Abstract. Glaciers with extensive surface debris cover respond differently to climate forcing than those without supraglacial debris. In order to include debris-covered glaciers in projections of glaciogenic runoff and sea level rise and to understand the paleoclimate proxy recorded by such glaciers, it is necessary to understand the manner and timescales over which a supraglacial debris cover develops. Because debris is delivered to the glacier by processes that are heterogeneous in space and time, and these debris inclusions are altered during englacial transport through the glacier system, correctly determining where, when and how much debris is delivered to the glacier surface requires knowledge of englacial transport pathways and deformation. To achieve this, we present a model of englacial debris transport in which we couple an advection scheme to a full-Stokes ice flow model. The model performs well in numerical benchmark tests, and we present both 2-D and 3-D glacier test cases that, for a set of prescribed debris inputs, reproduce the englacial features, deformation thereof and patterns of surface emergence predicted by theory and observations of structural glaciology. In a future step, coupling this model to (i) a debris-aware surface mass balance scheme and (ii) a supraglacial debris transport scheme will enable the co-evolution of debris cover and glacier geometry to be modelled.

pers, U., 2013. Thermal properties of a supraglacial debris layer with respect to lithology and grain size.ABSTRACT. This paper focuses on the impacts of debris cover on ice melt with regards to lithology and grain size. Ten test plots were established with different debris grain sizes and debris thicknesses consisting of different natural material. For each plot, values of thermal conductivity were determined. The observations revealed a clear dependence of the sub-debris ice melt on the layer thickness, grain size, porosity and moisture content. For the sand fraction the moisture content played a dominant role. These test fields were water saturated most of the time, resulting in an increased thermal conductivity. Highly porous volcanic material protected the ice much more effectively from melting than similar layer thicknesses of the local mica schist. However, the analysis of thermal diffusivities demonstrated that the vertical moisture distribution of the debris cover must be taken into consideration, with the diffusivity values being significantly lower in deeper layers.

Abstract. Glaciers with extensive surface debris cover respond differently to climate forcing than those without supraglacial debris. In order to include debris-covered glaciers in projections of glaciogenic runoff and sea-level rise, and to understand the paleoclimate proxy recorded by such glaciers it is necessary to understand the manner and timescales over which a supraglacial debris cover develops. As debris is delivered to the glacier by processes that are heterogeneous in space and time, and these debris inclusions are altered during englacial transport through the glacier system, correctly determining where, when, and how much, debris is delivered to the glacier surface requires that the englacial transport pathways and deformation can be known. To achieve this, we present a model of englacial debris transport in which we couple an advection scheme to a full-Stokes ice flow model. The model performs well in numerical benchmark tests, and we present both 2D and 3D steady-state glacier test cases that, for a set of prescribed debris inputs, reproduce the englacial features, deformation thereof, and patterns of surface emergence predicted by theory and observations of structural glaciology. In a future step, coupling this model to a (i) debris-aware surface mass-balance scheme and (ii) supraglacial debris transport scheme will enable the co-evolution of debris-cover and glacier geometry to be modelled.

Abstract. Like any gravitationally driven flow that is not constrained at the upper surface, glaciers and ice sheets feature a free surface, which becomes a free-boundary problem within simulations. A kinematic boundary condition is often used to describe the evolution of this free surface. However, in the case of glaciers and ice sheets, the naturally occurring constraint that the ice surface elevation (S) cannot fall below the bed topography (B) (S-B≥0), in combination with a non-zero mass balance rate complicates the matter substantially. We present an open-source numerical simulation framework to simulate the free-surface evolution of glaciers that directly incorporates this natural constraint. It is based on the finite-element software package FEniCS solving the Stokes equations for ice flow and a suitable transport equation, i.e. “kinematic boundary condition”, for the free-surface evolution. The evolution of the free surface is treated as a variational inequality, constrained by the bedrock underlying the glacier or the topography of the surrounding ground. This problem is solved using a “reduced space” method, where a Newton line search is performed on a subset of the problem (Benson and Munson, 2006). Therefore, the “constrained” non-linear problem-solving capabilities of PETSc's (Portable, Extensible Toolkit for Scientific Computation, Balay et al., 2019) SNES (Scalable Non-linear Equations Solver) interface are used. As the constraint is considered in the solving process, this approach does not require any ad hoc post-processing steps to enforce non-negativity of ice thickness and corresponding mass conservation. The simulation framework provides the possibility to divide the computational domain into different subdomains so that individual forms of the relevant equations can be solved for different subdomains all at once. In the presented setup, this is used to distinguish between glacierised and ice-free regions. The option to chose different time discretisations, spatial stabilisation schemes and adaptive mesh refinement make it a versatile tool for glaciological applications. We present a set of benchmark tests that highlight that the simulation framework is able to reproduce the free-surface evolution of complex geometries under different conditions for which it is mass-conserving and numerically stable. Real-world glacier examples demonstrate high-resolution change in glacier geometry due to fully resolved 3D velocities and spatially variable mass balance rate, whereby realistic glacier recession and advance states can be simulated. Additionally, we provide a thorough analysis of different spatial stabilisation techniques as well as time discretisation methods. We discuss their applicability and suitability for different glaciological applications.

Ongoing changes in mountain glaciers affect local water resources, hazard potential and global sea level. An increasing proportion of remaining mountain glaciers are affected by the presence of a surface cover of rock debris, and the response of these debris-covered glaciers to climate forcing is different to that of glaciers without a debris cover. Here we take a back-to-basics look at the fundamental terms that control the processes of debris evolution at the glacier surface, to illustrate how the trajectory of debris cover development is partially decoupled from prevailing climate conditions, and that the development of a debris cover over time should prevent the glacier from achieving steady state. We discuss the approaches and limitations of how this has been treated in existing modeling efforts and propose that “surrogate world” numerical representations of debris-covered glaciers would facilitate the development of well-validated parameterizations of surface debris cover that can be used in regional and global glacier models. Finally, we highlight some key research targets that would need to be addressed in order to enable a full representation of debris-covered glacier system response to climate forcing.