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A parameterization for the motion of ice-shelf fronts on a Cartesian grid in finite-difference land-ice models is presented. The scheme prevents artificial thinning of the ice shelf at its edge, which occurs due to the finite resolution of the model. The intuitive numerical implementation diminishes numerical dispersion at the ice front and enables the application of physical boundary conditions to improve the calculation of stress and velocity fields throughout the ice-sheet-shelf system. Numerical properties of this subgrid modification are assessed in the Potsdam Parallel Ice Sheet Model (PISM-PIK) for different geometries in one and two horizontal dimensions and are verified against an analytical solution in a flow-line setup.
Glacial-cycle simulations of the Antarctic Ice Sheet with the Parallel Ice Sheet Model (PISM)
(2020)
The Parallel Ice Sheet Model (PISM) is applied to the Antarctic Ice Sheet over the last two glacial cycles (approximate to 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 +/- 4.1m (or 6.5 +/- 2.0 x 10(6) km(3)), 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.
Glacial-cycle simulations of the Antarctic Ice Sheet with the Parallel Ice Sheet Model (PISM)
(2020)
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. <br /> 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. <br /> 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.
Higher resilience to climatic disturbances in tropical vegetation exposed to more variable rainfall
(2019)
With ongoing global warming, the amount and frequency of precipitation in the tropics is projected to change substantially. While it has been shown that tropical forests and savannahs are sustained within the same intermediate mean annual precipitation range, the mechanisms that lead to the resilience of these ecosystems are still not fully understood. In particular, the long-term impact of rainfall variability on resilience is as yet unclear. Here we present observational evidence that both tropical forest and savannah exposed to a higher rainfall variability-in particular on interannual scales-during their long-term past are overall more resilient against climatic disturbances. Based on precipitation and tree cover data in the Brazilian Amazon basin, we constructed potential landscapes that enable us to systematically measure the resilience of the different ecosystems. Additionally, we infer that shifts from forest to savannah due to decreasing precipitation in the future are more likely to occur in regions with a precursory lower rainfall variability. Long-term rainfall variability thus needs to be taken into account in resilience analyses and projections of vegetation response to climate change.
Droughts in tropical South America have an imminent and severe impact on the Amazon rainforest and affect the livelihoods of millions of people. Extremely dry conditions in Amazonia have been previously linked to sea surface temperature (SST) anomalies in the adjacent tropical oceans. Although the sources and impacts of such droughts have been widely studied, establishing reliable multi-year lead statistical forecasts of their occurrence is still an ongoing challenge. Here, we further investigate the relationship between SST and rainfall anomalies using a complex network approach. We identify four ocean regions which exhibit the strongest overall SST correlations with central Amazon rainfall, including two particularly prominent regions in the northern and southern tropical Atlantic. Based on the time-dependent correlation between SST anomalies in these two regions alone, we establish a new early-warning method for droughts in the central Amazon basin and demonstrate its robustness in hindcasting past major drought events with lead-times up to 18 months.
Consequences of twenty-first-century policy for multi-millennial climate
and sea-level change
(2016)
Most of the policy debate surrounding the actions needed to mitigate and adapt to anthropogenic climate change has been framed by observations of the past 150 years as well as climate and sea-level projections for the twenty-first century. The focus on this 250-year window, however, obscures some of the most profound problems associated with climate change. Here, we argue that the twentieth and twenty-first centuries, a period during which the overwhelming majority of human-caused carbon emissions are likely to occur, need to be placed into a long-term context that includes the past 20 millennia, when the last Ice Age ended and human civilization developed, and the next ten millennia, over which time the projected impacts of anthropogenic climate change will grow and persist. This long-term perspective illustrates that policy decisions made in the next few years to decades will have profound impacts on global climate, ecosystems and human societies - not just for this century, but for the next ten millennia and beyond.
Basal ice-shelf melting is the key driver of Antarctica's increasing sea-level contribution. In diminishing the buttressing force of the ice shelves that fringe the ice sheet, the melting increases the ice discharge into the ocean.
Here we contrast the influence of basal melting in two different ice-shelf regions on the time-dependent response of an isothermal, inherently buttressed ice-sheet-shelf system. In the idealized numerical simulations, the basal-melt perturbations are applied close to the grounding line in the ice-shelf's (1) ice-stream region, where the ice shelf is fed by the fastest ice masses that stream through the upstream bed trough and (2) shear margins, where the ice flow is slower.
The results show that melting below one or both of the shear margins can cause a decadal to centennial increase in ice discharge that is more than twice as large compared to a similar perturbation in the ice-stream region. We attribute this to the fact that melt-induced ice-shelf thinning in the central grounding-line region is attenuated very effectively by the fast flow of the central ice stream. In contrast, the much slower ice dynamics in the lateral shear margins of the ice shelf facilitate sustained ice-shelf thinning and thereby foster buttressing reduction.
Regardless of the melt location, a higher melt concentration toward the grounding line generally goes along with a stronger response. Our results highlight the vulnerability of outlet glaciers to basal melting in stagnant, buttressing-relevant ice-shelf regions, a mechanism that may gain importance under future global warming.
Projections of changes in Antarctic Ice Sheet (AIS) surface mass balance indicate a negative contribution to sea level because of the expected increase in precipitation due to the higher moisture holding capacity of warmer air(1). Observations over the past decades, however, are unable to constrain the relation between temperature and accumulation changes because both are dominated by strong natural variability(2-5). Here we derive a consistent continental-scale increase in accumulation of approximately 5 +/- 1% K-1, through the assessment of ice-core data (spanning the large temperature change during the last deglaciation, 21,000 to 10,000 years ago), in combination with palaeo-simulations, future projections by 35 general circulation models (GCMs), and one high-resolution future simulation. The ice-core data and modelling results for the last deglaciation agree, showing uniform local sensitivities of similar to 6% K-1. The palaeo-simulation allows for a continental-scale aggregation of accumulation changes reaching 4.3% K-1. Despite the different timescales, these sensitivities agree with the multi-model mean of 6.1 +/- 2.6% K-1 (GCMprojections) and the continental-scale sensitivity of 4.9% K-1 (high-resolution future simulation). Because some of the mass gain of the AIS is offset by dynamical losses induced by accumulation(6,7), we provide a response function allowing projections of sea-level fall in terms of continental-scale accumulation changes that compete with surface melting and dynamical losses induced by other mechanisms(6,8,9).
The past rapid growth of Northern Hemisphere continental ice sheets, which terminated warm and stable climate periods, is generally attributed to reduced summer insolation in boreal latitudes(1-3). Yet such summer insolation is near to its minimum at present(4), and there are no signs of a new ice age(5). This challenges our understanding of the mechanisms driving glacial cycles and our ability to predict the next glacial inception(6). Here we propose a critical functional relationship between boreal summer insolation and global carbon dioxide (CO2) concentration, which explains the beginning of the past eight glacial cycles and might anticipate future periods of glacial inception. Using an ensemble of simulations generated by an Earth system model of intermediate complexity constrained by palaeoclimatic data, we suggest that glacial inception was narrowly missed before the beginning of the Industrial Revolution. The missed inception can be accounted for by the combined effect of relatively high late-Holocene CO2 concentrations and the low orbital eccentricity of the Earth(7). Additionally, our analysis suggests that even in the absence of human perturbations no substantial build-up of ice sheets would occur within the next several thousand years and that the current interglacial would probably last for another 50,000 years. However, moderate anthropogenic cumulative CO2 emissions of 1,000 to 1,500 gigatonnes of carbon will postpone the next glacial inception by at least 100,000 years(8,9). Our simulations demonstrate that under natural conditions alone the Earth system would be expected to remain in the present delicately balanced interglacial climate state, steering clear of both large-scale glaciation of the Northern Hemisphere and its complete deglaciation, for an unusually long time.
More than half of Earth's freshwater resources are held by the Antarctic Ice Sheet, which thus represents by far the largest potential source for global sea-level rise under future warming conditions(1). Its long-term stability determines the fate of our coastal cities and cultural heritage. Feedbacks between ice, atmosphere, ocean, and the solid Earth give rise to potential nonlinearities in its response to temperature changes. So far, we are lacking a comprehensive stability analysis of the Antarctic Ice Sheet for different amounts of global warming. Here we show that the Antarctic Ice Sheet exhibits a multitude of temperature thresholds beyond which ice loss is irreversible. Consistent with palaeodata(2)we find, using the Parallel Ice Sheet Model(3-5), that at global warming levels around 2 degrees Celsius above pre-industrial levels, West Antarctica is committed to long-term partial collapse owing to the marine ice-sheet instability. Between 6 and 9 degrees of warming above pre-industrial levels, the loss of more than 70 per cent of the present-day ice volume is triggered, mainly caused by the surface elevation feedback. At more than 10 degrees of warming above pre-industrial levels, Antarctica is committed to become virtually ice-free. The ice sheet's temperature sensitivity is 1.3 metres of sea-level equivalent per degree of warming up to 2 degrees above pre-industrial levels, almost doubling to 2.4 metres per degree of warming between 2 and 6 degrees and increasing to about 10 metres per degree of warming between 6 and 9 degrees. Each of these thresholds gives rise to hysteresis behaviour: that is, the currently observed ice-sheet configuration is not regained even if temperatures are reversed to present-day levels. In particular, the West Antarctic Ice Sheet does not regrow to its modern extent until temperatures are at least one degree Celsius lower than pre-industrial levels. Our results show that if the Paris Agreement is not met, Antarctica's long-term sea-level contribution will dramatically increase and exceed that of all other sources. <br /> Modelling shows that the Antarctic Ice Sheet exhibits multiple temperature thresholds beyond which ice loss would become irreversible, and once melted, the ice sheet can regain its previous mass only if the climate cools well below pre-industrial temperatures.