On elliptical model for forest fire spread modeling and simulation

Glasa, Jan; Halada, Ladislav

doi:10.1016/j.matcom.2007.06.001

Cited by 36 publications

(23 citation statements)

References 19 publications

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“…Theorem 9.1 (Richards [20], Glasa and Halada [28]). A wildfire γ(s, t) on a given ellipse template field with Zermelo equivalent data a(u, v), b(u, v), C(u, v) = (c 1 (u, v), c 2 (u, v)), and θ(u, v) is determined by the following equations for the partial derivatives γ s (s, t) = (u s , v s ) and γ t (s, t) = (u t , v t ):…”

Section: Richards' Equationsmentioning

confidence: 99%

“…Following the pioneering works of G. D. Richards [20,21,22,23,24], van Wagner [25], Anderson et al [26], and Glasa-Halada [27,28,29,30,31], we will apply a number of assumptions to be satisfied by the wildfires. We will only consider 2-dimensional, regular, smooth and deterministic wildfires ignited at time t = 0 on a smooth and regular ignition fireline (or at an ignition point).…”

Section: Huyghens' Principlementioning

confidence: 99%

“…[20], [28]. In this setting, the representing ellipse field I p = E (u,v) is parametrized as follows in the tangent space basis {∂ u , ∂ v } at (u, v) in the parameter domain:…”

Section: The Randers-zermelo Elliptic Wildfiresmentioning

confidence: 99%

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A Finsler geodesic spray paradigm for wildfire spread modelling

Markvorsen

2016

Nonlinear Analysis: Real World Applications

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One of the finest and most powerful assets of Finsler geometry is its ability to model, describe, and analyze in precise geometric terms an abundance of physical phenomena that are genuinely asymmetric, see e.g. [1,2,3,4,5,6,7,8,9]. In this paper we show how wildfires can be naturally included into this family. Specifically we show how the celebrated and much applied Richards' equations for the large scale elliptic wildfire spreads have a rather simple Finsler-geometric formulation. The general Finsler framework can be explicitly 'integrated' to provide detailed -and curvature sensitive -geodesic solutions to the wildfire spread problem. The methods presented here stem directly from first principles of 2-dimensional Finsler geometry, and they can be readily extracted from the seminal monographs [10] and [11], but we will take special care to introduce and exemplify the necessary framework for the implementation of the geometric machinery into this new application -not least in order to facilitate and support the dialog between geometers and the wildfire modelling community. The 'integration' part alluded to above is obtained via the geodesics of the ensuing Finsler metric which represents the local fire templates. The 'paradigm' part of the present proposal is thus concerned with the corresponding shift of attention from the actual fire-lines to consider instead the geodesic spray -the 'fire-particles' -which together, side by side, mold the fire-lines at each instant of time and thence eventually constitute the local and global structure of the wildfire spread.

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Section: Richards' Equationsmentioning

confidence: 99%

Section: Huyghens' Principlementioning

confidence: 99%

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A Finsler geodesic spray paradigm for wildfire spread modelling

Markvorsen

2016

Nonlinear Analysis: Real World Applications

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“…A combination of weather and fuel calibration using fire perimeters has also been implemented using FARSITE (Finney 1998) and high-performance computing, showing great improvements and potential for long-term predictions (Wendt et al 2011;Artés et al 2014). Combining these ideas, Rios et al (2014) developed a data-driven algorithm based on Rothermel's RoS model (Rothermel 1972) and Huygens' elliptical propagation (Richards 1990;Glasa and Halada 2008) and proved that it provides a short-term highly accurate forecast of wind-driven wildfires when tested with synthetically generated data.…”

Section: Introductionmentioning

confidence: 99%

Short-term fire front spread prediction using inverse modelling and airborne infrared images

Rios

Pastor

Valero

et al. 2016

Int. J. Wildland Fire

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Abstract.A wildfire forecasting tool capable of estimating the fire perimeter position sufficiently in advance of the actual fire arrival will assist firefighting operations and optimise available resources. However, owing to limited knowledge of fire event characteristics (e.g. fuel distribution and characteristics, weather variability) and the short time available to deliver a forecast, most of the current models only provide a rough approximation of the forthcoming fire positions and dynamics. The problem can be tackled by coupling data assimilation and inverse modelling techniques. We present an inverse modelling-based algorithm that uses infrared airborne images to forecast short-term wildfire dynamics with a positive lead time. The algorithm is applied to two real-scale mallee-heath shrubland fire experiments, of 9 and 25 ha, successfully forecasting the fire perimeter shape and position in the short term. Forecast dependency on the assimilation windows is explored to prepare the system to meet real scenario constraints. It is envisaged the system will be applied at larger time and space scales.

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“…The propagation of wildfires has been studied in various mathematical papers: see, for example, [9,10], the survey articles [3,13], and the references therein. A related optimal control problem was considered in [12].…”

Section: Introductionmentioning

confidence: 99%

Existence of optimal strategies for a fire confinement problem

Bressan¹,

Lellis²

2008

Comm Pure Appl Math

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We consider a class of variational problems for differential inclusions related to the control of forest fires. The area burned by the fire at time t > 0 is modeled as the reachable set for a differential inclusion P x 2 F .x/ starting from an initial set R 0 . To block the fire, a barrier can be constructed progressively in time at a given speed. In this paper we prove the existence of an optimal strategy, which minimizes the value of the area destroyed by the fire plus the cost of constructing the barrier.

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On elliptical model for forest fire spread modeling and simulation

Cited by 36 publications

References 19 publications

A Finsler geodesic spray paradigm for wildfire spread modelling

A Finsler geodesic spray paradigm for wildfire spread modelling

Short-term fire front spread prediction using inverse modelling and airborne infrared images

Existence of optimal strategies for a fire confinement problem

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