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Predicting the Arrival of the Unpredictable: An Approach for Foreseeing the Transition to Chaos in Wildfire Propagation †

Depto. Matemática Aplicada y Ciencias de la Computación, Universidad de Cantabria, 39005 Santander, Spain
BCAM—Basque Center for Applied Mathematics, 48009 Bilbao, Spain
Ikerbasque, Basque Foundation for Science, 48013 Bilbao, Spain
Author to whom correspondence should be addressed.
Presented at the Third International Conference on Fire Behavior and Risk, Sardinia, Italy, 3–6 May 2022.
Environ. Sci. Proc. 2022, 17(1), 69;
Published: 11 August 2022
(This article belongs to the Proceedings of The Third International Conference on Fire Behavior and Risk)


Inspired by the success of weather forecasts in recent years, we wonder if in the future we can follow the same successful path for improving the prediction of wildfire propagation. Hence, in analogy with this story, we start this research program from the very beginning of the modern theory of the predictability of weather, namely by uncovering the chaotic nature of wildfires through the derivation of a low-dimensional model in the same spirit as the derivation of the Lorenz chaotic system. Specific applications of chaos theory to the predictability of the propagation of wildfires are very seldom. Here, a Lorenz-type chaotic system for wildfire propagation is derived. This chaotic system with three degrees of freedom (temperature, fuel concentration, and rate of spread) follows from a prototypical reaction-diffusion equation of the temperature field coupled with an equation of the fuel concentration and from a Langevin-like equation for the rate of spread. Then, the motion of the fire-front resembles Brownian-like motion, where the Gaussian noise is replaced by the combined effect of the temperature and of the fuel concentration. We show that it is possible to predict the “environmental” changes that generate a transition to chaos in a system that is initially predictable in spite of uncertainties in its initial state. Thanks to the physical meaning of the involved parameters, this approach can lead to the prediction of changes, e.g., variations in the mean wind or in the heat of the reaction, which turn a predictable propagation of wildfires into an unpredictable one. By studying the growth of the separation of the resulting fire-line positions, a quantitative ranking-of-risk can be established in view of the changes that may take place in the system; this allows for setting out an alternative method for real-time risk assessment.

Author Contributions

V.E. and G.P. contributed equally to this work. All authors have read and agreed to the published version of the manuscript.


This research is supported by the Basque Government through the BERC 2018–2021 program; by the Spanish Ministry of Economy and Competitiveness MINECO through the BCAM Severo Ochoa excellence accreditation SEV-2017-0718 and also through the project PID2019-107685RB-I00, and by the European Regional Development Fund (ERDF) and the Department of Education of the regional government, the Junta of Castilla y Léon, (Grant contract SA089P20).

Institutional Review Board Statement

Not Applicable.

Informed Consent Statement

Not Applicable.

Data Availability Statement

The study does not report any data.

Conflicts of Interest

The authors declare no conflict of interest.
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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MDPI and ACS Style

Egorova, V.; Pagnini, G. Predicting the Arrival of the Unpredictable: An Approach for Foreseeing the Transition to Chaos in Wildfire Propagation. Environ. Sci. Proc. 2022, 17, 69.

AMA Style

Egorova V, Pagnini G. Predicting the Arrival of the Unpredictable: An Approach for Foreseeing the Transition to Chaos in Wildfire Propagation. Environmental Sciences Proceedings. 2022; 17(1):69.

Chicago/Turabian Style

Egorova, Vera, and Gianni Pagnini. 2022. "Predicting the Arrival of the Unpredictable: An Approach for Foreseeing the Transition to Chaos in Wildfire Propagation" Environmental Sciences Proceedings 17, no. 1: 69.

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