Comparative Assessment of Wildland Fire Rate of Spread Models: Effects of Wind Velocity
Abstract
:1. Introduction
2. Materials and Methods
2.1. Semi-Empirical, Laboratory-Developed ROS Models
2.2. Empirical, Laboratory-Developed ROS Models
2.3. Wind Correction Empirical Sub-Models
2.4. Empirical, Field-Based Models and Wind Adjustment Factor
2.5. Laboratory Experimental Data
3. Results
3.1. Laboratory-Developed Models in Quiescent Conditions
3.2. Laboratory-Developed Models, Combined with Wind-Correction Sub-Models, against External Wind Conditions
3.3. Field-Developed Models against External Wind Conditions
3.4. Sensitivity Analysis
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
Symbol | Units | Description |
A, B, …, F | - | Empirically fitted constants or functions |
a, b, c | - | Fuel parameters, used in model F5 |
FC | % | Surface fuel cover |
fil | - | Ignition line length factor, used in sub-model W2 |
Hf | m | Flame height |
h | kJ/kg | Fuel lower calorific value |
hv | kJ/kg | Fuel’s pyrolysis gas lower calorific value |
IB | kW/m | Byram’s fireline intensity |
IP | kW/m2 | Propagation heat flux |
IR | kW/m2 | Reaction intensity |
ISI | - | Initial Spread Index, used in model F5 |
k | - | Moisture damping constant, used in model L3 |
Lig | kJ/m3 | Heat per unit volume required for ignition |
M* | - | Fuel moisture content—FMC (dry basis) |
Mc | - | Characteristic moisture, used in model L2 |
Mx | - | Moisture of extinction, used in model L1 |
kg/s·m | Rate of fuel added to combustion zone | |
mn″ | kg/m2 | Net fuel load |
md″ | kg/m2 | Dry fuel load |
nx | - | Extinction index |
- | Extinction adjustment factor | |
n | - | Total number of experiments |
Pf | - | Probability function for fire extinction |
Qp | kJ/kg | Heat of pyrolysis |
Qw | kJ/kg | Required heat to evaporate the fuel’s moisture |
R0 | m/s* | “Base” ROS in quiescent and horizontal conditions |
R | m/s* | Rate of spread |
Rexp | m/s* | Experimentally measured rate of spread |
Rpred | m/s* | Predicted rate of spread |
Ru | - | Wind correction factor, used in sub-model W2 |
Se | - | Effective mineral content |
St | - | Total mineral content |
s | m2/kg | Fuel particle specific surface |
Ta | °C | Ambient temperature |
U | m/s* | Wind velocity |
Uz | m/s* | Wind velocity measured at height z |
m/s* | Wind velocity at mid-flame height | |
W | m | Fuel bed width |
z | ft* | Wind velocity measuring height |
β | - | Fuel bed packing ratio |
Γ′ | min−1 | Potential reaction velocity |
δ | m | Fuel bed height |
ε | - | Effective heating number |
ηΜ | - | Moisture damping coefficient |
ηS | - | Mineral damping coefficient |
ξ | - | Propagating heat flux ratio |
ρb | kg/m3 | Fuel bed density |
ρp | kg/m3 | Fuel particle density |
σ | m−1 | Surface area-to-volume (SAV) ratio |
Φw | - | Wind correction factor, used in sub-model W1 |
* Properties may, in certain cases, be expressed in different units (see text). Numerical subscripts (in Table 1, Table A1, Table A2 and Table A6) indicate different constant or function. |
Appendix A. Detailed Forms of Equation Functions
Function | Units |
---|---|
(kJ/min·m2) | |
(min−1) | |
(kg/m2) | |
(kJ/m3) | |
σ | (cm−1) |
Function | Units |
---|---|
(kJ/m3) | |
(kJ/min·m2) | |
(min−1) | |
(kW/m2) | |
σ | (cm−1) |
Function | Units |
Function | Units |
Function | Units |
Uz | (km/h) |
Appendix B. Values of Empirical Parameters
Model | Parameter | Value | Model | Parameter | Value |
L4, L5 | A4 | 0.2859 | F1 | A8 | 40.982 |
A5 | 0.1557 | B8 | 1.399 | ||
B4,5 | −0.7734 | C8 | 1.201 | ||
C4,5 | 0.9440 | D8 | 1.699 | ||
D5 | 0.8173 | F2, F3 | A9 | 5.6715 | |
W2 | A7 | 2.143 × 10−5 | B9 | 0.9102 | |
B7 | 1.710 | C9 | 0.2227 | ||
C7 | −1.169 | D9 | 0.0762 | ||
D7 | −1.166 | A10 | 3.8320 | ||
F5 | α | 45 | B10 | 1.0927 | |
b | 0.0305 | C10 | −0.2098 | ||
c | 2 | D10 | 0.0721 | ||
A12 | 0.208 | E9,10 | 9 | ||
B12 | 0.05039 | F9,10 | 0.00316 | ||
C12 | 91.9 | F4 | A11 | 0.773 | |
D12 | −0.1386 | B11 | 0.707 | ||
E12 | 4.93 × 10−7 | C11 | −0.039 | ||
F12 | 5.31 | D11 | 0.188 |
References
- Sullivan, A.L. Wildland surface fire spread modelling, 1990–2007. 1: Physical and quasi-physical models. Int. J. Wildland Fire 2009, 18, 349–368. [Google Scholar] [CrossRef]
- Sullivan, A.L. Wildland surface fire spread modelling, 1990–2007. 2: Empirical and quasi-empirical models. Int. J. Wildland Fire 2009, 18, 369–386. [Google Scholar] [CrossRef]
- Sullivan, A.L. Wildland surface fire spread modelling, 1990–2007. 3: Simulation and mathematical analogue models. Int. J. Wildland Fire 2009, 18, 387–403. [Google Scholar] [CrossRef]
- Cruz, M.G.; Alexander, M.E. Uncertainty associated with model predictions of surface and crown fire rates of spread. Environ. Modell. Softw. 2013, 47, 16–28. [Google Scholar] [CrossRef]
- Viegas, D.X. On the existence of a steady state regime for slope and wind driven fires. Int. J. Wildland Fire 2004, 13, 101–117. [Google Scholar] [CrossRef]
- Weise, D.R.; Biging, G.S. A Qualitative comparison of fire spread models incorporating wind and slope effects. Forest Sci. 1997, 43, 170–180. [Google Scholar] [CrossRef]
- Weise, D.R.; Koo, E.; Zhou, X.; Mahalingam, S.; Morandini, F.; Balbi, J.H. Fire spread in chaparral-a comparison of laboratory data and model prediction in burning live fuels. Int. J. Wildland Fire 2016, 25, 980–994. [Google Scholar] [CrossRef]
- Cruz, M.G.; Alexander, M.E.; Sullivan, A.L.; Gould, J.S.; Kilinc, M. Assessing improvements in models used to operationally predict wildland fire rate spread. Environ. Modell. Softw. 2018, 105, 54–63. [Google Scholar] [CrossRef]
- Kolaitis, D.I.; Pallikarakis, C.N.; Founti, M.A. Effects of wind velocity on prediction of wildland fire rate of spread models: A comparative assessment using surface fuel fire tests. In Proceedings of the IX International Conference on Forest Fire Research, Coimbra, Portugal, 14–18 November 2022. [Google Scholar]
- Rothermel, R.C. A Mathematical Model for Predicting Fire Spread in Wildland Fuels; Res. Pap. INT-115; USDA Forest Service, Intermountain Forest and Range Experiment Station: Fort Collins, CO, USA, 1972. [Google Scholar]
- Wilson, R.A. Reexamination of Rothermel’s Fire Spread Equations in No-Wind and No-Slope Conditions; Res. Pap. INT-434; USDA Forest Service, Intermountain Research Station: Fort Collins, CO, USA, 1990. [Google Scholar]
- Catchpole, W.R.; Catchpole, E.A.; Butler, B.W.; Rothermel, R.C.; Morris, G.A.; Latham, D.J. Rate of spread of free-burning fires in woody fuels in a wind tunnel. Combust. Sci. Technol. 1998, 131, 1–37. [Google Scholar] [CrossRef]
- Rossa, C.G.; Fernandes, P.M. Empirical modeling of fire spread rate in no-wind and no-slope conditions. Forest Sci. 2018, 64, 358–370. [Google Scholar] [CrossRef]
- Rossa, C.G.; Fernandes, P.M. An empirical model for the effect of wind on fire spread. Fire 2018, 1, 31. [Google Scholar] [CrossRef]
- Burrows, N.; Gill, M.; Sharples, J. Development and validation of a model for predicting fire behaviour in spinifex grasslands of Arid Australia. Int. J. Wildland Fire 2019, 27, 271–279. [Google Scholar] [CrossRef]
- Anderson, W.R.; Cruz, M.G.; Fernandes, P.M.; McCaw, L.; Vega, J.A.; Bradstock, R.A.; Fogarty, L.; Gould, J.; McCarthy, G.; Marsden-Smedley, J.B.; et al. A generic, empirical-based model for predicting rate of fire spread in shrublands. Int. J. Wildland Fire 2015, 24, 443–460. [Google Scholar] [CrossRef]
- Fernandes, P.M.; Botelho, H.S.; Rego, F.C.; Loureiro, C. Empirical modelling of surface fire behavior in maritime pine stand. Int. J. Wildland Fire 2009, 18, 698–710. [Google Scholar] [CrossRef]
- Forest Canada Fire Danger Group. Development and Structure of the Canadian Forest Fire Behavior Prediction System; Information Report St-X-3; Forestry Canada, Science and Sustainable Development Directorate: Ottawa, Canada, 1992. [Google Scholar]
- Frandsen, W.H. Fire spread through porous fuels from conservation of energy. Combust. Flame 1971, 16, 9–16. [Google Scholar] [CrossRef]
- Byram, G.M. Combustion of Forest Fuels; McGraw-Hill: New York, NY, USA, 1959; pp. 61–89. [Google Scholar]
- Rossa, C.G.; Fernandes, P.M. Fuel-related fire-behaviour relationships for mixed live and dead fuels burned in the laboratory. Can. J. Forest. Res. 2017, 47, 883–889. [Google Scholar] [CrossRef]
- Albini, F.A.; Baughman, R.G. Estimating Windspeeds for Predicting Wildland Fire Behavior; Res. Pap. INT-221; USDA Forest Service, Intermountain Forest and Range Experiment Station: Ogden, UT, USA, 1979. [Google Scholar]
- Andrews, P.L. Modeling Wind Adjustment Factor and Midflame Wind Speed for Surface Fire Spread Model; Gen. Tech. Rep; RMRS-GTR-266; U.S. Department of Agriculture, Forest Service, Rocky Mountain Research Station: Ogden, UT, USA, 2012. [Google Scholar]
- Baughman, R.G.; Albini, F.A. Estimating Midflame Windspeed; Northern Forest Fire Laboratory: Missoula, MT, USA, 1980; pp. 88–92. [Google Scholar]
- Mendez-Lopez, J.M.; Ventura, J.M.; Amaral, J.M.P. Flame characteristics, temperature-time curves, and rate of spread in fires propagating in a bed of Pinus Pinaster needles. Int. J. Wildland Fire 2003, 12, 67–84. [Google Scholar] [CrossRef]
- Lozano, J.; Tachajapong, W.; Pan, H.; Swanson, A.; Kelley, C.; Princevac, M.; Mahalingam, S. Experimental investigation of the velocity field in a controlled wind-aided propagating fire using particle image velocimetry. In Proceedings of the Fire Safety Science-Proceedings of the 9th International Symposium, University of Karlsruhe, Karlsruhe, Germany, 21–26 September 2008; pp. 255–266. [Google Scholar]
- Anderson, W.R.; Catchpole, E.A.; Butler, B.W. Convective heat transfer in fire spread through fine fuel beds. Int. J. Wildland Fire 2010, 19, 284–298. [Google Scholar] [CrossRef]
- Korobenichev, O.; Tereshchenko, A.; Paletsky, A.; Shmakov, A.; Gonchikzhapov, M.; Chernov, A.; Kataeva, L.; Maslennikov, D.; Liu, N. The velocity and structure of the flame front at spread of fire across thepne needle bed depending on the wind velocity. In Proceedings of the 10th Asia-Oceania Symposium on Fire Science and Technology, Tsukuba, Japan, 5–7 October 2014; pp. 771–779. [Google Scholar]
- Korobeinichev, O.; Kumaran, S.M.; Shanmugasundaram, D.; Raghavan, V.; Trubachev, S.A.; Paletsky, A.A.; Shmakov, A.G.; Glaznev, R.K.; Chernov, A.A.; Tereshchenko, A.G. Experimental and numerical study of flame spread over bed of pine needles. Fire Technol. 2022, 58, 1227–1264. [Google Scholar] [CrossRef]
- Morandini, F.; Perez-Ramirez, Y.; Tihay, V.; Santoni, P.; Barboni, T. Radiant, convective and heat release characterization of vegetation fire. Int. J. Therm. Sci. 2013, 70, 83–91. [Google Scholar] [CrossRef]
- Tihay, V.; Morandini, F.; Santoni, P.A.; Perez-Ramirez, Y.; Barboni, T. Combustion of forest litters under slope condition: Burning rate, heat release rate, convective and radiant fractions for different loads. Combust. Flame 2014, 161, 3237–3248. [Google Scholar] [CrossRef]
- Finney, M.A.; McAllister, S.S.; Grumstrup, T.P.; Forthofer, J.M. Wildland Fire Behavior: Dynamics, Principles and Processes; CSIRO Publishing: Melbourne, Australia, 2021; pp. 15–45. [Google Scholar]
- Morvan, D.; Frangieh, N. Wildland fires behaviour: Wind effect versus Byram’s convective number and consequences upon the regime of propagation. Int. J. Wildland Fire 2018, 27, 636–641. [Google Scholar] [CrossRef]
- Cheney, N.P.; Gould, J.S.; Catchpole, W.R. The influence of fuel, weather and fire shape variables on fire-spread in grasslands. Int. J. Wildland Fire 1993, 3, 698–710. [Google Scholar] [CrossRef]
- Cheney, N.P.; Gould, J.S. Fire growth in grassland fuels. Int. J. Wildland Fire 1995, 5, 237–247. [Google Scholar] [CrossRef]
Model Type | Model | General Form | Ref. |
---|---|---|---|
ROS models developed using laboratory tests | L1 | [10] | |
L2 | [11] | ||
L3 | [12] | ||
L4 | [13] | ||
L5 | [13] | ||
“Wind correction” sub-models | W1 | [10] | |
W2 | [14] | ||
ROS models developed using field tests | F1 | [15] | |
F2 | [16] | ||
F3 | [16] | ||
F4 | [17] | ||
F5 | [18] |
Ref. | Fire Tests | No-Wind/Wind Tests | Fuel Type |
---|---|---|---|
[25] | 9 | 2/7 | Pine needles (Pinus Pinaster) |
[26] | 6 | 0/6 | Bamboo sticks |
[27] | 163 | 30/133 | Pine needles (Pinus Ponderosa)/Excelsior |
[28] | 7 | 1/6 | Pine needles (Pinus Sibirica) |
[29] | 18 | 4/14 | Pine needles (Pinus Sibirica) |
Model | RMSE | MAPE (%) | MBE |
---|---|---|---|
L1 | 3.5 | 42.8 | −2.8 |
L2 | 3.2 | 59.3 | 1.0 |
L3 | 4.7 | 71.6 | 1.5 |
L4 | 3.1 | 45.8 | −0.2 |
L5 | 2.9 | 50.9 | 0.3 |
Models | RMSE | MAPE (%) | MBE |
---|---|---|---|
L1-W1 | 40.1 | 46.5 | −25.3 |
L2-W1 | 51.5 | 59.2 | 14.8 |
L3-W1 | 91.8 | 49.3 | 30.8 |
L4-W1 | 40.2 | 52.0 | −6.7 |
L5-W1 | 42.1 | 43.1 | 1.2 |
L1-W2 | 143.8 | 78.0 | 34.4 |
L2-W2 | 127.8 | 105.3 | 35.2 |
L3-W2 | 101.0 | 67.1 | 26.8 |
L4-W2 | 131.3 | 94.9 | 33.7 |
L5-W2 | 124.5 | 90.1 | 33.0 |
Model | RMSE | MAPE (%) | MBE |
---|---|---|---|
F1 | 59.2 | 119.0 | −24.0 |
F2 | 44.4 | 67.5 | −21.2 |
F3 | 30.7 | 63.1 | −3.9 |
F4 | 51.5 | 231.3 | 35.2 |
F5 | 280.0 | 1278.3 | 251.6 |
Parameter | Model | −25% Change | Assumed Value | +25% Change |
---|---|---|---|---|
h | L1 | 4.42 (25.9%) | 3.51 | 2.67 (−23.8%) |
St | L1 | 3.46 (−1.5%) | 3.51 | 3.56 (1.5%) |
Se | L1 | 3.31 (−5.6%) | 3.51 | 3.65 (4.2%) |
Mx | L1 | 3.80 (8.3%) | 3.51 | 3.31 (−5.7%) |
hv | L2 | 2.82 (−13.0%) | 3.24 | 4.70 (45.3%) |
fil | W2 (L5-W2) | 85.70 (−31.2%) | 124.50 | 165.84 (33.2%) |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Kolaitis, D.I.; Pallikarakis, C.; Founti, M.A. Comparative Assessment of Wildland Fire Rate of Spread Models: Effects of Wind Velocity. Fire 2023, 6, 188. https://doi.org/10.3390/fire6050188
Kolaitis DI, Pallikarakis C, Founti MA. Comparative Assessment of Wildland Fire Rate of Spread Models: Effects of Wind Velocity. Fire. 2023; 6(5):188. https://doi.org/10.3390/fire6050188
Chicago/Turabian StyleKolaitis, Dionysios I., Christos Pallikarakis, and Maria A. Founti. 2023. "Comparative Assessment of Wildland Fire Rate of Spread Models: Effects of Wind Velocity" Fire 6, no. 5: 188. https://doi.org/10.3390/fire6050188