FIRE MODELING AND REMOTE SENSING:
CONVERGING TECHNOLOGIES
FRANCIS M. FUJIOKA1, Charles JONES2, and Philip J. RIGGAN1
SUMMARY
Fire managers will soon have ready access to weather and fire models to predict the behavior of fires whose
locations are known. The models result from many years of research and development, but they require
substantial computing support, which has become feasible for fire applications in recent years. The models,
however, are still subject to errors, so their output should be checked carefully and regularly. Model evaluation
benefits from recent innovations in remote sensing. We describe a thermal imaging system developed
especially to monitor wildland fires. The system sees the fire in infrared and visible bands, thus allowing the
determination of hot spots within the fire. We present a modeling and remote sensing system, and a risk
assessment framework that uses the model and image data to determine the expected net value change for an area
of interest. It involves a process for mapping the probability of fire spread, given a fire event at a known
location. Fire managers will benefit from a system which will better inform the decisionmaking process.
1. INTRODUCTION
Operational procedures in wildland fire management will change dramatically with new technologies
emerging from research and development. These technologies include computer modelling and remote sensing
tools that provide observations and predictions of fire and the fire environment with spatial and temporal detail
that go well beyond the capabilities of current operational systems. This paper describes an integrated
weather/fire modelling system and an airborne remote sensing platform designed to monitor wildland fire.
Each represents a distinct advance of fire technology in its own right; when used together, they offer a powerful
new system for fire risk assessment.
We envision this risk assessment system for tactical fire planning during the course of one or more fire
incidents. A weather model describes anticipated weather conditions on a grid covering the affected area, at
gridpoint spacings on the order of a kilometer or less. The model output includes all the weather variables
needed to describe weather effects on fire behavior. Fire behavior prediction is accomplished by a second
computer modelling system, which ingests the weather model output and accounts for fuel and terrain variations.
Recent examples show how this modelling approach has been applied. Some models not only account for the
weather effects on fire behavior, they also describe the feedback that the fire energy imposes on the atmosphere
in the immediate neighborhood of the fire (Clark et al. 1996, Linn et al. 2002). This paper focuses on a simpler
modelling approach which excludes the feedback mechanism, because the more complex models take longer to
run than operational constraints allow. A weather model generates predictions which feed into a fire behavior
model. The resultant fire spread predictions are checked against remote sensing images that show the actual
fire spread. Analysis of the errors in the fire spread predictions results in a spatial/temporal probability model
of the spread prediction errors, which enables an assessment of risk that the fire poses to the resources in its path.
1Forest
Fire Laboratory, USDA Forest Service, Riverside, California, USA
Email: ffujioka@fs.fed.us
2ICESS, University of California, Santa Barbara, California, USA
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November 30-December 2, 2005
The following sections describe in greater detail the weather model and the fire behavior modelling system
that comprise the modelling components for the risk assessment system in development at the USDA Forest
Service Forest Fire Laboratory in Riverside, California. The theory that underlies the risk assessment
procedure is explained. The modelling components, the remote sensing process, the probability analysis, and
the risk assessment process are presented as an integrated system.
2. WEATHER MODELING
The weather model we use to generate high resolution weather predictions is called MM5. It has its roots in
a weather model developed at Pennsylvania State University (Anthes and Warner 1978). The National Center
for Atmospheric Research in Colorado maintains the current version of the model, and supports its distribution
and use.
Figure 1 Nested grids for MM5 weather simulations at the University of California, Santa Barbara. Within the
boxes labelled D01, D02, and D03, the horizontal spacings between grid points are 36, 12, and 4 km,
respectively.
MM5 produces weather information on a grid with user-specified characteristics (grid spacing, location, map
projection, etc.). It uses a nested grid structure, where finer grids are embedded in coarser grids that provide
lateral boundary conditions for the former (Figure 1). The model is predictive, but it requires initial and lateral
boundary conditions, usually obtained from another weather model with coarser resolution. The user specifies
the number and spacing of the vertical levels in model runs. Near the earth’s surface, the model levels tend to
reflect the shape of the terrain, as depicted by the terrain elevation data at the prescribed horizontal grid spacing.
The MM5 model incorporates the laws that govern atmospheric processes, and draws on a rich heritage. In
the USA, weather models date back to the 1950s (Ross 1986). Early models had relatively simple physics,
suitable for computers available at the time. The MM5 model used for this paper is far more complex, based on
the theory of nonhydrostatic processes. The complexity is necessary to simulate weather at grid spacings on the
order of a kilometer.
Fundamentally, the MM5 model solves a set of time-dependent nonlinear partial differential equations that
express physical laws governing atmospheric processes (Perkey 1986). These include:
1.
2.
3.
4.
5.
6.
conservation of horizontal momentum
conservation of vertical momentum
mass continuity
ideal gas law
moist thermodynamics
conservation of cloud water
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November 30-December 2, 2005
The set of equations cannot be solved analytically, thus requiring numerical schemes. The calculus of the
governing equations are approximated by numerical differencing algorithms. This approach requires
extraordinary computing support, which parallel computing architecture facilitates. Fortunately, the vast
improvement in the price/performance ratio of cluster computers has made model applications like MM5 much
more accessible than they were even 5-10 years ago.
The fire modeling component requires weather information from the surface layer of the weather model.
We use the FARSITE version 3 fire modeling system (Finney 1998), which incorporates the Rothermel (1972)
fire spread model. The predicted weather variables passed to FARSITE from MM5 are hourly values on a 4 km
grid spacing of:
1. air temperature
2. relative humidity (percent)
3. wind direction (azimuth degrees)
4. wind speed
5. precipitation amount
6. cloud cover (percent)
The user can specify either metric or English units of measurement.
Figure 2 Web site at the University of California, Santa Barbara, with downloadable MM5 forecasts for use with
FARSITE
Currently, the University of California at Santa Barbara (UCSB) produces MM5 fire weather predictions
customized for FARSITE twice a day, for portions of northern and southern Calilfornia. The gridded prediction
fields can be downloaded from the Internet at http://www.icess.ucsb.edu/asr/farsite_files.htm (Figure 2). The
user can choose the type of map projection, datum, and forecast initialization time.
The UCSB web site also features animations of the predicted fire weather fields, georeferenced with major
city and road locations, and with topography. This allows the user to visualize the dynamics of the expected
Proceedings of Fifth NRIFD Symposium
November 30-December 2, 2005
weather conditions that can affect fire behavior. Alternatively, pull-down menus also facilitate frame-by-frame
inspection of the hourly weather fields (Figure 3).
Figure 3 MM5 predicted winds at 10 m and air temperature at 2 m above ground level for southern California,
19 July 2005. The first map is for 0600 Pacific Daylight Time, and the second map is for eight hours later.
The grid spacing is 4 km, but not all the grid points are shown.
Proceedings of Fifth NRIFD Symposium
November 30-December 2, 2005
Figure 4 FARSITE simulation of the 1996 Bee Fire in the San Bernardino National Forest, California. The
colors in the two-dimensional view represent different fuel types, also shown in the three-dimensional view.
The arrows represent the surface winds at a grid spacing of 2 km.
3. FIRE MODELING
As mentioned previously, the fire modeling component of this paper is FARSITE version 3, which predates
the current release. We favor the older version, because it allows gridded weather input of all the MM5
variables listed in the preceding section, whereas the current version does not. In addition to weather data,
FARSITE requires fuels and terrain elevation data for the area of interest. In California, these data are available
for national forests and other selected locations through the Forest Service Regional Office, Fire and Aviation
Management. This is not a trivial requirement, because the fuels and terrain data are typically used at a grid
spacing of 30 m for FARSITE simulations. The high resolution is necessary to capture the effects that spatially
variable fuels and terrain have on fire behavior.
The Rothermel fire spread model is the basis for the component of FARSITE which simulates surface fire
spread (Finney 1998):
R
I R 1  w  s 
b Qig
where
R  head fire steady-state spread rate
I R  reaction intensity
  propagating flux ratio
b  fuel ovendry bulk density
  effective heating number
Qig  heat of pre-ignition
w  wind coefficient
s  slope coefficient
(1)
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November 30-December 2, 2005
Figure 5 FARSITE simulation of the Troy Fire in San Diego County, California, 19 June 2002. This ongoing
study uses MM5 weather output at a horizontal grid spacing of 1.3 km, which is slightly larger than the 1 km
grid interval shown in the figure.
The Rothermel spread model is one-dimensional: it represents the spread rate only in the direction of
maximum spread. To simulate fire spread over the landscape, FARSITE applies Huygens’ principle, by
assuming that two-dimensional fire spread can be approximated locally by an ellipse, for which the Rothermel
model gives the head fire spread rate. The outer envelope of all such local ellipses represents the advancing fire
perimeter in two dimensions.
FARSITE effectively is a numerical integration over space and time of those variables that affect fire growth,
given the initial location of the fire. It requires parameters that control distance and time steps used in the
integration. FARSITE can simulate multiple fires simultaneously, and the coalescence of fires whose paths
converge. We have applied FARSITE in case studies of actual fires, the first of which was the 1996 Bee Fire,
which burned a portion of the San Bernardino National Forest in southern California (Figure 4). This was also
the first time we used a high resolution weather model (Mesoscale Spectral Model, or MSM; Chen et al. 1998)
with FARSITE to simulate fire spread. The simulated wind vectors at 1730 Pacific Daylight Time, 30 June
1996, appear in the left side of Figure 4.
Another case study is focusing on the Troy Fire, which burned in an area approximately 80 km east of the
city of San Diego in 2002. Figure 5 shows the FARSITE-simulated growth of the fire approximately six hours
after it started. A somewhat counterintuitive feature of the simulation is the accelerated downhill growth of the
fire on the right side of the two- and three-dimensional views. This fire is particularly interesting because we
have high resolution weather, fuels, and terrain data for fire spread simulations, and we also have high resolution
remote sensing imagery data of the fire as it grew in the afternoon of 19 June 2002. For the first time, we have
perimeters of the actual fire mapped at 10 minute intervals, from an airborne remote sensing system designed
specifically to study wildland fire. The next section describes the system used on the Troy Fire.
4. REMOTE SENSING BY FIREMAPPER™
Proceedings of Fifth NRIFD Symposium
November 30-December 2, 2005
FireMapper™ is an imaging system developed jointly by the USDA Forest Service and a contractor to
monitor wildland fires (Riggan and Hoffman 1999). Its sensors detect light in three infrared bands and two
visible bands. A microbolometer focal-plane array provides the capability for thermal-imaging without
cryogenic cooling, in infrared bands that wildland fires characteristically radiate. Two 1.6 megapixel cameras
are used to collect images in the visible bands. The system has been flown on a twin engine Piper Navajo
airplane. An onboard computer records the images together with GPS location information and aircraft speed
and heading. Flying at an elevation of 2770 m and a speed of 92 m/s (185 knots), FireMapper thermal-infrared
images are capable of 5 m resolution.
Figure 6 Two consecutive images of the Troy Fire from the FireMapper thermal imaging system. A ten minute
interval separates the time between the pictures, allowing analysis of the fire growth at high spatial and temporal
resolution.
Figure 6 shows two postprocessed infrared images from the Troy Fire, recorded on 19 June 2002. The first
image represents the fire at 1356 Pacific Daylight Time, and the second is at ten minutes later at 1406. The
brightness is a function of the radiance measured by the infrared sensors. The image can thus be used to
differentiate temperature zones within the fire. For the purposes of this study, we are primarily interested in the
spread of the fire, hence the perimeter that separates the burned area from the unburned area.
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November 30-December 2, 2005
Figure 7 FireMapper recorded this thermal image of the Old Fire, which burned into the city of San Bernardino,
California (lower right) and subsequently into the mountaintop community of Cedar Glen, in October 2003.
Several fires toward the end of October 2003 kept the FireMapper system busy in southern California. One
of the most destructive of those was the Old Fire (Figure 7), which started during the day on 25 October, north of
the city of San Bernardino, California. Driven by Santa Ana winds from the north, the fire quickly spread into
the city, where it burned over 200 homes by early evening. The FireMapper image shows the actively burning
areas of the fire as it made its way toward the city and up the mountain. Visit the web site at
www.fireimaging.com to view the other October 2003 fires in California, as well as fires from other years dating
back to 2001, and fires from Montana, Brazil, and Mexico.
5. USING MODELING AND REMOTE SENSING FOR RISK ASSESSMENT
The technologies of weather and fire modeling, and high resolution remote sensing of fire spread, provide the
necessary tools to evaluate the probability of fire spread on an incident. In turn, the probability information
enables a quantitative assessment of risk that a fire poses to the resource values in its path. We use the method
by Fujioka (2002) to obtain the probability information.
5.1 Probability Model
We assume the ability to run an objective procedure such as a model or models as described in the preceding
sections, to obtain a prediction of fire spread for a fire at a known location. We also assume an ability to obtain
accurate information efficiently, on the progression of the actual fire. Under conditions of mathematical
smoothness as described by Fujioka (2002), we compare the actual and simulated perimeters of the fire at time t.
If we can use polar coordinates unambiguously, with the origin at some reference point internal to the fire (e.g.
the ignition point), we define the model error G:
G ( j , t )  r ( j , t ) / R( j , t ),
where
R( j , t )  0
(2)
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 j  radian measure to j -th point on perimeter
t  time
r  radial distance to actual perimeter
R  radial distance to simulated perimeter
A stochastic model for the error of the simulations is given by
ln  G ( j , t )   ln r ( j , t )  ln R( j , t )  e( j , t )
(3)
where e is a zero mean random variable. The log transformation of Equation 2 in Equation 3 both linearizes the
model error formulation and potentially stabilizes the variance of the errors. Further assume the existence of a
probability model F(k) such that
ln  G( , t )  ~F (k )
(4)
where k is a parameter set for F. Our objective is to determine F in (4) from the actual and simulated perimeter
data in (3) For the Bee Fire case study, Fujioka (2002) used nonparametric methods to find the probability
distribution for ln(G(θj,t)). He used the probability information to construct confidence intervals on subsequent
fire spread predictions.
Figure 8 Three-dimensional view of the predicted perimeter growth of the 1996 Bee Fire, 45 minutes after
ignition, together with 95% confidence bounds on the location of the true fire perimeter. The pink polygon
marks the actual fire growth after 45 minutes.
One possible presentation of fire spread predictions and probability information is given in Figure 8. The
example shows the predicted 1996 Bee Fire perimeter, 45 minutes after ignition, embedded in 95% confidence
bounds as determined from the retrospective analysis of the simulated and actual fire behaviors by the method
outlined above. The light brown polygon in the lower left corner is the predicted burned area. The perimeters
of the small reddish polygon and the large yellow-brown polygon represent the 95% probability bounds on the
Proceedings of Fifth NRIFD Symposium
November 30-December 2, 2005
location of the true perimeter. The pink polygon is the actual area burned after 45 minutes. The utility of this
presentation derives not only from the prediction and attendant uncertainty information, it also provides visual
information of the resources in the potential path of the fire. This begins the process of risk assessment, which
can be extended as follows.
5.2 Risk Assessment Procedure
Given the location of an ongoing fire, an objective assessment of the risk to resources in vicinity of the fire
may be measured by the expected benefits from the fire versus the expected loss it might inflict. This quantity
is the expected net value change. Finney (2005) writes this quantity as
N
n
E[nvc]   p( Fi )  Bij  Lij 
(5)
i 1 j 1
where
p( Fi )  probability of the i -th fire behavior
Bij  benefit to the j -th resource from the i -th fire behavior
Lij  loss to the j -th resource from the i -th fire behavior
We can make this expression spatially and temporally explicit for the continuous case:
E nvc  A, t  

p(u, v, t ) aB (u, v, t ) B(u, v, t )  aL (u, v, t ) L(u, v, t ) dudv
(6)
u , vA
where A is the region of interest, (u,v) is the orthogonal spatial coordinate system, t is the time for which the
calculation is valid (a forecast time), and aB(•) and aL(•) are attenuation functions for B and L, respectively, that
express the proportionate effect that the fire has for the given place and time. Equation 5 might be considered a
special case of Equation 6, with aB(•)=aL(•)=1. The attenuation functions serve the purpose of accounting for
partial benefits or partial losses, when the fire does not exert its full effect.
An obviously essential component of Equation 6 is the probability p(•) of the fire behavior. Assume that the
aspect of fire behavior of interest is the passage of the surface fire front over the point (u,v), given the forecast at
time t. Equations 3 and 4 provide the probability information for this case. Without loss of generality, assume
that the simulated spread R(•) is an unbiased estimator for the actual spread. From Equation 3 and relation 4,
ln G  j , t   ln r  j , t   ln R  j , t  ~ F (k )
For fixed θj and t, ln G is a random variable.
P(ln G  g )  F ( g; k ),
  g  
(7)
Let g=ln G be the quantile of F such that
(8)
Recall from Equation 2 that G(θj,t) is the ratio of the radial distance traversed by the actual fire to the distance
traversed by the simulated fire at time t, in the direction of θj. Interpret t as the forecast lead time. From
Equations 2 and 8, for fixed in the direction of θj and t,
ln G  g
 ln r  ln R
ln r  ln R  g
r  R exp( g )
(9)
Hence,
P  r  R exp( g )   1  F ( g; k )
(10)
Equation 10 gives the probability that the actual fire will travel up to a distance of R exp(g) in the direction θj,
given the model forecast spread distance of R for time t. Recall that the spread model simulates a surface fire
burning through a continuous fuel bed. A simple example illustrates the concept. Assume that g for all θ is a
normal random variable with mean zero and variance  t2 , where the variance increases with t. Equation 6
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November 30-December 2, 2005
becomes
E  nvc  A, t  


u , A
1  FN  u  , g  ;0,  t2   aB (u, , t ) B(u, , t )  aL (u, , t ) L(u,  , t ) dud


(11)
where u  R( ) exp( g ) . The modeling and remote sensing components provide all the information required
for the probability calculation.
6. CONCLUSIONS
We describe a framework for assessing risk posed by a fire at a known location, using weather modeling, fire
modeling, and remote sensing to determine the probability distribution of the fire modeling errors. The
probability information is then used in a quantitative assessment of risk, specifically to determine the expected
net value change posed by the fire. The analysis assumes that the fire burns freely, without any suppression
response. It therefore provides a baseline estimate of the consequences if managementt takes no action.
It to be expected that the risk assessment is influenced by the environmental conditions that influence the fire,
the valuation of the resources at risk, and the potential positive and negative effects of the fire. It is also
important to note that the probability distribution that informs the assessment is a reflection of the ability of the
modeling system to predict fire behavior. Greater accuracy in the models enhances the risk assessment process.
Viewed in a decisionmaking context, where the consequences of good and bad decisions can be quantified, the
risk assessment procedure also provides a means to evaluate the value of accuracy in the modeling systems.
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