SWRA Model

Webster's dictionary defines risk as "The possibility of suffering harm or loss." As one can see, there needs to be both a likelihood and effect of an action or event before one can incur a risk. Two primary indices were assigned to each 30- by 30-m cell in all 13 southern States including Florida. These are the Level of Concern (LOC) Index and the Fire Response Accessibility Index (FRAI) (Figure on the right).

Within the risk assessment, the Level of Concern is the best measure of wildland fire risk. The Level of Concern Index is calculated from the likelihood of an acre burning, called the Wildland Fire Susceptibility Index (WFSI) and the expected effects of the fire (Fire Effects Index, or FEI). The FRA Index is a measure of the initial attack response time to a cell from existing initial dispatch locations for fire protection resources. Taken as a pair, these two indices define a cell’s accessibility and its vulnerability to wildland fire occurrence and effects.

As used in the Florida and Southern Fire Risk Assessment, the Wildland Fire Susceptibility Index is a value developed to represent an index related to the probability of an acre burning. The determination of an acre burning integrates the probability of an ignition and expected final fire size, the latter being affected by rates of fire spread in four weather categories and fire suppression effectiveness.

Fire Occurrence (Fire Occurrence Areas)

The first task to determine the WFSI is to determine the probability of an acre igniting. A Fire Occurrence Area (FOA) is an area where the probability of each acre igniting is the same. The historical fire ignition locations for a defined period of time are used. Pictorially, if one were to locate the point location for historic ignitions on a map of an FOA, the points would appear with randomly dispersed densities different from adjacent FOAs.

Fig. 1 - Flagler County, Fire
Occurrence Areas

A grid illustrating the probability of a wildfire igniting was developed using ArcMap by analyzing the location of historic ignitions from 1997 to 2003. Fire occurrence rates in Fire Occurrence Areas were described as the number of fire ignitions per 1,000 acres per year. A surface grid with fires per 1,000 acres per year was generated using a spatial filtering calculation available in ArcMap. FOAs were developed to identify areas where the probability of a fire igniting was similar. Hence, within an FOA, the probability of each acre igniting is the same.

An example of a FOA map for Flagler County in Florida is shown in Figure 1.

Weather Influence Zones

Fig. 2 - Weather Influence Zones
in Florida

To determine an estimate of fire spread upon fire ignition using a fire behavior model, environmental conditions are needed so that fuel moisture and wind speed values can be used in the fire behavior models. To determine these environmental conditions, areas of uniform weather conditions were defined and the weather conditions within each area determined. A Weather Influence Zone (WIZ) is an area where the weather on any given day is uniform. A fire weather meteorologist developed 20 Weather Influence Zones in Florida, and these are displayed in Figure 2.

Development of Percentile Weather Values

Within each WIZ, daily weather data is gathered for a defined period of time. This data was gathered from land management agency weather stations (National Fire Danger Rating System (NFDRS)) and from National Oceanographic and Atmospheric Administration (NOAA) maintained weather stations. A computer program developed by research meteorologist Dr. Scott Goodrick (Forestry Sciences Laboratory, 320 Green Street, Athens, GA 30602-2044) was used to change weather observations from NOAA stations to NFDRS standards. Another program developed by Dr. Goodrick was used to georeference the weather observations from the weather stations within a WIZ to the geographical center of the WIZ. Hence, one weather data set was developed with a weather observation for each day during the defined time period for each WIZ. From this weather data set, percentile weather was developed for each WIZ.

The weather observation data set was checked for errors and then imported into the USDA Forest Service’s FireFamilyPlus program. The NFDRS index Spread Component (SC) was calculated for each day. The fire season was set for each WIZ and the SC calculated using the NFDRS fuel model G. Fuel model G is used as it contains fuel loading in all of the dead (1-h, 10-h, 100-h and 1000-h) and live (herbaceous and woody) fuel categories. This allows for the influence in the Spread Component calculation of the fuel moisture values from all of the fuel categories. In addition, climate class 3 (subhumid/humid) and slope class most applicable to the WIZ were used.

The Spread Component was then divided into four commutative percentile categories: Low (0-15 percent), Moderate (16-90 percent), High (91-97 percent), and Extreme (98-100 percent). The median SC was determined for each category. The environmental values for 1-h, 10-h, 100-h timelag fuel moisture, live herbaceous fuel moisture, live woody fuel moisture, and the 20-foot, 10-minute average wind speed were determined as the average of the respective values on days when the SC was equal to the median SC. This allows for the determination of four percentile weather categories with the percent of occurrence of each category and with environmental values to define the weather conditions within each category.

Probability of a Fire Occurrence within Each FOA by Percentile Weather Category

We allow for the possibility that the higher percentile weather categories may be relatively more conducive to generating fire ignitions from ignition initiating sources. That is, if 15 percent of the days during the fire season are in the Low Percentile Weather Category, one cannot assume that 15 percent of the fires during the fire season will occur on the days in this percentile weather category. Four percentile weather categories were developed: Low, Moderate, High, and Extreme. The percent of days within each is 15 percent, 75 percent, 7 percent, and 3 percent, respectively.

Each fire within the fire occurrence database for all agencies within a Weather Influence Zone has a fire start date. Each historic fire was assigned a Spread Component based on the fire’s start date from the results of the FireFamily Plus runs. The four percentile weather categories were also developed using the same assumptions for SC, and the four categories have SC ranges. Hence, a correlation is made assigning each historic fire to one of the four percentile weather categories. From these assignments, the proportion of fires that occurred in each percentile weather category by WIZ was determined. For Florida, 14.2 percent, 74.1 percent, 8.1 percent, and 3.5 percent of the fires started within the Low, Moderate, High, and Extreme categories, respectively.

The probability of a fire within an FOA for each percentile weather category is the product of the total fire occurrence rate in the FOA by the proportion of fires within each percentile weather category.

Surface Fuel Models in Florida

Predicting fire behavior requires knowledge of fuels, weather, and topography. The previous section provides information on how the environmental conditions (weather) can be determined. The topographic conditions required are knowledge of slope steepness, aspect, and elevation. Aerial and surface fuel data that are required include canopy cover and the surface fuel model. If aerial fuel attributes are provided, then the occurrence and behavior of a crown (canopy) fire can be modeled. The aerial attributes needed are canopy base height (CBH), canopy bulk density, and stand height.

Data layers for the State were developed for slope, aspect, and elevation for USGS DEM information. Fuel models for Florida were developed in 2002 for the FRA using a process where actual satellite imagery was correlated with the surface fuel model. These fuel models were also used in the SWRA, and a statewide fuel model map is displayed in the figure on the right. An SFRA and FRA design requirement was to classify each acre of burnable land using the fuel models (Anderson 1982) in the Fire Behavior Prediction System (FBPS). A data layer defining the percent canopy cover was developed using satellite imagery for Florida. For the FRA and SFRA, none of the canopy fuel layers (Canopy Ceiling Height, Canopy Base Height and Canopy Bulk Density) were developed or used. All fire behavior predictions were based on surface fuel models.

Fire behavior outputs are a key component of the model used to estimate the WFSI. Potential fire behavior can be evaluated using a fire behavior prediction program, much like FARSITE (Fire Area Simulator) (Finney 1998) and FlamMap (Finney 2006). For the FRA, the FlamMap program was used.

The fire behavior program uses topographic information, fuel characteristics, and weather to calculate rate-of-spread, flame length, fire type, and other characteristics of fire behavior. Fire behavior prediction can also be done using a fire behavior dynamic link language (dll) program, which provides a more flexible and customizable method of calculating the required fire behavior outputs needed for the risk assessment model. The fb3.dll used in the SFRA has the advantage of providing tight integration capabilities with GIS systems and other programs.

The main fire behavior variable calculated by the fire behavior prediction programs such as the fb3.dll for the calculation of the WFSI is fire spread rate. This variable was developed because it can be used to estimate a fire’s expected size.

For further analysis and display, it is worthy to note that additional fire behavior outputs such as fire intensities and flame length are available outputs of the fb3.dll program. The FlamMap program and the fb3.dll calculate the behavior of a fire occurring in each 30- by 30-m cell under defined weather conditions. Fire behavior is described independently for each individual cell.

For a cell, the FOA designation provides an estimate of the cell igniting. To calculate the WFSI, the expected size of a fire needs to be determined. To do this, it is necessary to develop relationships between fire spread rates and the expected final fire size. The inputs to this relationship are the expected fire behavior, which depends on fuels, weather, and topography and a measure of suppression effectiveness of fire protection forces.

For each Weather Influence Zone, a relationship between the rate of spread and final fire size is developed using historic fire report data. This relationship can also be determined from the outputs of preparedness staffing modeling. Development using historic fire reports data requires the creating of several fire size classes where the time from fire start to fire containment can be estimated using fire report data. For all Weather Influence Zones, the time from fire start to fire containment for the benchmark fire sizes of 0.5, 2, 10, 50, 100, 500, and 1,000 acres were determined. Additional fire sizes greater than 1,000 acres are used when fires of these sizes occurred historically within a WIZ.

The average fire rate of spread for each benchmark fire size is estimated by using the double ellipse area model developed by Fons (1946) as documented by Anderson (1983). The model calculates fire size (Area) as: Area=K * D² where K is a constant dependent solely on midflame wind speed, and D is the distance the fire has traveled from its point of origin (D=rate of spread times containment time). A relationship between the fire size and average rate of spread values for the benchmark fire sizes is developed using multivariable regression using a power series equation form (Y=A+B*X^C+D*X^E where X=rate of spread, Y is the expected fire size and A-E are the regression coefficients). In some cases, a 4^th order polynomial equation form was utilized. In some WIZes, the constant term A was changed so that a 0.5-acre fire was expected when the rate of spread was 1 chain per hour (1.1 feet per minute). In addition, for each WIZ a maximum fire size was assigned.

Fig. 1 - Example WIZ and FOA

The cellular value for the probability of an acre burning (CPAB) is calculated for each percentile weather category for each 30- by 30-m cell on burnable acres within the State of Florida. The four values from the four Percentile Weather Categories are summed to obtain the total cellular value for the probability of an acre burning for a cell. The calculation is done for cells within an FOA and WIZ intersection. When the calculation is done for a cell, it is assumed that all cells in the FOA and WIZ intersection have the attributes of the cell. In essence, one is asking, “What would be the expected probability of an acre burning if all cells in the FOA and WIZ intersection were the same as the selected cell?”

To assist in the understanding of the calculation, an example is presented. Assume that the calculation is being done for a cell in FOA 1, WIZ 1 (Figure 1, bottom arrow directs reader to Table: Example Calculation of the Cellular WFSI). The data flow is shown via the example in (Table: Example Calculation of the Cellular WFSI).

Fig. 2 - Weather Influence Zones
in Florida

For the example, assume that the fire occurrence rate in FOA 1 is 0.1 fires / 1000 acres / year and assume there are 1,000,000 acres in the FOA 1, WIZ 1 intersection (Figure 2).

Note there are 100 fires per year. Row 1 of Table: Example Calculation of the Cellular WFSI gives the Percent of fires that have historically occurred within each of the Percentile weather categories. Multiplying the Proportion of fires in each Percentile weather category by the total number of fires in the FOA 1 / WIZ 1 intersection (100 fires) allows for determination of the Number of fires in each Percentile weather category, Row 2 of Table: Example Calculation of the Cellular WFSI.

Fig. 3 - Flagler County,
Cellular WFSI

The fire program (FlamMap for the FRA and the fb3.dll for the SFRA) has calculated a Rate of spread for each Percentile weather category (Row 3, Table: Example Calculation of the Cellular WFSI) and a Rate of spread versus expected Final fire size relationship (Row 4, Table: Example Calculation of the Cellular WFSI) has been determined. This allows for the determination of the expected Final fire size within each Percentile weather category.

Multiplying the Number of fires per year in each Percentile weather category by the expected Final fire size yields the Annual expected acres burned for each Percentile weather category (Row 5, Table: Example Calculation of the Cellular WFSI). Dividing the Annual expected acres burned for each Percentile weather category by the total acres within the FOA 1, WIZ 1 intersection (1,000,000 acres) yields the CPAB within each Percentile weather category (Row 6, Table: Example Calculation of the Cellular WFSI). The CPAB for the cell is the sum of the four Percentile weather category CPAB values (Figure 3).

Fig. 4 - Flagler County,
Roving Window WFSI

To consider the flammability of cells in the area of a given cell, a roving window (8 cells in radius) is drawn around each cell, and the average WFSI for all of the cells within that roving window is determined resulting in the roving window probability of an acre burning value (RWPAB) (Figure 4). This allows for integration of the nearby CPAB values to reflect the flammability of the cells around a given cell.