Temporal variations in rockfall and rock-wall retreat rates in a deglaciated valley over the past 11 k.y.

To calculate the power law predicted retreat rate, power law fit parameters must be defined. Previous studies have shown that above a certain magnitude, the frequency of rockfalls and landslides appears to decay as a power-law (Strunden et al., 2015; Barlow et al., 2012; Dussauge et al., 2003; Guzzetti et al., 2003; Hunger et al., 1999). Below this magnitude, which is commonly referred to as “rollover”, there is no clear trend. The rollover might be due to undersampling of small rockfalls by data collection methods (Lim et al., 2010; Stark and Hovius, 2001) or may have a physical explanation reflecting different slope failure processes (Stark and Guzzetti, 2009; Guthrie and Evans, 2004). To fit a power law distribution of the form: