Šume prekrivaju približno četvrtinu zemljine površine, i kao jedan od najvećih izvora kisika u prirodi važne su za opstanak života na Zemlji. Šumski požari kao vrlo važan fenomen za sam opstanak šuma, uz šumarstvo i ekologiju počeli su se proučavati i u fizici. U fizici je šumski požar prepoznat kao primjer kompleksnog sustava na velikim, kilometarskim skalama. Računalne simulacije omogućile su nova saznanja o šumskim požarima. U radu su korišteni podaci o broju požara i opožarenoj površini, prikupljeni u šumarijama Brač, Korčula i Rab, u razdoblju od 1991. godine do 2000. godine, koji su obrađeni primjenom fizikalnih modela, pomoću kojih se može saznati kako se požari šire, koji sve parametri i u kojoj mjeri utječu na širenje požara, te naj važnije – kako predvidjeti požare određenih razmjera. Rezultati istraživanja pokazuju da kumulativna raspodjela spaljenih površina na izabranim otocima slijedi zakon potencije u skladu s modelom Malamuda i drugih (1998). Logaritamski prikaz rezultata je pravac u najvećem dijelu. Nagib odgovara eksponentu a, jer je – dNCF/dAF~AFa. Prema navedenom modelu, ako su poznati zadani parametri nekog sustava možemo odrediti frekvenciju širenja požara, koja nam govori kolika je vjerojatnost pojave požara na nekoj površini. Skup podataka za naša tri otoka pokazuje da je s obzirom na dobiven nagib pravca za ukupan broj požara a = 1.02 ± 0.02 frekvencija širenja velika, što govori da je vjerojatnost širenja požara manja. Međutim, detaljnijom analizom dvije grupe podataka za veće požare dobije se veći nagib, što govori da je u idućih nekoliko godina rizik od požara velik, i to točno na područjima na kojima su izgorjele velike površine (na Korčuli čak do 55 km2). Iz dobivenih rezultata moguće je zaključiti da se vrijednosti nagiba pravca podudaraju za male i srednje požare, odnosno za veće frekvencije širenja kod primijenjenog modela, dok za veće požare postoje odstupanja kod primjene modela zbog konačnih dimenzija prostora. Dobiveni rezultati su poticaj za daljnja istraživanja, jer je pokazano da se poznavanjem utjecaja različitih parametara po vezanih sa širenjem požara na nekom prostoru mogu odrediti područja povećanog rizika od požara. Posebice ako je poznata raspodjela malih i srednjih požara.Forests cover approximately one fourth of the land’s surface. As one of the largest oxygen sources in the nature, they are very important for the survival of life on Earth. Forest fires have become an increasingly interesting issue not only for forestry and ecology, which study them as an important 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 de pends 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 li mited 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 increa ses and so does the number of fires. This provided a distribution of the cumu lative 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 corre sponds to the exponent ., because – dNCF/dAF.AF-.. According to the above model, if we know the parameters of the system we can determine fire propa gation 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 propa gation 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
