Fire Suppression Effectiveness--Rate of Spread vs Final Fire Size Relationships

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.