Multiscale mass conservative domain decomposition preconditioners for elliptic problems on irregular grids

Multiscale methods can in many cases be viewed as special types of domain decomposition preconditioners. The localisation approximations introduced within the multiscale framework are dependent upon both the heterogeneity of the reservoir and the structure of the computational grid. While previous works on multiscale control volume methods have focused on heterogeneous elliptic problems on regular Cartesian grids, we have tested the multiscale control volume formulations on two-dimensional elliptic problems involving heterogeneous media and irregular grid structures. Our study shows that the tangential flow approximation commonly used within multiscale methods is not suited for problems involving rough grids. We present a more robust mass conservative domain decomposition preconditioner for simulating flow in heterogeneous porous media on general grids.     

Late Weichselian to Holocene paleoenvironments in the Barents Sea

Paleoceanographic changes since the Late Weichselian have been studied in three sediment cores raised from shelf depressions along a north–south transect across the central Barents Sea. AMS radiocarbon dating offers a resolution of several hundred years for the Holocene. The results of lithological and micropaleontological study reveal the response of the Barents Sea to global climatic changes and Atlantic water inflow. Four evolutionary stages were distinguished. The older sediments are moraine deposits. The destruction of the Barents Sea ice sheet during the beginning of the deglaciation in response to climate warming and sea level rise resulted in proximal glaciomarine sedimentation. Then, the retreat of the glacier front to archipelagoes during the main phase of deglaciation caused meltwater discharge and restricted iceberg calving. Fine-grained distal glaciomarine sediments were deposited from periodic near-bottom nepheloid flows and the area was almost permanently covered with sea ice. The dramatic change in paleoenvironment occurred near the Pleistocene/Holocene boundary when normal marine conditions ultimately established resulting in a sharp increase of biological productivity. This event was diachronous and started prior to 10 ¹⁴C ka BP in the southern and about 9.2 ¹⁴C ka in the northern Barents Sea. Variations in sediment supply, paleoproductivity, sea-ice conditions, and Atlantic water inflow controlled paleoenvironmental changes during the Holocene.     

Mesan, an operational mesoscale analysis system

A system for mesoscale analyses of selected variables has been developed. The analysed parameters are of general interest in operational weather forecasting, but normally not available from NWP systems, or available, but with a significantly lower quality than achieved by the mesoscale analysis system. A supplementary objective is to produce initial information to be used for now-casting techniques. Examples of parameters are precipitation, temperature, humidity, visibility, wind and clouds. The basis of the analysis system is the optimal interpolation technique (OI). The use of observations from automatic stations, radars and satellites have been investigated. The investigation indicates that a dense network of ordinary precipitation gauge measurements can produce more accurate analyses than more elaborate systems like radar that suffers from anomalous echoes and other errors.     

Convergence of a symmetric MPFA method on quadrilateral grids

This paper investigates different variants of the multipoint flux approximation (MPFA) O-method in 2D, which rely on a transformation to an orthogonal reference space. This approach yields a system of equations with a symmetric matrix of coefficients. Different methods appear, depending on where the transformed permeability is evaluated. Midpoint and corner-point evaluations are considered. Relations to mixed finite element (MFE) methods with different velocity finite element spaces are further discussed. Convergence of the MPFA methods is investigated numerically. For corner-point evaluation of the reference permeability, the same convergence behavior as the O-method in the physical space is achieved when the grids are refined uniformly or when grid perturbations of order h ² are allowed. For h ²-perturbed grids, the convergence of the normal velocities is slower for the midpoint evaluation than for the corner-point evaluation. However, for rough grids, i.e., grids with perturbations of order h, contrary to the physical space method, convergence cannot be claimed for any of the investigated reference space methods. The relations to the MFE methods are used to explain the loss of convergence. Wheeler was partially supported by NSF grant DMS 0411413 and the DOE grant DE-FGO2-04ER25617. Yotov was supported in part by the DOE grant DE-FG02-04ER25618, the NSF grant DMS 0411694 and the J. Tinsley Oden Faculty Fellowship, The University of Texas at Austin.     

Downslope Displacement Rates of Ploughing Boulders in A Mid-Alpine Environment: Finse, Southern Norway.

Annual and seasonal displacements of ploughing boulders were investigated at Finse, southern Norway, by traditional surveying and differential carrier-phase global positioning system measurements. Annual displacement rates were mainly below 10 mm/year, although one particular season showed rates of 26 mm/year on average. There was a tendency for larger boulders to travel faster. Seasonal displacements were restricted to the annual freeze-thaw cycle. The frost heave seems to have a significant horizontal component, which does not necessarily point in the downslope direction. Thus, the concept of frost creep is not applicable to the investigated ploughing boulders. On the other hand, due to tilting of the boulders, a momentum may be gained during thaw consolidation that could induce downslope displacements. Such a process will work together with gelifluction.     

An Introduction to Multipoint Flux Approximations for Quadrilateral Grids

Control-volume discretizations using multipoint flux approximations (MPFA) were developed in the last decade. This paper gives an introduction to these methods for quadrilateral grids in two and three dimensions. The introduction is kept on a basic level, and a brief summary to more advanced results is given. Only the O-method with surface midpoints as continuity points is discussed. Flux expressions are derived both in physical and in curvilinear space. Equations for calculation of the transmissibility coefficients are given, and an explicit solution is shown for constant coefficients. K-orthogonality, stability and monotonicity are discussed, and an iterative solution technique is presented. Two numerical examples close the paper.     

Tidal amplification and along‐strike process variability in a mixed‐energy paralic system prograding onto a low accommodation shelf,Edgeøya,Svalbard

The study describes the depositional development and sediment partitioning in a prograding paralic Triassic succession. The deposits are associated with the advance of large prism‐scale clinoforms across a shallower platform area. Approaching the platform, the limited accommodation and associated relative higher rates of deposition generated straighter clinoforms with lower foreset angles. The vertical restriction across the platform is interpreted to have amplified the tidal signature. Sediment was redistributed from the coast into increasingly sandy delta‐front deposits, compared to offshore equivalents. The deposits comprise extensive compound dune fields of amalgamated and increasingly clean sandbodies up‐section. Rapid deposition of significant amounts of sand led to differential subsidence and growth‐faulting in the delta front, with downthrown fault blocks further amplifying the tidal energy through funnelling. A mixed‐energy environment created along‐strike variability along the delta front with sedimentation governing process‐regime. Areas of lower sedimentation were reworked by wave and storm‐action, whereas high sedimentation rates preserved fluvially dominated mouth bars. A major transgression, however, favoured tidally dominated deposits also in these areas, attributed to increasing rugosity of the coastline. Formation of an extensive subaqueous platform between the coast and delta front dampened incoming wave energy, and tidally dominated deposits dominate the near‐shore successions. Meanwhile formation of wave‐built sand‐bars atop the platform attest to continued wave influence. The strong tidal regime led to the development of a heterolithic near‐shore tidally dominated channel system, and sandier fluvial channels up‐river. The highly meandering tidal channels incising the subaqueous platform form kilometre wide successions of inclined heterolithic stratification. The fluvially dominated channels which govern deposition on the delta plain are narrower and slightly less deep, straighter, generally symmetric and filled with cleaner sands. This study provides important insight into tidal amplification and sand redistribution during shallowing on a wide shelf, along with along‐strike process‐regime variability resulting from variations in sediment influx.     

Model analysis of the measured concentration of organic gases in the Norwegian Arctic

A 2-D meridional model for the chemistry and transport in the troposphere is used to study the seasonal variation of the concentration of organic gases like C₂H₂, C₂H₆, C₃H₈, C₆H₆, C₇H₈. CHCl₃ and C₂Cl₄ at high latitudes. The anthropogenic sources for these species were estimated, and the temporal and latitudinal distribution of OH and O₃ was calculated using a complex photochemical reaction system. There is fair agreement between the calculated annual variation and the measured concentrations for C₂H₂, C₂H₆, C₃H₈, C₇H₈ and C₂Cl₄ at Spitsbergen during July 1982 and March/April 1983, with a distinct late winter maximum and summer minimum. For CHCl₃, the direct anthropogenic source is minor compared to indirect anthropogenic or natural sources. For benzene, emission in car exhaust is important, but other anthropogenic sources are required for the calculations to agree with the measurements. Measured C₂H₄ and C₃H₆ concentrations are much higher than the calculated ones based on anthropogenic emissions, and show opposite seasonal trends. This indicates biogenic sources for these compounds.A buildup of PAN (300 pptv) is calculated at high latitudes during winter. This makes it the dominant source for NO_x as the temperature increases in the spring. NO_x is found to be a limiting factor for O₃ production at high latitudes during spring.     

Nested intrashelf platform clinoforms—Evidence of shelf platform growth exemplified by Lower Cretaceous strata in the Barents Sea

Two nested clinoform set types of different scales and steepness are mapped and analysed from high-resolution seismic data. Restoration of post-depositional faulting reveals a persistent pattern of small-scale, high-angle clinoforms contained within platform-scale, low-angle clinothems, showing a combined overall progradational depositional system. The large clinoforms lack a well-defined platform edge, and show a gradual increase in dip from topset to foreset. A consistent recurring stratal pattern is evident from the architecture, and is considered a result of interplay between relative sea-level change and autocyclic switching of sediment delivery focal points that brought sediment to the platform edge. This un-interrupted succession records how intra-shelf platforms prograde. Quantitative clinoform analysis may assist in determining the most influential depositional factors. Post-depositional uplift and erosion requires restoration with re-burial to maximum burial depth. Backstripping, decompaction and isostatic correction was performed assuming a range of lithologic compositions, as no wells test the lithology. Nearby wells penetrate strata basinward of the clinoforms, proving mudstone content above 50%, which in turn guide restoration values. Typical restored platform heights are 250–300 m, with correspondingly sized platform-scale clinoform heights. Typical large-scale clinoform foreset dip values are 1.3°–2.4°. Small-scale clinothems are typically 100 m thick, with restored foreset dip angles at 4.4° - > 10°. The results suggest that intrashelf platform growth occurs in pulses interrupted by draping of strata over its clinoform profile. The resultant architecture comprises small-scale clinoforms nested within platform-scale clinothems.