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ŠUMARSKI LIST 5-6/2009 str. 77     <-- 77 -->        PDF

R. Rosavec, D. Dominko, D. Barčić, D. Starešinić, Ž. Španjol, K. Biljaković, M. Ožura, N. Marković, D. Bognolo: AN... Šum. list br. 5–6, CXXXIII (2009), 301-307
phenomenon for the survival of forests themselves, but also for physics. Physics
perceives forest fires as an example of a complex system on large, kilometer-
long scales. Faithful computer simulations can answer different questions, such
as how fires behave, what influences their propagation, how they follow the
power law and most importantly, how fires of different sizes can be predicted.


In our work we used the data from the forest administrations of Brač, Korčula
and Rab. The data, collected over the time period 1991 – 2000, relate to
the number of fires and the size of the burned area. We began with a model in
which a fire spreads in a two-dimensional (2D) grid developed by Malamud et
al. (1998). There is an accurately defined number of boxes in the grid (Ng), the
number of time steps (NS) and the number of fires (NF) for a given fire ignition
frequency. Computer simulation modeling provides a burned area AF (AF is
the number of trees destroyed in each fire). A non-cumulative number of fires
in a defined time period is NF/NS and is given as a function of AF on a 2D grid
of 128 x 128 for three frequencies: fS = 1/125, fS = 1/5000, fS = 1/2000. The
slope of direction represents the exponent a (the power law applies) which depends
on the frequency. The number of fires for every time interval is the function
of the number of trees burned in each of the fires. For every fire
propagation frequency there was the NS = 1.638x 109 of time intervals. There
is also a range from small to large fires, with the number of small fires far exceeding
that of large ones. Small and medium fires satisfy the power law, with
. = -1.02 to 1.09, while large fires exhibit bigger deviations (. = -1.16), as
manifested at frequency 1/2000 due to the finite grid dimensions. This is the limited
size effect, since the fire stops after it has spread across the entire grid.


In our application of the model to the data for Brač, Korčula and Rab, due
to the relatively small number of data we used cumulative distribution in order
to obtain qualitatively good results. By increasing the initial area interval that
contains a given number of fires (A1,………A10), the fire affected area increases
and so does the number of fires. This provided a distribution of the cumulative
area number NCF for an interval. The results of our research show that
the cumulative distribution of burned areas in the selected islands follows the
power law in accordance with the model by Malamud et al. (1998). A logarithmic
presentation of the results is a direction in its major part. The slope corresponds
to the exponent ., because – dNCF/dAF.AF-.. According to the above
model, if we know the parameters of the system we can determine fire propagation
frequency, which indicates the probability of fire occurrence in an area.
A data set for the three Croatian islands shows that, in relation to the obtained
slope of direction for the total number of fires . = 1.02 ± 0.02, the fire propagation
frequency is high, meaning that the probability of fire propagation is
lower. However, a more detailed analysis of the two data sets for larger fires
results in a greater slope, indicating a high risk of fire in the next several
years, particularly in the areas that have already been severely burned (e.g. as
many as 55 km2 on the island of Korčula). The obtained results allow us to
conclude that in the applied model, the direction slope values coincide for
small and medium fires, i.e. for higher spread frequencies, while the model
used for larger fires exhibits deviations due to the finite space dimensions. The
results provide a stimulus for further research, because it has been shown that
if the impact of different parameters related to fire spread in an area is known,
it is possible to identify areas with an increased fire risk, particularly in case
of small and medium fire distribution.


Key words: Adriatic islands, burned area, computer simulations, complex
systems, fire.