# Field-Scale Physical Modelling of Grassfire Propagation on Sloped Terrain under Low-Speed Driving Wind

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{wind}and ϕ

_{slope}are the factors for wind and slope, respectively. This model is considered applicable up to 0–37° upslope angles. There are two versions of the Rothermel model—“original” and “modified” [17,18]. The packing ratio and surface-to-volume ratio are the two important components of the model for ${RoS}_{0}$. The “modified” model incorporates an extinction index, which is a function of heat of vaporisation and fuel moisture content [18]. The details of ${RoS}_{0}$, ϕ

_{wind}, and ϕ

_{slope}for Rothermel models can be found in [17,18,19]. The detailed equations for both “original” and “modified” models are presented in supplementary document, Annexure A.

_{c}, (presented as Equation (6)) is a dimensionless parameter used to classify the mode of fire propagation as either wind-driven or buoyancy-driven [24,25].

^{2}), ${}_{g}$ = gas density (1.2 kg/m

^{3}), ${C}_{p}$ = specific heat of the air (1.0 kJ/kg/K). However, as N

_{c}is dimensionless, discretion is available in choosing the velocity at any relevant height to analyse the mode of fire propagation.

_{c}> 10, and wind-driven when Nc < 2. Fires with intermediate N

_{c}values are neither buoyancy-driven nor wind-driven. [26].

## 2. Simulation Methodology, Parameters, and Variables

_{10}(velocity at 10 m height), of 0.1 and 1 m/s, as outlined in Table 1.

^{2}was selected.

^{2}(triple the fuel load, in line with the increase in fuel height) are adopted in these simulations. Two sets of fuel parameters are used: “original” (Sets 1, 2, and 3) and “lighter & drier” (set 4). For the latter (Set 4), the ambient temperature is increased to 50 °C and relative humidity is reduced to 10% along with a reduced fuel moisture content, fuel density, and fuel load, as presented in Table 2. The fuel bulk density is maintained the same as is used in the other three sets of simulations. Arguably, a combination of increased ambient temperature and reduced fuel moisture content, relative humidity, and fuel load can significantly impact the rate of fire spread and heat release rate (HRR).

## 3. Postprocessing Methodology

#### 3.1. Isochrones, Pyrolysis Width, and Fire Propagation

#### 3.2. Visualisation of Plume Contours

#### 3.3. Determination of Flame Length

#### 3.4. Determination of Heat Flux

## 4. Results and Discussion

#### 4.1. Progression of Isochrones and Pyrolysis Width

^{2}exceeds 0.95 for all these relationships with the exception in linear relationship for Set 4, where R

^{2}= 0.88. Generally, the pyrolysis width was found to approximately double at every +10° increase in upslope, across all four sets, suggesting an exponential trend. It is to be noted that doubling of RoS at every +10° increase in slope is considered as a rule of thumb for Australian empirical models. Therefore, in Figure 3a, only exponential trend lines are displayed.

^{2}value shown in the figure) can be constructed between relative pyrolysis width and slope angle. The value of the coefficient is ~0.5 for all four curves and the exponent lies between 0.067 and 0.083. A stronger slope effect is observed for 0.1 m/s wind velocity cases (Set 1) compared with 1 m/s cases (Sets 2, 3, and 4) and the difference widens as the slope angle increases. This may be associated with longer residence times with the slower velocity. Generally, the pyrolysis width effect is found to be identical for 1 m/s wind velocity cases (Sets 2 and 3).

#### 4.2. Heat Release Rate (HRR) and Fire Intensity

^{2}value exceeds 0.97, indicating a strong fit. Given the negligible difference observed in the R

^{2}values among these relationships, an exponential relationship is deemed to represent the correlation between Q and slope angle, akin to that with pyrolysis width, as reasoned in Section 4.1. The exponential trend lines (for visual representation only) are shown in Figure 4a.

^{2}value of approximately 0.86 is observed. Alternatively, a logarithmic relationship can be formed, yielding an R

^{2}value of around 0.89. However, given the uncertainties inherent in simulations, it is reasonable to assert that these two parameters are linearly correlated.

#### 4.3. Fire Front Locations, Dynamic RoS, and RoS Calculations

#### 4.3.1. Fire Front Locations

#### 4.3.2. Dynamic RoS

#### 4.3.3. Averaged RoS

^{2}values are shown in the plots, Figure S5 of the supplementary document). As observed in [1], the relationship for 3 m/s scenarios can also be developed as exponential. This implies that the RoS vs slope angle relationship transitions to an exponential fit at lower wind velocities. It is plausible that as the driving wind velocity decreases, the relationship morphs into an exponential one, resonating with the exponential correlation reported in most of the experimental studies conducted with negligible or very low wind speeds [14,40,41]. The exponential relationship between RoS and slope angle are summarized in Table 3.

#### 4.3.4. Relative

^{2}> 0.99 for both functions at both wind velocities. The trend lines for the exponential relationship (as the Australian slope correction is exponential) between relative RoS and slope are shown in Figure 7.

#### 4.3.5. Fire Intensity Q as a Function of RoS

^{2}[1], while the load for the lower wind velocities of 0.1 and 1 m/s (Sets 1 and 3) in this study is 0.85 kg/m

^{2}(Table 2). Black circles in the plot denote values at no-slope cases for all wind velocities. As stated in Section 3.1, the fire front did not progress for 0°, +5°, and +10° at 0.1 m/s and 0°, +5° at 1 m/s and hence the related data were not included in the analysis.

#### 4.4. Plume and Flame Dynamics at Lower Wind Velocities

_{c}) analysis is performed to quantify the mode of fire propagation as wind-driven or buoyancy-driven.

#### 4.5. Mode of Fire Propagation

_{c}, is calculated using Equation (6) [25] for cases with all slope angles, at 1 m/s wind velocity (simulation Set 3). Only results with 1 m/s cases are presented in Figure 11, as meaningful values could not be obtained with 0.1 m/s wind velocity cases (with RoS values higher than U

_{10}, the denominator term (U

_{10}− RoS)

^{3}in Equation (6) gives negative values, resulting in negative N

_{c}values). Different N

_{c}values can be obtained using wind velocity at different reference heights and either dynamic or quasi-steady RoS, but none are significant enough to change the classification of the mode of fire propagation.

_{c}typically describes forces that are nominally perpendicular. However, wind and slope can incline flame towards the surface. Past studies used N

_{c}for assessing whether fire propagation is wind-driven or plume-driven. Therefore, it is rational to use N

_{c}for slope cases. However, caution needs to be exercised in interpreting the N

_{c}values obtained in this study for steep upslope cases.

_{c}values (Figure 11), all scenarios can be classified as buoyancy-driven, yet we observed attached flames for slope angles ≥ +20°. This agrees with flame and plume contours presented in Figure 9 and Figure 10 that for ≥+20° slopes, the flame and plume were found to be attached to the ground for a short period before transiting into a buoyancy-driven propagation. This indicates that Byram number analysis may not be sufficient to determine the mode of fire behaviour in greater upslopes. In contrast, the higher wind velocity cases presented in [2] demonstrated that, for the highest wind velocity of 12.5 m/s, the flame and near-surface flame appeared to be rising even though the plume was attached. For wind velocities of 12.5 and 6 m/s, the flame was found to be buoyancy-dominated near the ground, tended towards wind-dominated for a very short time, and then transited to a buoyancy-dominated regime as the fire progressed. The flame behaviour was found to be different from the overall plume behaviour [2].

#### 4.6. Flame Length

#### 4.7. Heat Fluxes

_{c}analysis in Section 4.5. The same trend is noted for +10° slope as well, though not as predominantly as observed with higher slope angles. The leading or lagging of the fire front by radiative heat flux provides information about where heat transfer occurs as the fire front moves and does not necessarily mean that the total heat flux is dominated by the radiative heat flux.

_{c}suggesting that all these fires are buoyancy-dominated. Although the boundary conditions, the scale of the fuel bed and fuel type were different, results from this study largely align with the heat flux results observed by Tihay et al. [39] in their experimental investigation (under the no-wind condition). Their heat flux measurements showed that, for a 20° slope, convection represented the major fraction of heat transfer (between 61.1% and 74.9% of the total heat transfer). Similarly, Sánchez-Monroy et al. [30], from their laboratory scale simulation, reported that for no-wind conditions on slopes above +30°, convective heat flux is larger.

## 5. Summary and Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

AS3959 | Australian Standard 3959 |

BF | boundary fuel |

CFD | computational fluid dynamics |

CSIRO | Commonwealth Scientific and Industrial Research Organization |

FDS | Fire Dynamic Simulator |

FMC | fuel moisture content |

FE | fuel element |

GFDI | Grassland Fire Danger Index Meter |

$\mathrm{H}\mathrm{R}\mathrm{R}$ | heat release rate |

LES | large eddy simulation |

RoS | rate of spread |

SEM | synthetic eddy methodology |

WFDS | Wildland–Urban Interface Fire Dynamics Simulator |

## References

- Innocent, J.; Moinuddin, K.; Sutherland, D.; Khan, N. Physics-based simulations of grassfire propagation on sloped terrain at field-scale: Motivations, model reliability, rate of spread and intensity. Int. J. Wildland Fire
**2022**, 32, 496–512. [Google Scholar] [CrossRef] - Innocent, J.; Sutherland, D.; Khan, N. Moinuddin, Physics-based simulations of grassfire propagation on sloped terrain at field-scale: Flame dynamics, mode of fire propagation and the heat fluxes. Int. J. Wildland Fire
**2022**, 32, 513–530. [Google Scholar] [CrossRef] - Mell, W.; Jenkins, M.; Gould, J.S.; Cheney, N.P. A physics-based approach to modelling grassland fires. Int. J. Wildland Fire
**2007**, 16, 1–22. [Google Scholar] - McGrattan, K.B.; Forney, G.P.; Hostikka, S.; McDermott, R.; Weinschenk, C. Fire Dynamics Simulator, User’s Guide, 6th ed.; Original Version 2013, Revised Version 6.3.2 in 2015; NIST Special Publication: Gaithersburg, MD, USA, 2013; p. 1019. [Google Scholar] [CrossRef]
- Morvan, D.; Accary, G.; Meradji, S.; Frangieh, N.; Bessonov, O. A 3D physical model to study the behavior of vegetation fires at laboratory scale. Fire Saf. J.
**2018**, 101, 39–52. [Google Scholar] - Sharples, J.J. Risk Implications of Dynamic Fire Propagation, A Case Study of the Ginninderry Region; Preliminary Report, June 2017; Ginninderra Falls Association: New South Wales, Australia, 2017. [Google Scholar]
- Hilton, J.E.; Miller, C.; Sharples, J.J.; Sullivan, A.L. Curvature effects in the dynamic propagation of wildfires. Int. J. Wildland Fire
**2016**, 25, 1238–1251. [Google Scholar] - Hoffman, C.M.; Canfield, J.; Linn, R.R.; Mell, W.; Sieg, C.H.; Pimont, F.; Ziegler, J. Evaluating Crown Fire Rate of Spread Predictions from Physics-Based Models. Fire Technol.
**2015**, 52, 221–237. [Google Scholar] - Moinuddin, K.; Khan, N.; Sutherland, D. Numerical study on effect of relative humidity (and fuel moisture) on modes of grassfire propagation. Fire Saf. J.
**2021**, 125, 103422. [Google Scholar] - Sutherland, D.; Sharples, J.J.; Moinuddin, K.A.M. The effect of ignition protocol on grassfire development. Int. J. Wildland Fire
**2020**, 29, 70. [Google Scholar] [CrossRef] - McArthur, A.G. Weather and Grassland Fire Behaviour. In Forestry and Timber Bureau; Department of National Development, Commonwealth: Canberra, Australia, 1966. [Google Scholar]
- McArthur, A.G. Fire Behaviour in Eucalypt Forests. In Forestry and Timber Bureau; Department of National Development, Commonwealth: Canberra, Australia, 1967. [Google Scholar]
- Cheney, N.P.; Gould, J.S.; Catchpole, W.R. Prediction of Fire Spread in Grasslands. Int. J. Wildland Fire
**1998**, 8, 1–13. [Google Scholar] [CrossRef] - Noble, I.R.; Gill, A.; Barry, G. McArthur’s fire-danger meters expressed as equations. Aust. J. Ecol.
**1980**, 5, 201–203. [Google Scholar] - Moinuddin, K.; Sutherland, D.; Mell, W. Simulation study of grass fire using a physics-based model: Striving towards numerical rigour and the effect of grass height on the rate-of-spread. Int. J. Wildland Fire
**2018**, 27, 800–814. [Google Scholar] [CrossRef] - Rothermel, R.C. A Mathematical Model for Predicting Fire Spread in Wildland Fuels; General Technical Report INT-115; Intermountain Forest and Range, USDA Forest Service: Ogden, UT, USA, 1972. [Google Scholar]
- Andrews, P.L. The Rothermel Surface Fire Spread Model and Associated Developments: A Comprehensive Explanation; General Techncial Report RMRS-GTR-371; United States Department of Agriculture, Forest Service: Washington, DC, USA, 2018. [Google Scholar]
- Wilson, R. Reexamination of Rothermels Fire Spread Equations in No-Wind and No-Slope Conditions; Research Paper INT-434; United States Department of Agriculture, Forest Service: Washington, DC, USA, 1990. [Google Scholar]
- Weise, D.; Biging, G. A Qualitative Comparison of Fire spread model incorporating wind and slope effects. For. Sci.
**1997**, 43, 170–180. [Google Scholar] - Cruz, M.; Alexander, M.E.; Kilinc, M. Wildfire Rates of Spread in Grasslands under Critical Burning Conditions. Fire
**2022**, 5, 55. [Google Scholar] [CrossRef] - Bishe, E.M.; Afshin, H.; Farhanieh, B. Modified Quasi-Physcial Grassland Fire Spread Model: Sensitivity Analysis. Sustainability
**2023**, 15, 13639. [Google Scholar] [CrossRef] - Cheney, N.; Gould, J.; Catchpole, W. The Influence of Fuel, Weather and Fire Shape Variables on Fire-Spread in Grasslands. Int. J. Wildland Fire
**1993**, 3, 31–44. [Google Scholar] [CrossRef] - Byram, G. Combustion of Forest Fuels. In Forest Fire: Control and Use; Davis, K.P., Ed.; McGraw-Hill: New York, NY, USA, 1959; pp. 61–89. [Google Scholar]
- Mell, W.; Simeoni, A.; Morvan, D.; Hiers, J.K.; Skowronski, N.; Hadden, R.M. Clarifying the meaning of mantras in wildland fire behaviour modelling: Reply to Cruz et al. (2017). Int. J. Wildland Fire
**2018**, 27, 770–775. [Google Scholar] [CrossRef] - Morvan, D.; Frangieh, N. Wildland fires behaviour: Wind effect versus Byram’s convective number and consequences upon the regime. Int. J. Wildland Fire
**2018**, 27, 636. [Google Scholar] [CrossRef] - Dupuy, J.-L.; Maréchal, J. Slope effect on laboratory fire spread: Contribution of radiation and convection to fuel bed preheating. Int. J. Wildland Fire
**2011**, 20, 289–307. [Google Scholar] [CrossRef] - Alexander, M.E.; Cruz, M.G. Interdependencies between flame length and fireline intensity in predicting crown fire initiation and crown scorch height. Int. J. Wildland Fire
**2012**, 21, 95–113, Supplementary Erratum in Int. J. Wildland Fire**2021**, 30, 70. [Google Scholar] [CrossRef] - Anderson, H.; Brackebusch, A.P.; Mutch, R.W.; Rothermel, R.C. Mechanisms of Fire Spread Research Progress Report No. 2; Research Paper INT-28; US Forest Service: Washington, DC, USA, 1966. [Google Scholar]
- Jarrin, N.; Benhamadouche, S.; Laurence, D.; Prosser, R. A synthetic-eddy-method for generating inflow conditions for large-eddy simulations. Int. J. Heat Fluid Flow
**2006**, 27, 585–593. [Google Scholar] [CrossRef] - Sánchez-Monroy, X.; Mell, W.; Torres-Arenas, J.; Butler, B.W. Fire spread upslope: Numerical simulation of laboratory experiments. Fire Saf. J.
**2019**, 108, 102844. [Google Scholar] [CrossRef] - AS 3959-2018; Construction of Buildings in Bushfire Prone Area. Australian Standard: Sydney, Australia, 2018.
- Overholt, K.J.; Cabrera, J.; Kurzawski, A.; Koopersmith, M.; Ezekoye, O.A. Characterization of Fuel Properties and Fire Spread Rates for Little Bluestem Grass. Fire Technol.
**2014**, 50, 9–38. [Google Scholar] [CrossRef] - Abu Bakar, A. Characterization of Fire Properties for Coupled Pyrolysis and Combustion Simulation and Their Optimised Use. Ph.D. Thesis, Victoria University, Melbourne, Australia, 2015. [Google Scholar]
- Morvan, D.; Dupuy, J.L. Modeling the propagation of a wildfire through a Mediterranean shrub using a multiphase formulation. Combust. Flame
**2004**, 138, 199–210. [Google Scholar] [CrossRef] - Cheney, N.P.; Gould, J.S. Fire Growth in Grassland Fuels. Int. J. Wildland Fire
**1995**, 5, 237. [Google Scholar] [CrossRef] - Davis, T.; Sigmon, K. MATLAB Premier, 7th ed.; Chapman & Hall/CRC: Boca Raton, FL, USA, 2005; Available online: www.dbeBooks.com (accessed on 1 June 2017).
- Cobian-Iñiguez, J.; Aminfar, A.; Weise, D.R.; Princevac, M. On the Use of Semi-empirical Flame Models for Spreading Chaparral Crown Fire. Front. Mech. Eng.
**2019**, 5, 50. [Google Scholar] [CrossRef] - Dupuy, J.L.; Mare’chal, J.; Portier, D.; Valette, J.-C. The effects of slope and fuel bed width on laboratory fire behaviour. Int. J. Wildland Fire
**2011**, 20, 272–288. [Google Scholar] [CrossRef] - Tihay, V.; Morandini, F.; Santoni, P.-A.; Perez-Ramirez, Y.; Barboni, T. Combustion of forest litters under slope conditions: Burning rate, heat release rate, convective and radiant fractions for different loads. Combust. Flame
**2014**, 161, 3237–3248. [Google Scholar] [CrossRef] - Beck, J.A. Equations For The Forest Fire Behaviour Tables For Western Australia. CALM Sci.
**1995**, 1, 325–348. [Google Scholar] - Pimont, F.; Dupuy, J.L.; Linn, R.R. Coupled slope and wind effects on fire spread with influences of fire size: A numerical study using FIRETEC. Int. J. Wildland Fire
**2012**, 21, 828–842. [Google Scholar] [CrossRef] - Sullivan, A.L.; Sharples, J.J.; Matthews, S.; Plucinski, M.P. A downslope fire spread correction factor based on landscape-scale fire behaviour. Environ. Model. Softw.
**2014**, 62, 153–163. [Google Scholar] [CrossRef] - Mendes-Lopes, J.M.C.; Ventura, J.M.P.; 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. [Google Scholar] [CrossRef] - Dold, J.W.; Zinoviev, A. Fire eruption through intensity and spread rate interaction mediated by flow attachment. Combust. Theory Model.
**2009**, 13, 763–793. [Google Scholar] [CrossRef]

**Figure 1.**The geometry of the original domain (360 × 120 × 60 m

^{3}): The burnable grass plot is 80 × 40 m (olive green region). The same boundary conditions are followed for the larger domain of 480 × 180 × 80 m

^{3}.

**Figure 2.**Progression of isochrones. Frames (

**a**–

**h**) original domain at 0.1 m/s (Set 1); Frames (

**i**–

**p**) original domain at 1 m/s (Set 2); Frames (

**q**–

**w**) large domain, original fuel parameters at 1 m/s (Set 3); and Frames (

**x**–

**ad**) large domain, changed (“lighter & drier”) fuel at 1 m/s (Set 4).

**Figure 4.**Fireline intensity vs. time: (

**a**) quasi-steady intensity vs slope angle; (

**b**) relative intensity vs. slope angle; (

**c**) quasi-steady intensity vs. pyrolysis width.

**Figure 5.**Fire front location vs. time: (

**a**) Set 1, original domain at 0.1 m/s; (

**b**) Set 2, original domain at 1 m/s; (

**c**) Sets 2 and 3, original and larger domain, at 1 m/s; (

**d**) Sets 3 and 4, original and changed (“lighter & drier”) fuel parameters, at 1 m/s.

**Figure 6.**RoS—slope angle: WFDS quasi-steady RoS values fitted with a margin of error (95% confidence bounds): (

**a**) at 0.1 m/s (Set 1); (

**b**) at 1 m/s, original fuel parameters (Set 3); (

**c**) at 1 m/s, changed (“lighter & drier”) fuel parameters (Set 4,whiskers look smaller than (a-b) because of the large y-axis range).

**Figure 7.**Comparison of slope effect: RoS/RoS (+10°) between WFDS results and empirical model values (

**a**) at 0.1 m/s (Set 1); (

**b**) at 1 m/s (Set 3); (

**c**) at 1 m/s (Set 4).

**Figure 9.**(

**a**–

**c**) Plume contour, upslopes at 0.1 m/s (Set 1): +10°, +20°, +30°. (

**d**–

**f**) Plume contour, upslopes at 1 m/s (Set 3): +10°, +20°, +30°. Plumes emanating from grass plot at +10°, +20°, and +30° upslopes, at wind velocities 0.1 and 1 m/s (Sets 1 and 3).

**Figure 10.**(

**a**–

**e**): +30° at 1 m/s (Set 3). (

**f**–

**j**): +10°at 1 m/s (Set 3). (

**k**–

**o**): +30°at 0.1 m/s (Set 1). (

**p**–

**t**): +10°at 0.1 m/s (Set 1). Flame contour (red) with temperature contour (yellow) in the background along with detachment location (black dot) and wind vector plots (white arrows) at various times.

**Figure 11.**Byram convective number (N

_{c}) vs slope angle, derived using quasi-steady RoS, based on U

_{10}at driving wind velocity of 1 m/s; termed as N

_{c10}in the figure.

**Figure 12.**(

**a**) Quasi-steady flame length L vs slope with empirically derived values for at 0.1 m/s (Set 1) and at 1 m/s (Set 3); (

**b**) quasi-steady L vs slope with empirical values for Sets 2, 3, and 4 at 1 m/s.

**Figure 13.**All simulated flame length (L) values against Q values for all five wind velocities: 12.5, 6, 3, 1, and 0.1 m/s.

**Figure 14.**Instantaneous heat flux contours are taken at different times as the fire front moves through the grass plot: “rad” and “conv” represent radiative and convective heat fluxes, respectively.

**Figure 15.**Quasi-steady heat fluxes vs slope angles (

**a**) Quasi-steady heat fluxes at 0.1 and 1 m/s—same fuel parameters (Sets 1 and 3); (

**b**) Quasi-steady heat fluxes at 1 m/s—original and “lighter & drier” fuel parameters (Sets 3 and 4).

Slope Angle (Degree) | Domain Size: 360 × 120 × 60 M | Domain Size: 480 × 180 × 80 M | |||
---|---|---|---|---|---|

Burnable grass plot 80 × 40 m | |||||

Wind velocity | 0.1 m/s, Set 1 | 1 m/s, Set 2 | 1 m/s, Set 3 | 1 m/s, Set 4 | |

Fuel parameters | Original | Original | Original | Changed | |

–10° | √ | √ | |||

0° | √ | √ | √ | √ | |

+5° | √ | √ | √ | √ | |

+10° | √ | √ | √ | √ | |

+15° | √ | √ | √ | √ | |

+20° | √ | √ | √ | √ | |

+25° | √ | √ | √ | √ | |

+30° | √ | √ | √ | √ |

Input Parameters | Values Used | Source and Reason | |
---|---|---|---|

Sets 1–3 | Set 4 | ||

Fuel—grass | Grass type: kerosene (Eriachne burkittii) [3,15,22] | ||

Heat of combustion | 16,400 kJ/kg | 16,400 kJ/kg | Bluestem grass [32] |

Soot yield | 0.008 g/g | 0.008 g/g | White pine (Australian Radiata pine) [33] |

Vegetation drag coefficient | 0.125 | assuming vegetation elements are spherical [34] | |

Vegetation load | 0.85 kg/m^{2} | 0.31 kg/m^{2} | |

Vegetation height | 0.6 m | 0.6 m | |

Vegetation moisture content | 0.065 | 0.024 | Experimental, Cheney et al. [3,22,35] |

Surface area-to-volume ratio of vegetation | 9770/m | 9770/m | Experimental, Cheney et al. [3,22,35] |

Vegetation char fraction | 0.17 | 0.17 | Average of Cheney and Gould [22] and Bluestem grass [32] |

Vegetation element density | 440 kg/m^{3} | 160 kg/m^{3} | Australian Radiata pine (Abu Bakar 2015) [33], hay or straw density |

Ambient temperature | 32 °C | 50 °C | Experimental ([22]), Cheney and Gould [24] |

Relative humidity | 40% | 10% | Experimental [3,22,35] |

Emissivity | 0.99 | 0.99 | Cheney and Gould (1995), [22] |

Pyrolysis temperature | 400–500 K | 400–500 K | Morvan et al. [34] |

Degree of curing | 100% | 100% | Assuming vegetation 100% cured |

Heat of pyrolysis | 200 kJ/kg | 200 kJ/kg | White pine (Australian Radiata pine) [33] |

RoS | Pattern | 0.1 m/s, Set 1 | 1 m/s, Set 3, Original Fuel | 1 m/s (Set 4), “Lighter & Drier” Fuel | |||
---|---|---|---|---|---|---|---|

Equation | R^{2} | Equation | R^{2} | Equation | R^{2} | ||

Dynamic RoS, average | Exponential | 0.0752e^{0.054x} | 0.998 | 0.1263e^{0.0411x} | 0.978 | 0.235e^{0.034x} | 0.984 |

Quasi-steady RoS | Exponential | 0.0711e^{0.0528x} | 0.990 | 0.1179e^{0.0405x} | 0.997 | 0.2025e^{0.0404x} | 0.992 |

Slope Angle | Driving Wind Velocity | ||
---|---|---|---|

0.1 m/s | 1 m/s | ||

Set 1 | Set 3 | Set 4 | |

+5° to +15° | 87% | 60% | 60% |

+10° to +20° | 87% | 55% | 53% |

+15° to +25° | 55% | 45% | 50% |

+20° to +30° | 59% | 45% | 44% |

Pattern | 0.1 m/s, Set 1 | 1 m/s, Set 3 | 1 m/s, Set 4 | |||
---|---|---|---|---|---|---|

Equation | R^{2} | Equation | R^{2} | Equation | R^{2} | |

Exponential | 0.6326e^{0.0528x} | 0.990 | 0.6675e^{0.0405x} | 0.997 | 0.6693e^{0.0404x} | 0.992 |

Polynomial | 0.0012x^{2} + 0.0496x + 0.4224 | 0.995 | 0.0007x^{2} + 0.0309x + 0.6253 | 0.999 | 0.0005x^{2} + 0.0383x + 0.582 | 0.998 |

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

**MDPI and ACS Style**

Innocent, J.; Sutherland, D.; Moinuddin, K.
Field-Scale Physical Modelling of Grassfire Propagation on Sloped Terrain under Low-Speed Driving Wind. *Fire* **2023**, *6*, 406.
https://doi.org/10.3390/fire6100406

**AMA Style**

Innocent J, Sutherland D, Moinuddin K.
Field-Scale Physical Modelling of Grassfire Propagation on Sloped Terrain under Low-Speed Driving Wind. *Fire*. 2023; 6(10):406.
https://doi.org/10.3390/fire6100406

**Chicago/Turabian Style**

Innocent, Jasmine, Duncan Sutherland, and Khalid Moinuddin.
2023. "Field-Scale Physical Modelling of Grassfire Propagation on Sloped Terrain under Low-Speed Driving Wind" *Fire* 6, no. 10: 406.
https://doi.org/10.3390/fire6100406