# CSIRO Grassland Models

The CSIRO Grassland rate of spread models were developed by CSIRO for predicting fire spread rates in Australian grasslands. There are three models for grasslands: natural/undisturbed pasture, cut/grazed pasture and eaten out pasture. These spread rates were published in the paper ‘Prediction of Fire Spread in Grasslands’ by Cheney, Gould and Catchpole in the International Journal of Wildfire, which can be found here.

Northern Australia woodland and open forest can also be modelled with adjustments to the natural/undisturbed pasture model based on Cheney and Sullivan (2008).

### Vegetation

Australian Grassland

### Fuel inputs

temp
rel_hum
curing
• Temperature (degrees C)
• Relative humidity (%)
• Curing (%)

### Code

```// CSIRO grasslands models - Cheney et al. (1998)

// Subclasses defined as the following sub type of grasslands:
// 1 - Eaten out
// 2 - Cut / grazed
// 3 - Natural / undisturbed
// 4 - Woodland
// 5 - Open forest

// -------------------------------------------
// Model parameters
// 1. Temperature, 'temp'  (input)
// 2. Relative humidity, 'rel_hum' (input)
// 3. Curing value, 'curing'
// -------------------------------------------

// Calculating the wind speed which is used to calculate head fire ROS
REAL wind_speed = length(wind_vector);

// Calculating the normalised dot product between the wind vector and the normal to the fire perimeter

// Calculate length-to-breadth ratio (LBR) which varies with wind speed
// Equations are curve fits adapted from Taylor (1997)
REAL LBR = 1.0;
if (wind_speed < 5){
LBR = 1.0;
} else {
LBR = 1.1*pow(wind_speed, 0.464);
}

// Determine coefficient for backing and flanking rank of spread using elliptical equations
// Where R_backing = cb * R_head, R_flanking = cf * R_head,
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));

// Calculate curing coefficient from Cruz et al. (2015)
REAL curing_coeff;
if ( curing < 20 )
curing_coeff = 0;
else
curing_coeff = 1.036 / ( 1 + 103.989 * exp( -0.0996 * (curing - 20) ) );

// Fuel moisture content approximated using McArthur (1966)
REAL GMf = 9.58-(0.205*temp) + (0.138*rel_hum);

// Calculate moisture coefficient from Cheney et al. (1998)
REAL moisture_coeff;
if ( GMf <= 12 ){
moisture_coeff = exp( -0.108 * GMf );
} else if ( wind_speed <= 10 ){
moisture_coeff = 0.684 - 0.0342 * GMf;
} else{
moisture_coeff = 0.547 - 0.0228 * GMf;}

// Defining coefficients for the various grasslands sub-types using different subclasses.
REAL CF_Backing_Slow;
REAL CF_Backing_Fast;
REAL CF_Wind_Slow;
REAL CF_Wind_Fast;
REAL speed_factor = 1;

if (subclass == 1) // Eaten out
{
CF_Backing_Slow = 0.027;
CF_Backing_Fast = 0.55;
CF_Wind_Slow = 0.1045;
CF_Wind_Fast = 0.3575;
}
else if (subclass == 2) // Cut or grazed
{
CF_Backing_Slow = 0.054;
CF_Backing_Fast = 1.1;
CF_Wind_Slow = 0.209;
CF_Wind_Fast = 0.715;
}
else if (subclass == 3) // Natural or undisturbed
{
CF_Backing_Slow = 0.054;
CF_Backing_Fast = 1.4;
CF_Wind_Slow = 0.269;
CF_Wind_Fast = 0.838;
}
else if (subclass == 4) // Woodland
{
CF_Backing_Slow = 0.054;
CF_Backing_Fast = 1.4;
CF_Wind_Slow = 0.269;
CF_Wind_Fast = 0.838;
speed_factor = 0.5;
}
else if (subclass == 5) // Open forest
{
CF_Backing_Slow = 0.054;
CF_Backing_Fast = 1.4;
CF_Wind_Slow = 0.269;
CF_Wind_Fast = 0.838;
speed_factor = 0.3;
}

// Calculate spread rate from Cheney et al. (1998) (converting spread rate to m/s from km/hr)
if ( wind_speed >= 5.0 )
head_speed = (CF_Backing_Fast + CF_Wind_Fast * pow( (wind_speed - 5), 0.844 ) ) * moisture_coeff * curing_coeff / 3.6;
else
head_speed = (CF_Backing_Slow + CF_Wind_Slow * wind_speed)* moisture_coeff * curing_coeff / 3.6;

// Adjust speed based on canopy layer for Northern Australia grassland types (woodland and open forest)
// Based on Cheney and Sullivan (2008)