Probabilistic forecasting of landslide displacement accounting for epistemic uncertainty: a case study in the Three Gorges Reservoir area, China

Accurate and reliable displacement forecasting plays a key role in landslide early warning. However, due to the epistemic uncertainties associated with landslide systems, errors are unavoidable and sometimes significant in traditional methods of deterministic point forecasting. Transforming traditional point forecasting into probabilistic forecasting is essential for quantifying the associated uncertainties and improving the reliability of landslide displacement forecasting. This paper proposes a hybrid approach based on bootstrap, extreme learning machine (ELM), and artificial neural network (ANN) methods to quantify the associated uncertainties via probabilistic forecasting. The hybrid approach consists of two steps. First, a bootstrap-based ELM is applied to estimate the true regression mean of landslide displacement and the corresponding variance of model uncertainties. Second, an ANN is used to estimate the variance of noise. Reliable prediction intervals (PIs) can be computed by combining the true regression mean, variance of model uncertainty, and variance of noise. The performance of the proposed hybrid approach was validated using monitoring data from the Shuping landslide, Three Gorges Reservoir area, China. The obtained results suggest that the Bootstrap-ELM-ANN approach can be used to perform probabilistic forecasting in the medium term and long term and to quantify the uncertainties associated with landslide displacement forecasting for colluvial landslides with step-like deformation in the Three Gorges Reservoir area.