Campbell-Lochrie, Zak

Gallagher, Michael

Hadden, Rory M.

Skowronski, Nicholas

English

Half a century after its introduction Rothermel’s flame spread model (Rothermel 1972) continues to find widespread use within fire modelling tools (e.g. BehavePlus, NEXUS, FARSITE) with few modifications incorporated (Albini 1976; Andrews et al. 2013). Rothermel’s model is underpinned by a physics-based framework based on conservation of energy, with the spread rate (R) described as the ratio between the energy transferred to the fuel (heat source) and the energy required for ignition (heat sink),R = (IR ξ (1 + ϕw + ϕs )) / (ρb ϵ Qig ) (1)where the energy transferred to the unburnt fuel incorporates reaction intensity (IR), propagating flux ratio (ξ), and wind (ϕw) and slope correction factors (ϕs). Energy required for ignition is given by the product of the oven-dry bulk density (ρb), effective heating number (ϵ), and heat of pre-ignition (Qig)

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     Edinburgh Research Explorer                                      Rothermel’s Model and the Role of Fuel Bed StructureCitation for published version:Campbell-Lochrie, Z, Gallagher, M, Skowronski, N & Hadden, RM 2023, Rothermel’s Model and the Role ofFuel Bed Structure. in Conference Proceedings Fire & Climate: Impacts, Issues & Futures. InternationalAssociation of Wildland Fire, Missoula, Montana, USA, pp. 154, Fire and Climate Conference 2022,Pasadena, California, United States, 23/05/22. <https://drive.google.com/file/d/1ne_Pnk-lr37UvQJdw9kCxeL3rz932l7n/view>Link:Link to publication record in Edinburgh Research ExplorerDocument Version:Publisher's PDF, also known as Version of recordPublished In:Conference Proceedings Fire & ClimateGeneral rightsCopyright for the publications made accessible via the Edinburgh Research Explorer is retained by the author(s)and / or other copyright owners and it is a condition of accessing these publications that users recognise andabide by the legal requirements associated with these rights.Take down policyThe University of Edinburgh has made every reasonable effort to ensure that Edinburgh Research Explorercontent complies with UK legislation. If you believe that the public display of this file breaches copyright pleasecontact openaccess@ed.ac.uk providing details, and we will remove access to the work immediately andinvestigate your claim.Download date: 26. Oct. 2023Proceedings for the Fire and Climate Conference May 23-27, 2022, Pasadena, California, USA and June 6-10, 2022, Melbourne, Australia Published by the International Association of Wildland Fire, Missoula, Montana, USA 154  Rothermel’s Model and the Role of Fuel Bed Structure   Zakary Campbell-Lochrie* The University of Edinburgh, Colin Maclaurin Road, Edinburgh, UK, z.campbell.lochrie@ed.ac.uk  Michael R. Gallagher USDA Forest Service, Northern Research Station, New Lisbon, New Jersey, USA, michael.r.gallagher@usda.gov  Nicholas Skowronski USDA Forest Service, Northern Research Station, Morgantown, West Virginia, USA, nicholas.s.skowronski@usda.gov  Rory M. Hadden The University of Edinburgh, Colin Maclaurin Road, Edinburgh, UK, r.hadden@ed.ac.uk  *Corresponding Author  Introduction Half a century after its introduction Rothermel’s flame spread model (Rothermel 1972) continues to find widespread use within fire modelling tools (e.g. BehavePlus, NEXUS, FARSITE) with few modifications incorporated (Albini 1976; Andrews et al. 2013). Rothermel’s model isunderpinned by a physics-based framework based on conservation of energy, with the spread rate (R) described as the ratio between the energy transferred to the fuel (heat source) and the energy required for ignition (heat sink),  R = (IR ξ (1 + ϕw + ϕs )) / (ρb ϵ Qig )    (1)  where the energy transferred to the unburnt fuel incorporates reaction intensity (IR), propagating flux ratio (ξ), and wind (ϕw) and slope correction factors (ϕs). Energy required for ignition is given by the product of the oven-dry bulk density (ρb), effective heating number (ϵ), and heat of pre-ignition (Qig).   Empirical values of reaction intensity (the heat release rate per unit area of the fire front) across a range of packing ratios were obtained through laboratory-based experiments in three fuel types (excelsior, ½ and ¼ inch sticks), however, the fuel loading was not held constant within or between the three different fuel types. This lack of systematic variation limits understanding of the independent effects of fuel loading and packing ratio despite the importance of both fuel properties on the fire behavior within surface fuel layers (Campbell-Lochrie et al. 2021; Gallagher et al. 2021) and it has been suggested that the model may be oversensitive to fuel height (Cruz and Fernandes 2008).  Proceedings for the Fire and Climate Conference May 23-27, 2022, Pasadena, California, USA and June 6-10, 2022, Melbourne, Australia Published by the International Association of Wildland Fire, Missoula, Montana, USA 155  Changes in fire management strategies, focusing on increasing prescribed burning, drive a need for improved fire behavior models to aid in planning, training, and strategy development (Hiers et al. 2020; Sample et al. 2022). It is therefore important to understand the implications of using a model developed using a small number of fuel types to predict the effect of fuel structure on the rate of spread across a range of natural fuel types. In this study, the performance of the Rothermel model across a range of (pine needle) fuel bed structures was investigated through comparison with an existing experimental dataset (Campbell-Lochrie et al. 2021).  Methods The effect of fuel bed structure on fire behavior in surface fuels was previously studied in a series of quiescent (no wind or slope) laboratory-based flame spread experiments (Campbell-Lochrie et al. 2021) involving linear flame spread (as shown in Figure 1). The spread rate was measured through video analysis of the flame front position over time. The Heat Release Rate was calculated using oxygen consumption calorimetry and converted to fireline intensity by dividing by the length of the fire front.   Figure 31. Example of linear flame spread experiments conducted in quiescent, laboratory environment  Fuel beds (1.5 m by 0.67 m) were constructed from either Pitch Pine (Pinus Rigida Mill.) or Pitch-Loblolly Pine hybrid (Pinus rigida x taeda) needles, with fuel moisture content measured prior to ignition. The fuel loading and bulk density of pine needle beds were independently varied (by controlling fuel height) and ranged from 0.2 to 1.6 kg/m2 and 10 to 40 kg/m3 respectively. The overall fuel bed structure was described by the single parameter ασδ which combines fuel bed porosity (α), surface-to-volume ratio (σ) and fuel bed height (δ) and was shown to be strongly correlated with spread rate.  For spread-rate predictions, Rothermel’s original model was used, however Albini’smodifications (Albini 1976) were incorporated along with conversion to SI units (Wilson 1980). The Albini modifications relevant to homogeneous fuel beds involve updated terms for the combustible dry fuel loading, mineral damping coefficient and reaction velocity variable. This model was implemented within MATLAB and verified through comparison with BehavePlus (Version 6).   Proceedings for the Fire and Climate Conference May 23-27, 2022, Pasadena, California, USA and June 6-10, 2022, Melbourne, Australia Published by the International Association of Wildland Fire, Missoula, Montana, USA 156  Results  Rate of Spread Experimental observations and Rothermel model predictions both indicate a positive trend between Rate of Spread (RoS) and either fuel loading or ασδ, and a negative trend between RoS and bulk density. As shown in Figure 2, predicted RoS values were typically lower than experimental observations. The model predicted flame spread at the lowest fuel loading (0.2 kg/m2) for Pitch-Loblolly hybrid pine needle fuel beds, however sustained flame spread did not occur in the experiments.  The deviation between experimental and observed RoS was calculated according to the Absolute Percent Error and ranged from -75 % to 12 %. As shown in Figure 2, the deviation varied with ασδ with the greatest under-predictions occurring in the lower ασδ range (ασδ =49 to ασδ =200) with little deviation at greater ασδ values (max. absolute deviation of 13 % for ασδ > 200).Deviation also increased at greater packing ratios (lower fuel heights) for a given fuel loading, which supports previous suggestions of an oversensitivity to compaction.   Figure 32. Comparison of predicted and experimentally observed Rate of Spread (RoS) for (left) Pitch Pine and (right) Pitch-Loblolly hybrid Pine Needles Reaction Intensity According to Equation 1, under-predictions of the RoS may occur due to under-prediction of the heat source term or over-prediction of the heat sink term. In this study, the experimentally observed fireline intensity allows further analysis of the suitability of the predicted reaction intensity across a range of fuel bed conditions.   Byram’s fireline intensity describes the heat release rate per unit length of the flame frontwhereas the reaction intensity describes the heat release rate per unit area of the fire front. The experimentally observed Byram fireline intensity (IB) was converted to a reaction intensity using  IB = (IR tR R) / 60     (2)  Proceedings for the Fire and Climate Conference May 23-27, 2022, Pasadena, California, USA and June 6-10, 2022, Melbourne, Australia Published by the International Association of Wildland Fire, Missoula, Montana, USA 157 where the residence time (tR) was estimated using (Anderson 1969)  tR = 8d = 384 / σ (3)  Diameter (d) and surface-to-volume ratio (σ) measurements for both species were used with the average residence time calculated (20 seconds).  As shown in Figure 3, comparison of the experimentally observed and predicted reaction intensity resulted in underestimates with increased divergence in the lower ασδ range (ασδ =49to ασδ =200). This suggests an under-prediction of the energy release within the flame front particularly in lower ασδ fuel beds in which the greatest deviations in predicted and observed spread rates occurred.   Figure 33. Ratio of predicted reaction intensity (IR(roth)) to experimentally observed reaction intensity (IR(exp)) for both pine needle species. Lowest fuel loading cases excluded due to the lack of sustained linear flame front.  Conclusions An oversensitivity of Rothermel’s flame spread model to fuel bed compaction was observed for low-intensity flame spread in pine needle beds. Comparison of experimental observations of spread rate with Rothermel model predictions resulted in increased divergence for fuel beds of lower ασδ values (ασδ =49 to ασδ =200). For fuel beds of constant fuel loading, greater under-predictions of spread rate occurred for compressed (lower fuel height, greater packing ratio) fuel beds. This appears to be at least in part due to the under-prediction of reaction intensity particularly in the lower ασδ range. Incorporating an increased understanding of the effect of fuel structure will aid the continued use of the Rothermel model in the planning of fuels management and prescribed fire operations by supporting the use of refined fuel representations and by Proceedings for the Fire and Climate Conference May 23-27, 2022, Pasadena, California, USA and June 6-10, 2022, Melbourne, Australia Published by the International Association of Wildland Fire, Missoula, Montana, USA 158 improving predictions of energy release outputs that subsequently drive flame-spread and fire-effects predictions. Acknowledgements This work was funded by the U.S. Department of Defense - Strategic Environmental Research and Development Program (SERDP) under project grant RC-2641.  References Albini FA (1976) Computer-based models of wildland fire behavior: A users’ manual. USDA Forest Service, Intermountain Forest and Range Experiment Station  Anderson HE (1969) Heat transfer and fire spread. USDA Forest Service, Research Paper INT -69.   Andrews PL, Cruz MG, Rothermel RC (2013) Examination of the wind speed limit function in the Rothermel surface fire spread model. International Journal of Wildland Fire 22, 959–969.   Campbell-Lochrie Z, Walker-Ravena C, Gallagher M, Skowronski N, Mueller EV, Hadden RM (2021) Investigation of the role of bulk properties and in-bed structure in the flow regime of buoyancy-dominated flame spread in porous fuel beds. Fire Safety Journal 120.  Cruz MG, Fernandes PM (2008) Development of fuel models for fire behaviour prediction in maritime pine (Pinus pinaster Ait.) stands. International Journal of Wildland Fire 17, 194–204.   Gallagher MR, Cope Z, Giron DR, Skowronski NS, Raynor T, Gerber T, Linn RR, Hiers JK (2021) Reconstruction of the spring hill wildfire and exploration of alternate management scenarios using QUIC-Fire. Fire 4.  Hiers JK, O’Brien JJ, Varner JM, Butler BW, Dickinson M, Furman J, Gallagher M, Godwin D,Goodrick SL, Hood SM, Hudak A, Kobziar LN, Linn R, Loudermilk EL, McCaffrey S, Robertson K, Rowell EM, Skowronski N, Watts AC, Yedinak KM (2020) Prescribed fire science: the case for a refined research agenda. Fire Ecology 16.  Rothermel RC (1972) A Mathematical Model for Predicting Fire Spread in Wildland Fuels. USDA Forest Service, Research Paper INT-115.  Sample M, Thode AE, Peterson C, Gallagher MR, Flatley W, Friggens M, Evans A, Loehman R, Hedwall S, Brandt L, Janowiak M, Swanston C (2022) Adaptation Strategies and Approaches for Managing Fire in a Changing Climate. Climate 10.  Wilson R (1980) Reformulation of Forest Fire Spread Equations in SI Units. USDA Forest Service, Research Note INT-292.    

Rothermel’s Model and the Role of Fuel Bed Structure

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Rothermel’s Model and the Role of Fuel Bed Structure

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