Polythermal Ice Sheet Research Articles

Greenland ice-sheet volume sensitivity to basal, surface and initial conditions derived from an adjoint model

AbstractWe extend the application of control methods to a comprehensive three-dimensional thermomechanical ice-sheet model, SICOPOLIS (SImulation COde for POLythermal Ice Sheets). Lagrange multipliers, i.e. sensitivities, are computed with an exact, efficient adjoint model that has been generated from SICOPOLIS by rigorous application of automatic differentiation. The case study uses the adjoint model to determine the sensitivity of the total Greenland ice volume to various control variables over a 100 year period. The control space has of the order 1.2 × 106 elements, consisting of spatial fields of basal flow parameters, surface and basal forcings and initial conditions. Reliability of the adjoint model was tested through finite-difference perturbation calculations for various control variables and perturbation regions, ascertaining quantitative inferences of the adjoint model. As well as confirming qualitative aspects of ice-sheet sensitivities (e.g. expected regional variations), we detect regions where model sensitivities are seemingly unexpected or counter-intuitive, albeit ‘real’ in the sense of actual model behavior. An example is inferred regions where sensitivities of ice-sheet volume to basal sliding coefficient are positive, i.e. where a local increase in basal sliding parameter increases the ice-sheet volume. Similarly, positive (generally negative) ice temperature sensitivities in certain parts of the ice sheet are found, the detection of which seems highly unlikely if only conventional perturbation experiments had been used. The object of this paper is largely a proof of concept. Available adjoint-code generation tools now open up a variety of novel model applications, notably with regard to sensitivity and uncertainty analyses and ice-sheet state estimation or data assimilation.

Circular moraine features on the Varanger Peninsula, northern Norway, and their possible relation to polythermal ice sheet coverage

This paper introduces a new hypothesis about the formation of circular moraine features (CMFs) on felsenmeer-covered plateaux of the Varanger Peninsula, northern Norway. CMFs and glacial lineations in the northwestern part of the Varanger Peninsula were mapped from aerial photographs. In two CMF-rich areas, Basečœrro-Plateau and Båtsfjordfjellet, the CMFs were investigated during fieldwork. The aim was to investigate possible entrainment, transport and deposition mechanisms of the CMFs in connection to ice sheet properties. The CMFs were deposited in connection with a polythermal ice cover. During glaciations, the ice sheet was cold-based on the boulder field plateaux and warm-based in valleys, especially in ice drainage pathways towards fjords. The CMF material was probably entrained en masse, on the Varanger Peninsula, in transition zones between warm- and cold-based ice. The debris transport took place close to the ice base. During deglaciation, the debris formed dirt cones, slowing down the melting of underlying dead-ice blocks. As material slid down the margins of the cones, the typical CMF shape was formed.

Asymptotic Theories of Large-Scale Motion, Temperature, and Moisture Distribution in Land-Based Polythermal Ice Sheets: A Critical Review and New Developments

A review is given of the theory of polythermal ice sheets, ie, ice masses of which the ice has submelting temperatures in certain subdomains and is at the pressure melting point in other subdomains. Cold ice is treated as a non-linearly viscous heat conducting fluid, temperate ice as a mixture of ice at the melting point and melt-water diffusing through the ice matrix. Cold and temperate ice are separated by a non-material singular Stefan-type surface. We repeat and partly amend the complicated field equations and boundary conditions as derived in the literature. These equations are subjected to a scale analysis that makes the creeping flow conditions and the shallow geometries of land-based ice sheets explicit. The small aspect ratio ε — typical depth to horizontal distance over which the geometry and/or stresses change appreciably — suggests a perturbation approach for a possible analytical or numerical solution which has been pursued to include second-order terms O(ε2). The lowest-order O(ε0) model equations, known as the shallow-ice approximation (SIA), are asymptotically valid in the entire ice sheet domain except a small marginal zone provided the topographic variations are shallow, ie, possess wave height to wavelength ratios that are O(ε1) and the constitutive relation for the stress deviator exhibits finite viscosity at zero effective shear stress (square root of second stress deviator invariant). We critically review earlier procedures and put them into the proper perspectives with regard to the original expansion procedures. We extend the zeroth-order theory to first and second order but present only those equations and deductions from them which lead to improved physical insight. In particular we derive stress formulas which show how the stresses depend on i) depth and surface slope, ii) surface topography and iii) stress deviator components, more complete than, and going beyond, known formulas of the literature. Finally we discuss numerically computed second-order stresses for the present state of the Greenland ice sheet. It turns out that they are typically three orders of magnitude smaller than the corresponding zeroth-order quantities, and that they are mainly determined by contributions due to zeroth-order stress deviators, rather than by topography effects. Their relative importance is largest close to the ice surface for the second-order pressure, and in the vicinity of ice domes for the horizontal, bed-parallel shear stresses. There are 229 references.

Numerical approach of temperature distribution in a free boundary model for polythermal ice sheets

A numerical method for solving the thermal subproblem appearing in the modelization of polythermal ice sheets is described. This thermal problem mainly involves three nonlinearities: a reaction term due to the viscous dissipation, a Signorini boundary condition associated to the geothermic flux and an enthalpy term issued from the two phase Stefan formulation of the polythermal regime. The stationary temperature is obtained as the limit of an evolutive problem which is discretized in time with an upwind characteristics scheme and in space with finite elements. The nonlinearities are solved either by Newton-Raphson method or by duality techniques applied to maximal monotone operators. The application of the algorithms provides the dimensionless temperature distribution approximation and allows to identify the cold and temperate ice regions.

Application of a Polythermal Three-Dimensional Ice Sheet Model to the Greenland Ice Sheet: Response to Steady-State and Transient Climate Scenarios

Abstract Steady-state and transient climate-change computations are performed with the author’s three-dimensional polythermal ice sheet model Simulation Code for Polythermal Ice Sheets for the Greenland Ice Sheet. The distinctive feature of this model is the detailed consideration of the basal temperate ice layer, in which the water content and its impact on the ice viscosity are computed; its transition surface to the cold ice region is accounted for by continuum-mechanical jump conditions on this interface. The simulations presented include steady states subject to a range of physical parameters and two different climates (present and glacial conditions), as well as three types of transient scenarios, namely (i) sinusoidal Milankovic-period forcing, (ii) paleoclimatic forcing from the Greenland Ice Core Project core reconstruction, and (iii) future greenhouse warming forcing.