Abstract. We present a novel approach to explain the complex scaling behavior of the Drossel-Schwabl forest-fire model in two dimensions. Clusters of trees are characterized by their size and perimeter only, whereas spatial correlations are neglected. Coalescence of clusters is restricted to clusters of similar sizes. Our approach derives the value of the scaling exponent τ of the event size distribution directly from the scaling of the accessible perimeter of percolation clusters. We obtain τ = 1.19 in the limit of infinite growth rate, in perfect agreement with numerical results. Furthermore, our approach predicts the unusual transition from a power law to an exponential decay even quantitatively, while the exponential decay at large event sizes itself is reproduced only qualitatively.

Abstract. The impact of forest fires on nature and civilisation is conflicting: on one hand, they play an irreplaceable role in the natural regeneration process, but on the other hand, they come within the major natural hazards in many regions. Their frequency-area distributions show power-law behaviour with scaling exponents α in a quite narrow range, relating wildfire research to the theoretical framework of self-organised criticality. Examples of self-organised critical behaviour can be found in computer simulations of simple cellular automaton models. The established self-organised critical Drossel-Schwabl forest fire model is one of the most widespread models in this context. Despite its qualitative agreement with event-size statistics from nature, its applicability is still questioned. Apart from general concerns that the Drossel-Schwabl model apparently oversimplifies the complex nature of forest dynamics, it significantly overestimates the frequency of large fires. We present a modification of the model rules that distinguishes between lightning-induced and man made forest fires and enables a systematic increase of the scaling exponent α by approximately 1/3. In addition, combined simulations using both the original and the modified model rules predict a dependence of the overall event-size distribution on the ratio of lightning induced and man made fires as well as a splitting of their partial distributions. Lightning is identified as the dominant mechanism in the regime of the largest fires. The results are confirmed by the analysis of the Canadian Large Fire Database and suggest that lightning-induced and man made forest fires cannot be treated separately in wildfire modelling, hazard assessment and forest management.

Abstract. The Olami-Feder-Christensen model is probably the most studied model in the context of self-organized criticality and reproduces several statistical properties of real earthquakes. We investigate and explain synchronization and desynchronization of earthquakes in this model in the nonconservative regime and its relevance for the power-law distribution of the event sizes (Gutenberg-Richter law) and for temporal clustering of earthquakes. The power-law distribution emerges from synchronization, and its scaling exponent can be derived as τ = 1.775 from the scaling properties of the rupture areas' perimeter. In contrast, the occurrence of foreshocks and aftershocks according to Omori's law is closely related to desynchronization. This mechanism of foreshock and aftershock generation differs strongly from the widespread idea of spontaneous triggering and gives an idea why some even large earthquakes are not preceded by any foreshocks in nature.