Santoni2011

Description

The Santoni wildfire spread model, presented by Santoni et al. in 2011 [1], is a physics-based approach developed to simulate wildfire dynamics in Mediterranean shrubland and forest fuels. The model distinguishes between dead and live fuels, a feature uncommon in typical rate of spread models, and integrates fundamental heat transfer mechanisms, such as radiation, to describe flame geometry, fuel consumption, and fire front propagation. By explicitly accounting for these physical processes, the Santoni model reliably predicts fire behavior in heterogeneous vegetation scenarios. The FireBench implementation follows [2].

Parameters

Input table

Variable name in model	Unit	Standard Variable Name	type	Bounds
dead_fuel_ratio	-	fuel_load_dead_ratio	float64	$$]0, 1]$$
fuel_dens_dead	kg m-3	fuel_density_dead	float64	$$]0, \infty[$$
fueldens_live	kg m-3	fuel_density_live	float64	$$]0, \infty[$$
fueldepth	m	fuel_height	float64	$$]0, \infty[$$
fuel_load_dry_total	kg m-2	fuel_load_dry_total	float64	$$]0, \infty[$$
fmc_dead	%	fuel_moisture_content_dead	float64	$$[0, 200]$$
fmc_live	%	fuel_moisture_content_live	float64	$$[0, 500]$$
savr_dead	m-1	fuel_surface_area_volume_ratio_dead	float64	$$]0, \infty[$$
savr_live	m-1	fuel_surface_area_volume_ratio_live	float64	$$]0, \infty[$$
slope	deg	slope_angle	float64	$$]-90, 90[$$
wind	-	wind_speed	float64	$$]-\infty, \infty[$$

Outputs

Variable name in model	Unit	Standard Variable Name	type	Bounds
ros	m s-1	rate_of_spread	float64	$$[0, 6]$$

Optional input table

Name in model	Standard Variable Name	Unit	Value
dens_air	air_density	kg m-3	$$1.125$$
temp_air	air_temperature	K	$$300$$
temp_ign	fuel_temperature_ignition	K	$$600$$

Internal parameters

Name in model	Description	Unit	Value
base_LAI	Base leaf area index	-	$$4$$
boltz	Stefan-Boltzman constant	W m-2 K-4	$$5.670373 \cdot 10^{-8}$$
chi0	Radiative factor	-	$$0.3$$
Cp	Specific heat of fuel	J kg-1 K-1	$$1200$$
Cpa	Specific heat of air	J kg-1 K-1	$$1150$$
delta_h	Heat of latent evaporation	J kg-1	$$2.3 \cdot 10^6$$
delta_H	Heat of combustion	J kg-1	$$1.7433 \cdot 10^7$$
r00	Model parameter		$$2.5 \cdot 10^{-5}$$
stoich_coeff	Stoichiometric coefficient	-	$$8.3$$
tau0	Anderson’s residence time coefficient	s m-1	$$75591$$

Usage

General use

The Santoni_2011 model is a class derived from firebench.ros_models.RateOfSpreadModel.

# Import rate of spread package from firebench
import firebench.ros_models as rm
# create the input dictionnary with the inputs listed above
model_inputs = {...}
# compute the rate of spread
ros = rm.Santoni_2011.compute_ros(model_inputs)
# compute the rate of spread with fuel category
ros = rm.Santoni_2011.compute_ros(model_inputs, fuel_cat = 1)

blockdiagram

Use with Anderson13 fuel model

The Anderson13 fuel model provides a set of fuel properties that can be linked to Santoni’s inputs. An example of use of Anderson fuel model with Santoni_2011:

import firebench as fb

# Define constant values as fb.Quantity (not pint.Quantity that does not share the same unit registry)
wind_speed_20ft = fb.Quantity(3.0, "m/s")
fuel_moisture_dead = fb.Quantity(12, "percent")
fuel_moisture_live = fb.Quantity(120, "percent")
slope = fb.Quantity(0, "degree")
fuel_class = 3  # one based index of the fuel class

# Select the rate of spread model class
ros_model = fb.ros_models.Santoni_2011

# Import Anderson data
fuel_data = fb.tools.import_anderson_13_fuel_model(add_complementary_fields=True)

# Use wind reduction factor from fuel model
wind_speed_midflame = fb.wind_interpolation.apply_wind_reduction_factor(
    wind_speed=wind_speed_20ft,
    wind_reduction_factor=fuel_data[fb.svn.FUEL_WIND_REDUCTION_FACTOR],
    fuel_cat=fuel_class,
)

# assume dead and live surface area to volume ratio is the same
savr_dead = fb.tools.get_value_by_category(fuel_data[fb.svn.FUEL_SURFACE_AREA_VOLUME_RATIO], fuel_class)
savr_live = fb.tools.get_value_by_category(fuel_data[fb.svn.FUEL_SURFACE_AREA_VOLUME_RATIO], fuel_class)

# assume dead and live fuel density ratio is the same
fuel_density_dead = fb.tools.get_value_by_category(fuel_data[fb.svn.FUEL_DENSITY], fuel_class)
fuel_density_live = fb.tools.get_value_by_category(fuel_data[fb.svn.FUEL_DENSITY], fuel_class)

# Merge the fuel dict and the constant inputs
input_dict = fb.tools.merge_dictionaries(
    {
        fb.svn.WIND_SPEED: wind_speed_midflame,
        fb.svn.FUEL_MOISTURE_CONTENT_DEAD: fuel_moisture_dead,
        fb.svn.FUEL_MOISTURE_CONTENT_LIVE: fuel_moisture_live,
        fb.svn.FUEL_SURFACE_AREA_VOLUME_RATIO_DEAD: savr_dead,
        fb.svn.FUEL_SURFACE_AREA_VOLUME_RATIO_LIVE: savr_live,
        fb.svn.FUEL_DENSITY_DEAD: fuel_density_dead,
        fb.svn.FUEL_DENSITY_LIVE: fuel_density_live,
        fb.svn.SLOPE_ANGLE: slope,
    },
    fuel_data,
)

# perform checks, conversion and magnitude extraction
final_input = fb.tools.check_data_quality_ros_model(input_dict, ros_model)

# compute the rate of spread
ros = ros_model.compute_ros_with_units(final_input, fuel_cat=fuel_class)

print(ros)

Compatibility with fire models

Compatibility levels for fuel models:

Full: The data contained in the fuel model covers all the fuel input needed by the fire model
Partial: The data contained in the fuel model covers some of the fuel input needed by the fire model
None: The data contained in the fuel model covers none of the fuel input needed by the fire model

Fire model	Category	Compatibility level
Anderson13	Fuel model	Full
ScottandBurgan40	Fuel model	Full

Benchmarks and workflows

References

[1] Santoni, P. A., Filippi, J. B., Balbi, J. H., & Bosseur, F. (2011). Wildland Fire Behaviour Case Studies and Fuel Models for Landscape‐Scale Fire Modeling. Journal of Combustion, 2011(1), 613424.

[2] Costes, A., Rochoux, M. C., Lac, C., & Masson, V. (2021). Subgrid-scale fire front reconstruction for ensemble coupled atmosphere-fire simulations of the FireFlux I experiment. Fire Safety Journal, 126, 103475.