7th Workshop on Forest Fire Management - EARSeL, European ...

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III - FIRE DETECTION AND FIRE MONITORING
2 - Methodology
The Fast Fourier Transform (FFT) is a method applied to time series data
that may present certain periodicity. Its application and analysis aims at
the attainment of two objectives. In the first place, to describe the temporal
behaviour of a magnitude whose data present short-term strong fluctuations
which are probably caused by “noise”. In the second place, the
Fourier Transform allows us to decompose the behaviour of a variable in different
terms with different weighting factors in the reproduction of the
series, which can be analyzed independently in order to draw conclusions
which are explained from the hidden effects caused by the variability of the
original data. The Fourier transform harmonics are calculated according to:
The Factor F A (n) is the Fourier Transform for frequency n, and there are N
frequencies corresponding to the harmonics of the series. F A (n) is calculated
from this already known time series. If there is a discrete variable A
which takes N values equi-spaced in time series, such variable can be represented
(the Inverse Fourier Transform) as:
3 - Results
Before establishing correlations with fire data, it was necessary to find a
yearly evolution curve of CO total column for years in the series 2005-08.
This analysis is a synoptic approximation to the CO behaviour in the Iberian
Peninsula. For this, a central geographical point in the Iberian Peninsula
was selected and a radial distance of 600 km was established to determine
CO column average values. After applying the FFT to the data, the spectral
energy of all 1460 harmonics in the series was analyzed in order to retrieve
the groups that would later provide the inverse Fourier transform. Thus, two
groups were chosen for this case comprising harmonics [1-10] and [1450-
1459] respectively. The adopted criteria, to explain this selection, were: i)
selection of biggest spectral energy of harmonics and ii) selection of harmonics
modulating the oscillation amplitude of values. The reference curve
found is finally calculated through:
where COS is the CO total column value for this synoptic curve, k represents
the day of the series (k = 1 is 1st January 2005 and k = 1460 is 31st