A comparison of the stability and performance of depth-integrated ice-dynamics solvers

In the last decade, the number of ice-sheet models has increased substantially, in line with the growth of the glaciological community. These models use solvers based on different approximations of ice dynamics. In particular, several depth-integrated dynamics solvers have emerged as fast solvers capable of resolving the relevant physics of ice sheets at the continental scale. However, the numerical stability of these schemes has not been studied systematically to evaluate their effectiveness in practice. Here we focus on three such solvers, the so-called Hybrid, L1L2-SIA and DIVA solvers, as well as the well-known SIA and SSA solvers as boundary cases. We investigate the numerical stability of these solvers as a function of grid resolution and the state of the ice sheet for an explicit time discretization scheme of the mass conservation step. Under simplified conditions with constant viscosity, the maximum stable time step of the Hybrid solver, like the SIA solver, has a quadratic dependence on grid resolution. In contrast, the DIVA solver has a maximum time step that is independent of resolution as the grid becomes increasingly refined, like the SSA solver. A simple 1D implementation of the L1L2-SIA solver indicates that it should behave similarly, but in practice, the complexity of its implementation appears to restrict its stability. In realistic simulations of the Greenland Ice Sheet with a nonlinear rheology, the DIVA and SSA solvers maintain superior numerical stability, while the SIA, Hybrid and L1L2-SIA solvers show markedly poorer performance. At a grid resolution of Delta x = 4 km, the DIVA solver runs approximately 20 times faster than the Hybrid and L1L2-SIA solvers as a result of a larger stable time step. Our analysis shows that as resolution increases, the ice-dynamics solver can act as a bottleneck to model performance. The DIVA solver emerges as a clear outlier in terms of both model performance and its representation of the ice-flow physics itself

An Investigation of a Method for the Analysis of Smokes According to Particle Size

An electrical precipitation method for the analysis of smokes according to particle size has been investigated. A thin stream of smoke particles moving under laminar conditions in a wind tunnel of rectangular cross section is electrically charged in a small region. The charged particles are then precipitated by the uniform field existing between the charged upper plate and the grounded lower plate of the wind tunnel as a long track along the lower plate. The size-frequency distributions of the particles precipitated at various points on the lower plate were determined from measurements on enlargements of electron-microscope photographs of samples of the smoke precipitated at various points. The agreement between theory and experiment is fair, but the range of sizes of the particles precipitated at a given point is rather large

Exploring the ability of the variable-resolution Community Earth System Model to simulate cryospheric–hydrological variables in High Mountain Asia

Earth system models (ESMs) can help to improve the understanding of climate-induced cryospheric–hydrological impacts in complex mountain regions, such as High Mountain Asia (HMA). Coarse ESM grids, however, have difficulties in representing cryospheric–hydrological processes that vary over short distances in complex mountainous environments. Variable-resolution (VR) ESMs can help to overcome these limitations through targeted grid refinement. This study investigates the ability of the VR Community Earth System Model (VR-CESM) to simulate cryospheric–hydrological variables such as the glacier surface mass balance (SMB) over HMA. To this end, a new VR grid is generated, with a regional grid refinement up to 7 km over HMA. Two coupled atmosphere–land simulations are run for the period 1979–1998. The second simulation is performed with an updated glacier cover dataset and includes snow and glacier model modifications. Comparisons are made to gridded outputs derived from a globally uniform 1∘ CESM grid, observation-, reanalysis-, and satellite-based datasets, and a glacier model forced by a regional climate model (RCM). Climatological biases are generally reduced compared to the coarse-resolution CESM grid, but the glacier SMB is too negative relative to observation-based glaciological and geodetic mass balances, as well as the RCM-forced glacier model output. In the second simulation, the SMB is improved but is still underestimated due to cloud cover and temperature biases, missing model physics, and incomplete land–atmosphere coupling. The outcomes suggest that VR-CESM could be a useful tool to simulate cryospheric–hydrological variables and to study climate change in mountainous environments, but further developments are needed to better simulate the SMB of mountain glaciers

Compensating errors in inversions for subglacial bed roughness: same steady state, different dynamic response

Subglacial bed roughness is one of the main factors controlling the rate of future Antarctic ice-sheet retreat and also one of the most uncertain. A common technique to constrain the bed roughness using ice-sheet models is basal inversion, tuning the roughness to reproduce the observed present-day ice-sheet geometry and/or surface velocity. However, many other factors affecting ice-sheet evolution, such as the englacial temperature and viscosity, the surface and basal mass balance, and the subglacial topography, also contain substantial uncertainties. Using a basal inversion technique intrinsically causes any errors in these other quantities to lead to compensating errors in the inverted bed roughness. Using a set of idealised-geometry experiments, we quantify these compensating errors and investigate their effect on the dynamic response of the ice sheet to a prescribed forcing. We find that relatively small errors in ice viscosity and subglacial topography require substantial compensating errors in the bed roughness in order to produce the same steady-state ice sheet, obscuring the realistic spatial variability in the bed roughness. When subjected to a retreat-inducing forcing, we find that these different parameter combinations, which per definition of the inversion procedure result in the same steady-state geometry, lead to a rate of ice volume loss that can differ by as much as a factor of 2. This implies that ice-sheet models that use basal inversion to initialise their model state can still display a substantial model bias despite having an initial state which is close to the observations

Surface mass balance downscaling through elevation classes in an Earth system model: application to the Greenland ice sheet

The modeling of ice sheets in Earth system models (ESMs) is an active area of research with applications to future sea level rise projections and paleoclimate studies. A major challenge for surface mass balance (SMB) modeling with ESMs arises from their coarse resolution. This paper evaluates the elevation class (EC) method as an SMB downscaling alternative to the dynamical downscaling of regional climate models. To this end, we compare EC-simulated elevation-dependent surface energy and mass balance gradients from the Community Earth System Model 1.0 (CESM1.0) with those from the regional climate model RACMO2.3. The EC implementation in CESM1.0 combines prognostic snow albedo, a multilayer snow model, and elevation corrections for two atmospheric forcing variables: temperature and humidity. Despite making no corrections for incoming radiation and precipitation, we find that the EC method in CESM1.0 yields similar SMB gradients to RACMO2.3, in part due to compensating biases in snowfall, surface melt, and refreezing gradients. We discuss the sensitivity of the results to the lapse rate used for the temperature correction. We also evaluate the impact of the EC method on the climate simulated by the ESM and find minor cooling over the Greenland ice sheet and Barents and Greenland seas, which compensates for a warm bias in the ESM due to topographic smoothing. Based on our diagnostic procedure to evaluate the EC method, we make several recommendations for future implementations. </div

Remapping of Greenland ice sheet surface mass balance anomalies for large ensemble sea-level change projections

Future sea-level change projections with process-based stand-alone ice sheet models are typically driven with surface mass balance (SMB) forcing derived from climate models. In this work we address the problems arising from a mismatch of the modelled ice sheet geometry with the geometry used by the climate model. We present a method for applying SMB forcing from climate models to a wide range of Greenland ice sheet models with varying and temporally evolving geometries. In order to achieve that, we translate a given SMB anomaly field as a function of absolute location to a function of surface elevation for 25 regional drainage basins, which can then be applied to different modelled ice sheet geometries. The key feature of the approach is the non-locality of this remapping process. The method reproduces the original forcing data closely when remapped to the original geometry. When remapped to different modelled geometries it produces a physically meaningful forcing with smooth and continuous SMB anomalies across basin divides. The method considerably reduces non-physical biases that would arise by applying the SMB anomaly derived for the climate model geometry directly to a large range of modelled ice sheet model geometries