The aim of the paper is to establish optimal stability estimates for the determination of sound-hard polyhedral scatterers by a minimal number of far-field measurements. This work is a significant and highly nontrivial extension of the stability estimates for the determination of sound-soft polyhedral scatterers by far-field measurements, proved by one of the authors, to the much more challenging sound-hard case.\ud The admissible polyhedral scatterers satisfy minimal apriori assumptions of Lipschitz type and may include at the same time solid obstacles and screen-type components. In this case we obtain a stability estimate with N far-field measurements, N being the space dimension. Important features of such an estimate are that we have an explicit dependence on the parameter h representing the minimal size of the cells forming the boundaries of the admissible polyhedral scatterers, and that the modulus of continuity, provided the error is small enough with respect to h, does not depend on h. If we restrict to N=2,3 and to polyhedral obstacles, that is to polyhedra, then we obtain stability estimates with fewer measurements, namely first with N-1 measurements and then with a single measurement. In this case the dependence on h is not explicit anymore and the modulus of continuity depends on h as well

The Greenland Ice Sheet (GrIS) mass balance is examined with an Earth system/ice sheet model that interactively couples the GrIS to the broader Earth system. The simulation runs from 1850 to 2100, with historical and SSP5-8.5 forcing. By the mid-21st century, the cumulative GrIS contribution to global mean sea level rise (SLR) is 23 mm. During the second half of the 21st century, the surface mass balance becomes negative in all drainage basins, with an additional SLR contribution of 86 mm. The annual mean GrIS mass loss in the last two decades is 2.7-mm sea level equivalent (SLE) year −1 . The increased SLR contribution from the surface mass balance (3.1 mm SLE year −1 ) is partly offset by reduced ice discharge from thinning and retreat of outlet glaciers. The southern GrIS drainage basins contribute 73% of the mass loss in mid-century but 55% by 2100, as surface runoff increases in the northern basins. Plain Language SummaryThe Greenland Ice Sheet (GrIS) gains mass at the surface from snowfall, and it loses mass from melting and runoff and from glacier calving at the ocean front. When these processes are in balance, the ice sheet does not contribute to global sea level change. Recent observations have shown that the ice sheet is losing mass and raising global mean sea level.This study uses a global Earth system model that calculates ice flow of the GrIS, as well as processes in the atmosphere, ocean, land, and sea ice. For a modern reference, the model is forced with atmospheric greenhouse gas concentrations for the period 1850-2014. Next, the model is forced for the rest of the 21st century following the SSP5-8.5 scenario to study how the GrIS and the Earth system respond to a worst-case scenario.By 2050, the GrIS loses mass that is equal to 23 mm of global mean sea level rise. During the second half of the 21st century, all regions of the GrIS lose mass because of increased surface melting and runoff, with the dry north playing a greater role. By 2100, the projected GrIS contribution to sea level rise is 109-mm sea level equivalent.

The Greenland Ice Sheet (GrIS) mass balance is examined with an Earth system/ice sheet model that interactively couples the GrIS to the broader Earth system. The simulation runs from 1850 to 2100, with historical and SSP5-8.5 forcing. By the mid-21st century, the cumulative GrIS contribution to global mean sea level rise (SLR) is 23 mm. During the second half of the 21st century, the surface mass balance becomes negative in all drainage basins, with an additional SLR contribution of 86 mm. The annual mean GrIS mass loss in the last two decades is 2.7-mm sea level equivalent (SLE) year −1 . The increased SLR contribution from the surface mass balance (3.1 mm SLE year −1 ) is partly offset by reduced ice discharge from thinning and retreat of outlet glaciers. The southern GrIS drainage basins contribute 73% of the mass loss in mid-century but 55% by 2100, as surface runoff increases in the northern basins. Plain Language SummaryThe Greenland Ice Sheet (GrIS) gains mass at the surface from snowfall, and it loses mass from melting and runoff and from glacier calving at the ocean front. When these processes are in balance, the ice sheet does not contribute to global sea level change. Recent observations have shown that the ice sheet is losing mass and raising global mean sea level.This study uses a global Earth system model that calculates ice flow of the GrIS, as well as processes in the atmosphere, ocean, land, and sea ice. For a modern reference, the model is forced with atmospheric greenhouse gas concentrations for the period 1850-2014. Next, the model is forced for the rest of the 21st century following the SSP5-8.5 scenario to study how the GrIS and the Earth system respond to a worst-case scenario.By 2050, the GrIS loses mass that is equal to 23 mm of global mean sea level rise. During the second half of the 21st century, all regions of the GrIS lose mass because of increased surface melting and runoff, with the dry north playing a greater role. By 2100, the projected GrIS contribution to sea level rise is 109-mm sea level equivalent.

The Greenland ice sheet (GrIS) is now losing mass at a rate of 0.7 mm of sea level rise (SLR) per year. Here we explore future GrIS evolution and interactions with global and regional climate under high greenhouse gas forcing with the Community Earth System Model version 2.1 (CESM2.1), which includes an interactive ice sheet component (the Community Ice Sheet Model v2.1 [CISM2.1]) and an advanced energy balance-based calculation of surface melt. We run an idealized 350-year scenario in which atmospheric CO 2 concentration increases by 1% annually until reaching four times pre-industrial values at year 140, after which it is held fixed. The global mean temperature increases by 5.2 and 8.5 K by years 131-150 and 331-350, respectively. The projected GrIS contribution to global mean SLR is 107 mm by year 150 and 1,140 mm by year 350. The rate of SLR increases from 2 mm yr −1 at year 150 to almost 7 mm yr −1 by year 350. The accelerated mass loss is caused by rapidly increasing surface melt as the ablation area expands, with associated albedo feedback and increased sensible and latent heat fluxes. This acceleration occurs for a global warming of approximately 4.2 K with respect to pre-industrial and is in part explained by the quasi-parabolic shape of the ice sheet, which favors rapid expansion of the ablation area as it approaches the interior "plateau."Plain Language Summary Observations show that the Greenland ice sheet (GrIS) has been losing mass at an accelerating rate over the last few decades and is currently one of the main contributors to global sea level rise. To understand the causes of GrIS mass loss, we must consider the Earth system as a whole. This study uses an Earth system model with an interactive GrIS model to explore (1) the extent to which the GrIS responds to warming and (2) the main processes that govern this response. The model is forced with an idealized greenhouse gas scenario in which the atmospheric CO 2 concentration increases by 1% per year until reaching four times the pre-industrial level; the CO 2 concentration is then kept constant for another two centuries. The GrIS responds nonlinearly to climate warming. The GrIS contributes about 100 mm of sea level rise by year 150, when CO 2 is stabilized and the global mean temperature has increased by 5.2 K. By year 350, when global warming has increased to 8.5 K, the GrIS contributes more than 1 m of additional sea level rise. The accelerated mass loss is mostly driven by summertime warming and increased melting of a darkening ice surface.

The Greenland ice sheet (GrIS) is now losing mass at a rate of 0.7 mm of sea level rise (SLR) per year. Here we explore future GrIS evolution and interactions with global and regional climate under high greenhouse gas forcing with the Community Earth System Model version 2.1 (CESM2.1), which includes an interactive ice sheet component (the Community Ice Sheet Model v2.1 [CISM2.1]) and an advanced energy balance-based calculation of surface melt. We run an idealized 350-year scenario in which atmospheric CO 2 concentration increases by 1% annually until reaching four times pre-industrial values at year 140, after which it is held fixed. The global mean temperature increases by 5.2 and 8.5 K by years 131-150 and 331-350, respectively. The projected GrIS contribution to global mean SLR is 107 mm by year 150 and 1,140 mm by year 350. The rate of SLR increases from 2 mm yr −1 at year 150 to almost 7 mm yr −1 by year 350. The accelerated mass loss is caused by rapidly increasing surface melt as the ablation area expands, with associated albedo feedback and increased sensible and latent heat fluxes. This acceleration occurs for a global warming of approximately 4.2 K with respect to pre-industrial and is in part explained by the quasi-parabolic shape of the ice sheet, which favors rapid expansion of the ablation area as it approaches the interior "plateau." Plain Language Summary Observations show that the Greenland ice sheet (GrIS) has been losing mass at an accelerating rate over the last few decades and is currently one of the main contributors to global sea level rise. To understand the causes of GrIS mass loss, we must consider the Earth system as a whole. This study uses an Earth system model with an interactive GrIS model to explore (1) the extent to which the GrIS responds to warming and (2) the main processes that govern this response. The model is forced with an idealized greenhouse gas scenario in which the atmospheric CO 2 concentration increases by 1% per year until reaching four times the pre-industrial level; the CO 2 concentration is then kept constant for another two centuries. The GrIS responds nonlinearly to climate warming. The GrIS contributes about 100 mm of sea level rise by year 150, when CO 2 is stabilized and the global mean temperature has increased by 5.2 K. By year 350, when global warming has increased to 8.5 K, the GrIS contributes more than 1 m of additional sea level rise. The accelerated mass loss is mostly driven by summertime warming and increased melting of a darkening ice surface.