Climate strongly influences global wildfire activity, and recent wildfire surges may signal fire weather-induced pyrogeographic shifts. Here we use three daily global climate data sets and three fire danger indices to develop a simple annual metric of fire weather season length, and map spatio-temporal trends from 1979 to 2013. We show that fire weather seasons have lengthened across 29.6 million km2 (25.3%) of the Earth's vegetated surface, resulting in an 18.7% increase in global mean fire weather season length. We also show a doubling (108.1% increase) of global burnable area affected by long fire weather seasons (>1.0 σ above the historical mean) and an increased global frequency of long fire weather seasons across 62.4 million km2 (53.4%) during the second half of the study period. If these fire weather changes are coupled with ignition sources and available fuel, they could markedly impact global ecosystems, societies, economies and climate.

Climate-induced variations in global wildfire danger from 1979-2013

Fire radiative energy for quantitative study of biomass burning: derivation from the BIRD experimental satellite and comparison to MODIS fire products.

Boundary conditions for displacement experiments through short laboratory soil columns [Dispersion coefficients]

In recent years, advances in computational power and spatial data analysis (GIS, remote sensing, etc) have led to an increase in attempts to model the spread and behaviour of wildland fires across the landscape. This series of review papers endeavours to critically and comprehensively review all types of surface fire spread models developed since 1990. This paper reviews models of a physical or quasi-physical nature. These models are based on the fundamental chemistry and/or physics of combustion and fire spread. Other papers in the series review models of an empirical or quasi-empirical nature, and mathematical analogues and simulation models. Many models are extensions or refinements of models developed before 1990. Where this is the case, these models are also discussed but much less comprehensively.

A review of wildland fire spread modelling, 1990-present, 1: Physical and quasi-physical models

Adaptive finite element methods (FEM) have been widely used in applications for over 20 years now. In practice, they converge starting from coarse grids, although no mathematical theory has been able to prove this assertion. Ensuring an error reduction rate based on a posteriori error estimators, together with a reduction rate of data oscillation (information missed by the underlying averaging process), we construct a simple and efficient adaptive FEM for elliptic partial differential equations. We prove that this algorithm converges with linear rate without any preliminary mesh adaptation nor explicit knowledge of constants. Any prescribed error tolerance is thus achieved in a finite number of steps. A number of numerical experiments in two and three dimensions yield quasi-optimal meshes along with a competitive performance. Extensions to higher order elements and applications to saddle point problems are discussed as well.

Keywords: A posteriori error estimators, data oscillation, adaptive mesh refinement, convergence, Stokes, Uzawa

AMS Subject Classifications: 65N12, 65N15, 65N30, 65N50, 65Y20


Published: SIAM Review, 44 (2002) 631--658.

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Convergence of Adaptive Finite Element Methods

SUMMARY The 2-D simplied wildlandre model presented here is based on conservation laws and takes into account radiation as the dominant thermal transfer mechanism, as well as convection, which represents the eect of the wind and the slope. The non-dimensional equations are obtained using the Frank- Kamenestkii change of variables. The existence of weak solutions of the non-linear reaction diusion problem obtained is established as a particular case of more general existence results using a compactness method. The uniqueness of the weak solution is shown for a given initial data andxed parameters of the equations. The approximate solution is obtained using a mixednite element method. This preserves the continuity of theux through the inter-element boundaries and allows to represent high gradients in the solution. Semi-discrete error estimation is presented. The convective term is solved by a splitting technique using Godunov's method. The numerical examples show the eciency of the algorithm in capturing there front, even for critical values of the parameters. Copyright ? 2002 John Wiley & Sons, Ltd.

On a wildland fire model with radiation

An adaptive refinement/derefinement algorithm of nested meshes is presented. Some definitions are introduced. The main properties of the derefinement algorithm are remarked upon and its efficiency is shown through two numerical examples: a time-dependent convection-diffusion problems with dominant convection and a quasistationary problem.

L. Ferragut

Papers

On a wildland fire model with radiation

Efficient refinement/derefinement algorithm of nested meshes to solve evolution problems

A numerical method for solving convection-reaction-diffusion multivalued equations in fire spread modelling

Adaptive strategies using standard and mixed finite elements for wind field adjustment

A convection model for fire spread simulation