Significant land uplift and horizontal motions have been recorded with Global Navigation Satellite Systems (GNSS) in areas such as Alaska, Iceland and the Northern Antarctic Peninsula (NAP) as a result of Glacial Isostatic Adjustment (GIA) due to ice melt after the Little Ice Age. Here, analysis of horizontal displacement rates can be of extra importance, as they are more sensitive to Earth properties in shallower layers than vertical displacement rates. Proper modelling of horizontal displacement rates with dedicated GIA models requires a spherical Earth with compressible rheology. However, in these small areas, the used GIA models are often incompressible using a Cartesian geometry to ease computation and in some cases allow for lateral viscosity changes or more complex rheology. We investigate the validity of modelled horizontal displacement rates using different approximations, that is using spherical or Cartesian Earth structures, and incompressible, material compressible or compressible rheology. Although the lack of self-gravity and sphericity compensate each other in the vertical, this is less the case for the horizontal. For a disc ice sheet with a radius just over 200 km and a thickness of 1000 m, differences due to sphericity are minimal and the modelled horizontal displacement rates of compressible Cartesian models differ from those simulated by a compressible spherical model by 0.63 mm a-1. Thus, compressible Cartesian GIA models can be applied for modelling horizontal displacement rates of small ice sheets like those in Alaska, Iceland and NAP. Unfortunately, the implementation of compressibility in Abaqus that we use here cannot be extended to spherical models as gravity can not be specified for a spherical body. Other modelling approaches are recommended in such cases.

The redistribution of past and present ice and ocean loading on Earth's surface causes solid Earth deformation and geoid changes, known as glacial isostatic adjustment. The deformation is controlled by elastic and viscous material parameters, which are inhomogeneous in the Earth. We present a new viscoelastic solid Earth deformation model in ASPECT (Advanced Solver for Problems in Earth's ConvecTion): a modern, massively parallel, open-source finite element code originally designed to simulate convection in the Earth's mantle. We show the performance of solid Earth deformation in ASPECT and compare solutions to TABOO, a semianalytical code, and Abaqus, a commercial finite element code. The maximum deformation and deformation rates using ASPECT agree within 2.6% for the average percentage difference with TABOO and Abaqus on glacial cycle (∼100 kyr) and contemporary ice melt (∼100 years) timescales. This gives confidence in the performance of our new solid Earth deformation model. We also demonstrate the computational efficiency of using adaptively refined meshes, which is a great advantage for solid Earth deformation modeling. Furthermore, we demonstrate the model performance in the presence of lateral viscosity variations in the upper mantle and report on parallel scalability of the code. This benchmarked code can now be used to investigate regional solid Earth deformation rates from ice age and contemporary ice melt. This is especially interesting for low-viscosity regions in the upper mantle beneath Antarctica and Greenland, where it is not fully understood how ice age and contemporary ice melting contribute to geodetic measurements of solid Earth deformation.

Long-term climate variations have the potential to amplify or dampen (human-induced) trends in temperature. Understanding natural climate variability is therefore of vital importance, especially since the variability itself may change with a changing climate. Here, we quantify the magnitude and other characteristics of interannual to decadal variability in Arctic temperature and their dependence on the climate state. Moreover, we identify the processes responsible for the state dependency of the variations, using five quasi-equilibrium climate simulations of a state-of-the-art global climate model with 0.25, 0.5, 1, 2, and 4 times present-day atmospheric CO₂ forcing. The natural fluctuations in Arctic temperature, including their dependence on the state of the climate, are linked to anomalous atmospheric and oceanic heat transports toward the Arctic. Model results suggest that atmospheric heat transport leads (and also controls) Arctic temperature variations on interannual time scales, whereas oceanic transport is found to govern the fluctuations on decadal time scales. This time-scale transition of atmospheric to oceanic dominance for Arctic temperature variations is most obvious when there is interannual to decadal variability in Arctic sea ice cover. In warm climates (without Arctic sea ice cover), there is no correlation between oceanic transport and surface air temperature on any time scale. In cold climates (with full Arctic sea ice cover), interaction between ocean and atmosphere is limited, leaving poleward atmospheric heat transport to be the primary driver on all time scales (interannual and decadal).