationships (Figure 16).

Figure 13. Spatial semivariogram statistics for each fuel component across all sites.

Range

Fuel Component

Duff/Litter Herbs Shrubs 1 hour 10 hour 100 hour 1000 hour

Range (m)

0

50

100

150

200

250

300

Big Hole

Silver Mountain

Colville

Ninemile

Lubrecht

Tenderfoot

Nugget

Fuel Component

Duff/Litter Herbs Shrubs 1 hour 10 hour 100 hour 1000 hour

Nugget 0

1

2

3

4

5

Big Hole

Silver Mountain

Colville

Ninemile

Lubrecht

Tenderfoot

Moran's I

Fuel Component

Duff/Litter Herbs Shrubs 1 hour 10 hour 100 hour 1000 hour

Moran's I -0.2

0.0

0.2

0.4

Big Hole

Silver Mountain

Colville

Ninemile

Lubrecht

Tenderfoot

Sill

Fuel Component

Duff/Litter Herbs Shrubs 1 hour 10 hour 100 hour 1000 hour

Sill 0

2

4

6

Big Hole

Silver Mountain

Colville

Ninemile

Lubrecht

Tenderfoot

a. b.

c. d.
36 USDA Forest Service RMRS-RP-98. 2012.

Most sites and fuel components had low Moran’s I values (<0.2) and Geary 

C values near 1.0, indicating that there was little spatial structure in the northern 

Rocky Mountain fuelbeds sampled in this study (Table 12). The highest Moran’s 

I values tended to be found in fine fuels, especially shrubs (0.3 at LF and 0.4 

at SM) and 1 hr woody (0.24 for LF and 0.33 for TF), for which these values 

were statistically significant (p<0.05). Logs had the least spatial structure, with 

the Moran’s I statistic less than 0.05 on all sites. Litter+duff results unexpectedly 

showed Moran’s I less than 0.2 for all sites because this layer is somewhat homogeneous and often exhibits some spatial structure over small distances. Geary’s C 

values showed nearly the same results even though this statistic was supposed to 

adjust for local settings (Table 12). The components with the least spatial structure 

were large woody fuel components (10, 100, 1000 hr components) and litter+duff 

because they had Geary’s C values between 0.95 and 1.05, but fine fuels, such as 

1 hr, shrub, and herbs, tended to have more spatial structure (values between 0.7 

to 0.9).

Canopy Fuels

Semivariance values are highly variable across each of the sites for CBD as 

show by the scatter of the points used to build the model (Figure 14). Most sites 

had excellent model fits (NM, LF, TF), but the CF pine savanna site had a poor fit 

with widely scattered semivariances. Exponential models were used for the three 

Montana sites, but the lack of distance-semivariance relationships for TF, CF, and 

SM required using a spherical, Gaussian, and pure nugget model, respectively 

(Table 13).

 The characteristics of spatial variograms for the three canopy fuel characteristics seemed remarkably similar across sites (Table 13; Figure 15). For the 

semivariogram range, values ranged from 100 to 440 m for CBD, 310 to 600 m 

for CFL, and 230 to 407 m for CC. Lowest ranges were in the closed forests of LF 

and TF (lodgepole), while the highest values were for the open SM and CF forests. CFL had the highest patch sizes (450 to 600 m), and these were significantly 

different from CBD and CC (Figure 15). The sill and nugget were significantly 

different across the three canopy characteristics, with CBD consistently having the 

lower semivariance and CC with the highest (Figure 15), probably due to differences in how each are estimated. Moran’s I statistics were also quite low for the 

canopy fuel characteristics with the highest value at 0.17 in the TF lodgepole pine 

site indicating a lack of spatial structure in canopy characteristics (Table 13). In 

general, Moran’s I was highest on the TF and SM sites, with values around 0.1, 

and lowest on the CF pine savanna, with values less than 0.08, for all three canopy 

fuel characteristics. Moran’s I values, however, were statistically similar across 

the three canopy characteristics with CC having the greatest variation in spatial 

structure (Figure 15).

It appears that canopy fuel characteristics are somewhat related to the inherent 

patch sizes (semivariogram range) of larger woody fuel (Figure 16). Large woody 

fuel ranges appeared to increase as canopy fuel increases in loading, bulk density, 

and cover, yet there seemed to be no relationship between canopy characteristics 

and litter+duff, shrubs, and fine woody debris ranges. It is odd that herb variogram 

ranges seemed to increase with canopy material, but this may be explained by the 
USDA Forest Service RMRS-RP-98. 2012. 37 Figure 14. Semivariograms for canopy bulk density across all sites in the study (a) Lubrecht Forest, (b) Tenderfoot Forest, (c) Colville Forest, (d) Ninemile, and (e) Silver Mountain. a) Lubrecht Forest b) Tenderfoot Forest c) Colville Forest d) Ninemile e) Silver Mountain
38 USDA Forest Service RMRS-RP-98. 2012.

 Table 13. Spatial semivariogram statistics for the three canopy fuel characteristics across the six sample sites. 

 Model indicates the type of model used to fit the semivariogram. 

Statistic

Bighole 

Valley 

(BV)

Sagebrush

Grassa

Silver

Mountain

(SM)

PinyonJuniper

Colville 

Forest

(CF)

Pine

Savannah

Ninemile 

(NM)

Pine-Fir

Lubrecht 

Forest (LF)

Pine-FirLarch

Tenderfoot 

Forest

(TF)

Lodgepole

Pine

Canopy Bulk Density (CBD, kg m-3)

Modelb - gaussian

pure 

nugget exponential exponential exponential

Range (m) - 440 - 412 100 120

Sill - 0.008 - 0.0014 0.001 0.0024

Nugget - 0.013 0.00014 0.0008 0.0001 0.0006

Moran’s I - *0.118 *0.083 *0.102 *0.045 0.0919

Geary’s C *0.861 1.065 *0.778 *0.721 *0.732

Canopy Fuel Loading (CFL, kg m-2)

Model2 - gaussian

pure 

nugget exponential exponential spherical

Range - 560 - 600 310 560

Sill - 0.0497 - 0.020 0.0172 0.0102

Nugget - 0.0501 0.0056 0.026 0.0154 0.0062

Moran’s I - *0.146 *0.058 *0.092 *0.052 *0.174

Geary’s C *0.814 1.033 0.892 *0.805 *0.782

Canopy Cover (CC, percent)

Model2 - gaussian

pure 

nugget pure nugget exponential gaussian

Range - 407 - - 230 300

Sill - 0.159 - - 0.048 0.0302

Nugget - 0.202 0.107 0.1197 0.103 0.0266

Moran’s I - *0.122 *0.069 *0.034 0.027 *0.162

Geary’s C *0.789 0.963 0.989 0.807 0.812

a

No tree canopy existed on the Bighole Valley site.

 bNo existent anisotropy was examined.

 *Indicates statistic is significant at p<0.01.
USDA Forest Service RMRS-RP-98. 2012. 39

Figure 15. Box and whisker plots of the four spatial statistics (a) range, (b) sill, (c) nugget, and (d) Moran’s I for the three 

canopy fuel components: canopy bulk density (CBD, kg m-3); canopy fuel loading (CFL, kg m-2); canopy cover (CC, %).

a. Range (m) b. Sill

c. Nugget d. Moran’s I
40 USDA Forest Service RMRS-RP-98. 2012.

Figure 16. Semivariogram range 

statistics for loading of each surface 

fuel component by the average 

canopy fuel characteristics computed 

across all plots on all sites.

Range versus canopy bulk density

CBD (kg m-3)

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Range (m)

0

50

100

150

200

250

300

1 hour

10 hour

100 hour

1000 hour

Herbs

Shrubs

Duff/Litter

Range versus canopy cover

Canopy cover (%)

10 15 20 25 30 35 40 45 50

Range (m)

0

50

100

150

200

250

300

1 hour

10 hour

100 hour

1000 hour

Herbs

Shrubs

Duff/Litter

Range versus canopy loading

Canopy loading (kg m-2)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Range (m)

0

50

100

150

200

250

300

1 hour

10 hour

100 hour

1000 hour

Herbs

Shrubs

Duff/Litter

(a)

(b)

(c)
USDA Forest Service RMRS-RP-98. 2012. 41

patchiness of herb coverage. CBD seemed to have the best fit with log loading 

semivariogram range.

Discussion

Perhaps the most important characteristic about wildland fuel is not its loading 

but the variability of that loading across the landscape, and this variability occurs 

at multiple scales depending on the size and type of fuel. The great heterogeneity 

of the fuel loading within small areas has more of an effect on fire behavior than 

the average loading (Parsons and others 2010) because fine-to-coarse scale spatial fuel distributions may influence fire spread and intensity more than the actual 

amount of that fuel. Moreover, the impact of this highly variable spread and intensity on the biophysical environment leaves behind a complex mosaic of fire effects 

that is governed not only by the scale of the fuel variability but also by the scale of 

the fire. Understanding this variability is the key to predicting complex, interacting 

fire behavior and effects.

Several important results from this study provide insight into understanding 

general fuel variability. First, and most obvious, is that all fuels are highly variable (Tables 7, 9). Most surface fuel components have properties that are highly 

variable: loading, for example, had variabilities that are often more than twice 

the mean, and we confined sampling to homogeneous stands. Second, it appears 

that this variability increases with fuel particle size; larger surface fuel properties 

are more variable than finer fuel properties (Table 7). Canopy fuel properties, on 

the other hand, have significantly lower variabilities than surface fuel components 

(less than 100 percent of mean), and this variability appears to be consistent across 

all canopy fuel characteristics (Table 9). It also appears that surface fuel loadings 

are not correlated to canopy fuel variables, general stand characteristics, and other 

surface fuel components (Table 11), but all canopy fuel variables were correlated 

to some commonly used stand characteristics (Table 10). Last, it appears that fuel 

loadings are rarely normally distributed with skewness statistics often greater than 

1.0 for many components and sites (Table 7). These results are not new, nor are 

they unexpected, and they somewhat agree with results from other studies (Brown 

and Bevins 1986; Delisle and others 1988; Thaxton and Platt 2006; King and others 2008).

The findings of this study that are new concern the spatial distribution of this 

variability across the surface and canopy fuel components. It appears that surface 

fuel components vary across different spatial scales with finer fuels of litter, duff, 

herbs, shrubs, and fine woody fuels varying at scales of meters to tens of meters, 

and larger surface fuels, such as 100 and 1000 hr fuels, vary at scales of tens 

to hundreds of meters (Table 12). Canopy fuels vary at still coarser scales (100 

to 400 m) (Table 13). Moreover, this spatial variability differs across sites, with 

closed canopy sites having somewhat smaller patch sizes than open canopies and 

rangeland settings (i.e., fuel component variability is highly variable across ecosystems). Larger fuels have less spatial structure than fine fuels as indicated by 

the low values of Moran’s I (less than 0.2; Table 12), and spatial distribution of 

logs are somewhat related to canopy fuels (Figure 15). This difference in scale and 

spatial distribution across surface fuel components could partly explain the lack of 

correlation of most surface fuels to canopy fuel variables and stand characteristics 

even though the forest canopy is the source for most of the litter that falls on the 

surface fuelbed.
42 USDA Forest Service RMRS-RP-98. 2012.

So, why are wildland fuels so variable? We feel that this variability is a result of 

many factors acting across different time and space scales. Most importantly, the 

sources of fuels, namely the plants, are often distributed across space in clumps 

or heterogeneous patches (Pukkala and Kolstrom 1991; Pacala and Deutschman 

1995; Rochefort and Peterson 1996). Large fuels, such as large branches and tree 

boles, tend to accumulate directly under the plant sources, especially trees, but 

small fuels, such as needles and twigs, can be blown away from the plant by wind, 

creating a more homogeneous distribution (Harmon and others 1986). Smaller 

fuels decompose quickly, which may influence spatial variability, while large fuels decompose slowly over decades and tend to accumulate directly under plants, 

thereby increasing variability across space (Keane 2008a). However, it is the impact of disturbances, such as windthrow, wildland fires, and insect outbreaks, and 

their patterns, that are probably the most important factor that influences spatial 

fuel distributions (Brown and Bevins 1986). In mixed species stands, for example, 

fuels can unevenly accumulate underneath the dead individuals killed by mountain 

pine beetle (Page and Jenkins 2007; Jenkins and others 2008). Fires can kill and 

injure plants and consume fuels in a patchwork of burned and unburned areas that 

will subsequently influence the colonization of future plants over long time periods 

(King and others 2008).

One interesting dilemma resulting from this study is that if this spatial variability is so important in describing fuels, then why have the current fuel inputs 

to fire models continued to satisfy fire managers and researchers? None of the fire 

models account for the large variability in fuel characteristics, yet predictions from 

these models are used extensively in fire management with acceptable results. This 

could be because the one major factor influencing fire behavior and effects during large fire events is weather, not fuel, and weather might drive fire behavior 

predictions under severe drought, high temperatures, strong wind, and steep slope 

conditions (Bessie and Johnson 1995). Another reason may be that all fire behavior 

and effects models used in management are one-dimensional point models that are 

designed to be used for small, homogeneous areas on the landscape, and the high 

extrapolation error of point estimates across space may overwhelm the variability 

of fuel characteristics. These one-dimensional fire behavior and effects models 

may not have sufficient resolution to recognize subtle changes in fuel properties 

across space. It could also be that the fuel information is often calibrated or adjusted to compute values that match observed fire behavior (Burgan and Rothermel 

1984), and this calibration has accounted for both loading and its variability. After 

all, fuels information in the fire behavior fuel models created by Anderson (1982) 

and Scott and Burgan (2005) are actually abstract representations of perceived fire 

behavior. Still, another reason might be that the high uncertainty in fuel sampling 

and fire behavior measurements make it difficult to actually validate the fire behavior and effects predictions. One thing is certain, if fire managers and researchers 

want more accurate and consistent estimates of fire at multiple scales, future fire 

models must account for fuel variability to comprehensively simulate fire behavior 

and effects (Thaxton and Platt 2006; Parsons and others 2010).

Study Findings

There are many aspects of our study results that need additional explanation to 

fully understand the findings. Our measured surface fuel loadings were consistent 

with those found in the literature, indicating that these sites had typical fuelbeds for 

northern Rocky Mountain sites (Brown and Bevins 1986). Moreover, the canopy 

fuel characteristics calculated in this study compared well with those studies that 
USDA Forest Service RMRS-RP-98. 2012. 43

destructively measured canopy fuels (Scott and Reinhardt 2005; Reinhardt and 

others 2006), except for the SM pinyon-juniper site, which had a very high CFL 

and CBD because of the overestimation of canopy biomass using the allometric 

equations implemented in FUELCALC (Reinhardt and others 2006).

The high particle densities measured for the 1 and 10 hr downed woody fuels 

were comparable to values found in the literature. Our fine woody particle densities ranged from 482 to 657 kg m-3 with large ranges and variations (Table 7). 

In the most comprehensive compilation of fine woody particle densities, Harmon 

and others (2008) reported values ranging from approximately 400 to 650 kg m-3

for similar tree species encountered in this study. Nalder and others (1999) measured 430 to 620 kg m-3 for fine fuels in the boreal forests of western and northern 

Canada, and Nalder and others (1997) measured 493 to 607 kg m-3 for spruce fine 

fuels in the boreal forests of Alberta and Northwest Territories. Sackett (1980) 

measured particle densities of southwestern tree species and found they ranged 

from 390 to 635 kg m-3, while Van Wagtendonk and others (1996) measured densities of 530 to 670 kg m-3 for Sierra Nevada conifers, and Ryan and Pickford (1978) 

measured mixed conifer fine wood densities of 340 to 620 kg m-3 in the Blue 

Mountains of Oregon and Washington. Interestingly, the ranges and variation of 

fine woody particle densities reported from these studies compares well with the 

variations calculated in our study.

The variability and mean of particle densities of the large woody fuels measured 

in this study also compared well with those measured in other studies. We found 

particle densities of 100 and 1000 hr size classes for downed woody ranged from 

178 to 522 kg m-3 with lower variation than fine woody debris (Table 7). Harmon 

and others (2008) compiled ranges of approximately 200 to over 600 kg m-3, and 

Green and others (1999) measured ranges of 300 to 550 kg m-3 for the same species encountered in our study. Our low coarse woody debris bulk densities are due 

to the high number of rotten logs found on our study sites, especially on the treated 

sites where rotten snags had fallen from thinning activities. The high particle densities measured at the SM site for pinyon-juniper downed wood seem consistent 

with values measured in Harmon and others (2008).

Most puzzling, however, were our measurements for bulk densities of the duff 

and litter layers (66 to 416 kg m-3 for CF and LF, respectively). They were much 

higher than the L-layer (only litter) bulk densities measured by Brown (1981), 

which ranged from 21 to 51 kg m-3, higher than those measured by Snell (1979), 

which ranged from 23 to 32 kg m-3, and higher than those measured by Brown 

(1970b), which ranged from 5 to 43 kg m-3 for xeric habitat types similar to those 

found in this study (these studies measured mostly the litter layer). However, our 

values tended to agree with the high bulk densities measured by Stephens and others (2004), which ranged from 54 to over 300 kg m-3 for California Sierra mixed 

conifer stands. Our values are high because of the presence of woody material and 

mineral soil within the litter+duff layer, especially on sites that had been thinned or 

grazed (LF, SM). Many woody fuel particles were embedded in the litter+duff layer and we decided to include these woody sticks in the computation of litter+duff 

bulk density even though these heavy woody particles substantially increased 

litter+duff bulk density on many plots. In fact, our high values compared well 

with the bulk densities of masticated fuel beds found by Kane and others (2009), 

which were 46 to 141 kg m-3 with high variability. We thought it was appropriate 

to include these woody particles since woody fuel particles must be above the 

duff layer to be sampled using standard methods (Lutes and others 2006). Our 

litter+duff profiles also had substantial amounts of mineral soil mixed with duff 
44 USDA Forest Service RMRS-RP-98. 2012.

based on the high estimations of mineral content (greater than 40 percent on three 

sites).

The high magnitude and variability of the measured mineral contents of woody 

and litter+duff components were a result of a number of factors. The high litter+duff 

mineral contents (22 to 47 percent) were probably from the mixing of mineral soil 

into the litter+duff layer by soil fauna, freeze-thaw cycles, grazing, and management 

activities (fuel treatments). We also found it difficult to identify the duff-mineral 

soil interface on many plots, so some mineral soil could have been mixed with the 

litter+duff sample profile during collection. Our values somewhat agree with Hood 

and Wu (2006) who found duff mineral contents were approximately 32 percent 

in Jeffrey pine-white fir forests and 42 percent in pine-oak woodlands. We believe 

that the reason 1 hr woody fuels had higher mineral contents than the larger woody 

fuels was because mineral soil residue on fine woody fuels contributed more to 

the overall particle weight than the mineral soil on larger fuel particles, probably 

explaining why our fine woody fuel particle densities were much higher than those 

presented in the literature. Ragland and others (1991) found clean wood mineral 

contents ranged from 0.1 to 0.6 percent, which agrees with our findings for 1000 

hr logs. But our fine woody fuels ranged from 1 to 8 percent, which is an order of 

magnitude more than clean wood. This could be from mineral soil residue on the 

fine woody material, or it could be from the bark on some of these small particles 

because bark mineral contents can range from 3 to 5 percent (Ragland and others 

1991). Default values for mineral contents in fire behavior fuel models are set at 

5.5 percent across all woody size classes (Burgan and Rothermel 1984; Scott and 

Burgan 2005), yet we found great variation in mineral contents across sites and 

components (Table 7), which can have great implications for the simulation of fire 

behavior because high mineral contents dampen fire behavior.

Study Limitations

This study has some limitations that may have influenced the results. First, out 

of logistical necessity, we sampled the woody fuel in the size classes commonly 

used by fire behavior models, which may be major source of variation in the study 

results (Table 1). Loadings in the 100 hr fuels, for example, can be highly variable 

because particle diameters range from 2.5 cm to 8 cm, resulting in a near ten-fold 

range in volume or loading. To further compound this problem, branch size distributions differ by species and position in the canopy. Subalpine fir, for example, 

has smaller branches than ponderosa pine (Minore 1979; Reinhardt and others 

2006) and, as a result, there is little chance that fir branches can be big enough to 

represent the entire range of 100 hr fuel. This problem has haunted wildland fuel 

science and management for some time because size class variability isn’t fully 

represented in fuel models, sampling methods, or fuel maps. In results from this 

study that are reported elsewhere, we explored using the distribution of loading 

across fuel particle sizes as a means to correct conventional fuel loading estimates 

and to develop new sampling methods (Keane and others 2012). Smoke emissions 

predictions, carbon inventories, and fuel consumption would be improved if fuels 

were sampled at size classes that are appropriate for the resolution of the sampling 

method and the ecology of downed woody debris (Harmon and others 1986). For 

example, size classes could be based on volume, the resolution of newly developed 

sampling methods, or variability of particle or component density. We are trying to 

develop a method that uses a fuel size-loading distribution relationship to calculate 

loading from particle counts in fixed area plots.
USDA Forest Service RMRS-RP-98. 2012. 45

Another concern is the low nanoplot, microplot, and subplot sampling densities 

at small scales. Due to logistical and cost constraints, there were only four intensive microplot grids (4 x 25 m2 = 100 m2

) in the 1 km2 sample grid. This 1 percent 

sample could be too small for accurate descriptions of spatial variability of surface 

fuels at fine scales. The distance between subplots for log loadings may have also 

been too great to accurately describe log spatial variability. However, extensive 

statistical analysis of our data revealed that the subplot size was large enough to 

minimize log fuel sampling variability, but we could have had more intensive sampling at 5-, 10-, and 15-m distances for fine woody fuels and logs.

Plot sizes used in this study may have been inappropriate for some fuel components. For logistical reasons, we only used four sampling frames for describing 

fuels, when in reality, the surface fuelbed may have components that are not effectively sampled at these scales. Large branches (100 hr), for example, may be 

more appropriately sampled with a 10 m2 microplot because of their rarity within a 

stand and because the estimated inherent patch size was 1 to 5 m (Table 12). This 

is somewhat evident in the high spatial variogram nugget values (Table 12). The 

high measurement error could be a result of inappropriate sample frames or ineffective measurement techniques (photoload adjustments). However, the ranges of 

many of the surface and canopy fuel properties appeared to compare well with our 

sampling design: (1) macroplot size of 400 m2 matched with 80 to 400 m canopy 

fuel patch size, (2) subplot size of 100 m2 matched with the 22 to 200 m patch 

sizes, and (3) microplots (1 m2) matched with shrub, herb, 1 hr, and 10 hr woody 

patch sizes (0.5 to 2 m). Those that didn’t match were the 100 hr microplots that 

had a 1 to 3.6 m patch size, and nanoplots (0.25 m2) that had litter+duff patch sizes 

of 0.5 to 8 m (Table 12)

This study was only implemented on six study sites that represented a small 

number of forest and range vegetation types in the northern Rocky Mountains. 

As a result, these study results are probably only specific to the few sites that we 

sampled. It took well over a month to conduct the measurements on one study 

site, so our sampling time was limited because of cost concerns. Moreover, it was 

difficult to find study sites that fit our selection criteria because the complex interactions among wildland fire, management activities, and topography rarely created 

the large, flat, homogeneous sites needed for this study. In the future, we will relax 

site selection criteria and move from small homogeneous 1 km2 patches to entire 

landscapes such as the Tenderfoot Creek Experimental Forest (Figure 5).

We feel that the somewhat higher particle densities measured in this study are 

primarily a result of the inaccurate measurement of particle volume using the water displacement method to estimate volume (Fasth and others 2010). While this 

method is better than calculating volume using diameter and length measurements, 

it tends to under-estimate volume, which results in over-estimations of particle 

densities because the mass of the particle is divided by the volume. Small wood 

particles tend to absorb water in small cracks and fissures, causing less displacement and resulting displacement values are so low that small errors in volume 

estimates result in large errors in the calculation of density. These twigs weigh so 

little and have such low volumes that minor measurement errors of 0.1 cm3 can 

cause large changes in particle density. A 6 g twig, for example, that displaces 

0.5 cm3 of water would have a density of approximately 120 kg m-3, but if the 

displacement is 0.4 cm3, the density would be 150 kg m-3, over 25 percent higher. 

Another reason particle densities were high was because of the residual mineral 

soil present on some of the sticks. We decided to leave this mineral soil on the particles because it is more representative of its condition in the fuelbed.
46 USDA Forest Service RMRS-RP-98. 2012.

Our decision to sample the duff and litter as one component was also a major 

limitation of the study. We found that it is difficult to consistently and accurately 

differentiate between the duff and litter fuel both in the field and in the office 

because the organic soil profile is more a gradient of decomposed material rather 

than a set of two distinctly different fuel components. This profile is constantly 

being mixed by animals, disturbance, and soil micro- and macro-fauna, making 

it difficult to find the subtle seam between litter and duff (Harmon and others 

1986). Rather than introducing the additional uncertainty of litter-duff differentiation, we decided to group litter and duff together. Unfortunately, most fire behavior 

and effects models require separate litter and duff inputs (Reinhardt and Keane 

1998), and most of the values found in the literature are separated by litter and duff 

(Brown 1970b, 1981; Snell 1979).

Last, the estimation of canopy fuel characteristics has some major limitations. 

Both CFL and CBD were indirectly estimated using the allometric canopy fuel 

equations contained in FUELCALC, and while most of our tree species in the study 

were represented in FUELCALC, equations for the species on the SM site (pinyon 

pine and juniper) were missing and substituted with other equations from similar 

species. This resulted in an overestimation of canopy fuel because the clumpy 

nature of pinyon-juniper trees was not properly represented in FUELCALC. 

Moreover, the visual estimation of CC was done using 10 percent cover classes (5 

to 15 percent, 15 to 25 percent, for example), and this also increased variation of 

this canopy variable.

Research and Management Implications

The findings from this study may have great implications to fire management 

and research that could fundamentally change the way we describe fuels and model fire in the future. Most importantly, it is clear that wildland fuel components vary 

greatly across different scales. This means that fuel sampling and mapping must 

accommodate the inherent scales of each fuel component. Counting intersects of 

all sizes of woody fuels crossing a sampling plane, for example, may ineffectively 

characterize fuel loadings, and similarly, using satellite imagery with only one resolution may not accommodate the accurate estimation of fuel loadings across all 

components. Future field methods must integrate scale into the sampling design, 

such as using nested fixed area sampling techniques designed to fit fuel particle 

patch sizes, to improve accuracies. Fine fuels, for example, should be sampled 

with a frame that is large enough to minimize spatial sampling bias (1 to 2 m2). 

Hierarchically nested fixed-area plot designs, similar to the one used in this study, 

may be needed where fine fuels are sampled within 1 to 2 m2 microplots, logs are 

sampled on 50 to 100 m2 plots, and canopy fuels are sampled on 400 to 1000 m2

plots. Critical research is needed to develop methods that efficiently quantify fuels 

within fixed plots and are also easy for management to use with minimal training 

and resources.

Quantification of wildland fuel loadings is often accomplished using standard 

fuel sampling protocols that are greatly dependent on woody fuel particle densities 

and shrub, herb, and litter+duff bulk densities (Brown and others 1982). Particle 

and bulk densities are used extensively in field sampling methods to estimate loading (Lutes and others 2006). The great variability that we found in these density 

measurements (Table 7) across both sites and fuel components suggests that estimating fuel loadings is even more difficult than previously thought since most fuel 

sampling methods use an average wood density value to calculate loadings for all 

woody components (Brown 1970a, 1974). Results from this study show that not 
USDA Forest Service RMRS-RP-98. 2012. 47

only are wood densities different across components; they are also highly variable 

within a component (Table 7; Figure 10). This complicates an already complex 

procedure for sampling fuels in that it now appears that wood density must also be 

assessed at the sample site to get accurate loading estimates. Innovative techniques 

are needed to quickly assess particle densities to accurately estimate fuel loadings. 

The same is true with field sampling litter+duff, shrub, and herbaceous loadings. 

Our bulk density values were highly variable and site specific, so new methods are 

needed to adjust bulk densities for local situations to accurately compute loadings 

from depth measurements. Photographs, for example, can be taken of shrub, herb, 

and litter+duff fuelbeds with measured bulk densities, and field people can select 

the picture that best matches the fuelbed conditions (Keane and Dickinson 2007a, 

2007b; Ottmar and Vihnanek 2000).

Fuel maps are now essential tools for predicting fire spread and intensity 

(Reeves and others 2006), but few of these maps incorporate scale and variability 

of fuel components in their design (Keane and others 2001). Variability of fine fuels within the 30-m pixel size commonly used in land management may be so great 

that it will overwhelm fuel quantification, compromise accuracy assessments, and 

ineffectively predict fire behavior and effects. Fine scale variations in fuel loadings and structure can also affect fire spread and subsequent fire intensity (Parsons 

and others 2010). There are at least two alternatives for spatially describing fuel 

components at their inherent scale. First, the resolution of imagery, modeling, and 

GIS analysis should match the appropriate resolution of the fuel component being mapped; twigs, for example, should be mapped using 1 to 5 m pixel imagery. 

Second, the fire behavior and effects models that use fuel maps could internally intensify the mapping grid with algorithms that stochastically distribute fuels 

across space at the appropriate resolutions. While this spatial stochastic modeling 

approach would not create the actual fuelbed for that pixel, it would create a fuelbed with the same variability and distributional characteristics. We created maps 

that distributed fuels at their appropriate scale and variability based on the spatial 

statistics computed in this study to show how future fuel maps can be developed 

(Figure 17).

Fuel classifications, such as fire behavior fuel models (Scott and Burgan 2005), 

fuel loading models (Lutes and others 2009), or fuel characteristics classification 

system (Ottmar and others 2007), may be inappropriate for future fire behavior and 

effects applications because they lack a description of fuel variability across space. 

These classifications are “point” estimations of fuel loadings, yet many mapping 

efforts assign categories from these classifications to entire areas, such as stands, 

polygons, or landscapes, ignoring the influence of the high fuel variability on fire 

prediction. The assignment of one classification category to a polygon discounts 

the fact that fuel components vary across different scales within that polygon and 

that they are highly variable across space. Moreover, most mapping efforts assign 

fuel classification categories to the categories of other vegetation classifications 

(Keane and others 1999), yet this study found that surface fuel components are 

rarely correlated to each other or to stand and canopy characteristics (Table 11) 

and that the variability of the vegetation, as described by canopy fuel variables, is 

rarely at the same scale as the surface fuel (Figure 16). We are conducting research 

in the possible development of the next generation of fuel models that contain the 

statistical properties of the spatial distribution of fuel components so that effective 

fuel maps can be developed at any scale and resolution (Figure 17).
48 USDA Forest Service RMRS-RP-98. 2012.

Figure 17. An example of maps of the four down dead woody fuel components created using statistical stochastic algorithms 

parameterized from findings of this study.

(a) (b)

(c) (d)
USDA Forest Service RMRS-RP-98. 2012. 49

Summary and Conclusions

It comes as no surprise to anyone who works in wildland fuel science and management that the properties and characteristics of fuels are highly variable. Most 

things in nature are highly variable to ensure their continued existence. Fuels, however, seem to take variability to another level, especially in a spatial and temporal 

context. Not only do wildland fuels have a variability that exceeds twice the mean 

within small areas, but this variability is distributed across space at unique scales 

for each fuel component with smaller fuels having smaller inherent patch sizes 

of 1 to 10 m than large fuels which are distributed in 100 to 500 m patch sizes. 

And these inherent patch sizes for each fuel component can change across different sites, becoming larger in forests with discontinuous canopies, for example. 

Moreover, it appears surface fuel loadings are rarely normally distributed, rendering parametric statistics inappropriate for many fuel analyses, and surface fuel 

loadings are poorly correlated with any canopy fuel or stand-level characteristic, 

which means that stand and vegetation characteristics may not be useful for mapping surface fuels, but they may be useful for canopy fuel characteristics.

These findings further complicate the process of describing and quantifying 

fuels for fire management and research. It appears that designing accurate, onesize-fits-all sampling, classification, and mapping approach for describing wildland 

fuels will be difficult because of high spatial variability. Each component must be 

sampled at its own scale to reduce a large amount of variation introduced because 

the resolution of the sampling approach did not match the scale of the data. And 

the high variation in fuel properties, such as particle density, may preclude cost-effective, generalized approaches at quantifying fuel loadings. If the particle density 

varies by a factor of two within an individual particle, then estimating accurate 

fuel loadings may require complex and costly sampling methods for determining 

particle density, which may be impractical for fire management.

Fire management and research may want to take a different approach for describing fuel characteristics, such as loading, in the future. Instead of using the 

central tendency statistics, such as the mean, median, or mode, to describe fuels in 

an area, future wildland fuel analyses should account for the high spatial variation 

by using novel statistical approaches, such as stochastic modeling of fuel loading 

probability distributions, to capture the full impact of fuel variability in space. This 

also means that point-level fire behavior and effects modeling probably will not 

improve in accuracy without explicit representation of spatial distributions even 

though these models are constantly refined and modified to include additional 

detail in combustion simulation because spatial fuel variability will overwhelm 

minor changes in model design. Future fire models will need a three-dimensional 

implementation to fully account for fuel variability in their simulations.

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use with Rothermel’s surface fire spread model. General Technical Report RMRSGTR-153, USDA Forest Service, Rocky Mountain Research Station, Fort Collins, CO.

Scott, J. H. 1999. NEXUS: A system for assessing crown fire hazard. Fire Management 

Notes 59:21-24.

Scott, J. H. and E. D. Reinhardt. 2005. Stereo photo guide for estimating canopy fuel 

characteristics in conifer stands. General Technical Report RMRS-GTR-145, USDA 

Forest Service, Rocky Mountain Research Station, Fort Collins, CO.

Sikkink, P. and R. E. Keane. 2008. A comparison of five sampling techniques to estimate 

surface fuel loading in montane forests. International Journal of Wildland Fire 

17:363-379.

Snell, J. A. K. 1979. Direct estimation of surface fuel bulk density and loading in western 

Montana and northern Idaho. Thesis, University of Montana, Missoula.

Sokal, R. R. and F. J. Rohlf. 1981. Biometry. W.H. Freeman and Company, San 

Francisco, CA, USA.

Stephens, S. L., M. Finney, and H. Schentz. 2004. Bulk density and fuel loads of 

ponderosa pine and white fir forest floors: Impacts of leaf morphology. Northwest 

Science 78:93-104.
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Thaxton, J. M. and W. J. Platt. 2006. Small-scale fuel variation alters fire intensity and 

shrub abundance in a pine savanna. Ecology 87:1331-1337.

Thorhallsdottir, T. E. 1990. The dynamics of a grassland community: a simultaneous 

investigation of spatial and temporal heterogeneity at various scales. Journal of 

Ecology 78:884-908.

Townsend, D. E. and S. D. Fuhlendorf. 2010. Evaluating relationships between spatial 

heterogeneity and the biotic and abiotic environments. The American Midland 

Naturalist 163:351-365.

van Wagner, C. E. 1977. Conditions for the start and spread of crown fire. Canadian 

Journal of Forest Research 7:23-34.

Van Wagtendonk, J. W., J. M. Benedict, and W. M. Sydoriak. 1996. Physical properties of 

woody fuel particles of Sierra Nevada conifers. International Journal of Wildland Fire 

6:117-123.

Van Wagtendonk, J. W., W. M. Sydoriak, and J. M. Benedict. 1998. Heat content variation 

of Sierra Nevada conifers. International Journal of Wildland Fire 8:147-158.

Woodall, C. W. and L. M. Nagel. 2006. Coarse woody type: A new method for analyzing 

coarse woody debris and forest change. Forest Ecology and Management 227:115-121.

Woodard, P. M. and R. E. Martin. 1980. Duff weight and depth in a high elevation Pinus 

contorta Dougl. forest. Canadian Journal of Forest Research 10:7-9.

The Rocky Mountain Research Station develops scientific information and 

technology to improve management, protection, and use of the forests and 

rangelands. Research is designed to meet the needs of the National Forest 

managers, Federal and State agencies, public and private organizations, 

academic institutions, industry, and individuals. Studies accelerate solutions to 

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technology, multiple use economics, wildlife and fish habitat, and forest insects 

and diseases. Studies are conducted cooperatively, and applications may be 

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