At the junction between deep learning and statistics of extremes: formalizing the landslide hazard definition

TL;DR

The paper tackles landslide hazard by unifying the three core components—location (susceptibility), size (intensity), and trigger frequency—into a single probabilistic framework where the local hazard is $h_q(s,t)=p(s,t)×i_q(s,t)$. Susceptibility is predicted with a deep neural network, while intensity is modeled with an extended Generalised Pareto Distribution for area density, with a scale parameter σ(s,t) learned by the network; the tail probability i_q(s,t) is derived from the eGPD, enabling estimation across multiple exceedance levels. The frequency component uses return levels RL_P(s) for precipitation obtained from two eGPD models fitted to annual max and mean precipitation, allowing scenario-based hazard projections under SSP245 and SSP585 for return periods $P∈{5,10,15,20}$. The model is trained on 30 years of Nepal rainfall-triggered landslide data, producing hazard maps and enabling risk-informed planning, including uncertainty in tail events and future climate change impacts. Data and code are openly shared to support reproducibility and extension to other regions and triggers.

Abstract

The most adopted definition of landslide hazard combines spatial information about landslide location (susceptibility), threat (intensity), and frequency (return period). Only the first two elements are usually considered and estimated when working over vast areas. Even then, separate models constitute the standard, with frequency being rarely investigated. Frequency and intensity are intertwined and depend on each other because larger events occur less frequently and vice versa. However, due to the lack of multi-temporal inventories and joint statistical models, modelling such properties via a unified hazard model has always been challenging and has yet to be attempted. Here, we develop a unified model to estimate landslide hazard at the slope unit level to address such gaps. We employed deep learning, combined with a model motivated by extreme-value theory to analyse an inventory of 30 years of observed rainfall-triggered landslides in Nepal and assess landslide hazard for multiple return periods. We also use our model to further explore landslide hazard for the same return periods under different climate change scenarios up to the end of the century. Our results show that the proposed model performs excellently and can be used to model landslide hazard in a unified manner. Geomorphologically, we find that under both climate change scenarios (SSP245 and SSP885), landslide hazard is likely to increase up to two times on average in the lower Himalayan regions while remaining the same in the middle Himalayan region whilst decreasing slightly in the upper Himalayan region areas.

Figures (10)

• Figure 1: Map showing the study area, mapping units, and observed landslide inventory (top) for 1988--2018. The bivariate histogram plot (bottom right) shows the intensity of landslides in individual slope units over the mapping period, together with the landslide frequency.
• Figure 2: Samples of SUs in 2D map with shaded relief (left) and 3D shaded relief (right) with camera angle of $30 ^\circ$ from south to north. Highlighted SUs in both maps show the same location.
• Figure 3: Empirical distribution of the landslide area density (histogram) and the best-fitting extended Generalised Pareto Distribution (eGPD) probability density function (dotted red).
• Figure 4: Distribution of Mean Precipitation (mm/day; top left), Maximum Precipitation (mm/day; top right) and Mean NDVI (unitless; bottom left) over 30 years pooling the data from all SUs together, obtained using Kernel Density Estimation.
• Figure 5: Overall performance of the developed model. (a) The model performance on the classification of landslides (i.e., landslide susceptibility), and (b) the Q-Q plot of displaying model-based vs empirical quantiles.