The presence of a supraglacial debris layer affects the melt of underlying ice which causes debris-covered glaciers to respond differently to climate forcing compared to clean-ice glaciers. To further complicate matters, supraglacial debris cover is not constant in time, but changes as a consequence of redistribution by ice flow, melt-out of englacial debris or redistribution by gravitational mass movements, to name a few out of a list of processes. To date, the dynamics of debris-covered glaciers, i.e. interaction of glacier mass balance rate, ice flow and dynamic debris evolution, are not fully understood and a comprehensive and unified treatment within modelling approaches is still missing.
In this thesis, some of the open questions regarding the model representation of debris-covered glaciers are tackled and the fundamental feedback processes are critically scrutinized. In the first part, a numerical model for the computation of englacial debris transport is presented, where debris concentration is modelled using an advection equation including a full-Stokes representation of ice flow. In this manner, the location as well as rate of debris emergence to the glacier surface can be computed for a wide range of potential debris inputs, from spatially confined to widely spread, from continuous to infrequent or instantaneous. In order to be able to benefit from this detailed information to derive supraglacial debris cover evolution with time, also a high level of detail is required in the representation of the free-surface evolution of the glacier geometry itself. For this purpose, in the second part, a numerical model for the simulation of glacier geometry change due to ice flow and surface mass balance rate, directly accounting for the constraint of bedrock elevation on surface elevation is presented. This tool also provides the option to use different spatial stabilisation schemes as well as time discretizations in order to identify the best working setup for the desired application. To complement the presentation of these modelling tools, in the third part of this thesis, a more conceptual perspective is employed to study how the glacier-climate relationship is affected by the presence of debris within the glacier system. This is done by examining the fundamental processes that lead to a change in debris cover characteristics for a simple 2D glacier long profile and how this will affect a glacier’s response also to a prescribed constant climate. This part concludes with a review on existing modelling approaches highlighting remaining research issues.