Bayesian Multilevel Models for Learning Seasonal Landslide Activity from Inventories with Observation Bias

Abstract:

Most landslide prediction research seeks to estimate where slopes are likely to fail; far fewer studies have looked into when landslides occur and how to predict their timing. In this study, we use a Bayesian multilevel model to explore seasonal changes in the rates of rainfall-triggered landslides in the Pacific Northwest region of the United States. We work with a compilation of more than 6000 landslides with daily time stamps, drawn from four published inventories.

We model landslides as a Poisson process, which describes a sequence of independent slope failures. The model has a single rate parameter: the average number of landslides per day. We hypothesize that this average rate of landsliding varies seasonally, and use a Bayesian multilevel model to learn this parameter from the data. We then use the model to estimate the probability of observing a number of landslides in a given time period or the probability of waiting a certain amount of time before the next landslide occurs.

In the model, the data is grouped by season, and a posterior distribution of rate parameters is learned for each group. We find credible differences (94% highest density interval) in seasonal landslide rates in the Pacific Northwest, with an order of magnitude difference between average rates in winter (highest) and fall (lowest). This means that on average, we would expect to wait ~10 times longer before observing the next landslide in fall than in winter.

Grouping the data by inventory, however, highlights how incomplete data affects this prediction. Rates between inventories span three orders of magnitude, a discrepancy that arises in large part from observation bias. In one inventory, the model expects hundreds of landslides everyday because the data used to train it are primarily from regional episodes where hundreds of landslides occurred on the same day. Bayesian multilevel models can be used to handle datasets with partly unobserved or inhomogenous data, and future research will focus on expanding the model to estimate the role of unobserved landslides and to quantify how this uncertainty changes predictions.

We argue that this approach can improve our ability to predict landslide timing by aiding seasonal landslide forecasts, and by helping us to shift from static susceptibility maps to dynamic landslide appraisals.