Fire disturbance is an important landscape process. Fires appear to be stochastic for a single site, but have repeated patterns in terms of ignition, location, size, and shape at landscape scales. It has long been noted that some areas are more fire-prone than others. The differences are often represented by using mean fire-return intervals; the mean number of years for fire to recur on a given area (Johnson 1992, Johnson et al. 1990, Pickett and Thompson 1978, Pickett and White 1985, Pickett et al. 1989). Depending on their extent, large landscapes can be stratified into ecoregions, relatively homogeneous sub-areas that are characterized by different climate, topography, and soils with similar fire characteristics. Such ecoregions can be used as the fire regime map in LANDIS in which each fire regime unit is characterized by its attributes in the fire regime attribute file.
As a disturbance module, a fire disturbance simulation module in LANDIS must address when and where such a disturbance occurs, how such a disturbance spreads over the landscape, and what effects it has on the forest landscape. Therefore, a fire module must include the following three major components:
The fire module also reads its own input and writes its own output just as the other modules do.
The fire module in LANDIS 4.0 uses a hierarchical fire frequency model to simulate temporal patterns of fire regimes. This differs from past approaches (Baker et al. 1991, He and Mladenoff 1999a, Johnson 1992, Turner et al. 1994), which use a statistical distribution of fire frequency to simulate fire occurrence. The hierarchical fire frequency model divides a fire occurrence into two consecutive events-fire ignition and fire initiation (fig. 4). A fire occurrence begins with an ignition attempt from an external heat source that heats the forest fuel complex up to its ignition temperature. Fire ignition agents are either natural (lightning) or anthropogenic (e.g., arson or accidental). A fire initiation event starts with the ignition and is successful when an area equal to the cell size is burned (Li 2000, 2001). Whether a fire ignition can result in fire initiation is dependent on the fuel loading, fuel arrangement, and fuel moisture content.
For a given time step (e.g., year 10), LANDIS first generates the number of ignitions (X) in the given fire regime unit from the Poisson distribution with the parameter ignition density λ (i.e., average fire ignitions per decade per hectare). For each ignition, LANDIS performs a Bernoulli trial, whose result is denoted by Yi (ignition result), with the parameter fire initiation probability Pi, whose value is determined by the time since last fire of the ignited cell if the fuel module is turned off (equation 1), or fine fuel class if the fuel module is turned on (specified in fire parameter file):
P(t) = 1 - e-t/FC (1)
where FC is fire cycle, t is time since last fire, P is fire initiation probability. If the ignition becomes an initiation, we assign 1 to Yi, otherwise we assign 0 to Yi. The summation of the result of all ignitions generated for a given fire regime unit per decade (ΣYi, i = 1,2,...,X ) is then the number of fire occurrences per decade for the given fire regime unit. For each initiation, LANDIS will randomly select a fire size, denoted by Z, from a log-normal distribution (fig. 4) with parameters μ (Mean Fire Size: MFS) and σ2 (Standard Deviation of Fire Size: STD) to simulate fire spread. The overall structure is depicted in figure 5.
Figure 4.-Fire size follows log-normal distribution with small fires occurring more frequently than large fires.
Since a landscape often consists of more than one fire regime unit, it is possible that a fire starts from one fire regime unit and spreads to another. When a fire reaches another fire regime unit, LANDIS will use a new fire ignition from the ignition pool of this new fire regime unit. If such a new ignition becomes a fire initiation, LANDIS will randomly draw another fire size from the fire size distribution defined on this new fire regime unit. Such a fire will be recorded as one single fire event in the fire log files, but it actually consists of two fire occurrences.
Figure 5.-The overview of the fire occurrence simulation design.
LANDIS 4.0 has two algorithms to simulate fire spread. The first one is a percolation algorithm similar to the algorithms of Gardner et al. (1999), Clarke et al. (1994), and Wimberley et al. (2000) to simulate fire spread. Fires simulated by the percolation algorithms spread from a burning cell to forested cells in the cardinal directions (up, down, left, and right). These cells are entered into a priority queue in a random order. The first cell in the queue has a higher priority of fire spread. The fire will continue to spread until it reaches its predetermined size. LANDIS does not allow a forested site to be burned more than once within one time step, and nonactive land types or ecoregions (e.g., roads, lakes) may serve as fuel breaks in the landscape. Therefore, it is possible for a fire to be extinguished prior to burning its predetermined size if the fire reaches fuel breaks or newly burned sites. In a real landscape, fires may spread across the boundaries of fire regime units where the fire size distribution changes. When a fire spreads into a different fire regime unit, the module will simulate a new ignition. If the new ignition results in an active fire, a new predetermined fire size will be selected based on the fire size distribution for the new fire regime unit.
The second algorithm used in LANDIS 4.0 is similar to Hargrove et al. (2000), a modified percolation method with a fire front, which can simulate fire spread behavior with respect to fuel configuration, topography, and prevailing wind. A fire front is defined as t he part of a fire within which continuous flaming combustion is taking place. The fire front in LANDIS is assumed to be the edges of the fire perimeter. Fire will spread out from the fire front along eight directional (N, NE, E, SE, S, SW, W, NW) neighbor sites. The directional spread probability in each site is computed by its own fuel quality and quantity, biased with topographical aspect and slope, and wind direction and speed:
P = 1 - e -( 1 + r1) y ( 1 + r2 ) Z ( 1 + r3 ) wkx (2)
where r1 is wind coefficient, which serves as an adjustment so that the user can increase or decrease wind effect on the directional spread probability calculation. If r1 = 0, then there is no wind effect on the directional spread probability calculation no matter how much wind speed ( y ) is. Similarly, r2 is the topography coefficient, r2 is the predefined fire size distribution coefficient, and k is the fuel coefficient. In LANDIS parameter files, k is surrogated by the base probability for fuel class 3 (denoted by prbase) when there are no other factors on spread probability (i.e. r1, r2, r3, are all 0). Equation 4 shows the relation between k and base probability:
k = log (1 - prbase) / (-3) (3)
Equation 3 denotes the relation between fuel coefficient and base probability for fuel class 3. There are four independent variables in the fire spread probability equation: y is wind speed class (0, 1, 2, 3, 4, 5), z is topographical slope ( - π / 2 to π / 2 ), is fuel class (i.e., the potential fire intensity class (0, 1 ~ 5) in the fuel module), and w is predefined fire size effect, a normalized ratio of current fire size to predefined fire size (equation 4) used for indicating how much effect current fire size can affect fire spread probability. The range of w is from 1 to negative infinity. However, in LANDIS practical simulations, w usually ranges from 1 (when current fire size equals 0) to –1 (when current size equals predefined size). It decreases when current size increases, and it will be zero when fire spread reaches half of predefined size.
w = 1 - 2CS / FS (4)
where CS is current simulated fire size, and FS is predefined fire size.
Fire intensity is determined by the quantity and quality of fuel. When the fuel module is turned off, a simple framework (fire curves defined on fire regime unit level, please refer to 13.2 for details) is designed to reflect the relationship between fuel quantity and years of accumulation on different fire regime units. Fire intensity is categorized into 6 classes (0 ~ 5, with a class 5 fire the most intense). When the fire module is on, LANDIS will directly use potential fire-intensity class calculated in the fuel module instead.
Fire is a bottom-up disturbance, such that fires of low intensity affect only younger age classes first. Also, fire tolerance varies among species fire-tolerance classes. To implement these two characteristics, species fire-tolerance classes, containing five categories from 1 to 5, are designed to reflect the differences of fire tolerance among species. Species fire-susceptibility classes are designed to reflect differences related to age. A fire of a given intensity interacts with individual species and age cohorts through the species fire tolerance and age susceptibility. The interactions of fire with species fire tolerance and age susceptibility have been explicitly defined in He and Mladenoff (1999a) (e.g., fig. 6).
Figure 6.-Fire intensity vs. fire tolerance (species classes) and susceptibility (age classes). Each individual bar represents the removal range of species of a given age class under fire-intensity class three.