Interactive visualization of 3D mantle convection

The current availability of thousands of processors at many high performance computing centers has made it feasible to carry out, in near real time, interactive visualization of 3D mantle convection temperature fields, using grid configurations having 10–100 million unknowns. We will describe the technical details involved in carrying out this endeavor, using the facilities available at the Laboratory of Computational Science and Engineering (LCSE) at the University of Minnesota. These technical details involve the modification of a parallel mantle convection program, ACuTEMan; the usage of client–server socket based programs to transfer upwards of a terabyte of time series scientific model data using a local network; a rendering system containing multiple nodes; a high resolution PowerWall display, and the interactive visualization software, DSCVR. We have found that working in an interactive visualizastion mode allows for fast and efficient analysis of mantle convection results. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Permeability and stress in crystalline rocks

Groundwater from crystalline rocks is a significant resource in many areas of the world. It is also an important medium for contaminant transport from, for example, deep nuclear waste repositories. Stress distributions in fractured rocks are important in controlling groundwater flow in several ways: (i) palaeostress fields are responsible for the evolution of fracture systems which transmit groundwater; (ii) current in situ stress fields will influence the shape and aperture of fractures; (iii) humans can influence the natural stress field in a rock mass to enhance fracture flows. The significance of stresses for groundwater flow can be investigated by field techniques (hydraulic fracturing), laboratory techniques (stress cells) or by numerical modelling.     

Flux comparison of Eulerian and Lagrangian estimates of Agulhas leakage: A case study using a numerical model

Estimating the magnitude of Agulhas leakage, the volume flux of water from the Indian to the Atlantic Ocean, is difficult because of the presence of other circulation systems in the Agulhas region. Indian Ocean water in the Atlantic Ocean is vigorously mixed and diluted in the Cape Basin. Eulerian integration methods, where the velocity field perpendicular to a section is integrated to yield a flux, have to be calibrated so that only the flux by Agulhas leakage is sampled. Two Eulerian methods for estimating the magnitude of Agulhas leakage are tested within a high-resolution two-way nested model with the goal to devise a mooring-based measurement strategy. At the GoodHope line, a section halfway through the Cape Basin, the integrated velocity perpendicular to that line is compared to the magnitude of Agulhas leakage as determined from the transport carried by numerical Lagrangian floats. In the first method, integration is limited to the flux of water warmer and more saline than specific threshold values. These threshold values are determined by maximizing the correlation with the float-determined time series. By using the threshold values, approximately half of the leakage can directly be measured. The total amount of Agulhas leakage can be estimated using a linear regression, within a 90% confidence band of 12 Sv. In the second method, a subregion of the GoodHope line is sought so that integration over that subregion yields an Eulerian flux as close to the float-determined leakage as possible. It appears that when integration is limited within the model to the upper 300 m of the water column within 900 km of the African coast the time series have the smallest root-mean-square difference. This method yields a root-mean-square error of only 5.2 Sv but the 90% confidence band of the estimate is 20 Sv. It is concluded that the optimum thermohaline threshold method leads to more accurate estimates even though the directly measured transport is a factor of two lower than the actual magnitude of Agulhas leakage in this model.     

Holocene talus accumulation rates,—and their influence on rock glacier growth. A case study from Igpik,Disko—West Greenland

Frich, Povl and Brandt, Erik: Holocene talus accumulation rates,—and their influence on rock glacier growth. A case study from Igpik, Disko—West Greenland. Geografisk Tidsskrift 85: 32–44 Copenhagen, October 1985.

The Igpik area is located ten km east of Godhavn on the south-coast of the island Disko. Geologically the area is dominated by Tertiary basalt formations.

A general geomorphological classification of this area, which covers approximately three square kms, has been made. Based on radiocarbon ages of former marine levels in the Disko Bugt area, the beginning of talus accumulation has been determined for two talus cones situated on raised beaches. They have ages of 5800 and 7900 ¹⁴C y. B.P. Using theodolite readings, the volumes of three different talus cones have been determined and two average talus accumulation rates have been calculated for the cones located on raised beaches. These values are transformed into an average Holocene rockwall retreat rate of 0.0005 and 0.0015 m/year, respectively. The total volume of two lobate rock glaciers is calculated to be 2.2 mill, cu.m and as they are located inside 9000 years old local moraines, the average Holocene mass-transfer through the third talus cone has been estimated to 1.4 10⁶ tons×m/sq.km/y. Finally the results are discussed, with reference to other areas, and as a possible threshhold for the initiation of rock glaciers.     

Numerical simulation of flow around a circular cylinder close to a flat seabed at high Reynolds numbers using a k–ε model

High Reynolds number flows around a circular cylinder close to a flat seabed have been computed using a two-dimensional standard high Reynolds number k–ε turbulence model. The effects of gap to diameter ratio, Reynolds number and flat seabed roughness for a given boundary layer thickness of the inlet flow upstream of the cylinder have been investigated. Hydrodynamic quantities and the resulting bedload transport have been predicted, and the vortex shedding mechanisms have been investigated. Predictions of hydrodynamic quantities around a cylinder located far away from the bed (so that the effect of the bed is negligible) are in satisfactory agreement with published experimental data and numerical results obtained for the flow around an isolated cylinder. Results for lower Reynolds number flows have also been computed for comparison with the high Reynolds number flow results. Overall it appears that the present approach is suitable for design purposes at high Reynolds numbers which are present near the seabed in the real ocean.     

Extreme storm surge modelling in the North Sea

This study shows that storm surge model performance in the North Sea is mostly unaffected by the application of temporal variations of surface drag due to changes in sea state provided the choice of a suitable constant Charnock parameter in the sea-state-independent case. Including essential meteorological features on smaller scales and minimising interpolation errors by increasing forcing data resolution are shown to be more important for the improvement of model performance particularly at the high tail of the probability distribution. This is found in a modelling study using WAQUA/DCSMv5 by evaluating the influence of a realistic air-sea momentum transfer parameterization and comparing it to the influence of changes in the spatial and temporal resolution of the applied forcing fields in an effort to support the improvement of impact and climate analysis studies. Particular attention is given to the representation of extreme water levels over the past decades based on the example of the Netherlands. For this, WAQUA/DCSMv5 is forced with ERA-Interim reanalysis data. Model results are obtained from a set of different forcing fields, which either (i) include a wave-state-dependent Charnock parameter or (ii) apply a constant Charnock parameter (α _{C h} =?0.032) tuned for young sea states in the North Sea, but differ in their spatial and/or temporal resolution. Increasing forcing field resolution from roughly 79 to 12 km through dynamically downscaling can reduce the modelled low bias, depending on coastal station, by up to 0.25 m for the modelled extreme water levels with a 1-year return period and between 0.1 m and 0.5 m for extreme surge heights.     

Use of stream response functions to determine impacts of replacing surface-water use with groundwater withdrawals

A regional-scale numerical groundwater model is used to study the impacts of replacing surface-water use with groundwater wells to improve low-flow stream conditions for endangered species within the Bertrand and Fishtrap watersheds, southern British Columbia, Canada and Washington, USA. Stream response functions ranging from 0 to 1.0 were calculated for individual wells placed within a steady-state groundwater flow model at varying distances from the streams to determine the impact that these replacement wells, operating under sustained pumping rates, would have on summer instream flows. Lower response ratios indicate groundwater pumping will have less of an impact on streamflow than taking an equivalent amount of water directly from a surface-water source. Results show that replacing surface-water use with groundwater withdrawals may be a viable alternative for increasing summer streamflows. Assuming combined response factors should be ≤0.5 for irrigators to undergo the expense of installing new wells, ~57% of the land area within 0.8 km of Bertrand Creek would be suitable for replacement wells. Similarly, 70% of the land area within 0.8 km of Fishtrap Creek was found to be appropriate. A visual analysis tool was developed using STELLA to allow stakeholders to quickly evaluate the impact associated with moving their water right.     

Concepts for reference frames in geodesy and geodynamics: The reference directions

Modern high accuracy measurements of the non-rigid earth are to be referred to four-dimensional, i.e., time- and space-dependent reference frames. Geodynamic phenomena derived from these measurements are to be described in a terrestrial reference frame in which both space- and time-like variations can be monitored. Existing conventional terrestrial reference frames (e.g. CIO, BIH) are no longer suitable for such purposes. The ultimate goal of this study is the establishment of a reference frame, moving with the earth in some average sense, in which the geometric and dynamic behavior of the earth can be monitored, and whose motion with respect to inertial space can also be determined. The study is conducted in several parts. In the first part problems related to reference directions are investigated, while subsequent parts deal with positions, i.e., with reference origins and scale. Only the first part is treated in this paper. The approach is based on the fact that reference directions at an observation point on the earth surface are defined by fundamental vectors (gravity, earth rotation, etc.), both space and time variant. These reference directions are interrelated by angular parameters, also derived from the fundamental vectors. The interrelationships between these space- and time-variant angular parameters are illustrated in a commutative diagram, tower of triads, which makes the derivation of the various relationships convenient. In order to determine the above parameters from observations using least squares techniques, a model tower of triads is also presented to allow the formation of linear observation equations. Although the model tower is also space and time variant, its variations are described by adopted parameters representing our current knowledge of the earth.