Fractal Methods in the Investigation of the Time Dynamics of Fires: An Overview

Fires represent one of the most critical issues in the context of natural hazards. Yearly, they affect large areas worldwide causing loss of biodiversity, decrease in forests, alteration of landscape, soil degradation, increase in greenhouse, etc. Most of these fires have anthropic causes, however there are natural factors, above all summer drought, that strongly influence fire ignition and spread. The investigation of the time dynamics of fires can be carried out considering the fire process per se or focusing on some signal whose variability can be informative of a fire occurrence. In the first case, fires are described by a stochastic point process, whose events are identified by spatial location, occurrence time and size of burned area, or amount of loss. In the second case, time-continuous signals are employed to reveal indirectly the occurrence of fires; one of the mostly used signals is the satellite normalized difference vegetation index (NDVI) that gives information about the "health" of vegetation and, thus, is suited to enhance the status of vegetation after a fire stress. In both cases, the concept of fractal can be used to qualitatively and quantitatively characterize the time dynamics of fires. Fractals are featured by power-law statistics, and, if applied to time series, can be a powerful tool to investigate their temporal fluctuations, in terms of correlation structures and memory phenomena. In the present review we describe fractal methods applied to fire point processes and satellite time-continuous signals that are sensitive to fire occurrences.