Knowledge of the ice thickness distribution of glaciers and ice caps is an important prerequisite for many glaciological and hydrological investigations. A wealth of approaches has recently been presented for inferring ice thickness from characteristics of the surface. With the Ice Thickness Models Intercomparison eXperiment (ITMIX) we performed the first coordinated assessment quantifying individual model performance. A set of 17 different models showed that individual ice thickness estimates can differ considerably – locally by a spread comparable to the observed thickness. Averaging the results of multiple models, however, significantly improved the results: on average over the 21 considered test cases, comparison against direct ice thickness measurements revealed deviations on the order of 10 ± 24 % of the mean ice thickness (1σ estimate). Models relying on multiple data sets – such as surface ice velocity fields, surface mass balance, or rates of ice thickness change – showed high sensitivity to input data quality. Together with the requirement of being able to handle large regions in an automated fashion, the capacity of better accounting for uncertainties in the input data will be a key for an improved next generation of ice thickness estimation approaches.

We describe and test a two-horizontal-dimension subglacial hydrology model which combines till with a distributed system of water-filled, linked cavities which open through sliding and close through ice creep. The addition of this sub-model to the Parallel Ice Sheet Model (PISM) accomplishes three specific goals: (a) conservation of the mass of water, (b) simulation of spatially and temporally variable basal shear stress from physical mechanisms based on a minimal number of free parameters, and (c) convergence under grid refinement. The model is a common generalization of four others: (i) the undrained plastic bed model of Tulaczyk et al. (2000b), (ii) a standard "routing" model used for identifying locations of subglacial lakes, (iii) the lumped englacial–subglacial model of Bartholomaus et al. (2011), and (iv) the elliptic-pressure-equation model of Schoof et al. (2012). We preserve physical bounds on the pressure. In steady state a functional relationship between water amount and pressure emerges. We construct an exact solution of the coupled, steady equations and use it for verification of our explicit time stepping, parallel numerical implementation. We demonstrate the model at scale by 5 year simulations of the entire Greenland ice sheet at 2 km horizontal resolution, with one million nodes in the hydrology grid.

The climate in Svalbard is undergoing amplified change compared to the global mean. This has major implications for runoff from glaciers and seasonal snow on land. We use a coupled energy balance–subsurface model, forced with downscaled regional climate model fields, and apply it to both glacier-covered and land areas in Svalbard. This generates a long-term (1957–2018) distributed dataset of climatic mass balance (CMB) for the glaciers, snow conditions, and runoff with a 1 km×1 km spatial and 3-hourly temporal resolution. Observational data including stake measurements, automatic weather station data, and subsurface data across Svalbard are used for model calibration and validation. We find a weakly positive mean net CMB (+0.09 m w.e. a⁻¹) over the simulation period, which only fractionally compensates for mass loss through calving. Pronounced warming and a small precipitation increase lead to a spatial-mean negative net CMB trend (−0.06 m w.e. a⁻¹ decade⁻¹), and an increase in the equilibrium line altitude (ELA) by 17 m decade⁻¹, with the largest changes in southern and central Svalbard. The retreating ELA in turn causes firn air volume to decrease by 4 % decade⁻¹, which in combination with winter warming induces a substantial reduction of refreezing in both glacier-covered and land areas (average −4 % decade⁻¹). A combination of increased melt and reduced refreezing causes glacier runoff (average 34.3 Gt a⁻¹) to double over the simulation period, while discharge from land (average 10.6 Gt a⁻¹) remains nearly unchanged. As a result, the relative contribution of land runoff to total runoff drops from 30 % to 20 % during 1957–2018. Seasonal snow on land and in glacier ablation zones is found to arrive later in autumn (+1.4 d decade⁻¹), while no significant changes occurred on the date of snow disappearance in spring–summer. Altogether, the output of the simulation provides an extensive dataset that may be of use in a wide range of applications ranging from runoff modelling to ecosystem studies.

Since the first estimates of Svalbard-wide glacier mass balance were made in the early 2000s, there has been great progress in remote sensing and modelling of mass balance, existing field records have been extended, field records at new locations have been added, and there has been considerable environmental change. There is a wide spread in the available estimates of both total mass balance and climatic mass balance, but there is overall agreement that the glaciers on Svalbard have been losing mass since the 1960s, with a tendency towards more negative mass balance since 2000. We define criteria to select data that are representative and of high credibility; this subset shows a more coherent evolution and reduced spread. In addition, we combine individual field mass balance records collected by different groups into a single dataset that samples glaciers across Svalbard and a range of different size classes. We find a close relationship between measured glacier mass balance and size of the glacier, in such a way that smaller glaciers experience more negative climatic mass balances. A qualitatively similar relationship between the accumulation area ratio and glacier area is found for all glaciers in the Svalbard, suggesting that the relation derived from glaciological records is not only an artefact caused by the limited number of samples (n=12). We apply this relation to upscale measured climatic mass balance for a new estimate for all glaciers of Svalbard. Our reconciled estimates are for the climatic mass balance -7 ± 2 Gt a-1 (2000-2019) and a total mass balance of -8 ± 6 Gt a-1. From the difference and the related uncertainty, we derive an estimate of frontal ablation amounting to ca. 5-10 Gt a-1. While this is similar to a previous estimate of Svalbard-wide frontal ablation, the uncertainties are large. Furthermore, several large and long-lasting surges have had considerable and multi-year impact on the total mass balance, and in particular on calving rates, emphasizing the need for better-resolved and more frequently updated estimates of frontal ablation.

A distributed energy balance model is coupled to a multi-layer snow model in order to study the mass balance evolution and the impact of refreezing on the mass budget of Nordenskiöldbreen, Svalbard. The model is forced with output from the regional climate model RACMO and meteorological data from Svalbard Airport. Extensive calibration and initialisation are performed to increase the model accuracy. For the period 1989–2010, we find a mean net mass balance of −0.39 m w.e. a⁻¹. Refreezing contributes on average 0.27 m w.e. a⁻¹ to the mass budget and is most pronounced in the accumulation zone. The simulated mass balance, radiative fluxes and subsurface profiles are validated against observations and are generally in good agreement. Climate sensitivity experiments reveal a non-linear, seasonally dependent response of the mass balance, refreezing and runoff to changes in temperature and precipitation. It is shown that including seasonality in climate change, with less pronounced summer warming, reduces the sensitivity of the mass balance and equilibrium line altitude (ELA) estimates in a future climate. The amount of refreezing is shown to be rather insensitive to changes in climate.