McArthur

Vegetation

Fuel inputs

• Temperature (degrees C)
• Relative humidity (%)
• Drought factor (range from 1 to 10)
• Fuel load (t/ha)

Code

// Dry Eucalypt model - McArthur Mk V

// -------------------------------------------
// Model parameters
// These must be defined below, or included as a user-defined layer
//
// 1. Temperature, 'temp' (input)
// 2. Relative humidity, 'rel_hum' (input)
// 3. Drought factor, 'D'
// 4. Fuel load, 'fuel_load' (input)
// -------------------------------------------

// Backing and flanking coefficients compared to head fire ROS
REAL wind_speed = length(wind_vector);
REAL wdot = dot(normalize(wind_vector),advect_normal_vector);

// Calculate length-to-breadth ratio (LBR)
REAL LBR = 1.0;
if (wind_speed < 5){
    LBR = 1.0;
} else if (wind_speed < 25){
    LBR = 0.9286 * exp(0.0505 * wind_speed); 
} else {
    LBR = 0.1143 * wind_speed + 0.4143; 
} 

// Determine coefficient for flank rank of spread, Rf = cf * Rh, using Andrew's LBR equations 
REAL cc = sqrt(1.0-pow(LBR, -2.0)); 
REAL cb = (1.0-cc)/(1.0+cc); 
REAL a_LBR = 0.5*(cb+1.0);
REAL cf = a_LBR/LBR; 

// Determine shape parameters 
REAL f = 0.5*(1.0+cb); 
REAL g = 0.5*(1.0-cb); 
REAL h = cf; 

// Now calculate a speed coefficient using normal flow formula 
REAL speed_fraction = (g*wdot+sqrt(h*h+(f*f-h*h)*wdot*wdot)); 

// Calculating FFDI using McArthur and Noble et al. (1980)
REAL FFDI = 2 * exp(-0.450 + 0.987*log(D) - 0.0345*rel_hum + 0.0338*temp + 0.0234*wind_speed);

// Calculate spread rate in km/h using McArthur's Mk 5 and Noble et al. (1980)
REAL head_speed = 0.0012 * FFDI * fuel_load;

// Converting spread rate into m/s
head_speed = speed / 3.6;

// Adjust for calculated speed coefficient for fire flanks
speed = head_speed * speed_fraction;