Physics-based simulations of grassfire propagation on sloped terrain at field-scale: a combined wind and slope effect study

The rate of spread of fire (RoS) depends on various topographical, weather and fuel parameters. The wind speed and slope of the terrain are among the two major weather and topographical factors that determine the rate of fire spread. These two parameters are investigated in this study to obtain an insight into grassfire behaviour in respect to wind and slope variables, which may then be used to improve operational and empirical models, improve prediction of real wildfires, and subsequently alleviate the risks of wildfire impact. A fully physics-based modelling study of grassfire behaviour over flat and sloped terrain has been conducted at field-scale. The purpose was to investigate the combined effect of slope and wind on grassfire behaviour and attempt to capture the physical processes governing fire propagation. The simulations are performed using physics-based model, Wildland-urban Interface Fire Dynamics Simulator (WFDS version svn 9977), at driving wind velocities of 12.5, 6, 3, 1 and 0.1 m.s–1 and slope angles varying from –30° to +30°. This research primarily analyses the RoS, alongside other quantities such as fire isochrones, fire intensity, flame dynamics, mode of fire propagation and heat transfer. Although the focus of this study is to compare quasi-steady fire behaviour with empirical models, an attempt is also made to analyse the dynamic beahviour of fire, as the fire intensity and the expansion of the isochrones even though RoS may remain roughly constant. Slope correction for grassfire propagation in empirical models are presented in two ways: multiplicative and additive. For the former, RoS is calculated for no-slope (under the influnce of wind) and then a multiplied by a slope correction factor developed from studies conducted with no-wind conditions (i.e. doubling RoS for every 10° slope as given by Noble et al. (1980)). For the latter, RoS under the influnce of no-wind is determined to which the wind and slope factors are added (Rothermel 1972 model). Within the simulations conducted in this research, the RoS and fire intensity are found to have a positive correlation with respect to the slope angles, besides with the wind velocity. RoS comparisons have been made with common empirical models: Australian models with ‘slope correction’ multiplication (CSIRO model and McArthur models MKIII and MKV), and Rothermel models (‘Original’ and ‘Modified’ models). At different slope angles and driving wind velocities, different empirical quasi-steady RoS broadly matches with particular dynamic maximum, minimum (the upper and lower bounds of instantaneous RoS are provided as whiskers to present uncertainty to the averaged RoS values) and averaged RoS values from this study. The dynamic nature of grassfire propagation and challenges related to capturing this dynamism in experimental studies are likely reasons for any observed discrepancies. Within the slope angles and driving wind velocities examined in this study, for higher wind velocities, a second-order polynomial relationship exists between the quasi-steady RoS and slope angle, which is also the case for Rothermel models. However, for lower wind velocities, the RoSslope angle relationship is closer to an exponential fit, consistent with the exponential relationship reported with most of the experimental studies that are conducted at no or very low wind speeds. The slope correction for RoS in Australian empirical correlations is also exponential, which are likely to be derived from very low wind laboratory-scale slope studies. The relative RoS (RoS on any slope divided by RoS at a reference slope) results shows that, at higher wind velocities, the relative RoS from WFDS are closer to Rothermel models than the Australian correlations. The Rothermel model shows very little slope-effect under the influence of strong wind, whereas, as the wind-velocity reduces, a greater effect can be observed. The opposite is noted for Australian slope function models. It is due to multiplicative nature of Australian correlations compared to Rothermel models’ additive nature. Under lower or near zero wind velocities, the Australian model’s slope function is closer to the WFDS quasi-steady RoS results, whereas there are significant discrepancies in the results for higher wind velocities. Hence, the multiplicative nature of the Australian model’s slope function (especially for upslopes at higher wind velocities) may need strong scrutiny. Generally, the RoS, headfire width, fire intensity and flame length are all strongly correlated to wind velocity and slope angle. This study also analyses the RoS-fire intensity and fire intensityflame length relationships. In most cases, the RoS-fire intensity relationship is found to be linear (as expected from Byram’s correlation for no-slope scenarios). However, the relationship deviates from linearity for higher upslopes. Generally, Byram intensity (Q = fuel load x heat of combustion x RoS) was satisfied with approximately 42% fuel load consumed instead of 100% fuel load. A power-law correlation is found between the simulated flame lengths and fire intensities as observed by many previous researchers. However, various researchers proposed different exponents. The flame length results from this study match closest to the empirical model proposed by Anderson et al. (1966). This study also analyses the grass fire propagation with varied ignition fire line widths, at different upslope angles, at 1 m.s–1 wind speed. Comparing the pyrolysis region contours for varied ignition fire lines, for higher upslopes, the contour pattern with wider ignition lines appears to give sharper convex curvature. The simulation results, in general, show similarity with the experimentally observed results of Dupuy et al. (2011). The narrower the ignition fire line is, the slower is fire propagation and a convergence is obtained at about 30 m ignition line in terms of RoS, fire intensity and flame length. The interaction of wind and fire on a sloped terrain is always complex due to mechanisms of heat transfer and flame dynamics. Heating of unburned vegetation by attached flames may increase the rate of spread. The relative intensities of convective and radiative heat fluxes may change the fire behaviour significantly. This study presents a detailed analysis of flame dynamics, mode of fire propagation and surface radiative and convective heat fluxes on sloped terrain, at various wind speeds. With the increase of slope angles and wind velocity, the plume inclines more towards the ground and becomes elongated in upslope cases, whereas in downslopes, the plume rises from the ground at a shorter distance from the fire line. The flame dynamics results at higher wind velocities indicate that eruptive growth of fires occur in higher upslopes. For higher wind velocities, the flame and near-surface flame dynamics appear to be up-rising, even though the plume is attached. The flame contour results for higher wind velocities indicate that the near-surface flame dynamics are difficult to characterise using the Byram number analysis. Finally, the heat transfer analyses demonstrated that the convective heat fluxes are more relevant at wind-driven fire propagation and at higher upslopes, whereas, both fluxes are equally significant at lower driving wind velocities compared with higher wind velocities. This tendency agrees with that observed in the literature. Overall, the finding from this research provide insight into physical and parametric observations with fire isochrone progression, RoS, the flame dynamics, mode of fire propagation and heat flux parameters. This can lead to further extensive studies to improve the approach of combined wind and slope effects within operational models.