A Finite-Element Model of Basal Water Generated by Melting in an Ice Sheet Model

It is well known that water is produced at the bed of an ice sheet when the temperature of the bed reaches the pressure melting point. The current ice sheet model, with its ability to calculate temperatures throughout the ice sheet, is also able to calculate melt rates at the bed. By incorporating a model of the continuity equation for the basal-water flow, this project will attempt to follow the movement of this water under the ice sheet as it flows from source regions to sink regions. The ability to predict wet-based regions is important to the understanding of the occurrence of the sliding mechanism, which is thought to control ice stream dynamics. The primary task will be to ascribe physical meaning to the parameters of the basal-water continuity equation. This will involve extracting, from observational evidence, the laws governing the flow of subglacial water. These will need to capture the essence of the underlying physics and yet remain simple enough to be treatable within the discretized and generalized snapshot of reality provided by numerical simulations. The primary effort will focus on compiling and analyzing the existing observational and theoretical constraints on ice-sheet hydrology. These data will be used to evaluate which modes of subglacial water flow are the most important and what values of parameters must be used to best incorporate the subglacial processes into the ice sheet model

Thermal Conditions at the Bed of the Laurentide Ice Sheet in Maine During Deglaciation: Implications for Esker Formation

The University of Maine Ice Sheet Model was used to study basal conditions during retreat of the Laurentide ice sheet in Maine. Within 150 km of the margin, basal melt rates average similar to 5 mm a(-1) during retreat. They decline over the next 100km, so areas of frozen bed develop in northern Maine during retreat. By integrating the melt rate over the drainage area typically subtended by an esker, we obtained a discharge at the margin of similar to 1.2 m(3) s(-1). While such a discharge could have moved the material in the Katahdin esker, it was likely too low to build the esker in the time available. Additional water from the glacier surface was required. Temperature gradients in the basal ice increase rapidly with distance from the margin. By conducting upward into the ice all of the additional viscous heat produced by any perturbation that increases the depth of flow in a flat conduit in a distributed drainage system, these gradients inhibit the formation of sharply arched conduits in which an esker can form. This may explain why eskers commonly seem to form near the margin and are typically segmented, with later segments overlapping onto earlier ones

Embedded Ice Sheet Model

This award supports the development of an embedded ice sheet model, one where a section of the ice sheet (at a mesoscale) is modeled at higher resolution, but is driven by output from a lower-resolution model of the entire ice sheet (at a global scale). In addition to giving higher resolution results, it will be better able to capture the behavior of small-scale, but dynamically important, systems such as ice streams. It will also be possible with the new embedded model to include more complete physics (such as longitudinal stresses). This project will enable the continued development and application of a scientific tool, the University of Maine Ice Sheet Model (UMISM). This tool enables a better understanding of the ice sheet and the processes that control mesoscale features of the ice sheet system, such as ice streams. The key to the development of a truly predictive model is a bridge between the larger-scale physics of an ice sheet and the smaller-scale processes that exert such important control over the dynamic behavior of the ice sheet system. The results of this work will be disseminated at meetings and by publication in appropriate technical journals

Derived Quantities: A Coupled Dynamic/Thermodynamic Ice Sheet Model

This award is for support for a program of research involving the use of inverse modeling to derive information from the measured configuration of an ice sheet to yield important information about the conditions both at the bed and within the ice column. It is proposed to convert a column-averaged model to a column- integrated model that accounts explicitly for internal thermodynamics and variations of material properties that depend on this internal temperature field. An existing finite-element 3- D temperature solver will be coupled with an existing finite- element map-plane continuity solver. The result will allow more detailed analysis of existing field data within the context of the assumptions of the model. This improved model will be used to derive quantities describing the basal conditions of the Antarctic ice sheet, with particular focus on the behavior of ice streams around the margin of the continent

Manufactured analytical solutions for isothermal full-Stokes ice sheet models

We present the detailed construction of a manufactured analytical solution to time-dependent and steady-state isothermal full-Stokes ice sheet problems. The solutions are constructed for two-dimensional flowline and three-dimensional full-Stokes ice sheet models with variable viscosity. The construction is done by choosing for the specified ice surface and bed a velocity distribution that satisfies both mass conservation and the kinematic boundary conditions. Then a compensatory stress term in the conservation of momentum equations and their boundary conditions is calculated to make the chosen velocity distributions as well as the chosen pressure field into exact solutions. By substituting different ice surface and bed geometry formulas into the derived solution formulas, analytical solutions for different geometries can be constructed. <br><br> The boundary conditions can be specified as essential Dirichlet conditions or as periodic boundary conditions. By changing a parameter value, the analytical solutions allow investigation of algorithms for a different range of aspect ratios as well as for different, frozen or sliding, basal conditions. The analytical solutions can also be used to estimate the numerical error of the method in the case when the effects of the boundary conditions are eliminated, that is, when the exact solution values are specified as inflow and outflow boundary conditions

Studying Byrd Glacier as a Rock-Floored Ice Stream Ending as a Calving Ice Shelf: Phase I

This award supports a one-year study of the floating part of Byrd Glacier, from its grounding line located halfway up a fjord through the Transantarctic Mountains to the end of its lateral rift zone on the Ross Ice Shelf beyond the fjord. Over this l00 km distance, the side boundary changes from rigid between the fjord sidewalls, to nearly free in the lateral rift zone, to deforming when the rifts are healed and Bryd Glacier becomes fully coupled to the Ross Ice Shelf. The stress field for these changing conditions will be calculated a using a gridpoint finite-element model for the Ross Ice Shelf (Thomas and MacAyeal, l982) and a flowband finite-difference model for smooth transitions from sheet flow to stream flow to shelf flow (Hughes, l998). Results of the two modeling approaches will be compared, using existing ice elevation and velocity data obtained from aerial photogrammetry, our unpublished surface mass balance data, and new velocity data obtained from Landsat imagery by the U. S. Geological Survey. This study will train one graduate student at the Masters level

Ice-Bed Coupling Beneath and Beyond Ice Streams: Byrd Glacier, Antarctica

Ice sheet thickness is determined mainly by the strength of ice-bed coupling that controls holistic transitions from slow sheet flow to fast streamflow to buttressing shelf flow. Byrd Glacier has the largest ice drainage system in Antarctica and is the fastest ice stream entering Ross Ice Shelf. In 2004 two large subglacial lakes at the head of Byrd Glacier suddenly drained and increased the terminal ice velocity of Byrd Glacier from 820 m yr(-1) to 900 m yr(-1). This resulted in partial ice-bed recoupling above the lakes and partial decoupling along Byrd Glacier. An attempt to quantify this behavior is made using flowband and flowline models in which the controlling variable for ice height above the bed is the floating fraction phi of ice along the flowband and flowline. Changes in phi before and after drainage are obtained from available data, but more reliable data in the map plane are required before Byrd Glacier can be modeled adequately. A holistic sliding velocity is derived that depends on phi, with contributions from ice shearing over coupled beds and ice stretching over uncoupled beds, as is done in state-of-the-art sliding theories

Evidence for a Frozen Bed, Byrd Glacier, Antarctica

Ice thickness, computed within the fjord region of Byrd Glacier on the assumptions that Byrd Glacier is in mass-balance equilibrium and that ice velocity is entirely due to basal sliding, are on average 400 m less than measured ice thicknesses along a radio-echo profile. We consider four explanations for these differences: (1) active glacier ice is separated from a zone of stagnant ice near the base of the glacier by a shear zone at depth; (2) basal melting rates are some 8 m/yr; (3) internal shear occurs with no basal sliding in much of the region above the grounding zone; or (4) internal creep and basal sliding contribute to the flow velocity in varying proportions above the grounding zone. Large gradients of surface strain rate seem to invalidate the first explanation. Computed values of basal shear stress (140 to 200 kPa) provide insufficient frictional heat to melt the ice demanded by the second explanation. Both the third and fourth explanations were examined by making simplifying assumptions that prevented a truly quantitative evaluation of their merit. Nevertheless, there is no escaping the qualitative conclusion that internal shear contributes strongly to surface velocities measured on Byrd Glacier, as is postulated in both these explanations

Derived Bedrock Elevations, Strain Rates and Stresses from Measured Surface Elevations and Velocities - Jakobshavns-Isbrae, Greenland

Jakobshavns Isbrae (69 degrees 10\u27N, 49 degrees 5\u27W) drains about 6.5% of the Greenland ice sheet and is the fastest ice stream known. The Jakobshavns Isbrae basin of about 10 000 km(2) was mapped photogrammetrically from four sets of aerial photography, two taken in July 1985 and two in July 1986. Positions and elevations of several hundred natural features on the ice surface were determined for each epoch by photogrammetric block-aerial triangulation, and surface velocity vectors were computed from the positions. The two flights in 1985 yielded the best results and provided most common points (716) for velocity determinations and are therefore used in the modeling studies. The data from these irregularly spaced points were used to calculate ice elevations and velocity vectors at uniformly spaced grid paints 3 km apart by interpolation. The field of surface strain rates was then calculated from these gridded data and used to compute the field of surface deviatoric stresses, using the flow law of ice, for rectilinear coordinates, X, Y pointing eastward and northward. and curvilinear coordinates, L, T pointing longitudinally and transversely to the changing ice-flow direction. Ice-surface elevations and slopes were then used to calculate ice thicknesses and the fraction of the ice velocity due to basal sliding. Our calculated ice thicknesses are in fair agreement with an ice-thickness map based on seismic sounding and supplied to us by K. Echelmeyer. Ice thicknesses were subtracted from measured ice-surface elevations to map bed topography. Our calculation shows that basal sliding is significant only in the 10-15 km before Jakobshavns Isbrae becomes afloat in Jakobshavns IsfJord

Global ice sheet modeling

The University of Maine conducted this study for Pacific Northwest Laboratory (PNL) as part of a global climate modeling task for site characterization of the potential nuclear waste respository site at Yucca Mountain, NV. The purpose of the study was to develop a global ice sheet dynamics model that will forecast the three-dimensional configuration of global ice sheets for specific climate change scenarios. The objective of the third (final) year of the work was to produce ice sheet data for glaciation scenarios covering the next 100,000 years. This was accomplished using both the map-plane and flowband solutions of our time-dependent, finite-element gridpoint model. The theory and equations used to develop the ice sheet models are presented. Three future scenarios were simulated by the model and results are discussed