GRAIL gravity field determination using the Celestial Mechanics Approach

The NASA mission GRAIL (Gravity Recovery and Interior Laboratory) inherited its concept from the GRACE (Gravity Recovery and Climate Experiment) mission to determine the gravity field of the Moon. We present lunar gravity fields based on the data of GRAIL’s primary mission phase. Gravity field recovery is realized in the framework of the Celestial Mechanics Approach, using a development version of the Bernese GNSS Software along with Ka-band range-rate data series as observations and the GNI1B positions provided by NASA JPL as pseudo-observations. By comparing our results with the official level-2 GRAIL gravity field models we show that the lunar gravity field can be recovered with a high quality by adapting the Celestial Mechanics Approach, even when using pre-GRAIL gravity field models as a priori fields and when replacing sophisticated models of non-gravitational accelerations by appropriately spaced pseudo-stochastic pulses (i.e., instantaneous velocity changes). We present and evaluate two lunar gravity field solutions up to degree and order 200 – AIUB-GRL200A and AIUB-GRL200B. While the first solution uses no gravity field information beyond degree 200, the second is obtained by using the official GRAIL field GRGM900C up to degree and order 660 as a priori information. This reduces the omission errors and demonstrates the potential quality of our solution if we resolved the gravity field to higher degree.

Pseudospectra in non-Hermitian quantum mechanics

We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT -symmetric quantum mechanics.

Patterns of landscape form in the upper Rhône basin, Central Swiss Alps, predominantly show lithologic controls despite multiple glaciations and variations in rock uplift rates

The development of topography depends mainly on the interplay between uplift and erosion. These processes are controlled by various factors including climate, glaciers, lithology, seismic activity and short-term variables, such as anthropogenic impact. Many studies in orogens all over the world have shown how these controlling variables may affect the landscape's topography. In particular, it has been hypothesized that lithology exerts a dominant control on erosion rates and landscape morphology. However, clear demonstrations of this influence are rare and difficult to disentangle from the overprint of other signals such as climate or tectonics. In this study we focus on the upper Rhône Basin situated in the Central Swiss Alps in order to explore the relation between topography, possible controlling variables and lithology in particular. The Rhône Basin has been affected by spatially variable uplift, high orographically driven rainfalls and multiple glaciations. Furthermore, lithology and erodibility vary substantially within the basin. Thanks to high-resolution geological, climatic and topographic data, the Rhône Basin is a suitable laboratory to explore these complexities. Elevation, relief, slope and hypsometric data as well as river profile information from digital elevation models are used to characterize the landscape's topography of around 50 tributary basins. Additionally, uplift over different timescales, glacial inheritance, precipitation patterns and erodibility of the underlying bedrock are quantified for each basin. Results show that the chosen topographic and controlling variables vary remarkably between different tributary basins. We investigate the link between observed topographic differences and the possible controlling variables through statistical analyses. Variations of elevation, slope and relief seem to be linked to differences in long-term uplift rate, whereas elevation distributions (hypsometry) and river profile shapes may be related to glacial imprint. This confirms that the landscape of the Rhône Basin has been highly preconditioned by (past) uplift and glaciation. Linear discriminant analyses (LDAs), however, suggest a stronger link between observed topographic variations and differences in erodibility. We therefore conclude that despite evident glacial and tectonic conditioning, a lithologic control is still preserved and measurable in the landscape of the Rhône tributary basins.