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A simple parametrization of mélange buttressing for calving glaciers
Both ice sheets in Greenland and Antarctica are discharging ice into the ocean. In many regions along the coast of the ice sheets, the icebergs calve into a bay. If the addition of icebergs through calving is faster than their transport out of the embayment, the icebergs will be frozen into a mélange with surrounding sea ice in winter. In this case, the buttressing effect of the ice mélange can be considerably stronger than any buttressing by mere sea ice would be. This in turn stabilizes the glacier terminus and leads to a reduction in calving rates. Here we propose a simple parametrization of ice mélange buttressing which leads to an upper bound on calving rates and can be used in numerical and analytical modelling.
Glacial-cycle simulations of the Antarctic Ice Sheet with the Parallel Ice Sheet Model (PISM) – Part 2: Parameter ensemble analysis
The Parallel Ice Sheet Model (PISM) is applied to the Antarctic Ice Sheet over the last two glacial cycles (≈210 000 years) with a resolution of 16 km. An ensemble of 256 model runs is analyzed in which four relevant model parameters have been systematically varied using full-factorial parameter sampling. Parameters and plausible parameter ranges have been identified in a companion paper (Albrecht et al., 2020) and are associated with ice dynamics, climatic forcing, basal sliding and bed deformation and represent distinct classes of model uncertainties. The model is scored against both modern and geologic data, including reconstructed grounding-line locations, elevation–age data, ice thickness, surface velocities and uplift rates. An aggregated score is computed for each ensemble member that measures the overall model–data misfit, including measurement uncertainty in terms of a Gaussian error model (Briggs and Tarasov, 2013). The statistical method used to analyze the ensemble simulation results follows closely the simple averaging method described in Pollard et al. (2016). This analysis reveals clusters of best-fit parameter combinations, and hence a likely range of relevant model and boundary parameters, rather than individual best-fit parameters. The ensemble of reconstructed histories of Antarctic Ice Sheet volumes provides a score-weighted likely range of sea-level contributions since the Last Glacial Maximum (LGM) of 9.4±4.1 m (or 6.5±2.0×106km3 ), which is at the upper range of most previous studies. The last deglaciation occurs in all ensemble simulations after around 12 000 years before present and hence after the meltwater pulse 1A (MWP1a). Our ensemble analysis also provides an estimate of parametric uncertainty bounds for the present-day state that can be used for PISM projections of future sea-level contributions from the Antarctic Ice Sheet.
Sensitivity of ice loss to uncertainty in flow law parameters in an idealized one-dimensional geometry
Acceleration of the flow of ice drives mass losses in both the Antarctic and the Greenland Ice Sheet. The projections of possible future sea-level rise rely on numerical ice-sheet models, which solve the physics of ice flow, melt, and calving. While major advancements have been made by the ice-sheet modeling community in addressing several of the related uncertainties, the flow law, which is at the center of most process-based ice-sheet models, is not in the focus of the current scientific debate. However, recent studies show that the flow law parameters are highly uncertain and might be different from the widely accepted standard values. Here, we use an idealized flow-line setup to investigate how these uncertainties in the flow law translate into uncertainties in flow-driven mass loss. In order to disentangle the effect of future warming on the ice flow from other effects, we perform a suite of experiments with the Parallel Ice Sheet Model (PISM), deliberately excluding changes in the surface mass balance. We find that changes in the flow parameters within the observed range can lead up to a doubling of the flow-driven mass loss within the first centuries of warming, compared to standard parameters. The spread of ice loss due to the uncertainty in flow parameters is on the same order of magnitude as the increase in mass loss due to surface warming. While this study focuses on an idealized flow-line geometry, it is likely that this uncertainty carries over to realistic three-dimensional simulations of Greenland and Antarctica.
The role of history and strength of the oceanic forcing in sea level projections from Antarctica with the Parallel Ice Sheet Model
Mass loss from the Antarctic Ice Sheet constitutes the largest uncertainty in projections of future sea level rise. Ocean-driven melting underneath the floating ice shelves and subsequent acceleration of the inland ice streams are the major reasons for currently observed mass loss from Antarctica and are expected to become more important in the future. Here we show that for projections of future mass loss from the Antarctic Ice Sheet, it is essential (1) to better constrain the sensitivity of sub-shelf melt rates to ocean warming and (2) to include the historic trajectory of the ice sheet. In particular, we find that while the ice sheet response in simulations using the Parallel Ice Sheet Model is comparable to the median response of models in three Antarctic Ice Sheet Intercomparison projects – initMIP, LARMIP-2 and ISMIP6 – conducted with a range of ice sheet models, the projected 21st century sea level contribution differs significantly depending on these two factors. For the highest emission scenario RCP8.5, this leads to projected ice loss ranging from 1.4 to 4.0 cm of sea level equivalent in simulations in which ISMIP6 ocean forcing drives the PICO ocean box model where parameter tuning leads to a comparably low sub-shelf melt sensitivity and in which no surface forcing is applied. This is opposed to a likely range of 9.1 to 35.8 cm using the exact same initial setup, but emulated from the LARMIP-2 experiments with a higher melt sensitivity, even though both projects use forcing from climate models and melt rates are calibrated with previous oceanographic studies. Furthermore, using two initial states, one with a previous historic simulation from 1850 to 2014 and one starting from a steady state, we show that while differences between the ice sheet configurations in 2015 seem marginal at first sight, the historic simulation increases the susceptibility of the ice sheet to ocean warming, thereby increasing mass loss from 2015 to 2100 by 5 % to 50 %. Hindcasting past ice sheet changes with numerical models would thus provide valuable tools to better constrain projections. Our results emphasize that the uncertainty that arises from the forcing is of the same order of magnitude as the ice dynamic response for future sea level projections.
Glacial-cycle simulations of the Antarctic Ice Sheet with the Parallel Ice Sheet Model (PISM) – Part 1: Boundary conditions and climatic forcing
Simulations of the glacial–interglacial history of the Antarctic Ice Sheet provide insights into dynamic threshold behavior and estimates of the ice sheet's contributions to global sea-level changes for the past, present and future. However, boundary conditions are weakly constrained, in particular at the interface of the ice sheet and the bedrock. Also climatic forcing covering the last glacial cycles is uncertain, as it is based on sparse proxy data. We use the Parallel Ice Sheet Model (PISM) to investigate the dynamic effects of different choices of input data, e.g., for modern basal heat flux or reconstructions of past changes of sea level and surface temperature. As computational resources are limited, glacial-cycle simulations are performed using a comparably coarse model grid of 16 km and various parameterizations, e.g., for basal sliding, iceberg calving, or for past variations in precipitation and ocean temperatures. In this study we evaluate the model's transient sensitivity to corresponding parameter choices and to different boundary conditions over the last two glacial cycles and provide estimates of involved uncertainties. We also discuss isolated and combined effects of climate and sea-level forcing. Hence, this study serves as a “cookbook” for the growing community of PISM users and paleo-ice sheet modelers in general. For each of the different model uncertainties with regard to climatic forcing, ice and Earth dynamics, and basal processes, we select one representative model parameter that captures relevant uncertainties and motivates corresponding parameter ranges that bound the observed ice volume at present. The four selected parameters are systematically varied in a parameter ensemble analysis, which is described in a companion paper.