Consistent comparison of full-Stokes and higher-order approximation in the central North East Greenland Ice Stream

Modelling ice sheet flow is at best modelled using the full-Stokes (FS) equations. However, it rarely sees application even in recent years due to its high computational demand and problems in numerical convergence due to the thin aspect ratio of ice sheets. For this reason, the modelling community has relied on simplified mathematical models, such as the three-dimensional Higher-Order (HO) approximation which neglects horizontal gradients of vertical velocities and bridging effects. Here, we conduct an analysis of the difference in stresses and velocity fields solving the FS system of equation and using two different types of HO approximations equivalent to LMLa (known as Blatter-Pattyn type) and LTSML according to Hindmarsh (2004). Our intention was to avoid any bias from a difference in discretization or implementation, therefore we implemented it in a single ice sheet model to avoid effects arising from discretization and implementation. We selected a subset of the North East Greenland Ice Stream (NEGIS) as investigation area. As differences between FS and HO emerge in regions with steep bedrock gradients or high aspect ratios, we step-wise increase spatial resolution from 12.8 km down to 0.1 km. Our analysis reveals that surface velocity differences between the FS and HO solution emerge below 1km horizontal resolution and increase with resolution. Compared to the absolute ice flow velocity, the relative error between FS and HO remains small. We present an in-depth analysis, that reveals that different factors are affected by the approximation, such as basal drag and rheology

References:
Hindmarsh, R. C. A.: A numerical comparison of approximations to the Stokes equations used in ice sheet and glacier modeling, Journal of Geophysical Research: Earth Surface, 109, https://doi.org/10.1029/2003JF000065, 2004