Application of a copula approach to quantify rainfall-induced rockfall

Rockfall hazards threaten coastal infrastructure, particularly under high rainfall conditions that accelerate slope degradation. This paper presents a copula-based statistical analysis of the relationship between rainfall and rockfall volume at Susan Gilmore Beach, Newcastle, NSW, Australia. Over a two-year monitoring period, drone-based photogrammetry surveys captured volumetric changes across 28 time intervals. To emphasise larger, more hazardous events, the 75th percentile of daily rainfall was paired with the 75th percentile of observed rockfall volumes. Correlation measures (Pearson’s 𝑟 and Kendall’s 𝜏) indicated moderate to strong dependencies, prompting assessment of three Archimedean copulas (Gumbel, Clayton, and Frank). Goodness-of-fit tests identified the Gumbel copula as the best model for capturing upper-tail dependence, linking high rainfall to substantial rockfall volumes. Joint and conditional probabilities derived from the copula framework revealed that extreme precipitation markedly elevates the likelihood of significant rockfalls, surpassing insights from conventional linear correlation. The findings underscore the value of nonlinear, tail-focused statistical approaches in hazard characterisation. The conditional probability provides explicit likelihoods of specific rockfall volumes for given rainfall amounts, offering the potential to define risk thresholds and inform targeted mitigation strategies. By integrating high-resolution 3D monitoring with an advanced copula-based model, this study provides a robust methodological template for analysing rainfall-triggered instability in coastal cliff environments.