FARSITE Technical References

If you want to know more about how FARSITE works or the assumptions of the models, you've come to the right place. Usually a user will find their way to the Technical References via links from the Reference or Users Guides but feel free to navigate through this section on your own. More details on equations and fire behavior models in FARSITE are available in the publication:

Finney, M.A. 1998. FARSITE: Fire Area Simulator-- Model Development and Evaluation. USDA For. Serv. Res. Pap. RMRS-RP-4.

Modeling Fire Growth (technical documentation)

The FARSITE model (Fire Area Simulator) simulates fire growth as a spreading elliptical wave. The fire is propagated over a finite time step using points, that define the fire front, as independent sources of small elliptical wavelets. These small ellipses can be thought of as forming an envelope around the original perimeter, the outer edge representing the new fire front. This process has been referred to as Huygens' principle (Anderson et al. 1982). Huygens' principle is named for the 17th century Dutch mathematician Christian Huygens who proposed it for describing the travel of light waves.

The reliance on an assumed fire shape, in this case an ellipse, is necessary because the spread rate of only the heading portion of a fire is predicted by the present fire spread model (Rothermel 1972). Fire spread in all other directions is inferred from this forward spread rate using the mathematical properties of the ellipse. An elliptical shape would not have to be assumed if the spread rate in all directions could be computed independently from the fuels, weather, and topography.

Two examples of Huygens' principle with elliptical fire shapes. Winds are uniform from the southwest.

The metaphor of a fire front spreading as a wave is intuitively attractive for several reasons:

This approach differs considerably in concept from the cellular models, or cellular automata, that simulate fire spread as a contagion process between cells (Kourtz and O'Regan 1971, Kourtz et al. 1977, Green 1983). Cellular models solve for ignition times of cells at known regular spacing. The position of the fire front at a given time must be interpreted from cells having similar arrival times. This type of model has some inherent difficulties. Among the most critical, appear to be the distortion of fire shapes caused by the gridded landscape geometry (Ball and Guertin 1992), and absence of information on spread between cells; the latter becomes vital to synchronizing effects of temporal changes in weather or fuel moisture around the fire perimeter. None of the cellular models adequately simulated fire spread under test conditions with spatial and temporal heterogenities (French 1992). Techniques recommended by (French 1992) for reducing geometric distortion have included enlarging the "search radius" for interacting cells (increasing the number of "adjacent cells"), and decreasing the time step (depending on the specific cellular algorithm in use). Cellular models may be deterministic, or have probabilistic or fractal modifications (Clark et al. 1994) to spread rates and/or directions. Non-deterministic models would require multiple runs to generate a risk map (event-probability map) for a given scenario because outputs change between individual simulations having identical input parameters.

The concept of applying Huygens' principle to model fire growth simply involves using the fire environment at each perimeter point to dimension and orient an elliptical wave around each point on a fire front at each time step. The shape and direction of the ellipse is determined by wind-slope vector while the size (e.g. spread rate) is determined by the fuel conditions. The implementation of this in a practical fire growth model is, however, considerably more complex.

Huygens' principle has been applied to fire growth modeling in various forms. The earliest published application was the "radial fire propagation model" by Sanderlin and Sunderson (1975). This was a computerized method for projecting fire perimeter growth over complex landscapes. It used a 3 dimensional wind field, a rasterized landscape of fuels and topography, and provided reasonable projections of fire growth (Sanderlin and Sunderson 1975, Sanderlin and Van Gelder 1977). The essential mathematics and many of the complications of this approach were first identified here. Anderson et al. (1982) brought the terminology and concept of Huygens' principle to the fire literature. They described the mathematics and applied Huygens' principle to perimeter data from a test fire, finding it suitable as a fire growth model. French et al. (1990) and French (1992) employed a graphical technique which used computer graphics block-copy techniques to produce fire fronts. The "four-point" technique (Beer 1990, French 1992) uses 4 points on an elliptical perimeter that correspond to its major and minor axes as the propagation points that form the new fire perimeters. Richards (1990) analytically derived a differential equation that propagates any point using an elliptical fire shape. Richards (1990) technique is employed in the FARSITE model and uses the vertices of the fire perimeter polygon as the propagation points. The same result is achieved by the method of Roberts (1989; discussed by French 1992) in which the line segments between the vertices are the objects of propagation. Knight and Coleman (1993), Dorrer (1993), and Wallace (1993) also developed procedures for computing fire perimeter positions based on Huygens' principle of wave propagation. Recently, Richards (1995) has extended his equations to expand fire shapes different from the simple ellipse (lemniscate, double ellipse etc).

Essential as it is, the method chosen to implement Huygens' principle really becomes a minor part of the whole simulation process. The outline of the process control used in FARSITE illustrates this; Richards' (1990) equation is used only in step 5 of the surface fire calculations and step 7 of the crown fire calculations.

Huygens' Principle (technical documentation)

The method chosen for implementing Huygens' principle in FARSITE was developed by G.D. Richards (1990). His differential equation solves for the spread vector (rate and direction) of each point knowing its orientation on the fire perimeter and the heading, flanking, and backing dimensions of an elliptical fire originating at that point. The elliptical dimensions are obtained from empirical models for the length to width ratio determined by the wind-slope vector (Anderson 1983, Alexander 1985). These dimensions are given units of fire spread rate from the predicted rate of forward spread (Rothermel 1972). The calculated spread rates are then multiplied by the time-step to obtain the positions of all points on the fire front at the end of the time-step.

Several modifications to this procedure are used in FARSITE to increase control over the simulation. The most important change is the concept of a dynamic time-step that is implemented through distance checking. Distance checking ensures the spread distance of any point on a fire is less than the maximum distance in a given time step. Without this procedure, there would be no control over the amount of spatial information used by the simulation. Faster moving heading portions of a fire would automatically use a coarser scale of landscape information than slower portions of a fire; important landscape information within a time step such as a river or change in fuel type could be ignored. Distance checking allows control over the minimum level of spatial detail used in a simulation.

When you are simulating multiple fires at a time, distance checking can be done in 2 different ways: fire-level and simulation-level. The fire-level distance checking uses the fastest moving point on each fire independently to regulate the growth of that fire front. The simulation-level distance checking uses the fastest moving point among all fires and regulates the growth of all fronts at the level. With fire-level distance checking, slow moving fires can accomplish their growth in one calculation per time-step while faster moving fires may take several steps. Merging is accomplished after the end of the actual time step. With simulation-level distance checking, the same internal time step used for all fire fronts (determined by the fastest vertex among all fronts) and merging can then be accomplished many times per actual time step. The simulation-level time step is required for calculating post-frontal combustion to remove the effects of overlap among fronts after merging of several fire fronts.

During distance checking, the working value or internal value of the time step is constantly changing. If during a time step the distance check is exceeded by any point on a fire, the minimum time from all points to spread that distance is used as the new time step. The original time step is then decreased by that amount, and the process repeated until the original time step is consumed. The time step then becomes important only as a consistent interval for:

In Richards (1990) application of his differential equation, he uses a single correcting iteration to compensate for the changing orientation of each point after a given time step. The orientation of each point on the fire front is a required input to the equation, but is changed as a result of the solution. Thus, an average orientation from the two time steps is used for each point in a second and final round of computations. This process can be repeated more often within a time step if greater averaging of the orientation is desired. At present, no correcting iterations are performed in FARSITE. This will be an area of further investigation as an option for the simulation.

Wind Profiles (technicial documentation)

Wind speed is input to FARSITE at the reference height of 20 feet above the vegetation. Speed is assumed to vary with height above the vegetation according to a logarithmic wind profile (Albini and Baughman 1979). Wind direction is assumed to remain constant with height. Beneath the canopy, winds are greatly reduced depending on the canopy cover and stand height (Albini and Baughman 1979). Recommended wind reduction factors, e.g. multipliers for the 20ft wind to obtain representative midflame winds, are 0.1-0.2 for sheltered fuels, but 0.4-0.6 for fully exposed fuels (e.g. no canopy) (Rothermel 1983). In FARSITE, the wind reduction factors are calculated at each location based on the canopy cover and the canopy height (Albini and Baughman 1979), irrespective of the surface fuel model. Thus, brush fuels (fuel model 4 or 5), that are normally exposed, can be sheltered if the canopy cover and height are both high. Timber understory fuels (8, 9, 10) can be exposed in the canopy cover and height are low. No accounting is made for topographic variation in wind exposure (e.g. ridge top vs. valley vs. slope).

Dead Fuel Moisture (technical documentation)

The change in moisture content of dead and downed woody surface fuels throughout the day is critical to calculating the changes in fire behavior. In general, drier fuels increase fire spread rate, fireline intensity, and fuel consumption. FARSITE uses a model to calculate fuel moisture during the simulation in response to changing weather conditions. Moisture contents of live fuels are assumed to remain constant in FARSITE throughout the simulation (but these can be changed in the .FMS file during the simulation). Dead fuel moisture is an important input to two sub-models used in FARSITE:

Fuel Size Classes

The rate of change of the moisture content is dependent on the diameter of the woody fuel particle and the amount of change in environment conditions. Historically, the diameters of the woody fuel particles have been classified according to their "time lag". Time lag refers to the length of time that a particle responds to within 63.2% (1-1/e) of the new equilibrium moisture content (either drying or wetting). Larger diameter fuels generally have longer time-lags, meaning they respond more slowly to changes in environmental conditions. The time lag categories traditionally used for fire behavior and fire danger rating are specified as: 1hr, 10hr, 100hr, and 1000hr and correspond to round woody fuels in the size range of: 0-¼", ¼"-1", 1"-3", and 3"-8" (0-.635cm, 0.635-2.54cm, 2.54-7.62cm, and 7.62-20.32cm) respectively. Loadings (weight/area) of dead fuels in these size-classes are required to describe surface fuels for fire modeling (Anderson 1982).

Environmental Effects on Dead Fuel Moisture

The environmental factors that determine the fuel moisture of a fuel particle are:

These are heavily dependent on the local topographic and environmental site factors for the fuel particle:

As a FARSITE simulation progresses, the moisture contents of the four fuel size classes are adjusted for the changing weather conditions over time at the local site. To do this, FARSITE uses the dead fuel moistures supplied as "initial fuel moistures" from the .FMS file (for 1hr, 10hr, and 100hr time lag categories) and modifies them according to the changes in temperature, humidity, and rainfall in the weather (.WTR) file, cloud cover in the wind (.WND) file, and the local site conditions (elevation, slope, aspect, canopy cover) from the landscape (.LCP) file.

Diurnal variation of fuel moistures

Graph of fuel moisture content over time (about 3 days) for three time-lags of dead woody fuel sticks. The fuel moistures were calculated using the model from Nelson (2000). Greater moisture response amplitude is produced for the smaller time-lags.

Since the moisture content of 1000hr fuels are only used for fuel consumption and post-frontal combustion, their initial moisture content is obtained from the coarse woody profile (.CWD) file. The moisture content of fuels larger than the 1000hr size class (specified in a coarse woody profile (.CWD) file for fuel consumption and emissions) are assumed to remain constant throughout the simulation because of their long time lags.

The air temperature and relative humidity are modified for elevation assuming a fixed lapse rate (Rothermel et al. 1986). Solar radiation is modified for slope steepness and orientation and reduced by the percentage of canopy cover and cloud cover specified in the wind (.WND) file. Rainfall is assumed constant across the coverage of the weather (.WTR) file.

To account for the spatial variation in local site conditions (from the landscape (.LCP) file), FARSITE generates a catalogue of representative fuel "particles" for all combinations of categories of each site factor (elevation, slope, aspect, canopy cover) and initial moisture content for each size class of fuel. This is necessary because the fuel particles have a state "memory" of moisture and temperature at all internal positions (within the particle) that are unique to a given local site. The size ranges for categories for each site factor can be adjusted at run time (see Models > Dead Fuel Moisture). The moisture model is used to update the moisture content of each representative particle in the catalogue at each simulation time step. Actual values used for calculating fire behavior at an arbitrary time and point on the fire front are obtained from the catalogue by interpolation.

Modeling Dead Fuel Moisture

FARSITE version 4.0 has implemented a new model for calculating dead fuel moisture content of 10hr fuels (Nelson 2000). As used here, it also handles other fuel size-classes (1hr, 100hr, and 1000hr) with modifications by Nelson. This model replaces those developed by Rothermel et al. (1986) for BEHAVE (Andrews 1986) and Deeming et al. (1977) for the NFDRS (Bradshaw et al. 1983) as used in previous versions of FARSITE (Finney 1998). The new fuel moisture model (Nelson 2000) calculates the exchange of water between the environment and the surface of a round wooden stick and transport of water within the stick itself. The stick is assumed to be without bark and located above ground. For computational efficiency, the 1hr fuel moisture in FARSITE is obtained from a calculation involving the equilibrium moisture content (Bradshaw et al. 1983) instead of Nelson's 1hr calculation. There is yet no general duff moisture model so the empirical relationship developed by Harrington (1982) is used to predict duff moisture content from the 100hr fuel moisture value.

As implemented in FARSITE, Nelsons (2000) model is used to calculate fuel moistures a each time step in the simulation or to "precalculate" fuel moistures for the range of dates and times specified. Precalculation takes place before the fire simulation begins and allows more rapid display and calculation of the fire behavior. In either case, the moistures do not need to be recalculated for repeated simulations unless modifications are made to the .WTR or .FMS files, the duration settings (Simulate > Duration), or the options for dead fuel moisture (Model > Dead Fuel Moisture). All fuel moistures will be saved when a bookmark is created or updated.

Use of Conditioning Period

At the beginning of a FARSITE simulation, the dead fuels of all size classes in each fuel model will not reflect the influences of the local site conditions. Fuels for a particular fuel model all have identical moisture contents obtained from the .FMS file regardless of where on the landscape the fire behavior is calculated. As the simulation progresses for a few hours or a day, however, the moisture content of the finer fuels (1hr, 10hr) will increasingly reflect the local site conditions because of their short time-lag. The influence of the constant initial conditions on fire simulations varies by the size and growth rate of the fire, spatial variation in topography and canopy cover, and the length of the simulation. The effect will be minor for long simulations (more than a few days) for slow moving fires ignited from a point source. The effect will be most significant for fires starting from an existing large perimeter in complex topography and simulated for only few hours.

To minimize the effect of this period of fuel "conditioning" on a fire simulation, the Simulate > Duration setting allows for a "conditioning period" to be inserted before the start of the simulation. The conditioning period can be set for several days to allow the catalogue of fuel moistures to reflect the range of local site conditions before the fire is simulated. When the fire simulation begins after the conditioning period, the landscape will contain spatial variation in dead fuel moisture with less influence of the initial fuel moisture input conditions.

Wind-Slope Vector (technical documentation)

The easiest way to vector the mid-flame wind speed and effect of slope on fire spread was to compute and vector the dimensionless wind and slope coefficients in the Rothermel model. This method was used by Sanderlin and Sunderson (1975). The resultant vector is dimensionless, and can be converted to an effective mid-flame wind speed by solving for wind speed in the wind coefficient equation.

Elliptical Dimensions (technical documentation)

A number of empirical relationships between fire shape and wind speed have been developed (Alexander 1985). Some of the relationships use midflame wind speed and others an open wind speed at 20ft or 10m above the vegetation. At present, FARSITE employs Anderson's (1983) model for length to width ratio of the ellipse because it uses mid-flame wind speed and because of its stated applicability to any fuel type. A simple ellipse is used, however, rather than the double ellipse. The midflame wind speed is a simpler value to obtain in the simulation because the wind-slope vector (above) is a midflame value. The appropriate open wind vector would have to be inferred from this midflame value.

Anderson's model does not yield a circular fire with zero wind and slope. Thus, as implemented in FARSITE, the length to breadth ratio from Anderson's model is adjusted by subtracting 0.397 from the predicted length to width ratio. This is not seen as a serious problem. Variation in wind direction at higher frequencies than represented in the wind stream will decrease the eccentricity of an elliptical fire. Simard and Young (1978) developed a model of fire shapes that accounted for Gaussian variation in wind direction. They recommended using a standard deviation of 10 degrees for all wind speeds (Alexander 1985). Their model has recently been found to agree reasonably well with a theoretical analysis of effects of wind variation on elliptical fire shape ( Richards 1993). All other models assume wind speed and direction to be constant. However, the empirical nature of some of these relationships suggests that wind variation must have affected the original field data to some degree.

Most of the work using elliptical fire shapes assumes the origin of a fire is at the rear focus of an ellipse (Anderson 1983, Alexander 1985, Andrews 1986). This provides an implicit means to calculate the backing fire spread rate.

Catchpole et al. (1982), Alexander (1985), and Bilgili and Methven (1990) suggest however, that this assumption has not been adequately examined; using the focus as the ignition point may under predict backing fire spread. It also appears to produce a temporary decrease in fire area for small length to breadth ratios as wind speed increases ( Bilgili and Methven 1990). On the other hand, using the no wind-no slope spread rate as the backing rate may over predict spread with increasing slope or winds ( Byram 1959). Van Wagner (1988) and Cheney (1981) show that backing spread decreases as slope inclines to about 20+ degrees. In effect, spread may be faster down steeper slopes because of ignition by rolling or sliding debris.

Post-Frontal Combustion (technical documentation)

Post-frontal combustion refers to the burning of woody surface fuels, litter, and duff behind the moving forward edge of the flaming zone. This is an important process in many forest fuel types and activity fuels (e.g. slash) because it accounts for a large proportion of the total fuel consumed and most of the gaseous emissions. It is also critical to lofting of smoke and predicting interactions between the fire and the atmosphere (Rothermel 1991, 1994, Linn and Harlow 1998). Post-frontal combustion can last for hours or even days. Both flaming and smoldering combustion occur in the post-frontal zone. Post-frontal combustion is minimal in uniform fine fuels like grass, unless duff is present and dry enough to burn. The models for post-frontal combustion do not yet account for prolonged smoldering of stumps or buried rotten roots or wood.

The important aspects of post-frontal combustion are the same as for fire behavior in the frontal zone, namely, how much, how fast, and how long. These quantities are obtained from a model of burning, and interaction of burning, among woody fuels and duff (Albini and Reinhardt 1995, Albini et al. 1995). The “Burnup” model accounts for these interactions and produces a combustion history for a unit-area of fuel bed.

Example curve showing the combustion history produced by Burnup. Flaming and smoldering contribute to the total fuel weight consumed (remaining) at any given time.

The combustion history describes fuel weight loss over time, or intensity over time, and total fuel consumption at the time of extinguishment. The rate of burning of each fuel size class in a particular fuel bed is determined by modeling the heat transfer at intersections with other fuel particles and with the combustion of duff (Albini and Reinhardt 1995). Duff combustion in this model was treated by simply assuming a constant rate of burning for a given moisture content (Frandsen 1991). The Burnup model was modified to distinguish flaming from smoldering phases of combustion for each intersecting pair of fuel elements, based on prescribed fire data suggested that flaming combustion could not be sustained lower than about 15 kW m^-2.

The combustion zone (flaming and smoldering) of a spreading two-dimensional fire is produced when a combustion history curve is applied to the vertex trajectories of the fire polygons generated by FARSITE.

diagram of combustion zone

The purpose of incorporating post-frontal combustion into FARSITE was to permit heat production and emissions to be calculated in a spatially and temporally explicit manner. This would allow simulation of heat and smoke production from multiple ignition sources and configurations as well as for heterogeneous landscapes and changing weather conditions. As described above, the Burnup model produces a time-dependent combustion history for a unit-area of the fuel complex. However, to estimate the amount of combustion occurring behind a two-dimensional moving fire front this combustion history had to be incorporated into the spatial framework of fire growth in FARSITE. The method of simulating fire growth in FARSITE involves the expansion of the edge of one or more fire polygons based on models for fire spread rate (Rothermel 1972, 1991, Van Wagner 1977). The fire polygon is defined by a series of vertices that move across the landscape according to the local fuels, weather, and topography. The trajectories of these vertices, or paths that a given vertex follows as it moves in space and time, are critical to the accurate construction of a two-dimensional combustion zone behind the fire front (see figure). The trajectories represent the progress of the fire front over time and therefore are equivalent to the X-axis of the combustion history generated by a vertex regardless of the distances they travel.

Once the combustion histories are assigned to a trajectory, the amount or rate of post-frontal products over a given time period can be obtained by integrating the change in volume under the curves across the entire fire front for that time period. This was done numerically for both the fuel weight remaining and the fraction of flaming combustion. The integration method accounts for arbitrary settings for time step, distance resolution, and perimeter resolution.

Implementing post-frontal combustion in FARSITE requires using "simulation-level" distance checking (see Huygens' principle). To account for overlap in burned areas among multiple fire fronts during a time-step, mergers among multiple fire fronts must be accomplished after a single timestep for all fires. Then the area overlapping among fire fronts is normalized by the original area to eliminate "double-counting" of burned area and emissions.

Emissions

By distinguishing fuel weight consumed in flaming and smoldering phases of combustion, the Burnup model allows emission factors to be applied separately to the fuel consumed in each phase. Emission factors for particulate and chemical emission species (Ward et al.. 1993) were applied to the fuel consumed in flaming and smoldering combustion assuming the values of combustion efficiencies of 0.95 for flaming and 0.75 for smoldering. Thus, the total is combined from the emissions calculated separately from fuel weight consumed in flaming and smoldering.

Mergers and Crossovers (technical documentation)

Crossovers

After a fire has burned for a given time step the fire perimeter is processed for crossovers. Crossovers are formed when locally concave portions of the fire perimeter intersect during a given time step (Sanderlin and Sunderson 1975, Richards 1990, Knight and Coleman 1993, Wallace 1993, Richards and Bryce 1995). This happens because the spread directions of points in a concavity are oriented inward; spread from unburned fuel to burned fuel is not automatically detected by the perimeter expansion algorithms. These crossovers must be removed to preserve the meaningful exterior portions of the fire front. Sometimes, an enclave or island is formed by a crossover. This represents a region of the perimeter in which the points are ordered in an opposite rotation. These enclaves essentially become separate fire fronts burning inward as a natural result of their orientation in Richards' (1990) differential equation.

Regardless of the methods chosen, the process of crossover removal is expensive in terms of time and computing power. A number of ways of removing illogical artifacts of the perimeter expansion have been proposed. Richards (1990) used a clipping strategy that excised the illogical portions of the fire perimeter from the fire polygon. Knight and Coleman (1993) and Wallace (1993) describe similar methods. Most recently, Richards and Bryce (1995) describe an algorithm that leaves intact the offending perimeter vertices but renders them inert. The methods described below are more similar to the clipping routines. This approach is used in FARSITE because it enables orderly storage of only meaningful fire perimeter information and facilitates export of fire polygons for GIS uses.

Version 1.X

The algorithm used for clipping loops and crossovers in FARSITE versions 1.X, processes the order of segment crosses to find enclaves and correct the outer fire front.

Five examples of crossovers occurring along concave portions of a fire front. Enclaves are formed by crossovers in the last four configurations.

The simplest example is the first diagram in Figure 10.2. that involves crossing of segments 2 and 11 (identified by the first vertex on the span). If crosses are computed for each span with each other span on the fire perimeter, the number of crosses would be 2, resulting in the order of intersections listed below the diagram (segment 2 crosses segment 11, and segment 11 crosses with 2). Knowing the number of intersections to be 2, and finding the match between segment 2 as Span A for the first intersection and segment 2 as Span B for the second intersection, the algorithm would clip all points from 3 through 11, replacing them with the intersection point.

Other general types of crossovers have a pattern that is recognizable regardless of other crosses within the bounds of these intersections. Some of these are shown above. Enclaves are identified in each of these patterns and written to separate arrays as separate fires. These enclaves may still contain crossovers themselves and must be processed through the same algorithm to clean these perimeters. This process may again result in enclaves being divided to form separate inward burning perimeters.

A limitation of this technique involves the spread distance possible within any given time step. Too much spread relative to the resolution of the fire perimeter will produce a spaghetti-like fire front or create complex knots that cannot be resolved logically by the above algorithms. Hence the need for a dynamically adjustable distance check that depends on the average resolution of a given fire. This feature attempts to limit the spread so that the crossovers fall within the limits of complexity solvable by the algorithms.

Version 2.0

A new algorithm was developed for version 2.0 to process crossovers on fire perimeters. It appears to more accurately determine enclaves. It is also tolerant of complex fire perimeter knots or "spaghetti ignitions" that are input by the user or arise naturally on complex landscapes.

The new algorithm corrects a fire polygon by following the outer edge starting from an extreme point. An extreme point is defined as one of the polygon vertices that is the farthest west, east, north, or south, and thus determines the bounding rectangle of the polygon. For an outward burning fire it proceeds with each perimeter segment (pair of vertices) counterclockwise until an intersection with another segment is encountered (clockwise if processing an inward fire). Vertices are written to a separate array containing the corrected fire polygon. If the process finds an intersection, the algorithm decides the rotation direction produced by the intersection with the new perimeter segment and whether the intersection produces a locally convex or concave region. These criteria are used to determine the next vertex to be processed (either in the original direction around the fire polygon or in the reverse direction). The intersection point is written as the next point on the new fire polygon. The process is continued until the algorithm arrives back at the starting point. This determines the vertices that now define the outermost fire perimeter.

After processing the vertices for the outermost fire polygon, the algorithm looks for perimeter segments that have crossed but not yet been processed. These will occur if an enclave is formed. If one of these intersections is found, the new intersection serves as the starting point for the same algorithm to again follow the edge of the fire polygon. This process determines if a new inward fire has been created within the original fire perimeter polygon (an enclave). Each enclave is written as a separate fire if it has more than 2 vertices and is oriented clockwise. This process is repeated until there are no more unprocessed crosses on the original fire perimeter polygon.

Mergers

Searching for fire mergers is accomplished at the end of a time step after all fires have spread and crossovers removed. This is a computationally intensive process that first compares the bounding rectangles for each fire. If rectangles for two fires overlap, it examines within the overlapping region, segments of the first fire for intersections with those of the second fire.

As with crossovers, the intersection coordinates and average fire characteristics of the intersecting segments are stored, as well as the order of segments in each fire that cross.

Examples of fire mergers. Mergers "B" and "C" form enclaves and thus one outward burning fire and one that burns inward.

This information is used by one of two algorithms. If there are only 2 crosses between fires, then no enclaves can be formed and the simpler, faster algorithm merges these fires (diagram "A" in Figure 10.3). Merging fires with more than two intersections uses the comparatively complex algorithm to write segments alternately from each fire between intersection points. There can be only one outward burning fire perimeter, so all subsequent fire perimeters must be inward burning enclaves (diagrams "B" and "C" above).

The algorithms for merging fires will perform mergers between 1) two separate outward burning fire polygons, and 2) between an inward burning fire polygon and an outward burning polygon. The latter situation develops where spot fires are burning within an inward burning polygon (that defines the fire front around an enclave). The spot fires will burn as independent fires until they merge with each other or with the wall of the enveloping inward burning fire. No situation can logically develop where two inward burning fire polygons could merge.

The process of merging fires proceeds first with mergers among all outward burning fires, and then for mergers between enclaves and outward burning perimeters. This sequence eliminates illogical overlaps between outward burning fires that could influence how enclaves are processed when they contain spot fires.

Slope Correction (technical documentation)

In sloping terrain, the topographic slope and direction of spread on that slope are used to translate the surface coordinates of the fire front to horizontal coordinates. This step is necessary because the Rothermel (1972) spread equation predicts the forward steady-state fire spread rate along the ground surface. As modified by the wind-slope vector, the forward spread rate is used in the acceleration functions to produce an average spread rate for a given time step. This in turn is used to produce the elliptical dimensions in units of surface spread rate that input to Richards’ differential equation. The resulting time derivatives for the X and Y coordinates are applied to give the spread of a particular point in units of surface spread distance. These must be converted to the horizontal coordinates. The horizontal projection of an elliptical fire burning on steep ground will appear flattened in the up- and down-hill directions because of this conversion.

Slope Effects:

Crown Fire (technical documentation)

A surface fire may make the transition to some form of crown fire depending on the surface intensity and crown characteristics (Van Wagner 1977, 1993) . The crown characteristics that are used to compute crown fire activity are;

Lower crown base height (including ladder fuels) facilitates ignition of the crown fuels by the surface fire and then, transition to some form of crown fire. Crown bulk density is used to determine threshold values for active crown fire, which spreads much faster than a surface fire. Crown height is used as the upper level of the crown space for determining crown fuel loading and the starting height for lofting embers.

After determining the surface spread characteristics, the fireline intensity is compared with the intensity threshold that is critical to involving the overlying crown fuels. If the threshold is met or exceeded, some form of crown fire has occurred. To determine what "type" of crown fire (Van Wagner 1977), the equilibrium rate of crown fire spread is computed for the current spread direction (Rothermel 1991), modified by the "crown fraction burned" (Van Wagner 1993) and compared with the critical rate of spread required for an active crown fire. If this threshold is not met or is exceeded, the crown involvement is assumed limited to torching trees (a passive crown fire), else it becomes an active crown fire.

Some method was required for linking the numbers of trees torching at once to the fire and canopy characteristics. It was assumed that more trees would torch as a group when both the "crown fraction burned" factor and canopy cover increased. The numbers of trees torching in a group affects the flame height and duration important to lofting of embers (Albini 1979). The following rules below were subjectively assigned.

Number of Trees Torching at Once

`	Crown Fraction Burned
Canopy Cover	< 50%	50% to 80%	80% +
<50%	1	2	3
50% to 80%	2	3	6
80%+	3	6	10

Spotting (technical documentation)

At present, spotting in FARSITE is simulated only from torching trees (Albini 1979). Maximum spot distances of embers from burning slash piles (Albini 1981), and line fires (Albini 1983a, 1983b, Morris 1987) are calculated in BEHAVE, but are not present in FARSITE. As originally implemented in BEHAVE, the spotting component of FARSITE is intended to compute the maximum spotting distance from a given point on a fire front if torching occurs. It is not intended to simulate the numbers of embers, exact locations embers would land, or locations of resulting spot fires.

Spotting is achieved as a 3 step process. The first step determines the maximum lofting height of cylindrical embers of 16 size classes (1/16" to 1 inch) that originate at the top of a tree or group of trees (see above). Some embers may be too heavy to be lofted by the given plume generated by the tree(s). The burning characteristics of a tree (flame height and duration) are determined by size and species of the trees (Albini 1979). For all lofted embers, the position, size, and time of lofting are stored until the end of a timestep.

After embers from all portions of all fire fronts are lofted in a given time step, each ember is iteratively descended until it is extinguished or contacts the ground. The iteration assumes that each ember falls at its terminal velocity determined by diameter and the time since it began falling. Using 50ft steps for vertical drop, the iteration accounts for change in the ground elevation, wind speed as a function of height above ground, and time of flight. Embers are assumed to follow the ambient wind direction. An ember will be extinguished if it is airborne longer than the burning duration determined by its size (Albini 1979). Above the canopy height, a logarithmic wind profile is assumed. This may overestimate spot distance if the terrain is not forest covered (Albini 1981). Below the canopy, the midflame wind speed is assumed vertically constant.

The third step involves ignition of spot fires and checking for impact of the embers within existing fire perimeters. At present, all embers burning at impact are considered ignitions. The probability of ignition (Bradshaw et al. 1984) is present, but not activated in this version of the simulation, given the intent to show locations of potential ignitions rather than their result.

Fire Acceleration (technical documentation)

Fire acceleration is defined as the rate of increase in fire spread rate. It affects the amount of time required for a fire spread rate to achieve the theoretical steady state spread rate given 1) its existing spread rate, and 2) constant environmental conditions. This usage only applies to fire spread under constant environmental conditions (e.g. fuel moisture constant, winds constant, fuel availability constant). Other definitions of acceleration also exist (e.g. Cheney and Gould 1997) but these don't separate effects of changing fire environment from physical process of build-up rate. Changes in the fire environment that lead to increases in available fuel and spread rate are simulated explicitly as separate fire behavior processes by the simulation.

Fire acceleration rates are distinguished simply by "ignition type". Point source fires have slower acceleration than line source fires (Johansen 1987). These ignition types are used in FARSITE for convenience, although both types are really elements of a continuum of fire spread from a 1-dimensional source. Even this is simplistic, however, for most fires have 2-dimensional curving fronts with alternating convex and concave regions; small concave regions would be expected to have more rapid acceleration than convex regions as a result of different heat transfer ahead of the front. Similarly, fire acceleration from multiple separate fires with nearby fronts would also be increased. No 2-dimensional effects of fire shape on acceleration are addressed in FARSITE.

The lack of independence between portions of a fire front technically violates this assumption of Huygens' principle. Unlike light waves that interfere little among sources, fire propagation can interact along curving fronts and between multiple sources. It is not known what, if any, corrections are required to model fire growth and behavior for the practical applications intended for FARSITE.

Fire acceleration is currently implemented as a two step process using the model of the Canadian Forest Fire Behavior Prediction System (Alexander et al. 1992). The first calculation is always performed. It computes the final forward spread rate by accelerating the fire from its current rate toward the new equilibrium over the given time step. The average spread rate is computed from the distance traveled divided by the time step.

A second calculation becomes necessary only if the distance check was used to truncate the fire spread distance within the time step. Here, the average and final spread rates are calculated using the actual spread distance (the distance check) and initial rate of spread. This is done numerically using Newton's method to iterate travel time over the check distance.

Fire acceleration rates can be adjusted for each fuel type. Grass fuels are expected to have more rapid acceleration rates (shorter time to reach equilibrium) than fuel types will larger woody material (slash etc).

Raster Data Generation (technical documentation)

Because the fire front and its characteristics are computed as a vector, raster representation of fire growth must be obtained by interpolation. FARSITE contains a routine for generating variable resolution raster information from the fire perimeters. The routine is tightly integrated with the control structure of the simulation; rasterizing is performed between distance checks (sub-time steps). This increases the proximity of vector information used for interpolating the fire behavior and arrival time at each raster. The raster algorithm interpolates the value for arrival time and fire behavior characteristics for the center point of each raster cell falling within two successive fire perimeters.

Method for interpolating fire behavior and time of arrival for raster centroids.

The interpolation for fire arrival time is a simple inverse-distance weighted average of the radial distance between a given raster centroid and the corresponding fire perimeter segments. The fire behavior interpolation uses an inverse-area weighted average to obtain a value for fireline intensity, flame length, spread rate, or heat per unit area for each raster. Each raster centroid is contained within a quadrilateral defined by four perimeter points, 2 successive points on perimeters at each time step. Each point has values for fireline intensity and spread rate in their respective spread directions. The interpolation computes the inverse proportional areas of 4 component quadrilaterals formed between each corner and the raster centroid. The fire behavior value for the raster centroid is calculated as the weighted average of fire behavior at each corner.

Attack Simulation (technical documentation)

Ground Attack Simulation

A number of analyses have shown the effects of fire suppression on fire growth where the fire shape remains constant (Albini et al. 1978, Bratten 1978, Mees 1985, Anderson 1989, Fried and Fried 1996). Effects of direct attack and parallel attack have shown that attacking the head of a fire reduces burned area more than an attack from the back and can result in different fire shapes. Direct attack occurs at the flaming front whereas parallel attack maintains a constant distance from the active fire front. Although none of the analytical models can be applied to fire shapes that arise under non-uniform environmental conditions, they do give ready comparisons for output of simulations of suppression with uniform fire conditions.

Many factors are known to affect the rate of fireline production. Fuel type, soil type, topography, weather influences on working conditions, crew size, equipment, fatigue, and crew experience have been found to have an effect (Hirsch and Martell 1996). Of these factors, most of the variation in line construction rate can probably be explained from fuel type, crew size, and equipment. Their effect on line production has also been the most consistently documented compared to other possible factors (Haven et al. 1982, Phillips and Barney 1984, Phillips et al. 1988, Quintilio et al. 1988, Fried and Gilless 1989, Barney et al. 1992, Hirsch and Martell 1996). Simulation control over line production rate was restricted to these factors.

The simulation of horizontal rate of fireline production is assumed only to be a function of fuel type and slope for an arbitrary crew type and size. On sloping terrain the horizontal rate is computed as the product of the horizontal rate and the cosine of slope in the direction of travel. This assumes that the horizontal rate is constant in a plane parallel with the slope but that less line will be produced on steep slopes in the horizontal plane.

Direct Attack

The effect of direct attack on an active fire front is simulated using the known fire perimeter positions at two successive time steps t1 and t2. The idea is to compute the position at t2 of an attack crew building line at a given rate from its position on the fire perimeter at t1 (Figure X). The computation assumes that the range of possible solutions is defined by a quadrilateral of perimeter vertices (2 successive points at t1 and their new positions at t2). The fire perimeter points will move to their respective positions at t2 without suppression. Because this quadrilateral is obtained while adhering to the time and space resolutions set for the simulation, the suppression effects on the fireline will also be calculated within those tolerances.

On flat terrain, the effect of suppression can be represented as an circle or arc of potential solutions with a constant radius L determined by the product of the line construction rate and the time difference between t2 and t1. On sloping terrain, the arc would be eccentric along the fall-line of the slope given the above assumption of constant line production. Solutions to the suppression problem occur where the arc of suppression intersects the legs of the quadrilateral. Some potential solutions are illogical. Different methods are required to obtain some solutions depending on the length of the suppression line L relative to the dimensions of the quadrilateral.

The first case occurs when the suppression arc intersects the fire perimeter segment of t2 within bounds of the quadrilateral (L is smaller than the diagonal of the quadrilateral but greater than the spread distance). Solving for this point is done iteratively (item A in Figure). The second case occurs if the suppression arc exceeds the bounds of the quadrilateral without intersecting it. This happens when the line production rate is large compared to the spread rate and larger than the diagonal of the quadrilateral. The solution in this case is to incrementally compute the progress of line building over shorter time steps such that the length L falls within the quadrilateral (item B in Figure). The third case occurs when the rate of line production is much slower than the fire spread rate. In reality, a flanking action would be taken by a fire crew. The simplest way to "flank" the fire spread is to compute the point at which the line production parallels the route of the suppression starting point from t1 to t2 (item C in Figure).

Indirect Attack

Indirect attack is simulated by the incremental lengthening of an impermeable fireline along a predetermined route. The length of line produced is determined by 1) the rate of line production in a given fuel type, 2) the slope in the direction of travel, and 3) the time step. The distance resolution set for the simulation will interrupt the line production, forcing it to sample the landscape for information on fuel type and topography, if the length of the line in a given time step exceeds that resolution. The distance resolution also determines the width of the fireline that can't be breached by the fire spread distance in a given time step. The constructed fireline is represented as a closed stationary polygon for which mergers with active fire fronts are computed as described above (see Mergers). When a merger is detected, the vertices from the fire that have entered the interior of the fireline polygon are "turned off".

Burnout, "firing out", or "back firing" is simulated on one side of the indirect line by adding a line fire incrementally to the simulation, but behind the advancing edge of the fireline by an adjustable distance. Each incremental line fire is then merged with the existing fire fronts.

Parallel Attack

A parallel or tangential attack is simulated using a combination of the direct and indirect methods discussed above. Since a parallel attack is designed to maintain line production at a fixed distance from the fire front, the algorithm from the Direct Attack methods is used to calculate the fireline path. As described by Fried and Fried (1996), this tactic has the same theoretical solution as for direct attack. The path taken by the parallel attack in FARSITE is however, computed along the convex hull of a fire perimeter. A convex hull is the ordered set of vertices that defines the globally convex outermost edge of a polygon. The convex hull will be the same as all or part of a fire that is convex (eg. an ellipse or circle). This feature has the benefit of minimizing the horizontal length of fireline constructed and it allows for automatic burnout of unburned fuels in concave regions. Once the route for fireline production is computed, the fireline is constructed the same way as for the Indirect Attack. Burnout is accomplished in the same fashion as with the Indirect Attack methods described above.

Aerial Attack Simulation

Numerous studies have shown that the effectiveness of a retardant drop depends on density of the retardant applied to a specific fuel type. Heavy fuels such a timber or slash require higher retardant densities or coverage levels than uniformly fine fuels such as grass. George (19...) classifies retardant densities into six coverage levels. Coverage levels 1-6 correspond to 1-6 US gallons per 100 ft2 of ground surface (George ..).

Both simulations and field trials have shown that the length of a drop pattern is related to the volume of retardant and the density of its application (George...). Aircraft with multiple tanks or compartments can choose to open all tanks at once to apply a high concentration of retardant onto a short pattern or combinations of sequential discharges for lesser coverage and a longer pattern. For a given volume of retardant, higher densities are found toward the middle of the drop pattern and have substantially shorter length of coverage. The relationships between retardant volume, drop height, air speed, aircraft type have been incorporated into simple slide calculators (George19..).

There is a finite duration of effectiveness for all retardant applications regardless of the type (water, thickened, or foam). As retardant dries, its effectiveness in stopping fire spread is reduced. The limited duration is an important tactical consideration in scheduling retardant drops. Drops too far ahead of the fire may evaporate or dry before the fire gets there. Retardant applied to timber fuels with holdover potential may not be effective without subsequent attention from ground crews.

Obviously there are many other factors that actually affect the application and effectiveness of air attack. Air temperature, wind speed and direction, angle of aircraft approach, drop height, aircraft speed, and fire behavior

Process Control (technical documentation)

Surface fire Calculations

Crown Fire Calculations

Spot Fire Calculations

Limitations and Assumptions (technical documentation)

Fire arrival and behavior at a given point on the landscape is dependent on the behavior and time of travel en route to that location. This means that fire growth projections should generally worsen with time and spread distance because errors will be compounded, regardless of the accuracy or resolution of temporal or spatial data. That is, unless errors to one extreme are compensated by equal errors to the opposite.

Logically, however, a fire growth simulation should be most accurate when using accurate data at high spatial and temporal resolution. An "optimum" resolution for each landscape parameter, fire behavior type, and simulation purpose, probably exists so that the pertinent variability is preserved without irrelevant detail. The sensitivity of spatial fire simulation to the resolution and qualities of different fire input parameters on the landscape, however, remains to be tested.

Winds, Weather, and Fuel Moistures

The present version of FARSITE is capable of using two types of weather/wind inputs; 1) weather/wind streams and 2) gridded weather/winds.

Weather/Wind streams

As with previous versions, FARSITE can use the simplified weather and wind input streams. Here, the open-winds you provide are assumed parallel to the terrain and spatially constant but can vary in speed and direction over time. Spatial variability in winds is accomplished only through use of multiple data streams. Wind speeds are adjusted for mid-flame height based on canopy characteristics and fuel model. The weather streams specify daily maximum and minimum temperatures and humidities and the elevation of the observations. The time of the maximum temperature is assumed to be coincident with the minimum humidity. This will probably not be accurate for the period where thunderstorms occur or during frontal passage.

Temperature and humidity observations are interpolated with a sine-curve (sensu Rothermel et al. 1986) to acquire temperatures and humidities throughout the day. A sine-exponential interpolation (Beck and Trevitt 1989) may be an improvement, but this will have to be tested. A lapse-rate (3.5F/1000ft) is used to adjust these observations to other elevations on the landscape. Daily precipitation amounts are included in the weather stream and assumed constant across the landscape. Solar radiation at the ground surface is computed using canopy coverage and terrain information; in this version of FARSITE, all other canopy characteristics (height, height to live crown base, crown bulk density, and foliar moisture content) are assumed spatially constant except where optional spatial data themes have been provided (height, height to live crown base, and crown bulk density).

Dead fuel moistures are calculated using the procedures implemented in BEHAVE (Rothermel et al. 1986). The calculations for daily fine fuel moistures (at 1400 hours) are different from the calculations for hourly fuel moistures at other times of the day. This results in an abrupt shift in the fuel moistures at 1400 hours. It is not known how critical this inconsistency is to the results of long term fire behavior spread simulations. Live fuel moistures are assumed to remain constant throughout the simulation unless manually changed. There are currently no general models for all species of live fuels that describe moisture variation either diurnally or seasonally.

The limitations to fire spread projections of the simplified weather data are not really known. Obviously, model results would be expected to suffer where strong interactions of wind and terrain are present. Furthermore, calculations that depend on fuel temperature and moisture may not be accurate where shadows are cast by topography, precipitation varies elevationally or spatially, or water availability is significantly is altered (e.g. higher fuel moistures near streams) .

Gridded Weather/Winds

As of version 3.0, you can provide weather and/or just winds in gridded formats. see Gridded Weather for an explanation of these data.

Spread Patterns

Fire spread patterns generated using Huygens' principle with an elliptical wave have been found to agree reasonably well with observed surface fire spread under relatively simple conditions (Anderson et al. 1982, French 1992). Wind changes produced fire spread shifts close to those observed for fires spreading in grass fuels with essentially no influence of topography. It is not yet confirmed how well Huygens' principle itself simulates fire growth on complex landscapes. Sanderlin and Sunderson (1975) were apparently the first to apply a "radial" perimeter expansion technique, now generally referred to as Huygens' principle, to simulating wildland fire spread. From a comparison of predictions with observed perimeters of the Potrero wildfire (September 1973) in Southern California, they concluded that their technique was acceptable for fire growth modeling in complex situations. The only other indications from complex circumstances are from some preliminary validations of FARSITE in which observed fire spread patterns were compared against surface fire spread predicted by the model (Finney 1994, Finney and Ryan 1995, Finney and Andrews 1996). These early comparisons were promising but the many potential sources of error in the observed data (fuel maps, perimeter maps, weather data etc.) preclude definite conclusions. More validations are planned and will be necessary before the "window" of applicability might be defined.

For practical purposes, the most important result of the FARSITE tests to date has been that spread rates for all fuel models tended to be over predicted by the Rothermel spread equation (Rothermel 1972). Sanderlin and Sunderson (1975) made a similar observation and ascribed the cause to problems relating wind speed to elliptical dimensions. Some problems may be a result of inaccurate data on fuel moistures, fuel descriptions (e.g. models), and weather. Also, wind reduction factors for forested areas and lee-side topographic sheltering can undoubtedly cause errors for spread rate calculations on some parts of a landscape.

However, given all input data to be accurate, the problem with over prediction may persist; the scale of time and space-averaged winds (e.g. hourly) and spatially homogenized fuels within rasters may be too coarse to reflect fine-scale variability in fire environment (temporal or spatial) that keeps fire actually spreading at variable rates. This could force the average fire spread rate over large areas and long time spans to be over predicted. The nonlinear relationship between wind speed, fire acceleration, and fire spread rate means that the average wind speed cannot be expected to predict the average spread rate (Richards 1993). Fluctuating wind directions also cause over prediction of spread in the heading direction because they reduce the eccentricity of the fire shape compared to the ellipse (see #6 below).

The simple approach to correcting the spread rates, perhaps too simplistic for complex landscapes, is to assign rate of spread adjustment factors to each fuel type (Rothermel and Rinehart 1983). These factors must be based on empirical observations of previous fires, or of phases of growth of the existing fire, in patches of homogeneous fuels. They should be based on the heading portion of the fire, given that spread in other directions is dependent on the elliptical dimensions. It would be possible however, to compute the spread rate for one fuel type in a mixture of fuels if the following were known: 1) the fractional distance occupied by fuel type, 2) the average spread rate for the fuel mixture, and 3) the individual spread rates of other fuel components of the mixture. Then the equation for the harmonic mean (Martin 1988, Fujioka 1985) can be solved for the unknown spread rate. The adjustment factors, however, may not be constant throughout the duration of a fire. Average spread rates may change if wind variations change frequency compared to the conditions used to obtain the adjustment factor. For example, adjustment factors determined from fire spread before a cold front may be not be adequate during and after the front passes because there may be more variability in wind speed or direction than before. FARSITE provides a means to apply and change fuel model-specific adjustment factors or fuel model parameters throughout the simulation.

A number of assumptions are critical to modeling fire growth using Huygens' principle. As discussed below, some of these assumptions are probably violated by current modeling methods. The degree to which a technical violation limits the practical application of a model, however, is not yet known. This is the critical question, because models will never be fully valid at all scales or for all purposes, but may be useful nonetheless if the scope of the assumptions are clearly understood by the user. The following paragraphs present a discussion of some major assumptions of the modeling method used for FARSITE. A detailed treatment of the subject was also written by Andre and Viegas (1994).

Multiple Fires

Although FARSITE will handle up to 5,000 simultaneous fires, the fire spread patterns of neighboring fires will not necessarily be accurately represented because fire interaction with weather and fuels is not accounted for. For example, behavior resulting from "back fires" set for suppression purposes, or a prescribed fire ignition pattern that is applied to "draw" the fire together at different times, places, or stages of build-up will not be addressed by FARSITE. Extreme fire behavior, e.g. plume dominated fires, that are affected by feedback between the weather and fire behavior are not intended to be simulated by FARSITE. Users should not assume that ignition patterns used for prescribed burning will result in correct simulation of fire behavior!!

Crown Fire

The crown fire models of Van Wagner (1977, 1993, and Alexander 1988) have been implemented in FARSITE. This approach requires information on crown fuels and the forest canopy, including:

Although FARSITE presently requires a canopy cover theme, the above crown-fuel characteristics must be constant for areas having canopy coverage, unless the optional crown fuel themes have been provided to the .LCP file.

Van Wagner (1993) notes that the height to live crown base is a difficult parameter to measure. The height to live crown base is really an "effective" number that incorporates ladder fuels (see Fahnestock 1970) and understory fuels such as small trees that assist the transition to crown fire. Thus, height to live crown base will not be a simple measurement in multi-storied stands.

Heat required to ignite the crown is based only on fuel sizes on the 100hr time lag and smaller (<3" diameter). This limitation may underestimate the potential for crowning or torching because larger woody fuels (1000 hr+) and their contributions to radiative and convective heating of overstory fuels are ignored. Rothermel (1991, 1994) discusses the contribution of large woody fuels to the development of convection columns and consequent crown fire behavior.

The wind-slope vectoring for crown fire has not been tested and may not be realistic. FARSITE presently uses the wind-slope vector direction from the understory surface fire with midflame winds. The reason is that transition to crown fire in Van Wagner's (1977, 1993) model is dependent first on the surface fire behavior that is determined by midflame winds. The problem with later combining an open-wind vector with the surface slope effect is that the range of data used to develop the slope coefficient in the Rothermel (1972) model may not be applicable to crown fire. The slope coefficient depends on fuel bed parameters not accounted for by the canopy fuels in which the fire is then burning. This situation needs further work and testing.

Spotting

The existing spotting models (Albini 1979, 1981, 1983a, 1983b, Morris 1987) were originally devised to predict the maximum distance burning embers would travel over flat and regularly undulating terrain. The maximum spotting distance is determined by the balance between particle size, burnout rate, and time or distance traveled. Smaller particles are lofted higher and transported further, but burnout sooner than larger particles. Thus, as published, Albini's equations for the maximum spotting distance cannot be implemented for complex topography because winds, terrain, and forest canopy can all vary.

At present only the model for spotting from torching trees (Albini 1979) is present in FARSITE. The purpose of the spotting capability of FARSITE is to compute the maximum distances that particles of different sizes would travel over complex landscapes. These indicate the potential distances ahead of the fire that spotting could be found, assuming winds vary only as a function of height above ground or as specified spatially by the weather/wind grid. Nevertheless, this greatly oversimplifies reality in mountainous terrain.

Depending on topography, Albini's equations may suggest the farthest spotting distances are produced by larger particles that aren't transported over deep ravines. The spotting model in FARSITE does not intend to predict the number of embers produced, or exact locations that embers will land, only the direction and distance embers might land.

Spotting is produced whenever some form of crown fire develops (torching and running crown fire). You must recognize, however, that the torching tree model of ember lofting was not intended for representing ember lofting from a running crown fire. It will likely underestimate both the ember sizes, lofting height, and ultimate spotting distances under conditions of running crown fire.

Ground Attack Simulation

The mechanics of simulating direct and indirect tactics are described in the Attack Simulation section of the Technical References. As with fire growth simulation, the techniques used here assume that variations in the fire environment in time or space at scales finer than those specified by the model parameters will not necessarily have influence over the progress of fire suppression. Thus, fuel variations or fire characteristics that normally would affect suppression efforts cannot be simulated at finer scales than the fire growth simulation. There are no slope limitations to the operation of mechanized equipment such as dozers.

Fire suppression activities are not affected by areas of non-fuel (barren, rock, lakes etc) in terms of travel time across them or in changing decision tactics when they are encountered. If indirect line is routed across a lake, the crew will merely skip to the other side of the water when it encounters the lake (resuming suppression along the remaining part of the route) and not count the travel time required to circumnavigate the lake.

Line production rates are maintained independently when more than one crew is assigned to the same portion of a given fire. Two crews that attack the same part of an active fireline will essentially "leap frog" each other, attacking alternating segments of the active fire perimeter. For example, if a slow crew and a fast crew are working on the same portion of the perimeter, the suppression line will alternate between fast and slow segments.

Users are responsible for providing their own line production rates. The values in any example files are for demonstration only.

A direct attack will continue on the original fire front until finished or until the user reassigns it. For example, if an attack is initiated against an outward burning fire front it will always remain on the outside of the fire front even if it begins attacking a concave portion of the fire perimeter that then becomes isolated as an enclave. This keeps the direct attack faithful to its original intent, that of limiting the expansion of the fire. You can however, attack an inward burning fire front (enclave).

A parallel attack cannot be assigned to an inward-burning fire front (e.g. an enclave). Instead, the direct attack can be used to suppress inward fire fronts.

Air Attack Simulation

It is assumed by the simulation that a retardant pattern will always be impermeable to an approaching fire front until its user-defined effectiveness has expired. In reality, most applications of retardant are supported by ground crews to ensure fire doesn't breach the treated area. Furthermore, the effectiveness of a retardant drop is not sensitive to fire behavior, although spot fires can be initiated beyond the fire line.

The user is responsible for selecting realistic performance parameters for the aircraft, the coverage level and line length, and the effective duration. No explicit consideration is given for factors affecting retardant longevity such as air temperature, shading, or fuel type. The user can however, implicitly incorporate such elements into the setting for effective duration.

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Passive or Torching	Active	Independent

Low windspeed, low Crown Bulk Density & Cover, high Crown Base Height.	Higher windspeed, high Crown Bulk Density & Cover, low Crown Base Height.	Very high windspeed, very high Crown Bulk Density & Cover.
Types of Wind Driven Crown Fire

For each timestep (date and time specified)
{	For each fire
	{	For each vertex (X, Y)
		{	Get the fire environment (fuels, weather, topography)
			Calculate fuel moistures from initial conditions
			Calculate vertex orientation angle
			Calculate surface fire (below)
			if (Canopy Cover > 0) Calculate crown fire (below)
		}
		Preform Direct and Parallel Attacks
		Update Raster Output Maps (arrival time, fire intensity, etc.)
		Correct crossovers
		Compute area and perimeter
	}
}
Ember flight, ignition, growth from time of contact
Perform Indirect and Aerial Attacks
Merge all fires

{	Compute forward equilibrium spread rate
	Vector wind and slope
	Compute elliptical dimensions using resultant wind-slope vector
	Compute spread rate R by accelerating fire over timestep
	Compute average spread rate of fire over timestep
	Compute spread differentials
	Slope transformation
	Compare fire spread with distance resolution
	if (fire spread is truncated to distance resolution)
	{	Compute time to spread distance resolution with acceleration
		Adjust spread distance to distance resolution
		Reduce time elapsed to accomplish distance resolution
	}
}

{	Calculate Critical Surface Fire Intensity Io
	if (actual surface intensity>= Io)
	{	Compute crown fraction burned
		Compute acceleration constant for crown fire spread
		Compute maximum crown fire spread rate
		Vector open wind and slope
		Compute elliptical dimensions using resultant wind-slope vector
		Compute critical crown fire spread rate
		Compute actual crown fire spread rate
		if (actual crown fire spread >= critical crown fire spread rate
		{	Accelerate crown spread rate
			Compute crown spread differentials
			Slope Transformation
			Compare fire spread to distance resolution
			if (crown fire spread is truncated to distance resolution)
			{	Fire acceleration as a function of distance resolution
				Adjust spread distance to distance resolution
				Reduce time elapsed because of increased spread rate
			}
			Compute Crown Fire Intensity
			Ember Lofting from Active Crown Fire
		}
		else
		{	Compute Crown Fire Intensity
			Ember Lofting from Torching Trees
		}
	}
}

{	Lofting
	{	Determine plume characteristics (for torching tree)
		Loft embers
	}
	Flight
	{	Iterate horizontal and vertical ember flight path
	}
	Ignition
	{	Determine if ember lands inside existing fires
		Ignition Frequency
	}
}