The small ice cap instability in seasonal energy balance models

Results from a two-dimensional energy balance model with a realistic land-ocean distribution show that the small ice cap instability exists in the Southern Hemisphere, but not in the Northern Hemisphere. A series of experiments with a one-dimensional energy balance model with idealized geography are used to study the roles of the seasonal cycle and the land-ocean distribution. The results indicate that the seasonal cycle and land-ocean distribution can influence the strength of the albedo feedback, which is responsible for the small ice cap instability, through two factors: the temperature gradient and the amplitude of the seasonal cycle. The land-ocean distribution in the Southern Hemisphere favors the small ice cap instability, while the land-ocean distribution in the Northern Hemisphere does not. Because of the longitudinal variations of land-ocean distribution in the Northern Hemisphere, the behavior of ice lines in the Northern Hemisphere cannot be simulated and explained by the model with zonally symmetric land-ocean distribution. Model results suggest that the small ice cap instability may be a possible mechanism for the formation of the Antarctic icesheet. The model results cast doubt, however, on the role of the small ice cap instability in Northern Hemisphere glaciations. Offprint requests to: J Huang     

A 3-D model for the Antarctic ice sheet: a sensitivity study on the glacial-interglacial contrast

On the longer climatic time scales, changes in the elevation and extent of the Antarctic ice sheet have an important role in modulating global atmospheric and oceanographic processes, and contribute significantly to world-wide sea levels. In this paper, a 3-D time-dependent thermomechanical model for the entire ice sheet is presented, that is subsequently used to examine the effects of glacial-interglacial shifts in environmental boundary conditions on its geometry. The model takes into account a coupled ice shelf, grounding-line dynamics, basal sliding and isostatic bed adjustment and considers the fully coupled velocity and temperature fields. Ice flow is calculated on a fine mesh (40 km horizontal grid size and 10 layers in the vertical) for grounded and floating ice and a stress transition zone in between at the grounding line, where all stress components contribute in the effective stress in the flow law. There is free interaction between ice sheet and ice shelf, so that the entire geometry is internally generated. A simulation of the present ice sheet reveals that the model is able to yield realistic results. A series of sensitivity experiments are then performed, in which lower temperatures, reduced accumulation rates and lower global sea level stands are imposed, either singly or in combination. By comparing results of pairs of experiments, the effects of each of these environmental changes can be determined. In agreement with glacial-geological evidence, we found that the most pronounced changes show up in the West Antarctic ice sheet configuration. They appear to be essentially controlled by variations in eustatic sea level, whereas typical glacial-interglacial changes in temperature and ice deposition rates tend to balance one another. These findings support the hypothesis that the Antarctic ice sheet basically follows glacial episodes in the northern hemisphere by means of sea-level teleconnections. Grounding occurs more readily in the Weddell sea than in the Ross sea and long time scales appear to be involved: it may take up to 30–40000 years for these continental shelf areas to become completely grounded after an initial stepwise perturbation in boundary conditions. According to these reconstructions, a steady state Antarctic ice sheet may contribute some 16 m to global sea level lowering at maximum glaciation.     

Response of the Antarctic ice sheet to future greenhouse warming

Possible future changes in land ice volume are mentioned frequently as an important aspect of the greenhouse problem. This paper deals with the response of the Antarctic ice sheet and presents a tentative projection of changes in global sea level for the next few hundred years, due to changes in its surface mass balance. We imposed a temperature scenario, in which surface air temperature rises to 4.2° C in the year 2100 AD and is kept constant afterwards. As GCM studies seem to indicate a higher temperature increase in polar latitudes, the response to a more extreme scenario (warming doubled) has also been investigated. The mass balance model, driven by these temperature perturbations, consists of two parts: the accumulation rate is derived from present observed values and is consequently perturbed in proportion to the saturated vapour pressure at the temperature above the inversion layer. The ablation model is based on the degree-day method. It accounts for the daily temperature cycle, uses a different degree-day factor for snow and ice melting and treats refreezing of melt water in a simple way. According to this mass balance model, the amount of accumulation over the entire ice sheet is presently 24.06 × 10¹¹ m³ of ice, and no runoff takes place. A 1°C uniform warming is then calculated to increase the overall mass balance by an amount of 1.43 × 10¹¹ m³ of ice, corresponding to a lowering of global sea level with 0.36 mm/yr. A temperature increase of 5.3°C is needed for the increase in ablation to become more important than the increase in accumulation and the temperature would have to rise by as much as 11.4°C to produce a zero surface mass balance. Imposing the Bellagio-scenario and accumulating changes in mass balance forward in time (static response) would then lower global sea level by 9 cm by 2100 AD. In a subsequent run with a high-resolution 3-D thermomechanic model of the ice sheet, it turns out that the dynamic response of the ice sheet (as compared to the direct effect of the changes in surface mass balance) becomes significant after 100 years or so. Ice-discharge across the grounding-line increases, and eventually leads to grounding-line retreat. This is particularly evident in the extreme case scenario and is important along the Antarctic Peninsula and the overdeepened outlet glaciers along the East Antarctic coast. Grounding-line retreat in the Ross and Ronne-Filchner ice shelves, on the other hand, is small or absent.     

Short‐term volume changes of the Greenland ice sheet in response to doubled CO2 conditions

This paper focuses on the rôle of accumulation and cloudiness changes in the response of the Greenland ice sheet to global warming. Changes in accumulation or cloudiness were often neglected, or coupled to temperature changes. We used model output on temperature, precipitation and cloudiness from a GCM (ECHAM4 T106). The GCM output was used to drive the Greenland model that exists of a vertically averaged ice flow model, coupled to a 1D surface energy balance model that calculates the ablation. Variables are temperature, accumulation and cloudiness. Sensitivity experiments with this model show that changes in accumulation are very important for the ice sheet mass balance, whereas cloudiness is of secondary importance. If the Greenland model is forced by the GCM output, the Greenland model is found to contribute 70% less to sea level rise after 70 years than is indicated by the results presented in the IPCC report. This large discrepancy is mainly due to the fact that the enhanced ablation is strongly compensated by increased accumulation. Comparing the result obtained here with changes in mass balance derived directly from the same general circulation model, indicates a 20% larger contribution to sea level. This increase is due to changes in ice flow, and a different method for the ablation calculation.     

Applying the energy- and water balance model for incorporation of the cryospheric component into a climate model. Part II. Modeled mass balance on the green land ice sheet surface

The Greenland ice sheet is a very important potential source of fresh water inflow to the World Ocean under warming climate conditions. Apparently, it was the same during the Last Interglacial 130-115 thousand years ago. In order to quantify input of the Greenland ice sheet to the rise of the global mean sea level in the past or in the future, we include a surface mass balance model block into the Earth System Model. The computational algorithm is based on the calculation of energy balance on the ice sheet surface. The key tuning parameter of the model is the daily amplitude of air surface temperature. It defines the area and the rate of snow or ice melting. The range of possible values of this parameter is determined during a series of numerical experiments. High sensitivity of meltwater runoff volume to surface air temperature amplitude is revealed.     

Thresholds for irreversible decline of the Greenland ice sheet

The Greenland ice sheet will decline in volume in a warmer climate. If a sufficiently warm climate is maintained for a few thousand years, the ice sheet will be completely melted. This raises the question of whether the decline would be reversible: would the ice sheet regrow if the climate cooled down? To address this question, we conduct a number of experiments using a climate model and a high-resolution ice-sheet model. The experiments are initialised with ice sheet states obtained from various points during its decline as simulated in a high-CO₂ scenario, and they are then forced with a climate simulated for pre-industrial greenhouse gas concentrations, to determine the possible trajectories of subsequent ice sheet evolution. These trajectories are not the reverse of the trajectory during decline. They converge on three different steady states. The original ice-sheet volume can be regained only if the volume has not fallen below a threshold of irreversibility, which lies between 80 and 90% of the original value. Depending on the degree of warming and the sensitivity of the climate and the ice-sheet, this point of no return could be reached within a few hundred years, sooner than CO₂ and global climate could revert to a pre-industrial state, and in that case global sea level rise of at least 1.3 m would be irreversible. An even larger irreversible change to sea level rise of 5 m may occur if ice sheet volume drops below half of its current size. The set of steady states depends on the CO₂ concentration. Since we expect the results to be quantitatively affected by resolution and other aspects of model formulation, we would encourage similar investigations with other models.     

Sensitivity of a Greenland ice sheet model to ice flow and ablation parameters: consequences for the evolution through the last climatic cycle

Sensitivity experiments are conducted to test the influence of poorly known model parameters on the simulation of the Greenland ice sheet by means of a three dimensional numerical model including the mechanical and thermal processes within the ice. Two types of experiments are performed: steady-state climatic conditions and simulations over the last climatic cycle with a climatic forcing derived from the GRIP record. The experiments show that the maximum altitude of the ice sheet depends on the ice flow parameters (deformation and sliding law coefficients, geothermal flux) and that it is low when the ice flow is fast. On the other hand, the maximum altitude is not sensitive to the ablation strength and consequently during the climatic cycle it is driven by changes in accumulation rate. The ice sheet extension shows the opposite sensitivity: it is barely affected by ice flow velocity and the ice covered area is smaller for large ablation coefficients. For colder climates, when there is no ablation, the ice sheet extension depends on the sea level. An interesting result is that the variations with time of the altitude at the ice divide (Summit) do not depend on the parameters we tested. The present modelled ice sheets resulting from the climatic cycle experiments are compared with the present measured ice sheet in order to find the set of parameters that gives the best fit between modelled and measured geometry. It seems that, compared to the parameter set most commonly used, higher ablation rate coefficents must be used. Received: 19 September 1995 / Accepted: 30 May 1996     

Numerical experiments on ice age climates

Numerical experiments with a hemispheric thermodynamic model are carried out, using present and ice age conditions. The computed surface temperatures for 18,000 years ago are in good agreement with the CLIMAP values. It is shown that the snow-ice cap that existed in the summer 18,000 years ago created a feedback mechanism which was responsible for perpetuating these ice age conditions. The increase of insolation due to orbital variations was responsible, at least in part, for the shrinkage of the snow-ice cap from 18,000 to 8,000 years ago. It is shown that the effect on the earth-atmosphere system of the changes in insolation due to the orbital variations depends on the preexisting snow-ice cap. It is significant for the ice cap that existed 18,000 years ago and insignificant for present conditions. The numerical experiments suggest that the evolution of climate depends in an important way on the initial snow-ice conditions. Therefore, according to the model the problem of simulating the evolution of climate is not determined if one does not prescribe these snow-ice conditions. Lamont Doherty Geological Observatory contribution No. 3115. Visiting Senior Research Associate at Lamont Doherty Geological Observatory, Columbia University.     

The initiation of ice sheet growth,Milankovitch solar radiation variations,and the 100 ky ice age cycle

Much work has gone into deciphering the causes of the large scale glacial/interglacial variations in the climate system over the last 900 000 years. While variations on the 41 thousand year (ky) and 23 ky time scales seem to be linearly linked to the variations in the distribution of solar radiation at the top of the atmosphere, Milankovitch solar radiation variations, the causes of the dominant 100 ky cycle in the geologic record are still unknown. One of the aspects of this cycle that is not well understood is how large scale ice sheet growth is initiated. Here we describe the mechanisms by which large scale ice sheet growth may have been initiated by the changes in the seasonal and latitudinal distribution of solar radiation over the past 160 ky. This is done through the use of a coupled energy balance climate-thermodynamic sea ice model that includes a hydrologic cycle which computes precipitation, and a land surface energy balance which determines the net accumulation of snow and ice. Results indicate that the initiation of ice sheet growth is possible during times of extremely low summer solstice solar radiation as a result of a large decrease in ablation during the critical melt season.     

Sensitivity of open-water ice growth and ice concentration evolution in a coupled atmosphere-ocean-sea ice model

A coupled atmosphere-ocean-sea ice model is applied to investigate to what degree the area-thickness distribution of new ice formed in open water affects the ice and ocean properties. Two sensitivity experiments are performed which modify the horizontal-to-vertical aspect ratio of open-water ice growth. The resulting changes in the Arctic sea-ice concentration strongly affect the surface albedo, the ocean heat release to the atmosphere, and the sea-ice production. The changes are further amplified through a positive feedback mechanism among the Arctic sea ice, the Atlantic Meridional Overturning Circulation (AMOC), and the surface air temperature in the Arctic, as the Fram Strait sea ice import influences the freshwater budget in the North Atlantic Ocean. Anomalies in sea-ice transport lead to changes in sea surface properties of the North Atlantic and the strength of AMOC. For the Southern Ocean, the most pronounced change is a warming along the Antarctic Circumpolar Current (ACC), owing to the interhemispheric bipolar seasaw linked to AMOC weakening. Another insight of this study lies on the improvement of our climate model. The ocean component FESOM is a newly developed ocean-sea ice model with an unstructured mesh and multi-resolution. We find that the subpolar sea-ice boundary in the Northern Hemisphere can be improved by tuning the process of open-water ice growth, which strongly influences the sea ice concentration in the marginal ice zone, the North Atlantic circulation, salinity and Arctic sea ice volume. Since the distribution of new ice on open water relies on many uncertain parameters and the knowledge of the detailed processes is currently too crude, it is a challenge to implement the processes realistically into models. Based on our sensitivity experiments, we conclude a pronounced uncertainty related to open-water sea ice growth which could significantly affect the climate system sensitivity.     

针对冰盖的定向地球工程研究

针对冰盖的定向地球工程研究旨在增强冰盖稳定性和减缓冰盖物质流失,从源头上减少冰盖对海平面上升的贡献,有望为应对气候变化和保护海岸线争取几百年的时间。冰盖地球工程主要作用在冰底和冰架-海洋界面上,主要途径如下：(1)排干或冻结冰盖底部水来干燥冰床,增强冰盖底部摩擦力;(2)在海洋中建造人造岛来支撑漂浮的冰架;(3)在冰架前端建造水下隔离墙,阻止温暖的海水到达冰川底部以减缓其融化。冰盖地球工程包括数值模拟、方案设计、工程试验和政治法律等诸多方面的研究。国际上的研究团队正在开展数值模拟和方案设计方面的研究,工程试验和政治法律等方面的研究尚未起步。预计工程试验的难度阶梯很可能是从实验室试验开始,到小尺度的野外试验,接着到格陵兰冰盖的入海冰川,最后到南极冰盖的入海冰川。针对冰盖的定向地球工程研究很有可能成为21世纪全球变化领域新兴的研究方向。     

Small ice cap instability in the presence of fluctuations

Phenomena associated with small ice cap instability (SICI) are investigated using a general circulation model (GCM: NCAR Community Climate Model version 0) and a noise-forced nonlinear energy balance model (EBM). Both make use of idealized boundary conditions consisting of an all-land planet without topography and mean annual insolation. Ice is prescribed to exist on surface areas for which the instantaneous temperature lies below freezing. The adjustable parameters of the EBM were chosen to match the GCM solutions. For the regions in parameter space where SICI might occur we do not find the corresponding icefree steady state solution with the GCM. Our simulations with the EBM show that SICI phenomena in the presence of fluctuations are strongly dependent on the amplitude of the noise forcing. When the strength of noise forcing is adjusted to match the fluctuations in the GCM, we do not find a SICI in the EBM. With weaker levels of forcing the SICI reappears. In all cases steady stable ice caps smaller than a critical size are not found to exist.     

The effect of snow on Antarctic sea ice simulations in a coupled atmosphere-sea ice model

 The effect of a snow cover on sea ice accretion and ablation is estimated based on the ‘zero-layer’ version sea ice model of Semtner, and is examined using a coupled atmosphere-sea ice model including feedbacks and ice dynamics effects. When snow is disregarded in the coupled model the averaged Antarctic sea ice becomes thicker. When only half of the snowfall predicted by the atmospheric model is allowed to land on the ice surface sea ice gets thicker in most of the Weddell and Ross Seas but thinner in East Antarctic in winter, with the average slightly thicker. When twice as much snowfall as predicted by the atmospheric model is assumed to land on the ice surface sea ice also gets much thicker due to the large increase of snow-ice formation. These results indicate the importance of the correct simulation of the snow cover over sea ice and snow-ice formation in the Antarctic. Our results also illustrate the complex feedback effects of the snow cover in global climate models. In this study we have also tested the use of a mean value of 0.16 Wm^-1 K^-1 instead of 0.31 for the thermal conductivity of snow in the coupled model, based on the most recent observations in the eastern Antarctic and Bellingshausen and Amundsen Seas, and have found that the sea ice distribution changes greatly, with the ice becoming much thinner by about 0.2 m in the Antarctic and about 0.4 m in the Arctic on average. This implies that the magnitude of the thermal conductivity of snow is of considerable importance for the simulation of the sea ice distribution. An appropriate value of the thermal conductivity of snow is as crucial as the depth of the snow layer and the snowfall rate in a sea ice model. The coupled climate models require accurate values of the effective thermal conductivity of snow from observations for validating the simulated sea ice distribution under the present climate conditions. Received: 20 November 1997/Accepted: 27 July 1998     

The effect of atmospheric CO2 and ice sheet topography on LGM climate

The role of reduced atmospheric CO₂ concentration and ice sheet topography plus its associated land albedo on the LGM climate is investigated using a coupled atmosphere-ocean-sea ice climate system model. The surface cooling induced by the reduced CO₂ concentration is larger than that by the ice sheet topography plus other factors by about 30% for the surface air temperature and by about 100% for the sea surface temperature. A large inter-hemispheric asymmetry in surface cooling with a larger cooling in the Northern Hemisphere is found for both cases. This asymmetric inter-hemispheric temperature response is consistent in the ice sheet topography case with earlier studies using an atmospheric model coupled with a mixed-layer ocean representation, but contrasts with these results in the reduced CO₂ case. The incorporation of ocean dynamics presumably leads to a larger snow and sea ice feedback as a result of the reduction in northward ocean heat transport, mainly as a consequence of the decrease in the North Atlantic overturning circulation by the substantial freshening of the North Atlantic convection regions. A reversed case is found in the Southern Ocean. Overall, the reduction in atmospheric CO₂ concentration accounts for about 60% of the total LGM climate change.     

Impact of freshwater discharge from the Greenland ice sheet on North Atlantic climate variability

Using a coupled ocean–atmosphere general circulation model, we investigated the impact of Greenland ice sheet melting on North Atlantic climate variability. The positive-degree day (PDD) method was incorporated into the model to control continental ice melting (PDD run). Models with and without the PDD method produce a realistic pattern of North Atlantic sea surface temperature (SST) variability that fluctuates from decadal to multidecadal periods. However, the interdecadal variability in PDD run is significantly dominated in the longer time scale compared to that in the run without PDD method. The main oscillatory feature in these experiments likely resembles the density-driven oscillatory mode. A reduction in the ocean density over the subpolar Atlantic results in suppression of the Atlantic Meridional Overturning Circulation (AMOC), leading to a cold SST due to a weakening of northward heat transport. The decreased surface evaporation associated with the cold SST further reduces the ocean density and thus, simultaneously acts as a positive feedback mechanism. The southward meridional current associated with the suppressed AMOC causes a positive tendency in the ocean density through density advection, which accounts for the phase transition of this oscillatory mode. The Greenland ice melting process reduces the mean meridional current and meridional density gradient because of additional fresh water flux, which suppress the delayed negative feedback due to meridional density advection. As a result, the oscillation period becomes longer and the transition is more delayed.     

The role of sea ice in the temperature-precipitation feedback of glacial cycles

The response of the hydrological cycle to climate variability and change is a critical open question, where model reliability is still unsatisfactory, yet upon which past climate history can shed some light. Sea ice is a key player in the climate system and in the hydrological cycle, due to its strong albedo effect and its insulating effect on local evaporation and air-sea heat flux. Using an atmospheric general circulation model with specified sea surface temperature and sea-ice distribution, the role of sea ice in the hydrological cycle is investigated under last glacial maximum (LGM) and present day conditions, and by studying its contribution to the “temperature-precipitation feedback”. By conducting a set of sensitivity experiments in which the albedo and thickness of the sea ice are varied, the various effects of sea ice in the hydrological cycle are isolated. It is demonstrated that for a cold LGM like state, a warmer climate (as a result of reduced sea-ice cover) leads to an increase in snow precipitation over the ice sheets. The insulating effect of the sea ice on the hydrological cycle is found to be larger than the albedo effect. These two effects interact in a nonlinear way and their total effect is not equal to summing their separate contribution.     

A continuous simulation of global ice volume over the past 1 million years with 3-D ice-sheet models

Sea-level records show large glacial-interglacial changes over the past million years, which on these time scales are related to changes of ice volume on land. During the Pleistocene, sea-level changes induced by ice volume are largely caused by the waxing and waning of the large ice sheets in the Northern Hemisphere. However, the individual contributions of ice in the Northern and Southern Hemisphere are poorly constrained. In this study, for the first time a fully coupled system of four 3-D ice-sheet models is used, simulating glaciations on Eurasia, North America, Greenland and Antarctica. The ice-sheet models use a combination of the shallow ice and shelf approximations to determine sheet, shelf and sliding velocities. The framework consists of an inverse forward modelling approach to derive a self-consistent record of temperature and ice volume from deep-sea benthic δ¹⁸O data over the past 1 million years, a proxy for ice volume and temperature. It is shown that for both eustatic sea level and sea water δ¹⁸O changes, the Eurasian and North American ice sheets are responsible for the largest part of the variability. The combined contribution of the Antarctic and Greenland ice sheets is about 10 % for sea level and about 20 % for sea water δ¹⁸O during glacial maxima. However, changes in interglacials are mainly caused by melt of the Greenland and Antarctic ice sheets, with an average time lag of 4 kyr between melt and temperature. Furthermore, we have tested the separate response to changes in temperature and sea level for each ice sheet, indicating that ice volume can be significantly influenced by changes in eustatic sea level alone. Hence, showing the importance of a simultaneous simulation of all four ice sheets. This paper describes the first complete simulation of global ice-volume variations over the late Pleistocene with the possibility to model changes above and below present-day ice volume, constrained by observations of benthic δ¹⁸O proxy data.     

Equilibrium ice sheet scaling in climate modeling

A set of simple scaling formulas related to ice sheet evolution is derived from the dynamic and thermodynamic equations for ice and is used to consider two common situations: (a) when we wish to estimate potential ice sheet characteristics given the prescribed net snow accumulation over an area; and (b) when we wish to reconstruct net snow accumulation and vertical temperature difference within the ice sheet given empirical data only concerning ice sheet area and volume. The scaling formulas are applied to the present day Antarctic and Greenland ice sheets, as well as to some ancient ice sheets, and are used to estimate the potential global sea level change due to greenhouse warming.     

Global dynamics of the Antarctic ice sheet

The total mass budget of the Antarctic ice sheet is studied with a simple axi-symmetrical model. The ice-sheet has a parabolic profile resting on a bed that slopes linearly downwards from the centre of the ice sheet into the ocean. The mean ice velocity at the grounding line is assumed to be proportional to the water depth. The accumulation rate is a linear function of the distance to the centre. Setting the total mass budget to zero yields a quadratic equation for the steady-state ice-sheet radius R. Analysis of the equilibrium states sheds light on the sensitivity of the ice-sheet radius to changes in sea level (S) and precipitation with respect to the present state (P_rel). For model parameters obtained by matching the analytical model to the present state of the Antarctic ice sheet, the sensitivity values are dR/dS = -2400 and dR/dP_rel = 4000 m/%. The model can also be used to study transient behaviour of the ice sheet. The characteristic relaxation time (e-folding time scale) is about 3500 years. Forcing the model with a sea-level and accumulation history over the past few hundred thousands of years yields Antarctic ice-volume curves that are similar to those obtained by comprehensive numerical modelling. The current imbalance predicted by the model corresponds to a sea-level rise of 0.25 mm yr^-1.