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approaches will be compared, using existing ice elevation and velocity data obtained from aerial photogrammetry, our unpublished surface mass balance data, and new velocity data obtained from Landsat imagery by the U. S. Geological Survey.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

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

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

Pre-LGM Northern Hemisphere ice sheet topography

We here reconstruct the paleotopography of Northern Hemisphere ice sheets during the glacial maxima of marine isotope stages (MIS) 5b and 4.We employ a combined approach, blending geologically based reconstruction and numerical modeling, to arrive at probable ice sheet extents and topographies for each of these two time slices. For a physically based 3-D calculation based on geologically derived 2-D constraints, we use the University of Maine Ice Sheet Model (UMISM) to calculate ice sheet thickness and topography. The approach and ice sheet modeling strategy is designed to provide robust data sets of sufficient resolution for atmospheric circulation experiments for these previously elusive time periods. Two tunable parameters, a temperature scaling function applied to a spliced Vostok–GRIP record, and spatial adjustment of the climatic pole position, were employed iteratively to achieve a good fit to geological constraints where such were available. The model credibly reproduces the first-order pattern of size and location of geologically indicated ice sheets during marine isotope stages (MIS) 5b (86.2 kyr model age) and 4 (64 kyr model age). From the interglacial state of two north–south obstacles to atmospheric circulation (Rocky Mountains and Greenland), by MIS 5b the emergence of combined Quebec–central Arctic and Scandinavian–Barents-Kara ice sheets had increased the number of such highland obstacles to four. The number of major ice sheets remained constant through MIS 4, but the merging of the Cordilleran and the proto-Laurentide Ice Sheet produced a single continent-wide North American ice sheet at the LGM

Collaborative Research: Did the Laurentine Ice Sheet Control Abrupt Climate Change?

This is a collaborative project with the University of Maine and Ohio State University. The Principal Investigators will model the late glacial Laurentide Ice Sheet from near steady-state equilibrium at - 25,000 BP (years before present), through reversible stadial/interstadial transitions associated with Laurentide iceberg outbursts (Heinrich events 2 and 1), and across the threshold of irreversible Laurentide collapse after the last iceberg outburst at - 1 1,000 BP (Heinrich event 0). The goals are to determine if ice-sheet changes could have triggered climate changes by abrupt ice sheet change and to investigate the structure of these changes. The Principal Investigators will isolate mechanisms of abrupt change over hundreds of years in the ice sheet that are large enough to trigger climate changes captured as time snapshots by coupled global and regional atmospheric climate models. Specific modeling tasks are: 1) to provide the climate settings surrounding the Laurentide Ice Sheet at snapshots of time during this late glacial period. This includes the wind field over the ice sheet, proglacial lakes along the border, the fine-resolution mesoscale climate of North America, and global climate; 2) to provide the basal boundary conditions that, together with the internal flow and temperature fields, are used to calculate the basal mass balance. This includes the pattern of basal temperatures, melting and freezing rates, and the associated subglacial hydrology; 3) to model the Laurentide Ice Sheet basal thermal, hydrological, and mechanical conditions within the imposed and basal boundary constraints for the chosen timeframe; and 4) to determine whether modeling will isolate mechanisms of abrupt change that allow rapid advance and retreat of Laurentide ice, with areal, elevation, and volume changes large enough to trigger climate changes that are captured by our snapshots of regional and global climate.This project has significance for educational outreach and the possible behavior of present-day ice sheets. The education outreach program will be interactive with high school students. They will be able to manipulate the major variables so that they can view three-dimensional computer simulations of how the Laurentide Ice Sheet responds to each variable. This program will be disseminated on the world-wide web. If fluctuations in the Laurentide Ice Sheet triggered climate changes, then the possibility exists that present-day ice sheets covering Greenland and Antarctica could trigger similar climate changes, with major social, economic, and political consequences. A way to assess this possibility is to understand the internal instability mechanisms that could have caused abrupt changes in Laurentide ice extent, and to tie them firmly to known late glacial climate changes

Global modelling of the early Martian climate under a denser CO2 atmosphere: Water cycle and ice evolution

We discuss 3D global simulations of the early Martian climate that we have performed assuming a faint young Sun and denser CO2 atmosphere. We include a self-consistent representation of the water cycle, with atmosphere-surface interactions, atmospheric transport, and the radiative effects of CO2 and H2O gas and clouds taken into account. We find that for atmospheric pressures greater than a fraction of a bar, the adiabatic cooling effect causes temperatures in the southern highland valley network regions to fall significantly below the global average. Long-term climate evolution simulations indicate that in these circumstances, water ice is transported to the highlands from low-lying regions for a wide range of orbital obliquities, regardless of the extent of the Tharsis bulge. In addition, an extended water ice cap forms on the southern pole, approximately corresponding to the location of the Noachian/Hesperian era Dorsa Argentea Formation. Even for a multiple-bar CO2 atmosphere, conditions are too cold to allow long-term surface liquid water. Limited melting occurs on warm summer days in some locations, but only for surface albedo and thermal inertia conditions that may be unrealistic for water ice. Nonetheless, meteorite impacts and volcanism could potentially cause intense episodic melting under such conditions. Because ice migration to higher altitudes is a robust mechanism for recharging highland water sources after such events, we suggest that this globally sub-zero, `icy highlands' scenario for the late Noachian climate may be sufficient to explain most of the fluvial geology without the need to invoke additional long-term warming mechanisms or an early warm, wet Mars.Comment: Minor revisions to text, one new table, figs. 1,3 11 and 18 redon

Seasonal melting and the formation of sedimentary rocks on Mars, with predictions for the Gale Crater mound

A model for the formation and distribution of sedimentary rocks on Mars is proposed. The rate-limiting step is supply of liquid water from seasonal melting of snow or ice. The model is run for a O(10^2) mbar pure CO2 atmosphere, dusty snow, and solar luminosity reduced by 23%. For these conditions snow only melts near the equator, and only when obliquity >40 degrees, eccentricity >0.12, and perihelion occurs near equinox. These requirements for melting are satisfied by 0.01-20% of the probability distribution of Mars' past spin-orbit parameters. Total melt production is sufficient to account for aqueous alteration of the sedimentary rocks. The pattern of seasonal snowmelt is integrated over all spin-orbit parameters and compared to the observed distribution of sedimentary rocks. The global distribution of snowmelt has maxima in Valles Marineris, Meridiani Planum and Gale Crater. These correspond to maxima in the sedimentary-rock distribution. Higher pressures and especially higher temperatures lead to melting over a broader range of spin-orbit parameters. The pattern of sedimentary rocks on Mars is most consistent with a Mars paleoclimate that only rarely produced enough meltwater to precipitate aqueous cements and indurate sediment. The results suggest intermittency of snowmelt and long globally-dry intervals, unfavorable for past life on Mars. This model makes testable predictions for the Mars Science Laboratory rover at Gale Crater. Gale Crater is predicted to be a hemispheric maximum for snowmelt on Mars.Comment: Submitted to Icarus. Minor changes from submitted versio