Multiscale Gravitational Field Recovery from GPS-Satellite-to-Satellite Tracking

The purpose of GPS-satellite-to-satellite tracking (GPS-SST) is to determine the gravitational potential at the earth's surface from measured ranges (geometrical distances) between a low-flying satellite and the high-flying satellites of the Global Positioning System (GPS). In this paper, GPS-satellite-to-satellite tracking is reformulated as the problem of determining the gravitational potential of the earth from given gradients at satellite altitude. The uniqueness and stability of the solution are investigated. The essential tool is to split the gradient field into a normal part (i.e. the first-order radial derivative) and a tangential part (i.e. the surface gradient). Uniqueness is proved for polar, circular orbits corresponding to both types of data (first radial derivative and/or surface gradient). In both cases gravity recovery based on satellite-to-satellite tracking turns out to be an exponentially ill-posed problem. Regularization in terms of spherical wavelets is proposed as an appropriate solution method, based on the knowledge of the singular system. Finally, the extension of this method is generalized to a nonspherical earth and a non-spherical orbital surface, based on combined terrestrial and satellite data.     

Catchments of German surface water bodies

The European Water Framework Directive demands to assess and report the chemical and ecological status of water bodies (WB). Linking their status to drivers and pressures and deriving suitable mitigation measures require knowledge of the shape and area of WB catchments. We derived a network of 26 570 WB catchments in Germany using the hydrologically-defined drainage basins of the German federal states. We established a network of 338 149 drainage basins. This network underwent plausibility checks and a validation with the catchment areas of 348 monitoring stations across Germany. To this network, we assigned the longest intersecting or the next downstream WB code. To account for geometric inaccuracies we revised spurious intersections resulting in splittings and cycles in the WB network. As WB may be ecologically but not hydrologically well defined, we split them at confluences and intersections. The network of drainage basins matched the monitoring stations with a Nash-Sutcliffe efficiency of 1.00. The final WB network contained 11 005 out of the 11 586 original WBs longer than 1 m. The corresponding local catchment areas range from <<0.0001 to 446 km², with a median of 10 km². The dataset combines the requirements of hydrological and ecological modelling applications at basin or national scales with the needs of the EU reporting which can foster their acceptance by state authorities and river-basin management.     

Dual models of pore spaces

We present a model for pore spaces that consists of two parts related by duality: (1) a decomposition of an open polyhedral pore space into open contractible pore bodies separated by relatively open interfaces and (2) a pore network that is homotopy equivalent to the pore space. The dual model is unique and free of parameters, but it relies on regularity conditions for the pore space. We show how to approximate any pore space by the interior of a polyhedral complex such that the regularity conditions are fulfilled. Thus, we are able to calculate the dual model from synthetic porous media and images of real porous media. The pore bodies are unions of relatively open Delaunay cells with respect to the corners of the pore boundary, and the pore network consists of certain at most two-dimensional (2D) Voronoi cells with respect to the corners of the pore boundary. The pore network describes the neighborhood relations between the pore bodies. In particular, any relatively open 2D Delaunay face f separating two pore bodies has a unique (relatively open) dual network edge. In our model, f is a pore throat only if it is hit by its dual network edge. Thus, as opposed to widespread intuition, any pore throat is convex, and adjacent pore bodies are not necessarily separated by pore throats. Due to the duality between the pore network and the decomposition of the pore space into pore bodies it is straightforward to store the geometrical properties of the pore bodies [pore throats] as attributes of the dual network vertices [edges]. Such an attributed network is used to perform 2D drainage simulations. The results agree very well with those from a pore-morphology based modeling approach performed directly on the digital image of a porous medium. Contractibility of the pore bodies and homotopy equivalence of the pore space and the pore network is proven using discrete Morse theory and the nerve theorem from combinatorial topology.     

Rapid decrease of soil erosion rates with soil formation and vegetation development in periglacial areas

High mountainous areas are geomorphologically active environments which are strongly shaped by redistribution of sediments and soils. With the projected climate warming in the twenty-first century and the continued retreat of glaciers, the area of newly exposed, highly erodible sediments and soils will increase. This presents a need to better understand and quantify erosion processes in young mountainous soils, as an increase in erodibility could threaten human infrastructure (i.e. hydroelectric power, tourist installations and settlements). While soil development is increasingly well understood and quantified, a coupling to soil erosion rates is still missing. The aim of this study was, therefore, to assess how soil erosion rates change with surface age. We investigated two moraine chronosequences in the Swiss Alps: one in the siliceous periglacial area of Steingletscher (Sustenpass), with soils ranging from 30 a to 10 ka, and the other in the calcareous periglacial area of Griessgletscher (Klausenpass) with surfaces ranging from age of 110 a to 13.5 ka. We quantified the erosion rates using the ^239+240Pu fallout radionuclides and compared them to physical and chemical soil properties and the vegetation coverage. We found no significant differences between the two parent materials. At both chronosequences, the erosion rates were highest in the young soils (on average 5−10 t ha^-1 a^-1 soil loss). Erosion rates decreased markedly after 3−5 ka of soil development (on average 1−2.5 t ha^-1 a^-1 soil loss) to reach a more or less stable situation after 10−14 ka (on average 0.3–2 t ha^-1 a^-1). Climate change not only causes glacier retreat, but also increased sediment dynamics. Depending on the relief and vegetational development, it takes up to at least 10 ka to reach soil stability. The establishment of a closed vegetation cover with dense root networks seems to be the controlling factor in the reduction of soil erodibility. © 2020 John Wiley & Sons, Ltd.     

Tectono‐sedimentary evolution of lower to middle Miocene half‐graben basins related to an extensional detachment fault (western Crete,Greece)

Crustal extension in the overriding plate at the Aegean subduction zone, related to the rollback of the subducting African slab in the Miocene, resulted in a detachment fault separating high‐pressure/low‐temperature (HP‐LT) metamorphic lower from non‐metamorphic upper tectonic units on Crete. In western Crete, detachment faulting at deeper crustal levels was accompanied by structural disintegration of the hangingwall leading to the formation of half‐graben‐type sedimentary basins filled by alluvial fan and fan‐delta deposits. The coarse‐grained clastic sediments in these half‐grabens are exclusively derived from the non‐metamorphic units atop the detachment fault. Being in direct tectonic contact with HP‐LT metamorphic rocks of the lower tectonic units today, the basins must have formed in the period between c. 20 and 15 Ma, prior to the exposure of the HP‐LT metamorphic rocks at the surface, and juxtaposed with the latter during ongoing deformation.     

The Western European PSSA—Testing a unique international concept to protect imperilled marine ecosystems

Particularly Sensitive Sea Areas (PSSAs) are a tool designed to protect vulnerable marine areas from vessel-source pollution through measures approved by the governing body, the International Maritime Organisation. Recent developments triggered by the proposal to designate, amongst others, a large part of the Western European Atlantic a PSSA have brought the instrument to a decisive stage. Although the proposal appears to be lawful, its implications for the concept, which this paper seeks to assess, are questionable. The significance of the instrument is at risk if it is overused. As a consequence, new protective mechanisms should be contemplated.