Ice stream sticky spots: A review of their identification and influence beneath contemporary and palaeo-ice streams

Rapidly-flowing ice streams are the arterial drainage routes in continental ice sheets and exert a major influence on ice sheet mass balance. Recent observations have revealed that ice stream flow exhibits considerable variability, with relatively rapid changes taking place in speed and direction. This spatial and temporal variability is intimately linked to the conditions at the base of the ice streams and the distribution of localised patches of basal friction, known as ‘sticky spots’. In this paper, we provide a detailed review of sticky spot observations from both contemporary and palaeo-ice stream beds in order to better understand their nature and influence. Observations and theoretical considerations reveal four primary causes of ‘stickiness’: (i), bedrock bumps; (ii), till-free areas; (iii), areas of ‘strong’ (well drained) till; and (iv), freeze-on of subglacial meltwater. These may act together in one location, or in isolation; and a progressive increase in their distribution could lead to ice stream shut-down. Bedrock bumps are influential under active ice streams, where they provide form drag and can create thinner ice which increases the likelihood of basal freeze-on. Increased bed roughness may prevent the lateral migration of some ice streams but bedrock bumps are unlikely to cause ice stream shut-down because, over long time-scales, ice stream erosion might be expected to reduce their amplitude. The influence of till-free areas beneath an ice stream will depend critically on the amount of water that might be drawn out of the surrounding till to lubricate such areas. They are likely to be most important in ice stream onset zones but their identification has proved difficult beneath active ice streams. If an ice stream operates solely by till deformation, it is conceivable that a progressive increase in the exposure of till-free areas could lead to shut-down through a process of sediment exhaustion. Areas of strong, well drained till have been identified beneath both active and ancient ice streams and are most likely to result from the reorganisation of subglacial meltwater. The collapse of an inefficient ‘cannalised’ system to a more efficient ‘channelised’ system can occur rapidly and this mechanism has been hypothesised as a candidate for ice stream shut-down in both contemporary and palaeo-settings. Basal freeze-on has also been observed and inferred from beneath modern and palaeo-ice streams, and a reduction in basal meltwater supply coupled with ice stream drawdown and the advection of cold ice increases the likelihood of switching off an ice stream. A paucity of data from ice stream sticky spots limits a better understanding of their nature, distribution and evolution beneath ice streams. Future technological advances are likely to improve the resolution of the data collected from the beds of modern ice streams but well-preserved palaeo-ice stream beds also hold potential for investigating their influence on ice stream flow and we present simple landsystems models to aid their identification. Such data will considerably enhance the basal boundary condition in ice stream models which will, ultimately, refine our predictions of the response of contemporary ice sheets to future changes in climate.     

Reconstructing the last Irish Ice Sheet 1: changing flow geometries and ice flow dynamics deciphered from the glacial landform record

The glacial geomorphological record provides an effective means to reconstruct former ice sheets at ice sheet scale. In this paper we document our approach and methods for synthesising and interpreting a glacial landform record for its palaeo-ice flow information, applied to landforms of Ireland. New, countrywide glacial geomorphological maps of Ireland comprising >39,000 glacial landforms are interpreted for the spatial, glaciodynamic and relative chronological information they reveal. Seventy one ‘flowsets’ comprising glacial lineations, and 19 ribbed moraine flowsets are identified based on the spatial properties of these landforms, yielding information on palaeo-ice flow geometry. Flowset cross-cutting is prevalent and reveals a highly complex flow geometry; major ice divide migrations are interpreted with commensurate changes in the flow configuration of the ice sheet. Landform superimposition is the key to deciphering the chronology of such changes, and documenting superimposition relationships yields a relative ‘age-stack’ of all Irish flowsets. We use and develop existing templates for interpreting the glaciodynamic context of each flowset – its palaeo-glaciology. Landform patterns consistent with interior ice sheet flow, ice stream flow, and with time-transgressive bedform generation behind a retreating margin, under a thinning ice sheet, and under migrating palaeo-flowlines are each identified. Fast ice flow is found to have evacuated ice from central and northern Ireland into Donegal Bay, and across County Clare towards the south-west. Ice-marginal landform assemblages form a coherent system across southern Ireland marking stages of ice sheet retreat. Time-transgressive, ‘smudged’ landform imprints are particularly abundant; in several ice sheet sectors ice flow geometry was rapidly varying at timescales close to the timescale of bedform generation. The methods and approach we document herein could be useful for interpreting other ice sheet histories. The flowsets and their palaeo-glaciological significance that we derive for Ireland provide a regional framework and context for interpreting results from local scale fieldwork, provide major flow events for testing numerical ice sheet models, and underpin a data-driven reconstruction of the Irish Ice Sheet that we present in an accompanying paper – Part 2.     

Streamlined bedrock terrain and fast ice flow, Jakobshavns Isbrae, West Greenland: implications for ice stream and ice sheet dynamics

This study investigates the marginal subglacial bedrock bedforms of Jakobshavns Isbrae, West Greenland, in order to examine the processes governing bedform evolution in ice stream and ice sheet areas, and to reconstruct the interplay between ice stream and ice sheet dynamics. Differences in bedform morphology (roche moutonnee or whaleback) are used to explore contrasts in basal conditions between fast and slow ice flow. Bedform density is higher in ice stream areas and whalebacks are common. We interpret that this is related to higher ice velocities and thicker ice which suppress bed separation. However, modification of whalebacks by plucking occurs during deglaciation due to ice thinning, flow deceleration, crevassing and fluctuations in basal water pressure. The bedform evidence points to widespread basal sliding during past advances of Jakobshavns Isbrae. This was encouraged by increased basal temperatures and melting at depth, as well as the steep marginal gradients of Jakobshavns Isfjord which allowed rapid downslope evacuation of meltwater leading to strong ice/bedrock coupling and scouring. In contrast to soft-bedded ice stream bedforms, the occurrence of fixed basal perturbations and higher bed roughness in rigid bed settings prevents the basal ice subsole from maintaining a stable form which, coupled with secondary plucking, counteracts the development of bedforms with high elongation ratios. Cross-cutting striae and double-plucked, rectilinear bedforms suggest that Jakobshavns Isbrae became partially unconfined during growth phases, causing localised diffluent flow and changes in ice sheet dynamics around Disko Bugt. It is likely that Disko Bugt harboured a convergent ice flow system during repeated glacial cycles, resulting in the formation of a large coalesced ice stream which reached the continental shelf edge.     

Paleoglaciological reconstructions for the Tibetan Plateau during the last glacial cycle: evaluating numerical ice sheet simulations driven by GCM-ensembles

The Tibetan Plateau is a topographic feature of extraordinary dimension and has an important impact on regional and global climate. However, the glacial history of the Tibetan Plateau is more poorly constrained than that of most other formerly glaciated regions such as in North America and Eurasia. On the basis of some field evidence it has been hypothesized that the Tibetan Plateau was covered by an ice sheet during the Last Glacial Maximum (LGM). Abundant field- and chronological evidence for a predominance of local valley glaciation during the past 300,000 calendar years (that is, 300 ka), coupled to an absence of glacial landforms and sediments in extensive areas of the plateau, now refute this concept. This, furthermore, calls into question previous ice sheet modeling attempts which generally arrive at ice volumes considerably larger than allowed for by field evidence. Surprisingly, the robustness of such numerical ice sheet model results has not been widely queried, despite potentially important climate ramifications. We simulated the growth and decay of ice on the Tibetan Plateau during the last 125 ka in response to a large ensemble of climate forcings (90 members) derived from Global Circulation Models (GCMs), using a similar 3D thermomechanical ice sheet model as employed in previous studies. The numerical results include as extreme end members as an ice-free Tibetan Plateau and a plateau-scale ice sheet comparable, in volume, to the contemporary Greenland ice sheet. We further demonstrate that numerical simulations that acceptably conform to published reconstructions of Quaternary ice extent on the Tibetan Plateau cannot be achieved with the employed stand-alone ice sheet model when merely forced by paleoclimates derived from currently available GCMs. Progress is, however, expected if future investigations employ ice sheet models with higher resolution, bidirectional ice sheet-atmosphere feedbacks, improved treatment of the surface mass balance, and regional climate data and climate reconstructions.     

中国极地冰盖数值模拟研究进展北大核心CSCD

冰盖数值模拟是一种基于多源观测数据,通过构建并求解冰流动力学方程组,理解冰流运动物理机制以及诊断和预估其演化过程的方法,目前已被广泛应用于冰盖变化研究。本文简要介绍了极地冰盖数值模拟方法,归纳综述了近十余年我国学者在极地冰盖数值模拟方面的研究进展,厘清我国在冰盖数值模拟领域遇到的瓶颈和关键问题。阐述了如何与我国的极地冰盖科考优势区域深度结合,协同多源强化观测和数值模拟,研发和改进冰盖模式,提高冰盖模拟能力,对定量估算极地冰盖的物质平衡及其对未来海平面上升的影响做出实质贡献。通过逐步发展冰盖模式的研究能力,有望将来在冰盖关键动力过程和机制的科学认识上有所突破。     

Tracer transport in the Greenland ice sheet: three-dimensional isotopic stratigraphy

Polar ice cores can provide both a record of climate history and a sharp test of the performance of numerical ice dynamics models. The stratigraphic structure of an ice sheet is an expression of its full depositional and dynamic history and thus presents a greater challenge to computer models than merely matching the contemporary ice thickness and areal extent. We describe a coupled model of ice and tracer dynamics that is realized by adding a semi-Lagrangian tracer transport scheme to a conventional thermomechanical ice dynamics model. Model skill is demonstrated by using ice core data from the GRIP site near Summit Greenland to successfully predict the isotopic stratigraphy of ice cores at other deep drilling sites. The success of this effort indicates that, when compensated for the effects of ice flow and elevation, all the deep cores relate a coherent glacial history over the past 120,000 years. According to the simulation results, the oldest Greenland ice lies beneath the GRIP, GISP2 and NorthGRIP sites although comparably old ice may also be found in North Greenland and East Central Greenland.     

Short Communication: A numerical method for diffusive transport with moving boundaries and discontinuous material properties

A method for the numerical simulation of diffusive transport with moving boundaries is developed and tested. The variable domain is mapped onto a fixed region, which introduces a term of convective form to the transformed governing equation. The resulting convection/diffusion equation is solved by a finite-difference method. An ‘Immersed Interface’ Method (IIM) is introduced in order to retain second-order accuracy near discontinuities in material properties, where the solution is not smooth. The method performs well in benchmark calculations against an analytical solution. The IIM scheme is capable of treating a strong discontinuity in the gradient, and it is readily extended to two or three dimensions. The methods are illustrated through a calculation for the temperature profile in a growing continental ice sheet, in which the thermal properties are discontinuous at the rock/ice interface. © 1997 by John Wiley & Sons, Ltd.     

Switching of a paleo-ice stream in northwest Svalbard

Ice streams are the fast-flowing zones of ice sheets that can discharge a large flux of ice. The glaciated western Svalbard margin consists of several cross-shelf troughs which are the former ice stream drainage pathways during the Pliocene–Pleistocene glaciations. From an integrated analysis of high-resolution multibeam swath-bathymetric data and several high-resolution two-dimensional reflection seismic profiles across the western and northwestern Svalbard margin we infer the ice stream flow directions and the deposition centres of glacial debris that the ice streams deposited on the outer margin. Our results show that the northwestern margin of Svalbard experienced a switching of a major ice stream. Based on correlation with the regional seismic stratigraphy as well as the results from ODP 911 on Yermak Plateau and ODP 986 farther south on the western margin of Spitsbergen, off Van Mijenfjord, we find that first a northwestward flowing ice stream developed during initial northern hemispheric cooling (starting ～2.8–2.6 Ma). A switch in ice stream flow direction to the present-day Kongsfjorden cross-shelf trough took place during a glaciation at ～1.5 Ma or probably later during an intensive major glaciation phase known as the ‘Mid-Pleistocene Revolution’ starting at ～1.0 Ma. The seismic and bathymetric data suggest that the switch was abrupt rather than gradual and we attribute it to the reaching of a tipping point when growth of the Svalbard ice sheet had reached a critical thickness and the ice sheet could overcome a topographic barrier.     

冰川动力学模式模型进展及研究

冰冻圈是气候系统中的一个重要圈层, 其中冰川又是冰冻圈的重要组成部分, 冰川、 尤其是山地冰川的本构方程和建模一直是冰川动力学的核心任务。首先, 简要回顾冰川模型的研究和发展, 简要介绍了基于Navier-Stokes方程耦合温度场的三维冰川模型。然后, 介绍了冰川建模过程中的常用的静水压力近似、 一阶近似、 浅冰近似等的基本概念, 总结了冰川的动力数值模式建立的主要方法, 对于常用的GLIMMER冰盖模式的物理框架及其应用进行了介绍。最后, 针对目前的简化模型难以准确地描述山地冰川的物理过程及其变化的问题, 提出了一个基于全Navier-Stokes方程的山地冰川模型及其动力框架、 边界条件处理的设想。本文可为建立、 发展冰川及冰架模型, 尤其建立和发展山地冰川模型提供基础知识和参考。     

南极冰盖GLIMMER模式移动边界试验研究

利用欧洲冰盖比较计划(EISMINT)的移动边界条件EISMINT-1测试集,通过三维有限差分南极冰盖GLIMMER模式,采用浅冰近似计算了一个定义在方形冰盖积分区域的流场特征量,研究了冰盖在大尺度长时间序列条件下对气候变化的反馈,考察了稳定态下冰盖演化的周期性行为.试验表明:GLIMMER模式在EISMINT-1移动边界条件下可以模拟出气候强迫下的冰盖演化趋势,在长时间尺度上可以刻画出气候变化的反馈机制.同时,对南极冰盖数值模拟面临的问题、GLIMMER模式以及EISMINT冰盖比较计划的内容和框架做了说明,对EISMINT比较计划目前的发展状况和遇到的问题做了分析,并且对GLIMMER模式下一步的研究方向做了一些探讨.     

东南极冰盖/冰架变化监测与预测技术研究

南北极是研究全球变化的关键区域。＂十一五＂期间我国在南极地区系统开展了东南极冰盖/冰架变化监测与预测技术研究,对认识全球气候变化具有重要作用。通过项目实施,建立和发展了一批现场观测体系,发展了冰盖观测新技术并集成应用于东南极冰盖的综合观测,拓展了对冰穹A地区的新认识和新发现;在冰穹A边缘地区钻取的一支浅冰芯恢复了过去约780年的气候记录,记录了东南极地区存在小冰期的明显证据;发展了东南极冰盖积累和等时年层流动模型,研究在冰盖浅层、中层和深部的变化特征,反演了冰穹A地区的古积累率分布。本文概要介绍该项目基本情况。     

河流冰塞数值模拟进展

冰塞是高纬度地区河流凌汛的主要诱因.为防凌减灾,围绕着河冰问题的试验研究、原型观测和数值模拟,国内外学者展开了大量的研究.就数值模拟方面,综述了国内外学者在河冰一维、二维数值模拟方面的研究成果;重点描述了Shen的一维模型和模拟冰塞体溃决的二维模型及其在实际中的应用;在评述和分析各模型特点的基础上,尝试提出了今后的发展方向.     

Ice-avalanche scenario elaboration and uncertainty propagation in numerical simulation of rock-/ice-avalanche-induced impact waves at Mount Hualcán and Lake 513, Peru

The interest in numerical simulation of cascading processes involving mass movements and lakes has recently risen strongly, especially as the formation of new lakes in high-mountain areas as a consequence of glacier recession can be observed all over the world. These lakes are often located close to potentially unstable slopes and therewith prone to impacts from mass movements, which may cause the lake to burst out and endanger settlements further downvalley. The need for hazard assessment of such cascading processes is continuously rising, which demands methodological development of coupled numerical simulations. Our study takes up on the need for systematic analysis of the effect of assumptions taken in the simulation of the process chain and the propagation of the corresponding uncertainties on the simulation results. We complemented the research of Adv Geosci 35:145-155, 2014 carried out at Lake 513 in the Cordillera Blanca, Peru, by focusing on the aspects of (a) ice-avalanche scenario development and of (b) analysis of uncertainty propagation in the coupled numerical simulation of the process chain of an impact wave triggered by a rock/ice avalanche. The analysis of variance of the dimension of the overtopping wave was based on 54 coupled simulation runs, applying RAMMS and IBER for simulation of the ice avalanche and the impact wave, respectively. The results indicate (a) location and magnitude of potential ice-avalanche events, and further showed (b) that the momentum transfer between an avalanche and the impact wave seems to be reliably representable in coupled numerical simulations. The assessed parameters—initial avalanche volume, friction calibration, mass entrainment and transformation of the data between the models—was decisive of whether the wave overtopped or not. The overtopping time and height directly characterize the overtopping wave, while the overtopping volume and the discharge describe the overtopping hydrograph as a consequence of the run-up rather than the wave. The largest uncertainties inherent in the simulation of the impact wave emerge from avalanche-scenario definition rather than from coupling of the models. These findings are of relevance also to subsequent outburst flow simulation and contribute to advance numerical simulation of the entire process chain, which might also be applied to mass movements other than rock/ice avalanches.     

Calving processes and the dynamics of calving glaciers

Calving of icebergs is an important component of mass loss from the polar ice sheets and glaciers in many parts of the world. Calving rates can increase dramatically in response to increases in velocity and/or retreat of the glacier margin, with important implications for sea level change. Despite their importance, calving and related dynamic processes are poorly represented in the current generation of ice sheet models. This is largely because understanding the ‘calving problem’ involves several other long-standing problems in glaciology, combined with the difficulties and dangers of field data collection. In this paper, we systematically review different aspects of the calving problem, and outline a new framework for representing calving processes in ice sheet models. We define a hierarchy of calving processes, to distinguish those that exert a fundamental control on the position of the ice margin from more localised processes responsible for individual calving events. The first-order control on calving is the strain rate arising from spatial variations in velocity (particularly sliding speed), which determines the location and depth of surface crevasses. Superimposed on this first-order process are second-order processes that can further erode the ice margin. These include: fracture propagation in response to local stress imbalances in the immediate vicinity of the glacier front; undercutting of the glacier terminus by melting at or below the waterline; and bending at the junction between grounded and buoyant parts of an ice tongue. Calving of projecting, submerged ‘ice feet’ can be regarded as a third-order process, because it is paced by first- or second-order calving above the waterline.First-order calving can be represented in glacier models using a calving criterion based on crevasse depth, which is a function of longitudinal strain rate. Modelling changes in terminus position and calving rates thus reduces to the problem of determining the ice geometry and velocity distribution. Realistic solutions to the problem of modelling ice flow therefore depend critically on an appropriate choice of sliding law. Models that assume that basal velocities are controlled by basal drag can replicate much of the observed behaviour of calving glaciers with grounded termini, but an important limitation is that they cannot be used to model floating glacier termini or ice shelves. Alternative sliding laws that parameterise drag from the glacier margins provide more flexible and robust ways of representing calving in ice sheet models. Such models can explain a remarkable range of observed phenomena within a simple, unifying framework, including: downglacier increases in velocity and strain rates where basal and/or lateral drag diminishes; flow acceleration in response to thinning through time; the tendency for glaciers to stabilise at ‘pinning points’ in relatively shallow water or fjord narrowings; the constraints on ice shelf stability; and the contrasts in calving rates between tidewater and freshwater calving glaciers. Many unresolved issues remain, however, including the role played by the removal of backstress in the acceleration of retreating calving glaciers, and the controls on melting at and below the waterline.     

On the reconstruction of pleistocene ice sheets: A review

Pleistocene ice sheets can be reconstructed through three separate approaches: (1) Evidence based on glacial geological studies, such as erratic trains, till composition, crossing striations and exposures of multiple tills/nonglacial sediments. (2) Reconstructions based on glaciological theory and observations. These can be either two- or three-dimensional models; they can be constrained by ‘known’ ice margins at specific times; or they can be ‘open-ended’ with the history of growth and retreat controlled by parameters resting entirely within the model. (3) Glacial isostatic rebound after deglaciation provides a measure of the distribution of mass (ice) across a region. A ‘best fit’ ice sheet model can be developed that closely approximates a series of relative sea level curves within an area of a former ice sheet; in addition, the model should also provide a reasonable sea level fit to relative sea level curves at sites well removed from glaciation.This paper reviews some of the results of a variety of ice sheet reconstructions and concentrates on the various attempts to reconstruct the ice sheets of the last (Wisconsin, Weischelian, Würm, Devensian) glaciation. Evidence from glacial geology suggests flow patterns at variance with simple, single-domed ice sheets over North America and Europe. In addition, reconstruction of ice sheets from glacial isostatic sea level data suggests that the ice sheets were significantly thinner than estimates based on 18 ka equilibrium ice sheets (cf. Denton and Hughes, 1981). The review indicates it is important to differentiate between ice divides, which control the directions of glacial flow, and areas of maximum ice thickness, which control the glacial isostatic rebound of the crust upon deglaciation. Recent studies from the Laurentide Ice Sheet region indicate that the center of mass was not over Hudson Bay; that a major ice divide lay east of Hudson Bay so that flow across the Hudson Bay and James Bay lowlands was from the northeast; that Hudson Bay was probably open to marine invasions two or three times during the Wisconsin Glaciation; and that the Laurentide Ice Sheet was thinner than an equilibrium reconstruction would suggest.     

Reconstructing the last Irish Ice Sheet 2: a geomorphologically-driven model of ice sheet growth,retreat and dynamics

The ice sheet that once covered Ireland has a long history of investigation. Much prior work focussed on localised evidence-based reconstructions and ice-marginal dynamics and chronologies, with less attention paid to an ice sheet wide view of the first order properties of the ice sheet: centres of mass, ice divide structure, ice flow geometry and behaviour and changes thereof. In this paper we focus on the latter aspect and use our new, countrywide glacial geomorphological mapping of the Irish landscape (>39 000 landforms), and our analysis of the palaeo-glaciological significance of observed landform assemblages (article Part 1), to build an ice sheet reconstruction yielding these fundamental ice sheet properties. We present a seven stage model of ice sheet evolution, from initiation to demise, in the form of palaeo-geographic maps. An early incursion of ice from Scotland likely coalesced with local ice caps and spread in a south-westerly direction 200 km across Ireland. A semi-independent Irish Ice Sheet was then established during ice sheet growth, with a branching ice divide structure whose main axis migrated up to 140 km from the west coast towards the east. Ice stream systems converging on Donegal Bay in the west and funnelling through the North Channel and Irish Sea Basin in the east emerge as major flow components of the maximum stages of glaciation. Ice cover is reconstructed as extending to the continental shelf break. The Irish Ice Sheet became autonomous (i.e. separate from the British Ice Sheet) during deglaciation and fragmented into multiple ice masses, each decaying towards the west. Final sites of demise were likely over the mountains of Donegal, Leitrim and Connemara. Patterns of growth and decay of the ice sheet are shown to be radically different: asynchronous and asymmetric in both spatial and temporal domains. We implicate collapse of the ice stream system in the North Channel – Irish Sea Basin in driving such asymmetry, since rapid collapse would sever the ties between the British and Irish Ice Sheets and drive flow configuration changes in response. Enhanced calving and flow acceleration in response to rising relative sea level is speculated to have undermined the integrity of the ice stream system, precipitating its collapse and driving the reconstructed pattern of ice sheet evolution.     

Late Quaternary record of sea-level changes in the Antarctic

The Late Quaternary sediment sequence of the continental margin in the eastern Weddell Sea is well suited for palaeoenvironmental reconstructions. Two cores from the upper slope, which contain the sedimentary record of the last 300 ky, have been sedimentologically investigated. Age models are based on lithostratigraphy and are correlated with the stable isotope record. As a result of a detailed analysis of the clay mineral composition, grain size distributions and structures, this sedimentary record provides the first marine evidence that the Antarctic ice sheet extended to the shelf edge during the last glacial.The variations in volume and size of the ice sheet were also simulated in numerical models. Changes in accumulation rate and ice temperature are of some importance, but the model revealed that fluctuations are primarily driven by changes in eustatic sea-level and that the ice edge extended to the shelf edge during the last glacial maximum. This causal relationship implies that the maximum ice extension strongly depends on the magnitude and duration of the sea-level depression during a glacial period. The results of the sedimentological investigations and of the numerical models show that the Antarctic ice sheet follows glacial events in the northern hemisphere by teleconnections of sea level. Correspondence to: H. Grobe     

Evaluation of a numerical model of the British–Irish ice sheet using relative sea‐level data: implications for the interpretation of trimline observations

The glacial isostatic adjustment (GIA) of the British Isles is complex due to the interplay between local and non‐local signals. A number of recent studies have modelled the GIA response of the British Isles using relative sea‐level data. This study extends these previous analyses by using output from a numerical glaciological model as input to a GIA model. This is a necessary step towards more realistic GIA models, and although there have been similar studies for the major late Pleistocene ice sheets, this is the first study to do so for the British Isles. We test three reconstructions, classed as ‘minimal’, ‘median’ and ‘maximal’ in terms of their volume at maximum extent, and find it is possible to obtain good data–model fits. The minimal reconstruction is clearly preferred by the sea‐level data. The ice reconstructions tested were not constrained by geomorphological information of past ice extent (lateral and vertical). As a consequence, the reconstructions extend further than much of this information suggests, particularly in terms of ice thickness. It is notable, however, that the reconstructions produce good fits to many sea‐level data from central, mountainous regions (e.g. Scottish highlands), which lends support to the suggestion that trimlines, often used as an constraint on the palaeo ice surface location, are in fact features formed at the transition from warm‐ to cold‐based ice and so mark a minimum constraint on the ice surface altitude. Based on data–model misfits, suggestions are made for improving the ice model reconstructions. However, in many locations, the cause of the misfit could be due to non‐local, predominantly Fennoscandian ice and so interpretation is not straightforward. As a result, we suggest that future analyses of this type consider models and observations for both Fennoscandia and the British Isles. Copyright © 2012 John Wiley & Sons, Ltd.     

更新世冰盖与大洋碳储库相互作用的箱式模型模拟

全球大洋深海有孔虫碳同位素(δ13C)记录中广泛发现40万年周期,这一周期可能与偏心率长周期的轨道驱动有关.1.6 Ma以来,δ13C的这一长周期拉长到50万年,且重值期不再与偏心率低值对应.目前对δ13C 40万年周期的成因及其周期拉长的机制还不明确.这里使用了包含9个箱体的箱式模型,用于研究热带过程与冰盖相互作用及其对大洋碳循环的影响.模拟结果显示当北半球高纬海区海冰迅速增大时冰盖迅速融化,进入冰消期,而当海冰快速消失后,冰盖则重新缓慢增长.冰盖变化具有冰期长,间冰期短的非对称形态.在季节性太阳辐射量的驱动下冰盖变化具有10万年冰期-间冰期旋回.当冰盖融化速率受北半球高纬夏季太阳辐射量控制时,冰盖变化的岁差周期明显加强,相位与地质记录一致,说明轨道驱动可以通过非线性相位锁定机制使冰盖变化与其在相位上保持一致.海冰的阻隔效应使大气中CO₂在冰消期时增多.冰期时大洋环流减弱使大气中CO₂逐渐减少.当模型只有ETP驱动的风化作用而不考虑冰盖变化时,模拟的δ13C记录显示极强的40万年周期,体现了大洋碳储库对热带风化过程的响应.当同时考虑冰盖变化和风化作用时,模拟的δ13C结果中40万年周期减弱而10万年周期加强,并且40万年周期上碳储库与偏心率的相位与不考虑冰盖变化时的相位也存在差异,反映了冰盖变化引起的洋流改组压制了大洋碳循环对热带过程的响应.