On the long-term stability of terrestrial reference frame solutions based on Kalman filtering

The Global Geodetic Observing System requirement for the long-term stability of the International Terrestrial Reference Frame is 0.1 mm/year, motivated by rigorous sea level studies. Furthermore, high-quality station velocities are of great importance for the prediction of future station coordinates, which are fundamental for several geodetic applications. In this study, we investigate the performance of predictions from very long baseline interferometry (VLBI) terrestrial reference frames (TRFs) based on Kalman filtering. The predictions are computed by extrapolating the deterministic part of the coordinate model. As observational data, we used over 4000 VLBI sessions between 1980 and the middle of 2016. In order to study the predictions, we computed VLBI TRF solutions only from the data until the end of 2013. The period of 2014 until 2016.5 was used to validate the predictions of the TRF solutions against the measured VLBI station coordinates. To assess the quality, we computed average WRMS values from the coordinate differences as well as from estimated Helmert transformation parameters, in particular, the scale. We found that the results significantly depend on the level of process noise used in the filter. While larger values of process noise allow the TRF station coordinates to more closely follow the input data (decrease in WRMS of about 45%), the TRF predictions exhibit larger deviations from the VLBI station coordinates after 2014 (WRMS increase of about 15%). On the other hand, lower levels of process noise improve the predictions, making them more similar to those of solutions without process noise. Furthermore, our investigations show that additionally estimating annual signals in the coordinates does not significantly impact the results. Finally, we computed TRF solutions mimicking a potential real-time TRF and found significant improvements over the other investigated solutions, all of which rely on extrapolating the coordinate model for their predictions, with WRMS reductions of almost 50%.     

A numerical exercise for the definition under undrained conditions of the deep tunnel front characteristic curve

In spite of the increasing diffusion of tunnel boring machines, conventional tunnelling is still largely employed in the excavation of both deep and shallow tunnels characterized by a particularly irregular tracing. Under difficult ground conditions, in conventional tunnelling, the front is frequently reinforced by using fibreglass tubes partially removed during the excavation. This technique is expensive, time-consuming and its design is based on either empirical or very simplified theoretical formulas. Thus, the ultimate objective of the research developed by the authors is to introduce a more sophisticated design approach for this front reinforcement technique. A first step in this direction is this numerical study, in which the mechanical response of deep tunnel faces under undrained conditions is analysed by employing the front characteristic curve: a useful tool largely employed in the literature in analogy with what done for the cavity. The main result of this paper is the “Front Mother Characteristic” curve, obtained by introducing appropriate non-dimensional variables, allowing the designer, once both the system geometry and the soil mechanical properties are assigned, to assess the displacements of tunnel fronts without performing any numerical analysis.     

High-resolution monitoring of water temperature and oxygen concentration in Lake Murten (Switzerland)

Lake Murten is located in the Lake District in western Switzerland and so far, it has been poorly investigated. The Environmental Service of Fribourg (SEn) has monitored this lake once a month for several years by water profiles (water temperature, pH, dissolved oxygen, conductivity) at its deepest part. The SEn identified the stratification of water masses as one of the main causes for oxygen consumption in the hypolimnion. In the present study, a Lander System was deployed in Lake Murten from April to September 2015 at 20 m depth at the northwestern part of the lake to monitor water temperature and dissolved oxygen at higher resolution (30 s interval). These records were compared with time series of atmospheric parameters like atmospheric temperature, wind speed and precipitation. A clear correlation of lake temperatures with wind speed was observed during the Spring and Autumn. The water mass stratification evolved through the season and reached its peak during Summer, preventing surface turbulences to reach the deeper part (20 m) of the water column and to partially oxygenate the metalimnion.     

The RUSLE erosion index as a proxy indicator for debris flow susceptibility

Debris flows represent dangerous occurrences in many parts of the world. Several disasters are documented due to this type of fast-moving landslides; therefore, natural-hazard assessment of debris flows is crucial for safety of life and property. To this aim, much current work is being directed toward developing geotechnical-hydraulic models for the evaluation of debris flow susceptibility. A common base for such current models is parameterization of background predisposing and triggering factors such as inherent characteristics of geo-materials, topography, landscape and vegetation cover, rainfall regime, human activities, etc. which influence the occurrence of these processes on slopes. The same factors are also taken into account in soil erosion prediction models. Consequently, it seems worth investigating the effectiveness of the soil erosion index as debris flows susceptibility indicator. To this aim, a logistic regression analysis was carried out between the erosion index assessed by means of the Revised Universal Soil Loss Equation (RUSLE) model and the inventory of debris flows that have occurred in an area in Sicily (Southern Italy). Model assumptions were verified and validated by means of a series of statistical tools. Different possible scenarios were also evaluated by considering hypothetical changes in soil erosion rate under different rain erosivity conditions. Notwithstanding the rough approximations in model data collection, the outcomes appear encouraging.     

Late Quaternary colluvial deposits in the Bocaina Plateau,southeastern Brazil highlands: age and palaeoenvironmental consequences

Despite the generalized occurrence of colluvial deposits in the humid tropical areas of southeastern Brazil, regional correlation is difficult because the deposits are discontinuous, and chronological data are very scarce and scattered. For the first time, colluvial deposits in the Bocaina Plateau are described, including 18 radiocarbon ages from 12 profiles. The plateau is located on the eastern flank of the Continental Rift of Southeastern Brazil and is the highest part of the Serra do Mar, with elevations up to 2000 m above sea level. Because the Bocaina Plateau is part of the summit surfaces of southeastern Brazil, it was subjected to specific climatic conditions during the Quaternary. Colluvial deposits on the lower hillslopes and edges of amphitheatres can show complex sequences with up to three intercalated dark humic horizons, corresponding to Late Pleistocene and Holocene phases of morphodynamic activity and pedogenesis. Ages of palaeosols vary from 650±50 a BP to 36 880±980 a BP. Landforms and colluvia on the Bocaina Plateau are very similar to those found on the opposite flank of the continental rift, on the Campos do Jordão Plateau. Ages of buried soils point to similar soil formation and colluviation episodes in the two plateaus. As in Campos do Jordão, the succession of erosive, depositional and pedogenetic processes on the altos campos hillslopes is probably related to late Quaternary climate changes.     

Periodic Solutions for any Planar Symmetric Perturbation of the Kepler Problem

We consider perturbations of the Kepler problem that are symmetric with respect to the origin and admit a first integral of motion which is also symmetric with respect to the origin. It has been proved that each circular solution of the unperturbed problem gives rise to a periodic solution of the perturbed system.