United States

Department

of Agriculture

Forest Service

Rocky Mountain

Research Station

Research Paper

RMRS-RP-29

September 2001

Assessing Crown Fire Potential

by Linking Models of Surface

and Crown Fire Behavior

Joe H. Scott

Elizabeth D. Reinhardt
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 Authors

Joe H. Scott has been a Forester with Systems for Environmental Management, a nonprofit research group based in Missoula,

MT, since 1996. He has a B.S. degree in forestry and resource management from the University of California at Berkeley and

an M.S. degree in forestry from the University of Montana. Joe has participated in investigations of surface and canopy fuels,

fire behavior modeling, and crown fire hazard assessment.

Elizabeth D. Reinhardt is a Research Forester in the Prescribed Fire and Fire Effects Project at the Rocky Mountain Research

Station, Missoula Fire Sciences Laboratory, Missoula, MT. She has degrees in English (A.B., 1978, Harvard University) and

forestry (M.S., 1982, and Ph.D., 1991, University of Montana). Her research has included studies of fuel consumption, tree

mortality, and prescription development.

Abstract

Scott, Joe H.; Reinhardt, Elizabeth D. 2001. Assessing crown fire potential by linking models of

surface and crown fire behavior. Res. Pap. RMRS-RP-29. Fort Collins, CO: U.S. Department

of Agriculture, Forest Service, Rocky Mountain Research Station. 59 p.

Fire managers are increasingly concerned about the threat of crown fires, yet only now are

quantitative methods for assessing crown fire hazard being developed. Links among existing

mathematical models of fire behavior are used to develop two indices of crown fire hazard—the

Torching Index and Crowning Index. These indices can be used to ordinate different forest stands

by their relative susceptibility to crown fire and to compare the effectiveness of crown fire mitigation

treatments. The coupled model was used to simulate the wide range of fire behavior possible in a

forest stand, from a low-intensity surface fire to a high-intensity active crown fire, for the purpose of

comparing potential fire behavior. The hazard indices and behavior simulations incorporate the

effects of surface fuel characteristics, dead and live fuel moistures (surface and crown), slope

steepness, canopy base height, canopy bulk density, and wind reduction by the canopy. Example

simulations are for western Montana Pinus ponderosa and Pinus contorta stands. Although some of

the models presented here have had limited testing or restricted geographic applicability, the

concepts will apply to models for other regions and new models with greater geographic applicability.

Keywords: canopy fuels, hazard assessment, fireline intensity, rate of spread, crown fraction

burned, fire potential
USDA Forest Service September 2001

Research Paper RMRS-RP-29

Assessing Crown Fire Potential by

Linking Models of Surface and

Crown Fire Behavior

Joe H. Scott

Elizabeth D. Reinhardt
ii

Acknowledgments

We thank Mark A. Finney and Patricia Andrews of the Missoula Fire Sciences Laboratory, Rocky Mountain Research Station;

David B. Sapsis of the University of California at Davis and California Department of Forestry and Fire Protection; and Jim K.

Agee of the University of Washington for thoughtful reviews of an earlier draft of this report.

This research was supported by funds provided by the Interior Fire Coordination Committee, United States Department of

the Interior; the Rocky Mountain Research Station, United States Department of Agriculture, Forest Service; Seymour Johnson

Air Force Base, United States Department of Defense; and Systems for Environmental Management, under cooperative

agreements (RJVA 96-094 and RJVA 98-575).

Software Availability

The NEXUS spreadsheet and its documentation can be obtained at www.fire.org/nexus/nexus.html. Information about other

fire modeling systems described in the text can be obtained at the Fire Management Tools Online Web site at www.fire.org/

perl/tools.cgi.
Contents

INTRODUCTION .......................................................................................................................... 1

CHARACTERIZING CANOPY FUELS................................................................................................. 4

EXISTING MODELS OF SURFACE AND CROWN FIRE BEHAVIOR .......................................................... 7

QUANTIFYING THE HAZARD ....................................................................................................... 15

SIMULATING OVERALL SPREAD RATE AND INTENSITY ..................................................................... 19

HYSTERESIS IN CROWN FIRE: THE CONDITIONAL SURFACE FIRE...................................................... 21

EXAMPLE SIMULATIONS USING THE COUPLED MODEL .................................................................... 27

DISCUSSION ........................................................................................................................... 34

REFERENCES.......................................................................................................................... 34

APPENDIX A: CROWN FRACTION BURNED ............................................................................... 39

APPENDIX B: GLOSSARY ...................................................................................................... 43

APPENDIX C: ENGLISH/METRIC UNIT CONVERSION FACTORS ..................................................... 47

APPENDIX D: NOMOGRAMS .................................................................................................. 49

iii
USDA Forest Service Research Paper RMRS-RP-29. 2001. 1

INTRODUCTION

Crown fires present special problems to managers. Crown fires are more difficult

to control than surface fires. Their rate of spread is several times faster than surface

fires (Rothermel 1983). Spotting is frequent and can occur over long distances. Larger

flames from crown fires dictate larger firefighter safety zones (Butler and Cohen

1998). Spotting and increased radiation make structures more difficult to defend from

crown fire than surface fire (Cohen and Butler 1998). Effects of crown fire are more

severe and lasting than surface fire. Near total tree mortality should be expected.

Smoke production will be greater, and foliar nutrients may be lost from the site.

Crown fires can occur in a wide variety of forest types throughout the United

States (Agee 1996). Increasingly, crown fires are taking place in forest types not

historically prone to crown fires, such as ponderosa pine forests (Mutch and others

1993). A significant risk to life and property exists wherever forest stands prone to

crown fire lie in proximity to residential or recreational development. Therefore, assessing the susceptibility of forest stands to crown fire and designing fuel and silvicultural treatments to reduce susceptibility have become priorities for many land

management agencies.

Accepted methods exist for predicting surface fire behavior (Rothermel 1972,

1983) and crown fire behavior (Rothermel 1991a), but not for predicting the

transition between them. In this paper we explore the use of Van Wagner’s crown

fire transition criteria (Van Wagner 1977, 1989, 1993), elements of which are

used in the Canadian Forest Fire Behavior Prediction (FFBP) System (Forestry

Canada Fire Danger Group 1992), to link Rothermel’s separate surface fire and

crown fire spread models. By linking these models we derive indices of crown

fire hazard and simulate the full range of potential fire behavior possible in a

forest stand—surface through active crowning.

Other models of surface fire behavior (Catchpole and others 1998) and crown

fire behavior (Albini 1996; Grishin 1997; Gomes da Cruz 1999) and transition

to crown fire (Alexander 1988; Gomes da Cruz 1999) are in various stages of

development and testing. Until a robust fire behavior model is developed that

internally simulates surface fire behavior, transition to crown fire, and crown

fire behavior, we will need to rely on the links between these separate models.

From the array of available models, we chose to couple the most widely used for

this analysis: Rothermel’s (1972) surface and (1991a) crown fire models, and Van

Wagner’s (1977) models of transition to crown fire. The concepts we present, solving for critical environmental conditions that lead to crown fire and producing fullrange estimates of fire behavior, can be applied to other models in the future.

Assessing Crown Fire Potential by

Linking Models of Surface and

Crown Fire Behavior

Joe H. Scott and Elizabeth D. Reinhardt
2 USDA Forest Service Research Paper RMRS-RP-29. 2001

The coupled model produces seamless, full-range estimates of fire behavior

(whether surface or crown). However, the purpose of those fire behavior estimates is to compare the relative susceptibility of different stands to crown fire,

not to predict the behavior of an actual fire. The method we developed allows

direct, quantitative comparison of the relative crown fire potential of different

stands from a description of surface fuels, canopy fuels, site characteristics, and

environmental conditions.

Conceptual Approach to Quantifying Crown Fire Hazard

The concept of hazard has been defined many ways in the wildland fire literature (Bachman and Allgöwer 1999). Fire hazard is sometimes referenced to the

specific fuel element that most contributes to the potential fire behavior of a

given site. For example, the increased potential fire behavior caused by activity

fuels left behind after timber harvesting is sometimes referred to as a “slash hazard.”

The field of technical risk engineering defines hazard more generally as a

physical situation with a potential for human injury, damage to property, or

damage to the environment. Crown fire hazard, therefore, is a physical situation (fuels, weather and topography) with potential for damage or injury caused

by crown fires. The nature of crown fires—intense, fast-moving, and destructive—suggests that potential for damage is great whenever a crown fire occurs.

Assessing the hazard posed by crown fire is therefore a matter of assessing

the potential for their occurrence—of identifying the physical situations that

lead to crown fire occurrence.

The potential for crown fire occurrence does not depend on any single element of

the fuel complex, nor on any one element of the fire environment. Rather, crown fires

result from certain combinations of fuels, weather, and topography that lead to the

development and continued spread of crown fires. The concepts and models we discuss in this paper are geared toward determining those combinations, without attempting to determine which component contributes most to the hazard.

This is not the first attempt to assess crown fire potential. Fahnestock (1970)

developed a heuristic key to rate crowning potential based largely on canopy

closure, (individual tree) crown density, and the presence or absence of ladder

fuels. Kilgore and Sando (1975) showed a decrease in crown fire potential following prescribed burning in a giant sequoia/mixed-conifer forest by comparing

canopy fuel weight, crown volume ratio, mean height to canopy base, and the

vertical profile of canopy fuel packing ratio before and after a prescribed fire.

Taylor and others (1998) assessed temporal changes in crown fire hazard at the

landscape scale by noting the change in relative frequency of different types of

crown fire in different time periods.

The mathematical nature of surface and crown fire models allows us to link them

together and solve for the critical conditions that lead to crown fires. The crown fire

hazard assessment method we develop in this paper is based on the determination of

critical environmental conditions that lead to different types of crown fire activity.

In the next two sections we review fire behavior concepts and models pertinent to quantitative crown fire hazard assessment. In later sections we present the

derivation and interpretation of two indices of stand-level crown fire hazard,

discuss methods of obtaining the necessary canopy fuel inputs, and introduce

seamless surface/crown fire behavior simulations that can be used to assess the

likely range of fire behavior at a site and the nature of the transition from surface

to crown fire. In addition, we introduce the concept of hysteresis in the crown fire

phenomenon.
USDA Forest Service Research Paper RMRS-RP-29. 2001. 3

Types of Wildland Fire

Fire scientists and managers recognize three general types of wildland fire, depending on the fuel stratum in which the fire is burning. A ground fire is one that burns

in ground fuels such as duff, organic soils, roots, rotten buried logs, and so forth.

Ground fuels are characterized by higher bulk density than surface and canopy fuels.

Ground fires burn with very low spread rates but can be sustained at relatively high

moisture contents (Frandsen 1987, 1991). Fuel consumption through ground fire can

be great, causing significant injury to trees and shrubs. Although ground fuels can be

ignited directly, they are most commonly ignited by a passing surface fire.

A surface fire is one that burns in the surface fuel layer, which lies immediately above the ground fuels but below the canopy, or aerial fuels. Surface fuels

consist of needles, leaves, grass, dead and down branch wood and logs, shrubs,

low brush, and short trees (Brown and others 1982). Surface fire behavior varies

widely depending on the nature of the surface fuel complex.

A crown fire is one that burns in the elevated canopy fuels. Canopy fuels

normally consumed in crown fires consist of the live and dead foliage, lichen,

and fine live and dead branchwood found in a forest canopy. They have higher

moisture content and lower bulk density than surface fuels. We generally recognize three types of crown fire: passive, active, and independent (Van Wagner

1977).

A passive crown fire, also called torching or candling, is one in which individual

or small groups of trees torch out, but solid flame is not consistently maintained in the

canopy (fig. 1a). Passive crowning encompasses a wide range of fire behavior, from

the occasional tree torching out to a nearly active crown fire. The increased radiation

b

a

Figure 1—Passive crowning (a) involves individual or small groups of trees, whereas during active crowning (b) the whole fuel complex

burns as a unit. Photo (a) by Duncan Lutes; photo (b) by Jim Kautz.
4 USDA Forest Service Research Paper RMRS-RP-29. 2001

to surface fuels from passive crowning increases flame front spread rate, especially at

the upper end of the passive crown fire range. Embers lofted during passive crowning

can start new fires downwind, which makes containment more difficult and increases

the overall rate of fire growth. Passive crowning is common in many forest types,

especially those with an understory of shade-tolerant conifers.

An active crown fire, also called a running or continuous crown fire, is one in

which the entire surface/canopy fuel complex becomes involved (fig. 1b), but the

crowning phase remains dependent on heat from the surface fuels for continued

spread. Active crown fires are characterized by a solid wall of flame extending

from the fuel bed surface through the top of the canopy. Greatly increased radiation and short-range spotting of active crown fires lead to spread rates much

higher than would occur if the fire remained on the surface. Medium and longrange spotting associated with active crowning leads to even greater rates of fire

growth.

An independent crown fire is one that burns in canopy fuels without aid of a

supporting surface fire. Independent crown fires occur rarely and are short lived

(Van Wagner 1993), requiring a combination of steep slope, high windspeed, and

low foliar moisture content. Many apparently independent crown fires may actually be active crown fires in which the canopy phase is momentarily pushed ahead

of the surface phase under the influence of steep slope or strong wind.

Few cases of independent crown fire have been documented. The 1987 South

Mowich fire occurred over a spring snowpack on the slopes of Mount Rainier,

WA (Huff 1988). However, the primary mechanism of fire spread during that fire

was crown-to-crown spread in which lichens ignited first, then the foliage after

being preheated by burning lichen. Radiation from the torching tree then ignited

lichen on an adjacent tree. Spread rate was low—the fire took 2 days of uncontained

spread to reach 25 ha.

We do not address independent crown fires in this paper because they occur

so rarely and because no model of their behavior is available.

The Canadian Forest Fire Behavior Prediction System (Forestry Canada Fire Danger

Group 1992) uses the term “intermittent crown fire” to describe a fire that alternates

in space and time between continuous crowning and surface fire or passive crowning.

Such a phenomenon could result from spatial variability in surface and canopy fuels,

or temporal variability in windspeed, especially when conditions are near the threshold for active crowning.

CHARACTERIZING CANOPY FUELS

Assessing crown fire potential requires the most accurate estimates of canopy fuel

characteristics possible. However, the literature provides little guidance for determining these characteristics at the stand level. A rich body of literature does exist on quantification of tree crown and forest canopy characteristics for purposes other than fuel

characterization for crown fire modeling.

Reinhardt and others (2000) are attempting to accurately measure canopy fuel

characteristics in a range of forest types and stand densities. These accurate measurements will then be compared with estimates made using two indirect approaches: instrument-based optical techniques and inventory-based techniques.

The indirect techniques have proven useful in a modeling framework. They now

need to be calibrated and verified for operational use. In addition, photographs

made of the sample stands will provide a good start for a canopy fuel photo

guide.

Three main characteristics of canopy fuels must be quantified to use the coupled

models: canopy bulk density, canopy base height, and foliar moisture content.

Canopy bulk density is the mass of available canopy fuel per unit canopy volume. It is a bulk property of the stand, not an individual tree. We use the term
USDA Forest Service Research Paper RMRS-RP-29. 2001. 5

crown bulk density for reference to the bulk fuel properties of an individual tree.

Canopy base height is more difficult to define, but it too is a bulk property of a

stand, whereas crown base height is a property of an individual tree.

Alternative techniques for estimating canopy bulk density and base height are

described below. We do not yet know the relative accuracy of these methods.

Inventory-based techniques hold promise for highest accuracy, but other methods are better for mapping large areas. Pending further research, we suggest using inventory-based techniques where possible.

Canopy Bulk Density

With Rothermel’s (1972) surface fire model we specify the fuels that may

potentially be consumed in the flaming fire front (Wo

), and the model then estimates what portion of that fuel actually contributes to propagation of the fire

front. However, with canopy bulk density (CBD) we specify, before the fact, the

canopy fuels that would be consumed in the flaming front of a fully active crown

fire. It is reasonable to assume that the foliage, lichen, and moss are consumed in

the flaming front of a fully active crown fire. Some portion of the live and dead

branch wood less than 6 mm diameter should also be consumed in the flaming

front (Brown and Bradshaw 1994; Brown and Reinhardt 1991; Reinhardt and

others 1997). A model by Call and Albini (1997) suggests that 65 percent of

canopy fuel 0 to 6 mm diameter at 100 percent moisture content would be consumed in a crown fire. However, Call and Albini acknowledge that their model

overpredicts consumption in small size classes.

For uniform stands, CBD can be computed as the available canopy fuel load

divided by canopy depth (Keane and others 1998). This method carries the implicit assumption that canopy biomass is distributed uniformly within the stand

canopy, which is unlikely to be true even in stands with simple structures;

multistoried stands are probably even more poorly represented by this procedure.

Following Sando and Wick (1972), the Fire and Fuels Extension to the Forest Vegetation Simulator (FFE-FVS, Beukema

and others 1997) uses a technique to estimate “effective” CBD

in nonuniform stands from a stand inventory that does not assume a uniform vertical distribution of canopy fuel. Therefore,

CBD does not necessarily equal canopy load divided by canopy

depth. In FFE-FVS, CBD was defined as the maximum 4.5-m

deep (15-foot) running mean of canopy bulk density for layers

0.3 m (1 ft) thick (fig. 2). This method yielded encouraging and

realistic results when applied to stand exam data on the Idaho

Panhandle National Forests. However, we have no way of knowing if the results are accurate because canopy fuels have never

been measured directly.

A number of studies exist that predict foliar and branch biomass from tree dimensions, typically diameter, sometimes in

combination with height, crown ratio, or sapwood thickness.

Brown (1978) provides predictive equations for the common conifer tree species of the Inland West; Snell and Brown (1980)

provide similar methods for Pacific Northwest conifers. A large

number of allometric equations of this type from many research

studies are summarized in the computer software BIOPAK

(Means and others 1996). These equations, together with a list

of trees representing a stand, may be used to estimate foliage

load, as well as the load of branchwood of various sizes.

Canopy bulk density, kg m-3

0.0 0.1 0.2 0.3

0

5

10

15

20

25

5-m running mean

foliage and fine branches

Height above ground, m

fine branches

foliage

fine branches

foliage and

Figure 2—Vertical profile of canopy bulk density in a

lodgepole pine (Pinus contorta) stand on the Bitterroot National Forest, Montana. Effective canopy

bulk density is taken to be the maximum 5-m running mean (0.21 kg m-3).
6 USDA Forest Service Research Paper RMRS-RP-29. 2001

An alternative method of estimating foliage load is to first estimate leaf area index

(LAI) using onsite measurement. Several optical instruments are available for estimating LAI (Fassnacht and others 1994; Smith and Somers 1993; Welles 1990). Leaf

area index can be converted to an estimate of foliar biomass using specific leaf area

factors (for example, Keane and others 1996). Published values for specific leaf area

exist for many conifer species.

A canopy fuel photo guide would help managers quantify canopy bulk density in the field. Further research into the nature and properties of canopy fuels is

needed before we can fully exploit existing and future models of crown fire behavior.

Canopy Base Height

Crown base height is a simple characteristic to measure on an individual tree.

Canopy base height (CBH ) is not well defined or easy to estimate for a stand.

Neither the lowest crown base height in a stand nor the average crown base height

is likely to be representative of the stand as a whole. Canopy base height is difficult to measure in multistory stands and stands with ladder fuels. Van Wagner

(1993) reduced observed CBH to account for ladder fuels in a two-story stand.

Defined in terms of its consequences to crown fire initiation, CBH is the lowest

height above the ground at which there is sufficient canopy fuel to propagate fire

vertically through the canopy. Using this definition, ladder fuels such as lichen,

dead branches, and small trees are incorporated. Sando and Wick (1972) estimated canopy base height of nonuniform stands based on the height at which a

minimum bulk density of fine fuel (100 lb acre-1 ft-1, 0.037 kg m-3) is found.

The Fire and Fuels Extension to the Forest Vegetation Simulator (Beukema

and others 1997) uses the Sando and Wick approach in combination with Brown’s

(1978) equations to estimate canopy base height and canopy bulk density. Canopy

base height was defined as the lowest height above which at least 30 lb acre-1 ft-1

(0.011 kg m-3) of available canopy fuels is present.

Ladder fuels that increase the intensity of the surface fire, such as short understory trees, shrubs, and needle drape, are best accounted through custom surface

fuel modeling or by simple adjustment of simulated surface fire intensity to include their effect.

Foliar Moisture Content

Foliar moisture content (FMC) has less influence over crown fire initiation

than CBH , but its theoretical effect on crown fire spread rate through the foliar

moisture effect (Van Wagner 1993) is much stronger (Scott 1998). Numerous

studies of FMC have been conducted throughout North America (Alexander 1988).

Moisture content of conifer foliage varies among species and seasons (Philpot

and Mutch 1971), but not from day to day (Hartford and Rothermel 1991) or year

to year (Philpot and Mutch 1971). The Forestry Canada Fire Danger Group (1992)

related the timing of seasonal changes in FMC to latitude, longitude, and elevation.

In old foliage (at least 1 year old), the lowest moisture contents have been

found in Picea mariana (Chrosciewicz 1986; Springer and Van Wagner 1984),

and Picea glauca, Picea banksiana, and Abies balsamea (Chrosciewicz 1986),

each with a low FMC near 75 percent (though the lowest FMC may occur outside

the fire season). Highest old-foliage moisture content was found in Pinus clausa

(Hough 1973) and Abies balsamea (Kozlowski and Clausen 1965; Little 1970),

with values near 150 percent. The range of old-foliage FMC for most species

straddles 100 percent, so this value has been used as a default FMC if no other

information is available (Finney 1998; Scott 1998). Future research should be
USDA Forest Service Research Paper RMRS-RP-29. 2001. 7

directed at compiling existing FMC data for Western conifers, then conducting

field research to fill in gaps in the data. Larger errors in estimating effective FMC

probably result from variable amounts of dry dead fuels and lichen in the canopy.

Van Wagner (1993) estimated effective FMC by computing the loading-weighted

average moisture content of the foliage and fine dead canopy fuels. Until better

data exist, using 100 percent for FMC is a reasonable approach, especially given

the relative insensitivity of the models to this parameter.

EXISTING MODELS OF SURFACE AND CROWN FIRE BEHAVIOR

The basic behavior of surface and crown fires can be described by fireline

intensity (I), forward rate of spread (R), and heat (release) per unit area (HPA). (A

complete list of symbols used in this paper can be found in table 1.) Fireline

intensity is the rate of heat release in the flaming front per unit length of fire

front. Byram (1959) defines fireline intensity, I, as

60

HW R

I f = (1)

where H is the heat yield of the fuel (kJ kg-1), Wf

 is the weight of fuel consumed

in the flaming front (kg m-2), R is the forward rate of spread of the fire (m min-1),

and 60 is a conversion factor so that the units for I reduce to kW m-1(kJ m-1 min-1).

Byram uses the term “available fuel” to describe Wf

, but he evidently refers to the

weight of fuel available to the flaming fire front, not the total amount consumed

in flaming and smoldering combustion. In the remainder of this paper, intensity

should be taken to mean Byram’s fireline intensity as defined in equation 1.

Heat (release) per unit area is the product of the heat yield of fuels, H, and the

weight of fuel consumed in the flaming front, Wf

. Therefore, HPA is identical to

the quantity HWf

 in equation 1. Heat per unit area can also be expressed (Andrews

and Rothermel 1982) as

HPA I t = R R

(2)

where IR is reaction intensity (kJ min-1 m-2) and t

R is residence time in minutes

(Anderson 1969)

t R = 12 595 .

σ

 (3)

where σ is the characteristic surface-area-to-volume ratio (cm-1) of the fuel bed.

Neither Rothermel’s (1972) model nor BEHAVE (Andrews 1986) explicitly

computes Wf

, but because HWf in equation 1 is equivalent to HPA, Wf can be

computed as

W

HPA

H f = (4)

Fuel Consumption at the Flaming Front

Conflicting and ambiguous terminology has led to confusion in determining

Wf

 for use in equation 1 and its variants (see table 2). Total fuel load, Wt, is the

maximum amount of fuel, including duff and large woody fuels (>76 mm diameter), that could possibly be consumed in a hypothetical fire of the highest intensity in the driest fuels (Byram 1959). Available fuel, Wa

, is that portion of the
8 USDA Forest Service Research Paper RMRS-RP-29. 2001

total fuel load that is consumed in a given fire; it must always be less than or

equal to Wt (fig. 3). Unless otherwise specified, Wa includes the consumption of

duff and large woody fuels, most of which takes place after passage of the fire

front. Equation 1 requires Wf

, the usually much smaller quantity of fuel that is

consumed in the flaming fire front. The Forestry Canada Fire Danger Group

(1992) uses equation 1 to define frontal fire intensity (as opposed to Byram’s

fireline intensity) in the Canadian Forest Fire Behavior Prediction System by

using Wa (total fuel consumption) in place of Wf

. In forest fuel complexes with

duff and coarse fuels, Wa can be many times larger than Wf

, so values of frontal

Table 1—Symbols and variables used in the text.

Symbol Definition

B,C,E Terms in Rothermel’s (1972) model, all functions of 

s

CBD Canopy bulk density, kg m-3

CBH Canopy base height, m

CFB Crown fraction burned

FMC Crown foliar moisture content, percent

FME Foliar moisture effect

HPA Heat (release) per unit area, kJ m-2

H Heat yield of fuel, kJ kg-1

I Byram’s fireline intensity, kW m-1

I'initiation Critical I for initiating a crown fire, kW m-1

I

R Reaction intensity, kW m-2

O Open (6.1-m) windspeed, km hr-1

O'active Critical open windspeed for sustaining fully active crown fire, km hr-1

O'cessation Critical open windspeed for crown fire cessation, km hr-1

O'initiation Critical open windspeed for crown fire initiation, km hr-1

Qig Heat of preignition, kJ kg-1

R Forward rate of spread, m min-1

Ractive R for a fully active crown fire, m min-1

R'active Critical R for sustaining an active crown fire, m min-1

Rfinal R for any type of fire: surface, passive crown, or active crown, m min-1

R'initiation Critical R for initiating a crown fire, m min-1

Rsurface R for a surface fire, m min-1

S Mass-flow rate of crown fuel, kg m-2 s-1

t

R Flame residence time, min

U Midflame windspeed, km hr-1

Wa Available fuel, or total fuel consumption, kg m-2

Wc Fuel available for convection, kg m-2

Wcanopy Weight of available canopy fuel, kg m-2

Wf Weight of fuel consumed in the flaming front, kg m-2

Wn Wo with the mineral content removed, kg m-2

Wo Fine fuel that can potentially contribute to flaming front, kg m-2

Wt Total fuel load, kg m-2

WRF Wind reduction factor

b Fuelbed packing ratio

bop Optimum fuelbed packing ratio

e Effective heating number

x Propagating flux ratio

rb Oven-dry fuel bed bulk density, kg m-3

s Surface-area-to-volume ratio of fuel particles, cm-1

fs Slope factor

fw Wind coefficient

f'

w (initiation) Critical wind coefficient for crown fire initiation
USDA Forest Service Research Paper RMRS-RP-29. 2001. 9

Table 2—Definition of fuel loading, consumption and availability terms and variables. All quantities are

measured in mass per unit area (kg m-2).

Term Symbol Definition

Total biomass The total amount of living and dead vegetation per unit

area, including vegetation that is never consumed in a

fire, such as live tree boles and large live branches.

Total fuel load Wt The maximum amount of fuel per unit area that can

possibly be consumed in a fire of the highest possible

intensity in the driest possible fuels.

Available fuel Wa The total amount of fuel per unit area that is consumed by

a fire, including the post-frontal consumption of duff,

organic soils, and large woody fuels like logs.

Fuel available for Wc The amount of fuel per unit area that is consumed in a

convection short enough time and with enough intensity to contribute

to the convection column. It is usually larger than Wf

 but

smaller than Wa

 because only a fraction of postfrontal

combustion contributes to convection.

Fuel consumed Wf The amount of fuel per unit area that is consumed within

 within the and contributes to fire behavior in the flaming front of the

 flaming front fire. In Rothermel’s (1972) surface fire model this only

includes fuels less than 7.6 mm diameter.

Total fine fuel loada Wo The amount of surface fuel per unit area less than 7.6 mm

diameter. This term is used in the Rothermel (1972)

surface fire spread model.

Net fuel load Wn The net amount of surface fuel per unit area less than 7.6 mm

diameter after the mineral fraction has been sub

tracted. It is always slightly less than Wo

. Wn is also a term

from the Rothermel spread model.

a

This term was originally called total fuel load in the Rothermel (1972) model; we modified it here to avoid conflict with

Byram’s definition of Wt.

Fuel load, kg m-2

0 2 4 6 8 10 12 14

duff 

surface < 7.6cm

surface > 7.6cm 

canopy fuel 

Wt

Fuel load terms

Fuel consumption

surface fire

crown fire

Wo

Wn

Wa

Wc

Wf

Wa

Wc

Wf

Figure 3—Comparison of fuel

loading, consumption, and availability terms for a hypothetical

fuel complex under conditions of

(a) high dead fuel moisture that

leads to surface fire, and (b) low

dead fuel moisture that leads to

active crown fire. Terms are defined in table 2.
10 USDA Forest Service Research Paper RMRS-RP-29. 2001

fire intensity should also be many times larger than the fireline intensity used in

this paper. Values of frontal fire intensity from the Canadian FFBP System are

therefore not directly comparable to values of fireline intensity reported here.

Rothermel (1991a) resurrected Byram’s concept of the “power of the fire” to

identify potential plume-dominated fire conditions. To compute the power of the

fire, Rothermel (1991a) estimated the amount of fuel consumed in a short enough

time and with enough intensity to contribute to the convection column, Wc

.

Rothermel refers to the energy produced by Wc

 (that is, H * Wc) as the unit energy, which is analogous to heat per unit area in the surface fire model. Rothermel’s

analysis using Albini’s (1976) BURNOUT model indicated that Wc

 was only

slightly greater than Wf

.

Further confusion is brought about by variable names from the Rothermel

surface spread model (1972). In that model, Wo

, which Rothermel called total

fuel load, is actually a subset of the total fuel load defined by Byram. Unlike Wt

,

Wo

 includes only those fuel components that contribute significantly to fire behavior at the flaming front. By convention, only the dead fuels less than 76 mm

diameter and live fuels less than 6 mm diameter are included in Wo

 (Rothermel

1972). In the Rothermel (1972) model, Wn

 is the net weight of Wo after the mineral fraction has been subtracted. Mineral fraction is usually held constant at

0.055, so Wn

 = Wo (1 – 0.055). Some authors have incorrectly used Wn in place of

Wf

 (for example, Bessie and Johnson 1995, equation 12). This error can result in

a many-fold over-calculation of intensity, because the Rothermel model predicts

that Wf

is only a small fraction of Wn in forest fuels.

For crown fires, Wf

is the combined weight of surface and canopy fuels consumed in the flaming front. An active crown fire consumes nearly all of the fine

crown fuels in a given area, while a passive or intermittent crown fire consumes

only a portion (Van Wagner 1993).

It will later be necessary to estimate the spread rate that leads to a given fireline

intensity by rearranging equation 1. The difficulty of determining Wf for use in

equation 1 and its derivatives can be avoided by replacing HWf

 with HPA in equation 1.

I

HPA R = *

60

 (5)

The Rothermel surface fire spread model was developed to predict spread

rate; only through combination with a model of residence time (Anderson 1969)

can the Rothermel spread model be used to estimate HPA and I (Andrews and

Rothermel 1982). As such, estimates of I are not as reliable as those of R from the

Rothermel model. However, the Rothermel model is the best choice currently

available for estimating the fireline intensity in surface fires. With testing, the

BURNUP model (Albini and Reinhardt 1995; Albini and others 1995) may prove

useful in estimating fuel consumed in the flaming front of surface fires.

Surface Fire Behavior

For this analysis surface fire spread rate is simulated with Rothermel’s (1972)

model as adjusted by Albini (1976) and implemented in BEHAVE (Andrews 1986),

FARSITE (Finney 1998), NEXUS (Scott 1999), and other fire modeling systems. Headfire rate of spread for upslope winds is expressed (Rothermel 1972)

R

I

Q surface

w s

b ig

R

= ξ φφ + +

ρ ε

( ) 1 (6)
USDA Forest Service Research Paper RMRS-RP-29. 2001. 11

The Rothermel model has many input factors. Fuelbed characteristics have

been combined into standard fuel models (Anderson 1982) that represent stylized fuelbeds. Custom fuel models can be created from a fuel inventory or by

adjusting one of the standard fuel models (Burgan 1987; Burgan and Rothermel

1984). As employed in this analysis, the Rothermel model can be used with either standard or custom fuel models to simulate surface fire behavior. Standard

fuel models often do not accurately simulate both spread rate and fireline intensity simultaneously for a given simulation. Even custom models are difficult to

calibrate so that both rate of spread and fireline intensity are accurately simulated

over a range of environmental conditions. For assessing crown fire hazard using

the models outlined in this paper, accurate simulation of surface fireline intensity

is more important than spread rate accuracy. The selection of a standard model or

calibration of a custom model should reflect this importance.

Crown Fire Behavior

Foresters and ecologists use the term crown in reference to the branches and

foliage of individual trees, and the term canopy when referring to the aggregation

of crowns at the group or stand level. Technically, a crown fire is one that consumes the crowns of individual trees (a passive crown fire), while a canopy fire

would be one that burns in the whole canopy stratum as a unit (active or continuous crowning). However, we customarily refer to both types of fires as crown

fires. We will continue to use the term crown fire to refer to both crown and

canopy fires because the modifiers passive and active distinguish the two types.

Several models of active crown fire spread rate are now available (Albini 1996;

Gomes da Cruz 1999; Grishin 1997; Rothermel 1991a). Each model carries problems or assumptions that limit its application. Despite its shortcomings, we use

the Rothermel (1991a) procedure to estimate crown fire spread rate because it is

the most widely used of the available models.

The Rothermel (1991a) correlation was intended for the Northern Rocky Mountains and other areas with similar fuels, climate, and topography. He used linear regression to relate coarse-scale observed crown fire spread rates to predictions made

with his surface fire model using fuel parameters from Fire Behavior Fuel Model

(FM) 10 (Anderson 1982). Midflame windspeed was set to 40 percent of the observed 6.1-m (20-ft) windspeed. In simple form, the Rothermel (1991a) correlation

for average crown fire spread rate is

( ) 10 40% Ractive = 3.34 R (7)

where (R10)40% is the spread rate predicted with Rothermel’s (1972) surface fire

model using the fuel characteristics for FM 10 and midflame windspeed set at 40

percent of the 6.1-m windspeed.

The input factors from FM 10 must be used to predict crown fire spread rate

using Rothermel’s method, not the actual surface fuel characteristics. Bessie and

Johnson (1995) used actual surface fuel characteristics, which can result in errors

of nearly an order of magnitude, depending on the nature of the actual surface

fuels. However, the mandatory use of FM 10 applies only to simulating crown

fire spread rate with Rothermel’s (1991a) correlation—surface fire spread rate

can still be simulated with any appropriate standard or custom fuel model. The

midflame windspeed for use in the correlation must be set at 40 percent of the

open windspeed, not at the midflame wind that would be used for simulating

surface fire behavior. For surface fires, midflame winds are estimated by multiplying the open wind (6.1-m in the United States) by a wind reduction factor,

WRF, the ratio of midflame to open windspeeds. In forest stands on level ground,
12 USDA Forest Service Research Paper RMRS-RP-29. 2001

Albini and Baughman (1979) estimate WRF from stand height and crown filling

fraction (the fraction of the canopy volume that is occupied by tree crowns). The

WRF for forest stands is most often in the range 0.10 to 0.3 (Rothermel 1983).

Rothermel’s correlation is limited to wind-driven crown fires—plume-dominated crown fires are not predicted by this or any other crown fire spread model.

We must make additional assumptions before applying Rothermel (1991a) to

the coupled model. First, we assume the Rothermel crown model estimates the

spread rate of fully active crown fires, though some of his fires, such as the 1989

Black Tiger fire (NFPA 1990), were likely not fully active. In that respect the

Rothermel correlation might underestimate the spread rate of a true fully active

crown fire. Second, we assume that the correlation simulates the flame front

spread rate alone, without the effect of spotting. However, the observed spread

rates used in the correlation included the effect of short- and medium-range spotting on overall fire spread rate. In that respect the correlation should overpredict

spread rate of the flame front itself. Last, we use the average spread rate from

Rothermel (1991a) rather than the maximum he observed. Therefore, crown fire

runs with spread rates faster than the coarse-scale average are possible and will

be underpredicted in our method. The combined effects of fires with significant

spotting and less than fully active crowning in the Rothermel correlation on simulated active crown fire spread rate is uncertain.

Despite these limitations, the lack of practical alternative models requires

that we use Rothermel’s (1991a) method to simulate spread rate of a fully active

crown fire flame front. Different models of active crown fire spread rate—an

improved empirical model (Gomes da Cruz 1999) or a metamodel derived from

a physical model—can be substituted as they become available.

To derive an index of crown fire potential, equation 7 must be written in its

mathematical form

R

I

Q active

R ws

b ig FM

=  + +













 3 34

1

10

. ξ φφ ( )

ρ ε

 (8)

where all terms are evaluated for the characteristics of FM 10. In Rothermel’s

correlation, crown fire rate of spread depends only on open windspeed, surface

fuel moisture contents, and slope steepness, but not on actual surface or canopy

fuel characteristics. Active crown fire spread rate probably also varies with other

canopy characteristics such as foliar moisture content (Van Wagner 1974, 1989)

and canopy bulk density. However, the models that include canopy bulk density

show contradictory effects of canopy bulk density on spread rate. Grishin’s (1997)

physical model indicates increasing spread rate with decreasing canopy bulk density, whereas the empirical model developed by Gomes da Cruz (1999) shows a

direct relationship. Albini’s crown fire model has not yet been exercised sufficiently to determine how it will respond to variation in canopy bulk density. Until

the conflicting effects of canopy bulk density on crown fire spread rate can be

resolved, using a model that does not include this variable is not unreasonable.

Foliar Moisture Effect

The Rothermel correlation can be extended to include the theoretical effect of

foliar moisture content, FMC, on crown fire spread rate using the foliar moisture

effect, FME, defined by Van Wagner (1974, 1989, 1993) as

( )

( ) FME

FMC

FMC = −

+





 



 15 00275

460 25 9

4 . .

. (9)
USDA Forest Service Research Paper RMRS-RP-29. 2001. 13

The FME is always applied as a ratio of FME to a normal value, FMEo, which

is based on the FMC in the data used to construct the crown spread rate model.

The FMC of the fires used in the Rothermel correlation was not documented and

surely varied among the fires. Therefore, using the FME concept with Rothermel’s

model will require a derivation of FMEo

 based on some alternative FMC, such as

an overall average FMC among all species during the fire season in the Northern

Rocky Mountains. Taking the range of FMC to be 85 to 120 percent and assuming an average of 100 percent, the ratio FME/FMEo

 would range from 0.714 to

1.31. Incorporating the FME concept, equation (8) becomes

R

FME

FME

I

Q active

o

R ws

b ig FM

= 



 





 + +













 3 34

1

10

. ξ φφ ( )

ρ ε

 (10)

where FMEo

 is 0.0007383 for a reference FMC of 100 percent. The foliar moisture effect will not be used further in this paper. However, FME is included as an

option in NEXUS; interested readers can examine its effect on crown fire spread

rate and the Torching and Crowning Indices themselves.

Criterion for Crown Fire Initiation

Several models of crown fire initiation are available. Most are semiempirical

with a basis in convection theory (Alexander 1998; Van Wagner 1977;

Xanthopoulous 1990) that consequently need estimates of heat release rate (fireline

intensity) for determining the upward heat flux. Gomes da Cruz (1999) developed a logistic regression model based largely on fuel strata gap (similar to canopy

base height) and total surface fuel consumption (as a surrogate for Wf

). Gomes da

Cruz used total surface fuel consumption to avoid difficulties in estimating fireline

intensity. However, surface fuel consumption is itself difficult to estimate.

Alexander’s model is similar to Van Wagner’s, but accounts for the effects of

flaming residence time, plume angle, and fuel bed characteristics. While these

additional inputs may improve predictions, they are difficult to estimate, so their

inclusion is of dubious value. Because of the lack of high quality observations,

none of these crown fire initiation models has been rigorously tested against

independent data.

We selected Van Wagner’s (1977) model of crown fire initiation because it is the

most widely used of the potential models, if only because it is one of the oldest. Van

Wagner (1977) theorized that canopy fuels ignite when heat supplied by a surface fire

drives off their moisture and raises them to ignition temperature. He identified the

critical (minimum) fireline intensity of a surface fire, I'initiation, that will initiate a crown

fire. Van Wagner’s (1977) separate equations can be combined as follows to compute

I'initiation in kW m-1:

( ) ′ =  +



 

 I  CBH FMC

initiation

460 259

100

3

2 . (11)

where CBH is the canopy base height (m). The coefficient 100 in the denominator is an empirical constant based on a single observation.

For further analysis, I'initiation is converted to its equivalent rate of spread, R'initiation,

by rearranging equation 5 and substituting I'initiation for I, following the concepts in

the Canadian FFBP System (Forestry Canada Fire Danger Group 1992) and Van

Wagner (1993)

′ = ′ R

I

HPA initiation

initiation 60 (12)
14 USDA Forest Service Research Paper RMRS-RP-29. 2001

Because HPA is a function of fuel characteristics, R'initiation will also vary with

surface fuel characteristics, even if I'initiation is the same.

Van Wagner’s crown fire initiation criterion has not been well tested, but it

includes the major variables important to initiating a crown fire—height of canopy

fuels above the ground, their moisture content, and the intensity of the surface

fire (fig. 4). I'initiation depends on foliar moisture content and canopy base height.

In the Rothermel surface fire model, surface fire intensity depends on surface

fuel characteristics (load, surface-area-to-volume ratio, heat content, packing ratio, and moisture contents), midflame windspeed, and slope steepness. Different

fuel complexes can have the same value of I'initiation (for example, similar CBH

and FMC) but different surface fire intensities.

Criterion for Active Crown Fire Spread

By rearranging a basic heat balance equation applicable to fire spread in any

fuel complex, Van Wagner (1977) theorized that solid flames would form in the

canopy (active crowning) if a critical horizontal mass-flow rate of fuel into the

flaming zone, S, is exceeded

S R CBD = active

 (13)

where Ractive is the after-crowning forward rate of spread and CBD is the canopy

bulk density (kg m-3). Van Wagner (1977) found a critical mass flow rate of 0.05

kg m-2 sec-1 for one fire in a red pine plantation, slightly lower than the values

given for experimental fuel beds by Thomas (1963). Until more data on the critical mass flow rate for crown fires in a wide range of forest types are available we

will rely on Van Wagner’s critical mass-flow rate of 0.05 kg m-2 sec-1. Rearranging equation 12, substituting Van Wagner’s value of 0.05 for S, and multiplying

by 60 to compute R'active in m min-1 (Alexander 1988), the critical (minimum) rate

of spread for active crowning, R'active, is

R′ = CBD active

30. (14)

The only factor affecting the critical spread rate needed to sustain an active

crown fire is CBD (fig. 5).

Figure 4—Van Wagner’s crown fire initiation criterion (following Alexander 1988) expressed

as critical surface fireline intensity (a), and critical flame length using Byram’s (1959) flame

length model (b). Note that critical flame length is less than canopy base height (CBH) for

CBH greater than about 1 m. Example: a stand with CBH of 3 m and 100 percent FMC

requires surface fireline intensity of 875 kW m-1 (flame length 1.7 m) to initiate crowning.

2000

Crown base height, m

0 2 4 6 8 10 12

0

4000

6000

8000

10000

Crown base height, m

0 2 4 6 8 10 12

0

1

2

3

4

5

6

(a) (b)

FMC FMC

I'initiation, kW hr -1

120

100

80

120

100

80

Critical flame length, m
USDA Forest Service Research Paper RMRS-RP-29. 2001. 15

Quantitative Crown Fire Classification

Following Van Wagner (1977) and Alexander (1988), we use the criteria for

initiation and sustained spread of crown fires to classify a fire as surface, passive

crown, or active crown fire. In the classification, two criteria must be met in

order to have an active crown fire. First, a surface fire of sufficient intensity must

ignite the canopy fuels; Isurface must exceed I'initiation. Using equation 11, the required intensity is a function of foliar moisture content and height to the base of

the canopy. If this criterion cannot be met, the fire will remain on the surface.

Second, if a crown fire can indeed initiate, the potential crown fire spread rate for

the conditions specified must be sufficient to meet the mass-flow requirement

(equation 13).

The expected type of fire then follows from simulated surface fire intensity

and crown fire spread rate (fig. 6). If the classification is followed strictly, all

situations in which the surface fire intensity criterion is not met are classified as

surface fires. However, an alternative classification splits the surface fire class

into two subclasses. These will be discussed later in the section on hysteresis.

QUANTIFYING THE HAZARD

Our objective is to produce a method of quantitatively assessing the relative

crown fire hazard of different stands by coupling the existing fire behavior modCanopy bulk density, kg m-3

0.0 0.1 0.2 0.3 0.4

0

20

40

60

80

100

active crown fire possible

active crown fire

not possible

R' active, m min -1

Figure 5—Van Wagner’s criterion for sustained

active crown fire spread based on a minimum

horizontal mass-flow rate of 0.05 kg m-2 min-1.

Example: a stand with CBD of 0.2 kg m-3 requires a spread rate of 15.0 m min-1 to sustain

active crowning.

Active

crown fire

Surface

fire

low high

low

high

Passive

crown

fire

Crown fire spread rate, 

Ractive

Isurface

R'active

I'initiation

Figure 6—Fire classification based on Van

Wagner (1977) and Alexander (1988). A fire

for which surface fire intensity (I surface) is less

than critical (I' initiation) falls in the surface fire

class; one for which I surface exceeds I' initiation

is either a passive or active crown fire depending on the crown fire spread rate criterion. Passive crowning occurs where a

crown fire initiates (I surface > I' initiation) but cannot be sustained (Ractive < R'active). An active

crown fire occurs where both criteria are

exceeded.
16 USDA Forest Service Research Paper RMRS-RP-29. 2001

els presented above. At any given site, fuels and topography can be considered

constant in the short term. Weather, however, varies significantly throughout a

day, from day to day, and throughout a season.

In the fire behavior models presented above, weather is manifested in two

basic inputs: windspeed and dead fuel moisture content. From a description of

the surface fuels, canopy fuels, and site characteristics needed for the above models, we can define critical combinations of dead fuel moisture and windspeed that

result in surface, passive crown, and active crown fires. Consider a simulation

for a hypothetical stand with the characteristics shown in table 3. The passive

crown fire region is fairly narrow (fig. 7), and active crowning can occur under

moderate burning conditions.

While it is possible to compute all combinations of dead fuel moisture and

windspeed that lead to crown fire activity for a given fuel complex, for purposes

of a relative hazard assessment it is sufficient to set fuel moistures constant at

values that represent some moisture condition of interest (for example, actual,

typical, or extreme moisture conditions). Windspeed is highly variable and probably the most important environmental factor affecting crown fire initiation, sustained active spread, and final rate of spread. Therefore, we will determine the

critical open wind, O (6.1-m above the canopy), that leads to crown fire activity

for a set of site characteristics, surface and canopy fuel characteristics, and fuel

moisture conditions. Sites that can initiate or sustain a crown fire at lower

windspeeds are more prone to crown fire. Critical open windspeeds for crown

fire initiation and active spread are stand-specific indicators of crown fire hazard. Note that although we use critical windspeeds as indices, the site conditions

(surface and canopy fuels, slope steepness, and so forth), not the weather, are

being rated.

σφ

Table 3—Simulation inputs for a hypothetical stand to be

used in examples throughout this paper.

 Input Value

Fuel model 10 (timber litter)

Slope 0 percent

Canopy bulk density 0.15 kg m-3

Canopy base height 1.5 m

Foliar moisture content 100 percent

Wind reduction factor 0.15

Live fuel moisture Normal summera

a

See table 4 for a listing of fuel moisture content by size class.

Weighted-average dead

fuel moisture content, percent

4 6 8 10 12 14

0

10

20

30

40

50

60

70

active crown fire

surface fire

Open windspeed, km/hr

passive crown fire

Figure 7—Van Wagner’s (1977) crown fire classification under varying open windspeed and

dead surface fuel moisture conditions for the

example stand. For this example, a passive

crown fire region separates surface fire and

active crown fire. Inputs: fuel model 10 (timber litter and understory, Anderson 1982),

canopy base height = 1.5 m, canopy bulk density = 0.15 kg m-3, foliar moisture content =

100 percent, live surface fuel moisture = 78

percent, and wind reduction factor = 0.15.
USDA Forest Service Research Paper RMRS-RP-29. 2001. 17

Two Indices of Crown Fire Hazard

The Torching Index (TI) is the 6.1-m windspeed at which crown fire is expected to

initiate based on Rothermel’s (1972) surface fire model and Van Wagner’s (1977)

crown fire initiation criteria. TI is a function of surface fuel characteristics (fuel model),

surface fuel moisture contents, foliar moisture content, canopy base height, slope steepness, and wind reduction by the canopy.

The Crowning Index (CI) is the 6.1-m windspeed at which active crowning is

possible, based on Rothermel’s (1991a) crown fire spread rate model and Van Wagner’s

(1977) criterion for active crown fire spread. CI is a function of canopy bulk density,

slope steepness and surface fuel moisture content.

The Torching and Crowning Indices can be determined graphically by plotting Rsurface, Ractive, R'initiation and R'active over a range of open windspeeds (fig. 8),

holding moisture content at some specified level—in this example we use

Rothermel’s (1991a) normal summer condition (table 4). The TI is the windspeed

where the lines for Rsurface and R'initiation cross. The CI is where the lines for Ractive

and R'active cross. Van Wagner’s fire classification is also shown on the chart. At

windspeeds less than TI a surface fire is expected. If the windspeed is greater

than TI but less than CI we expect a passive crown fire. Finally, windspeeds

greater than CI result in active crown fire.

Table 4—Fuel moisture content values (percent) by size class for five seasonal moisture conditions, from Rothermel (1991a).

 Seasonal moisture condition

 Early spring Late spring Normal Drought Late summer

Class before greenup after greenup summer summer severe drought

1-h 8 9 6 4 3

10-h 14 11 8 5 4

100-h 18 15 10 7 6

live 65 195 117 78 70

Crown fire assessment chart

Open (6.1-m) windspeed, km hr-1

0 5 10 15 20 25 30 35 40 45 50

0

5

10

15

20

25

30

35

40

45

50

surface fire

active

crown

fire

Spread rate, m min-1

R'active

R'initiation

R'SA

Rsurface

Ractive

passive

crown

fire

Torching index (O'initiation)

Crowning index (O'iactive)

Figure 8—The Torching and Crowning Indices can

be determined graphically on a crown fire assessment chart. The open windspeed at which Rsurface

exceeds R' initiation (same as I surface > I' initiation) is the

Torching Index (TI). The open windspeed at which

Ractive exceeds R'active is the Crowning Index. A surface fire is expected at windspeeds below TI.

Windspeeds greater than TI but less than CI lead

to passive crowning. Active crown fire is expected

at windspeeds above CI. The theoretical surface

fire spread at CI (R'SA) is shown; that quantity will

be used later in the paper. Inputs: fuel model 10

(timber litter and understory, Anderson 1982),

canopy base height = 1.5 m, canopy bulk density

= 0.15 kg m-3, foliar moisture content = 100 percent, normal summer surface fuel moisture condition (Rothermel 1991, table 4), and wind reduction factor = 0.15.

σφ
18 USDA Forest Service Research Paper RMRS-RP-29. 2001

The quantity R'SA, the simulated surface fire spread rate when the windspeed =

O'active is also shown in figure 8; it will be referenced in the discussion of crown

fraction burned in appendix A.

The effects of slope are difficult to generalize because slope can either increase or decrease fire spread rate depending on wind direction. In his analysis of

crown fire spread, Rothermel (1991a) suggests assuming level ground for modeling average crown fire behavior over large areas, and assuming upslope winds

for worst-case analysis. One might want to examine effects of wind direction

with respect to slope on crown fire potential. Equations for determining TI and

CI for cross-slope winds are on file with the authors at the Rocky Mountain

Research Station, Missoula Fire Sciences Lab. The derivations of critical

windspeed for crown fire initiation and sustained spread for upslope winds will

be shown below.

Torching Index—The Torching Index is the open windspeed at which I'initiation

= Isurface. Assuming that Wf is independent of windspeed, as it is in the Rothermel

surface fire model, then TI is also the windspeed at which R'initiation= Rsurface. Combining equations 6 and 12 allows us to express R'initiation = Rsurface as

60 ′ 1 = I + ′ +

HPA

I

Q

initiation R w initiation s

b ig

ξφ φ

ρ ε

( ) ( ) (15)

where φ '

w (initiation) is the critical wind coefficient for crown fire initiation. Solving

equation 15 for φ '

w (initiation) gives

′ = ′ φ − − ρ ε

ξ w initiation φ initiation b ig

R

s

I Q

HPA I ( )

60

1 (16)

Rothermel (1972), expressed in SI units by Wilson (1980) with midflame

windspeed (U) in km hr-1, defines φ w

φ β

β w

B

op

E

= C U 















−

(. ) 54 683 (17)

where C, B, and E are constants for any given surface fuel complex that depend

only on σ , and ß/ßop is the ratio of actual to optimum packing ratio of the fuel

bed (Rothermel 1972). Combining equations 16 and 17 and converting to the

open windspeed gives us O'initiation.

TI O

WRF

I Q

HPA I

C

initiation

initiation b ig

R

s

op

E

B

= ′ = 



 





′ − −













































−

1

54 683

60

1

1

.

ρ ε

ξ φ

β

β

 (18)

The Torching Index can be computed for any combination of surface fuels,

fuel moistures, canopy base height, wind reduction factor, and foliar moisture

content.
USDA Forest Service Research Paper RMRS-RP-29. 2001. 19

Crowning Index—Similarly, to derive the Crowning Index, O'active, we solve

for O'active such that Ractive equals R'active, which in turn is expressed in terms of

canopy bulk density (equation 13). Solving first for the critical midflame

windspeed,

′ = 



 









 





− −





















































U −

CBD Q

I

C

active

b ig

R

s

op

E

B

1

54 683

3 0

3 34

1

1

.

.

.

ρ ε

ξ φ

β

β

 (19)

As in equation 8, the terms from Rothermel’s crown fire rate of spread equation are evaluated only for FM 10, so all terms are constant except I

R and ε Qig,

which vary with fuel moisture, and CBD and φ s

. Simplifying equation 19, substituting fuel characteristics for FM 10 and converting to open wind, we have

CI O

Q

I CBD

active

ig

R

s

= ′ =

− − 























0 0457

164 8

1

001612

0 7

.

.

.

. ε

φ

 (20)

where the terms are evaluated for the fuel characteristics of FM 10.

Nomograms for computing TI and CI for flat ground have been created (see

appendix D). For more complex situations, the spreadsheet NEXUS (Scott 1999,

www.fire.org/nexus/nexus.html) can be used. The Torching and Crowning Indices have been incorporated into FFE-FVS, and have been coded to operate directly in ArcInfo GIS.

SIMULATING OVERALL SPREAD RATE AND INTENSITY

Methods for simulating surface fire behavior, active crown fire behavior, and

the thresholds for crown fire initiation and active crown fire spread for the Northern Rocky Mountains were described earlier. In this section we simulate the behavior of a fire as it makes the transition from surface to crown fire as burning

conditions worsen.

Overall Spread Rate

An elusive goal of fire modelers has been to simulate the full range of fire

behavior exhibited in forest stands using one model or system of models. Any

single model is unlikely to adequately simulate surface fire behavior, transition

to crown fire, and crown fire behavior in the near future. However, existing models can be linked together to produce such simulations. Final rate of fire spread

(Rfinal), whether surface or crown, is computed following Van Wagner (1989, 1993)

and the Forestry Canada Fire Danger Group (1992) as

R R CFB R R final surface active surface =+ − ( ) (21)
20 USDA Forest Service Research Paper RMRS-RP-29. 2001

where CFB is a transition function, termed “crown fraction burned,” that ranges

from 0 for a surface fire to 1 for a fully active crown fire (Van Wagner 1993). (In

the Canadian FFBP System, the Forestry Canada Fire Danger Group [1992] defines a surface fire as having CFB > 0.1 and an active crown fire as having CFB

> = 0.9.) Conceptually, CFB is the fraction of canopy fuels consumed in a fire.

Several alternative derivations of CFB are available (Finney 1998; Forestry Canada

Fire Danger Group 1992; Van Wagner 1989, 1993), but none are based on observed (for example, Stocks 1987, 1989) or modeled (for example Call and Albini

1997) canopy fuel consumption. Instead, CFB is simply a transition function to

estimate final spread rate from simulations for surface and fully active crown

fires, and to estimate of the degree of crowning (Van Wagner 1989, 1993). In all

of the above models, the proportion of canopy fuels burned (for estimating fireline

intensity, for example) is assumed to equal the value of the transition function.

We used a linear CFB transition function for scaling spread rate between Rsurface

and Ractive. A detailed discussion of alternative methods of estimating CFB can be

found in appendix A. For the example stand described earlier, Rfinal and CFB are

plotted on the crown fire hazard assessment chart (fig. 9). Crown fraction burned

is zero until the windspeed equals the TI, then increases linearly to 1.0 where the

windspeed equals the CI. For windspeeds less than TI, a surface fire is expected

and Rfinal equals Rsurface. For windspeeds in excess of CI, a fully active crown fire

is expected, and Rfinal equals Ractive. In the passive crown fire region between TI

and CI, passive crowning is expected, and Rfinal is scaled between Rsurface and Ractive

(equation 21) based on CFB.

Crown fire assessment chart

Open (6.1-m) windspeed, km hr-1

0 5 10 15 20 25 30 35 40 45 50

0

5

10

15

20

25

30

0.0

0.2

0.4

0.6

0.8

1.0 CFB

crown fraction burned

surface fire

active

crown

fire

Spread rate, m min-1

R'active

R'initiation Rsurface

Ractive

passive

crown

fire

Rfinal

Figure 9—Final spread rate (Rfinal) and crown fraction burned (CFB) plotted over a range of

windspeeds. Crown fraction burned (right-hand Y-axis) is 0 until windspeed reaches the

TI, then increases to 1 where windspeed reaches CI. In the surface fire region, Rfinal =

Rsurface. In the passive crown fire region, final spread rate is scaled between Rsurface and

Ractive. In the active crown fire region, Rfinal = Ractive. Inputs: fuel model 10 (timber litter and

understory, Anderson 1982), canopy base height = 1.5 m, canopy bulk density = 0.15 kg

m-3, foliar moisture content = 100 percent, normal summer surface fuel moisture condition

(Rothermel 1991a, table 4), and wind reduction factor = 0.15.
USDA Forest Service Research Paper RMRS-RP-29. 2001. 21

Overall Fireline Intensity

Final fireline intensity is computed by modifying equation 5 as follows:

( ( ))

60

surface canopy canopy final

final

HPA W H CFB R

I

+ = (22)

where Wcanopy is the available canopy fuel load, and Hcanopy is the heat yield of

canopy fuels (including a reduction for moisture content). Following FARSITE

(Finney 1998) we assume a heat yield of 18,000 kJ kg-1 for canopy fuels.

HYSTERESIS IN CROWN FIRE: THE CONDITIONAL SURFACE FIRE

Conventional wisdom is that a surface fire must first go through a passive

crown fire phase before becoming active as burning conditions worsen (for example, as windspeed increases), and that any stand not capable of initiating a

crown fire would not support an active crown fire under the same conditions.

However, the links among models of surface and crown fire behavior indicate a

different possible behavior during transition to crown fire. In this section we

discuss the evidence of hysteresis in the linked surface and crown fire models

and its potential impact on fire behavior and crown fire hazard assessment.

For many stand conditions, such as those with low canopy base height (which

makes initiation easier) and low canopy bulk density (which makes active crowning more difficult), a period of passive crowning would be experienced as conditions worsen and active crowning is approached. In these situations the Torching

Index is less than the Crowning Index; the region between the two indices is the

passive crown fire region (fig. 8). In stands that have higher canopy base height

or higher canopy bulk density, such as those associated with dense, single-storied

stands, the TI can be higher than the CI. That is, stronger winds may be required

to initiate crowning than are needed to sustain active crowning once started. For

example, by modifying characteristics of our example stand so that CBH = 2 m

and CBD = 0.25 kg m-3, the TI is 45 while the CI is only 26 (fig. 10). This “reversal” of TI and CI only occurs with certain combinations of CBH and CBD. The

combinations of those variables where TI = CI (for level ground, normal summer

R'active

Crowning index (O'iactive

surface fire )

active

crown

fire

conditional

crown

fire

Crown fire assessment chart

0 5 10 15 20 25 30 35 40 45 50

0

5

10

15

20

25

30

35

40

45

50

Open (6.1-m) windspeed, km hr-1

Spread rate, m min-1

R'initiation

Ractive

Torching index (O'initiation)

Rsurface

Figure 10—In conditions of relatively high CBH

and CBD, the CI is less than the TI. That is,

more extreme conditions (of wind and fuel

moisture) are required to initiate crown fire than

to maintain active crown fire. This situation can

lead to a hysteresis in spread rate and intensity. Inputs: fuel model 10 (timber litter and

understory, Anderson 1982), canopy base

height = 2.0 m, canopy bulk density = 0.25 kg

m-3, foliar moisture content = 100 percent, normal summer surface fuel moisture condition

(Rothermel 1991a, table 2), and wind reduction factor = 0.15.
22 USDA Forest Service Research Paper RMRS-RP-29. 2001

fuel moisture conditions and WRF = 0.15) can be plotted for a range of surface

fuel models (fig. 11). For the example in figure 11, if the CBD = 0.2 kg m-3 there

can be a hysteresis if CBH is greater than about 0.2 m for fuel model 8, 1.5 m for

fuel model 10, and 3.5 m for fuel model 12. Many stands of that CBD have CBH

greater than those critical values, so the hysteresis may not be a rare phenomenon.

Following Van Wagner’s (1977) classification, any stand for which surface fireline

intensity does not meet the initiation criterion is classed as a surface fire (that is, when

the windspeed is less than the TI). For a before-the-fact classification of the type of

fire, surface fireline intensity is estimated from a model of surface fire behavior (for

example, Rothermel 1972), which implicitly assumes that the origin of the fire in the

stand of interest is a surface fire. But what if fire spreads to the stand of interest as a

crown fire, having made the transition earlier or elsewhere? How then should fireline

intensity be estimated for the stand of interest?

In applying his classification model to experimental fires in mature and immature stands of jack pine, Van Wagner (1993) calculates surface fireline intensity as the product of fuel consumption and observed spread rate. That is, he

computed the contribution of surface fuels to the total fireline intensity, whether

the fire was on the surface or in the crowns. Therefore, surface fireline intensity

depended in large part on the type of fire observed, with the higher spread rates

associated with crown fire leading to higher surface fireline intensity. According

to Rothermel’s (1991a) model, crown fire spread rate can be as many as six to

eight times faster than that of a surface fire burning in the same conditions (Scott

1998), which means that surface fuel contribution to fireline intensity would also

be as much as six to eight times greater during active crowning than for normal

surface fire spread.

With separate models of surface and crown fire behavior, we need to know the

type of fire before applying the classification to determine exactly that—the type of

fire. This circularity occurs only when the Torching Index is greater than the Crowning Index. In that case, when the windspeed is between the two indices, two different

results are possible—surface fire or active crown fire—depending on the type of

originating fire. Rothermel described this phenomenon as a cusp catastrophe in an

unpublished paper presented at the 1999 National Fire Behavior Workshop (March

1–5, 1999; Phoenix, AZ).

If the fire begins as a surface fire, then the former classification would correctly predict surface fire until the wind reached the TI, at which time active

crowning would begin almost immediately, without experiencing a period of passive crown fire, because both criteria are met. However, if the fire spreads into

the stand as an already-initiated crown fire, then the higher spread rate of the

Canopy base height, m

012345

0.0

0.1

0.2

0.3

0.4

FM11

Canopy bulk density, kg m-3

FM8

FM9

FM5

FM10

FM12

Figure 11—Combinations of canopy

base height (CBH ) and canopy bulk

density (CBD) for which the Torching Index equals the Crowning Index,

for various surface fuel models.

Combinations of CBH and CBD that

fall above the lines will exhibit a hysteresis in some range of environmental conditions. Inputs: level ground,

100 percent foliar moisture content,

and normal summer fuel moisture

condition (Rothermel 1991a).
USDA Forest Service Research Paper RMRS-RP-29. 2001. 23

crown fire is used to estimate the contribution of surface fuels to fireline intensity. This higher intensity may be sufficient to meet the crown fire initiation criterion at a lower windspeed. The type of fire experienced therefore depends on

the origin of fire in the subject stand.

We call the region of the classification where the active crowning criterion is

met but the initiation criterion is not a “conditional surface fire” (fig. 12). This is

equivalent to the range between the CI and TI when TI > CI. If the fire originates

as a surface fire, then it is expected to remain so. If the fire originates as an active

crown fire in an adjacent stand, then we compare the contribution of surface fuels

to overall fireline intensity (using the higher crown fire spread rate) against the

threshold for crown fire initiation. If the intensity is greater than critical, then the

active crown fire could continue through the stand, otherwise the fire is expected

to drop to the ground.

The contribution of surface fuels to total fireline intensity during a crown fire

is the product of HPAsurface and Ractive. For any given surface fuel model, HPAsurface

varies only with fuel moisture. Using Rothermel’s crown fire spread correlation,

Ractive varies primarily with windspeed, but also with slope and surface fuel moisture. For level ground and 100 percent foliar moisture content, the critical open

windspeed that could be expected to cause cessation (O'cessation) increases with

CBH (fig. 13).

Active

crown fire

Surface

fire

low high

low

high

Passive

crown

fire

Crown fire spread rate, 

Ractive

Isurface

R'active

I'initiation

Conditional

surface fire Figure 12—Extension of Van Wagner’s (1977) original

classification to include conditional surface fire.

Cases in which CBD is sufficient to support active

crowning but surface fire intensity (from Rothermel’s

surface fire model) is below the threshold for initiation fall into the conditional surface fire class. Within

this class, the type of fire observed depends on the

origin of the fire in the subject stand; surface fires

are expected to remain on the surface, and active

crown fires remain fully active.

normal summer

severe drought

early spring before greenup

drought summer

late spring after greenup

Canopy base height, m

0 2 4 6 8 10 12

0

10

20

30

40

50

O' cessation , km hr -1

Figure 13—Theoretical open windspeeds for

crown fire cessation using Van Wagner’s

(1977) initiation criterion for a range of

canopy base heights and a variety of

dead fuel moisture conditions (Rothermel

1991a). Fireline intensity computed as the

product of heat per unit area from fuel

model 10 (Anderson 1982) and active

crown fire spread rate from Rothermel

(1991a). Inputs: Slope = 0 percent, foliar moisture content = 100 percent.
24 USDA Forest Service Research Paper RMRS-RP-29. 2001

Conditions for Crown Fire Cessation

The process of crown fire cessation has not yet been studied on its own. However, Van Wagner’s two criteria for crown fire initiation can be modified and

applied to cessation. There are again two criteria to check; failure to meet either

one will lead to crown fire cessation.

Mass-Flow Rate too Low—The mass-flow rate through the canopy must be

at least 3.0 kg m-2 s-1, which leads to a critical spread rate (equation 14). If the

product of the potential active crown fire spread rate and canopy bulk density

does not meet this threshold, then active crowning is not possible and active

crowning ceases. Cessation from failure to meet the mass-flow requirement is

quantified by the Crowning Index. If the windspeed falls below CI then an active

crown fire could be expected to cease.

Intensity in Surface Fuels too Low—The after-crowning contribution of

surface fuels to fireline intensity must be sufficient to meet the threshold for

initiation (equation 11). If the product of Ractive and HPAsurface falls below the threshold for crown fire initiation, we assume that the crown fire could not continue.

Using the criterion in this way implies that crown fire spread can be modeled as

a series of crown fire initiations, similar in concept to assumptions made for

surface fire spread (Rothermel 1972). It is not known whether this mechanism is

realistic for crown fires.

Assuming flat ground and normal summer surface fuel moisture condition

(Rothermel 1991a), the open windspeed that leads to cessation of active crown

fire depends on surface fuel model and CBH (fig. 14). We use equation 5 for

determining the contribution of surface fuels to fireline intensity; R is Ractive, but

HPA is determined in the Rothermel surface fire model from surface fuel characteristics. Cessation from failure to meet the initiation criterion is quantified by

O'cessation, the open windspeed at which the product of HPAsurface and Ractive equals

the minimum necessary for crown fire initiation.

In formulating crown fire mitigation strategies, forest managers are just as

concerned with causing crown fire cessation as limiting its initiation. Crown fire

cessation is indexed as the higher of CI and O'cessation, which we call the Surfacing

Index (SI). The Surfacing Index can be plotted on the crown fire assessment

chart along with TI and CI (fig. 15). In the example in figure 15, CI is greater

than O'cessation so SI = CI.

Canopy base height, m

0 2 4 6 8 10 12

0

10

20

30

40

50

O' cessation , km hr -1

FM 12: medium logging slash

FM 11: light logging slash

FM 9: hardwood and long-needle pine litter

FM 10: timber litter and understory

FM 5: brush (2 feet)

FM 8: closed timber litter

Figure 14—Theoretical open windspeed for

crown fire cessation using Van Wagner’s

(1977) initiation criterion for a range of

canopy base heights and a variety of surface fuel models (Anderson 1982).

Fireline intensity is computed as the

product of heat per unit area from the

various fuel models and active crown fire

spread rate from Rothermel (1991a). Inputs: slope = 0 percent, live fuel moisture = 100 percent, foliar moisture content = 100 percent, dead fuel moisture

content = 5 percent.
USDA Forest Service Research Paper RMRS-RP-29. 2001. 25

It is helpful to know whether CI or O'cessation is the limiting factor in crown fire

cessation, which depends mainly on CBH and CBD. For level ground, fuel model

10 (Anderson 1982), and normal summer fuel moisture conditions, the combinations of CBH and CBD where CI (O'active) equals O'cessation can be found graphically (fig. 16). For those conditions, if CBD = 0.2 kg m-3 then O'cessation is limiting

only if CBH is greater than about 7.5 m. We get a better picture of the tradeoffs

by plotting the intersections of O'active and O'cessation for a variety of fuel models

(fig. 17). With fuel model 12 (medium logging slash) for example, O'cessation is

limiting only if CBH is greater than about 8 m even if CBD = 0.3 kg m-3. By

contrast, the low HPA for fuel model 8 means that O'cessation is limiting if CBH is

greater than about 2 m; otherwise cessation is determined by the mass-flow rate

requirement.

surface fire

active

crown

fire

conditional

surface

fire

Torching index

Crown fire assessment chart

0 5 10 15 20 25 30 35 40 45 50

0

5

10

15

20

25

30

35

40

45

50

Open (6.1-m) windspeed, km hr-1

Spread rate, m min-1

O'cessation

O'active

O'initiation

Surfacing index

Figure 15—The Surfacing Index (SI)

is the higher of O'cessation and O' active,

In this example, O' active is higher

than O' cessation, so SI = CI. A crown

fire is expected to surface when

the windspeed drops below SI.

Inputs: fuel model 10 (timber litter and understory, Anderson

1982), canopy base height = 2.0

m, canopy bulk density = 0.25 kg

m-3, foliar moisture content = 100

percent, normal summer surface

fuel moisture condition (Rothermel

1991a, table 4), and wind reduction factor = 0.15.

Canopy base height, m

012345678

0

10

20

30

40

50

60

O'active (CBD = 0.1 kg m-3)

Open windspeed, km/hr-1

O'active (CBD = 0.2 kg m-3)

O'active (CBD = 0.3 kg m-3)

O'active (CBD = 0.4 kg m-3)

O'cessation

Figure 16—The open windspeed for crown

fire cessation (O' cessation) and sustained

active crown fire spread (O'active) plotted for a range of canopy base heights

(CBH) and a variety of canopy bulk

densites (CBD). The intersections of

plots for O' cessation and O' active indicate

combinations of CBH and CBD where

they equally limit continued crown fire

spread. Inputs: level ground, 100 percent foliar moisture content, normal

summer fuel moisture condition

(Rothermel 1991a), and wind reduction

factor = 0.15.
26 USDA Forest Service Research Paper RMRS-RP-29. 2001

With separate sets of criteria for initiation and cessation, a hysteresis is possible in which the path of fire behavior as windspeed increases may be different

from the path as it decreases (see fig. 15). Two behaviors are possible in the conditional surface fire region depending on whether the region is approached from

the lower windspeeds as a surface fire or as a crown fire from the higher

windspeeds. Even with constant winds, spatial variability in surface fuels, canopy

fuels, and topography can lead to the incidence of active crown fire where the

former classification always predicts a surface fire.

Implications of Hysteresis in Crown Fire

This procedure for determining the actual type of fire within the conditional surface fire class is an untested theoretical extension of Van Wagner’s (1993) classification. The mechanisms of crown fire cessation are poorly understood. This approach

simulates two possible mechanisms. However, not using this revised classification

leads to expectation of surface fire when crown fire may be encountered. Stands that

are considered safe from crown fire initiation cannot necessarily be relied upon to

cause crown fire cessation.

This phenomenon has several important consequences that should be further

investigated. The conditions that lead to crown fire initiation may be quite different from the conditions that lead to crown fire cessation. If initiation and cessation of crown fires follow different paths, then a hysteresis is created in which a

crown fire can be sustained even if conditions ameliorate. Hysteresis could explain the persistence of crown fires well into the night during major crown fire

runs, such as those that occurred in Yellowstone National Park, WY, in 1988

(Hartford and Rothermel 1991).

The transition from surface fire spread to active crown fire spread can occur

as an abrupt change, with no period of passive crowning to act as a warning.

Even small changes in the fire environment can cause a surface fire to become

fully active quickly. Sudden changes in fire behavior have contributed to the

entrapment of many wildland firefighters.

The fire environment is highly variable in space and time. A hysteresis in the

crown fire phenomenon could take advantage of this variability by initiating crown

fire activity during the short periods when conditions are most favorable, yet

continue with active spread through the lulls. Large fires may be more likely to

Canopy bulk density, kg m-3

0.0 0.1 0.2 0.3 0.4

0

2

4

6

8

10

FM8

Canopy base height, m

FM5

FM9

FM11

FM10

FM12 Figure 17—Combinations of canopy

base height (CBH) and canopy

bulk density (CBD) where they

equally limit continued crown fire

spread, for a variety of surface fuel

models. A combination of CBH and

CBD that falls above the line for

the appropriate fuel model indicates that CBH is more limiting

than CBD. Inputs: level ground,

100 percent foliar moisture content, normal summer fuel moisture

condition (Rothermel 1991a), and

wind reduction factor = 0.15.
USDA Forest Service Research Paper RMRS-RP-29. 2001. 27

exhibit crown fire activity than smaller ones because, with more perimeter length,

large fires are more likely to encounter fuel and topographic conditions conducive to crown fire initiation (Rothermel 1991b). Once initiated, it may be possible for crown fire to spread through adjacent stands that could not initiate crown

fire on their own. This has implications for how we determine model inputs in

the face of spatial and temporal variability. The extremes of the fire environment

become much more important than the mean when identifying thresholds.

Hysteresis in crown fire initiation and cessation is not proven to exist. However, in light of the evidence of hysteresis in high intensity wildland fire, fire

managers should consider its possibility until further investigations can be carried out.

EXAMPLE SIMULATIONS USING THE COUPLED MODEL

All models we used in deriving the indices of crown fire potential and overall

spread rate and intensity have already been tested and verified to some degree,

though not comprehensively. Proper validation of the indices and coupled model

requires numerous observations of surface and crown fire behavior coupled with

accurate, stand-level descriptions of surface and canopy fuels, weather, and topography. Unfortunately, wildfire documentation, the sole source of crown fire

spread observations in the United States, does not contain enough information to

provide useful data. Too many vital model inputs must be inferred or estimated

after the fact rather than observed. In those cases one cannot determine whether

fire behavior observations that deviate from simulations result from errors in the

model or from errors in estimating inputs or fire behavior.

We used data from a few well-documented fires that exhibited various degrees of

crowning (1990 Dude Fire, 1974 Burnt Fire, 1977 Pattee Canyon Fire) in an attempt

to verify that our method was performing reasonably. However, even those fires left

significant gaps in pertinent information (for example, fuel moisture, onsite windspeeds,

stand-specific surface, and canopy fuel data), and contained only coarse-scale observations of fire behavior. Despite encouraging results of the trials, the lack of complete

data sets (and the attendant need to substitute estimates) renders the verification meaningless, so it is not presented here. Validation data of good quality are difficult to

come by; their collection on wild, prescribed, and experimental fires in the United

States should become a high priority for research and management.

In this section we will demonstrate the application of the indices and fire

behavior simulations by comparing the relative crown fire potential of two contrasting forest stands on the Bitterroot National Forest, MT. No observations of

crown fire activity are available for these stands.

We examine the effects of fuel treatments on crown fire potential and discuss

the implications of individual fuel treatment options on crown fire hazard. Finally, we couple the indices with diurnal weather and fuel moisture data to determine the expected type of fire throughout the day.

Crown Fire Hazard in Two Stands on the Bitterroot National Forest

The application of the linked models is demonstrated by comparing crown

fire hazard and simulated fire behavior in two contrasting stands on the Bitterroot National Forest, Montana. Both stands are on the east slope of the Bitterroot

Range, near the town of Hamilton, MT. Stand A (PIPO) is a midelevation stand

of old-growth ponderosa pine (Pinus ponderosa) with under and middle stories

of Douglas-fir (Pseudotsuga menzeizii), grand fir (Abies grandis), subalpine fir

(Abies lasiocarpa), and lodgepole pine (Pinus contorta). Stand B (PICO) is higher

elevation (table 5) and dominated by lodgepole pine (fig. 18). The PIPO stand is
28 USDA Forest Service Research Paper RMRS-RP-29. 2001

wholly within the B-4 plot described by Arno and others (1995). It had a pre1900 mean fire return interval of 13 years, with the last recorded fire in 1908.

Analysis—Canopy fuel load and bulk density were estimated using allometric

equations (Brown 1978). Rather than assume a uniform vertical distribution of canopy

fuels, we estimated CBD in thin layers (0.3 m in height) by summing the crown fuel

load in these horizontal layers (Kilgore and Sando 1975, Sando and Wick 1972). The

“effective” CBD for use in the coupled models was the maximum 4.5-m (15-ft) running mean CBD within the canopy, as in the Fire and Fuels Extension to the Forest

Vegetation Simulator. This is illustrated for stand B in figure 2.

Following Sando and Wick (1972), “effective” canopy base height (that is,

with ladder fuels incorporated) was estimated by computing the minimum height

above ground where a CBD of 0.037 kg m-3 (100 lbs acre-1 ft-1) occurs. Although

the critical canopy bulk density set by Sando and Wick was arbitrary, the results

for these stands agree with visual inspections.

Table 5—Summary of stand and site characteristics for a Pinus ponderosa stand

(A) and Pinus contorta stand (B) in the Bitterroot Mountains, Montana, U.S.A.

Characteristic Stand A Stand B

Slope, percent 20 20

Aspect E NE

Elevation, m 1,520 1,860

Total basal area, m2/ha 29.8 36.4

Surface fuel model 5 10

Canopy characteristics

 CBH , m 1.5 0.9

 CBD, kg/m3 0.06 0.21

 Wcanopy, kg/m2 1.22 2.25

 Hcrown, kJ/kg 18,000 18,000

 FMC, percent 100 100

 WRF 0.15 0.12

Surface fuel moisture, percent

 0-6 mm dia. class 5 8

 6-25 mm dia. class 6 9

 25-76 mm dia. class 8 10

 Fine live fuels 117 117

Figure 18—Structure of example Pinus ponderosa (a) and Pinus contorta (b) stands on the Bitterroot

National Forest, Montana. Note: the y-axis scales are different for the two stands.

100

ABGR, ABLA, PICO

(a) stand Pinus ponderosa

Diameter class midpoint (cm)

0 10 20 30 40 50 60 70 80

0

200

300

400

500

Diameter class midpoint (cm)

0 10 20 30 40 50 60 70 80

0

500

1000

1500

2000

2500

PSME

PICO

ABLA

(b) stand Pinus contorta

Trees per hectare

Trees per hectare

PSME

PIPO
USDA Forest Service Research Paper RMRS-RP-29. 2001. 29

Moisture contents of fine dead surface fuels were estimated using the moisture tables from the Fire Behavior Field Reference Guide for a July day with high

temperature of 30 o

C and low relative humidity of 20 percent at 1600 hours at the

elevation of the PIPO stand (table 5). Differences in dead fuel moisture between

the PIPO and PICO stands arise primarily from differences in elevation and sheltering from sun. Live surface fuel moisture content was set at Rothermel’s “normal summer” value of 117 percent for both stands.

Foliar moisture content varies with species and time of year. For the species

present and time of year of the simulation, FMC is near 100 percent (Brown

1978; Philpot and Mutch 1971), so we used a value of 100 percent for both stands.

We assumed a nominal value of 18,000 kJ kg-1 for Hcrown (Finney 1998; Forestry

Canada Fire Danger Group 1992). We estimated wind reduction factor from the

degree of sheltering (Rothermel 1983), with guidance from Albini and Baughman

(1979). Based on visual inspection, surface fuels were best represented by FM 5

in the PIPO stand and FM 10 in the PICO stand.

Results—The results of this simulation are shown in table 6. We estimated

type of fire and potential fire behavior at a windspeed of 40 km hr-1. Surface fire

spread rate and fireline intensity are estimated to be higher in the PIPO stand.

However, the higher CBH in the PIPO stand also requires a higher I'initiation and

R'initiation. On balance, the PIPO stand is not expected to initiate a crown fire until

the open wind reaches 28 km hr-1 (the Torching Index), whereas the PICO stand

can initiate crown fire activity at a windspeed of only 16 km hr-1.

Table 6—Intermediate and final output values for the example simulation. Site, fuel and

environmental conditions are as described in Table 5, with open windspeed of 40 km/hr

for both stands.

Parameter Source Stand A Stand B

Surface fire

 I surface, kW m-1 Equation 5 470 313

 I' initiation, kW m-1 Equation 11 309 144

 HPAsurface, kJ m-2 Equation 2 6 13

 Rsurface, m min-1 Equation 6 4.6 1.4

 R' initiation, m min-1 Equation 12 3.0 0.6

 R'SA, m min-1 Figure 8 9.2 1.1

Crown fire

 Ractive, m min-1 Equations 7, 8 23.1 20.4

 R' active, m min-1 Equation 14 50 14

Final, or overall

 Type of fire Figure 12 Passive Active

 CFB Equation 28 (Appendix A) 0.25 1.00

 Rfinal, m min-1 Equation 21 9.2 20.4

 Ifinal, kW m-1 Equation 22 1,788 18,337

Crown fire hazard indices

Torching Index, km hr-1 Equation 18 28 16

Crowning Index, km hr-1 Equation 20 70 30

Surfacing Index, km hr-1 70 30
30 USDA Forest Service Research Paper RMRS-RP-29. 2001

Potential crown fire spread rate is not different in the stands; Rothermel’s

(1991a) correlation does not take into account the possible effect of variation in

canopy bulk density on spread rate. Foliar moisture content is the same in both

stands, so nothing in this example would be gained by using Van Wagner’s foliar

moisture effect. Because Ractive is similar in the stands, the Crowning Index is

mainly a function of CBD, which differs considerably in the two stands. The

PIPO stand, with its relatively open canopy, would not support active crowning

until the open windspeed reached 70 km hr-1. In contrast, the dense canopy of the

PICO stand would support active crowning at windspeeds of only 30 km hr-1.

Crown fraction burned is 0.25 in the PIPO stand and 1.0 in the PICO stand.

Therefore, under the conditions specified, we could expect a passive crown fire

in the PIPO stand and a fully active crown fire in the PICO stand. Final spread

rate in the PICO stand is estimated to be 20.4 m min-1, roughly twice that in the

PIPO stand. Fireline intensity in the PIPO stand is only 1,788 kW m-1, but 18,337

kW m-1 in the PICO stand. For reference, the limit of mechanical fire control is

3,459 kW m-1 (1,000 BTU ft-1 s-1).

At windspeeds less than 20 km/hr, spread rate in the PIPO stand is slightly

greater than in the PICO stand (fig. 19a), due to the more open forest cover. Above

that windspeed, though, crowning in the PICO stand leads to much higher spread

rates than in the PIPO stand. The difference in fireline intensity is even greater

(fig. 19b), largely because HPAsurface and Wcanopy in the PICO stand are much greater

than in the PIPO stand. The limit of mechanical control is exceeded in the PICO

stand at a windspeed of about 22 km hr-1, whereas a fire in the PIPO stand would

not exceed that intensity until windspeed reached about 46 km hr-1. Because winds

exceeding 22 km hr-1 occur far more frequently than winds exceeding 46 km hr-1,

we could expect fires burning under the dry, summer conditions simulated to be

controllable less often in the PICO stand than the PIPO stand. Knowledge of the

wind climatology of the site would improve this assessment by indicating how

often we might expect the critical wind/fuel moisture combinations to occur.

Discussion—The purpose of the fire behavior simulations is to assess the

relative fire potential in these stands, not to predict the behavior of an actual fire.

From the above simulation it is clear that both stands can experience some kind

of crown fire activity under moderate winds during the summer. However, the

PIPO stand is likely to attain only passive crowning even under high winds,

whereas the PICO stand can support fully active crowning under even moderate

winds.

Figure 19—Final rate of spread (a) and fireline intensity (b) for the two example stands on the

Bitterroot National Forest, Montana. The limit of mechanical control (3500 kW m-1) is indicated.

Stand B

limit of

mechanical

control

10

15

Open (6.1-m) windspeed, km hr-1

0 10 20 30 40 50 60 70

0

5

20

25

30

35

40

0 10 20 30 40 50 60 70

0

10000

20000

30000

40000

(a) (b)

Open (6.1-m) windspeed, km hr-1

Final spread rate, m min-1

Final fireline intensity, kW m-1

Stand A

Stand B

Stand A
USDA Forest Service Research Paper RMRS-RP-29. 2001. 31

Assessing the Effects of Alternative Treatments

Managers who wish to reduce crown fire hazard must determine how different fuel treatments affect torching and crowning. This is done by first simulating

the effects of a treatment on the inputs to the coupled model. Fuel treatments that

reduce crown fire hazard involve a combination of thinning, pruning, pile burning, broadcast burning, lopping, and chipping. The effects of these treatments

change over time. For example, a broadcast burn reduces surface fuels immediately after the burn. However, depending on stand structure, resulting mortality

and needle scorch may lead to higher fuel load a few years after the burn. As fuels

decompose, fuel load may again decrease. Managers must consider the time frame

of interest when comparing treatments. The Fire and Fuels Extension to the Forest Vegetation Simulator (Beukema and others 1997) simulates longer term effects of fuel treatments. Surface and canopy fuel treatments have variable effects

on the factors affecting torching and crowning (table 7). Foliar moisture content

is assumed to be independent of fuel treatment.

A thinning designed to reduce crown fire hazard will usually raise the effective CBH . However, in a partial harvest such as selection or crown thinning,

mainly large trees with high crown bases are removed, so the effective CBH may

not change. Similarly, a broadcast burn will usually increase CBH by scorching

lower branches. However, a broadcast burn under moderate burning conditions

may be patchy and of insufficient intensity to raise effective CBH for the whole

stand. Understory removal is the harvest of submerchantable trees in the lower

stratum of a multistoried stand. This story usually consists of shade-tolerant conifers with low crowns. Where the understory is well developed, its removal may

also reduce the effective CBD of the stand.

A combination of treatments, such as thinning with broadcast burning, is simulated by adding the individual effects. The overall effect of a combination of

treatments on a factor where the individual effects are in opposition (such as the

effects of thinning with whole-tree harvest on fuel load) must be determined by

computing TI and CI and simulating fire behavior in the treated and untreated

stands.

When simulating the effect of fuel treatments on potential crown fire behavior, it is important to simulate effects on midflame windspeed and fuel moisture.

Thinning to reduce canopy bulk density reduces the moderating effect of the

canopy on windspeed, so midflame windspeed will increase. The increased fuellevel windspeed coupled with increased insolation also leads to lower dead fuel

moisture in treated stands during summer. These two factors tend to exacerbate

surface fire behavior. However, properly executed treatments also tend to reduce the crown fire potential. Crown fire mitigation treatments often represent a tradeoff—the decrease in crown fire potential comes at the expense of

Table 7—The immediate-term effects of fuel treatments on factors that affect the Torching and Crowning Indices

(from Scott 1998). A blank cell in the table indicates no effect. I = increase, D = decrease, NE = no effect. The

whole-tree yarding treatment is only applicable in conjunction with a harvest.

 Canopy Wind Canopy

 Surface Dead fuel base reduction bulk

Fuel treatment fuel load moisture height factor density

Overstory thinning I D I or NE I D

Understory removal I I D or NE

Pruning I I

Pile burning D

Whole-tree yarding D

Broadcast burning D I or NE
32 USDA Forest Service Research Paper RMRS-RP-29. 2001

increased surface fire spread rate and intensity. The greatly increased spread rate

and intensity of crown fires makes this tradeoff reasonable.

Assessing Crown Fire Potential Throughout a Day

In planning for crown fires it is helpful to know at what time of the day crowning

might begin and how long such conditions would persist, and perhaps compare

these estimates for different treatments. For such an analysis we need diurnal

fuel moisture and windspeed data. As an example we use the published diurnal

weather measured on the North Fork Fire in Yellowstone National Park in August

1988 (Hartford and Rothermel 1991a). Temperature, relative humidity, and fine

fuel moisture were measured for 48 hours in late August (fig. 20). By coupling

the moisture data with the stand characteristics for the Bitterroot PIPO and PICO

stands and a hypothetical trace of open windspeed (fig. 21), we plotted potential

spread rate and intensity throughout the period (fig.22). This type of analysis

may be useful where the timing and duration of a crown fire run needs to be

estimated, or where proposed tactics must be weighed against potential fire behavior. However, calibration of such simulations with onsite observations must

be done before attempting to use this analysis operationally.

0

10

20

30

40

50

60

70

80

90

100

0

2

4

6

8

10

12

1600 midnight 0800 1600 midnight 0800 1600

25 August 26 August 27 August

Temperature (F) or relative humidity (percent)

temperature

relative humidity

fuel moisture

Fine fuel moisture (percent)

Figure 20—Temperature, relative humidity, and fine dead fuel moisture measured for a 48-hour

period on the North Fork Fire, Yellowstone National Park, Wyoming, 1988 (Hartford and

Rothermel 1991a).
USDA Forest Service Research Paper RMRS-RP-29. 2001. 33

Figure 21—Critical windspeeds for crown fire initiation, sustained active spread, and cessation for the diurnal

weather depicted in figure 20 for a ponderosa pine stand (a) and lodgepole pine stand (b) on the Bitterroot

National Forest, Montana. For demonstration, a hypothetical trace of “actual” windspeed is shown.

0

10

20

30

40

50

60

70

80

90

100

0

10

20

30

40

50

60

70

80

90

100

actual

actual

(a) ponderosa pine (b) lodgepole pine

1600 midnight 1600 midnight 0800 1600 0800

25 August 26 August 27 August

1600 midnight 1600 midnight 0800 1600 0800

25 August 26 August 27 August

Open windspeed, km hr-1

Open windspeed, km hr-1

O'initiation

O'active

O'cessation O'initiation

O'active

0

5000

10000

15000

20000

0

5000

10000

15000

20000

0

5

10

15

20

25

30

0

5

10

15

20

25

30

(a) ponderosa pine

(b) lodgepole pine

P S P S

P S P A P S P S P A P S

P S P S

1600 midnight 1600 midnight 0800 1600 0800

25 August 26 August 27 August

Final spread rate, m min-1 Final spread rate, km hr-1

1600 midnight 1600 midnight 0800 1600 0800

25 August 26 August 27 August

1600 midnight 1600 midnight 0800 1600 0800

25 August 26 August 27 August

1600 midnight 1600 midnight 0800 1600 0800

25 August 26 August 27 August

Final fireline intensity, kW m-1 Final fireline intensity, kW m-1

Figure 22—Final rate of spread and fireline intensity for the diurnal weather depicted in figure 20 and the

hypothetical windspeed shown in figure 21 for the ponderosa pine stand (a) and lodgepole pine stand (b)

on the Bitterroot National Forest, Montana. Fire classification is also shown: S = surface fire, P = passive

crown fire, A = active crown fire.
34 USDA Forest Service Research Paper RMRS-RP-29. 2001

DISCUSSION

Crown fire is a complex phenomenon; we are only beginning to understand

the processes of crown fire development, spread, and cessation. Accurate description of canopy fuels and reliable simulation of these processes remain elusive. Yet crown fires present special problems for managers today. Crown fires’

high spread rates and resistance to control lead to high acreage burned and significant adverse effects. We must take steps now to assess and mitigate crown

fire potential.

This paper presents a method of assessing crown fire potential by linking

separate models of surface fire spread and intensity, crown fire spread rate, and

transition to crown fire. Three indices of crown fire potential are computed from

a description of surface fuels, canopy fuels, and site characteristics. The Torching Index is the open windspeed at which the transition from surface to crown

fire is expected. The Crowning Index is the open windspeed at which fully active

crown fire is possible. The Surfacing Index is the open windspeed at which an

active crown fire is expected to cease, either from failure to meet the minimum

mass-flow rate or from failure of the after-crowning contribution of surface fuels

to fireline intensity to meet the minimum necessary for crown fire initiation.

From the linked models we also seamlessly simulate the wide range of surface and crown fire behavior that occurs in forest stands. These simulations are

used for comparing relative fire behavior of different stands or after treatments to

mitigate crown fire, not for operational prediction of the behavior of a going fire.

The accuracy of simulations can be improved by calibrating model results with

onsite observations.

Due to a lack of high-quality validation data, this and similar methods have

not been validated. As such, users should apply results cautiously. Gathering highquality data from prescribed and wild fires for building and testing models of fire

behavior should be made a high priority.

Calculation of the indices for simple cases can be made in the field with nomograms (appendix D) or by using NEXUS (Scott 1999), which also allows simulation of the full range of surface and crown fire behavior encountered in forest

stands.

The links among the existing models indicate the potential for a hysteresis in

the crown fire phenomenon; the conditions for crown fire cessation may be quite

different from those for crown fire initiation. If so, many forest stands that seem

to be safe from crown fire because they cannot initiate a crown fire may still be

susceptible to active crown fire if a crown fire has initiated elsewhere. Spatial

and temporal variability in the fire environment leads to higher crown fire activity than predicted using average conditions.

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USDA Forest Service Research Paper RMRS-RP-29. 2001. 39

APPENDIX A: CROWN FRACTION BURNED

The equation commonly used for the CFB transition function (Finney 1998;

Van Wagner 1989, 1993; Forestry Canada Fire Danger Group 1992) is of the

general form

( ) CFB e ax = − − 1 (23)

where a is a scaling factor and x is based on the difference between predicted and

critical spread rates. In this section we will review the alternative implementations of this CFB transition function and derive a new form of our own.

The concept of a transition function for scaling between surface and crown

fire spread rate predictions was first proposed by Van Wagner (1989). In that

model, x = Rsurface –R'initiation and a = 0.23 in order to force CFB = 0.9 when Rsurface

exceeds R'initiation by an arbitrary 10 m min-1. Van Wagner does not state how the

10 m min-1 threshold was selected. The functional form of Van Wagner’s (1989)

CFB equation is thus

( ) ( ) CFB e R R surface initiation

= − − −′ 1 .23 (24)

In the Canadian FFBP System, the Forestry Canada Fire Danger Group (1992)

employs the CFB concept for both two-equation and one-equation models of

crown fire spread rate. In the two-equation model for Conifer Plantation Fuel

Type C-6, the Forestry Canada Fire Danger Group (1992) uses equation 24 directly. In the one-equation models, a single equation describes spread rate for the

full range of fire behavior, surface through crown. Thus, Rfinal is estimated directly—intermediate estimates of Rsurface and Ractive are avoided — and the implicit

CFB equation is

( ) ( ) CFB e R R final initiation

= − − −′ 1 .23 (25)

In this one-equation model, CFB is used only to estimate the degree of crowning and final fire intensity, but not the final fire spread rate as in equation 21.

Although the Forestry Canada Fire Danger Group (1992) sets the value of a at

0.23 such that CFB = 0.9 when Rsurface exceeds R'initiation by 10 m min-1, this same

value of a is used in equation 23, which is based on the amount by which Rfinal

(rather than Rsurface) exceeds R'initiation.

Van Wagner (1993) modified his CFB concept to allow dynamic calculation

of the coefficient a to account for variation in canopy fuel characteristics. In that

paper he states that the coefficient a was “based on the difference between [R'initiation]

and [R'active], that is, on the difference between the point where crown consumption begins and the point where it becomes complete” (p. 446). Van Wagner (1993)

set the value of a such that CFB = 0.9 for Rfinal = 90 percent of the difference

between R'active and R'initiation. 

(Due to the form of the CFB equation [equation 24],

CFB approaches 1.0 asymptotically, so the point at which CFB = 1.0 cannot be

specified.) Thus, a is

( )

( ) a

R R active initiation

= −

′ − ′

















ln .

.

01

0 9

(26)

For Van Wagner’s (1993) immature jack pine data set, R'initiation was 2.15 m

min-1 and R'active was 12.89 m min-1, the difference between these being 10.74 m

min-1. Ninety percent of this difference (9.666 m/min) yields a = 0.238 in the
40 USDA Forest Service Research Paper RMRS-RP-29. 2001

above model. This value, however, is only valid in stands where 90 percent of

(R'active R'initiation) is about 9.666 m/min. To that end, Van Wagner also estimated a

for a mature stand of jack pine where R'initiation = 1.45 m min-1 and R'active = 25.14 m

min-1 and obtained a = 0.108. Van Wagner’s (1993) CFB equation is of the same

functional form as equation 24, but with different values of a for the immature

and mature stands.

For assessing crown fire hazard CFB should vary with fuel characteristics

believed to be important in determining crown fire behavior and be consistent

with Van Wagner’s (1977) crown fire initiation and sustained spread thresholds.

In other words, the CFB function should be scaled such that CFB approaches 1.0

at the point where active crowning is expected.

Each of the above implementations has a problem of internal consistency,

especially when applied to stands with different surface or canopy fuel characteristics. The problem is the inconsistency between the derivation of a and the subsequent formulation of x in equation 23.

First, we must determine whether x in equation 23 should be Rfinal – R'initiation,

as in the one-equation model used in the Canadian FFBP System, or Rsurface –

R'initiation, which is used in all the other formulations. In the Canadian FFBP System and Van Wagner (1989), the derivation of a is said to be based on the difference between Rsurface and R'initiation. Given that, using x = Rsurface – R'initiation seems

reasonable. However, CFB in the one-equation model of the Canadian FFBP System, with the same value of a as the two-equation model, is instead computed

using x = Rfinal – R'initiation. Because Rfinal > = Rsurface, their one-equation model will

over-predict CFB relative to the two-equation model.

A more pressing problem for making crown fire hazard assessments is the

proper scaling of a to correctly represent various stand conditions. Using a single

value of a implies that progress toward fully active crowning is independent of

CBD. In contrast, Van Wagner (1977) suggests a critical mass-flow rate through

the canopy (a function of CBD) must be met before fully active crowning can

occur. Van Wagner’s (1993) dynamic computation of the parameter a accounts

for differing canopy characteristics in a way that makes consistency with a critical mass-flow rate possible.

However, because Van Wagner (1993) scaled the coefficient a between R'initiation

and R'active, consistency is most logically achieved by using x = Rfinal – R'initiation

rather than x = R'initiation in the CFB equation. For practical purposes the predicted

Rsurface is usually much less than R'active using the standard U.S. Fire Behavior Fuel

Models commonly associated with conifer forests fuels.

This inconsistency is best illustrated with an example. Consider a dense forest

stand with CBD = 0.20 kg m-3, CBH = 2 m, WRF = 0.15, and surface fuels

characterized by FM 10, on level terrain. Such a stand is obviously susceptible to

active crown fire. For this stand R'active = 15 m min-1 (equation 14), R'initiation = 1.08

m min-1 (equation 12), and a = 0.184 (equation 26). Even under the most extreme

environmental conditions (fine dead fuel moisture 3 percent, live surface fuel

moisture 70 percent, open [6.1-m] windspeed 70 km/hr), predicted surface fire

spread rate is only 6.0 m/min. Following Van Wagner (1993), with a as above,

CFB would be only 0.60. Following the two-equation CFB model of the Canadian FFBP System (equation 23), CFB would be only 0.68. Under the extreme

conditions specified, we could reasonably expect fully active crowning, so CFB

should be much closer to 1. Rothermel’s (1991a) crown fire correlation predicts

that Ractive will equal R'active, at an open windspeed of only 21 km hr-1. At that

windspeed, the Van Wagner (1993) predicts CFB = 0.06 and Forestry Canada

Fire Danger Group (1992) models predict CFB = 0.07. In Van Wagner’s model,

this problem results because the coefficient a is based on x = R'active – R'initiation, but

CFB is scaled by x = Rsurface – R'initiation. In the Canadian FFBP System, the problem

is the use of a single value of a to represent the wide range of stand conditions we

need to evaluate.
USDA Forest Service Research Paper RMRS-RP-29. 2001. 41

We can avoid this inconsistency in two ways. First, we can scale a following

equation 26 but use x = Rfinal – R'initiation in equation 23. Unfortunately, Rfinal is itself

a function of CFB (equation 21), resulting in a problem of circularity that can be

solved by iteration.

Alternatively, we can keep x = Rsurface – R'initiation for the CFB equation but

provide an alternative derivation of a that will properly scale CFB to equal or

approach 1 when the critical mass-flow rate is met. For example,

( )

( ) a

R R SA initiation

= −

′ − ′

















ln . 01 (27)

where R'SA is the predicted surface fire spread rate that corresponds to the environmental conditions for which Ractive = R'active (see fig. 8 in text). In equation 27

we drop the 0.9 factor so that the point at which Ractive = R'active corresponds exactly to CFB = 0.9. This is satisfying because the Canadian FFBP System defines

an active crown fire as one having CFB > 0.9. In other words, this approach is

consistent with the Van Wagner (1977) and the Canadian FFBP System classifications and will properly predict active crown fire spread rates when the critical

mass-flow rate is met (Van Wagner 1977).

All of the above approaches are based on the assumption that the CFB transition function should follow the negative exponential form of equation 23. However, no empirical evidence suggests what equation form best represents the

transition to active crown fire. Assuming a straight line function for CFB, as did

Stocks (1987, 1989) when relating canopy fuel consumption to Initial Spread

Index, might be better than assuming a more complex shape. The equivalent

straight-line CFB equation is

( )

( ) CFB

R R

R R

surface initiation

SA initiation

= − ′

′ − ′

(28)

In this paper, the purpose of predicting crown fire behavior is to assess the

relative crown fire potential of different stand structures. Therefore, we use equation 28 for estimating CFB and equation 21 for Rfinal because that approach (1)

assumes the simplest shape for the CFB function in the absence of empirical

evidence to the contrary, (2) correctly bounds CFB such that CFB = 1.0 where

Ractive = R'active, (3) does not require iteration, and (4) varies logically with most

surface and canopy fuel characteristics believed to influence crown fire development.
42 USDA Forest Service Research Paper RMRS-RP-29. 2001
USDA Forest Service Research Paper RMRS-RP-29. 2001. 43

APPENDIX B: GLOSSARY

Active crown fire—A crown fire in which the entire fuel complex becomes involved, but the crowning phase remains dependent on heat released from the surface fuels for continued spread. Also called running and continuous crown fire.

Available canopy fuel—The mass of canopy fuel per unit area consumed in a crown

fire. There is no post-frontal combustion in canopy fuels, so only fine canopy

fuels are consumed. We assume that only the foliage and a small fraction of the

branchwood is available.

Available fuel—The total mass of ground, surface and canopy fuel per unit area

consumed by a fire, including fuels consumed in postfrontal combustion of duff,

organic soils, and large woody fuels.

Canopy base height—The lowest height above the ground at which there is a sufficient amount of canopy fuel to propagate fire vertically into the canopy. Canopy

base height is an effective value that incorporates ladder fuels such as shrubs and

understory trees. See also fuel strata gap and crown base height.

Canopy bulk density—The mass of available canopy fuel per unit canopy volume. It is a bulk property of a stand, not an individual tree.

Canopy fuels—The live and dead foliage, live and dead branches, and lichen of

trees and tall shrubs that lie above the surface fuels. See also available canopy

fuel.

Conditional surface fire—A potential type of fire in which conditions for sustained

active crown fire spread are met but conditions for crown fire initiation are not. If

the fire begins as a surface fire then it is expected to remain so. If it begins as an

active crown fire in an adjacent stand, then it may continue to spread as an active

crown fire.

Continuous crown fire—See active crown fire.

Crown base height—The vertical distance from the ground to the bottom of the live

crown of an individual tree. See also canopy base height.

Crown bulk density—The mass of available fuel per unit crown volume. In this

paper it is a property of an individual tree, not a whole stand. See also canopy

bulk density.

Crown fire—Any fire that burns in canopy fuels.

Crown fire cessation—The process by which a crown fire ceases, resulting in a

surface fire. Crown fire cessation is a different mechanism than crown fire initiation, possibly leading to hysteresis.

Crown fire hazard—A physical situation (fuels, weather, and topography) with

potential for causing harm or damage as a result of crown fire.

Crowning Index—The open (6.1-m) windspeed at which active crown fire is possible for the specified fire environment.
44 USDA Forest Service Research Paper RMRS-RP-29. 2001

Environmental conditions—That part of the fire environment that undergoes shortterm changes: weather, which is most commonly manifest as windspeed and dead

fuel moisture content.

Fire environment—The characteristics of a site that influence fire behavior. In fire

modeling the fire environment is described by surface and canopy fuel characteristics, windspeed and direction, relative humidity, and slope steepness.

Fire hazard—A physical situation (fuels, weather, and topography) with potential

for causing harm or damage as a result of wildland fire.

Fire intensity—See frontal fire intensity. Contrast with fireline intensity.

Fireline intensity—The rate of heat release in the flaming front per unit length of

fire front (Byram 1959).

Flaming front—The zone at a fire’s edge where solid flame is maintained.

Foliar moisture content—Moisture content (dry weight basis) of live foliage, expressed as a percent. Effective foliar moisture content incorporates the moisture

content of other canopy fuels such as lichen, dead foliage, and live and dead

branchwood.

Foliar moisture effect—A theoretical effect of foliar moisture content on active

crown fire spread rate (Van Wagner 1974, 1979, 1983).

Frontal fire intensity—Similar to fireline intensity, it is the rate of heat release per

unit length of fire front, including the additional heat released from postfrontal

flaming and smoldering combustion (Forestry Canada Fire Danger Group 1992).

Fuel complex—The combination of ground, surface, and canopy fuel strata.

Fuel model—A set of surface fuel bed characteristics (load and surface-area-tovolume-ratio by size class, heat content, and depth) organized for input to a fire

model. Standard fuel models (Anderson 1982) have been stylized to represent

specific fuel conditions.

Fuel strata gap—The vertical distance between the top of the surface fuel stratum

and the bottom of the canopy fuel stratum.

Fuel stratum—A horizontal layer of fuels of similar general characteristics. We

generally recognize three fuel strata: ground, surface, and canopy.

Full-range fire behavior simulation—The simulated behavior of a wildland fire

whether it is a surface fire, passive crown fire, or active crown fire. Ground fire

behavior is usually not included.

Ground fire—A slow-burning, smoldering fire in ground fuels. Contrast with surface fire.

Ground fuels—Fuels that lie beneath surface fuels, such as organic soils, duff, decomposing litter, buried logs, roots, and the below-surface portion of stumps.

Compare with surface fuels.

Hysteresis—The failure of a property that has been changed by an external agent to

return to its original value when the cause of the change is removed. In crown fire,
USDA Forest Service Research Paper RMRS-RP-29. 2001. 45

hysteresis is expressed in the persistence of active crowning after the fire environment has changed such that a crown fire could no longer initiate.

Independent crown fire—A crown fire that spreads without the aid of a supporting

surface fire.

Intermittent crown fire—A crown fire that alternates in space and time between

active crowning and surface fire or passive crowning. See also passive crown

fire.

Mass-flow rate—The rate of fuel consumption (kg m-2 s-1) through a vertical plane

(oriented parallel with the fireline) within the fuel bed. It is the product of spread

rate (m s-1) and fuel bed bulk density (kg m-3).

Passive crown fire—A crown fire in which individual or small groups of trees torch

out, but solid flaming in the canopy cannot be maintained except for short periods. Passive crown fire encompasses a wide range of crown fire behavior from

the occasional torching of an isolated tree to a nearly active crown fire. Also

called torching and candling. See also intermittent crown fire.

Plume-dominated fire-—A fire for which the power of the fire exceeds the power

of the wind, leading to a tall convection column and atypical spread patterns. The

models used in this paper do not address plume-dominated fire behavior. Contrast

with wind-driven fire.

Running crown fire—See active crown fire.

Site characteristics—The characteristics of a location that do not change with time:

slope, aspect, elevation.

Surface fire—A fire spreading through surface fuels.

Surface fuels—Needles, leaves, grass, forbs, dead and down branches and boles,

stumps, shrubs, and short trees.

Surfacing Index—The higher of O'active and O'cessation. The Surfacing Index is the

open windspeed at which an active crown fire can be expected to drop to the

surface, either due to insufficient mass-flow rate through the canopy or insufficient contribution of surface fuels to fireline intensity.

Torching Index—The open (6.1-m) windspeed at which crown fire activity can

initiate for the specified fire environment.

Total biomass—The mass per unit area of all living and dead vegetation at a site.

Total fuel load—The mass of fuel per unit area that could possibly be consumed in

a hypothetical fire of the highest intensity in the driest fuels.

Wind-driven fire—A wildland fire in which the power of the wind exceeds the

power of the fire, characterized by a bent-over smoke plume and a high length-towidth ratio.

Wind reduction factor—The ratio of the midflame windspeed to the open (6.1-m)

windspeed. For convenience of measurement eye-level winds are usually substituted for midflame winds.
46 USDA Forest Service Research Paper RMRS-RP-29. 2001
USDA Forest Service Research Paper RMRS-RP-29. 2001. 47

APPENDIX C: ENGLISH/METRIC UNIT CONVERSION

FACTORS

weight

from to=> g oz lb kg ton M g

g 1 0.035 2.205E-03 0.001 1.102E-06 1.000E-06

oz 28.35 1 0.06251 2.835E-02 3.125E-05 2.835E-05

lb 453.6 16 1 0.4536 5.000E-04 4.536E-04

kg 1000 35.30 2.205 1 1.10E-03 0.001

ton 9.072E+05 3.202E+04 2000 907.2 1 0.9072

M g 1.E+06 3.530E+04 2205 1000 1.102 1

length

from to=> m m cm inch feet yard m eter chain km m ile

m m 1 0.1 3.937E-02 3.281E-03 1.094E-03 0.001 4.971E-05 1.E-06 6.214E-07

cm 10 1 0.3937 3.281E-02 1.094E-02 0.01 4.971E-04 1.E-05 6.214E-06

inch 25.40 2.540 1 0.08333 0.02778 0.02540 0.001 2.540E-05 1.578E-05

feet 304.8 30.48 12 1 0.3333 0.3048 0.01515 3.048E-04 1.894E-04

yard 914.4 91.44 36 3 1 0.9144 4.545E-02 9.144E-04 5.682E-04

m eter 1000 100 39.37 3.281 1.094 1 0.04971 0.001 6.214E-04

chain 2.012E+04 2.012E+03 7.920E+02 66 22 20.12 1 2.012E-02 1.250E-02

km 1.E+06 1.E+05 3.937E+04 3.281E+03 1.094E+03 1000 49.71 1 0.6214

m ile 1.609E+06 1.609E+05 6.336E+04 5280 1760 1.609E+03 80 1.609 1

area

from to=> cm 2 in2 ft2 yd2 m 2 acre ha km 2 m i2

cm 2 1 0.1550 1.076E-03 1.196E-04 0.0001 2.471E-08 1E-08 1E-10 3.861E-11

in2 6.452 1 6.944E-03 7.716E-04 6.452E-04 1.594E-07 6.452E-08 6.452E-10 2.491E-10

ft2 929.0 144 1 0.1111 0.09290 2.296E-05 9.290E-06 9.290E-08 3.587E-08

yd2 8361 1296 9 1 0.8361 2.066E-04 8.361E-05 8.361E-07 3.228E-07

m 2 1.E+04 1550 10.76 1.196 1 2.471E-04 1.E-04 1E-06 3.861E-07

acre 4.047E+07 6.273E+06 4.356E+04 4840 4047 1 0.4047 4.047E-03 1.563E-03

ha 1.E+08 1.550E+07 1.076E+05 1.196E+04 1.E+04 2.471 1 0.010000045 3.861E-03

km 2 1.E+10 1.550E+09 1.076E+07 1.196E+06 1.E+06 247.1 100 1 0.3861

m i2 2.590E+10 4.014E+09 2.788E+07 3.098E+06 2.590E+06 640.0 259.0 2.590 1

from to=> ton/(ac-ft) kg/m3 ton/(ac-in) lb/ft3 gm /cm 3

ton/(ac-ft) 1 0.7355 0.08333 0.04591 7.355E-04

kg/m 3 1.360 1 0.1133 0.06243 0.001

ton/(ac-in) 12 8.826 1 0.5510 8.826E-03

lb/ft3 21.78 16.02 1.815 1 0.01602

gm /cm 3 1360 1000 113.3 62.43 1

from to=> kJ/(m 2-m in) kW /m 2 BTU/(ft2-s) cal/(cm 2-s)

kJ/(m 2-m in) 1 0.01667 1.469E-03 3.984E-04

kW /m 2 60 1 0.08811 0.02390

BTU/(ft2-s) 680.9 11.35 1 0.2712

cal/(cm 2-s) 2510 41.84 3.687 1

from to=> kJ/kg BTU/lb cal/gm

kJ/kg 1 0.4303 0.2390

BTU/lb 2.324 1 0.5555

cal/gm 4.184 1.800 1

from to=> ft/m in ch/hr cm /s m/m in km /hr ft/sec m i/hr knot m /sec

ft/m in 1 0.9091 0.5080 0.3048 0.01829 0.01667 0.01136 9.875E-03 5.080E-03

ch/hr 1.100 1 0.5588 0.3353 0.02012 0.01833 0.01250 0.01086 5.588E-03

cm /s 1.968 1.790 1 0.6000 0.03600 0.03281 0.02237 0.01944 0.01

m /m in 3.281 2.983 1.667 1 0.06000 0.05468 0.03728 0.03240 0.01667

km /hr 54.68 49.71 27.78 16.67 1 0.9113 0.6214 0.5400 0.2778

ft/sec 60 54.55 30.48 18.29 1.097 1 0.6818 0.5925 0.3048

m i/hr 88 80 44.70 26.82 1.609 1.467 1 0.8690 0.4470

knot 101.3 92.06 51.44 30.87 1.852000037 1.688 1.151 1 0.5144

m /sec 196.8 179.0 100 60 3.6 3.281 2.237 1.944 1

heatcontent

M ultiplication factors

area intensity

rate ofspread,speed

bulk density
48 USDA Forest Service Research Paper RMRS-RP-29. 2001

from to=> J/(ft-sec) cal/(cm -sec) kW /m BTU/(ft-sec) kcal/(m -sec)

J/(ft-sec) 1 7.841E-03 3.281E-03 9.485E-04 7.841E-04

cal/(cm -sec) 127.5 1 0.4184 0.1210 0.1

kW /m 304.8 2.390 1 0.2891 0.2390

BTU/(ft-sec) 1054 8.268 3.459 1 0.8268

kcal/(m -sec) 1275 10 4.184 1.210 1

from to=> J cal kJ BTU

J 1 0.2390 0.001 9.485E-04

cal 4.184 1 4.184E-03 3.968E-03

kJ 1000 239.0 1 0.9485

BTU 1054 252.0 1.054 1

fuelload

from to=> g/m 2 M g/ha tons/ac kg/m2 lbs/ft2

g/m 2 1 0.01 4.461E-03 0.001 2.048E-04

M g/ha 100 1 0.4461 0.1 0.02048

tons/ac 224.2 2.242 1 0.2242 0.04591

kg/m 2 1000 10 4.461 1 0.2048

lbs/ft2 4882 48.82 21.78 4.882 1

basalarea

from to=> ft2/ac m 2/ha

ft2/ac 1 0.2296

m 2/ha 4.356 1

angles

from to=> degrees radians

degrees 1 0.01745

radians 57.30 1

from to=> J/ft2 kJ/m 2 BTU/ft2 kcal/m 2 cal/cm 2

J/ft2 1 0.01076 9.479E-04 2.572E-03 2.572E-04

kJ/m 2 92.96 1 0.08811 0.2391 0.02391

BTU/ft2 1055 11.35 1 2.713 0.2713

kcal/m 2 388.9 4.183 0.3686 1 0.1

cal/m 2 3889 41.83 3.686 10 1

fireline intensity

heat,energy

heatperunitarea
USDA Forest Service Research Paper RMRS-RP-29. 2001. 49

APPENDIX D: NOMOGRAMS

Figure D-1—Chart for determining Crowning Index from canopy bulk density and stylized surface fuel moisture. Level ground is

assumed. Fuel moisture conditions are described in table 4.

Canopy bulk density (kg m ) -3

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

0

10

20

30

40

50

60

70

80

90

100

1

2

3

5

4

1 late spring after greenup

2 normal summer

3 early spring before greenup

4 drought summer

5 severe drought

Crowning index ( ), km hr O'active -1

Figure D-2—Example use of figure D-1. For normal summer fuel moisture condition (Rothermel 1991a) and canopy bulk density = 0.15

kg m-3, the Crowning Index is 38. That is, an open windspeed of at least 38 km hr-1 is needed to sustain active crowning.

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

0

10

20

30

40

50

60

70

80

90

100

1

2

3

5

4

1 late spring after greenup

2 normal summer

3 early spring before greenup

4 drought summer

5 severe drought

38

Canopy bulk density (kg m ) -3

Crowning index ( ), km hr O -1 'active
50 USDA Forest Service Research Paper RMRS-RP-29. 2001

crown base height, m

0 2 4 6 8 10

0

10

20

30

40

50

60

70

80

90

100

Fuel model 5

Brush (2 feet)

Foliar

moisture

content

Surface fuel

moisture condition

(Rothermel 1991)

Wind reduction

(Rothermel 1983)

Instructions:

Begin in upper-right chart.

Draw vertical line from crown base

height to appropriate foliar moisture

content.

From that intersection draw a

horizontal line to the appropriate

surface fuel moisture condition.

Draw a vertical line down to the

line corresponding to the degree

of sheltering.

Draw a horizontal line and read the

Torching Index on the vertical axis. 

NOTE: this chart assumes a head fire on

level ground. For other conditions, use

NEXUS (see text for more details).

normal summer

spring before greenup

drought summer

severe drought

spring after greenup

FMC = 120 percent

FMC = 100 percent

FMC = 80 percent

unsheltered (WRF = 0.4)

partially sheltered (WRF = 0.3)

fully sheltered: open stand (WRF = 0.2)

fully sheltered: dense stand (WRF = 0.1)

Torching index (

O' initiation), km hr -1

Figure D-3—Nomogram for determining the Torching Index for fuel model 5 (Brush 2 feet).
USDA Forest Service Research Paper RMRS-RP-29. 2001. 51

Instructions:

Begin in upper-right chart.

Draw vertical line from crown base

height to appropriate foliar moisture

content.

From that intersection draw a

horizontal line to the appropriate

surface fuel moisture condition.

Draw a vertical line down to the

line corresponding to the degree

of sheltering.

Draw a horizontal line and read the

Torching Index on the vertical axis. 

NOTE: this chart assumes a head fire on

level ground. For other conditions, use

NEXUS (see text for more details).

crown base height, m

0.0 0.5 1.0 1.5 2.0

0

10

20

30

40

50

60

70

80

90

100

Fuel model 8

Closed timber litter

Foliar

moisture

content

Surface fuel

moisture condition

(Rothermel 1991)

Wind reduction

(Rothermel 1983)

normal summer

severe drought

drought summer

spring before greenup

spring after greenup

FMC = 120 percent

FMC = 100 percent

FMC = 80 percent

unsheltered (WRF = 0.4)

partially sheltered (WRF = 0.3)

fully sheltered: open stand (WRF = 0.2)

fully sheltered: dense stand (WRF = 0.1)

Torching index (

O' initiation), km hr -1

Figure D-4—Nomogram for determining the Torching Index for fuel model 8 (closed timber litter).
52 USDA Forest Service Research Paper RMRS-RP-29. 2001

crown base height, m

0 2 4 6 8 10

0

10

20

30

40

50

60

70

80

90

100

Fuel model 9

Hardwood and long-needle

pine litter

Instructions:

Begin in upper-right chart.

Draw vertical line from crown base

height to appropriate foliar moisture

content.

From that intersection draw a

horizontal line to the appropriate

surface fuel moisture condition.

Draw a vertical line down to the

line corresponding to the degree

of sheltering.

Draw a horizontal line and read the

Torching Index on the vertical axis. 

NOTE: this chart assumes a head fire on

level ground. For other conditions, use

NEXUS (see text for more details).

Foliar

moisture

content

Surface fuel

moisture condition

(Rothermel 1991)

Wind reduction

(Rothermel 1983)

normal summer

drought summer

spring before greenup

spring after greenup

FMC = 120 percent

FMC = 100 percent

FMC = 80 percent

unsheltered (WRF = 0.4)

partially sheltered (WRF = 0.3)

fully sheltered: open stand (WRF = 0.2)

fully sheltered: dense stand (WRF = 0.1)

severe drought

Torching index (

O' initiation), km hr -1

Figure D-5—Nomogram for determining the Torching Index for fuel model 9 (hardwood and long-needle pine litter).
USDA Forest Service Research Paper RMRS-RP-29. 2001. 53

crown base height, m

0 2 4 6 8 10

0

10

20

30

40

50

60

70

80

90

100

Fuel model 10

Timber (litter and understory)

Instructions:

Begin in upper-right chart.

Draw vertical line from crown base

height to appropriate foliar moisture

content.

From that intersection draw a

horizontal line to the appropriate

surface fuel moisture condition.

Draw a vertical line down to the

line corresponding to the degree

of sheltering.

Draw a horizontal line and read the

Torching Index on the vertical axis. 

NOTE: this chart assumes a head fire on

level ground. For other conditions, use

NEXUS (see text for more details).

Foliar

moisture

content

Surface fuel

moisture condition

(Rothermel 1991)

Wind reduction

(Rothermel 1983)

normal summer

spring before greenup

drought summer

spring after greenup

FMC = 120 percent

FMC = 100 percent

FMC = 80 percent

unsheltered (WRF = 0.4)

partially sheltered (WRF = 0.3)

fully sheltered: open stand (WRF = 0.2)

fully sheltered: dense stand (WRF = 0.1)

severe drought

Torching index (

O' initiation), km hr -1

Figure D-6—Nomogram for determining the Torching Index for fuel model 10 (timber litter and understory).
54 USDA Forest Service Research Paper RMRS-RP-29. 2001

crown base height, m

0 2 4 6 8 10

0

10

20

30

40

50

60

70

80

90

100

Fuel model 11

Light logging slash

Instructions:

Begin in upper-right chart.

Draw vertical line from crown base

height to appropriate foliar moisture

content.

From that intersection draw a

horizontal line to the appropriate

surface fuel moisture condition.

Draw a vertical line down to the

line corresponding to the degree

of sheltering.

Draw a horizontal line and read the

Torching Index on the vertical axis. 

NOTE: this chart assumes a head fire on

level ground. For other conditions, use

NEXUS (see text for more details).

Foliar

moisture

content

Surface fuel

moisture condition

(Rothermel 1991)

Wind reduction

(Rothermel 1983)

normal summer

drought summer

spring before greenup

spring after greenup

FMC = 120 percent

FMC = 100 percent

FMC = 80 percent

unsheltered (WRF = 0.4)

partially sheltered (WRF = 0.3)

fully sheltered: open stand (WRF = 0.2)

fully sheltered: dense stand (WRF = 0.1)

severe drought

Torching index (

O' initiation), km hr -1

Figure D-7—Nomogram for determining the Torching Index for fuel model 11 (light logging slash).
USDA Forest Service Research Paper RMRS-RP-29. 2001. 55

crown base height, m

0 2 4 6 8 10

0

10

20

30

40

50

60

70

80

90

100

Fuel model 12

Medium logging slash

Instructions:

Begin in upper-right chart.

Draw vertical line from crown base

height to appropriate foliar moisture

content.

From that intersection draw a

horizontal line to the appropriate

surface fuel moisture condition.

Draw a vertical line down to the

line corresponding to the degree

of sheltering.

Draw a horizontal line and read the

Torching Index on the vertical axis. 

NOTE: this chart assumes a head fire on

level ground. For other conditions, use

NEXUS (see text for more details).

Foliar

moisture

content

Surface fuel

moisture condition

(Rothermel 1991)

Wind reduction

(Rothermel 1983)

normal summer

spring before greenup

drought summer

spring after greenup

FMC = 120 percent

FMC = 100 percent

FMC = 80 percent

unsheltered (WRF = 0.4)

partially sheltered (WRF = 0.3)

fully sheltered: open stand (WRF = 0.2)

fully sheltered: dense stand (WRF = 0.1)

severe drought

Torching index (

O' initiation), km hr -1

Figure D-8—Nomogram for determining the Torching Index for fuel model 12 (medium logging slash).
56 USDA Forest Service Research Paper RMRS-RP-29. 2001

crown base height, m

0 2 4 6 8 10

0

10

20

30

40

50

60

70

80

90

100

Fuel model 10

Timber (litter and understory)

32

Instructions:

Begin in upper-right chart.

Draw vertical line from crown base

height to appropriate foliar moisture

content.

From that intersection draw a

horizontal line to the appropriate

surface fuel moisture condition.

Draw a vertical line down to the

line corresponding to the degree

of sheltering.

Draw a horizontal line and read the

Torching Index on the vertical axis. 

NOTE: this chart assumes a head fire on

level ground. For other conditions, use

NEXUS (see text for more details).

Foliar

moisture

content

Surface fuel

moisture condition

(Rothermel 1991)

Wind reduction

(Rothermel 1983)

normal summer

spring before greenup

drought summer

spring after greenup

FMC = 120 percent

FMC = 100 percent

FMC = 80 percent

unsheltered (WRF = 0.4)

partially sheltered (WRF = 0.3)

fully sheltered: open stand (WRF = 0.2)

fully sheltered: dense stand (WRF = 0.1)

severe drought

WRF = 0.15

Torching index (

O' initiation), km hr -1

Figure D-9—Example nomogram for determining the Torching Index. Inputs: fuel model 10 (timber litter and understory), slope = 0,

canopy base height = 1.5 m, foliar moisture content = 100 percent, normal summer fuel moisture condition (Rothermel 1991a), and

wind adjustment factor = 0.15. The Torching Index is 32, indicating that an open windspeed of at least 32 km hr-1 is needed to initiate

crown fire activity in the stand.
USDA Forest Service Research Paper RMRS-RP-29. 2001. 57

crown base height, m

0 2 4 6 8 10

0

10

20

30

40

50

60

70

80

90

100

Normal summer

fuel moisture

Instructions:

Begin in upper-right chart.

Draw vertical line from crown base

height to appropriate foliar moisture

content.

From that intersection draw a

horizontal line to the appropriate

surface fuel moisture condition.

Draw a vertical line down to the

line corresponding to the degree

of sheltering.

Draw a horizontal line and read the

Torching Index on the vertical axis. 

NOTE: this chart assumes a head fire on

level ground. For other conditions, use

NEXUS (see text for more details).

Foliar

moisture

content

Standard

fuel model

Wind reduction

(Rothermel 1983)

FM 12: medium logging slash

FM 11: light logging slash

FM 9: hardwood litter

FMC = 120 percent

FMC = 100 percent

FMC = 80 percent

unsheltered (WRF = 0.4)

partially sheltered (WRF = 0.3)

fully sheltered: open stand (WRF = 0.2)

fully sheltered: dense stand (WRF = 0.1)

FM 10: timber (litter and understory)

FM 5: brush (2 feet)

FM 8: closed timber litter

Torching index (

O' initiation), km hr -1

Figure D-10—Nomogram for determining the Torching Index for normal summer fuel moisture condition (Rothermel 1991a).
58 USDA Forest Service Research Paper RMRS-RP-29. 2001

crown base height, m

0 2 4 6 8 10

0

10

20

30

40

50

60

70

80

90

100

Normal summer

fuel moisture

32

Instructions:

Begin in upper-right chart.

Draw vertical line from crown base

height to appropriate foliar moisture

content.

From that intersection draw a

horizontal line to the appropriate

surface fuel moisture condition.

Draw a vertical line down to the

line corresponding to the degree

of sheltering.

Draw a horizontal line and read the

Torching Index on the vertical axis. 

NOTE: this chart assumes a head fire on

level ground. For other conditions, use

NEXUS (see text for more details).

Foliar

moisture

content

Standard

fuel model

Wind reduction

(Rothermel 1983)

Torching index (

O' initiation), km hr -1

FM 12: medium logging slash

FM 11: light logging slash

FM 9: hardwood litter

FMC = 120 percent

FMC = 100 percent

FMC = 80 percent

unsheltered (WRF = 0.4)

partially sheltered (WRF = 0.3)

fully sheltered: open stand (WRF = 0.2)

fully sheltered: dense stand (WRF = 0.1)

FM 10: timber (litter and understory)

FM 5: brush (2 feet)

FM 8: closed timber litter

WRF = 0.15

Figure D-11—Example nomogram for determining the Torching Index for normal summer fuel moisture condition (Rothermel 1991a).

Inputs: fuel model 10 (Timber litter and understory), slope = 0, canopy base height = 1.5 m foliar moisture content = 100 percent,

normal summer fuel moisture condition (Rothermel 1991a), and wind adjustment factor = 0.15. The Torching Index is 32, indicating

that an open windspeed of at least 32 km hr-1 is needed to initiate crown fire activity in the stand.
USDA Forest Service Research Paper RMRS-RP-29. 2001. 59

Canopy base height, m

012345678

0

10

20

30

40

50

60

70

80

90

100

O' cessation , km hr -1

FM 12: medium logging slash

FM 11: light logging slash

FM 9: hardwood and long-needle pine litter

FM 10: timber litter and understory

FM 5: brush (2 feet)

FM 8: closed timber litter

Figure D-12—Chart for determining the open windspeed (O' cessation) at which the contribution of surface fuels to fireline intensity is too

low to maintain crown fire spread, for a variety of surface fuel models. The contribution of surface fuels to fireline intensity is

computed as the product of HPAsurface and Ractive. Normal summer fuel moisture condition (Rothermel 1991a) is assumed.

Canopy base height, m

012345678

0

10

20

30

40

50

O' cessation , km hr -1

normal summer

late summer severe drought

early spring before greenup

drought summer

late spring after greenup

Figure D-13—Chart for determining the open windspeed (O' cessation) at which the contribution of surface fuels to fireline intensity is too

low to maintain crown fire spread, for a variety of fuel moisture conditions (Rothermel 1991a). Surface fuel model 10 was used in this

chart. The contribution of surface fuels to fireline intensity is computed as the product of HPAsurface and Ractive.
Rocky Mountain Research Station

240 W. Prospect Road

Fort Collins, CO 80526
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 National Forest managers,

Federal and State agencies, public and private organizations,

academic institutions, industry, and individuals.

Studies accelerate solutions to problems involving ecosystems, range, forests, water, recreation, fire, resource inventory, land reclamation, community sustainability, forest engineering technology, multiple use economics, wildlife and fish

habitat, and forest insects and diseases. Studies are conducted cooperatively, and applications may be found worldwide.

Research Locations

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*Station Headquarters, Natural Resources Research Center,

2150 Centre Avenue, Building A, Fort Collins, CO 80526

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