Fire sub-model

Design concepts

The fire sub-model has been designed to allow the fire spread rate to partially depend on the main factors determining fire shapes in real landscapes (Rothermel, 1972). Specifically, fire spread rate is calculated as function of fuel load (using time since fire as a proxy), topography, wind direction and burnable covers. Therefore, the shape of a fire arises as a result of distinct rates of fire spread from one cell to the other (Figure 1). In contrast, fire size is primarily determined by applying a top-down approach in which the potential burnt area by each fire is selected from an input distribution of fire sizes (as in Pennanen and Kuuluvainen, 2002). Potential fire size distribution depends on the climatic severity of the year. Adverse years are characterized by a high number of weather risk days (Piñol et al., 1998). Therefore, the statistical distribution of fire sizes in adverse years has a higher probability for large wildfires compared to normal (non-adverse) years (Pausas and Paula, 2012). Total area burnt per year is also drawn annually from a statistical distribution that differs in adverse compared to normal years.

The explicit inclusion of processes leading to fire extinction may help gaining insight on the factors determining fire size distributions (Loepfe et al., 2011). In the MEDFIRE model, two distinct fire suppression strategies are implemented, both related to the concept of fire fighting opportunity, which is defined as instances in which low fire intensity allows fire fighters to control and extinguish it. The first suppression strategy (active suppression) concerns opportunities generated in areas where spread rate (an indicator of fire intensity) is below a certain threshold and therefore low enough to allow fire-fighting crews to stop fire from further spreading. The second suppression strategy (opportunistic suppression) is based on opportunities derived from recent fire scars. In these areas, previous detailed knowledge of their location and low fuel loads allow a very high increase in fire-fighting capacity. The two suppression strategies differ in the mechanisms driving such reductions in effective area burnt: while opportunistic fire suppression strategy accounts for opportunities derived from past fire history, active fire suppression mimics overall fire fighting capacity under slow fire propagation conditions. We have distinguished these two strategies because while active fire suppression effectiveness may depend on the amount of resources allocated to fire fighting, the effectiveness of opportunistic fire suppression is in fact only dependent on historical fire patterns. Therefore, it is important to identify to which degree the impact of fire suppression may be explained by the interaction with previous fire history or due to the increase of funding allocated to fire-fighting. Both suppression strategies lead to an effective fire size that is smaller than the potential fire size (Figure 2). As a consequence, effective area burnt is an important emergent property of the MEDFIRE model and allows assessing the role of climatic variability (i.e. proportion of climatic adverse years) and fire suppression in the determining fire impact and fire size distributions.

Details

The fire sub-model is responsible for simulating a fire regime in the study area. This landscape event is scheduled once every year in summer. The sub-model begins by determining either from a preselected distribution or an input table whether the current summer is climatically normal or adverse. After that, a total annual extent to be burnt is drawn from a statistical distribution, which differs depending on whether the summer is climatically normal or adverse (AnnualBurnDistNorm and AnnualBurnDistSevr). For each fire, the sub-model stochastically selects an ignition point, the target fire size and a spread type (either relief- or wind-driven). As for the total annual extent to be burnt, distinct fire size distributions are used for climatically normal and adverse years (FireSizeDistNorm and FireSizeDistSevr). If fire suppression is not active, the fire is allowed to spread from its ignition point until the burnt extent equals the fire size (all burnable LCTs are counted when calculating burnt extents). In contrast, if fire suppression is active not all the cells potentially affected by a fire will be effectively burnt. Ignitions starts and fires spread one after the other sequentially until the total annual extent to be burnt is reached.

Ignition point and fire size

Ignition points are restricted to occur among cells with burnable LCT (i.e. urban, water and rock covers are excluded). In order to determine the spatial distribution of ignitions the model uses an input layer that describes the probability of ignition for each grid cell (ProbIgnition) based on a basic fire risk index. The spread type layer contains the proportion of relief-driven vs. wind.driven fires for each cell in the grid. A Bernouilli trial with the probability of relief-driven fires taken from this proportion is used to determine the spread type (Castellnou et al., 2009).

Fire spread, burn and extinction

Before starting a given fire, a value for its fire size is drawn from a statistical fire size distribution. This value sets the target extent to be burnt. The process of fire spread is as follows. A given cell that is set to burn is called an active cell. The first active cell is the grid cell selected as ignition point. For each active cell, its eight immediate neighbors are considered as cells where the fire can spread. We refer to these as spreading cells. For every spreading cell the model calculates a spread rate (SR > 0), which is a dimensionless number but is used to determine the order in which spreading cells are processed (removed from the event queue). Cells with low SR values are processed later than those with high SR values. When a given spreading cell is processed, the model then calculates the probability of burning (Pburning) and determines whether the cell burns or not using a Bernouilli trial. If the cell burns it becomes an active cell, and the spreading algorithm is processed for that cell. Otherwise the fire front at this point is stopped. The spatial pattern of a given fire arises as a result of differences among cells in the rate of spread and probability of burning. In other words, different combinations of spread rate and propensity to burn control fire shape and the proportion of unburned islands. Fires generally burn until their burnt extent equals the pre-specified fire size. Hence, the fire extent may be reached before slow-spreading cells are processed. Once the target extent is reached, all active cells on the front are stopped and the fire is completed. To ensure that fires do no stop before the target extent is reached, cells on the front that do not burn are kept in a randomly sorted list and the fire front is re-ignited if needed from these cells. Otherwise, these remain unburned. The following describes how the rate of spread and the probability of burning are calculated.

A) Rate of spread

There are two kinds of fire spread, relief- and wind-driven, which imply different ways of calculating a basic rate of spread (Base). In order to model the influence of fuel load in the rate of spread, the Base value is modified according to LCT, TSF and Aspect values of the spreading cell.

a1) Relief-driven spread

The basic spread rate in a relief-driven fire is modeled as follows: First, the difference in altitude between the spreading cell and the active cell is assessed. This difference allows calculating the slope of the burning front (estFireSlope), which is afterwards bounded between –0.5 and +0.5 (±50%). The slope of the burning front is used to calculate a base rate of spread following:

Base = (1+rSlope) ^ (estFireSlope+0.5) (eq. 1)

where rSlope specifies the extent to which slope modulates the spread rate. Note that Base = 1 when the slope of the burning front is -0.5 (downhill) and Base > 1 for higher values of slope.

a2) Wind-driven spread

The basic spread rate for a wind-driven fire is calculated as follows: First, fire spread direction is defined as the vector from a fire anchor point to the spreading cell. The model then measures the angle (in degrees) between the direction of fire spread and the wind direction vector (degreesOffWind). This value, which ranges from 0 to 180 degrees, is used to calculate the basic spread rate following the function:

Base = (1+rWind) ^ ((180 – degreesOffWind) /180) (eq. 2)

where rWind specifies the extent to which degreesOffWind modulates the spread rate. Using this formula, Base = 1 when the fire is spreading against the wind (degreesOffWind = 180) whereas Base > 1 for fire fronts with lower angles between the wind direction and the direction of fire spread. The initial fire anchor point for any fire is the ignition point. As fire spreads, however, if the local fire spread direction deviates significantly (> 45 degrees) from the direction from the anchor point (e.g. due to barriers such as urban or rock, or due to slower spread or local fire extinctions), the anchor point is updated. In this way broad scale fire direction can reduce bias from spreading within a grid (to eight neighbours on 45 degree angles), yet local effects that influence direction can be included to ensure fire direction responds to landscape structure. The fire anchor points tend to be located in areas that cause discontinuous changes in fire direction, such as non-burnable LCTs, areas with slower spread or low probabilities of burning, areas with local fire suppression, etc). After passing such areas, fire spread rate increases again in the direction of the wind.

a3) Fuel load

Fuel load (Fuel) is calculated using the LCT, TSF and Aspect values of the spreading cell. TSF values are re-scaled to the [0-1] interval and the result is stored as TSFExp. Aspect is used to modulate fuel load by setting AspExp = -1 when the spreading cell is oriented to North, AspExp = +1 when it is oriented to South and AspExp = 0 otherwise. Each burnable LCT has its corresponding fuel quality parameter, fLCT, assessed by calibration. The fuel load is then calculated as:

Fuel = (1+rAspect) ^ (AspExp) · (1+rTSF) ^ (TSFExp) · (rLCT · fLCT) (eq. 3)

where rAspect, rTSF, and rLCT specify the extent to which differences in Aspect, TSF and LCT respectively modulate the fuel load.

a4) Spread rate

The Base and Fuel values are combined to calculate the rate of spread (SR) as:

SR = 1 - exp(-Base · Fuel) (eq. 4)

Note that rSlope, rWind, rAspect or rFuel equals 0, and rLCT equals 1, implies no driver effect on the spread rate.

B) Probability of burning

Whether a cell burns or not mainly depends on the spread rate. Slower fires are assumed to be more likely to go out due to local conditions (slow fires are most likely lower intensity, such as heading downhill, against the wind, across lower flammable types, etc.). The probability of burning is simply calculated as:

Pburning = SR ^ SR_BurnExp (eq. 5)

where exponent SR_BurnExp controls the relationship (linear, quadratic, …) between spread rate and probability of burning.

Fire suppression

Two distinct fire suppression strategies are implemented, both related to the concept of fire fighting opportunity. The first suppression strategy concerns opportunities generated in areas where SR is lower than a pre-specified threshold (SRThreshFF). The second suppression strategy is related to opportunities given by low fuel loads and consists in suppressing the fire whenever TSF is lower than a pre-specified threshold (TSFTreshFF). For any of the two fire suppression strategies, if a cell is said to burn but complies with the required condition it will not burn. However, the model allows the fire to continue spreading from that cell (but without effectively burning), so that areas that would have been reached via spread beyond the suppression opportunity point also do not burn.

Fire effects

Cells that are effectively burned have TSF set to 0. The fire extent is calculated as the number of cells that effectively burned plus the number of cells that would have burned but did not because of fire suppression of all burnable LCT cells reached via spread.

Figures

Figure 1: Two replicates of fire patches simulated by MEDFIRE in the period 1989 - 1999

Figure 2: Patches of observed and simulated fires (a): dark grey areas are recent burn perimeters which time since last fire is less than 15 years and light grey extension are ancient patches. The footprint of a simulated fire (b) which effective burnt area (light grey) does not reach all the target extension because of fire fighting opportunities generate suppressed areas (dark grey).

References

Castellnou, M., Pagés, J., Miralles, M., Pique, M., 2009. Tipificación de los incendios forestales de Cataluña. Elaboración del mapa de incendios de diseño como herramienta para la gestión forestal. In: Proceedings of the 5th Congreso Forestal Español. Ávila, Spain.

Loepfe, L., Martinez-Vilalta, J., Piñol, J., 2011. An integrative model of human-influenced fire regimes and landscape dynamics. Environmental Modelling & Software 26, 1028–1040.

Pausas, J.G., Paula, S., 2012. Fuel shapes the fire–climate relationship: evidence from Mediterranean ecosystems. Global Ecology and Biogeography.

Pennanen, J., Kuuluvainen, T., 2002. A spatial simulation approach to natural forest landscape dynamics in boreal Fennoscandia. Forest Ecology and Management 164, 157–175.

Piñol, J., Terradas, J., Lloret, F., 1998. Climate warming, wildfire hazard, and wildfire occurrence in coastal eastern Spain. Climatic change 38, 345–357.

Rothermel, R.C., 1972. A mathematical model for predicting fire spread in wildland fuels, USDA Forest Service Research Paper INT USA.