How sample size can effect landslide size distribution

Abstract

Background: Landslide size distribution is widely found to obey a negative power law with a rollover in the smaller size, and has been exploited by many researchers to inspect landside physics or to assess landslide erosion and landslide hazard. Yet, sample size has effect on the statistics of landslide size even though we manage to avoid complications associated with landslide datasets and statistical treatments. Results: In this paper, a series of stochastic simulations were implemented to explicitly and systematically quantify the effect of sample size. The results show that, the errors of parameters estimated based on small sample size can be considerably large. For a sample size of 100, the relative error of the estimated landslide erosion rate that has a probability of 50 % can approach 100 %. In addition, small sample size also obscures the statistical significance of the variances in parameters between different subsets of the same dataset. Although inconsistency was found regarding how the power exponent varies with rainfall intensity, numerical results suggest that the variance observed in a dataset with a small sample size may be not statistically significant. Conclusions: This paper not only reveals the potential effect of sample size on exploiting landslide size distribution but also presents procedures for quantifying this issue in future studies.