## 1. Introduction

[2] Landslides cover an enormous range of sizes from small rockfalls of less than one cubic meter to several cubic kilometers, such as the Flims rockslide in the Alps with a volume of about 8 cubic kilometers [e.g., *von Poschinger*, 2011]. They can be classified by the mechanism of movement (e.g., falling or sliding) and by the involved material (rock or an unconsolidated regolith layer above the bedrock). Following the majority of the references cited in this paper, the term rockfalls is used for all types of rapid rock mass movements, in particular rockfalls and rockslides, in the following.

[3] While a variety of approaches to predict the runout of rockfalls is available (for a review see, e.g., *Volkwein et al.* [2011]), very little is known about the probability that a rockfall of a given size occurs in a certain region. Available statistical data [*Wieczorek et al.*, 1992; *Noever*, 1993; *Dussauge et al.*, 2003; *Guzzetti et al.*, 2003; *Malamud et al.*, 2004; *Brunetti et al.*, 2009; *Bennett et al.*, 2011] indicate that rockfall sizes are power-law distributed,

where *V* is the involved volume and *p*(*V*) is the probability density of the size distribution. In the studies mentioned above, values of the scaling exponent *α* in the range between 1.07 and 1.75 were found for the non-cumulative probability density function.

[4] Similar power-law distributions occur in several natural hazards such as earthquakes, wildfires and regolith landslides, so that all these processes have been viewed in the context of self-organized criticality (SOC). The relationship to SOC is well established, although still in discussion for earthquakes [*Olami et al.*, 1992] and for wildfires [*Drossel and Schwabl*, 1992; *Malamud et al.*, 1998], and there have been some modeling approaches to link regolith landslides to SOC [*Densmore et al.*, 1998; *Hergarten and Neugebauer*, 1998, 2000; *Piegari et al.*, 2006] as well as laboratory experiments [e.g., *Katz and Aharonov*, 2006; *Juanico et al.*, 2008]. However, the scaling exponents found for regolith landslides are significantly larger than those of rockfalls [*Hovius et al.*, 1997; *Hergarten*, 2003; *Malamud et al.*, 2004], namely *α* ≈ 2.4 with respect to area and *α* ≈ 2 with respect to volume.

[5] As a consequence of the strongly different scaling exponents found for rockfalls and regolith landslides, the modeling approaches mentioned above cannot be directly transferred to explain or predict the statistics of rockfalls. There was some discussion whether the simplest model of SOC, the so-called “sandpile model” [*Bak et al.*, 1987], could be applied to rockfalls. But apart from the exponent being too low, the physical relationship between this model and gravity-driven mass movements seems to be rather weak [*Hergarten*, 2002, 2003; *Dussauge et al.*, 2003; *Malamud et al.*, 2004]. In their laboratory experiments originally focusing on regolith landslides, *Katz and Aharonov* [2006] found block sliding with a rather low scaling exponent *α* = 1.13 under certain conditions. Although their results suffer from a small range of scales and limited statistics, this seems to be the greatest progress towards understanding the power-law distribution of rockfalls so far. Beyond this, there seems to be no consistent model to reproduce the power-law distribution of rockfalls (and rockslides) quantitatively so far.