United States

Department

of Agriculture

Forest Service

Rocky Mountain

Research Station

Research Paper

RMRS-RP-58

May 2006

Comparison of Crown Fire

Modeling Systems Used in

Three Fire Management

Applications

Joe H. Scott
Abstract ________________________________________

The relative behavior of surface-crown fire spread rate modeling systems used in three fire

management applications—CFIS (Crown Fire Initiation and Spread), FlamMap and NEXUS—

is compared using fire environment characteristics derived from a dataset of destructively

measured canopy fuel and associated stand characteristics. Although the surface-crown

modeling systems predict the same basic fire behavior characteristics (type of fire, spread rate)

using the same basic fire environment characteristics, their results differ considerably. Across

the range of inputs used in these comparisons, CFIS predicted the highest incidence of crown

fire and the highest resulting spread rates, whereas FlamMap predicted the lowest crown fire

incidence and lowest spread rates. NEXUS predictions fell between those two systems.

Keywords: forest fire behavior modeling, transition, crown fraction burned, rate of spread,

FlamMap, NEXUS, CFIS

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Author ______________________________________________________

Joe H. Scott is a Research Forester, Systems for Environmental Management, Missoula, Montana. Joe

has more than 15 years experience in wildland fire science research and development, including 10 years with

Systems for Environmental Management in Missoula, MT. He has conducted investigations of surface and

canopy fuel characteristics, fire behavior modeling, and crown fire hazard assessment. Joe is the lead

developer of NEXUS, a computer system for assessing crown fire potential; lead developer of FireWords, an

annotated, illustrated glossary of wildland fire science terminology; co-developer of FuelCalc, a system for

computing summarizing and formatting ground, surface and canopy fuel characteristics; and lead developer

of a new set of standard fire behavior fuel models for national application. Joe earned a B.S. in Forestry and

Resource Management from the University of California at Berkeley, an M.S. in Forestry from the University

of Montana, and is a Certified ForesterTM as recognized by the Society of American Foresters.

Acknowledgments ____________________________________________

Preparation of this manuscript was supported by the Fire Modeling Institute, Missoula Fire Sciences

Laboratory, Rocky Mountain Research Station, USDA Forest Service; and by Systems for Environmental

Management. I am grateful for the review comments provided by James Agee, University of Washington; Patricia

Andrews, Missoula Fire Sciences Lab; Miguel Cruz, ADAI, Portugal; Mark Finney, Missoula Fire Sciences Lab;

Pete Fule, University of Arizona; Russ Parsons, Missoula Fire Sciences Lab; and Jan Van Wagtendonk, USGS

Yosemite Field Station.

Scott, Joe H. 2006. Comparison of crown fire modeling systems used in three fire

management applications. Res. Pap. RMRS-RP-58. Fort Collins, CO: U.S. Department of

Agriculture, Forest Service, Rocky Mountain Research Station. 25 p.
Table of Contents

Page

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

Study Areas..................................................................................................... 2

Fire Environment ....................................................................................... 3

Background: Component Models .................................................................... 6

Crown Fire Spread Rate ............................................................................ 6

Crown Fire Occurrence or Initiation ........................................................... 8

Sustained Active Crown Fire Spread ....................................................... 11

Final (Surface-Crown) Spread Rate ........................................................ 13

Crown Fire Modeling Systems ...................................................................... 13

FlamMap .................................................................................................. 13

NEXUS .................................................................................................... 14

CFIS (Crown Fire Initiation and Spread).................................................. 15

Results .......................................................................................................... 15

Crown Fire Occurrence............................................................................ 15

Potential for Active Crown Fire ................................................................ 15

Type of Fire.............................................................................................. 18

Final Rate of Spread ................................................................................ 18

Discussion ..................................................................................................... 22

Management Implications ............................................................................. 23

References .................................................................................................... 24
USDA Forest Service Res. Pap. RMRS-RP-58. 2006 1

Comparison of Crown Fire

Modeling Systems Used in

Three Fire Management

Applications

Joe H. Scott

Introduction ______________________________________________________

Early efforts to predict wildland fire behavior characteristics were focused on

surface fires, primarily their rate of spread and intensity. Later research and development efforts have produced several physics-based research models (Albini 1996,

Butler and others 2004, Grishin 1997, Linn and others 2002) and operational models

(Cruz and others 2004, 2005, Forestry Canada Fire Danger Group 1992, Rothermel

1991)for predicting crown fire occurrence and spread rate. The physics-based models,

based on principles of combustion chemistry, fluid dynamics, and heat transfer, are

calculation intensive and costly to operate, precluding their application to most fire

management problems. However, physics-based models could be used to study a

variety of wildland fire phenomena (Linn and others 2002), including fire-atmosphere

interactions, plume domination, ember transport, steady-state spread, and initiation

and cessation of crown fire. Operationalmodels of crown fire spread rate, based largely

on empirical data collected on both unplanned and experimental fires, are simple

mathematical models whose great speed of calculation and relative ease of use allows

application to importantfiremanagement problems at large spatial and temporalscales

(for example, assessing fire potential across a large landscape, or predicting large fire

growth over many days). Unlike the physics-based models, which enjoy broader

applicability, valid use of empirical models is restricted to situations similar to those

on which the models were built.

For purposes ofthis paper, a fire model is defined as amathematicalrelationship that

describes a single aspect of a fire (Andrews and Queen 2001). Rothermel’s (1972)

model for predicting flame front spread rate at the head of a surface fire is a notable

example. A fire modeling system is a series of fire models used in concert to predict

another aspect of fire. For example, separate models of surface fireline intensity and

minimum fireline intensity crown fire initiation are used together to predict whether

a crown fire can initiate (Alexander 1988, Van Wagner 1977). A fire management

application is one or more models or systems applied coherently to support fire

management decisionmaking. FARSITE, for example, is a fire management application incorporating dozens of models and modeling systems to simulate fire growth

across a two-dimensional landscape; its output is used to support decisions regarding

appropriate response on wildfires and wildland fire use incidents.

A variety of surface-crown spread rate modeling systems have been incorporated

into fire management applications over the past decades, including BehavePlus

version 3 (Andrews and others 2005), the Canadian Forest Fire Behavior Prediction

System (CFFBPS; Forestry Canada Fire Danger Group 1992), FARSITE (Finney

1998), FlamMap (Finney and others 2006), FFE-FVS (Reinhardt and Crookston

2003), FMAplus(Carlton 2005), NEXUS (Scott 1999, Scott and Reinhardt 2001), and
2 USDA Forest Service Res. Pap. RMRS-RP-58. 2006

CFIS (Crown Fire Initiation and Spread; Cruz and others 2005). The surface-crown

spread rate system in each of those applications integrates separate models of surface

fire behavior characteristics (intensity or fuel consumption), transition to crown fire

(or crown fire occurrence), and crown fire spread rate. Of the eight systems identified

above, six (all but CFIS and CFFBPS) are built upon a common set of component fire

modelsthat includes Rothermel’s(1972)surface fire spread rate and (1991) crown fire

spread rate models, and Van Wagner’s(1977) crown fire initiation and spread models.

Of those six systems, FlamMap and FARSITE employ identicalsurface-crown spread

rate systems. FlamMap 3.0 and FARSITE 4.1.05 now include a switch that enables the

user to select between their standard method (Finney 1998) and a new method based

largely on NEXUS (Scott and Reinhardt 2001). The FlamMap and FARSITE implementation of Scott and Reinhardt (2001) does not include condition crown fire, but in all

other respects is identical to the results of NEXUS. This paper will help a user interpret

the impact of that switch on fire behavior simulations. The surface-crown systems in

FFE-FVS and BehavePlus are consistent with that of NEXUS. FMAplus can be set, at

the user’s discretion, to use the surface-crown system of either FARSITE/FlamMap or

NEXUS. Therefore, detailed comparison of the surface-crown spread rate systems in

FlamMap, NEXUS, CFIS, and CFFBPS coversthe range ofsurface-crown spread rate

systems used in current fire management applications. For most fuel types, the

CFFBPS integratessurface and crown fire spread ratesinto a single predictive equation

that encompasses the full range of behavior, whether surface or crown. However, for

fuel type C-6 (conifer plantation), separate equations are used for surface and crown

fire behavior, and a transition function is used to scale between the separate predictions

– the first implementation of such a dual-equation approach in an operational system.

However, due to fundamental differences in inputs between the CFFBPS and the

others, I do not include the CFFBPS in the detailed comparisons.

The purpose of this paper is to compare the primary outputs of the surface-crown

spread rate systems used in CFIS, FlamMap, and NEXUS. The descriptions and

comparisons presented in this paper will be useful for interpreting output from those fire

management applications.

Study Areas ______________________________________________________

Rather than exercise each system through the entire range of possible input values, as

in a sensitivity analysis, I made the comparisons for five intensively sampled conifer

stands for which stereo photographs, stand data, and canopy fuel characteristics were

readily available (Scott and Reinhardt 2005):

• ponderosa pine/Douglas-fir (PPDF)

• pure ponderosa pine (PP)

• Douglas-fir (DF)

• lodgepole pine (LP)

• Sierra Nevada mixed conifer (SNMC).

The multi-storied PPDF stand is located on a gentle NE-facing slope west of Missoula,

Montana. The ponderosa pine overstory is approximately 120 years old. Douglas-fir has

established in the under- and middle-story, creating continuous canopy fuel from the

ground to the top of the canopy. The single-storied PP stand is located on a gentle slope

near Flagstaff, Arizona. Ponderosa pine is both the existing and potential natural

vegetation type, even without fire; no other conifer species are present in this forest. The

plot was established in the densest part of a dense stand, thus the high initial basal area

(BA = 69.0 m2 ha–1; table 1). The single-storied DF stand is located on a moderately steep

southeast-facing slope southwest of Salmon, Idaho. Douglas-fir dominates the plot, with
USDA Forest Service Res. Pap. RMRS-RP-58. 2006 3

a small amount of lodgepole pine. The single-storied LP stand is located on a gentle slope

east of Helena, Montana. A shade-tolerant understory of subalpine fir was only

beginning to establish in this stand. The SNMC stand (composed of white fir, incense

cedar, ponderosa pine, and Douglas-fir) is located at Blodgett Forest Research Station,

SE of Auburn, California. This stand originated after clearcut logging around 1910, and

was treated with commercial thinning about 20 years prior to sampling. Despite the

origin and management of this stand, its canopy fuel profile is more similar to a multistoried stand than single-storied, due in part to the high productivity of the site and

presence of shade tolerant species. Scott and Reinhardt (2002, 2005) describe these five

stands and their associated canopy fuel characteristics in more detail.

I also compared system outputs for the PPDF stand at various levels of residual basal

area (BA) resulting from low thinning (Scott and Reinhardt 2005). The first level,

understory removal (UR), simulates removal of all trees less than 5 cm d.b.h. Subsequent

levels simulated progressive removal, from below (smallest diameter trees first), of 25,

50, and 75 percent of the initial BA.

Fire Environment

Measured, estimated, or assumed fire environment characteristics (fuel, weather,

and topography) are described below and summarized for each stand (table 1), and for

the PPDF stand across different levels of simulated canopy fuel reduction treatment

(table 2).

Table 1—Stand and fuel characteristics of five conifer stands. Site and stand characteristics are

from Scott and Reinhardt (2002). Canopy fuel characteristics are from Scott and

Reinhardt (2005). Surface fuel and miscellaneous characteristics are assumed or

calculated from other inputs.

PPDF PP DF LP SNMC

Site characteristics

Slope (pct) 6 11 25 7 7

Aspect NNE S SE NE NNE

Elevation (m) 1050 2308 2300 2290 1300

Stand characteristics

SD (# ha–1) 481 2070 1178 1146 382

BA (m2 ha–1) 30.4 69.0 36.3 42.7 46.8

SH (m) 23 16 17 20 34

CC (pct) 59 69 70 52 74

Canopy fuel characteristics

CBD (kg m–3) 0.089 0.166 0.257 0.112 0.101

CBH (m) 0 5 1 1 2

CFL (kg m–2) 1.40 0.93 2.09 1.00 1.72

FMC (pct) 100 100 100 100 100

Surface fuel characteristics

FBFM 10 10 10 10 10

EFFM (pct) 6 6 6 6 6

LFM (pct) 80 80 80 80 80

SFC (kg m–2) 1.5 1.5 1.5 1.5 1.5

Miscellaneous

WAF (fraction) 0.10 0.11 0.10 0.10 0.10

Notes: SD = stem density (greater than 10 cm d.b.h.), BA= basal area, SH = stand height, CC = canopy cover,

CBD = canopy bulk density, CBH = canopy base height, CFL = canopy fuel load, FMC = foliar moisture

content, FBFM = fire behavior fuel model, EFFM = estimated fine dead fuel moisture, LFM = live fuel moisture,

SFC = surface fuel consumption, and WAF = wind adjustment factor.
4 USDA Forest Service Res. Pap. RMRS-RP-58. 2006

Fuel—Canopy fuel characteristicsfor each stand were taken directly from Scott and

Reinhardt(2005).Canopy bulk density (CBD)was defined asthemaximum3-mvertical

running mean bulk density of available canopy fuel, which includes the foliage,

0-3 mm live branchwood, and 0-6 mm dead branchwood. CBD varies from a low of

0.089 kg m–3 in the PPDF stand to 0.257 kg m–3 in the DF stand (table 1). In the PPDF

stand, CBD decreased to 0.022 kg m–3

after removal of 75 percent of the initial basal

area (table 2). Canopy base height (CBH) is defined as the lowest height above the

ground at which the canopy bulk density exceeds a threshold of 0.011 kg m–3

. Using

this criterion, initial CBH varies from 0 m in the PPDF stand to 5 m in the PP stand

(table 1). In the PPDF stand, CBH increased to 12 m after removal of 75 percent of the

initial BA (table 2). Foliar moisture content (FMC) is assumed to be 100 percent for all

species at all sites (Philpot and Mutch 1971). (Table 3 contains a complete list of

variables used in this paper.)

To focus the analysis on the relative behavior of the models and systems (as opposed

to the stands themselves), I assumed that surface fuels in each of the stands are

represented by fire behavior fuel model 10 (FBFM 10; Albini 1976, Anderson 1982).

Further, I assumed that FBFM 10 would still represent surface fuels after each level of

canopy fuel reduction in the PPDF stand.

Fine dead surface fuel moisture (EFFM) was estimated using Rothermel’s (1983) fuel

moisture tables, assuming a late summer, mid-afternoon fire, using the same general

weather condition (temperature and humidity) for all simulations. The tables indicated

Table 2—Stand and fuel characteristics of a ponderosa pine-Douglas-fir stand through progressive levels of basal area

(BA) removal. Site and stand characteristics are from Scott and Reinhardt (2002). Canopy fuel characteristics

are from Scott and Reinhardt (2005). Surface fuel and miscellaneous characteristics are assumed or

calculated from other inputs

Initial Understory 25% Basal 50 % Basal 75% Basal

stand removed area removed area removed area removed

Site characteristics

Slope (pct) 6 6 6 6 6

Aspect NNE NNE NNE NNE NNE

Elevation (m) 1050 1050 1050 1050 1050

Stand characteristics

SD (# ha–1) 481 481 226 113 57

BA (m2 ha–1) 30.4 30.0 23.3 16.6 9.2

SH (m) 23 23 23 23 23

CC (pct) 59 59 50 30 19

Canopy fuel characteristics

CBD (kg m–3) 0.089 0.086 0.055 0.037 0.022

CBH (m) 0 1 5 11 12

CFL (kg m–2) 1.40 1.33 0.76 0.40 0.24

FMC (pct) 100 100 100 100 100

Surface fuel characteristics

FBFM 10 10 10 10 10

EFFM (pct) 6 6 5 4 3

LFM (pct) 80 80 80 80 80

SFC (kg m–2) 1.5 1.5 1.5 1.5 1.5

Miscellaneous

WAF (fraction) 0.10 0.10 0.11 0.18 0.22

Notes: SD = stem density (greater than 10 cm d.b.h.), BA = basal area, SH = stand height, CC = canopy cover, CBD = canopy bulk

density, CBH = canopy base height, CFL = canopy fuel load, FMC = foliar moisture content, FBFM = fire behavior fuel model, EFFM

= estimated fine dead fuel moisture, LFM = live fuel moisture, SFC = surface fuel consumption, and WAF = wind adjustment factor.
USDA Forest Service Res. Pap. RMRS-RP-58. 2006 5

an EFFM of 6 percent for the initial condition for allstands(table 1). In the PPDF stand,

EFFM was estimated to be 3 percent after removal of 75 percent of initial basal area

(table 2).Canopy coverremained unchanged afterremoval ofthe understory; therefore

the initial condition and UR treatment were given the same EFFM value of 6 percent.

The two intermediate levels of treatment were assigned EFFM of 4 and 5 percentso that

EFFM decreased evenly with treatment (table 2). For use in Rothermel’s surface fire

spreadmodel, 10-hrtimelagmoisturecontentwasassumedtobe1percentagepoint higher

than EFFM; 100-hr timelag moisture content was assumed to be 2 percentage points

higher than EFFM (Rothermel 1983). Live surface fuel moisture content was assumed

to be 80 percent, representing dry, late summer conditions.

An estimate of surface fuel consumption (SFC) is required for the Cruz and others

(2004) crown fire occurrence model, which classifies SFCinto three categories. Because

I do not have estimates of surface fuel load to use for estimating SFC, I simply assigned

SFC to the middle category (1 – 2 kg m–2) for all stands and all levels of BA removal.

Weather—I assumed an afternoon temperature of 21–32  ̊C and relative humidity of

15–19 percent for all stands and levels of BA removal. Wind speeds above and below the

forest canopy are important variables in the models and systems being compared. Rather

than assume a single wind speed for the comparisons, I computed system outputs over

a range of open wind speeds (U10; wind speed measured 10 m above the forest canopy),

and the U10 at which the systems predict a certain type of crown fire would occur.

Mid-flame wind speed is a required input for predicting surface fire spread rate in

Rothermel’s (1972) model. I estimated mid-flame wind speed by multiplying U10 by a

wind adjustment factor (WAF), which is the ratio of open to mid-flame wind speed. WAF

was estimated using Albini and Baughman’s (1979) model for forested areas on flat

ground, with a lower limit of 0.10. Unconstrained, the Albini and Baughman (1979)

model indicates WAF = 0.09 for the DF stand and 0.08 for the SNMC stand. Their model

Table 3—Complete list of variables.

CBD canopy bulk density (kg m–3)

CBH canopy base height (m)

CD canopy depth (m)

CFB crown fraction burned (dimensionless)

CFL canopy fuel load (kg m–2)

EFFM estimated fine (dead) fuel moisture content (percent)

FBFM fire behavior fuel model (categorical)

FMC foliar moisture content (percent)

FSG fuel strata gap (m)

I fireline intensity (kW m–1)

I’ s critical surface fireline intensity to initiate crown fire (kW m–1)

R rate of spread (m min–1)

Ra rate of spread of an active crown fire (m min–1)

Ra(max) near-maximum rate of spread of an active crown fire (m min–1)

Rfinal final fire rate of spread, whether surface or crown (m min–1)

R’ a critical crown fire rate of spread to sustain active crown fire (m min–1)

Rp passive crown fire rate of spread (m min–1)

Rs surface fire rate of spread (m min–1)

R’ s critical surface fire rate of spread to initiate crown fire (m min–1)

R’ sa surface fire rate of spread for U10 = CI (m min–1)

S mass flow rate (kg m–2 min–1)

SFC surface fuel consumption (kg m–2)

U10 wind speed 10 m above the surrounding vegetation (km hr–1)

WAF wind adjustment factor (dimensionless)
6 USDA Forest Service Res. Pap. RMRS-RP-58. 2006

computes WAF assuming open wind speed is measured at 6.1 m rather than 10 m. U10

was converted to U6.1 by dividing by 1.15 (Turner and Lawson 1978). WAF varied from

0.10 to 0.11 for the initial condition of all stands (table 1), which is consistent with the

Rothermel (1983) guideline for dense canopies on flat ground. For the PPDF stand, WAF

increased from a minimum of 0.10 for the initial condition (table 1) to 0.22 for the most

open treatment level (table 2). Wind direction was assumed to be upslope in all cases.

Topography—Slope steepness at each site was gentle; only the DF site exceeded

11 percent slope (table 1).

Background: Component Models ____________________________________

It is helpful to first review the relative behavior of the component models that

comprise each spread rate modeling system before comparing them.

Crown Fire Spread Rate

Following significant crown fire events of the 1988 fire season, Rothermel (1991)

constructed a simple statistical model of the behavior of sustained crown fire runs in the

northern Rocky Mountains. The dataset consisted of eight crown fire runs on seven

documented wildfires. Duration of crown fire runs varied from 45 minutes to several

hours. Observed average crown fire spread rate was estimated as the total distance of the

run divided by its duration. In addition to this average spread rate for the run, Rothermel

also estimated the maximum crown fire spread rate observed during the run (these data

were available for only five of the eight runs). Slope steepness, open (6.1-m) wind speed,

and dead and live surface fuel moistures were estimated for each run. The observed

average crown spread rate was correlated linearly with predictions made with the

Rothermel (1972) surface fire spread model as adjusted by Albini (1976), using FBFM

10 (Albini 1976, Anderson 1982). FBFM 10 was used for the correlation in all cases, even

though a different FBFM might have better represented actual surface fuels. Wind speeds

at 6.1 m were adjusted by a factor of 0.4 to estimate mid-flame wind speed (even though

a different wind adjustment factor might have been chosen for actual conditions) because

it better represented “mid-flame” wind speed of an active crown fire. In Rothermel’s

correlation, average crown fire spread rate is 3.34 times faster than the predictions made

with FBFM 10 using a 0.4 wind adjustment factor.

Ra Rs FBFM WAF = ! ( = = ) 3 34 10 0 4 . ; . (1)

Where Rs(FBFM=10; WAF=0.4) is the surface fire spread rate predicted with FBFM 10 using

a 0.4 wind adjustment factor. Near-maximum spread rate is 1.7 times faster than the

average spread rate.

Ra(max) Ra = 1.7 (2)

During crown fire runs of those durations, medium- or long-distance spotting could

have contributed to overall fire growth and, therefore, to its estimated spread rate.

However, there is no way to determine the magnitude of the spotting effect on spread

rate, if any, on any of the fires in Rothermel’s analysis. In that respect, compared to

crown fire spread rate models developed withoutspotting (that is, forshorter durations

or on smaller fires,such as experimental crown fires), Rothermel’s model might overpredict spread rate. On the long runs used in the correlation, which covered many

thousands of acres each, canopy and surface fuels, topography, and wind speed likely

varied considerably. The fires may have experienced lulls, periods of surface spread,

or only passive crowning at times during the run, potentially leading to underprediction of fully active crown fire spread rate. Rothermel’s near-maximum spread
USDA Forest Service Res. Pap. RMRS-RP-58. 2006 7

rate model, based on shorter, higher spread rate runs, would be less affected by

temporal and spatial variability in the fire environment.

Rothermel’s average and near-maximum crown fire spread rate models predict little

variation in spread rate among sites (fig. 1a). The only input that varied among sites was

slope steepness, so variation in that input accounted for all of the variation in predicted

output. The DF stand is predicted to have slightly higher spread rate than the others due

to its steeper slope. In the PPDF stand, predicted spread rate increased as the canopy was

opened (BA removed) due to treatment (fig. 1b), because surface fuel moisture was

predicted to decrease.

Using a database of 25 active crown fires, Cruz and others (2005) constructed a nonlinear regression model to predict active crown fire spread rate from U10, EFFM, and

CBD. Data for the regression consisted of small-scale experimental crown fires (smallscale only in relation to the typical size of a naturally occurring crown fire) in mature and

immature jack pine (Pinus banksiana), black spruce (Picea mariana), and red pine

(Pinus resinosa) plantations. A fire was considered an active crown fire if its spread rate

was at least 90 percent of that needed to maintain a massflow rate of 3.0 kg m–2 min–

1 (0.05 kg m–2 s–1) for the observed CBD (Van Wagner 1977). Predicted active crown

fire spread rate is

R U CBD e a

EFFM = ! ! ! (" ) 11 02 10

0 9 0 19 0 17 . . . . (3)

Figure 1—Potential active crown fire rate of spread (Ra) as predicted by three different models for a range of open wind speeds (U10)

in (a) five different conifer stands, and (b) a ponderosa pine/Douglas-fir stand as basal area (BA) is removed to simulate low thinning.

Complete model inputs are described in tables 1 and 2. Forest types include: PPDF = ponderosa pine/Douglas-fir; PP = ponderosa

pine; DF = Douglas-fir; LP = lodgepole pine; and SNMC = Sierra Nevada mixed-conifer.
8 USDA Forest Service Res. Pap. RMRS-RP-58. 2006

The Cruz and others (2005) spread rate model does not include slope as a predictive

factor;most ofthe fires used in the regression were on essentially flat ground (< 11 percent

slope).

Because EFFM was the same for the initial condition of all sites, variation in predicted

active crown fire spread rate with the Cruz and others (2005) model is due entirely to

variation in CBD; the DF stand has the highest predicted spread rates because it has the

highest CBD(fig. 1a). As the PPDF canopy was opened, EFFMand CBDboth decreased.

Those variables have opposing effects on spread rate in the Cruz and others (????) model,

decreasing CBD leads to lower spread rate while decreasing EFFM leads to higher

spread rate. Potential crown fire spread rate was predicted to increase as the canopy is

progressively opened (fig. 1b) because the effect of EFFM overpowered that of CBD.

In summary, the two Rothermel (1991) models and the Cruz and others (2005) crown

fire spread rate model predicted the initial condition of the DF stand would have the

highest Ra of the five sites, but for different reasons; Rothermel’s for that stand’s

relatively steep slope, and Cruz and others for its relatively high CBD. There is no overlap

in predictions using the three models across the stands or simulated treatments. Predicted

Ra is primarily determined by model choice rather than by the range of inputs for the

example stands (fig. 1). Rothermel’s near-maximum spread rate model predicts (by

design) spread rate values 1.7 times the average. Over the range of U10 between 10 and

60 km h–1, the Cruz and others model predicts crown fire spread rate between 2.5 and 5.1

times the Rothermel average, and between 1.1 and 3.0 times the Rothermel nearmaximum. This variation in predicted spread rates is presumably due to differences in

nature of the fires used for constructing each model. Rothermel’s crown fires were longduration runs in coniferous forests of the western United States. Even the near-maximum

spread rates he used were of much longer duration than the observations used by Cruz

and others, and could have included periods of passive crown fire or surface fire spread.

By contrast, the fires used in the Cruz and others model were much shorter duration

experimental crown fires primarily in the northern forests of Canada. The experimental

crown fires were small compared to the usual size of a crown fire. In most cases, the linear

dimensions of the experimental plots were only three to five times the flame length. A

large free-burning crown fire might have a much different response to environmental

conditions than a small experimental crown fire.

The Rothermel models do not include CBD as a predictive factor, whereas CBD has

a small, directly proportional effect on Ra in the Cruz and others model. By contrast,

Grishin (1997) found that increasing CBD would lead to a decrease in Ra, due to the

higher energy requirement to heat the additional fuel. Albini’s (1996) radiation-driven

crown fire spread rate model predicts Ra inversely proportional to CBD for small CBD

values, then directly proportional for higher values (Butler and others 2004).

Crown Fire Occurrence or Initiation

In this section I review the operational aspects of a model of crown fire initiation

(Van Wagner 1977) and one of crown fire occurrence (Cruz and others 2004). Detailed

review of the history and development of models to predict the transition to crown fire

can be found elsewhere (Alexander 1998, Cruz 1999, Cruz and others 2004). The

distinction between crown fire initiation and occurrence may be important when

interpreting model and system output. Crown fire initiation is the onset of crowning; a

crown fire initiation model predicts whether a surface fire will transition to some kind of

crown fire for a given fire environment. Crown fire occurrence is the observation of some

kind of crown fire (for example, passive or active). A crown fire occurrence model

predicts whether some kind of crown fire will be observed for a given fire environment.

The distinction can be important in cases where a crown fire cannot initiate (due to high
USDA Forest Service Res. Pap. RMRS-RP-58. 2006 9

CBH or low fireline intensity, for example) but an active crown fire can still occur if

initiated elsewhere (due to high CBD or strong wind). If such a conditional crown fire is

possible (Scott and Reinhardt 2001), crown fire may occur where it cannot initiate. The

possibility of conditional crown fire is important for both wild and experimental crown

fires. For example, the purpose of the International Crown Fire Modeling Experiment

(ICFME; Stocks and others 2004) was to observe and measure active crown fire

characteristics, so a TerraTorch was used to ignite a crown fire rather than see if one

would ignite further into the experimental plot. There is no guarantee that a crown fire

could have initiated on its own under the same conditions. If a similar situation existed

for the experimental fires comprising a crown fire occurrence database, then overprediction of the onset of crowning relative to a crown fire initiation model is possible.

Van Wagner (1977) theorized that canopy fuels would ignite when the heat supplied

by a surface fire drives off their moisture and raises them to ignition temperature. Using

a single observation of crown fire initiation in a jack pine stand to estimate an empirical

constant, Van Wagner identified the minimum surface fireline intensity required to ignite

canopy fuels, I’s (kW m–1), as a function of height of canopy fuels above the ground

(CBH) and foliar moisture content (FMC).

# = $ +

%

& '

(

) I CBH FMC s

(460 25.9

100

3

2

(4)

Because FMC is held constant for all cases, variation in I’s results solely from

variation in CBH, the variable to which the model is most sensitive (Alexander 1988,

Scott 1998). Using Van Wagner’s (1977) model, I’s = 0 kW m–1 in the initial PPDF

stand (eq. 4) because CBH = 0 (table 4). I’s increased as BA was removed from the

PPDF stand (table 4) because CBH increased.

Van Wagner’s transition model alone does not provide enough information to

determine if transition occurs—an estimate of Is for comparison with I’s is also required.

To more directly compare the results of Van Wagner’s model with those of Cruz and

others, I computed Is with Rothermel’s surface fire spread model. For more direct

comparison with the Cruz and others (2004) crown fire occurrence model (see below),

Table 4—Critical fireline intensity (I’s; kW m–1) as

calculated with Van Wagner’s (1977)

crown fire initiation model for the initial

condition of five conifer stands and for a

ponderosa pine/Douglas-fir stand

through several levels of basal area

(BA) removal.

Five stands, initial condition

PPDF 0.0

PP 1883

DF 168

LP 168

SNMC 476

PPDF stand

Initial condition 0.0

Understory removed 168

25% BA removed 1883

50% BA removed 6145

75% BA removed 7002
10 USDA Forest Service Res. Pap. RMRS-RP-58. 2006

I compute the transition ratio (Is/I’s), the ratio of predicted surface fireline intensity to the

critical fireline intensity needed to initiate a crown fire (Andrews and others 2004).

A crown fire is predicted to initiate if Is/I’s * 1.

In the PPDF initial condition, the transition ratio (Andrews and others 2004), Is/I’s,

was infinity and crown fire initiation is therefore expected at all combinations of U10

and EFFM. Initiation of crown fire was also predicted to occur easily in the DF stand

due to the combination of relatively steep slope and low CBH, and was most difficult

in the PP stand due to the relatively high CBH (fig. 2a). After removing the PPDF

understory, CBH increased but canopy cover (and therefore WAF) remained the same,

so crown fire would now initiate only if U10 is greater than about 18 km h–1 (fig. 2b).

After only 25 percent of the BA had been removed, CBH was raised to 5 m, and crown

fire would not be expected to initiate even as U10 reached 60 km h–1 (fig. 2b). The last

treatment level, which left only 25 percent of the initial BA, showed an increase in the

ease with which crown fire would initiate compared to the 50 percent basal area level.

This is because the CBH did not change much between the two levels (11 m to 12 m),

but the EFFM decreased and WAF increased (table 2), resulting in higher surface fire

intensity.

Figure 2—Ratio of predicted to critical fireline intensity (Is/ I’s) over a range of U10 in (a) five different conifer stands, and (b) a

ponderosa pine/Douglas-fir stand as basal area (BA) is removed to simulate low thinning. On both charts, the PPDF initial condition

is not plotted because CBH = 0 m, so the transition ratio is infinity and initiation occurs at any U10. Complete model inputs are

described in tables 1 and 2. Forest types include: PPDF = ponderosa pine/Douglas-fir; PP = ponderosa pine; DF = Douglas-fir;

LP = lodgepole pine; and SNMC = Sierra Nevada mixed-conifer. Although not part of Van Wagner’s (1977) crown fire initiation model,

Rothermel’s (1972) surface fire spread model, as adjusted by Albini (1976), is used here for predicted fireline intensity (Is) .
USDA Forest Service Res. Pap. RMRS-RP-58. 2006 11

Cruz and others (2004) took a new approach by using logistic regression to predict the

probability of observing crown fire behavior (see also Cruz 1999, Cruz and others 2002).

The dataset on which the model was built included surface, passive crown, and active

crown fires. Rather than predict crown fire initiation (ignition of canopy fuel), the model

predicts the probability of observing passive or active crown fire (as opposed to surface

fire). Predictive variables include U10, fuel strata gap (FSG), surface fuel consumption

(SFC, kg m–2), and EFFM.

Fuel strata gap as conceptually defined by Cruz and others (2004) is identical to the

Scott and Reinhardt (2001) definition of CBH; both terms refer to the vertical distance

from the ground to the height within the canopy at which there is sufficient fuel to

propagate fire vertically. Because the terms refer to the same quantity, I will use CBH in

place of FSG because it is used by a majority of the models and systems described.

Surface fuel consumption, being a fire characteristic that must be predicted (as opposed

to a fuel characteristic that can be observed), is treated as a coded categorical variable

(< 1.0, 1.0 – 2.0, and > 2.0 kg m–2). The Cruz model of crown fire occurrence is

P e

e crownfire

g x

( ) g x

( )

( ) =

1+

(5)

where P(crownfire) is the probability of observing some type of crown fire, and

g(x) = 4 236 + 0 357U " 0 710CBH " 0 331EFFM " SFCf 10 . . . . actor (6)

where SFCfactor is determined from an estimate of SFC as follows

SFC criteria SFCfactor

SFC < 1.0 kg m–2 4.613

1.0 + SFC + 2.0 kg m–2 1.856

SFC > 2.0 kg m–2 0.000

The primary output of the Cruz and others model is probability of crown fire

occurrence. To use the model deterministically, Cruz and others (2002) apply a threshold

probability of 0.5; if P(crownfire) < 0.5 then a surface fire is expected; if P(crownfire) * 0.5

then crown fire behavior is expected.

Because EFFM and SFC were assumed to be the same for the initial condition at all

sites, variation in P(crownfire) results from variation in CBH and U10. The model predicted

crown fire in the PPDF initial condition at any wind speed, due to its low CBH. In the PP

stand, with a CBH of 5 m, the model predicted crown fire occurrence if wind speed

exceeds 8 km h–1 (fig. 3a). Canopy base height rises significantly as the PPDF canopy

is opened, but EFFM decreases (table 2). In this example, the effect of rising CBH was

stronger, so crown fire occurrence became less likely as the PPDF stand was opened

(fig. 3b).

I assumed a value of SFCfrom the middle category (1 – 2 kg m–2). If SFCwere actually

less than 1 kg m–2, these results would slightly over-estimate the true model predictions.

Sustained Active Crown Fire Spread

There is general agreement on the conceptual validity of a minimum mass-flow rate

required for maintaining an active crown fire (Van Wagner 1977). All three surfacecrown fire systems discussed here employ that concept. Van Wagner rearranged a basic

heat balance equation and theorized that solid flames would form in the canopy space

(that is, active crown fire) if a minimum horizontal mass-flow rate of fuel into the flaming

zone, S (kg m–2 min–1), is exceeded

S = Ra *CBD (7)
12 USDA Forest Service Res. Pap. RMRS-RP-58. 2006

where Ra is the predicted flame front spread rate of an active crown fire spread rate

(m min–1)o and CBD (kg m–3) is the bulk density of canopy fuels available for

consumption in the flaming fire front. Van Wagner observed a critical mass-flow rate

of 3.0 kg m–2 min–1 in a red pine plantation, slightly lower but similar in magnitude to

the values given by Thomas (1963) for experimental fuelbeds. Substituting 3.0 for S, the

critical spread rate for active crown fire (m min–1) is

R# = CBD a

3.0

(8)

An active crown fire is possible for all cases in which potential Ra exceeds R’a. In

estimating the mass-flow rate observation for the above equation, Van Wagner computed

CBD by dividing canopy fuel load (foliage) by canopy depth, with canopy depth being

the difference between stand height and CBH (exact method of calculating CBH was not

specified, and different methods produce very different results, especially when applied

to stands with diverse structures). By contrast, the dataset on which these comparisons

are based calculated CBD as the maximum 3-m vertical running mean through the

canopy space, a method which usually produces a slightly higher value than Van

Wagner’s. Because of that difference, all systems could over-predict mass-flow rate

relative to the threshold calculated by Van Wagner. However, comparing the relative

behavior of the systems is still valid because the same CBD estimation method was used

for all systems.

Figure 3 – Probability of crown fire occurrence predicted by the Cruz and others (2004) model over a range of U10 in (a) five different

conifer stands, and (b) a ponderosa pine/Douglas-fir stand as basal area (BA) is removed to simulate low thinning. Complete model

inputs are described in tables 1 and 2. Forest types include: PPDF = ponderosa pine/Douglas-fir; PP = ponderosa pine; DF = Douglasfir; LP = lodgepole pine; and SNMC = Sierra Nevada mixed-conifer. The DF and LP stands have the same model inputs and are

therefore plotted as the same line. Some type of crown fire is said to occur if P(occurrence) = 0.5.
USDA Forest Service Res. Pap. RMRS-RP-58. 2006 13

Final (Surface-Crown) Spread Rate

FlamMap and NEXUS employ Van Wagner’s (1989, 1993) transition function for

scaling spread rate between predictions of surface and crown fire behavior, though the

exact implementation varies. Van Wagner called the transition function “crown fraction

burned” (CFB)—a fraction between 0 and 1 representing the degree of crowning—where

0 indicates no crowning and 1 indicates fully active crown fire. Final spread rate was

defined as

Rfinal = Rs " CFB!(Ra " Rs ) (9)

For CFB = 0 (a surface fire) eq. (9) reduces to Rfinal = Rs; for CFB = 1 (active crown

fire), Rfinal = Ra. At intermediate values of CFB, Rfinal is scaled proportionally between

Rs and Ra. For example, for CFB = 0.5, Rfinal is halfway between the values predicted for

Rs and Ra.

The Crown Fire Initiation and Spread (CFIS) surface-crown system does not use the

CFB concept for determining Rfinal with eq. (9). Instead, passive crown fire spread rate

in their system is a function only of Ra and R’a.

Crown Fire Modeling Systems _______________________________________

FlamMap

FlamMap calculates potential fire behavior across a landscape, incorporating spatial

variability in fuels and topography and temporal variability in environmental conditions

(wind speed and direction, fuel moisture). FlamMap uses the same surface-crown fire

behavior system as FARSITE (Finney 1998). Unlike FARSITE, however, FlamMap

does not simulate spotting or spot fire growth, an important distinction. The primary

purpose of FARSITE is to predict where the fire perimeter will be, and when; the how

(type of fire, fire behavior characteristics) is of secondary importance (though not

unimportant). By contrast, FlamMap is not concerned with determining fire perimeter

locations, only with mapping how a fire might burn a given area.

FlamMap uses the Rothermel (1972) surface fire spread model as adjusted by Albini

(1976) for predicting spread rate and intensity of a surface fire. Although FARSITE can

utilize surface-fuel-model-specific multiplication factors for adjusting spread rate predictions, FlamMap does not need them because it is not projecting fire growth.

In FlamMap, some kind of crown fire is expected if Is * I’s (eq. 4), and surface fire if

not. For crown fires, if Rfinal (eq. 9) * R’a (eq. 8) then active crown fire is expected,

otherwise passive crown fire is expected. Passive crown fires are assigned spread rate of

Rs on the reasoning that passive crown fires are controlled by the surface phase (Finney

1998). CFB for use in eq. (9) is calculated following Van Wagner (1989), who proposed

a transition function of the form

CFB e ax = " (" ) 1 (10)

where a is a scaling factor and x is based on the difference between predicted and critical

spread rates. In the original Van Wagner model

x = Rs " Rs

# (11)

and a = 0.23 such that CFB = 0.9 when Rs exceeds R’

s by 10 m min–1. R’s is the spread

rate associated with I’s (eq. 4).

# = #

$

%

&

'

(

) R I R

I s s s

s (12)
14 USDA Forest Service Res. Pap. RMRS-RP-58. 2006

Using eqs. (10) through (12), spread rate transition toward fully active crown fire is

independent of the critical or predicted active crown fire spread rate. Depending on

surface fuel model and CBH, eqs. (10) through (12) can result in low CFB even if

potential crown fire spread rate indicates active crown fire is possible, and CFB can be

high even though potential active crown fire spread rate may be well below the minimum

needed for active crowning.

Van Wagner (1993) modified the CFB equation to permit dynamic calculation of the

coefficient a to account for variable canopy fuel characteristics. He states that a was

“based on the difference between [R’

s] and [R’a], that is, on the difference between the

point where crown consumption begins and where it becomes complete” (p. 446). The

value of a was set such that CFB = 0.9 when Rfinal is 90 percent of (R’a - R’s)

a

Ra Rs

= "

( # " #)

$

%

&

'

(

)

ln( . )

.

0 1

0 9 (13)

Dynamic calculation of the coefficient a only partially solves the problem described

above where CFB is independent of predicted and critical mass-flow rates. FlamMap

calculates CFB with eqs. (10) through (13).

NEXUS

NEXUS (Scott 1999) was designed for assessing relative crown fire potential by

linking separate models of surface and crown fire behavior (Scott and Reinhardt 2001).

In addition to predicting surface-crown fire spread and intensity, NEXUS computes

indices for rating crown fire potential—Torching Index (TI) and Crowning Index (CI).

The TI is defined as the open wind speed (U10) at which the predicted surface fire intensity

equals the minimum required for crown fire initiation (Van Wagner 1977). The CI is the

U10 at which the predicted active crown fire spread rate equals the minimum needed to

maintain solid flame through the canopy (Van Wagner 1977).

NEXUS includes an additional type of fire—conditional crown fire—that represents

the situation in which the component models predict an active crown fire is possible but

initiating one is not. In that case, NEXUS suggests that two outcomes are possible for the

conditional crown fire type: surface fire behavior, if fire enters the stand as a surface fire;

or active crown fire, if fire enters the stand as a passive or active crown fire (that is, if a

crown fire has already initiated).

If Ra (eq. 1) *R’a (eq. 8) then an active or conditional crown fire is expected, otherwise

surface fire or passive crown fire is expected. For active or conditional crown fires, if

Is * I’s (eq. 4) then NEXUS predicts active crown fire, otherwise conditional crown fire

is predicted. For surface fires or passive crown fires (Ra + R’a), if Is * I’s then NEXUS

predicts passive crown fire, otherwise surface fire.

For all fire types, final spread rate is determined by eq. (9). For conditional crown fires,

CFB = 1. Otherwise, NEXUS assumes a simple linear transition function

CFB R R

R R

s s

sa s

= " #

# " # (14)

where R’sa is the surface fire spread rate at the environmental conditions for which Ra =

R’a. CFB must be bounded such that 0 + CFB + 1.

By default, NEXUS uses Rothermel’s average crown fire spread rate model (eq. 1),

but can also be set to use Rothermel’s near-maximum crown fire spread rate (eq. 2).
USDA Forest Service Res. Pap. RMRS-RP-58. 2006 15

CFIS (Crown Fire Initiation and Spread)

The Cruz and others (2005) stepwise process for determining surface-crown spread

rate has been implemented in a calculation tool called CFIS V1.0. It uses the Cruz and

others (2004) crown fire occurrence model and the Cruz and others (2005) crown fire

spread rate model.

If P(crownfire) (eqs. 5 and 6) *0.5 then passive or active crown fire is expected, otherwise

surface. For passive or active crown fires, if Ra (eq. 3) * R’a (eq. 8) then active crown fire

is expected, otherwise passive. Surface fires can be given Rs from any (unspecified)

model. In CFIS, estimates of surface fire behavior (other than surface fuel consumption)

do not affect other model outputs. Although CFIS does not estimate Rs itself, I plotted

Rs using Rothermel’s (1972) model for FM10, just as for FlamMap and NEXUS. Passive

crown fires in CFIS are given a spread rate Rp as follows (Cruz and others 2005)

R R e p a

R

R

a

a = ! " # $

%

& '

(

) (15)

where Ra is from eq. (3) and R’a is from eq. (8).

Results __________________________________________________________

Crown Fire Occurrence

Although the FlamMap and NEXUS methods are computationally and theoretically quite different from CFIS, it is nonetheless possible to compare their output by

computing TI. Only NEXUS computes TI directly, but each system has an implicit

TI. Because FlamMap and NEXUS use the same crown fire initiation models in the

same way, their TI values were identical in all cases (fig. 4), ranging from zero for

the PPDF initial condition (because CBH = 0) to 155 km h–1 in the PP stand due to its

relatively high CBH. The very high value of TI in the PP stand (i.e., TI > 100 km h–1)

indicates a very low potential for initiating a crown fire. TI increased quickly as the

PPDF stand was opened; with removal of just 25 percent of the initial BA, TI was

greater than 100 km h–1, indicating it is nearly impossible to initiate crown fire.

CFIS also implied TI = 0 for the PPDF initial condition. However, it produced much

lower values of TI than the other models for all remaining stands (fig. 4a). Where the

other systems suggested that crown fire initiation is impossible in the PP stand, CFIS

indicated crown fire could occur if U10 exceeds only 8 km h–1.

Despite drastic differences in actual values of TI between CFIS and FlamMap/

NEXUS, ordinal ranking of crown fire potential in the five stands and five levels of BA

removal as indexed by TI was similar for all systems.

Potential for Active Crown Fire

Despite diverse implementations of crown fire spread rate models, we can compare

how the systems predict the relative ease of sustaining an active crown fire by calculating

CI. CFIS predicted the highest active crown fire potential of all the systems (the lowest

values of CI). Despite not accounting for the relatively steep slope, CFIS estimated active

crown fire would be possible for the DF initial condition if U10 exceeds 4 km h–1, whereas

NEXUS indicated CI of 23 km h–1 (fig. 5). The implied FlamMap CI was much higher

than both NEXUS and CFIS, 55 km h–1 for the DF initial condition. For all stands and

levels of simulated treatment, FlamMap CI was at least twice that of NEXUS, and

roughly eight times that of CFIS (fig. 5).
16 USDA Forest Service Res. Pap. RMRS-RP-58. 2006

Figure 4—Torching Index (TI), defined as the open wind speed (U’10) at which different surface-crown systems predict crown fire

initiation or occurrence, for (a) five different conifer stands, and (b) a ponderosa pine/Douglas-fir stand as basal area (BA) is

removed to simulate low thinning. Complete model inputs are described in tables 1 and 2. High values of U’ 10 indicate low potential

for crown fire initiation or occurrence. Forest types include: PPDF = ponderosa pine/Douglas-fir; PP = ponderosa pine; DF =

Douglas-fir; LP = lodgepole pine; and SNMC = Sierra Nevada mixed-conifer. Simulated BA reduction levels include: IC = initial

condition; UR = understory removal (all trees < 5 cm dbh); 25 = 25 percent of initial BA removed; 50 = 50 percent BA removal;

and 75 = 75 percent BA removed. Y-axis is truncated at U’10 = 100 km h–1. Wind speeds above 100 km h-1 occur so rarely that

crown fire can be considered nearly impossible to initiate for U’10 > 100 km h–1.

Figure 5—Crowning Index (CI), defined as the open wind speed (U’10) at which active crown fire spread is possible, for (a) five

different conifer stands, and (b) a ponderosa pine/Douglas-fir stand as basal area (BA) is removed to simulate low thinning.

Complete model inputs are described in tables 1 and 2. High values of U’ 10 indicate low potential for active crown fire spread.

Forest types include: PPDF = ponderosa pine/Douglas-fir; PP = ponderosa pine; DF = Douglas-fir; LP = lodgepole pine; and

SNMC = Sierra Nevada mixed-conifer. Simulated BA reduction levels include: IC = initial condition; UR = understory removal

(all trees < 5 cm dbh); 25 = 25 percent of initial BA removed; 50 = 50 percent BA removal; and 75 = 75 percent BA removed.

Y-axis is truncated at U’10 = 100 km h–1. Wind speeds above 100 km h–1 occur so rarely that active crown fire can be considered

nearly impossible to sustain for U’10 > 100 km h–1.
USDA Forest Service Res. Pap. RMRS-RP-58. 2006 17

Again, despite drastic differences in actual values of CI, ordinal ranking of crown fire

potential based on CI was similar for the three systems. Only FlamMap deviated from

the others, and then only in the ranking of the PPDF and PP stands. FlamMap’s highest

CI occurred in the PP stand, whereas the other systems predicted the highest CI in the

PPDF stand (because it has the lowest CBD). This occurred because of the effect of the

PP stand’s high CBH on CFB as computed with eqs. (10) through (13). Despite the PPDF

stand having the lowest CBD, FlamMap assigned it a moderate CI because of its very

low CBH.

Because all systems are using the same R’a threshold (Van Wagner 1977), variation

in CI among systems arises from the calculation of Ra. The Cruz and others (2005) model

used in CFIS predicts the highest crown fire spread rates, therefore CFIS produced the

lowest values of CI. The relatively high values of CI in FlamMap result from two factors:

• calculation of CFB independent of Ra and R’a

• reduction of Ra by CFB (eq. 9) before comparing Rfinal against R’a

By directly using eqs. (10) through (13), FlamMap’s calculation of CFB does not

depend greatly on CBD or Ra. Instead, CFB is primarily a function of predicted surface

fire spread rate, available surface fuel, and CBH. FlamMap CFBnever exceeds 0.4 in any

of the stands, even at very high wind speeds (fig. 6). As CBH increases with treatment

in the PPDF stand (table 2), CFB is reduced further; by the time 25 percent of the initial

BA has been removed, CFB never rises above zero at U10 less than 60 km h–1. Although

CBD is also falling with treatment, it has little effect on the reduction in CFB. The only

effect of CBD on CFB is though calculation of the parameter a (eq. 13).

Figure 6—Crown Fraction

Burned (CFB) as calculated in

NEXUS and FlamMap for the

initial condition at five conifer

sites (left charts), and at the

PPDF site at progressive levels

of treatment (right charts). After

25 percent of the initial BA was

removed from the PPDF stand,

both FlamMap and NEXUS

predicted CFB = 0.
18 USDA Forest Service Res. Pap. RMRS-RP-58. 2006

FlamMap computes Rfinal by eq. (9) and CFBas calculated above, then compares Rfinal

against R’a to see if an active crown fire is possible. Of the three systems, only FlamMap

applies the CFB reduction before determining whether an active crown fire is possible;

the others compare Ra against R’a. Because the FlamMap CFB calculation results in

relatively small values, the result is lower potential crown fire spread rate compared to

NEXUS.

Type of Fire

All systems classify type of fire as surface, passive crown, or active crown fire. In

addition to these fire types, NEXUS includes a conditional crown fire type, which

represents a situation in which an active crown fire is possible (Ra * R’a), but one would

not be predicted to initiate (Is < I’s, or P(occurrence) < 0.5 in CFIS). Two outcomes are

possible in that situation: surface fire if the fire starts in the stand as a surface fire, or active

crown fire if fire enters the stand as an active crown fire (for example, if a crown fire has

initiated elsewhere and spread into the stand of interest). All other systems classify that

situation as a surface fire. NEXUS reports the spread rate of a conditional crown fire

as if it were an active crown fire. (The original spreadsheet version of NEXUS

classified this situation as a conditional surface fire and reported spread rate as if it

were a surface fire.)

CFISpredictedactivecrownfireinallfivestandsforU10>18kmh–1,whereas FlamMap

predicted active crown fire only in theDF stand, and then only forU10 > 55 kmh–1 (fig. 7a).

All systems showed progressive reduction in passive and active crown fire as BA was

removed from the PPDF stand (fig. 7b), though CFIS showed a lesser reduction than the

other systems.

Final Rate of Spread

All aspects of how each system simulates surface-crown fire behavior are expressed

in predictions of Rfinal over a range of U10 (figs. 8 and 9). Note that all systems use the

same R’a threshold to distinguish active crowning. The primary difference among the

systems is how each predicts Ra for comparison with R’a.

In five conifer stands—For the PPDF initial condition, all systems predicted crown

fire is possible even with no wind. CFIS predicted passive crown fire spread rate for the

region 0 < U10 < 18 km h–1, then active crown fire at higher wind speeds (fig. 8). In the

passive crown fire range, Rfinal, as computed with eq. (15), asymptotes to the value R’a

* 0.37, then jumps to R’a and follows Ra for U10 > 18 km h–1. NEXUS predicted passive

crown fire for the region 0 < U10< 53 km h

–1, then active crown fire at higher wind speeds.

FlamMap predicted passive crown fire for the entire region 0 < U10 < 60 km h–1. For

passive crown fires in FlamMap, Rfinal = Rs.

For the PP stand, CFIS predicted surface fire for the region 0 < U10 < 9 km h–1, then

active crowning at higher wind speeds. Note that there is no region of passive crowning

because the wind speed at which active crowning is possible (8 km h–1) is less than that

for which crown fire was predicted to initiate. NEXUS predicted surface fire for the

region 0 < U10< 33 km h–1, then conditionally active crown fire spread rate at higher wind

speeds. FlamMap predicts surface fire spread for the entire range U10< 60 km h–1 because

Is < I’s for that range.

In theDFstand,CFISpredicted passive crown fire forthe region 1<U10<4 kmh–1,with

surface fire at lower wind speed and active crown fire at higher wind speeds. In the

passive crown fire region, Rfinal asymptoted to 4.3 m min–1, then jumped to Ra. NEXUS

predicted passive crown fire spread for the region 4 < U10< 22 km h–1, with surface spread

at lower wind speeds and active crown fire spread at higher wind speeds. FlamMap
USDA Forest Service Res. Pap. RMRS-RP-58. 2006 19

Figure 7—Predicted type of fire for (a) five different conifer stands, and (b) a ponderosa pine/Douglas-fir

stand as basal area (BA) is removed to simulate low thinning. Complete model inputs are described in tables

1 and 2. Forest types include: PPDF = ponderosa pine/Douglas-fir; PP = ponderosa pine; DF = Douglas-fir;

LP = lodgepole pine; and SNMC = Sierra Nevada mixed-conifer. Simulated BA reduction levels include:

IC = initial condition; UR = understory removal (all trees < 5 cm d.b.h.); 25 = 25 percent of initial BA removed;

50 = 50 percent BA removal; and 75 = 75 percent BA removed.

predicted passive crown fire spread for the range 4 < U10 < 55 km h–1. Because

FlamMap assigns Rs to passive crown fire spread rate, Rfinal = Rs for the whole range

0 < U10 < 55 km h–1, above which Rfinal is computed using eqs. (9) through (13).

In the LP stand, CFIS predicted passive crown fire for the wind speed range 1 < U10

< 13 km h–1, with surface spread below and active crown fire spread above that range.

Passive crown fire spread rate asymptotes to 9.9 m min–1. NEXUS predicted passive

crown fire spread in the range 21 < U10 < 45 km h–1, with surface spread below and active

crown fire spread above that range. FlamMap predicted passive crown fire spread in the

range 21<U10<60 kmh–1,with surface spread below that range.Rfinal=Rs overthewhole

range 0 < U10 < 60 km h–1.
20 USDA Forest Service Res. Pap. RMRS-RP-58. 2006

Figure 8—Final (surface-crown) spread rate predicted by CFIS, FlamMap, and NEXUS for five different

conifer stands. Complete model inputs are described in table 1. Forest types include: PPDF = ponderosa

pine/Douglas-fir; PP = ponderosa pine; DF = Douglas-fir; LP = lodgepole pine; and SNMC = Sierra Nevada

mixed-conifer. R’a is the minimum spread for maintaining active crown fire.

In the SNMC stand, CFIS predicted passive crown fire for the range 3 < U10 < 15 km h–1,

with surface spread below and active crown spread above that range. Passive crown fire

spread rate asymptotes to 12.5 m min–1. The initial value for passive crown fire spread

rate is computed independent of surface fire spread rate (eq. 15), so spread rate jumps

abruptly at both TI and CI. NEXUS predicted surface fire spread for U10< 48 km h–1, with

conditionally active crown fire spread above that range. FlamMap predicted surface fire

spread for U10 < 59 km h–1, with passive crown fire spread (for which Rfinal = Rs) above

that range.
USDA Forest Service Res. Pap. RMRS-RP-58. 2006 21

Figure 9—Final (surface-crown) spread rate predicted by CFIS, FlamMap, and NEXUS for a

ponderosa pine/Douglas-fir stand as basal area (BA) is removed to simulate low thinning. Complete

model inputs are described in table 2. R’a is the minimum spread for maintaining active crown fire; for

75 percent BA removed, R’a is 136 m min–1.

Following simulated treatments—Using CFIS, predicted Rfinal changed little after

removal of the understory in the PPDF stand. In the remaining systems, surface fire

spread was then predicted for U10 < 21 km h

–1

, with passive or active spread above that

range (fig. 9).

After removal of 25 percent of the initial BA, CFIS then predicted passive crown fire

for the range 8 < U10 < 28 km h–1, with surface spread below and active crown spread

above that range. The values for passive crown fire spread rate began at 13 m min–1 and

asymptoted to 20m min–1. NEXUS and FlamMap both predicted surface fire spread for U10

< 60 km h–1, because Is < I’s for that range.
22 USDA Forest Service Res. Pap. RMRS-RP-58. 2006

After removal of 50 percent of the initial BA, CFIS predicted passive crown fire spread

for the range 19 < U10 < 39 km h–1, with surface spread below and active spread above

that range. The values for passive crown fire spread rate began at 25 m min–1 and

asymptoted to 30 m min–1. All other systems predicted surface fire spread for U10 < 60

km h–1, because Is < I’s for that range.

After removal of 75 percent of the initial BA, CFIS predicted passive crown fire

spread for U10 > 20 kmh–1, with surface spread below thatrange.The valuesfor passive

crown fire spread rate began at 34 m min–1 and asymptoted to 50 m min–1 (which would

be reached at U10 = 65 km h–1). All other systems predicted surface fire spread for U10

< 60 km h–1, because Is < I’s for that range.

Discussion _______________________________________________________

Although the surface-crown modeling systems in CFIS, FlamMap, and NEXUS are

all designed to predict the same basic fire behavior characteristics (fire type, spread rate),

their results for the same fire environment differ considerably. Across the range of inputs

used in these comparisons, CFIS predicts the highest incidence of crown fire and the

highest resulting spread rates, whereas FlamMap predicts the lowest crown fire incidence and lowest spread rates. NEXUS outputs fall between those two systems.

The FlamMap and NEXUS surface-crown modeling systems are very similar in

architecture, but subtle differences in implementation lead to significantly less predicted

crown fire activity in FlamMap than NEXUS. Those differences arise from two sources:

(1) in FlamMap, passive crown fire flame front spread rate is set to that of the surface fire,

whereas NEXUS follows Van Wagner (1993) by estimating passive crown fire spread

rate by scaling between surface and crown fire spread rates; and (2) the FlamMap method

of calculating CFB results in much lower values than NEXUS, resulting in lower

predictions of crown fire spread rate. Even under high to extreme environmental

conditions in dense stands, CFB as computed in FlamMap rarely rises to 0.5, whereas an

active crown fire would logically have CFBnear 1.0. Therefore, FARSITE and FlamMap

users are accustomed to adjusting fire environment characteristics in order to obtain

accurate simulation results. For example, it is common to use higher open wind speeds,

higher CBD, or lower CBH than observed in order to force a simulation to predict the

higher spread rates associated with active crown fire. In FARSITE, where the primary

purpose is to predict fire front location, the simulation of ember transport and spot fire

growth can compensate for any possible under-prediction of crown fire spread rate by

increasing overall fire growth. This spotting mechanism is not present in FlamMap.

Spread rate and intensity of active crown fire, in the few situations where FlamMap

predicts it will occur, are much lower than the Cruz and others (2005) model, and are

usually lower than the Rothermel (1991) model upon which it is built.

CFIS output is notable for its comparatively high incidence of crown fire and

subsequent crown fire behavior. Fully active crown fire in CFIS is predicted to have

spread rates even greater than Rothermel’s near-maximum spread rates. Clearly, the

difference in scale between data used to develop each model must play a role in

explaining this difference. Even the relatively short-duration crown fire runs used in

Rothermel’s near-maximum spread model were much larger and longer than the

experimental crown fires used in building the model used in CFIS. In the Rothermel

near-maximum model, duration and extent are long enough that the fire environment

cannot reasonably be assumed constant—factors such as slope steepness, surface and

canopy fuel characteristics, and wind speed and direction may have varied within the

run,so it is difficult to associate the observed behavior with a specific fire environment.

The experimental fires in the Cruz and others (2005) dataset are small enough that fire

environment can be assumed constant, but their small size may preclude direct
USDA Forest Service Res. Pap. RMRS-RP-58. 2006 23

application to real crown fires. Those experimental fires were in units whose sides were

just a few tree-heights in length, and even fewer flame-heights. To contain the experimental fires, wide areas around each unit were necessarily cleared of trees, resulting in

drastic change in wind flow into the burn unit from all sides. A free-burning line fire in

the same conditions might, therefore, exhibit lower spread rate.

The CFIS final spread rate system exhibits curious behavior as wind speed increases,

especially for higher values of CBH (figs. 8 and 9). In such cases, abrupt changes in

spread rate occur at both the surface-passive and passive-active transitions (TI and CI).

Passive crown fire spread rate depends on predicted and critical active crown fire spread

rates (Ra and R’a), but not on surface fire spread rate. The CFIS passive crown fire spread

rate equation form leads to an initial rapid rise in Rfinal, then a gradual increase as R

approaches R’a asymptotically. At the point where predicted active crown fire equals the

critical value (Ra = R’a), passive crown fire spread rate = 0.37 * R’a, due to the assumed

form of the passive crown fire equation. This predicted behavior appears to be an artifact

of the system rather than intentional design, as the authors offer no physical explanation

for the behavior.

Because NEXUS is designed to assess crown fire potential of different stands and

treatments, it would be more appropriate to use Rothermel’s near-maximum crown fire

spread rate model rather than the long-range average, as is currently used. Doing so

would reduce the chance of under-predicting crown fire potential (NEXUS can emulate

the use of Rothermel’s maximum spread rate model by setting ROSMhigh to 1.7.)

Switching to the near-maximum model would not affect TI, but would reduce computed

values of CI, indicating higher potential for crown fire, and would also predict higher

potential passive and active crown fire spread rates. CFIS, however, would still predict

even greater crown fire potential that NEXUS with the near-maximum model.

Management Implications___________________________________________

CFIS, FlamMap, and NEXUS predict very different surface-crown fire behavior for

the same fire environment. Despite the significant differences in crown fire behavior

predictions, the ordinal ranking of crown fire potential (by implicit TI and CI) in the five

stands and five treatments is similar among the three systems, so users can rely on the

relative fire behavior potential estimated from any of the systems. However, absolute fire

potential, not just the relative potential among stands, is critical for many fire management applications such as determining acceptable levels of hazard, prioritizing areas for

fuel treatment, and quantifying the benefit of fuel treatments. Therefore, the output from

these systems must be compared with observation and experience to determine the

suitability of the system.

FlamMap and NEXUS were built on the same component fire behavior models, but

minor differences in implementation (the calculation of CFB) lead to very different

simulation results. For the same independently determined fire environment characteristics, FlamMap under-predicts the incidence and behavior of active crown fire compared to NEXUS.

The FlamMap surface-crown fire modeling system is identical to that of FARSITE,

which has a different primary purpose (fire growth simulation vs. fire potential mapping). Unlike FARSITE, however, FlamMap does not simulate the effects of ember

transport and spotting on overall fire growth, and therefore under-predicts the effects of

crown fire on fire growth compared to FARSITE.

CFIS and NEXUS were built on different component models, which were in turn built

with different types of data gathered at different scales. It is not surprising, then, that those

systems predict very different fire behavior for the same fire environment inputs. An

individual user has no control over which system is used in a particular application; these
24 USDA Forest Service Res. Pap. RMRS-RP-58. 2006

comparisons cannot be used to select the appropriate system. However, these comparisons may be useful in determining inputs and interpreting output from the different

systems, and perhaps in the development of future surface-crown fire modeling systems.

Finally, this analysis comparesthe modeling systems only with each other, not with

“the truth;” we do not know the truth. From this analysis alone, one cannot conclude

that a particular system or approach is necessarily any better or more accurate than

another, just how and why their results are different. The spread rate modeling systems

described and compared here are artful applications of existing knowledge; they do not

attempt to explain the physics or mechanics of crown fire initiation and spread. As the

science of surface and crown fire behavior advances, so too will our fire management

applications.

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