Build up phase

Most of the published rate-of-spread models are for the quasi-steady or potential speed that the fire can reach in that specific vegetation under given conditions. Depending on the vegetation type and condition this may not happen for minutes or even hours. A key factor of this is the fire needing to develop a large enough front for its potential to be reached. Below is an example of a build-up function which can be used to estimate the rate-of-spread of the fire before the quasi-steady speed has been achieved. A logistic function is used in this example.

Vegetation

Not vegetation specific

Code

// Logistic fire acceleration (build-up) model

// Vegetation specific inputs
REAL shape_factor = 0.5; // Shape factor range for acceleration function [0.4, 1.4]
REAL steady_state_time_mins = 60; // Time in minutes for fire to reach steady state speed [15, 120]
REAL inflection_frac = 0.5; // Fraction of steady state time taken to reach inflection point of acceleration function [0.2, 0.8]

// Example RoS
speed = 1;

// Acceleration function - Logistic function template used
REAL acceleration_factor = 1;
if (time < steady_state_time_mins*60){
    acceleration_factor = 1 / (1 + exp(-1*shape_factor*((12*(time/60)/steady_state_time_mins - 6) - (12*inflection_frac - 6))));
}

speed = speed * acceleration_factor;