Modelling wildland fire propagation by tracking random fronts

Abstract

Abstract. Wildland fire propagation is studied in the literature by two alternative approaches, namely the reactiondiffusion equation and the level-set method. These two approaches are considered alternatives to each other because the solution of the reaction-diffusion equation is generally a continuous smooth function that has an exponential decay, and it is not zero in an infinite domain, while the levelset method, which is a front tracking technique, generates a sharp function that is not zero inside a compact domain. However, these two approaches can indeed be considered complementary and reconciled. Turbulent hot-air transport and fire spotting are phenomena with a random nature and they are extremely important in wildland fire propagation. Consequently, the fire front gets a random character, too; hence, a tracking method for random fronts is needed. In particular, the level-set contour is randomised here according to the probability density function of the interface particle displacement. Actually, when the level-set method is developed for tracking a front interface with a random motion, the resulting averaged process emerges to be governed by an evolution equation of the reaction-diffusion type. In this reconciled approach, the rate of spread of the fire keeps the same key and characterising role that is typical of the level-set approach. The resulting model emerges to be suitable for simulating effects due to turbulent convection, such as fire flank and backing fire, the faster fire spread being because of the actions by hot-air pre-heating and by ember landing, and also due to the fire overcoming a fire-break zone, which is a case not resolved by models based on the level-set method. Moreover, from the proposed formulation, a correction follows for the formula of the rate of spread which is due to the mean jump length of firebrands in the downwind direction for the leeward sector of the fireline contour. The presented study constitutes a proof of concept, and it needs to be subjected to a future validation.

Towards predictive data-driven simulations of wildfire spread – Part I: Reduced-cost Ensemble Kalman Filter based on a Polynomial Chaos surrogate model for parameter estimation

“…The second part of this series of two articles ) is dedicated to the evaluation of a state estimation approach that is able to account for both anisotropic uncertainties and modeling uncertainties. While out of the scope of this series of two articles, a proper representation of the model errors could be performed in the EnKF by introducing a model error covariance matrix (Trémolet, 2007), which could be modeled using a stochastic model such that proposed by Pagnini and Mentrelli (2014) for the transport of firebrands.…”

“…For instance, Finney et al (2011) describes an ensemble-based forecasting capability, in which a large number of fire spread scenarios (i.e., the ensemble members) are generated based on a probabilistic uncertainty in the weather conditions and in the moisture content of biomass fuels. Model uncertainties are a combination of epistemic errors that express an imperfect knowledge of the input parameters of the ROS model (that could in theory be removed), and of aleatoric errors that result from natural and unpredictable stochastic variabilities of the physical system (that can be addressed by stochastic models, see for instance Reference by Pagnini and Mentrelli (2014), whose model relies on a stochastic component to represent the transport of firebrands). These uncertainties translate inevitably into errors in the output variables of interest (e.g., time-evolving position of the front, burnt area, maximum value for the ROS).…”

RandomFront 2.3: a physical parameterisation of fire spotting for operational fire spread models – implementation in WRF-SFIRE and response analysis with LSFire+

“…A mathematical model to represent the random effects associated with the wildland fires has been developed by Pagnini and co-authors (Pagnini and Massidda, 2012b, a;Pagnini, 2013Pagnini andMentrelli, 2016, 2014;Kaur et al, 2015Mentrelli and Pagnini, 2016). This formulation describes the motion of the fire line as a composition of the drifting part and the fluctuating part.…”

“…In this article, the authors proceed with the RandomFront statistical formulation for including the effects of random processes in wildfire simulators, namely turbulence and firespotting phenomena. The chronology of this approach refers to the following papers: v1.0 includes only turbulence, with no parameterisation (Pagnini and Massidda, 2012a, b); v2.0 includes turbulence and fire spotting with literature parameterisation for fire spotting (Pagnini and Mentrelli, 2014); v2.1 includes turbulence and fire spotting with parameterisation for turbulence ; and v2.2 includes turbulence and fire spotting with a first physical parameterisation of fire spotting . Finally, in the present version v2.3 the parameterisation of fire spotting has been modified and corrected (also in view of a remark by one of the referees) with respect to the previous version.…”

“…The proposed parameterisation has been implemented into WRF-SFIRE (Coen et al, 2012;Mandel et al, 2014) and a paradigmatic test case has been simulated. Moreover, the proposed formulation for including random process and the corresponding physical parameterisations are implemented into a much simpler fire spread simulator, also based on the LSM, namely LSFire+ (Pagnini and Massidda, 2012a, b;Pagnini and Mentrelli, 2014;Chu and Prodanović, 2009;Bevins, 1996). Results from different test cases with LSFire+ are presented to highlight the sensitivity of the simple parameterisation in simulating the generation of secondary fires by fire spotting under different wind conditions, fire intensities and firebrand radii.…”