Flame shape and heat flux mediate conditions of fuel and terrain affect surface fire spread rate

Abstract

Flame shape and heat flux are crucial indicators for evaluating forest combustion conditions. Variations in surface fire spread rate caused by changes in fuel and terrain conditions correspond to distinct flame shape and heat flux characteristics. However, little is known about the relationships among flame shape, heat flux, and surface fire spread rate after alterations in fuel conditions (such as moisture content and load) and slope. We selected Pinus koraiensis, P. sylvestris var. mongolica, Quercus mongolica, and Juglans mandshurica in Heilongjiang Province, China, whose surface fuel bed structures and fuel types differ. We analyzed the impacts of changes in fuel moisture content, load, and slope on the surface fire spread rate, flame shape, and heat flux characteristics. Additionally, we evaluated the relationships among flame shape, heat flux, and surface fire spread rate under varying moisture content, load, and slope conditions. Moisture content is negatively correlated with the surface fire spread rate, flame shape, and heat flux characteristics, while fuel load exhibits the opposite trend. Slope is positively correlated only with flame size (height and length) and indicators of total and convective heat fluxes. Increases in moisture content and slope exert direct negative and positive impacts on surface fire spread rate respectively. In contrast, an increase in fuel load produces only an indirect positive impact on the spread rate through the peak total heat flux and flame height, with no significant direct effect. Both increases in moisture content and slope indirectly negatively affect the spread rate through flame height. However, the negative impact of slope is offset by its positive effect through the peak total heat flux, resulting in an overall positive indirect effect. The surface fire spread rate directly responds to changes in moisture content and slope and indirectly enhances its responsiveness through flame shape and heat flux. In contrast, the response of the spread rate to changes in fuel load is mediated by flame shape and heat flux. This study enhances the understanding of the theoretical mechanisms by which changes in fuel and terrain conditions influence the surface fire spread rate.

Keywords

Forest fire / Indoor simulated combustion / Moisture content / Slope / Heat transfer / Flame height

References

[1] Alexander ME, Cruz MG. Interdependencies between flame length and fireline intensity in predicting crown fire initiation and crown scorch height. Int J Wildland Fire, 2012, 21(2): 95-113.

[2] Andrews PL, Cruz MG, Rothermel RC. Examination of the wind speed limit function in the Rothermel surface fire spread model. Int J Wildland Fire, 2013, 22(7): 959-969.

[3] Asensio MI, Cascón JM, Laiz P, Prieto-Herráez D. Validating the effect of fuel moisture content by a multivalued operator in a simplified physical fire spread model. Environ Model Softw, 2023, 164. ArticleID: 105710

[4] Brown PT, Hanley H, Mahesh A, Reed C, Strenfel SJ, Davis SJ, Kochanski AK, Clements CB. Climate warming increases extreme daily wildfire growth risk in California. Nature, 2023, 621(7980): 760-766.

[5] Cheney NP, Gould JS, Catchpole WR. Prediction of fire spread in grasslands. Int J Wildland Fire, 1998, 8(1): 1-13.

[6] Cruz MG, Alexander ME. Uncertainty associated with model predictions of surface and crown fire rates of spread. Environ Model Softw, 2013, 47: 16-28.

[7] Di Giuseppe F, McNorton J, Lombardi A, Wetterhall F. Global data-driven prediction of fire activity. Nat Commun, 2025, 16: 2918.

[8] Duane A, Piqué M, Castellnou M, Brotons L. Predictive modelling of fire occurrences from different fire spread patterns in Mediterranean landscapes. Int J Wildland Fire, 2015, 24(3): 407-418.

[9] Duane A, Castellnou M, Bachfisher M, Brotons L (2024) Fire rate of spread and growth rate in a set of 30 global wildfires: new evidence of extreme fire behavior. J Environ Inform 44(2). https://doi.org/10.3808/jei.202400526

[10] Dube OP. Global wildfire activity re-visited. Glob Environ Change, 2024, 89. ArticleID: 102894

[11] Dupuy JL, Larini M. Fire spread through a porous forest fuel bed: a radiative and convective model including fire-induced flow effects. Int J Wildland Fire, 2000, 9(3): 155-172.

[12] Dupuy JL, Maréchal J. Slope effect on laboratory fire spread: contribution of radiation and convection to fuel bed preheating. Int J Wildland Fire, 2011, 20(2): 289-307.

[13] Dupuy JL, Maréchal J, Portier D, Valette JC. The effects of slope and fuel bed width on laboratory fire behaviour. Int J Wildland Fire, 2011, 20(2): 272-288.

[14] Fidanova S, Marinov P. The impact of slope on fire spread simulation. Environ Eng Manag J, 2016, 15(3): 505-510.

[15] Finney MA, Grumstrup TP. Effect of flame zone depth on the correlation of flame length with fireline intensity. Int J Wildland Fire, 2023, 32(7): 1135-1147.

[16] Fons WL. Analysis of fire spread in light forest fuels. J Agric Res, 1946, 72: 92-121

[17] Frandsen WH. Fire spread through porous fuels from the conservation of energy. Combust Flame, 1971, 16(1): 9-16.

[18] Geng DT, Yang G, Ning JB, Li A, Li ZG, Ma SJ, Wang XY, Yu HZ. Modification of the Rothermel model parameters–the rate of surface fire spread of Pinus koraiensis needles under no-wind and various slope conditions. Int J Wildland Fire, 2024, 33(4): WF23118.

[19] Geng DT, Yang G, Ning JB, Ma SJ. Study on a predictive model for carbon consumption of surface fuels based on the Byram model. J Tsinghua Univ Sci Technol, 2025, 65(4): 664-671. in Chinese).

[20] Guo HW, Xiang D, Kong LY, Gao YJ, Zhang YC. Upslope fire spread and heat transfer mechanism over a pine needle fuel bed with different slopes and winds. Appl Therm Eng, 2023, 229. ArticleID: 120605

[21] Guo HW, Xiang D, Zhang PY, Gao YJ, Zhang YC, Kong LY. Effects of wind on heat transfer and spread of different fire lines across a pine needle fuel bed. Combust Sci Technol, 2025, 197(4): 782-802.

[22] Guo XR, Yan C, Wang XR, Zhang H, Miao SG. Rapid simulation of grassland fire spread with parameterized flame plume entrainment effects. Sci China Earth Sci, 2025, 68(5): 1458-1468.

[23] Guo Y (2024) Experimental and theoretical study on forest surface fire spread. PhD thesis, Northeast Forestry University

[24] Hoffman CM, Linn R, Parsons R, Sieg C, Winterkamp J. Modeling spatial and temporal dynamics of wind flow and potential fire behavior following a mountain pine beetle outbreak in a lodgepole pine forest. Agric for Meteorol, 2015, 204: 79-93.

[25] Hu T, Han Y, Köster K, Wang J, Hu H, Dou X, Sun L, Ding Y. Prescribed burning alters soil microbial community structure by changing soil physicochemical properties in temperate forests of northern China. J for Res, 2024, 35(1): 141.

[26] Jhariya MK, Bargali SS, Swamy SL, Kittur B. Vegetational structure, diversity and fuel load in fire affected areas of tropical dry deciduous forests in Chhattisgarh. Vegetos, 2012, 25(1): 210-224

[27] Jhariya MK, Bargali SS, Swamy SL, Kittur B, Bargali K, Pawar GV. Impact of forest fire on biomass and carbon storage pattern of tropical deciduous forests in Bhoramdeo Wildlife Sanctuary, Chhattisgarh. Int J Ecol Environ Sci, 2014, 40(1): 57-74.

[28] Kenny BJ, Matthews S, Sauvage S, Grootemaat S, Hollis JJ, Fox-Hughes P. Australian Fire Danger Rating System: implementing fire behaviour calculations to forecast fire danger in a research prototype. Int J Wildland Fire, 2024, 33(4): WF23142.

[29] Khastagir A, Hossain I, Aktar N. Evaluation of different parameter estimation techniques in extreme bushfire modelling for Victoria, Australia. Urban Clim, 2021, 37. ArticleID: 100862

[30] Kittur BH, Swamy SL, Bargali SS, Jhariya MK. Wildland fires and moist deciduous forests of Chhattisgarh, India: divergent component assessment. J for Res, 2014, 25(4): 857-866.

[31] Korobeinichev OP, Kumaran SM, Raghavan V, Trubachev SA, Paletsky AA, Shmakov AG, Glaznev RK, Chernov AA, Tereshchenko AG, Loboda EL, Kasymov DP. Investigation of the impact of Pinus silvestris pine needles bed parameters on the spread of ground fire in still air. Combust Sci Technol, 2023, 195(13): 3072-3094.

[32] Lemos NSA, Cunha JM, Campos MCC, Filho EGB. Forest fire distribution standard in the south of Amazonas state. Nat Hazards J Int Soc Prev Mitig Nat Hazards, 2025, 121(5): 6011-6042

[33] Li WR, Bai YQ, Chen ZY, Lou SH, Liao YH. Spatiotemporal analysis of wildfires in Alberta, Canada over the past sixty years: increased wildfire frequency by human activities. J Environ Manage, 2025, 380. ArticleID: 124963

[34] Liu NA, Wu JM, Chen HX, Xie XD, Zhang LH, Yao B, Zhu JP, Shan YL. Effect of slope on spread of a linear flame front over a pine needle fuel bed: experiments and modelling. Int J Wildland Fire, 2014, 23(8): 1087-1096.

[35] Magee RS, Mcalevy RF, Wrubel JA (1967) Flame spreading at elevated pressures over the surface of igniting solid propellants in oxygen/inert environments. Presented at the The Spring Meeting of Western States Section Combustion Institute.

[36] Man ZY, Sun L, Hu HQ, Zhang YL. Prediction model of the spread rate of eight typical surface dead fuel in southern China under windless and flat land. Sci Silvae Sin, 2019, 55(7): 197-204. in Chinese).

[37] Masinda MM, Sun L, Wang GY, Hu TX. Moisture content thresholds for ignition and rate of fire spread for various dead fuels in northeast forest ecosystems of China. J for Res, 2021, 32(3): 1147-1155.

[38] McArthur AG. Control burning in eucalypt forests (leaflet No.80), 1962. Canberra, ACT, Commonwealth of Australia, Forestry and Timber Bureau

[39] Morandini F, Perez-Ramirez Y, Tihay V, Santoni PA, Barboni T. Radiant, convective and heat release characterization of vegetation fire. Int J Therm Sci, 2013, 70: 83-91.

[40] Ning JB (2023) Smoke exposure levels prediction following laboratory combustion of Pinus koraiensis. PhD thesis,Northeast Forestry University

[41] Ning JB, Yang G, Liu XY, Geng DT, Wang LX, Li ZG, Zhang YL, Di XY, Sun L, Yu HZ. Effect of fire spread, flame characteristic, fire intensity on particulate matter 2.5 released from surface fuel combustion of Pinus koraiensis plantation–A laboratory simulation study. Environ Int, 2022, 166. ArticleID: 107352

[42] Niu HC (2014) Pyrolysis kinetics and flammability study of forest fuels. PhD thesis, University of Science and Technology of China

[43] Pan Y, Li MH, Luo XJ, Wang CJ, Luo QT, Li JC. Analysis of heat transfer of spilling fire spread over steady flow of n-butanol fuel. Int Commun Heat Mass Transf, 2020, 116. ArticleID: 104685

[44] Pinto P, Cabrera A, Cruz JJ, Contreras J, Severino G, Demarco R, Elicer-Cortés JC, Fuentes A. Effects of wildland fuel moisture content on radiant heat flux emitted by a laminar non-premixed flame. Appl Therm Eng, 2020, 181. ArticleID: 115968

[45] Radcliffe DC, Bakker JD, Churchill DJ, Alvarado EC, Peterson DW, Laughlin MM, Harvey BJ. How are long-term stand structure, fuel profiles, and potential fire behavior affected by fuel treatment type and intensity in Interior Pacific Northwest forests?. For Ecol Manage, 2024, 553: 121594.

[46] Razmjooei B, Ravangard AR, Momayez L, Ferchichi M. The influence of heat transfer due to radiation heat transfer from a combustion chamber. J Therm Anal Calorim, 2022, 147(3): 1901-1917.

[47] Ren ML, Guo Y, Chen BX, Fan JL, Hu TX, Sun L. Prediction models of fire spread rate of Pinus koraiensis plantation’s surface fuel. J Appl Ecol, 2023, 34(8): 2091-2100.

[48] Rothermel RC (1972) A mathematical model for predicting fire spread in wildland fuels (No. INT-115) USDA Forest Service, Intermountain Forest and Range Experiment Station, Ogden, UT, USA.

[49] Simpson CC, Sharples JJ, Evans JP. Sensitivity of atypical lateral fire spread to wind and slope. Geophys Res Lett, 2016, 43(4): 1744-1751.

[50] Sneeuwjagt RJ, Peet GB. Forest fire behaviour tables for Western Australia, 1985, Third edition. ed, Perth, Western Australia, Department of Conservation and Land Management

[51] Tang F, Li LJ, Wang Q, Shi Q. Effect of cross-wind on near-wall buoyant turbulent diffusion flame length and tilt. Fuel, 2016, 186: 350-357.

[52] Wang ZF. The measurement method of the wildfire initial spread rate. Mt Res Dev, 1983, 1(2): 42-51.

[53] Wang ZL, Zhang TH, Huang XY. Predicting real-time fire heat release rate by flame images and deep learning. Proc Combust Inst, 2023, 39(3): 4115-4123.

[54] Wu JM (2014) Experimental and theoretical study on surface fire spread under effect of wind and slope. PhD thesis, University of Science and Technology of China

[55] Xie XD (2014) Experimental and theoretical research on upslope surface fire spread. PhD thesis, University of Science and Technology of China

[56] Yang H, Cai HY, Yang G, Geng DT, Sun L. Predicting the rate of spread of mixed-fuel surface fires in northeastern China using the Rothermel wildfire behaviour model: a laboratory study. J for Res, 2024, 35(1): 108.

[57] Yip A, Haelssig JB, Pegg MJ. Multicomponent pool fires: trends in burning rate, flame height, and flame temperature. Fuel, 2021, 284. ArticleID: 118913

[58] Yuan XS (2020) Modelling and experimental study on upslope surface fire spread of wildland fuels. PhD thesis, University of Science and Technology of China

[59] Zhao J, Yue C, Wang JM, Hantson S, Wang XL, He BB, Li GY, Wang L, Zhao HF, Luyssaert S. Forest fire size amplifies postfire land surface warming. Nature, 2024, 633(8031): 828-834.

[60] Zhao K, Chen W, Li ST, Lin ZM, Wang HK. The effect of fire-wall distance on the flame attachment characteristics and flame height of near-wall fires. J Build Eng, 2024, 98. ArticleID: 111292

[61] Zheng HN. Forest combustion loop and network system, 2003. Harbin, Northeast Forestry University Press

[62] Zheng HN, Hu HQ. Forest burning link. J Northeast for Univ, 1987, 15(5): 1-6.

[63] Zong XZ, Tian XR. Impacts of fuel treatment on potential fire behavior of main forest types in Daxing’anling. Sci Silvae Sin, 2021, 57(2): 139-149

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