Refining inventory-based frequency-ratio landslide susceptibility using multivariate conditional likelihood ratios and event-based rainfall amplification

Landslide Inventory Maps (LIMs) are the essential starting point for any hazard assessment, yet their statistical quality is often assumed rather than verified. A persistent issue in susceptibility modeling, particularly with the widely used Frequency Ratio (FR) method, is the assumption of conditional independence among factors. This simplification not only overlooks complex inter-dependencies between geology and terrain but also tends to hide the inherent limitations and biases of the underlying inventory.

 

In this study, we propose a shift toward a Multivariate Conditional Likelihood Ratio (MCLR) framework to explicitly evaluate and manage inventory representativeness. By estimating likelihoods over joint combinations of geomorphic, hydrologic, and land-cover factors, MCLR preserves the multivariate signals that drive landslide occurrence. Crucially, we treat the resulting "empirical sparsity" (data-poor environmental units) not as a mathematical hurdle, but as a diagnostic strength. By imposing minimum support criteria, we can pinpoint specific environmental domains where the inventory lacks representative power, effectively "exposing" the quality constraints of the input data.

 

To test how these patterns perform under real-world forcing, we introduce an event-based Rainfall Amplification Factor (RAF) as a diagnostic stress test. Using a terrain-trend-plus-residual interpolation, we capture the spatial heterogeneity and orographic enhancement of precipitation to dynamically modulate the MCLR-based susceptibility. This allows us to track how inventory limitations propagate from static maps into event-scale hazard interpretations.

 

Our findings demonstrate that MCLR produces more physically interpretable patterns than marginal FR, especially in complex landscapes where terrain and geology are tightly coupled. The RAF analysis further reveals where susceptibility models remain robust and where representativeness gaps become critical during extreme events. Ultimately, this framework provides a transparent bridge between static susceptibility mapping and event-oriented hazard assessment, offering a quantitative basis for evaluating the reliability of landslide inventory products under extreme forcing conditions.