United States 

Department of 

Agriculture

Forest Service

Pacific Southwest 

Research Station

Research Paper

PSW-RP-259

January 2009

Using HFire for Spatial 

Modeling of Fire in 

Shrublands

Seth H. Peterson, Marco E. Morais, Jean M. Carlson, 

Philip E. Dennison, Dar A. Roberts, Max A. Moritz, and 

DEPA

David R. Weise R TMENT OF AGRICULT URE
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water, forage, wildlife, and recreation. Through forestry research, cooperation with the 

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Grasslands, it strives—as directed by Congress—to provide increasingly greater service 

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Authors 

Seth H. Peterson is a Ph.D. candidate, Jean M. Carlson is a professor, Department of Physics, and Dar A. Roberts is a professor, Department of Geography, 

University of California, Santa Barbara, CA 93106. Marco E. Morais is a computer programmer, Aerospace Corporation, 2350 East El Segundo Boulevard, El 

Segundo, CA 90245. Philip E. Dennison is an assistant professor, Department 

of Geography, University of Utah, Salt Lake City, UT 84112. Max A. Moritz is 

an adjunct professor, Department of Environmental Science, Policy and Management, University of California, Berkeley, CA 94720. David R. Weise is a supervisory research forester, U.S. Department of Agriculture, Forest Service, Pacific 

Southwest Research Station, Forest Fire Laboratory, 4955 Canyon Crest Drive, 

Riverside, CA 92507.
Abstract

Peterson, Seth H.; Morais, Marco E.; Carlson, Jean M.; Dennison, Philip E.; 

Roberts, Dar A.; Moritz, Max A.; Weise, David R. 2008. Spatial modeling of 

fire in shrublands using HFire. Res. Pap. PSW-RP-259. Albany, CA: U.S. Department of Agriculture, Forest Service, Pacific Southwest Research Station. 44 p.

An efficient raster fire-spread model named HFire is introduced. HFire can simulate 

single-fire events or long-term fire regimes, using the same fire-spread algorithm. 

This paper describes the HFire algorithm, benchmarks the model using a standard 

set of tests developed for FARSITE, and compares historical and predicted fire 

spread perimeters for three southern California fires. HFire is available for download at http://firecenter.berkeley.edu/hfire. 

Keywords: Fire spread model, raster, Rothermel, wildfire, southern California, 

chaparral.
Summary

A raster-based, spatially explicit model of surface fire spread called HFire is introduced. HFire uses the Rothermel fire spread equation to determine one-dimensional 

fire spread, fit to two dimensions using the solution to the fire containment problem 

and the empirical double ellipse formulation of Anderson. HFire borrows the idea 

of an adaptive time step from cell contact raster models and permits fire to spread 

into a cell from all neighboring cells over multiple time steps as is done in the heat 

accumulation approach. The model has been developed to support simulations of 

single-fire events and long-term fire regimes. The model implements equations for 

surface fire spread and is appropriate for use in grass or shrubland functional types. 

Model performance on a synthetic landscape, under controlled conditions was 

benchmarked using a standard set of tests developed initially to evaluate FARSITE. 

Additionally, simulations of three southern California fires spreading through 

heterogeneous fuels under realistic conditions showed similar performance between 

HFire and FARSITE, good agreement to historical reference data, and shorter 

model run times for HFire.
Contents

1 Introduction

1 Background

1 Rothermel Rate-of-Spread Model 

2 Two-Dimensional Fire-Spread Modeling Approaches

4 The HFire Model 

4 Model Description

5 Model Inputs 

7 Two-Dimensional Fire Spread 

9 Adaptive Time Step

10 Modeling Fire-Spread at Subcell Resolutions

11 Methods

12 Synthetic Landscape Tests

14 Historical Fires

18 Run Time Efficiency

18 Results

18 Synthetic Landscape Tests

26 Historical Fires

34 Run Time Efficiency

34 Discussion

38 Conclusions

39 Acknowledgments

39 English Equivalents

39 References

Using HFire for Spatial Modeling of Fire in Shrublands

Introduction

Interest in predictive models of wildland fire spread has existed since the late 

1930s, and a substantial body of related information has been published on such 

models (Catchpole and DeMestre 1986, Finney 1998, Fons 1946, Pitts 1991, Weber 

1991, Yassemi et al. 2008). The culmination of this accumulated knowledge is 

encapsulated in the U.S. fire prediction system. The fire-spread predictions used 

by the current system are based on a semiempirical formulation first presented by 

Rothermel in 1972. The Rothermel equation has been implemented operationally 

in the form of programmable hand-held calculators in the late 1970s (Rothermel 

1983), the BEHAVE minicomputer program in the middle 1980s (Andrews 1986), 

and the FARSITE fire-spread model in the middle 1990s (Finney 1998). FARSITE 

is unique because it is the first component of the national system that provides 

spatially explicit predictions of fire spread. In addition to the use of the Rothermel 

equation for modeling surface fire spread, FARSITE adds crown fire and spot fire 

modules for use during extreme wildfire conditions.

HFire (a highly optimized tolerance fire-spread model) is a spatially explicit 

model of surface fire spread through shrubland fuels for real-time use during complex fire situations. HFire, like FARSITE, uses the Rothermel equation, but HFire 

uses a more computationally efficient raster-based algorithm to model fire spread 

in two dimensions. This allows for (1) real-time fire behavior prediction of active 

fires, (2) fire behavior prediction at regional spatial scales, and (3) multicentury 

fire regime modeling. 

This paper introduces and describes the HFire fire-spread algorithm, benchmarks the model using a standard set of tests developed by Finney (1998) for 

FARSITE, and compares historical and predicted fire-spread perimeters for three 

southern California fires, for the raster (HFire) and vector (FARSITE) implementations of the Rothermel equation.

Background

Rothermel Rate-of-Spread Model

Fire-spread models can be classified according to the degree to which they are 

based on empirical data or physical principles (Weber 1991). Fully empirical 

models do not attempt to simulate the physical phenomena and instead rely on 

statistical correlation between variables known to influence fire spread (e.g., 

windspeed or slope). A very simple empirical model of fire spread might be

R = aU b ,

where the rate of fire spread, R (m/s), is the product of the windspeed, U (m/s), 

The fire-spread 

predictions used 

by the current 

system are based 

on a semiempirical 

formulation first 

presented by 

Rothermel in 1972.
2

GENERAL TECHNICAL REPORT PSW-RP-259 

raised to an empirically determined power, b (unitless), and an empirically 

determined constant, a (unitless). Nelson and Adkins (1988) used dimensional 

analysis to construct a similar model from data collected during laboratory and 

field experiment wind-driven fires. A weakness of any fully empirical model is 

that predictions made for fire spread under conditions that were not explicitly 

tested may be unreliable.

Fully physical models differentiate among the different modes of heat transfer 

from burning to unburned fuel and link to the meteorological equations of motion 

in a way that captures the feedback between the fire and local weather conditions 

(Linn 1997, Linn et al. 2002). These types of models offer high fidelity, but are 

computationally intense and thus not suitable for use in a real-time operational 

setting or for multiyear simulations of fire regime (Hanson et al. 2000).

Semiempirical/semiphysical models are a blend of the two approaches. In a 

fully physical model, a heat-transfer calculation is used to estimate the rate of fire 

spread from the ratio of flux between burning and unburned fuels (Williams 1976). 

The Rothermel equation (1972) resembles the heat-transfer equation, but substitutes 

the flux components with representative empirically derived terms,

 , (1)

where IR is the reaction intensity (J·s-1·m2), x is the propagating flux ratio, Фw is the 

wind factor, Фs is the slope factor, ρf is the fuel bed bulk density (kg/m3), ε is the 

effective heating number, and Qig is the heat of preignition (J/kg). The Rothermel 

equation computes the steady-state rate of fire spread in the direction of maximum 

fire spread and assuming wind and slope are aligned in this direction. As a result, 

some other models must be used to compute the rate of fire spread in other directions and when wind and slope are not aligned with the direction of maximum 

spread.

Two-Dimensional Fire-Spread Modeling Approaches

Both vector and raster-based approaches have been used to model fire spread in 

two dimensions. The vector-based approach simulates fire spread as a continually 

expanding fire polygon (Anderson et al. 1982) and is the basis for the FARSITE 

model. Raster schemes of two-dimensional fire growth partition the modeling 

domain into regularly spaced square or hexagonal lattices, and fire spreads from 

neighboring cell to neighboring cell, using cell contact or heat accumulation methods (Ball and Guertin 1992, Berjak and Hearne 2002, Clarke et al. 1994, Frandsen 

and Andrews 1979, Green et al. 1990, Hargrove et al. 2000, Kourtz and O’Regan 

1971, Yassemi et al. 2008). 

f ig

R w s

Q

I

R

ρ ε

ξ (1+ Φ + Φ ) =
Using HFire for Spatial Modeling of Fire in Shrublands

In the vector approach to modeling fire spread, the fire perimeter at any point in 

time is represented by an infinitely thin arc consisting of a set of n coordinate pairs, 

known as vertices, in a Cartesian plane. The maximum rate of spread is computed 

at each vertex, and empirical relationships developed by Anderson (1983) are used 

to predict the elliptical shape of fire spread from the maximum rate of fire spread 

and the local wind and slope conditions. The convex hull about the n fire-prediction 

ellipses defines the perimeter of the fire for the next time step. The number of coordinate pairs, n, relative to the length of the perimeter, l, dictates the spatial resolution of the predicted fire spread; referred to as “perimeter resolution” in FARSITE. 

One of the weaknesses of the vector approach is the difficulty in choosing an 

appropriate perimeter resolution. Clarke et al. (1994) observed from historical fire 

scars that fire perimeter length is strongly dependent upon scale, and this suggests 

a uniform perimeter resolution may not be appropriate. Another weakness of the 

vector approach is the need for a computationally expensive convex hull fire-spread 

perimeter generation procedure (Richards 1990) at the end of each time step in 

order to resolve fire crossovers and unburned islands. In a critical evaluation of 

a fire-spread model implementing Huygens’ Principle, French et al. (1990) found 

that the model performance suffered under increasingly heterogeneous conditions. Despite this, the most widely used fire-spread models in the United States 

(FARSITE) (Finney 1998), Canada (Prometheus) (Prometheus 2008), and Australia 

(SiroFire) (Coleman and Sullivan 1996) all use the vector approach to modeling fire 

spread.

Green (1983) identified two main approaches to determining fire spread in a 

raster domain: heat accumulation and cell contact. The cell contact approach, used 

by Kourtz and O’Regan (1971), Frandsen and Andrews (1979), and Green et al. 

(1990), is consistent with an interpretation of fire spread as a series of discontinuous 

ignitions spanning the length of an individual cell. The strength of this approach 

is that it is extremely computationally efficient because the simulation clock increments in nonuniform intervals based on the amount of time required to spread into 

an adjacent cell; this is sometimes referred to as the time-of-arrival (TOA) of the 

fire perimeter. This eliminates the redundant computations that are made when 

operating with a uniform time step. The weakness of the contact approach is that 

events are generated based only upon the influence of the single fastest spreading 

neighbor, and fire spread into a cell that is the cumulative effect of multiple neighboring cells or prior heating is neglected (Green 1983). 

The heat accumulation approach to raster fire spread mitigates the fundamental 

weakness of the cell contact approach by enabling the rate of spread of fire into a 

cell to be the sum of the contribution of neighboring ignited cells during prior time 
GENERAL TECHNICAL REPORT PSW-RP-259 

steps (Green 1983). The heat accumulation model iterates over fixed time intervals, 

known as the time step, visiting every cell in the simulation domain and tabulating 

the quantity of heat received by that cell from all of its neighbors. After receiving 

some threshold quantity of heat, a cell is considered ignited and begins delivering heat to neighboring cells. Although the phrase “heat accumulation” suggests 

that there is a physical basis for the method used to describe the ability of a cell 

to absorb and emit heat, all implementations to date have used fully empirical or 

semiempirical/semiphysical models of fire spread as surrogates for the physical 

properties and mechanisms of fire spread (Green et al. 1990). French et al. (1990) 

empirically evaluated the performance of a heat accumulation model (Green 

1983) and found that it was more computationally intensive than the cell contact 

approach because of the relatively small elapsed time step required to capture rapid 

fire spread. However, the added cost appeared worthwhile because the fire-spread 

perimeters produced from the heat accumulation model were less distorted in 

comparison to the cell contact models. Most recent raster fire-spread models use the 

heat accumulation approach (Anderson et al. 2007, Ball and Guertin 1992, Berjak 

and Hearne 2002, Clarke et al. 1994, Hargrove et al. 2000, Vasconcelos and Guertin 

1992, Yassemi et al. 2008). Yassemi et al. (2008) performed an analysis similar to 

our analysis. They compared a raster and a vector (Prometheus) implementation of 

the semiempirical fire-spread algorithm used by government agencies in Canada, 

finding the best agreement at high windspeeds.

The HFire Model

Model Description

HFire (Morais 2001) is a raster model of surface fire spread based on the Rothermel 

(1972) fire-spread equation and the empirical double ellipse formulation of Anderson (1983). HFire blends the strengths of the contact-based and heat accumulation 

raster fire-spread approaches; it borrows the idea of an adaptive time step from 

the cell contact models and permits fire to spread into a cell from all neighboring 

cells over multiple time steps as is done in the heat accumulation approach. A state 

machine is used to track the movement of the fire through the cells in the simulation 

domain. 

The model can be run in two modes, simulating single-fire events or longterm fire regimes. The fire-spread algorithm used in both modes of the operation 

is the same, resulting in no loss of fidelity whether the model is being run for a 

single event or for a scenario spanning several centuries. Single-event simulations 

driven by historical or predicted data are completely deterministic. Although not 

HFire is a raster 

model of surface 

fire spread based on 

the Rothermel firespread equation and 

the empirical double 

ellipse formulation of 

Anderson.
Using HFire for Spatial Modeling of Fire in Shrublands

5

discussed in this paper, the model can be used for multiyear simulations of fire 

regime (many hundreds of years) featuring stochastic historical weather patterns, 

ignition frequency and location, simulated Santa Ana wind events, and dynamic 

fuels regrowth (Moritz et al. 2005). Hfire has also been used to examine sensitivity 

to weather inputs (Clark et al., in press) and the effectiveness of fire suppression 

(Ntaimo et al. 2004). 

Model Inputs

HFire model inputs can be subdivided into three groups: (1) fuel variables, 

(2) terrain variables, and (3) environmental variables (table 1). 

Table 1—Variables required for predicting fire spread using HFire

Variable Type Units

Fuel load Fuel kg/m2

Surface area to volume (σ) Fuel m2/m3

Heat content Fuel J/kg

Total silica content Fuel Percent

Effective silica content Fuel Percent

Fuel bed depth Fuel m

Moisture of extinction Fuel Percent

Elevation Terrain m

Slope Terrain Percent

Aspect Terrain Degrees

Dead fuel moisture Environmental Percent

Live fuel moisture Environmental Percent

Windspeed Environmental m/s

Wind direction Environmental Degrees

Fuel variables require a value for each of the following size classes: dead 1-hour 

(<0.635 cm diameter), dead 10-hour (0.635 to 2.54 cm diameter), dead 100-hour 

(2.54 to 7.62 cm diameter), live herbaceous, and live woody fuels.

Fuel variables—

Fuels are described using the parameter sets (fuel models) for the Rothermel model 

developed by Albini (1976). The 13 Northern Forest Fire Laboratory (NFFL) 

standard fuel models (Albini 1976) or user-defined custom fuel models (Burgan and 

Rothermel 1984) can be used in HFire. A look-up table applied to the fuel model 

map provides fuel information across the landscape. Because the Rothermel equation assumes a homogeneous fuel bed, a method of averaging the collections of fuel 

particles used by the fuel modeling system is required. HFire uses the surface-areato-volume weighting scheme described by Rothermel (1972) to synthesize the fuel 

particle attributes into a single-characteristic value of the fuel bed. Although some 

fuel variables such as fuel load and depth vary annually owing to disturbance and 

seral stage, the change in these properties within a single year is small enough to 
GENERAL TECHNICAL REPORT PSW-RP-259 

justify holding them constant during a year of simulation time. Fuel moisture varies 

on a daily basis (dead) or seasonal basis (live) and is treated as an environmental 

variable by the model.

Terrain variables—

The terrain variables used by the model (elevation, slope, and aspect) are typically 

computed from a digital elevation model (DEM) using a geographic information 

system (GIS). These are held constant for the duration of single-event and multiyear 

simulations.

Environmental variables—

The environmental variables used by the model can vary in both time and space. 

Inputs can be specified to a minimum resolution of 1 hour,1 which is common for 

windspeed, wind azimuth, and dead fuel moisture. This constraint does not reflect 

a limitation of the internal simulation clock but is imposed because estimates for 

these parameters are commonly taken from Remote Automated Weather Stations 

(RAWS) that report data in 1-hour intervals. Live fuel moisture changes more 

slowly; it is measured in the field at 2-week intervals but can be input at any resolution up to hourly. The inputs can be constant on the landscape or maps of values. 

Spatially varying environmental inputs can be specified at a spatial resolution 

different from that of the terrain and fuels variables and up to a minimum temporal 

resolution of 1 hour. Diagnostic wind models are a potential source for spatially 

varying weather inputs (Butler et al. 2006), and remote sensing is a potential source 

for live fuel moisture maps (Dennison et al. 2003, 2005; Peterson et al., in press; 

Roberts et al. 2006). 

HFire assumes windspeed and direction data are measured at the conventional 

reference height for RAWS stations in the United States, 6.1 m above the top of the 

fuel bed. HFire uses an approximation2 to the logarithmic reduction formula given 

by Albini and Baughman (1979) to compute the windspeed experienced at midflame from the windspeed measured at the reference height,

1 This restriction will be relaxed in future versions of HFire to allow time tagged inputs 

specified at any resolution.

2 There is a slight discrepancy between the mid-flame windspeed computed from Albini 

and Baughman (1979) and the mid-flame windspeed computed using BEHAVEPlus. The 

windspeed adjustment factor (WAF) used in BEHAVEPlus (WAFBHP) can be recovered 

from the Albini and Baughman equation (WAFAB79) using the following linear equation: 

WAFBHP = WAFAB79 * 1.371817779 + 0.046171831. The results reported in this paper use 

the WAF from BEHAVEPlus.
Using HFire for Spatial Modeling of Fire in Shrublands

where Umid is the mid-flame windspeed (m/s), Uref is the windspeed measured at 

the reference height (m/s), href is the reference height (m), and hmid is the mid-flame 

height (m). In HFire, the mid-flame height, hmid, is assumed to be equal to twice 

the fuel bed depth. Although others have suggested that a logarithmic windspeed 

reduction profile may be less accurate during periods of local atmospheric 

instability (Beer 1990) and during nighttime conditions (Rothermel et al. 1986), 

HFire uses this adjustment throughout the duration of the simulation.

Two-Dimensional Fire Spread

There is widespread agreement that fire spread under steady homogeneous conditions and in the presence of wind and topography roughly approximates an expanding ellipse (Anderson 1983, Green 1983). Anderson (1983) described fire spread as 

a double ellipse, which allows for different equations for the forward and backward 

spreading ellipses. The length-to-width ratio of the ellipses is a function of the midflame windspeed.

Since Rothermel’s original fire-spread equation assumes that the wind is 

aligned directly with slope, the effect of cross-slope winds must be taken into 

account. HFire uses the technique defined in Rothermel (1983: fig. IV-8) to compute 

the cross-slope rate of spread vector by adding two rate-of-spread vectors, one 

computed using the observed winds without slope and another using the slope and 

no wind. The windspeed in the direction of the cross-slope rate of spread vector, 

termed the effective windspeed, Ueff (m/s), is used to compute the length-to-width 

ratio of an ellipse (Rothermel 1991: equation [9]),

 (2)

where L is equal to the length (m) and W is equal to the width (m) of the predicted 

elliptical dimensions. The coefficient k is an addition to Rothermel’s (1991) equation3

 that we have included in HFire and termed the ellipse adjustment factor 

(EAF). The EAF is included in HFire as a correction factor for grid-induced 

kUeff W

L = 1 + 0.5592

3 Equation 5 in Rothermel (1991) is a linearization of an exponential function suggested by 

Andrews (1983) where U is given in mi/hr. Equation 2 in this paper uses U in m/s and as a 

result the coefficient 0.25 in mi hr-1 has been divided by (1609.344 m/3600s) in order for L

and W to remain unitless. 

,





 



 + =

mid

ref mid

ref

mid

h

h h

U

U

0.13

(0.36 ) ln
GENERAL TECHNICAL REPORT PSW-RP-259 

effects associated with the raster-based algorithm. The raster-based algorithm 

generally produces narrower, more angular fire shapes than FARSITE when k = 1.0 

(i.e., no EAF correction); values of k less than 1.0 widen the fire front for HFire. 

The rationale for the EAF is explained in more detail following equation (3). 

Albini and Chase (1980) provided a formula (equation 8) for determining 

the eccentricity of an ellipse, E, such that 0 < E < 1 and using the length, L, and 

width, W:

 .

Given the predicted eccentricity, E, of the fire calculated from the effective 

windspeed and the rate of maximum fire spread calculated from the Rothermel 

equation, Rmax, the solution to the fire containment problem (Albini and Chase 

1980) provides the rate of fire spread at arbitrary angles from the maximum:

 , (3)

where Rθ is the rate of fire spread (m/s), at some angle θ (degrees), from the direction of the maximum rate of fire spread. The derivative of equation (3) with respect 

to the angle, θ, is largest at small angles, 0° < θ < ±45°. For example, the eccentricity for typical length-to-width ratios (12:1 to 3:1) is on the order of 0.9, and for this 

value, R45 is reduced to 27 percent of R0 using equation (3). Hence, for a raster 

model allowing fire spread to eight neighbors, where the values of the angle θ in 

equation (3) are restricted to multiples of 45° in the range [-180°, 180°], the region 

from 0° to ±45° is undersampled and poorly approximates the true shape of the 

function. As a result, the shape of the heading portion of the fire is angular rather 

than rounded, in comparison to a vector model (Ball and Guertin 1992, French et al. 

1990).

The EAF is introduced to compensate for this distortion. The effect of the 

EAF on predicted fire shapes on a landscape with flat terrain, homogeneous fuels, 

and under uniform wind conditions is shown in figure 1. In all cases, the distance 

spread in the direction of the maximum rate of fire spread (from the ignition point 

to the fire front) is unchanged, but the fire front is less pointed (EAF < 1.0) than 

the raster realization of Anderson’s (1983) standard fire-spread ellipse (EAF = 1.0). 

For example, for an effective windspeed of 5 m/s, R45 is reduced to 25 percent of 

R0 with EAF = 0.5 and to 11 percent with EAF = 1.0. When conditions are less 

simplified, the heading portion of the fire will become more blunted as the direction 

of the maximum rate of fire spread changes, and an EAF closer to 1.0 can be used. 

( )

( ) 1 2

W

L

W

L

E − =

(1 cos )

(1 ) max

θ θ − Ε

− Ε

R = R
Using HFire for Spatial Modeling of Fire in Shrublands

9

Recommendations for setting the EAF appropriately are made in the “Discussion” 

section.

In any three-by-three neighborhood of cells, a fire located at the center of the 

neighborhood has the potential of spreading to all eight adjacent neighbors. The 

fire-spread distance in the direction of a neighboring cell located at some angle θ, 

in degrees, from the cell center during the nth iteration dθ,n is equal to the rate of fire 

spread in the direction of the neighbor during the nth iteration Rθ,n multiplied by the 

duration of the time step tn:

 dθ,n = Rθ,n tn .

Under homogeneous conditions, an eight-sided figure will always emerge 

because the underlying raster provides eight degrees of freedom.

Adaptive Time Step

The cell size, ∆d, provides a lower limit on the distance between adjacent cells 

in the simulation. The terrain distance, dxyz, is necessary for tracking fire spread 

parallel to the ground and is computed from a pair of cells in three-dimensional 

Cartesian space {x1, y1, z1} and {x2, y2, z2} as:

The terrain distance between adjacent cells at the same elevation and connected 

via one of the four cardinal directions, 0 (north), 90 (east), 180 (south), or 270 (west) 

degrees, will always be equal to or longer than the cell size. Similarly, the terrain 

distance between cell centers connected by a diagonal will always be longer than 

the cell size. Thus, the cell size, ∆d, divided by the maximum rate of fire spread at 

all cells in the simulation domain during the nth iteration, max |Rmax,n,|, yields the 

minimum amount of time, in seconds, that can occur in the simulation before the 

fire may have traveled from one cell center to another during a single time step. 

This provides the basis4 for the size of the time step used during the nth iteration, tn:

 . (4)

Because the size of the time step will vary with fire behavior, incrementing 

more slowly when fire spread is rapid and vice-versa, this is referred to as an 

adaptive time step.

2

1 2

2

1 2

2

1 2 dxyz = (x − x ) + ( y − y ) + (z − z )

max | | max,n

n

R

d t ∆ =

4 The distance past a neighboring cell center that a fire spreads during a single iteration 

is termed the “slop over.” HFire properly handles “slop over,” but an attempt is made to 

minimize the frequency with which it occurs by scaling the time step computed using 

equation 4 by 0.25. More details are provided in the section on modeling fire spread at 

subcell resolutions.

.

In any three-by-three 

neighborhood of 

cells, a fire located 

at the center of the 

neighborhood has the 

potential of spreading 

to all eight adjacent 

neighbors.
10

GENERAL TECHNICAL REPORT PSW-RP-259 

Modeling Fire Spread at Subcell Resolutions

Given a method for computing the rate of fire spread in any direction and for 

determining an appropriate time step from the fastest spreading component of the 

fire, a state machine is used to track the movement of the fire through the cells in 

the simulation domain. At any instant in the simulation, all cells in the simulation 

domain are assigned one of four possible states.

• Cell is unburnable [U].

• Cell is flammable, but not currently ignited [N].

• Cell is flammable and is ignited, but fuel is not yet consumed [I].

• All fuel in cell has been consumed by the fire [C].

At the start of the simulation, all cells are in the unburnable [U] or not-currently-ignited [N] states. Unburnable cells [U] correspond to areas without the 

potential to burn, such as rock outcrops and water bodies, including the ocean, 

lakes, and perennial streams. There are no transitions to or from the unburnable 

state to any of the other three states. 

During the simulation, there are two possible events that can result in the transition of a cell from the not currently ignited state [N] to the ignited state [I]. The 

first type of transition event is an independent ignition that represents a new fire. 

Independent ignitions can be specified by the user in two ways. For single-event 

simulations, the user typically supplies a file containing the coordinates of cells that 

will be ignited [I] at the start of the first iteration in the simulation. For multiyear 

simulations, the user specifies two types of ignition probabilities: an overall temporal frequency for ignitions and a surface containing the relative probability of 

ignition for each cell. Ignitions occur stochastically in time and space. 

The second type of transition event occurs when a fire spreads into the cell 

from an adjacent cell. HFire implements fire spread as follows. The simulation 

maintains a list of all cells that are in the ignited state [I]. Two arrays are associated 

with each element of this list. The first array is used to accumulate the distance over 

multiple time steps that the fire has traveled in each of the eight possible directions. 

The second array is used to store the terrain distance, dxyz, between adjacent cells 

in each direction. When the accumulated distance in a direction exceeds the terrain 

distance in that direction, then the adjacent cell in that direction is transitioned from 

the not ignited state [N] to the ignited state [I]. Any excess distance, termed “slop 

over,” is applied to the array of accumulated distances for the newly ignited cell in 

the direction of fire spread.

During the simulation, there are two possible events that can result in the 

transition of a cell from the ignited state [I] to the consumed state [C]. The first type 
Using HFire for Spatial Modeling of Fire in Shrublands

11

of transition event is triggered when the eight neighbors of a cell are in the ignited 

state [I] or unburnable state [U]. Cells in this configuration are typically located in 

the interior portions of an expanding fire. This is not meant to imply that cells in the 

consumed state [C] are not undergoing postfrontal combustion, only that the energy 

released from these cells no longer contributes to the forward rate of spread of the 

fire. The second type of transition event occurs when a fire is extinguished; this is 

important for the multiyear model runs.

Fire does not burn in a cell indefinitely. Fire extinction refers to the transition of 

a cell from the ignited state [I] to the not-ignited state [N] or from the ignited state 

[I] to the consumed state [C]. The Rothermel model given in equation (1) does not 

describe the conditions under which a fire is extinguished. As a result, the simulation uses a few additional heuristics to trigger extinction. First, a cell in the ignited 

state [I] that has burned longer than a user-specified threshold without propagating 

to all adjacent burnable neighbors will trigger an extinction transition; this is implemented in the simulation by tracking the time since each cell was ignited. Second, 

a cell in the ignited state [I] with a maximum rate of fire spread that falls below a 

user-specified threshold will trigger an extinction transition. In both cases, the user 

controls whether all extinction transitions will go from ignited [I] to not ignited [N] 

or from ignited [I] to consumed [C].

Methods

In this section, we describe two sets of numerical simulations to evaluate the 

performance of HFire. First, a series of benchmarks on synthetic, homogeneous 

landscapes under simplified burning conditions were performed, following the 

initial landmark validation of the FARSITE implementation of the Rothermel equation (Finney 1998). For all of the HFire simulations, we ran comparison simulations 

with FARSITE, using the same inputs, enabling a direct comparison of the results. 

Second, simulations of three historical fires with mapped topography and vegetation and measured weather were performed, and HFire perimeters were compared 

to FARSITE perimeters and reference fire perimeters.

All tests were performed with the same inputs, with the exception of dead fuel 

moisture, which is input differently for HFire and FARSITE. HFire uses hourly 

10-hour dead fuel moisture data from RAWS stations, and the 1-hour and 100-

hour dead fuel moistures are determined from the 10-hour values ± a user-defined 

constant. For FARSITE 1-, 10-, and 100-hour dead fuel moistures are initialized at 

the beginning of the simulation period and are modified using a sinusoidal function 

whose shape is dictated by air temperature and humidity.

For all of the HFire 

simulations, we 

ran comparison 

simulations with 

FARSITE, using the 

same inputs, enabling 

a direct comparison 

of the results. 
12

GENERAL TECHNICAL REPORT PSW-RP-259 

FARSITE contains modules for predicting fire spread in grassland, shrubland, 

and forested landscapes, whereas HFire is designed for surface fire in chaparral 

landscapes comprising grasslands and shrublands only. FARSITE modules for 

forested landscapes that allow for spotting and crown fires are not applicable. In 

addition, the FARSITE fire acceleration module is disabled so that a comparison 

between the two model implementations of the Rothermel equation could be 

performed.

Agreement between HFire- and FARSITE-modeled fire perimeters, as well as 

between modeled and historical fire perimeters, was assessed using the Sørensen 

metric. The Sørensen metric (Greig-Smith 1983, Perry et al. 1999) measures agreement between two areas:

where a is the intersection of the area burned in the two models, b is the area 

burned by model A but not model B, and c the area burned by model B but not 

model A. A value of S = 1.0 indicates perfect agreement. All calculations are 

performed on cumulative area burned for an individual fire. Perry et al. (1999) used 

the Sørensen metric to assess the accuracy of a simulation of the 1995 Cass Fire in 

New Zealand.

Synthetic Landscape Tests

A series of simple, controlled tests were designed by Finney (1998) to illustrate 

the response of the FARSITE fire-spread model to the primary factors affecting 

fire spread. These factors include windspeed, wind direction, slope, fuel type, and 

fuel transitions. They are varied individually and in pairs under otherwise uniform 

conditions to illustrate model behavior under idealized, controlled conditions. To 

evaluate HFire, we replicated the burning conditions used by Finney (1998) to test 

the FARSITE model. 

In all of the tests, fuel moisture was held constant, spatial resolution was 10 m, 

and perimeters were output at hourly time steps. Unless otherwise specified, wind 

direction was from 180 degrees; values of EAF tested were 1, 0.66, 0.5, 0.4, and 

0.33; fuel model 15, a custom fuel model for mature chamise chaparral (Weise and 

Regelbrugge 1997), was used, and the terrain was flat. 

Test of different windspeeds—

This test isolates the effects of windspeed and the EAF. Twenty-one separate HFire 

simulations were run. Windspeed ranged from 0 to 20 m/s, in increments of 5 m/s. 

Five values of EAF were tested, except for the 0 m/s windspeed case, where EAF 

(2 )

2

a b c

a S

+ + = ,

A series of simple, 

controlled tests were 

designed by Finney 

(1998) to illustrate 

the response of the 

FARSITE fire-spread 

model to the primary 

factors affecting fire 

spread. 
Using HFire for Spatial Modeling of Fire in Shrublands

13

has no effect. For the zero m/s windspeed simulations, Fuel Model 1, grassland, was 

used to increase rate of spread, so the figure is less pixilated. 

Test of time varying wind direction—

This test isolates the effect of varying wind direction and EAF. Thirty HFire 

simulations were run, the five values of EAF were tested with six wind azimuths: 

winds having a constant azimuth of 180 degrees and five different wind azimuth 

scenarios, listed in table 2. For the first four scenarios, the wind direction is periodically and deterministically varied by fixed increments about the 180-degree average. In the last scenario, the wind direction switches between due north and due 

south. Windspeed was 5 m/s for all runs.

Table 2—Scenarios for alternating wind azimuth condition tests

Hour

Scenarioa 0 1 2 3 4 5 6 7 8

Degrees

1 180 190 170 185 175 180 190 170 180

2 180 210 150 195 165 180 210 150 180

3 200 220 170 210 130 190 220 140 180

4 180 225 135 225 135 225 135 180 180

5 180 360 180 360 180 360 180 360 180

a The first four scenarios involve perturbations about 180 degrees, the last involves alternating 

wind directions.

Test of different windspeeds and slopes, with up-slope winds—

This test combines the effects of changing both windspeed and slope. Twenty-four 

HFire and FARSITE simulations were run, with slopes (rise over run) of 0, 20, 

40, 60, 80, and 100 percent and constant upslope windspeeds of 0, 2.5, 5, and 7.5 

m/s. A fire burning uphill spreads faster as the heat from the fire front preheats the 

adjacent fuel, driving off vegetation moisture, reducing the energy required to raise 

the temperature of the fuel to ignition. HFire was run with the EAF set to 0.5. 

Test of different slopes and cross-slope winds—

This test combines the effects of changing slope and temporally varying wind 

direction. It is similar to the previous test with different windspeeds and slopes, 

with the modification that the wind direction is cross-slope. We tested two wind 

direction scenarios: winds from 270 degrees and winds from 270 degrees systematically perturbed ± 20 degrees. Only 7.5 m/s windspeed model runs are presented. 

HFire was run with the EAF set to 0.5. 
14

GENERAL TECHNICAL REPORT PSW-RP-259 

Test of different fuel model transitions—

This test isolates the effects of fuel model transitions and the EAF. Twenty HFire 

simulations were run with five values for the EAF and four landscape scenarios: a 

landscape solely comprising Fuel Model 15, and Fuel Model 15 with an inset block 

of three different fuel models (unburnable; a synthetic fuel model based on Fuel 

Model 15 but with reduced fine fuel loads so that it burns more slowly than Fuel 

Model 15; and Fuel Model 1, grassland, which results in faster fire spread). Windspeed was 7 m/s. 

Historical Fires

This section tests agreement between HFire, FARSITE, and reference fire perimeters when wind, fuels, and terrain vary under actual burning conditions. The 

initial stages of three historical chaparral fires were simulated. The Day Fire burned 

slowly for a month in southern California in 2006. The Simi Fire was part of a complex of fires burning under extreme Santa Ana conditions in southern California in 

late October of 2003. The Calabasas Fire was a short-lived Santa Ana wind-driven 

event. The initial stages of the Day Fire are presented first to demonstrate a relatively simple scenario involving low windspeeds that is intermediate in complexity 

between the synthetic landscapes and the more complex Simi and Calabasas Fires. 

Two types of comparisons are made in this section: model to model, and both 

HFire and FARSITE models to measured perimeters, all at hourly time steps. 

Model-to-model comparisons under realistic burning conditions serve as further 

benchmarks of HFire. Comparisons between modeled and reference perimeters 

build understanding and gain confidence. The accuracy of modeled perimeters 

is limited by the underlying semiempirical/semiphysical nature of the Rothermel equation, the spatial resolution of the landscape variables, and the temporal 

(hourly) and spatial (point) resolution of the wind data. Furthermore, historical fire 

suppression information is often not available or available in a way that is easily 

incorporated into the models. Finally, the accuracy of the reference historical fire 

perimeters differs and may not be the absolute standard needed. Hence, the primary 

benefit of the models vs. reality comparisons lies in developing a general understanding of fire modeling, and defining future directions for model refinement to 

improve model accuracy and predictive power. 

Day Fire—

The Day Fire was reported at 1355 hours on 4 September 2006 and was contained 

on 2 October 2006. It burned 65 871 ha, and cost $73.5 million to suppress. The fire 

initially spread slowly, burning only 5000 ha by 9 September. Major wind-driven 

runs occurred on the 12th, 16th through 19th, 22nd through 24th, and 27th of September. 

The initial stages 

of three historical 

chaparral fires 

were simulated.
Using HFire for Spatial Modeling of Fire in Shrublands

15

Only the first 58 hours of burning (1400 hours 4 September to 2300 hours 6 

September) are simulated as both fire-spread models dramatically overpredict 

initial fire growth, owing to effective fire suppression efforts at the initial stages 

of the actual event. 

The Day Fire burned through a southern California chaparral/coastal sage 

scrub (CSS) mosaic. The state of California Fire and Resource Assessment Program 

(FRAP) map was used to determine fuel models. Two different sets of fuel models 

were used to characterize the vegetation (table 3): the fuel models developed by 

Anderson (1983), formally called the NFFL models; and custom fuel models that 

were specifically developed for chaparral, the Riverside Fire Lab (RFL) fuel models 

(Weise and Regelbrugge 1997). The 1-, 10-, and 100-hour fuel size classes of table 3 

correspond to <1⁄4-, 1⁄4- to 1-, and 1- to 3-in diameter woody material, and are based 

on how quickly dead fuel moisture responds to changes in atmospheric relative 

humidity.

Table 3—Biomass and fuel bed depth for the fuel models used in this study

Fuel biomass

Dead Live

Fuel model Fuel model description 1-hr 10-hr 100-hr Herbaceous Woody Fuel bed depth

- - - - - - - - - - - - - - - - Mg/ha - - - - - - - - - - - - - - - Centimeters

NFFL 1 Grass 1.66 0 0 0 0 30.48

NFFL 2 Savana 4.49 2.25 1.12 0 1.12 30.48

NFFL 4 Shrub 11.25 9.01 4.49 0 11.25 182.88

NFFL 5 Shrub 2.25 1.12 0 0 4.49 60.96

NFFL 6 Shrub 3.37 5.61 4.49 0 0 76.20

NFFL 8 Timber 3.37 2.25 5.61 0 0 6.10

NFFL 10 Timber 6.76 4.49 11.25 0 4.49 30.48

RFL 15 Old chamise 4.48 6.73 2.24 1.12 4.48 91.44

RFL 16 Ceanothus 5.04 10.76 4.04 6.73 6.28 182.88

RFL 18 Sagebrush/buckwheat 12.33 1.79 0.22 1.68 5.6 91.44

FARSITE 99 Unburnable 0 0 0 0 0 0

Size classes are 1-hour (<0.635 cm diameter), 10-hour (0.635-2.54 cm diameter), 100-hour (2.54-7.62 cm diameter).

NFFL= Northern Forest Fire Laboratory.

RFL= Riverside Fire Laboratory.

The 30-m FRAP fuels map uses NFFL fuel models; however, the fuel models 

for shrubs were changed to the RFL chaparral fuel models for this analysis. NFFL 

Fuel Model 4 was converted to RFL 16 (Ceanothus chaparral), NFFL 6 to RFL 15 

(mature chamise chaparral), and NFFL 5 to RFL 18 (CSS). Fuel Models 28, 98, 15, 

and 97, which represent urban, water, desert, and irrigated agriculture, respectively, 

were reclassified to Fuel Model 99, the designated number for unburnable cells. 

Topographic variables were derived from a 30-m U.S. Geological Survey (USGS) 

DEM. Slope and aspect were derived using standard techniques. 
16

GENERAL TECHNICAL REPORT PSW-RP-259 

The weather data were obtained from the Cheeseboro, California, RAWS, 

which is located 48 km south of the final fire extent. The RAWS closer to the fire 

were not used because data were either missing or noisy. The RAWS data consist of 

daily precipitation, maximum/minimum temperature, maximum/minimum humidity, timing of maximum and minimum temperatures (hourly values are interpolated 

by FARSITE), and elevation of the weather station (needed to interpolate weather 

variables across the landscape, using environmental lapse rates). Live fuel moisture 

during the simulation was held constant at a value of 60-percent of ovendry weight 

(ODW) for live herbaceous material and for live woody material. Live fuel moisture 

in chaparral in the fall drops to the annual minimum value, which is on the order of 

60 percent (Countryman and Dean 1979, Roberts et al. 2006).

Accuracy was assessed using a perimeter derived from the MODIS active fire 

product, which uses data from both the Aqua and Terra satellites. It is produced 

four times a day, at 1-km cell resolution. The reference perimeter was generated 

by calculating a convex hull polygon about the set of all active fire cells from the 

MODIS active fire product (current and past) for the Day Fire as of 2300 hours on 

6 September.

Simi Fire—

The Simi Fire burned from October 25 to November 5, 2003, consumed 44 000 ha, 

destroyed 315 structures, and cost approximately $10 million to suppress. It was a 

Santa Ana wind-driven fire, which exhibited rapid westward growth on the 26th of 

October owing to high windspeeds. The first 34 hours of the fire were simulated, 

from 1300 hours on 25 October to 2300 hours on 26 October. The Simi Fire was 

chosen for simulation because it is representative of fires in chaparral, experiencing 

high windspeeds and high rates of spread.

The Simi Fire burned through a southern California chaparral/grassland 

mosaic. The state of California FRAP map was used to determine fuel models as 

described above for the Day Fire. Topographic variables were derived from a 30-m 

USGS DEM; slope and aspect were derived using standard techniques. Weather 

data were obtained from the Cheeseboro, California, RAWS Station, located 8 km 

south of the central portion of the final fire extent. 

Accuracy was assessed using perimeters derived from the MODIS active fire 

product. Convex hull polygons were generated from the set of all active fire cells 

(current and past) for each time step. These polygons were then clipped using the 

official final fire perimeter from the California Department of Forestry and Fire 

Prevention (CDF) to remove the presence of false positives in the MODIS product. 

The Simi Fire 

was chosen for 

simulation because 

it is representative 

of fires in chaparral, 

experiencing high 

windspeeds and high 

rates of spread.
Using HFire for Spatial Modeling of Fire in Shrublands

17

Calabasas Fire—

The 1996 Calabasas Fire burned 5159 ha in the Santa Monica Mountains, California. The Calabasas Fire was chosen for simulation based on the availability 

of hourly perimeter data for the fire, and availability of remote sensing data for 

mapping prefire fuels. The Calabasas Fire was a Santa Ana wind-driven event, 

typical of conditions under which the majority of burning takes place in shrublands 

of southern California (Keeley et al. 1999, Moritz et al. 2004). The fire was actively 

spreading from the time it started along U.S. Highway 101 on October 21, 1996, at 

approximately 1100 hours Pacific Daylight Time until contained on the morning of 

October 22. 

The northern and southern portions of the Calabasas Fire were modeled separately for comparison to the helicopter-based reference perimeters. The northern 

portion of the fire occurred between 1100 and 1500 hours. A second simulation 

period, from 1500 to 2200 hours, was also examined as a spot fire over Malibu 

Canyon Road acted as a point source for a “new” fire.

Historical windspeed, wind direction, and dead fuel moisture data during the 

fire are available on an hourly basis from the Cheeseboro RAWS, located 12 km 

from the fire. Live fuel moisture during the simulation was held constant at a value 

of 60-percent ODW for live herbaceous material and for live woody material. 

Use of the most up-to-date map of fuels for the Santa Monica Mountains is 

inappropriate in a historical reconstruction because the current fuel type in the 

area of the 1996 Calabasas Fire reflects early postfire succession. Instead, a technique was devised to produce a fuels map to reflect the conditions in 1996, prior 

to the arrival of the fire. First, a map of the potential natural vegetation (PNV), 

the ultimate floristic composition an area would attain many years after fire, was 

generated (Franklin 1997). Second, the fire history of the Santa Monica Mountains 

was retabulated to reflect the age of each cell prior to the arrival of the Calabasas 

Fire. Finally, tables of successional pathways, referred to as regrowth files (.rgr), 

were used to cross reference each chaparral PNV type with age to yield a fuel type. 

The regrowth files included custom chaparral fuel models (Weise and Regelbrugge 

1997) and were used to make maps showing custom fuels. Additionally, a custom 

fuel model for describing wildland-urban interface (WUI) was developed by 

combining the fuel loadings in the NFFL grass and southern rough fuel models. 

Terrain elevation for the entire domain is available at 10 m spatial resolution. 

Since the spatial resolution of the fuels data is no better than 30 m, the elevation 

data were resampled from 10 to 30 m using bilinear interpolation prior to calculating slope and aspect at that resolution. 
18

GENERAL TECHNICAL REPORT PSW-RP-259 

At 1-hour intervals during the course of the fire, a helicopter equipped with a 

global positioning system (GPS) receiver was used to map the location of the leading edge of the fire. These data serve as the historical record of fire spread to which 

the HFire and FARSITE simulations are referenced. The effects of suppression are 

unaccounted for in the simulations and therefore represent a potential source of 

error in comparing modeled and actual fire behavior. Suppression of the heading 

portion of the fire was largely unsuccessful during the first 4 hours of the fire, but 

suppression along the flanks of the fire during this time did have some effect.

Run Time Efficiency 

Run time efficiency is an important attribute of a fire-spread model, both for 

the simulation of individual fires and simulations of long-term fire regimes. The 

run-time performance of HFire was evaluated relative to FARSITE for each of the 

historical fire simulations described in this paper. All of the simulations used in the 

timing analysis were performed on a personal computer with an Intel Core2 Duo 

dual-core processor, 2 gigabytes of RAM, and running the Windows XP 32-bit 

operating system.5 Care was taken to ensure that the simulation was the only active 

task not associated with the operating system on the computer.

Results

Synthetic Landscape Tests

For all of the figures in this section, FARSITE perimeters are represented as black 

lines and HFire perimeters as colors representing regular intervals of fire progression. Sørensen metric values, quantitatively comparing HFire and FARSITE burned 

area at the final time step (Sf) for each model run, are included on the figures. 

Test of different windspeeds—

The results of this test are presented in figures 1 and 2. As expected, as windspeed 

increases, the fires become larger, and the length-to-width ratio decreases (fig. 1). 

The one-dimensional, forward rate of spread is identical in all cases for HFire and 

FARSITE, the difference is in the flanking rate of spread and the resulting twodimensional shape. FARSITE produces a rounded fire front, whereas HFire exhibits 

a triangular leading edge. Here, the increasingly sharp triangular edge corresponds 

to an increasingly stretched vertex of the eight-sided fire perimeter with increasing 

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

imply endorsement by the U.S. Department of Agriculture of any product or service.
Using HFire for Spatial Modeling of Fire in Shrublands

19

Figure 1—A test of varying 

windspeeds on flat terrain, 

showing HFire (colors) and 

FARSITE (lines) perimeters for 

(a) 5-m/s, (b) 10-m/s, (c) 15-m/s, 

and (d) 20-m/s winds; the lengthto-width ratio of the ellipses 

increases as windspeed increases; 

HFire shown for ellipse adjustment factors (EAFs) (k in eqn. 2) 

of 1.0, 0.66, 0.5, 0.4, and 0.33.

1 0.66 0.5 0.4 0.33

EAF

a

b

d

c

Sf = 0.545 0.726 0.841 0.881 0.868

Sf = 0.493 0.711 0.785 0.800 0.784

Sf = 0.505 0.704 0.766 0.758 0.718

Sf = 0.487 0.694 0.756 0.738 0.686
20

GENERAL TECHNICAL REPORT PSW-RP-259 

windspeed. The back edge of the perimeter corresponds to the remaining six sides 

of the eight-sided figure, and has flat edges, although it appears rounded because 

they are close together.

To minimize the difference between HFire and FARSITE results, we ran HFire 

with five values of EAF. Setting EAF to 1.0 corresponds to no adjustment; values 

less than 1.0 decrease the length-to-width ratio, increasing the flanking rate of 

spread (eqn. 2). An EAF of 0.4 maximized the Sørensen metric between HFire and 

FARSITE at lower windspeeds. An EAF setting of 0.5 maximized the metric at 

higher windspeeds. 

Figure 2 illustrates the special case of 0-m/s winds, in which the fire spreads in 

a circular pattern. Both HFire and FARSITE accurately capture the expected onedimensional Rothermel rate of spread. For FARSITE, the modeled shape is a circle. 

The HFire algorithm approximates the circular shape with an octagon. 

Sf = 0.979

Figure 2—Null windspeed test on flat terrain, showing HFire (colors) and 

FARSITE (lines) perimeters for 0 m/s winds; the fire is circular for FARSITE 

and octagonal for HFire.

Test of time varying wind direction—

Figure 3 shows that varying the wind inputs leads to HFire and FARSITE perimeters having closer agreement. Comparing the results of wind azimuth scenario 

1 (fig. 3b) with those from the constant azimuth case (fig. 3a) shows that perturbing the wind direction slightly (a maximum of ±10 degrees) widens the fire front 

noticeably, eliciting better agreement with the FARSITE perimeters. Wind azimuth 
Using HFire for Spatial Modeling of Fire in Shrublands

21

a

b

d

c

1 0.66 0.5 0.4 0.33

EAF

e

f

Sf = 0.545 0.726 0.841 0.881 0.868

Sf = 0.577 0.760 0.869 0.901 0.884

Sf = 0.647 0.801 0.899 0.929 0.910

Sf = 0.695 0.822 0.906 0.939 0.925

Sf = 0.761 0.848 0.918 0.947 0.942

Sf = 0.614 0.758 0.870 0.942 0.945

Figure 3—A test of differing 

azimuth scenarios for 5-m/s 

winds, showing HFire (colors) and FARSITE (lines) 

perimeters for (a) constant 

azimuth, (b) azimuth 

scenario 1, (c) scenario 2, 

(d) scenario 3, (e) scenario 4, 

(f) scenario 5; there is better 

agreement between HFireand FARSITE-modeled fire 

shapes as perturbations of 

the azimuth increase. HFire 

shown for ellipse adjustment 

factors (EAFs) of 1.0, 0.66, 

0.5, 0.4, and 0.33.
22

GENERAL TECHNICAL REPORT PSW-RP-259 

scenarios 2 and 3, which perturb the wind direction a greater amount, resulted 

in a smooth, nontriangular fire front for HFire (fig. 3c and 3d). Hence, agreement 

between HFire and FARSITE improved, with Sørensen metric values above 0.9. 

Scenario 4 systematically perturbed the wind azimuth ±45 degrees about 180 

degrees, leading to symmetric fire perimeters at the end of the simulation for both 

models, and a Sørensen metric value of 0.947 for an EAF of 0.4. Likewise, perturbing the wind ±180 degrees leads to symmetric shapes for both models, with a high 

Sørensen metric value of 0.942 (fig. 3f). 

Test of different windspeeds and slopes, with up-slope winds—

Starting from the case of zero windspeed and zero slope, increasing windspeed has 

a greater effect on forward rate of spread than does increasing the slope by approximately a factor of two (fig. 4). Steepening the slope has a large effect on forward 

rate of spread at low windspeeds, but the effect at higher windspeeds is reduced. In 

all cases, forward rate of spread is comparable between HFire and FARSITE, with 

FARSITE exhibiting greater spread on the flanks of the fire. 

Test of different slopes and cross-slope winds—

This test shows the largest difference between FARSITE and HFire perimeters as 

measured by the Sørensen metric. Differences arise because of the vector/eight 

nearest neighbor raster differences in the models. As the slope becomes steeper, the 

direction of fire propagation smoothly rotates from 90 degrees to approximately 60 

degrees in the FARSITE simulations (fig. 5). HFire suffers from some distortion 

when the direction of fire spread is not aligned with one of the eight cardinal directions of the underlying lattice--the angles to the eight adjacent pixels. For the 0-, 

20-, and 40-percent model runs, the true direction of fire propagation was approximately 90 degrees, so the HFire modeled perimeters are reasonable. For the 60- and 

80-percent slope runs, HFire modeled the true direction of spread of approximately 

75 degrees as a mixture of spread at 45 and 90 degrees. For the 100-percent slope, 

HFire modeled the true direction of spread (approximately 60 degrees) as propagating toward 45 degrees. Hence, agreement between modeled fire shapes is relatively 

poor (Sørensen metric values less than 0.8) for the 60-, 80-, and 100-percent slope 

comparisons. However, as demonstrated in the test of time varying wind direction, 

perturbing the wind azimuth (±20 degrees about 270 degrees) results in a more 

rounded fire front, leading to much closer agreement between the predicted fire 

shapes. The Sørensen metric values at the end of the simulation for the 60-, 80-, 

and 100-percent slope cases, where disagreement between FARSITE and HFire is 

highest, are 0.785, 0.718, and 0.669 for the constant 270 azimuth case but increase to 

0.904, 0.909, and 0.848 for the 270 ± 20 azimuth case. 

Increasing windspeed 

has a greater effect on 

forward rate of spread 

than does increasing 

the slope.
Using HFire for Spatial Modeling of Fire in Shrublands

23

Figure 4—A test of differing windspeed and slope, with up-slope winds, showing HFire (colors) and FARSITE (lines) 

perimeters. The length-to-width ratio of the ellipses increases as windspeed and slope steepness increase.

0 20 40 60 80 100

Slope (percent)

Win

d

s

p

e

ed (m/s)

0

2.5

5

7.5

0.741 0.800 0.915 0.891 0.836 0.786

0.869 0.874 0.879 0.857 0.814 0.784

0.848 0.838 0.845 0.823 0.785 0.768

Sf = 0.818 0.802 0.813 0.787 0.766 0.759

Sf =

Sf =

Sf =
24

GENERAL TECHNICAL REPORT PSW-RP-259 

Test of different fuel model transitions—

The case involving homogeneous fuels exhibits the expected pattern of equivalent 

forward rate of spread, with FARSITE producing a wider fire front (fig. 6a). In 

the case involving the unburnable block, the fire perimeters for both models are 

unchanged, except for in the block (fig. 6b). The case with the slower burning 

block shows, once again, that more heterogeneous conditions lead to a closer 

match between HFire and FARSITE. For the EAF of 0.4 model run, the flanking fire spread for HFire on the left side of the fire (where two different fuels are 

encountered) is less than 1 hour behind FARSITE, whereas on the right flank, it 

is more than 1 hour behind (fig. 6c). The scenario where a faster burning block of 

fuel is encountered exhibited the strongest agreement. Unlike the cases involving 

the unburnable and slow-burning blocks, agreement in fire spread on both flanks 

of the fire improved upon encountering the different block of fuels, and final 

Sørensen metric values were greater than 0.9. Sørensen metric values were lower 

for the other three scenarios owning to the triangular fire front.

0 20 40 60 80 100

Slope (percent)

Win

d

a

zim

uth

2

7

0 ±20

2

7

0

Sf = 0.828 0.843 0.844 0.785 0.718 0.669

Sf = 0.834 0.851 0.879 0.904 0.909 0.848

Figure 5—A test of 7.5-m/s windspeed, varying slope, and wind azimuth, with cross-slope winds, showing HFire (colors) and 

FARSITE (lines) perimeters. This test reveals raster-based limitations of HFire fire spread when the direction of spread is not in 

a cardinal direction; this effect is mitigated when wind azimuth is perturbed.
Using HFire for Spatial Modeling of Fire in Shrublands

25

a

b

d

c

EAF 1 EAF 0.66 EAF 0.5 EAF 0.4 EAF 0.33

Sf = 0.514 0.718 0.826 0.840 0.829

Sf = 0.553 0.767 0.877 0.854 0.812

Sf = 0.529 0.739 0.851 0.845 0.817

Sf = 0.763 0.899 0.959 0.949 0.920

Figure 6—A test of different blocks of fuels with 7-m/s winds, showing HFire (colors) and FARSITE (lines) perimeters for four fuel 

model (FM) maps: (a) uniform FM 15, (b) FM 15 plus unburnable, (c) FM 15 plus slower burning, (d) FM 15 plus faster burning. 

Increased heterogeneity in fuels leads to better agreement between HFire- and FARSITE-modeled perimeters. HFire shown for ellipse 

adjustment factors (EAFs) of 1.0, 0.66, 0.5, 0.4, and 0.33.
26

GENERAL TECHNICAL REPORT PSW-RP-259 

Historical Fires

Day Fire results—

Figure 7 shows FARSITE and HFire (EAF of 0.5, 0.66, 0.9) perimeters for the 

Day Fire from 4 July 1500 hours to 6 July 2300 hours. The modeled fires were all 

roughly circular, with the EAF 0.5 fire being largest and the EAF 0.9 fire being 

smallest. The effect of altering EAF clearly has a greater effect on fire size than 

fire shape in heterogeneous conditions. Sørensen metric values between HFire- and 

FARSITE-modeled perimeters were highest for the EAF 0.66 model run, with 

values generally above 0.9 for the first 2 days of burning, and above 0.8 on the 3rd

day. Complete Sørensen metric values are available in table 4.

a

c d

b

N

Figure 7—Simulated perimeters for the Day Fire; HFire shown for ellipse adjustment factors (EAFs) of (a) 0.5, (b) 0.66, (c) 0.9, 

and (d) FARSITE. The legend refers to fire perimeters at a given time, with time in DDHHMM format. Low windspeeds and a 

diurnal wind pattern lead to roughly circular fire shapes. HFire run with an EAF of 0.66 shows the best agreement with FARSITE 

perimeters; associated Sørensen metric scores are listed in table 4.
Using HFire for Spatial Modeling of Fire in Shrublands

27

Table 4—Sørensen metric values for HFire (EAF set to 0.5, 0.66, and 0.9) and FARSITE for the Day Fire

EAF 0.5 EAF 0.66 EAF 0.9

Time Sørensen Time Sørensen Time Sørensen Time Sørensen Time Sørensen Time Sørensen

41500 0.819 51900 0.835 41500 0.774 51900 0.904 41500 0.632 51900 0.772

41600 0.922 52000 0.829 41600 0.919 52000 0.911 41600 0.827 52000 0.787 

41700 0.898 52100 0.824 41700 0.899 52100 0.913 41700 0.792 52100 0.800

41800 0.875 52200 0.821 41800 0.877 52200 0.913 41800 0.725 52200 0.807

41900 0.889 52300 0.819 41900 0.907 52300 0.914 41900 0.729 52300 0.817

42000 0.902 60000 0.814 42000 0.915 60000 0.911 42000 0.732 60000 0.823

42100 0.918 60100 0.806 42100 0.94 60100 0.906 42100 0.777 60100 0.832

42200 0.92 60200 0.798 42200 0.959 60200 0.902 42200 0.813 60200 0.841

42300 0.914 60300 0.784 42300 0.965 60300 0.893 42300 0.833 60300 0.849

50000 0.905 60400 0.765 50000 0.966 60400 0.881 50000 0.853 60400 0.856

50100 0.898 60500 0.745 50100 0.962 60500 0.862 50100 0.861 60500 0.858

50200 0.89 60600 0.73 50200 0.96 60600 0.847 50200 0.859 60600 0.855

50300 0.878 60700 0.72 50300 0.962 60700 0.838 50300 0.853 60700 0.851

50400 0.876 60800 0.72 50400 0.958 60800 0.838 50400 0.849 60800 0.85

50500 0.876 60900 0.723 50500 0.959 60900 0.839 50500 0.859 60900 0.848

50600 0.864 61000 0.728 50600 0.957 61000 0.841 50600 0.869 61000 0.847

50700 0.857 61100 0.737 50700 0.957 61100 0.846 50700 0.868 61100 0.847

50800 0.855 61200 0.746 50800 0.96 61200 0.853 50800 0.865 61200 0.853

50900 0.847 61300 0.75 50900 0.949 61300 0.855 50900 0.859 61300 0.854

51000 0.838 61400 0.754 51000 0.937 61400 0.859 51000 0.855 61400 0.854

51100 0.835 61500 0.761 51100 0.925 61500 0.864 51100 0.832 61500 0.854

51200 0.839 61600 0.76 51200 0.911 61600 0.869 51200 0.809 61600 0.861

51300 0.846 61700 0.757 51300 0.904 61700 0.872 51300 0.789 61700 0.867

51400 0.85 61800 0.753 51400 0.898 61800 0.873 51400 0.779 61800 0.872

51500 0.845 61900 0.751 51500 0.899 61900 0.872 51500 0.779 61900 0.874

51600 0.843 62000 0.748 51600 0.894 62000 0.871 51600 0.776 62000 0.874

51700 0.839 62100 0.745 51700 0.89 62100 0.87 51700 0.767 62100 0.875

51800 0.84 62200 0.742 51800 0.892 62200 0.869 51800 0.763 62200 0.875

— — 62300 0.739 — — 62300 0.868 — — 62300 0.875

The EAF 0.66 model run shows the highest agreement with FARSITE, with Sørensen values on the order of 0.9.

Time in DHHHH format.

EAF = ellipse adjustment factor.

These simulations of the Day Fire demonstrate that HFire and FARSITE 

produce similar fire perimeters under low wind conditions. Low wind conditions 

during the early portion of the fire were amenable to successful fire suppression 

efforts, and the fire was actively suppressed. Because of the suppression, modeled 

HFire and FARSITE perimeters are approximately five times the size of a MODIS 

active fire product-derived reference perimeter for the same time step (fig. 8).
28

GENERAL TECHNICAL REPORT PSW-RP-259 

Figure 8—Day Fire perimeters at 2300 hours on 6 September: Hfire (white), 

FARSITE (black), MODIS (red). The green color represents available fuels, 

and the black color represents unburnable areas. The discrepancy in fire size 

between the modeled fires and the actual fire is attributable to fire suppression.

N

Simi Fire results—

Figure 9 shows HFire and FARSITE perimeters for the Simi Fire from 1400 hours 

on 25 October to 2300 hours on 26 October. HFire is shown for an EAF of 0.66, 

which provided the highest overall agreement. The shapes of initial fire progression to the southwest are very similar, with forward rate of spread slightly faster 

for FARSITE. The flanking rate of spread was slightly faster for HFire. The HFire 

simulation reached the western edge of Simi Valley (“b” on fig. 9) at 0900 hours on 

26 October, whereas the FARSITE simulation reaches the same landmark at 1200 

hours. Other features of note include the expansion of HFire perimeters into areas 

that FARSITE did not burn, to the north and to the west (marked a and b on fig. 9). 

HFire was better able to utilize narrow corridors to reach additional areas of fuel. 

FARSITE was run with a perimeter resolution of 99 m. A finer resolution may have 

allowed FARSITE to navigate these corridors; however, finer resolution results in 

very long model run times for FARSITE (on the order of 3 to 7 days) and the finest 

resolution that the model was successfully run at in prior research for the Simi Fire 

was 59 m (Peterson et al. 2005). This is twice the resolution at which HFire was 

run, 30 m, which is the native resolution of the landscape variables. Fire spread 

in the south-central portion of the fire (marked c on fig. 8) further illustrates this 

point. Both HFire and FARSITE show fire just north of point c at 1700 hours on 

25 October. HFire propagated fire to the southwest during the next hour, whereas 

FARSITE required 5 hours to get through the corridor. This has implications for 
Using HFire for Spatial Modeling of Fire in Shrublands

29

a

c

HFire

FARSITE

b

d

N

Figure 9—Simulated perimeters for the Simi Fire for HFire (EAF 0.66) and FARSITE. The legend refers to fire perimeters at a given 

time, with time in DDHHMM format. Sørensen metric scores are listed in table 5. FARSITE propagates the fire slightly faster in the 

forward-spread direction, whereas HFire is faster in the flanking direction; additionally, HFire is better able to navigate narrow fuel 

corridors, fire spread at point a and b is only present in the HFire perimeters, and fire spread at c and d occurs earlier in the HFire 

simulations.

fires in the WUI where narrow corridors may be common. Despite these areas of 

disagreement, Sørensen metric values were again high, generally on the order of 

0.85 to 0.9, because of the large area in the main body of the fire, which overlaps for 

the two models. Complete Sørensen metric values are available in table 5.

Figure 10 shows perimeters derived from HFire, FARSITE, and MODIS: 2300 

hours on 25 October for the models and 2233 hours on 25 October for MODIS, 

and 1200 hours on 26 October for the models and 1209 hours on 26 October for 

MODIS. For the first comparison, the HFire and FARSITE perimeters were nearly 
30

GENERAL TECHNICAL REPORT PSW-RP-259 

Table 5—Sørensen metric values for 

HFire (EAFa set to 0.66) and FARSITE for 

the Simi Fireb

Timec Sørensen Time Sørensen

251400 0.714 260700 0.854

251500 0.769 260800 0.852

251600 0.827 260900 0.845

251700 0.926 261000 0.847

251800 0.944 261100 0.84

251900 0.924 261200 0.838

252000 0.905 261300 0.837

252100 0.898 261400 0.842

252200 0.901 261500 0.846

252300 0.915 261600 0.851

260000 0.915 261700 0.856

260100 0.915 261800 0.859

260200 0.917 261900 0.862

260300 0.904 262000 0.864

260400 0.899 262100 0.865

260500 0.888 262200 0.865

260600 0.860 262300 0.866

a

EAF = ellipse adjustment factor. 

b

Accuracy is lower at the beginning and end of 

the model runs, at the beginning FARSITE is 

propagating the fire more quickly, at the end the 

HFIRE modeled fire is larger as it is better able to 

negotiate narrow fuel isthmuses.

c Time in DDHHHH format. 

identical on the east and west flanks of the fire. However, HFire 

exhibited greater spread to the southwest. Both modeled perimeters 

agreed well with MODIS (Sørensen metric values on the order of 

0.75). The value for HFire was slightly lower because of overburning to the southwest. Fire suppression during the Simi Fire is 

only anecdotally documented, but as mentioned in the previous 

paragraph, the area of overburning by HFIRE at point c is separated 

from the main body of the landscape by a narrow corridor, so fire 

suppression efforts could have been focused on the small area, 

enhancing success. Additionally, MODIS resolution is coarse at 1 

km, so the precision of the MODIS shape is uncertain.

For the second comparison, the modeled fires and the actual 

fire have reached the farthest western extent of the Simi Fire. HFire 

overburned farther to the west, whereas FARSITE was not able to 

negotiate the narrow fuel corridors to the west. Both modeled fires 

also overburn to the south and the southeast. This overburning of 

modeled fires relative to the MODIS perimeter likely reflects the 

presence of active fire suppression. Again, anecdotal information 

suggests that fire suppression was active to the south owing to the 

presence of the Ronald Reagan Presidential Library and other areas 

of high-value real estate. Sørensen metric values are lower for this 

comparison, owing to overburning.

Calabasas Fire results—

Figure 11 shows the fire perimeters for HFire (EAF 0.66) and FARSITE for the 

single-ignition case, with the fire igniting at 1100 hours and burning until 2200 

hours. As for the Day and Simi Fires, agreement was highest for the 0.66 EAF case, 

and only EAF of 0.66 results are presented. The FARSITE simulation reaches the 

southern boundary approximately 1 hour sooner than HFire, but, in general, the 

shape and size of the fires are very similar. Sørensen metric values were on the 

order of 0.8 to 0.9. 

However, comparing figures 11 and 12 reveals that agreement between the 

actual perimeters (fig. 12) and perimeters from both models (fig. 11) is poor. This is 

likely due to effective fire suppression efforts. The actual fire was much narrower 

during the initial 1100- to 1500-hours burning period, and was nearly controlled, 

before it spotted over Malibu Canyon road, igniting the second stage of the fire. 

Because of the compounding errors owing to not accounting for fire suppression, 

HFire and FARSITE were rerun, treating the northern and southern halves of the 

fire separately.
Using HFire for Spatial Modeling of Fire in Shrublands

31

Time Sørensen Comparison

252300 0.762 MODIS/Hfire

252300 0.780 MODIS/Farsite

261200 0.445 MODIS/Hfire

261200 0.566 MODIS/Farsite

25 2300

26 1200

N

Figure 10—Simi Fire perimeters: HFire (white), FARSITE (black), and MODIS reference (red), for 2 hours of the Simi Fire, 

2300 hours 25 October and 1200 hours 26 October. Times are in DDHHMM format. The green color represents available 

fuels, and the black color represents unburnable areas. Agreement is good for the first comparison; agreement for the second 

comparison is hindered because the actual fire was actively suppressed.
32

GENERAL TECHNICAL REPORT PSW-RP-259 

Figure 11—Simulated perimeters for the Calabasas Fire for (a) HFire (EAF 0.66) and (b) FARSITE. The legend refers to fire perimeters 

at a given time, with time in DDHHMM format. Sørensen metric scores are included. Agreement is high throughout the simulation 

period.

N

Unburnable

UUnburned nburned

10/21 1100

10/21 1200

10/21 1300

10/21 1400

10/21 1500

10/21 1600

10/21 1700

10/21 1800

10/21 2100

10/21 2200

Unburnable

Figure 12—Fire perimeters for the Calabasas Fire determined by helicopter reconnaissance. 

The pinched shape at 1500 hours is due to successful fire suppression efforts, which were nearly 

successful until the fire spotted over containment lines between 1500 and 1600 hours. The legend 

refers to fire perimeters at a given time, with time in MonthMonth/DD HHMM format.

a b Time Sørensen

211200 0.832

211300 0.858

211400 0.875

211500 0.840

211600 0.865

211700 0.880

211800 0.888

211900 0.903

212000 0.905

212100 0.919

212200 0.936

N

Unburned

211200

211300

211400

211600

211700

211800

211900

212000

212100

212200

Unburnable

Time

211200

211300

211400

211500

211600

211700

211800

211900

212000

212100

212200

Sørenson

0.832

0.858

0.875

0.840

0.865

0.880

0.888

0.903

0.905

0.919

0.936
Using HFire for Spatial Modeling of Fire in Shrublands

33

Figure 13 shows HFire, FARSITE, and actual perimeters at two times following the initial ignition at 1100 hours and two times following the spot fire ignition 

at 1500 hours. At 1300 and 1500 hours, both the azimuth and size of the modeled 

and actual fires differ. In contrast, modeled fire perimeters at the two later times, 

associated with the spot fire ignition, exhibit better agreement with the actual fire 

in both direction and magnitude of fire spread. Both the actual and modeled fires 

reached the southern end of the landscape (the Pacific Ocean) within the same hour. 

The modeled fires are narrower than the actual fire at 1800 hours but are on the 

same order of magnitude at 2200 hours. Sørensen metric values between HFire and 

the actual fire are also much higher at 1800 and 2200 hours than at 1300 and 1500 

hours, on the order of 0.7 vs. 0.2.

a, 1300 b, 1500

c, 1800 d, 2200

N

Time HFire FARSITE

211200 0.140 0.121

211300 0.211 0.199

211400 0.229 0.227

211500 0.298 0.282

 Sørensen

Time HFire FARSITE

211600 0.505 0.597

211700 0.513 0.524

211800 0.548 0.529

211900 0.764 0.742

212000 0.709 0.758

212100 0.750 0.799

212200 0.742 0.810

Sørensen

Figure 13—Calabasas Fire perimeters: HFire (white), FARSITE (black), and helicopter reference (red), for the initial ignition and the 

spot fire ignition. The green color represents available fuels, and the black color represents unburnable areas. The 1300- and 1500-hour 

perimeters result from the initial ignition at 1200 hours; the 1800- and 2200-hour perimeters result from the spot fire ignition at 1500 

hours, times are in DDHHMM format. Sørensen metric scores are included. The first set of simulations show poor agreement with reality because the wind azimuth recorded at the Cheeseboro remote automated weather station (RAWS) was not representative of the winds 

affecting the fire; agreement was better during the second simulation period.
34

GENERAL TECHNICAL REPORT PSW-RP-259 

Run Time Efficiency 

The wall clock times required for the simulation of 58 hours of the Day Fire, 35 

hours of the Simi Fire, and 12 hours of the Calabasas Fire were recorded. All FARSITE simulations were performed with perimeter and distance resolution set to 99 

m. Resolution values closer to the native resolution (30 m) of the input terrain and 

fuels significantly increase the run time without a substantial increase in accuracy 

(Peterson et al. 2005). FARSITE took 2.3 times as long as HFire (6.33 min) to 

complete the simulation of the Day Fire (14.83 min). The relatively small difference 

can be attributed to the relatively homogeneous landscape and low wind conditions 

used as inputs to these simulations. The Calabasas Fire was more complex, involving varying terrain and fuels and higher windspeeds. HFire (1.1 min) completed the 

simulation in approximately one-eighth the time for FARSITE (8.75 min). The Simi 

Fire was the most complex simulation, covering the largest area. HFire (6.1 min) 

completed the simulation approximately 162 times faster than FARSITE (16.5 h).

Figure 14 illustrates model run times for each hour of the Simi Fire with 

cumulative area burned (x-axis) plotted versus HFire and FARSITE run times on 

separate y-axes. The trend for HFire is approximately linear, which implies that the 

run time is proportional to the number of ignited cells. The trend for FARSITE is 

more complex. It is approximately linear from the time of ignition until 30 000 ha 

burned, which occurred at 200 hours on 26 October. During this initial period, the 

fire shape was relatively simple (fig. 9). The period from 400 to 1300 hours on 26 

October exhibits the steepest slope (longest model run time in comparison to the 

net area burned). During this period, the perimeter length and complexity increased 

relative to the area burned as the fire expanded to the south and southeast (points 

c and d on fig. 9). The increased perimeter length leads to longer calculation times 

because more vertices are added to the perimeter to meet the specified perimeter 

resolution. The inset on the main graph of figure 14, a log-log plot of run time vs. 

area burned, emphasizes these findings. 

Discussion

Predictions from HFire were similar to those obtained from FARSITE for a standard set of benchmarks developed by Finney (1998) for the testing of the FARSITE 

model. Although the predictions from HFire and FARSITE for the benchmarks 

are virtually identical in the direction of the maximum rate of fire spread, there 

are differences between the models in their predicted shapes, and hence for fire 

spread along the flanks. Similar shapes are shown in French et al. (1990) and Ball 

and Guertin (1992), and are inherent to eight-nearest-neighbors raster fire-spread 

Run time is 

proportional to 

the number of 

ignited cells.
Using HFire for Spatial Modeling of Fire in Shrublands

35

Figure 14—Model run times for the Simi Fire for HFire and FARSITE, on separate axes. HFire shows a consistent relationship between 

fire size and model run time throughout the 6-minute burn time. The model run time is 16.5 hours for FARSITE, with run time for a 

particular hourly time step being dependent on the fire shape. Inset is a log-log plot of run time with HFire and FARSITE run times on 

the same axis to emphasize differences.

0

1

2

3

4

5

6

7

0 10 000 20 000 30 000 40 000 50 000 60 000 70 000 80 000

0

100

200

300

400

500

600

700

800

900

1000

1100

HFire

FARSITE

-1.0

-0.5

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

2 2

Log HFire

Log FARSITE

Modeled burned area (ha)

HFir

e

m

o

del run ti

m

e (min)

FARSITE

model run ti

m

e (min)

Log of model run time (min)

Log of modeled burned area (ha)

.5 3 3 5 4 .5 5

models. There are raster models that better approximate an elliptical fire shape, 

such as FlamMap (Finney 2006) and the Finney minimum travel time model 

(Finney 2002). However, although both models allow for a heterogeneous landscape, weather conditions are held constant. The constant weather simplifies the 

fire-spread calculations, so a large neighborhood of pixels can be used to populate 

the available angles in equation (3) (as opposed to multiples of 45 degrees), and 

an elliptical shape is better realized. Owing to the constant weather requirement, 

neither model is used to simulate actual fires.

The differences in shape were reduced for the more complex benchmark tests, 

which are closer to conditions that could occur during an actual fire. In figure 3, 

Sørensen metric values are higher for the more varying wind scenarios (d, e, and f). 

In figure 5, varying the wind azimuth by ±20 degrees increased agreement between 

FARSITE- and HFire-modeled shapes dramatically for the steeper slope scenarios. 

In figure 6, it can be seen the models respond similarly to transitions to different 

fuel types. 
36

GENERAL TECHNICAL REPORT PSW-RP-259 

Similarly, the pointed shape that is observed in some of the predictions from 

HFire for the benchmarks on homogeneous landscapes is not apparent in the 

simulations of historical fires. For instance, both FARSITE and HFire modeled 

the Day Fire as having a generally circular shape, owing to low windspeeds and 

alternating wind directions during the simulation period (fig. 7). Lower windspeeds 

favor more circular fires (fig. 1 and 2) and from 1400 hours on 4 September to 2300 

hours on 6 September, windspeeds were greater than 5 m/s only 7 of 58 hours, the 

maximum windspeed was 6.7 m/s, and the median windspeed was 3.1 m/s. Additionally, because the wind alternates in a typical diurnal pattern between easterly 

in the mornings and westerly in the afternoons, wind did not have a net directional 

effect on fire spread. This is similar to the time varying wind direction test, where 

alternating wind conditions in Wind Azimuth Scenario 5 lead to an oval fire shape. 

HFire and FARSITE produced generally similar fire perimeters in simulations 

of the Simi Fire, although HFire is better able to negotiate narrow fuel corridors in 

the terrain, which led to extended fire perimeters to the north and west, and earlier 

expansion to the south. The general location of the modeled fire fronts with respect 

to the reference data was good, although the fire-spread models, which do not 

include information about fire suppression, tend to overpredict areas of fire spread. 

Additionally, for the Simi and Day Fires, there is a disconnect between the spatial 

resolution of the model (30 m) and MODIS reference data (1 km). Figure 10 shows 

that the MODIS-based perimeters are more angular. However, the differences 

between modeled and reference perimeters involve large areas, not subtle differences at the edges owing to resolution, so resolution is less of an issue. 

Simulations of the Calabasas Fire again demonstrate that HFire and FARSITE 

produce similar fire perimeters, and that correspondence between modeled and 

actual fire perimeters is affected by active fire suppression. Additionally, the wind 

data appear to have an effect on accuracy with respect to the reference perimeters, 

as the modeled direction of fire spread differed from the actual direction. The 

Cheeseboro RAWS is located 6 km northwest of the initial ignition point of the fire. 

Wind data from the Malibu RAWS, which is located 10 km south-southeast of the 

initial ignition point, were also examined but contained periods of winds blowing 

from the south, so predictions showed less agreement with the historical perimeters. 

The Santa Monica Mountains have complex topography, so it is plausible that 

the winds are subject to topographic steering, and only a RAWS within the 

same canyon as a fire would provide accurate wind azimuth data. An alternate 

explanation is that as RAWS “hourly” wind data are not actually hourly averages, 

but rather the average of the wind conditions 5 minutes prior to the reading, the 

data could be biased. 

Correspondence 

between modeled and 

actual fire perimeters 

is affected by active 

fire suppression.
Using HFire for Spatial Modeling of Fire in Shrublands

37

It is important to note that the 0.66 EAF model run led to the best agreement 

between HFire and FARSITE for all three historical fires. This differs from the 

synthetic landscape cases where EAF values of 0.4 and 0.5 were best (an EAF value 

closer to zero was needed to widen the fire shape in the homogeneous cases). The 

tests of time varying wind azimuth and different fuel model transitions demonstrated that HFire shows better agreement with FARSITE under shifting conditions. 

In actual fire conditions, where landscape and wind are varying simultaneously, the 

combined effect is to reduce the need for the EAF (a value closer to 1.0 is used). 

The tests on synthetic landscapes and historical fires demonstrate that the raster 

and vector implementations of the Rothermel equation perform similarly. Further, 

the agreement between HFire and FARSITE perimeters for all three historical fires 

is qualitatively comparable to the agreement shown between the raster and vector 

implementations of the Canadian fire-spread model in figures 13 and 14 of Yassemi 

et al. (2008). However, there were some systematic discrepancies when comparisons 

were made to reference perimeters. Finney (1998) noted three main problems when 

simulating actual fires: (1) the model input data (both fuels and weather) may contain errors, (2) the resolution (both spatial and temporal) of the input data is not fine 

enough to account for natural variability, and (3) validation is hindered by errors 

associated with the reference perimeters. To this list we would add the difficulty in 

acquiring fire suppression information and incorporating it into models. Nevertheless, comparisons for the Simi Fire and the spot fire of the Calabasas Fire show that 

fire-spread models do have the potential to accurately predict fire-spread rates. 

Similar to other raster models, the performance of HFire is proportional to the 

number of ignited cells and the rate of spread of the fastest burning cell. In contrast, 

FARSITE model performance is a function of the user-specified simulation 

resolution, the heterogeneity of the conditions through which the fire is burning 

(highly heterogeneous conditions increase the number of sub-time steps in a time 

step), and the amount and complexity of the fire perimeter crossovers, mergers, and 

islands to be resolved during the fire perimeter generation process. The effect of 

amount of crossovers to resolve can be seen for the Simi Fire. Differences in run 

time between HFire and FARSITE for the Simi Fire at the fourth time step are of 

the same order of magnitude as for the Calabasas Fire: HFire burned 10 000 ha in 

less than 1 minute, FARSITE in just under 10 minutes. The difference in run time 

between HFire and FARSITE for the Simi Fire became accentuated as the fire grew 

larger (fig. 14).

The tests on synthetic 

landscapes and 

historical fires 

demonstrate that 

the raster and vector 

implementations of the 

Rothermel equation 

perform similarly. 
38

GENERAL TECHNICAL REPORT PSW-RP-259 

Conclusions

To evaluate performance and improve understanding of optimal parameterization, 

we compared HFire to FARSITE over a series of synthetic landscapes with varying 

conditions and for three historical fires. In the synthetic landscape comparisons, 

HFire showed good agreement with FARSITE in the heading direction. Additionally, HFire- and FARSITE-predicted fire shapes showed good agreement when 

burning conditions were more complex. The two models also performed similarly 

in the historical fires tests, with Sørensen metric values at the final timestep of 

0.868, 0.866, and 0.936 for the Day, Simi, and Calabasas Fires, respectively. 

 HFire represents an attractive alternative to FARSITE because it provides a 

similar level of accuracy with orders of magnitude improvement in computation 

time, and very similar input data requirements. The increased algorithmic 

efficiency makes possible near real-time estimates of fire spread, such as might be 

available in a mobile or other embedded device that can be worn by firefighters 

on the fire line. It also provides a vehicle for quantitative estimate of fire risk for 

a locale through testing hundreds of different fuel treatment, fuel moisture, and 

fire suppression scenarios under different weather conditions (e.g., Finney 2001). 

Finally, HFire is ideal for mechanistic simulation of long-term fire regimes under 

different climate change and WUI expansion scenarios, enhancing our ability 

to understand underlying controls on fire patterns and to mitigate the effect of 

anthropogenic changes.

The comparisons between modeled and actual fire perimeters demonstrate 

the utility of fire models as a tool for wildland management, policy and hazard 

estimation. Future enhancements of HFire may include (1) modification of the 

fire-spread equation and rules (if Rothermel is updated or replaced), (2) addition 

of a spotting module, (3) addition of a suppression module that allows for scenario 

testing, (4) addition of a module for assessing the worth of fuel treatments.

The 2003 and 2007 southern California Wildfires have raised public awareness 

of the impact of wildfires on urban communities and increased concerns about 

potential future fire hazards associated with climate change. Given how little we 

know about climate change impacts on fire probabilities (Moritz and Stephens, 

in press) and the importance of fire-spread models as the basis of simulating 

ecological disturbance regimes, new and more physically based approaches are 

needed. The computational efficiency of the HFire algorithm creates opportunities 

for mechanistic fire models to play quantitative and dynamic roles in analysis of 

fire patterns. 

The computational 

efficiency of the 

HFire algorithm 

creates opportunities 

for mechanistic 

fire models to play 

quantitative and 

dynamic roles in 

analysis of 

fire patterns.
Using HFire for Spatial Modeling of Fire in Shrublands

39

Acknowledgments

This work was supported by the James S. McDonnell Foundation, the David and 

Lucile Packard Foundation, National Science Foundation Grant DMR-0606092, 

the Institute for Collaborative Biotechnologies through Army Research Office 

grant DAAD19-03-D-0004, and a National Aeronautics and Space Administration 

Regional Earth Science Application Center grant (CSDH NASA RESAC 447633-

59075). 

English Equivalents

When you know: Multiply by: To find: 

Centimeters (cm) 0.394 Inches

Meters (m) 3.28 Feet

Kilometers (km) 0.621 Miles

Square meters (m2) 10.76 Square feet

Hectares (ha) 2.47 Acres

Cubic meters (m3) 35.3 Cubic feet

Meters per second (m/s) 2.24 Miles per hour

Joules (J) 0.000952 British thermal units

Kilograms (kg) 2.205 Pounds

Kilograms per cubic meter (kg/m3) 0.0624 Pounds per cubic foot

Megagrams per hectare (Mg/ha) 0.446 Tons per acre

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