Glacial cycles and ice-sheet modelling

An attempt is made to simulate the Pleistocene glacial cycles with a numerical model of the Northern Hemisphere ice sheets. This model treats the vertically-integrated ice flow along a meridian, including computation of bedrock adjustment and temperature distribution in the ice. Basal melt water is traced and controls ice-mass discharge. The model produces asymmetric glacial cycles, even when it is not forced. Model parameters can be chosen such that cycles with a duration of about 100 000 yr occur. Due to the production of basal melt water and bedrock sinking, deglaciations are very rapid. The occurrence of glacial cycles in the model is a stable feature, but thephase of the cycles is very sensitive to the model parameters. The main conclusion is that ice-sheet dynamics may provide an explanation for the Pleistocene glacial cycles. However, the ‘predictability’ of the ice-volume record appears to be small.     

The Pangean ice age: studies with a coupled climate-ice sheet model

 Application of an ice sheet model developed for the Pleistocene to the extensive Carboniferous glaciation on Gondwana yields an ice sheet which has several features consistent with observations. While complete deglaciation is not achieved without CO₂ changes, the Milankovich-induced fluctuations in ice sheet volume are comparable to Pleistocene glacial/ interglacial signals. This result is shown to hold for a large fraction of physically reasonable parameter space. The model also exhibits multiple equilibria and sharp bifurcations, as infinitesimal changes in the solar constant or precipitation can lead to a qualitatively different climate. The success of the model in predicting ice location in an environment quite different from the Pleistocene provides additional support for the robustness of the basic model physics and suggests that the model can be applied with some confidence to other pre-Pleistocene glaciations. Received: 30 June 1998 / Accepted: 5 January 1999     

Ubiquity of the relative equilibrium line dynamic and amplified cyclicity in Earth sedimentary systems

A distinctive feature of Earth’s sedimentary systems is that they all involve the interaction between a nearly-horizontal “equilibrium line,” controlling mass supply, and a dynamic sedimentary surface. For glacial systems, this is the snow line or firn line, approximating a zero-degree atmospheric isotherm. For sedimentary basin systems it is sea level or baselevel. For deep ocean carbonate sediments it is the calcite compensation depth or lysocline. First-order considerations in each case suggest a positive feedback on mass supply as the surface builds upwards (and negative feedback if the surface drops). In the first two cases, outstanding paleo-climate problems exist wherein recorded past sedimentary cycles have asymmetric amplitudes that appear too large compared to deduced vertical movements of the respective equilibrium lines. These problems are familiarly known as the “100-kiloyear Pleistocene ice age cycle” and the “million year high-order Cretaceous relative sea level cycles.” Here, I discuss the emerging commonalities that surround these two amplified cycles, emphasizing the ubiquitous presence of a relative equilibrium line dynamic, and which for glacial systems has long been seen as providing a mass supply feedback that can reconcile the disparity between the forcing and the response. I suggest that, in the same way that continental ice sheets have been modeled as passive sedimentary systems that can freely oscillate with little or no snowline forcing, sedimentary basin systems may be capable of similar behavior without vertical sea level change and illustrate the concepts with a low-order model. Sedimentary indicators for relative sea level change may be displaying disproportionately large responses to small eustatic sea level changes, due to internal positive feedbacks.     

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.     

Coupled climate modelling of ocean circulation changes during ice age inception

Freshening of high latitude surface waters can change the large-scale oceanic transport of heat and salt. Consequently, atmospheric and sea ice perturbations over the deep water production sites excite a large-scale response establishing an oceanic "teleconnection" with time scales of years to centuries. To study these feedbacks, a coupled atmosphere-ocean-sea ice model consisting of a two dimensional atmospheric energy and moisture balance model (EMBM) coupled to a thermodynamic sea ice model and an ocean general circulation model is utilised. The coupled model reproduces many aspects of the present oceanic circulation. We also investigate the climate impact of changes in fresh water balance during an ice age initiation. In this experiment part of the precipitation over continents is stored within continental ice sheets. During the buildup of ice sheets the oceanic stratification in the North Atlantic is weakened by a reduced continental run-off leading to an enhanced thermohaline circulation. Under these conditions salinity is redistributed such that deep water is more saline than under present conditions. Once the ice sheets built up, we simulate an ice age climate without net fresh water storage on the continents. In this case the coupled model reproduces the shallow and weak overturning cell, an ice edge advance insulating the upper ocean, and many other aspects of the glacial circulation.     

A study of the climatic regimes of the Pleistocene using a stochastic resonance model

A global energy balance model employing the stochastic resonance mechanism, previously used to explain the climatic variability of the late Pleistocene, has now been extended to account for the climatic variations over the full Pleistocene. The possibility that extremely long-term changes (of the order of millions of years) in the boundary conditions of the climate system have altered the response of the Pleistocene climate to the external orbital forcing has been investigated. It is shown that, by slowly changing the only free parameter of the model, the system can undergo a pitchfork bifurcation. The bifurcation point separates a linear regime (identified with the early Pleistocene climate) from a strongly nonlinear regime (the late Pleistocene) where the stochastic resonance mechanism produces rapid and symmetric transitions between the two stable steady states of the system. The main differences in the dynamic features of the two regimes are the change in amplitude of the oscillations, the relative importance of the stochastic forcing, the change in shape of the probability distribution, and the corresponding change in the power centered around the 100000 year cycle: in qualitative agreement with the observed geological record. With the introduction of the external orbital forcing, now spectrally complete and included without requiring any additional hypothesis, the model reproduces the previous results, namely the good correlation with the isotopic record, the appearance of the dominant spectral peaks, as well as the redness of the power spectrum. In particular, it is shown that the orbital forcing in eccentricity acts as a pacemaker of the major glacial cycles of the late Pleistocene through the mechanism of stochastic resonance. A stochastic sensitivity analysis is then applied to validate the significance of the results and to investigate the predictability of the climate system over the time-scales of the orbital cycles.     

Multiple instabilities and modes of glacial rhythmicity in the plio-Pleistocene: a general theory of late Cenozoic climatic change

It has been noted that several distinct modes of glacial oscillation have existed during the past few million years, ranging from low-amplitude, high-frequency oscillations in the early Pliocene, through relatively high amplitude, predominantly near-40 ky period, oscillations in the late Pliocene and early Pleistocene, to the major near-100 ky period oscillations of the late Pleistocene. In addition to other plausible mechanisms suggested previously to explain aspects of this multirhythmic phenomenon, we now illustrate another possible contributor to this type of behavior based on the hypothesis that the slow-response climatic system is bistable and that two kinds of internal instability may be operative along with externally imposed forcing due to earth-orbital (Milankovitch) radiation changes and slow, tectonically-induced changes in atmospheric carbon dioxide. These two instabilities have been discussed previously: one is due to positive feedback in the global carbon cycle leading to near-100 ky free oscillations of the ice sheets, and the other is due to the potential for ice-calving catastrophes associated with bedrock variations that can lead to oscillations of a period near 40 ky, independent of obliquity forcing. Within the framework of a dynamical model containing the possibility for these two instabilities, as well as for stable modes, we show (1) how Milankovitch radiative changes or stochastic forcing influencing ice sheets can induce aperiodic (chaotic) transitions between the possible stable and unstable modes, and more significantly, (2) how progressive, long-term, tectonically-induced, changes in carbon dioxide, acting in concert with earth-orbital radiative variations in high Northern Hemisphere latitudes, can force systematic transitions between the modes. Such systematic changes can result in an ice mass chronology for the past 5 My that is qualitatively similar to the observed record of global ice mass. In essence, we have constructed a minimum dynamical model of the late Cenozoic climatic changes, containing what are believed to be the main physical factors determining these changes: ice mass, bedrock depression, atmospheric carbon dioxide concentration, deep ocean thermohaline state, Milankovitch radiation forcing, and slow tectonically-induced carbon dioxide forcing. This model forms the basis for a coherent theory for the complex climatic events of this long period.     

过去0.8 Ma期间的地表温度数值模拟研究

使用一个改进的二维能量平衡模式模拟了过去0.8 Ma冰期-间冰期旋回期间北半球各纬度带的地表温度,并以65°N的地表温度为代表与南极冰芯记录进行了比较.通过敏感性试验,分析了日射量、温室气体、沙尘气溶胶强迫和水汽反馈的辐射-气候效应.结果显示,日射量变化不足以解释冰期-间冰期旋回期间北半球的地表温度变化,大气温室气体(...     

Impact of dust aerosol on glacial-interglacial climate

The temperature anomaly and dust concentrations recorded from central Antarctic ice core records display a strong negative correlation. The dust concentration recorded from an ice core in central Antarctica is 50-70 times higher during glacial periods than interglacial periods. This study investigated the impact of dust aerosol on glacial-interglacial climate, using a zonal energy balance model and dust concentration data from an Antarctica ice core. Two important effects of dust, the direct radiative effect and dust-albedo feedback, were considered. On the one hand, the direct radiative effect of dust significantly cooled the climate during the glacial period, with cooling during the last glacial maximum being as much as 2.05℃ in Antarctica. On the other hand, dust deposition onto the ice decreased the surface albedo over Antarctica, leading to increased absorption of solar radiation, inducing a positive feedback that warmed the region by as much as about 0.9℃ during the glacial period. However, cooling by the direct dust effect was found to be the controlling effect for the glacial climate and may be the major influence on the strong negative correlation between temperature and dust concentration during glacial periods.     

Ice and climate modeling: An editorial essay

The growth and decay of ice sheets are driven by forces affecting the seasonal cycles of snowfall and snowmelt. The external forces are likely to be variations in the earth's orbit which cause differences in the solar radiation received. Radiational control of snowmelt is modulated by the seasonal cycles of snow albedo and cloud cover. The effects of orbital changes can be magnified by feedbacks involving atmospheric CO₂ content, ocean temperatures and desert areas. Climate modeling of the causes of the Pleistocene ice ages involves modeling the interactions of all components of the climate system; snow, sea ice, glacier ice, the ocean, the atmosphere, and the solid earth. Such modeling is also necessary for interpreting oxygen isotope records from ice and ocean as paleoclimatic evidence.     

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.     

Snowline instability in a general circulation model: application to Carboniferous glaciation

For over twenty years it has been known that energy balance models (EBMs) with snow-albedo feedback are characterized by unstable behavior in some areas of parameter space. This behavior leads to rapid changes in snow area due to small changes in forcing, and has been termed the small ice cap instability (SICI). It has never been clarified whether this behaviour reflects a real feature of the climate system or a limitation in EBMs. In this study we demonstrate that evidence for similar unstable behavior can also be found in an atmospheric general circulation model (GCM), using a realistic set of boundary conditions for the Carboniferous (300 Ma), one of the most extensive periods of glaciation in Earth history. When solar luminosity is sequentially lowered to near values appropriate for the Carboniferous, there is a discontinuous increase in summer snow area. The instability occurs in approximately the same area of parameter space as one previously found in an EBM. Analysis of selected fields indicates that the circulation is primarily affected in the area of snow increase; far-field effects are minimal. There is good agreement between model-generated summer snowcover and one reconstruction of Carboniferous ice cover. Although more work is required on this topic, our results provide increased support for the possibility that the snowline instability represents a real feature of the climate system, and that it may help explain some cases of glacial inception and abrupt transitions in Earth history.     

Weak oceanic heat transport as a cause of the instability of glacial climates

The stability of the thermohaline circulation of modern and glacial climates is compared with the help of a two dimensional ocean—atmosphere—sea ice coupled model. It turns out to be more unstable as less freshwater forcing is required to induce a polar halocline catastrophy in glacial climates. The large insulation of the ocean by the extensive sea ice cover changes the temperature boundary condition and the deepwater formation regions moves much further South. The nature of the instability is of oceanic origin, identical to that found in ocean models under mixed boundary conditions. With similar strengths of the oceanic circulation and rates of deep water formation for warm and cold climates, the loss of stability of the cold climate is due to the weak thermal stratification caused by the cooling of surface waters, the deep water temperatures being regulated by the temperature of freezing. Weaker stratification with similar overturning leads to a weakening of the meridional oceanic heat transport which is the major negative feedback stabilizing the oceanic circulation. Within the unstable regime periodic millennial oscillations occur spontaneously. The climate oscillates between a strong convective thermally driven oceanic state and a weak one driven by large salinity gradients. Both states are unstable. The atmosphere of low thermal inertia is carried along by the oceanic overturning while the variation of sea ice is out of phase with the oceanic heat content. During the abrupt warming events that punctuate the course of a millennial oscillation, sea ice variations are shown respectively to damp (amplify) the amplitude of the oceanic (atmospheric) response. This sensitivity of the oceanic circulation to a reduced concentration of greenhouse gases and to freshwater forcing adds support to the hypothesis that the millennial oscillations of the last glacial period, the so called Dansgaard—Oeschger events, may be internal instabilities of the climate system.     

A model for large glacial–interglacial climate-induced changes in dust and sea salt concentrations in deep ice cores (central Antarctica): palaeoclimatic implications and prospects for refining ice core chronologies

A semi-empirical model has been developed to reproduce glacial–interglacial changes of continental dust and marine sodium concentrations (factor of ∼50 and ∼5, respectively) observed in inland Antarctic ice cores. The model uses conceptual pathways of aerosols within the high troposphere; assumes the dry deposition of impurities on the Antarctic surface; uses estimates of aerosol transit times taken independent of climate; assumes a temperature-dependent removal process during aerosol pathways from the mid-latitudes. The model is fitted to the data over the last four climate cycles from Vostok and EPICA Dome C Antarctic sites. As temperature is cooling, the aerosol response suggests different modes of climate couplings between latitudes, which can be continuous or below temperature thresholds for sodium and dust, respectively. The model estimates a southern South America dust source activity two to three times higher for glacial periods than for the Holocene and a glacial temperature over the Southern Ocean 3–5 °C cooler. Both estimates appear consistent with independent observations. After removal of temperature effects, dust and sodium residuals for both sites show orbital frequencies in opposite phase at the precession timescale. Such long-term insolation-related modulation of terrestrial and marine aerosol input, could provide a chemical pacemaker useful for refining ice core chronologies.     

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.     

Glacial-Interglacial Atmospheric CO2 Change—The Glacial Burial Hypothesis

Organic carbon buried under the great ice sheets of the Northern Hemisphere is suggested to be the missing link in the atmospheric CO2 change over the glacial-interglacial cycles. At glaciation, the advancement of continental ice sheets buries vegetation and soil carbon accumulated during warmer pe-riods. At deglaciation, this burial carbon is released back into the atmosphere. In a simulation over two glacial-interglacial cycles using a synchronously coupled atmosphere-land-ocean carbon model forced by reconstructed climate change, it is found that there is a 547-Gt terrestrial carbon release from glacial maximum to interglacial, resulting in a 60-Gt (about 30-ppmv) increase in the atmospheric CO2, with the remainder absorbed by the ocean in a scenario in which ocean acts as a passive buffer. This is in contrast to previous estimates of a land uptake at deglaciation. This carbon source originates from glacial burial,continental shelf, and other land areas in response to changes in ice cover, sea level, and climate. The input of light isotope enriched terrestrial carbon causes atmospheric δ^13C to drop by about 0.3‰ at deglaciation,followed by a rapid rise towards a high interglacial value in response to oceanic warming and regrowth on land. Together with other ocean based mechanisms such as change in ocean temperature, the glacial burial hypothesis may offer a full explanation of the observed 80-100-ppmv atmospheric CO2 change.     

A two-dimensional energy balance climate model including radiation and ice caps-albedo feedback

A simplified two-dimensional energy balance climate model including the solar and infrared radiation transports, the turbulent exchanges of heat in vertical and horizontal directions and the ice caps-albedo feedback is developed The solutions show that if the atmosphere is considered as a grey body and the grey coefficient depends upon the distributions of absorption medium and cloudiness, both horizontal and vertical distributions of temperature are identical to the observation.On the other hand, comparing the models that the atmosphere is considered as a grey body with ones that the infrared radiation is parameterized as a linear function of temperature, as was considered by Budyko, Sellers(1969), then the results show that even though both of them can obtain the earth's surface temperature in agreement with the observation, the sensitiv ity of the climate to the changes of solar constant is very different. In the former case,the requirement for the ice edge to move southward from the normal 72°N to 50°N(i.e. where the glacial climate would take place) is that the solar constant should decrease by 13% to 16%. However, in the latter case, the climate is highly sensitive to the changes of solar radiation. In this case, the requirement of solar radiation occurring in the glacial climate should decrease by 2% to 6%. According to the investigations mentioned above we must be careful when the parameterizations of the radiation and other processes are conducted in a climate model, otherwise the reliability of the results is suspicious.     

Late Pleistocene variations in Antarctic sea ice II: effect of interhemispheric deep-ocean heat exchange

Variations in production rates of warm North Atlantic Deep Water (NADW) have been proposed as a mechanism for linking climate fluctuations in the northern and southern hemispheres during the Pleistocene. We have tested this hypothesis by examining the sensitivity of a thermodynamic/dynamic model for Antarctic sea ice to changes in vertical ocean heat flux and comparing the simulations with modified CLIMAP sea-ice maps for 18 000 B.P. Results suggest that changes in NADW production rates, and the consequent changes in the vertical ocean heat flux in the Antarctic, can only account for about 20%–30% of the overall variance in Antarctic sea-ice extent. This conclusion has been validated against an independent geological data set involving a time series of sea-surface temperatures from the subantarctic. The latter comparison suggests that, although the overall influence of NADW is relatively minor, the linkage may be much more significant at the 41 000-year obliquity period. Despite some limitations in the models and geological data, we conclude that NADW variations may have played only a modest role in causing late Pleistocene climate change in the high latitudes of the southern hemisphere. Our conclusion is consistent with calculations by Manabe and Broccoli (1985) suggesting that atmospheric CO₂ changes may be more important for linking the two hemispheres.     

Development of a new sea ice growth and lead parameterization

A thermodynamic sea ice model that has been numerically structured to take time steps on the order of a week has been shown to be sensitive to time step size. This sensitivity was caused by the extrapolation of initial ice growth rates over the long time step. A new parameterization of new sea ice growth on open ocean and in leads that can be used over a large range of time step sizes (at least from 0.3 to 12 days) is described here. In this parameterization new sea ice growth is computed as a power law function of the initial energy deficit in the ocean. This power law takes into account the rapid reduction of the ice growth rate as the sea ice gets thicker, and therefore reduces sensitivity to time step size. Tests of this parameterization show that this method does a good job of simulating the rate of new ice growth when compared to data from Mawson, Antarctica, and is relatively insensitive to the length of the time step.     

Properties of adjoint sea ice sensitivities to atmospheric forcing and implications for the causes of the long term trend of Arctic sea ice

Based on adjoint sensitivities of the coupled Massachusetts Institute of Technology ocean–sea ice circulation model, the potential influence of thermodynamic atmospheric forcing on the interannual variability of the September sea ice area (AREA) and volume (VOLUME) in the Arctic is investigated for the three periods 1980–1989, 1990–1999 and 2000–2009. Sensitivities suggest that only large forcing anomalies prior to the spring melting onset in May can influence the September sea ice characteristics while even small changes in the atmospheric variables during subsequent months can significantly influence September sea ice state. Specifically, AREA close to the ice edge in the Arctic seas is highly sensitive to thermodynamic atmospheric forcing changes from June to July. In contrast, VOLUME is highly sensitive to atmospheric temperature changes occurring during the same period over the central parts of the Arctic Ocean. A comparison of the sea ice conditions and sensitivities during three different periods reveals that, due to the strong decline of sea ice concentration and sea ice thickness, sea ice area became substantially more sensitive to the same amplitude thermodynamic atmospheric forcing anomalies during 2000–2009 relative to the earlier periods. To obtain a quantitative estimate of changes that can be expected from existing atmospheric trends, adjoint sensitivities are multiplied by monthly temperature differences between 1980s and two following decades. Strongest contributions of surface atmospheric temperature differences to AREA and VOLUME changes are observed during May and September. The strongest contribution from the downward long-wave heat flux to AREA changes occurs in September and to VOLUME changes in July–August. About 62 % of the AREA decrease simulated by the model can be explained by summing all contributions to the thermodynamic atmospheric forcing. The changing sea ice state (sensitivity) is found to enhance the decline and accounts for about one third of the explained reduction. For the VOLUME decrease, the explained fraction of the decrease is only about 37 %.