Articles | Volume 18, issue 3
Nonlin. Processes Geophys., 18, 381–388, 2011
https://doi.org/10.5194/npg-18-381-2011
Nonlin. Processes Geophys., 18, 381–388, 2011
https://doi.org/10.5194/npg-18-381-2011

Research article 21 Jun 2011

Research article | 21 Jun 2011

A semi-phenomenological approach to explain the event-size distribution of the Drossel-Schwabl forest-fire model

S. Hergarten and R. Krenn S. Hergarten and R. Krenn
  • Institut für Erdwissenschaften, Karl-Franzens-Universität Graz, Heinrichstraße 26, 8010 Graz, Austria

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.