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Publication
Fractional Dynamics in Forest Fires
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| 1.25 MB | Adobe PDF |
Advisor(s)
Abstract(s)
Every year forest fires consume large areas, being a major concern in many countries like
Australia, United States and Mediterranean Basin European Countries (e.g., Portugal,
Spain, Italy and Greece). Understanding patterns of such events, in terms of size and
spatiotemporal distributions, may help to take measures beforehand in view of possible
hazards and decide strategies of fire prevention, detection and suppression. Traditional
statistical tools have been used to study forest fires. Nevertheless, those tools might not be
able to capture the main features of fires complex dynamics and to model fire behaviour
[1]. Forest fires size-frequency distributions unveil long range correlations and long memory
characteristics, which are typical of fractional order systems [2]. Those complex correlations
are characterized by self-similarity and absence of characteristic length-scale, meaning
that forest fires exhibit power-law (PL) behaviour. Forest fires have also been proved to
exhibit time-clustering phenomena, with timescales of the order of few days [3]. In this
paper, we study forest fires in the perspective of dynamical systems and fractional calculus
(FC). Public domain forest fires catalogues, containing data of events occurred in Portugal,
in the period 1980 up to 2011, are considered. The data is analysed in an annual basis,
modelling the occurrences as sequences of Dirac impulses. The frequency spectra of such
signals are determined using Fourier transforms, and approximated through PL trendlines.
The PL parameters are then used to unveil the fractional-order dynamics characteristics
of the data. To complement the analysis, correlation indices are used to compare and find
possible relationships among the data. It is shown that the used approach can be useful to
expose hidden patterns not captured by traditional tools.