# Optimising rainfall characteristics for determining landslide thresholds

## TL;DR

This paper introduces a new framework for optimizing rainfall thresholds to predict landslides in areas with limited data.

## Contribution

The study introduces a Bayesian inference framework for deriving more stable landslide rainfall thresholds in data-limited regions.

## Key findings

- Bayesian-derived thresholds are more stable and produce fewer unrealistic curves compared to nonlinear least-squares methods.
- A minimum inter-event time of 48 hours provides the most robust landslide prediction results.
- Rainfall–Duration thresholds outperformed Intensity–Duration thresholds in predicting landslides.

## Abstract

This work contributes a new framework for establishing data-driven rainfall thresholds in high-risk, data-limited contexts. Rainfall thresholds are commonly used to characterise the precipitation needed to trigger landslides in a region. However, these empirical relationships are sensitive to the exact definition of a “rainfall event”, especially how the minimum inter-event time (MIT) and triggering event (TE) are defined. Using Bayesian inference (BI) and nonlinear least-squares (NLS) techniques, this study evaluates how variations in MIT and TE definitions affect rainfall threshold estimation, considering both Event Rainfall–Duration \documentclass[12pt]{minimal}
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\begin{document}$$\left( {E{-}D} \right)$$\end{document} and Intensity–Duration \documentclass[12pt]{minimal}
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\begin{document}$$\left( {I{-}D} \right)$$\end{document} spaces. The dataset includes 15-min rainfall measurements from 52 gauges recorded from 2005 to 2023, as well as a regional landslide dataset compiled from British Geological Survey records covering the South Wales coalfields. Findings reveal that BI-derived thresholds are more stable than NLS-based thresholds, showing smaller parameter changes and fewer unrealistic curves, particularly in I–D space, where NLS often produces near-flat thresholds. Overall, both BI and NLS approaches demonstrate their strongest performance at MIT = 48 h, emphasising the role of extended antecedent rainfall in triggering spoil tip failures. This study demonstrates how the integration of robust Bayesian methods facilitates the downscaling of global thresholds to data-scarce regions and how careful event delineation practices can improve landslide prediction.

Landslide rainfall thresholds were derived using Bayesian and nonlinear least-squares methods.

Rainfall–Duration (E–D) thresholds performed better than Intensity–Duration (I–D) thresholds.

Minimum inter-event time (MIT) of 48 h yielded the most robust prediction results.

The Bayesian approach generally outperformed the nonlinear least-squares method.