Parameterisation of relationships between climate and glacier mass balance is of considerable importance in understanding and modelling how temporal variability in climate affects the quantity of perennial snow and ice stored in glaciers, and the runoff from glacierised areas. Influences of year-to-year variations in air temperatures are pertinent in the absence of long records of measured energy balance and in view of predictions of future climate scenarios in terms of temperature. Measurements of temperature and precipitation from several stations in Alpine valleys in the Rhone basin, Wallis, Switzerland have been analysed to indicate trends in climate from 1930 to 1988. Actual measurements of mass balance of Griesgletscher, ablation calculated from runoff and net accumulation estimated from totalising rain gauges for Findelengletscher and Gornergletscher beginning in the late 1960s, and runoff from Aletschgletscher since 1930, were taken as annual glaciological responses to climatic variation. Variables to represent climatic elements and interactions between precipitation and temperature were selected according to degree of correlation with glacier response variables, and climate-glacier response relationships were assessed by multiple regression. Subsets of the data representing the coolest (1972–81) and warmest (1943–52) decades were also analysed to indicate whether relationships amongst climatic variables and between climate and mass balance remain the same under contrasting climatic conditions.

Overall, mean summer air temperature variables for the months May through September and June through August provide the highest levels of explanation of variance of ablation and mass balance respectively (75–82%). Addition of a precipitation variable (winter, spring or summer) in multiple regression increases explanation to a maximum of 91%. Spring and summer precipitation variables are negatively correlated with ablation. Positive degree days and temperature-summer snow functions provide alternatives to temperature. Event-based analysis of the coolest and warmest years selected by rank order invokes high precipitation in May and low May-June temperatures and summer snowfall events as significant variables.

Relationships between climatic variables indicate that warmer-than-average winters have higher precipitation, but at summer and annual time scales precipitation is slightly negatively associated with temperature. At the decadal level, warmer periods appear to be influenced by increased frequency of continental anticyclonic conditions, in an area subject to both maritime and continental influences. These analyses of climatic variables indicate that summer energy inputs dominate glacier mass balance. Relationships between precipitation and temperature are complex and were changeable during a fluctuation of about 1° over 40 years. Effects of a potentially warmer future on the form of precipitation in spring, summer and autumn are not clear, so estimates of changes of mass balance have been calculated for contrasting precipitation regimes.

The climatic record from Greenland boreholes is likely to extend well beyond the last interglacial only if the basal ice near the drilling sites has never reached its pressure melting point (−2°C). A simplified one-dimensional analysis (Paterson and Waddington, 1986) suggested that this would be true at Crête, Greenland, if the geothermal flux was less than 48 mW m−2. In that study, the vertical velocity pattern for an isothermal ice sheet was used. We have repeated the Crête calculations using the vertical velocity pattern derived by a finite element analysis. Using this temperature-dependent velocity pattern lowered the basal temperature by about 3°C.

We have carried out a similar analysis for the Summit coring site further north on the Greenland ice divide. Here we find that the basal ice does not melt if the geothermal flux is less than 54 mW m−2, using the same mass balance and surface temperature histories as the previous study. We are repeating these one-dimensional calculations with more recently compiled histories and plan to present results from a full two-dimensional temperature model that includes processes only parameterized in the one-dimensional models. Using two dimensions, we will more realistically incorporate the special ice-flow patterns found at divides (e.g. Raymond, 1983; Dahl-Jensen, 1989). In steady-state flow models these patterns lead to significant horizontal temperature gradients and a “hot spot” beneath an ice divide (Paterson and Waddington, 1986). In addition, we will more accurately determine the transient effects on basal temperature resulting from the interaction of these flow patterns and the changing climate. Our discussion will include sensitivity to geothermal heat flux, ice thickness and paleoenvironmental history.

Satellite data have proved suitable and cost-effective for ice and climate research in Antarctica. They have been used in numerous research efforts, including: monitoring coastal change, determining velocities of outlet glaciers, defining blue ice areas, tracking the movement of icebergs, and as a base for overlaying radar and other data. This paper reviews the data acquired since 1972 by the Landsat, SPOT and Sojuzkarta space systems and illustrates where good-quality (±10% cloud cover) data are available.

The Landsat 1, 2, and 3 satellites acquired approximately 10 000 multispectral scanner (MSS) (80 m resolution) and return-beam vidicon (RBV) (30 m resolution) photographic and digital images of Antarctica between 1972 and 1983. The quality of these images has been evaluated by USGS to determine the feasibility of using them for glaciological, climatological, and geological research. Results have been plotted on a base map of Antarctica and show about 45% of the nominal scene centers, or about 70% of the geographic area of the continent, to be covered by good-quality imagery. Landsat 4 started acquiring data in 1982 and Landsat 5 in 1984. Together the two satellites acquired more than 4 500 thematic mapper (TM) (30 m resolution) and MSS images of Antarctica through the 1988–89 austral summer season, which may be the last season of Landsat 4 and 5 acquisition. The majority of the scenes have been acquired by two major projects: the West German Institut für Angewandte Geodäsie project to acquire data from the Ronne Ice Shelf area to the Greenwich meridian, and the USGS project to acquire data of coastal Antarctica and the inland boundary of the ice shelves, for use by the Scientific Committee on Antarctic Research (SCAR) community. Landsat 4 and 5 have different orbital parameters from Landsat 1, 2, and 3. As a result Landsat 4 and 5 imagery have different areal coverage. The data also have been archived differently. While the Landsat 1, 2, and 3 data exist in film format, many Landsat 4 and 5 TM images exist only as high-density digital tapes, and, as a result, the scenes cannot be examined and evaluated before purchase. Computer evaluation of the Landsat 4 and 5 data indicate that about 1350 or about 30% of the images have 10% cloud cover or less. However, it is difficult for automatic systems or those unfamiliar with the area to discriminate between clouds and snow. Based on a sampling of the data, it is more likely that 10–15%, or about 500 scenes, are of good quality. Those scenes which have been examined and evaluated as part of the SCAR cooperative acquisition project and are known to be of good quality are plotted and compared with the earlier Landsat data. The combined plot gives accurate and reliable information on the location of good quality Landsat 1–5 data of Antarctica.

More than 7 000 Sojuzkarta scenes have been collected over Antarctica since 1976. The most useful data consist of photography from the KATE-200 system (20 m resolution) and the KFA-1000 system (6 m resolution). The data have been plotted by the U.S. Geological Survey and will soon be available as an open-file report. Those scenes which have been evaluated as having 10% cloud cover or less are plotted separately and overlaid on the Landsat plots. Scenes which have been examined are excellent, but an insufficient number of scenes have been inspected to evaluate the accuracy of the cloud cover estimation.

The Systeme Probatoire d'Observation de la Terre (SPOT) was launched in 1986 and has acquired more than 1200 scenes of Antarctica. SPOT data consist of multi-spectral (20 m resolution) and panchromatic (10 m resolution) photographic or digital imagery. SPOT also possesses a mechanical plane mirror which permits off-nadir imaging and the generation of stereoscopic images. The locations of these scenes are now being plotted by the U.S. Geological Survey. Scenes with 10% cloud cover or less will be combined with Landsat and Sojuzkarta data to provide an accurate summary of the availability and coverage of high-quality satellite data of Antarctica.

The important role played by ice on climate is recognized in the ice–albedo feedback effect which is incorporated in most climate models. But the ice under consideration is two-dimensional and only its surface area enters into the interaction. Whereas this applies well to the seasonal ice and sea ice, it does not to the permanent ice sheets on earth because they are three-dimensional. A new feature is the ice flow down the ice-sheet slope. This increases the amount of ice on the ice-sheet periphery above that produced by local precipitation that is considered in most climate models. As a result the ice–albedo effect will be greater than that given in most climate models. The latter (a positive feedback) is generally smaller than the major negative feedback due to the infrared effect and therefore stable equilibrium is achieved in most climate models. When the positive feedback is thus increased to an amount equal to the infrared negative feedback, stable equilibrium is destroyed and the system changes to netural equilibrium – a mildly unstable form. This may be just what is necessary to explain the advance and retreat of the ice sheets, which cannot be explained by most climate models because in stable equilibrium an ice sheet cannot advance and retreat.

The advance and retreat can be proven to be the manifestation of a neutral equilibrium. At any instant of time in an ice age, including the present time, the climate system is nearly in equilibrium. But as time goes on the equilibrium point shifts continuously, reflecting the advance of the ice sheet and the cooling of the ocean. Thus an ice age is represented by a continuous sequence of equilibrium points, which, by definition, constitutes a netural equilibrium. The argument is reinforced by the observation that the “cause” of ice ages is a very small perturbation – the variation of the eccentricity of the earth orbit. According to most climate models, this effect is one order of magnitude too small to generate the climate changes in an ice age. On the other hand in a neutral equilibrium a very weak perturbation can generate slow progressive changes, like the rolling of a cylinder on a plane. As a matter of fact, the small periodic changes of the eccentricity pace the advance and retreat of the ice sheets almost in phase; this is not possible in stable and unstable equilibrium and can be possible only in neutral equilibrium. The empirical conclusion of neutral equilibrium is solidly established. Any theory and any climate model must accommodate this fact.

A deeper understanding requires the pinpointing of the physical origin of the meutral equilibrium. The origin can be shown, though not obviously, to be just the phase equilibrium of water and ice, which is quasi-static and may be considered as neutral equilibrium in a mechanical analogy. The argument is complicated by the fact that the temperature does not remain constant as expected in phase equilibrium but does decrease in an ice age. However, this can be accounted for by the complication of the albedo effect. Hypothetically if ice were brown and without albedo effect, then in an ice age the temperature would not decrease and the situation would be just like ice-water phase equilibrium. The physical origin of neutral equilibrium clarifies the fundamental principle but is not necessary for the mathematical formulation of a dynamic theory of the ice sheets that is given as follows. Instead neutral equilibrium emerges naturally from that theory and the advance and retreat can be explained readily.

Most climate models are static models which cannot explain the advance and retreat – a manifestly dynamic process. A simple but adequate dynamic theory can be formulated considering the ice volume V(t) and the ocean surface temperature T(t) as the basic dynamic variables. The equations for their changes can be written down, making use of the latent heat of fusion of ice and the sensible heat capacity of the ocean mixed layer. Albedo positive feedback and infrared negative feedback will be included in the heat balance. The three-dimensional effect of the ice sheet will be introduced in the albedo effect. This involves the geometry of the ice sheet which will be specified in a constraint equation. Then a closed, deterministic set of intergral-differential equations may be formulated to describe the dynamics of the ice sheets. The equations may be solved without adjustable parameters. The solutions agree with the observed advance and retreat of ice sheets and the cooling and warming of the ocean. A close examination of the feedbacks involved reveals that the dynamics is indeed like a mechanical system in neutral equilibrium. However, the detailed mathematical theory shows that the netural equilibrium changes to stable when the ice sheets reach the middle latitudes. They thus stop there in maximum glaciation.

There is no limit on the other end. The northern ice sheet did melt completely. So could the Antarctic ice sheet though it has not in the ice ages. But before the Pleistocene in 99% of the geological time the earth was free of ice sheets. Then, why did the “cause” of ice ages, the eccentricity variations, not generate ice ages in 99% of the earth history? Ice and water can co-exist (in equilibrium) only under unusual conditions, which are not fulfilled generally. But in recent geological times Antarctica drifted to the pole position and high mountains arose on the continents so that permanent ice can survive the summer season and accumulate year after year. Most important, the CO2 content in the atmosphere has been decreasing (Budyko, 1974), cooling down the earth. Eventually the earth was cool enough in Pleistocene to satisfy the neutral equilibrium condition. Then the ice ages began.

But we are now burning fossil fuels to put CO2 back into the atmosphere, going back to pre-Pleistocene conditions. The Antarctic ice sheet will melt away; this will be the principal result of the greenhouse effect. However, current discussion of the greenhouse effect deals with only the warming of the earth and neglects the more serious effect of the melting of the Antarctic ice sheet because climatologists overlooked the effect of ice sheets on climate. This study will change the outlook.

A two-dimensional finite element model has been applied to Rutford Ice Stream, Antarctica, and part of Ronne Ice Shelf into which the ice stream flows. The model is an extension of one describing ice-shelf flow, and relies on vertical shear in the ice stream being small in some mathematically defined sense. This is equivalent to requiring the vertical shear to be confined to a basal layer or a deformable substrate.

Although there is no direct observational evidence for such a layer beneath Rutford Ice Stream, extensive surface surveys and estimates of the strength of the overlying ice show that some dynamically equivalent mechanism must occur. If basal shear stress is parameterised in terms of the thickness and viscosity of a linearly viscous substrate, as may be the case beneath Ice Stream Β in Antarctica, then going upstream from the grounding line, the thickness of this layer must decrease, and the viscosity increase (to retain a realistic thickness at the upstream limit), in order to reproduce the observed surface velocities. This physically reasonable picture is currently adopted as a working hypothesis.

Vertical shear in the body of the ice stream appears to be negligible for approximately 70 km above the grounding line. Sensitivity tests show that, in this lower section, ice-shelf back stress is an important restraining influence. A 10% reduction in back stress would produce an immediate 15% increase in grounding line flux. Further upstream, however, higher surface slopes and slightly lower surface velocities suggest that the neglect of vertical shear may be less appropriate. The effect of a reduction in ice-shelf back stream is not felt in this region immediately, as the gravitational driving force is almost balanced by local basal shear traction.

A complex surface morphology has been revealed by satellite imagery below the grounding line of Rutford Ice Stream. On the basis that this may be evidence of time dependent behaviour, the finite element model is being used to investigate the origin of the pattern. Ice-shelf back stress, basal melting, mass flux from tributary glaciers and substrate properties can all be varied in physically realistic ways to try to reproduce, qualitatively, the observed surface morphology.

Recently reported observations of a nine-year decrease in global sea-ice extent, obtained from the Scanning Multichannel Microwave Radiometer onboard the Nimbus-7 satellite during 1978–87 and averaged with an annual running mean, have been separated into Arctic and Antarctic components. The annually-averaged global extent decrease was 2.5%. Here it is shown that the greater part of this decrease occurred in the Arctic where there was a decline of 3.5% with a goodness of fit of 0.54.

Superimposed on this decline was a small oscillation with a period of about four years and an amplitude of about 1%. A significantly smaller and statistically insignificant decrease of 1.2% with a goodness of fit of 0.03 is observed in the annually averaged Antarctic sea-ice extent. However, three large oscillations with amplitudes of about 4% and periods of about three years occurred in phase with three El Niño events.

The process by which water flows from the surface ocean to the deep ocean is crucial in determining the structure and composition of the world ocean (Killworth, 1983). An important element in this process is the mechanism by which surface water on the Antarctic continental shelves becomes dense enough to sink to the abyssal ocean. These shelves are active sites of surface water modification because of the intense cooling and salt rejection due to sea-ice formation which occurs there during the winter.

Prior models of water mass modification on the Antarctic continental shelves have focused on either the wind-forced circulation (Killworth, 1973), or the density-forced circulation (Solomon, unpublished; Killworth, 1974). Solomon (unpublished) showed that the density-forced circulation alone is too weak to produce a flux of saline water to the deep sea which was consistent with observations. Killworth (1973) showed that the wind-forced circulation alone in the Weddell Sea was incapable of producing a large enough flux. In a complementary model of only the density-forced circulation, Killworth (1974) showed that the change in salinity of water parcels caused by regional density forcing was reasonable; but as in Solomon's (unpublished) model, the flux of modified water was too small. The result of these model studies was that either circulation alone, wind-forced or density-forced, is insufficient to produce the observed flux of saline shelf water. The conjecture based on the results of these studies was that, when combined, the density forcing determined the change of salinity in the shelf water and the wind-forced circulation determined the flux of the modified water.

To determine whether the combination of wind stress and density forcing is sufficient to produce a flux and salinity change consistent with observations, a simple model which responds to both forcings was developed. The model is essentially that used by Killworth (1974) with the addition of the flow forced by wind stress. A different density forcing is used because observations of the sea-ice cover (Zwally and others, 1983) suggest that the regions of coastal open water, and hence freezing, are much more localized than used in prior density-forced models. The localization of the density forcing was parameterized as being a Gaussian function of distance from and along the coast. The model (Grumbine, unpublished) predicts the velocity and salinity in two layers of equal depth in a square region with a flat bottom, subject to wind and density forcing. The east, south, and west boundaries represent coasts of an embayment analogous to the Weddell Sea continental shelf, with the continental shelf break in the middle, north-south, of the region, and an open northern boundary. The salinity is initially constant in each layer. The velocity is initialized to the equilibrium value of the wind-forced circulation. Then the salinity forcing is started and the evolution of the salinity fields is computed using the wind-forced velocity field and a diagnostically computed density-forced velocity field.

The model was run for three cases: wind stress forcing only, density forcing only, and wind stress and density forcing combined. The wind-forced circulation alone was incapable of producing a sufficient degree of water mass modification. With only density forcing, the change in salinity was consistent with observations, but the flux was too small. When the two forcings are combined, both the change in salinity and the flux of modified water are consistent with observations. The model is verified against the flux and composition values from observations by Foster and Carmack (1976) in the deep Weddell Sea. The observed flux value of 1 to 2.5 × 106 m3 s−1 corresponds to water with a mean salinity of 34.7‰. This is the salinity of the water which was able to reach the abyssal ocean off the Weddell Sea coast. Figure 1 gives the modelled seasonal cycle and annual mean of the equatorward flux of water which corresponds to a mean salinity of 34.7‰. The figure shows the flux for the last three years of a five- year run computed across the position of the continental slope. The mean annual flux of this modified water is 2.0 × 106 m3 s−1, compared to the observation of 1 to 2.5 × 106 m3 s−1. These results confirm the conjecture that the combination of wind and density forcing is sufficient to produce a degree of modification and flux of modified water consistent with observations.

The production of Antarctic Bottom Water is mainly influenced by Ice Shelf Water, which is formed through the modification of shelf water masses under huge ice shelves. To simulate this modification a two-dimensional thermohaline circulation model has been developed for a section perpendicular to the ice-shelf edge. Hydrographic data from the Filchner Depression enter into the model as boundary conditions. In the outflow region they also serve as a verification of model results.

The standard solution reveals two circulation cells. The dominant one transports shelf water near the bottom toward the grounding line, where it begins to ascend along the inclined ice shelf. The contact with the ice shelf causes melting with a maximum rate of 1.5 m a−1 at the grounding line. Freezing and therefore the accumulation of “sea ice” at the bottom of the ice shelf occurs at the end of the melting zone at a rate on the order of 0.1 ma−1. Both rates are comparable with values estimated or predicted by models concerning ice-shelf dynamics.

As one example of model sensitivity to changing boundary conditions, a higher sea-ice production in the southern Weddell Sea, as might be expected for a general climatic cooling event, is assumed. The resultant decrease/ increase in temperature/salinity of the inflow (Western Shelf Water) reduces the circulation under the ice shelf and therefore the outflow of Ice Shelf Water by 40%. The maximum melting and freezing rate decreases by 0.1 ma−1 and 0.01 m a−1, respectively. and the freezing zone shifts toward the grounding line by 100 km.

In general the intensity of the circulation cells, the characteristics of Ice Shelf Water, the distribution of melting and freezing zones and the melting and freezing rates differ from the standard results with changing boundary conditions. These are the temperature and salinity of the inflow, the surface temperature at the top, and the extension and morphology of the ice shelf.

Sea-ice drift and dynamics can significantly affect the exchanges of heat between the atmosphere and ocean and salt fluxes into the ocean. The ice drift and dynamics, in turn, can be modified by the ocean circulation. This is especially true of the ice margin location whose seasonal characteristics are largely controlled by the substantial oceanic heat flux in the Greenland Sea due to convective overturning.

A useful framework to analyze the interannual variability of ice–ocean interaction effects relevant to climatic change is the diagnostic ice–ocean model developed by Hibler and Bryan (1987). In this model, the oceanic temperature and salinity is weakly relaxed (except in the upper layer of the ocean which is essentially driven by the ice dynamic-thermodynamic sea-ice model) to climatological temperature and salinity data. This procedure allows seasonal and interannual variability to be simulated while still preventing the baroclinic characteristics of the ocean circulation from gradually drifting off into a total model defined state. However, in the work of Hibler and Bryan only the seasonal equilibrium characteristics of this model with the same forcing repeated year after year have been considered.

In order to begin to examine the interannual behavior of this model, we have carried out a three-year simulation for the Arctic Greenland and Norwegian seas over the time period 1981–83. (The geographical region is essentially the same as used by Hibler and Bryan.) This three year simulation is carried out after an initial two year spin up using the 1981 atmospheric forcing data. For comparison purposes, an ice model simulation with only a fixed depth mixed layer was also carried out over this time interval.

The results of these two simulations are analyzed with special attention to the ice margin characteristics in the Greenland and Norwegian seas to determine the role of ocean circulation on the variability there. The ice margin results are also compared to the variability in the northward transports of heat through the Faero-Shetland passage which in the fully-coupled model are calculated rather than specified.

The seasonal cycle of sea ice, especially the ice margin location in the East Greenland region, is significantly affected by ocean circulation. The ocean circulation in turn can be altered by ice dynamics which cause large amounts of ice to be transported to the ice margin to be melted, thus stratifying the ocean there. By responding to wind changes, the ice dynamics can also create rapid melting or freezing events which can destabilize the ocean.

In an earlier study, Hibler and Bryan (1987) carried out a diagnostic simulation of the Arctic ice-ocean system in which a coupled ice-ocean circulation model was integrated for about five years beginning with mean annual estimates by Levitus (1982) of the observed temperature and salinity fields. As a consequence of this short integration, the mean baroclinic circulation of the ocean deviated little from the initial fields, although seasonal and local effects due to the interactive models were simulated. One particularly interesting result of this study was the presence of fluctuations of oceanic heat flux at the ice margin, which appeared to coincide with strong wind events occurring over a few days which induced periods of freezing.

With this diagnostic model, good results for the location of the ice margin were obtained. However, a global budget analysis indicated that the net northward heat transport through the Faero–Shetland passage was not adequate to balance the heat loss to the atmosphere sustained by the ocean in the fifth year. Moreover, a 20-year simulation without diagnostic terms showed a degraduation of the baroclinic fields in the Arctic Basin possibly due to the very weak wind stress used for this particular years's wind forcing, or perhaps due to excessive damping in the ocean due to computational requirements imposed by the coarse grid.

As a first step in the development of a higher-resolution fully interactive prognostic model, we have modified this model and carried out two prognostic simulations of the Arctic ice ocean system by employing 50-year integrations. The ocean model used for this study is essentially that of Hibler and Bryan (1987). However, the boundary conditions, atmospheric forcing, and ice model have been changed. In particular, a much more robust wind forcing was obtained by replacing the monthly mean wind fields with a 30-year means in order to obtain a seasonal forcing closer to climatology. With regard to the ice rheology, a cavitating fluid model in spherical coordinates which fully conserves ice mass and air sea heat exchanges was employed. The idea here is to attenuate less of the stress into the ocean so that even though the circulation is somewhat sluggish due to large viscous damping, a reasonable current field for the Arctic Basin might be obtained.

Two types of prognostic circulation experiments were carried out with this model using different southern boundary conditions. In one case, a diagnostic relaxation near the boundary as used by Hibler and Bryan (1987) was employed. In this case, heat mass and salt transports through the southern boundary are essentially simulated. In the second case, the net burotropic flow through the Faero-Shetland passage and Denmark Strait were specified with the baroclinic transports partially specified by diagnostic relaxation terms. The results from both these models are analyzed with special attention to the ice edge location and the character of the baroclinic fields in the Arctic Basin.

A two-dimensional energy balance model (EBM) with a seasonal cycle and a realistic land–ocean distribution is used to study climate sensitivity and the properties of equilibrium climate states. The land–ocean distribution is represented by the heat capacity of the surface. The horizontal heat flux is parameterized by diffusion. Nonlinearity is introduced into the model by the albedo–temperature feedback. A multi-grid finite difference method is used to solve the model equation. This method shows great advantages compared to other numerical methods.

The sensitivity of snow cover to changes in the solar constant is examined. It is found that the climate is more sensitive in summer due to a more effective albedo–temperature feedback. The local annual mean temperature and the amplitude of the seasonal cycle depend on the land–ocean distribution. Because Eurasia has the largest annual cycle of temperature and is the coldest in winter, winter snow appears first in Eurasia as the solar constant is reduced. Wintertime snow appears next in Greenland because of its low annual mean temperature and last in North America. Perennial snow cover appears first in Greenland because of the low annual mean temperature and the small annual cycle, and next appears in North America. Perennial snow in Eurasia appears only when the solar constant is reduced to a very low value, since the Eurasian land mass is too hot in summer for perennial snow cover. The sensitivity of the model climate to changes in the orbital parameters is also investigated and discussed.

Small polar ice caps in one-dimensional mean-annual EBMs are unstable to small perturbations. The ice caps either vanish or grow to a stable finite size. This phenomenon, referred to as the small ice-cap instability (SICI), is a consequence of the multiple stable equilibrium states in one-dimensional models. The SICI may be related to glacial–interglacial transitions. However, numerical results with the two-dimensional EBM demonstrate that the existence of the SICI depends on the land–ocean distribution. The SICI exists in the southern hemisphere, but not in the northern hemisphere. This casts doubt on the role of the SICI in northern hemisphere glaciations. Experiments with a one-dimensional seasonal EBM with simplified geography have been made to analyze the two-dimensional results. Mechanisms for the existence of the SICI in seasonal EBMs are discussed.

On the seasonal time scales relevant to numerical investigations of climate, the rheology used in large-scale sea ice models significantly affects the ice thickness build-up and ice velocity fields. Plastic rheologies with a normal flow rule have been used to-date in seasonal dynamic thermodynamic simulations. These rheologies have proved useful in simulating discontinuous slip near the coast while still supplying relatively robust velocity fields in the central Arctic Basin. However, as indicated by limited numerical sensitivity studies with different types of elliptical yield curves, the amount of shear strength significantly affects the ice build-up and can possibly cause a stoppage of the ice outflow through Fram Strait. In addition to the shear strength issue, there is also the possibility that non-normal flow rule rheologies, such as the Mohr Coulomb failure criterion used in soil mechanics, may cause somewhat different types of flow patterns, especially in the Fram Strait region. However, to date no seasonal simulations with such non-normal flow rule rheologies have been carried out.

In order to investigate the role of different rheologies on the large-scale flow patterns in the Arctic Basin, a more general numerical scheme than that of Hibler (1979) is developed, which allows the simulation of the dynamic thermodynamic behavior of sea ice with a wide variety of different non linear rheologies. Using this numerical scheme, comparative simulations are carried out to seasonal equilibrium with several variations of the Mohr Coulomb rheology and compared to the more standard Elliptical yield curve results. In particular, the main control Mohr Coulomb case is a capped rheology in which the shear strength is taken to be proportional to the compressive stress. In this capped case only shear flow is allowed until a maximum allowable compressive stress is reached. This cap strength is parameterized to be a function of the ice thickness and compactness. For comparison, a simulation with a very large cap strength is also carried out, and an experiment with a similar compressive cap but much lower shear strength. Overall the results are analyzed to determine the sensitivity of the ice build-up to flow rule and shear strength magnitude. In addition special attention is given to the character of the flow and stoppage (if any) through Fram Strait.

All of the West Antarctic ice sheet draining into the Ross Ice Shelf lies on bedrock which is below sea level. This is thought to make it especially senstitive to rapid decay which could be triggered by an increase in atmospheric CO2 levels, ice stream B, one of the main outlets of the West Antarctic Ice Sheet, is thinning, possibly in response to changes in climate. However, Ice Stream C, its neighbor, is thickening.

One of the most effective ways to study ice streams is by repeat aerial photogrammetry. Thousands of velocity values and elevations are available for Ice Stream B using this technique. Two sections of the ice stream have repeat photogrammetry with control. Maps of elevations, velocity components and velocity gradients have been produced following the methods of Brecher (1986).

The area considered here is a 40 by 30 km block across a part of the ice stream. The maps show that most of the increase in longitudinal velocity occurs within about 6 km of the ice-stream margin and reaches a maximum of 460 m a-1 in the center of the stream. Strain rates in the shear margins reach 0.12 a-;1 and are an order of magnitude less in the main body of the stream.

The elevation maps show ridges and troughs. These features appear to be related to transverse velocities.

A detailed glaciological study of Ronne Ice Shelf has been undertaken along a flowline extending from Rutford Ice Stream grounding line to the ice front. Measurements of velocity, surface elevation, ice thickness, surface temperature and accumulation rate have been made at a total of 28 sites; at 17 of these ice deformation rates are also known. Although no direct measurements of basal conditions have been made, these can be deduced from observations made at the surface. Assuming the ice shelf to be in a steady state, the basal mass balance can be calculated at points where strain-rates are known. Information on the spatial distribution of basal saline ice layers can also be obtained from radio-echo sounding data. The derived pattern of basal melting and freezing influences both the ice shelf and the underlying ocean. Vertical heat advection modifies the temperature distribution within the ice shelf, which determines its dynamic response to driving and restraining forces through the temperature-dependent ice-flow law. Using measured strain-rates and calculated temperature profiles, the restraint generated by horizontal shear stresses can be derived for points on the flowline. It is the cumulative effect of these forces which controls the discharge of grounded ice from Rutford Ice Stream. Cooling of sea-water to its pressure melting point by melting of ice at depth has two important results. The outflow of cold, dense Ice Shelf Water, produced by this mechanism, is a major source of Antarctic Bottom Water, formed as it mixes at depth with the warmer waters of the Weddell Sea (Foldvik and Gammelsrod, 1988). If the cold water is forced up to shallower depths, frazil ice will be produced as the pressure freezing point rises, resulting in basal accretion if this occurs beneath the ice shelf.

Scharffenbergbotnen is a 3 × 6 km large basin of interior ice drainage on the north-western side of Heimefrontfjella in Dronning Maud Land, Antarctica. The elevation at the bottom of the depression is 1142 m a.s.l., while bedrock immediately to the south-east of this point rises to more than 2750 m. Ice enters the basin mainly from a low ice divide (1250 m a.s.l.) in the west but also through a 400 m high icefall in the east. Two separate blue-ice areas constitute approximately half the surface of the basin, while the other half is snow-covered.

As part of SWEDARP (Swedish Antarctic Research Programme) 1988 a research project to study the origin and mass balance of this basin has been initiated. A net of 28 stakes has been established for studies of ablation and ice movement (Fig. 1). The ice thickness was measured by radio-echo sounding (Fig. 2) and particular care was devoted to get the correct ice depths at the entrance to the basin. The ice thickness along a central section of the basin varied from 1000 m in the west to 400 m at the bottom of the depression.

In order to explain the ablation two automatic weather stations (Aanderaa 2700) were operated during the field season (mid-January to mid-February 1988). One was placed in the bottom of the depression, the other 13 km to the west in an area where a small net accumulation took place during the field season. The latter station should record “normal” weather. Sensors registering wind speed, wind gust, wind direction, incoming solar radiation, air temperature and relative humidity were installed at both weather stations, while reflected solar radiation, net radiation and air pressure were measured only at Scharffenbergbotnen. All sensors except the air pressure sensor were placed 270 cm above the ground, and all were read every 10 minutes.

Ablation measurements were carried out between 16 January and 18 February on 24 of the stakes. 12 of these stakes were standing in snow. All but one recorded ablation and, as no signs of melting could be seen, all ablation must be due to evaporation and perhaps for the snowy areas some wind erosion. The average ablation rate for the whole field season was 0.7 mm w.eq. per day with a standard deviation of 0.3. Stakes in blue ice showed slightly higher values than those in snow. For January, when air temperatures always were above −10°C, the average ablation rate was 1.2 mm w.eq. per day.

A regional difference in ablation rate across the depression was also measurable. Maximum ablation took place immediately below the arête forming the north-eastern boundary of the basin and diminished towards south-west. Below the arête the ablation rate was above 1 mm w.eq. per day for the whole field season and more than 2 mm w.eq. per day during January.

A comparison of weather data between the two stations showed the following main differences. In the depression the temperature showed no daily variation and relative humidity varied between 40 and 60%. The weather at the other station was characterised by colder nights and weaker winds as well as by a relative humidity between 60 and 80%. The reason for the regional variation in ablation can be explained by almost constant easterly winds during January and the drop in altitude (between 300 and 500 m) along the north-western arête.

On 11 February 1988 the weather station at Scharffenbergbotnen was converted into a system for satellite (Argos) transmission of weather data to Europe. The transmission seems to have been successful but the data are not yet processed. At present (January 1989) one of us is remeasuring the stakes (ablation and ice movement) during SWEDARP 1989. Preliminary results sent by radio point towards a yearly net ablation rate of 120 mm w.eq. for the blue-ice area in the bottom of the depression. 25% of the ablation took place during the field season 1988, but 75% has evaporated between 18 February 1988 and mid-January 1989. Probably most of the evaporation took place during December 1988 and January 1989, which means a very high daily evaporation rate (2.5 mm w.eq. per day).

The modern concensus outside of the glaciological community is that “greenhouse” gases, released by human activity, will cause an unprecedented temperature rise over the next 100 years and thereby cause a socially-threatening rise of sea level. With respect to ice the concept is simple: warmer means less. The relationship between glaciers and climate is much more complex than this. Warmer also means more vapour transport and there is ample evidence from both theory and ice-core data that snow accumulation rates in both Greenland and Antarctica were lower during the last glacial period. The problem is whether the increased accumulation rates will be exceeded by increased melting of ice in the ablation areas. Antarctica could play a dominant role because of its size and very low temperatures. Only a small percent of Antarctica will increase its meltwater run-off into the ocean. Furthermore, its dynamic response time is so large that the calving rate will not change over a 200-year period. Most of the increased melt will be absorbed in the firn and the question is how much the snow accumulation rate will increase over the major part of the continent.

In the northern hemisphere one has to consider the way in which the warming will manifest itself seasonally. Most of the “forecasts” indicate that most of the warming will occur in the winter rather than the summer. In this case one has to consider the balance between greatly increased winter snowfall rates and only slightly increased summer melt rates. In this respect a review of the snow accumulation and ice melt rates from different glaciers and ice caps in the Canadian Arctic Islands is pertinent. Over the past 20 to 30 years we see no sign of a trend of either side of the balance equation (accumulation, melt). Is this the effect of high noise levels or is there simply no trend?

Finally, we review the ground-ice potential in terms of sea-level change. Ground ice may not form a large part of the world's ice reserves but it covers a large area. Both increased snowfall rates in winter, and summer warming will move to increase the thickness of the active layer. This will result in run-off to the oceans.

Global circulation models might be modified to determine a “best guess” of future sea-level change. To do this they must incorporate all of the parameters considered in this paper.

The layered sequences of melt features preserved in inland polar ice sheets provide valuable proxy data on past variations in summer temperature. A continuous detailed light-table examination was made on the 2037 m-deep Dye 3 ice core immediately after core recovery. Melt features are products of high air temperatures or solar insolation which occur only at or near the snow surface during summer months. A correlation is made between these features and the extent and intensity of summer temperatures. Care must be exercised to identify and distinguish between all mm-thick radiation crusts and wind crusts contained in the record. The absence or presence of these discrete features serve respectively as indicators of total summer cloud cover and the extent of winter storm activity although they are difficult to differentiate from only light-table observations. In this analysis both thin radiation crusts and wind crusts are not in themselves significant indicators of long-term temperature trends, but may serve as incipient subsurface horizons or barrier crusts for the formation of thicker ice melt features caused by downward melt percolation during elevated surface temperature conditions.

More than 10 000 individual melt features, including ice layers, ice lenses and ice wedges (but excluding ice glands) were measured down to a depth of 1278 m; below this depth transformation of air bubbles to transparent air hydrate inclusions occurs (Shoji and Langway, 1987) and the megascopic melt features become obscure. The melt-feature data extends back to 1883 B.c. or approximately 3900 years B.P., based on the accurate time scale of continuous δ18O measurements (Dansgaard and others, 1985) For the entire core profile investigated the annual melt percentage is 5.7. Individual melt features range in thickness from 1 mm to 100 mm. A mean value for melt-feature thickness was calculated for continuous 30-year time intervals to consider the general long-term summer temperature trends with corrections made for progressive annual accumulation layer thinning due to ice flow.

Since the AMP parameter includes noise from radiation and wind crusts it appears that the simple average of melt-feature thickness per longer time-units is a better indication of air temperature paleodata. The average melt-feature thickness is 1.2 cm. The complete curve obtained shows a higher thickness value of about 1.5 cm for the period 1800 B.C. to 1300 B.C. A lower, almost constant thickness value of about 1cm is shown for the period 1000 B.c. to 1800 A.D., with a slight reduction in thickness recorded around 200 B.C., 400 A.D. and 1600 A.D. These long-term trends are coherent with those recorded in the δ18O profile for the same ice core.

A 2 200 m-deep ice core from Vostok Station (East Antarctica) has been used for a comprehensive study of a series of ions (Na+ NH4+, K+, H+, Ca2+, Mg2+, C1−, F−, NO3− and SO42−) originating from impurities deposited over the whole last climatic cycle (180 000 years) as depicted from the isotopic composition of the ice.

Concentration profiles confirm that both marine and terrestrial aerosol inputs were higher (up to five and 30 times the Holocene values respectively) during cold climatic conditions. Such large variations of marine and terrestrial aerosol concentrations measured in ice mainly reflect global (source strength and atmospheric transport efficiency) changes, and to a lesser extent local (deposition) changes.

As opposed to these primary aerosols, secondary aerosols or gases (HNO3, HC1) exhibit more moderate variations. Finally, variations of other minor ions such as NH4+ provide information on the capacity of ammonia to neutralize the natural acidity of the past background atmosphere.

Spectral analyses performed on our chemical profiles (200 samples) exhibit several specific periodicities (around 20 and 40 k year) close to the Earth's orbit tilt and precession frequencies which are discussed in terms of atmospheric response to climatic fluctuations.

A numerical model which simultaneously computes grounded and ice-shelf flow was used to develop an equilibrium ice-sheet–ice-shelf system over Eurasia and the Arctic region. Present-day net accumulation rates and mean annual and July temperature values were used as base values for climatic variable specifications. The values were adjusted during the model run to account for changes in the ice-surface elevation and atmospheric CO2 concentration. The model-determined equilibrium ice-sheet configuration was used as input for additional runs to observe what effect removing the Arctic ice shelf and increasing the CO2 concentration from glacial to present-day values has on the ice sheet.

At equilibrium, an ice shelf formed over the Arctic Ocean and Greenland and Norwegian seas. Ice easily grounded over the Barents, Kara, East Siberian, and Laptev seas. The grounded ice-sheet profile differs in Europe from most glacial geological reconstructions because the North Atlantic Current effect was not removed from the climatic adjustments. As a result, ice did not extend over the North Sea and onto the British Isles because of the North Atlantic Current's warming effect. Also, the precipitation rate over Europe was too high because of the moisture source the North Atlantic Current carries, and the ice sheet expanded beyond the field-determined ice-sheet margins in the region south-east of Finland.

Removing most of the Arctic region's ice-shelf cover had little effect on the grounded ice sheet unless it rested upon a deformable sediment layer. The ice sheet was able to collapse within 10 000 years, however, when the CO2 concentration was gradually increased toward present-day values using the Vostok ice core's CO2 record from the last 18 000 years. Initially, most mass loss resulted from surface melting. Once the thickness decreased enough over some regions for the grounded ice to become ungrounded, however, most mass loss resulted from the ice shelf rapidly transporting the ice to the ice-shelf front and discharging it to the sea.

An ice mass increasing its extent will generally also increase its mean surface elevation (anything else being unchanged). Since temperature drops rapidly with height this often implies a more positive mass balance and thus further growth. This powerful feedback loop is at least as important as the temperature-albedo feedback. In this work, we present a general study of the nature of the altitude-mass-balance feedback, with special attention for the role of differences in the bedrock geometry. One- and two-dimensional experiments on various bedrock topographies are run, using a numerical ice-sheet model based on plane shear flow of ice. Different climates are simulated by lowering or raising uniformly the mass-balance distribution over the ice sheet.

These studies were first done on steady state ice sheets. They show that some geometries can largely enhance this altitude mass-balance feedback. On an island, for instance, it is possible to have two different stable steady states under the same climatic environment: no ice sheet, or a large one over the whole island. When the geometry of the island becomes more complex, for instance with two hills of unequal heights, four different equilibria can be found for the same climatic conditions: no ice sheet, one small one, two small ones or a very large one. Which will develop depends entirely on the history of the mass-balance fluctuations.