In the past decades, many different approaches have been developed in the literature to quantify the load-carrying capacity and geotechnical stability (or the Factor of Safety, ) of variably saturated hillslopes. Much of this work has focused on a deterministic characterization of hillslope stability. Yet, simulated values are subject to considerable uncertainty due to our inability to characterize accurately the soil mantle's properties (hydraulic, geotechnical and geomorphologic) and spatiotemporal variability of the moisture content of the hillslope interior. This is particularly true at larger spatial scales. Thus, uncertainty-incorporating analyses of physically based models of rain-induced landslides are rare in the literature. Such landslide modeling is typically conducted at the hillslope scale using gauge-based rainfall forcing data with rather poor spatiotemporal coverage. For regional landslide modeling, the specific advantages and/or disadvantages of gauge-only, radar-merged and satellite-based rainfall products are not clearly established. Here, we compare and evaluate the performance of the Transient Rainfall Infiltration and Grid-based Regional Slope-stability analysis (TRIGRS) model for three different rainfall products using 112 observed landslides in the period between 2004 and 2011 from the North Carolina Geological Survey database. Our study includes the Tropical Rainfall Measuring Mission (TRMM) Multi-satellite Precipitation Analysis Version 7 (TMPA V7), the North American Land Data Assimilation System Phase 2 (NLDAS-2) analysis, and the reference 'truth' Stage IV precipitation. TRIGRS model performance was rather inferior with the use of literature values of the geotechnical parameters and soil hydraulic properties from ROSETTA using soil textural and bulk density data from SSURGO (Soil Survey Geographic database). The performance of TRIGRS improved considerably after Bayesian estimation of the parameters with the DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm using Stage IV precipitation data. Hereto, we use a likelihood function that combines binary slope failure information from landslide event and 'null' periods using multivariate frequency distribution-based metrics such as the False Discovery and False Omission Rates. Our results demonstrate that the Stage IV-inferred TRIGRS parameter distributions generalize well to TMPA and NLDAS-2 precipitation data, particularly at sites with considerably larger TMPA and NLDAS-2 rainfall amounts during landslide events than null periods. TRIGRS model performance is then rather similar for all three rainfall products. At higher elevations, however, the TMPA and NLDAS-2 precipitation volumes are insufficient and their performance with the Stage IV-derived parameter distributions indicate their inability to accurately characterize hillslope stability.

Ensemble Kalman filters are based on a Gaussian assumption, which can limit their performance in some non-Gaussian settings. This paper reviews two nonlinear, non-Gaussian extensions of the Ensemble Kalman Filter: Gaussian anamorphosis (GA) methods and two-step updates, of which the rank histogram filter (RHF) is a prototypical example. GA-EnKF methods apply univariate transforms to the state and observation variables to make their distribution more Gaussian before applying an EnKF. The two-step methods use a scalar Bayesian update for the first step, followed by linear regression for the second step. The connection of the two-step framework to the full Bayesian problem is made, which opens the door to more advanced two-step methods in the full Bayesian setting. A new method for the first part of the two-step framework is proposed, with a similar form to the RHF but a different motivation, called the 'improved RHF' (iRHF). A suite of experiments with the Lorenz-'96 model demonstrate situations where the GA-EnKF methods are similar to EnKF, and where they outperform EnKF. The experiments also strongly support the accuracy of the RHF and iRHF filters for nonlinear and non-Gaussian observations; these methods uniformly beat the EnKF and GA-EnKF methods in the experiments reported here. The new iRHF method is only more accurate than RHF at small ensemble sizes in the experiments reported here.

This paper proposes a new method to approach earthquake hypocenter studies based on Chaos Game Representation (CGR), a method initially used for making fractal structures and applied for studying DNA sequences. Applying the CGR method, this study aims at checking whether any relation exists between earthquakes occurring in different depth ranges in a seismically active area. For this purpose, the seismically active areas around the Indian tectonic plate were used. The CGR images gave characteristic patterns, implying that the occurrence of earthquakes in some specific depth range combinations showed higher preference. Statistical data on the frequency of different depth range combinations were derived from these plots. We put forward a mathematical value which we call proximity index, to compare the similarity between two different CGR plots. Proximity index values were used to compare the similarity in seismic activity in two different zones by comparing their respective CGR plots.

In reservoir simulation, it is important to understand the mechanical behaviour of fractured rocks and the effect of shear and tensile displacements of fractures on their aperture. Tensile opening directly enhances the fracture aperture, whereas shear of a preexisting rough-walled fracture creates aperture changes dependent on the local stress state. Since fracture dilatation increases reservoir permeability, both processes must be included in a realistic and consistent manner into the mechanical reservoir simulation model. Here, we use the extended finite volume method (XFVM) to conduct flow and geomechanics simulations. In XFVM, fractures are embedded in a poroelastic matrix and are modelled with discontinuous basis functions. On each fracture segment the tractions and compressive forces are calculated, and one extra degree of freedom is added for both the shear and tensile displacement. In this particular XFVM implementation we assume that linear elasticity and steady state fluid pressure adequately constrain the effective stress. In this paper, shear dilation is not calculated a posteriori, but it enters the equations such that aperture changes directly affect the stress state. This is accomplished by adding shear dilation to the displacement gradients and therefore ascertains a consistent representation in the stress-strain relations and force balances. We illustrate and discuss the influence of this extra term in two simple test cases and in a realistic layer-restricted two-dimensional fracture network subjected to plausible in situ stress and pore pressure conditions.