Impact of mapping strategies on rockfall frequency-size distributions

Rockfall frequency size distributions are used in Austria for the definition of a design block for the planning of technical rockfall protection. Rockfall size datasets are often incomplete. Here, we study fifteen catalogues of rockfall size in Austria, Italy, and the USA to analyse the impact of the data collection and mapping methods on the representativeness of the catalogues and on the estimates of frequency-size statistics. To describe and compare the catalogues of rockfall size, we first use Empirical Cumulative Distribution Functions (ECDFs), followed by parametric distribution estimates in the form of Probability Density Functions (PDFs), and Cumulative Distribution Functions (CDFs). We discuss the output of Kolmogorov-Smirnov tests, the position of the frequency-size distribution rollover, and the p-value and the standard errors associated to the distribution parameters estimates to determine the reliability of our model results. In addition, we analyse the variations in the modelled CDFs for different percentiles of the frequency-size distributions to describe and discuss the representativeness of the rockfall catalogues. Our results show that different mapping strategies may affect the estimates of frequency-size distribution of rock fall volume, a relevant information when evaluating the possible impacts of rockfall processes. We conclude offering recommendations for rockfall mapping, and the use and of a non-parametric statistical method being capable to deal with small datasets, which is very typical when dealing with rockfall data. Such recommendations help for a correct dimensioning of designing rockfall mitigation measures.