A physics-based hierarchical framework for landslide early warning

Early warning of catastrophic landslides remains challenging due to the multiscale and intermittent nature of precursory deformation. Existing warning systems often rely on empirical thresholds or short-term acceleration criteria, limiting their transferability and physical interpretability across sites and landslide types. Here, we propose a general, physics-based hierarchical framework for landslide forecasting that integrates complementary statistical diagnostics operating across distinct temporal horizons. The framework is grounded in principles of statistical physics and explicitly links observable statistical signatures to underlying transitions between system deformation regimes. For long-term forecasting (months to years), we track the temporal decline of the velocity b value—defined as the power law tail exponent of the probability density function of slope velocities—which reflects an increasing frequency of medium-to-large velocities and a progressive shift towards critical behaviour. For medium-term forecasting (weeks to months), we apply the log-periodic power law singularity (LPPLS) model combined with a Lagrange regularisation approach to objectively identify the onset of a critical phase, marking the transition from stable or quasi-stable behaviour to accelerating deformation. For short-term forecasting (days to weeks), we detect dragon-kings, defined as statistically exceptional outliers that deviate from the background power law scaling of slope velocities and emerge only during the final stage preceding failure. The framework is designed to operate on time-series monitoring data commonly available at landslide sites, without reliance on site-specific empirical thresholds. We test the approach on well-instrumented historical landslide events, demonstrating that the combination of long-, medium-, and short-term indicators provides a coherent and hierarchical early warning strategy. By explicitly linking statistical signatures to distinct stages of instability development, the proposed framework offers a pathway towards more robust, transferable, and physically interpretable landslide early warning systems.