Conditions for a steady ice sheet–ice shelf junction

This paper investigates the conditions under which a marine ice sheet may adopt a steady profile. The ice is treated as a linear viscous fluid caused to flow from a rigid base to and over water, treated as a denser but inviscid fluid. The solutions in the region around the point of flotation, or ‘transition’ zone, are calculated numerically. In-flow and out-flow conditions appropriate to ice sheet and ice shelf flow are applied at the ends of the transition zone and the rigid base is specified; the flow and steady free surfaces are determined as part of the solutions. The basal stress upstream, and the basal deflection downstream, of the flotation point are examined to determine which of these steady solutions satisfy ‘contact’ conditions that would prevent (i) the steady downstream basal deflection contacting the downstream base, and (ii) the upstream ice commencing to float in the event it was melted at the base. In the case that the upstream bed is allowed to slide, we find only one mass flux that satisfies the contact conditions. When no sliding is allowed at the bed, however, we find a range of mass fluxes satisfy the contact conditions. The effect of ‘backpressure’ on the solutions is investigated, and is found to have no affect on the qualitative behaviour of the junctions. To the extent that the numerical, linearly viscous treatment may be applied to the case of ice flowing out over the ocean, we conclude that when sliding is present, Weertman's ‘instability’ hypothesis holds.     

平面SV波在饱和土半空间中圆柱形孔洞周边的散射

在Biot饱和多孔介质动力学理论的基础上,利用Fourier—Bessel级数展开法,得到SV波在饱和土半空间中圆柱形孔洞周边的散射问题的解析解答。与已有相关问题的解析解答进行对比,验证了此解的正确性,并给出算例,分析了入射频率对柱面上的应力集中因子的影响。     

Topography and ice sheet growth

This paper uses a numerical ice sheet model to investigate the role of topography in influencing ice sheet growth. The model is applied to the maritime, mid-latitude uplands of Scotland and relies on a series of assumptions about mass balance, topography, and ice flow. It is driven by an imposed pattern of temperature change. The model is able to predict effectively the extent and thickness of the Loch Lomond ice sheet, using a palaeotemperature curve based on Coleoptera assemblages. A series of experiments with a stepped, constant July air temperature depression suggests that in Scotland a change in excess of ?3·0°C is necessary to initiate ice sheet growth; that steady state ice caps build up at changes of ?3 to ? 6·5°C; and that large ice sheets build up at changes of more than ? 6·625°C. The bifurcation revealed by the last two types of behaviour is the result of topography. Both the vertical amplitude and the spatial distribution of bedrock basins and ridges are important in determining the pattern, rate, and extent of ice sheet growth. The implication is that topography plays an important role in determining the dynamics of ice sheet growth.     

饱和土中孔列对平面快纵波的隔离效应

在Biot饱和土波动理论的基础上,用单排孔列作为屏障,对全空间饱和土中人射平面快纵波进行了隔离分析.采用波函数展开法,将人射波和散射波的势函数展开成Fourier-Bessel函数的无穷级数的形式,利用一组可以求解多散射问题的圆柱坐标系统和界面处位移连续的条件,得到问题的理论解.对影响隔离效果的孔间距和饱和土的渗透性等...     

基于远震接收函数的南极大陆冰盖厚度研究

冰盖厚度是研究南极冰盖质量、建立冰盖动力学模型的基本参数,对于冰川均衡调整、冰盖物质平衡及全球气候变化研究具有重要意义.基于地震学的远震接收函数和H-Kappa格网搜索方法可以用于地震台站下方冰盖厚度的可靠探测,不仅能与冰雷达获得的冰盖厚度进行独立对比,还可以与冰雷达方法相互补充,进一步填补南极大陆冰盖厚度探测空白区.本文利用布设于南极大陆冰盖上方的流动地震台阵记录到的远震波形数据,基于接收函数方法对台阵下方的冰盖厚度进行了研究.结果显示:基于远震接收函数方法的冰盖厚度与Bedmap2冰厚格网模型相比,二者差别大多在200 m以内;少数台站差值达到600 m左右,这一差别可能与Bedmap2测线分布空区、冰雷达测深不确定性以及冰盖内部复杂波速结构等因素有关.本文研究结果表明:利用南极大陆冰盖上方的流动地震台阵,基于远震接收函数方法可以获得比较可靠的南极冰盖厚度,为独立验证冰雷达的探测结果并弥补冰雷达探测空白区提供了有效方法.同时,部分台站接收函数波形的复杂性可能暗示了南极大陆数千米厚的冰盖内部结构不是均一的,仍然存在比较复杂的内部结构变化.因此,有必要进一步利用包括接收函数波形拟合、地震面波反演等方法对南极大陆冰盖厚度及其内部精细结构进行更为深入的研究.     

基于ICESat块域分析法探测2003～2008年南极冰盖质量变化

利用2003～2008年间的ICESat卫星激光测高数据,通过块域交叉点分析提取南极大陆冰盖表面高程变化信息,同时探讨了卫星激光测高不同任务间的系统偏差,结合冰盖地表粒雪密度模型探测南极大陆冰盖质量变化,并对其原因做了初步分析.结果显示南极大陆冰盖高度变化具有明显的年周期信号,平均周年振幅为2.21 cm.在南极大陆的...     

圆弧状凹陷地形对平面P波的散射:高频解答

利用波函数的Fourier-Bessel级数展开,推导了具有不同深宽比的圆弧状凹陷地形对入射平面P波二维散射问题的解析解.与现有解析解不同之处在于,为了使该解析解适用于更高的入射波频率,本文利用了柱函数的渐进性质,使得散射波的待定系数可以直接确定,避免了线性方程组的求解以及相关的数值计算问题,从而拓展了该解析解适用的频带范围.通过与现有解析解的比较,论证了该解析解的正确性,进而在一个较宽的频带范围内分析了圆弧状凹陷地形对入射平面P波的散射效应.     

Scattering of Plane P Waves by Circular-arc Canyon Topography:High-frequency Solution

Through the Fourier-Bessel series expansion of wave functions,the analytical solution to the two-dimensional scattering problem of incidental plane P waves by circular-arc canyon topography with different depth-to-width ratio is deduced.Unlike other existing analytical solutions,in order to ensure that the analytical solution is valid for higher frequency incident waves,the asymptotic properties of cylindrical functions are in this paper introduced to directly determine the unknown coefficients of scattering waves,avoiding the solution of linear equation systems and corresponding numerical issues,which in turn expand the frequency band in which the analytical solution is valid.Comparison with other existing analytical solutions demonstrates that the proposed analytical solution is correct.Furthermore,the scattering effects of a circular-arc canyon on the incident plane P wave are analyzed in a comparatively broad frequency band.     

Representing Grounding Line Dynamics in Numerical Ice Sheet Models: Recent Advances and Outlook

Recent satellite observations of the Antarctic and Greenland ice sheets show accelerated ice flow and associated ice sheet thinning along coastal outlet glaciers in contact with the ocean. Both processes are the result of grounding line retreat due to melting at the grounding line (the grounding line is the contact of the ice sheet with the ocean, where it starts to float and forms an ice shelf or ice tongue). Such rapid ice loss is not yet included in large-scale ice sheet models used for IPCC projections, as most of the complex processes are poorly understood. Here we report on the state-of-the art of grounding line migration in marine ice sheets and address different ways in which grounding line migration can be attributed and represented in ice sheet models. Using one-dimensional ice flow models of the ice sheet/ice shelf system we carried out a number of sensitivity experiments with different spatial resolutions and stress approximations. These are verified with semi-analytical steady state solutions. Results show that, in large-scale finite-difference models, grounding line migration is dependent on the numerical treatment (e.g. staggered/non-staggered grid) and the level of physics involved (e.g. shallow-ice/shallow-shelf approximation).     

利用ICESat数据解算南极冰盖冰雪质量变化

南极冰盖冰雪质量变化反映了全球气候变化,并且直接影响着全球海平面变化.ICESat测高卫星的主要任务之一就是要确定南北两极冰盖的质量变化情况并评估其对全球海平面变化的影响.本文利用2003年10月至2008年12月的ICESat测高数据,针对南极DEM分辨率有限的特殊性,通过求解坡度改正值,解决重复轨道地面脚点不重合的问题,计算了南极大陆(86°S以北区域,后文所述南极冰盖均不包括86°S以南区域)在这5年里的冰雪质量变化情况,得到东南极冰盖的质量变化为-18±20Gt/a,西南极-26±6Gt/a,南极冰盖的冰雪质量变化为-44±21Gt/a,对全球海平面上升的影响约为0.12mm·a~(-1).解算结果表明,南极冰盖质量亏损主要集中在西南极阿蒙森海岸附近冰川以及东南极波因塞特角区域.     

The scattering of Rossby waves from finite abrupt topography

The scattering of first mode linear baroclinic Rossby waves by a top-hat ridge in a continuously stratified ocean, with Brunt-Väisälä frequency that decays exponentially with depth below a surface mixed layer, is the subject of this study. A numerical mode matching technique is used to calculate the transmission coefficients for the propagating modes over the ridge. It is found that the scattered field depends crucially upon the stratification. For example, when the majority of the density variation is confined to a thin thermocline, corresponding to a small e-folding scale, gamma ^?1, for the Brunt-Väisälä frequency, a large amount of the incident wave energy is reflected by a small amplitude ridge. Appreciable energy conversion between the propagating barotropic and baroclinic modes takes place in this case. An asymptotic analysis for a small amplitude ridge is presented that confirms these numerical results. In the limit gamma ^?1→ 0, it is demonstrated that the scattered field in the continuously stratified ocean model differs markedly from the two-layer solution. The latter does not exhibit appreciable reflection of the incident wave energy for a small amplitude ridge. In conclusion, the application of a two-layer ocean model to describe Rossby wave scattering by ridges in place of a continuously stratified model cannot be recommended.     

A new series solution method for two-dimensional elastic wave scattering along a canyon in half-space

This paper presents a semi-analytical method for studying the two-dimensional problem of elastic wave scattering by surface irregularities in a half-space. The new method makes use of the member of a c-completeness family of wave functions to construct the scattering fields, and then applies equal but opposite tractions to those of the foregoing constructed scattering fields on the horizontal surface of the half-space to produce additional scattering fields. These additional scattering fields are a series of Lamb's solutions. Thus the whole scattering field constructed in the series automatically satisfies the Navier equations, the condition of zero traction on the half-space surface, and the radiation boundary conditions at infinity. Using the traction-free conditions along the canyon surface, the coefficients of the series solutions are determined via a least-squares method. For incident P, SV, and Rayleigh waves, the numerical results are presented for the scattering displacements in the vicinity of a semi-circular canyon in the half-space.     

Glacial isostatic adjustment at the Laurentide ice sheet margin: Models and observations in the Great Lakes region

Glacial Isostatic Adjustment (GIA) modelling in North America relies on relative sea level information which is primarily obtained from areas far away from the uplift region. The lack of accurate geodetic observations in the Great Lakes region, which is located in the transition zone between uplift and subsidence due to the deglaciation of the Laurentide ice sheet, has prevented more detailed studies of this former margin of the ice sheet. Recently, observations of vertical crustal motion from improved GPS network solutions and combined tide gauge and satellite altimetry solutions have become available. This study compares these vertical motion observations with predictions obtained from 70 different GIA models. The ice sheet margin is distinct from the centre and far field of the uplift because the sensitivity of the GIA process towards Earth parameters such as mantle viscosity is very different. Specifically, the margin area is most sensitive to the uppermost mantle viscosity and allows for better constraints of this parameter. The 70 GIA models compared herein have different ice loading histories (ICE-3/4/5G) and Earth parameters including lateral heterogeneities. The root-mean-square differences between the 6 best models and the two sets of observations (tide gauge/altimetry and GPS) are 0.66 and 1.57 mm/yr, respectively. Both sets of independent observations are highly correlated and show a very similar fit to the models, which indicates their consistent quality. Therefore, both data sets can be considered as a means for constraining and assessing the quality of GIA models in the Great Lakes region and the former margin of the Laurentide ice sheet.     

Glacial isostatic adjustment at the Laurentide ice sheet margin: Models and observations in the Great Lakes region

Glacial Isostatic Adjustment (GIA) modelling in North America relies on relative sea level information which is primarily obtained from areas far away from the uplift region. The lack of accurate geodetic observations in the Great Lakes region, which is located in the transition zone between uplift and subsidence due to the deglaciation of the Laurentide ice sheet, has prevented more detailed studies of this former margin of the ice sheet. Recently, observations of vertical crustal motion from improved GPS network solutions and combined tide gauge and satellite altimetry solutions have become available. This study compares these vertical motion observations with predictions obtained from 70 different GIA models. The ice sheet margin is distinct from the centre and far field of the uplift because the sensitivity of the GIA process towards Earth parameters such as mantle viscosity is very different. Specifically, the margin area is most sensitive to the uppermost mantle viscosity and allows for better constraints of this parameter. The 70 GIA models compared herein have different ice loading histories (ICE-3/4/5G) and Earth parameters including lateral heterogeneities. The root-mean-square differences between the 6 best models and the two sets of observations (tide gauge/altimetry and GPS) are 0.66 and 1.57 mm/yr, respectively. Both sets of independent observations are highly correlated and show a very similar fit to the models, which indicates their consistent quality. Therefore, both data sets can be considered as a means for constraining and assessing the quality of GIA models in the Great Lakes region and the former margin of the Laurentide ice sheet.     

南极冰盖内部结构特性研究——基于三维各向异性电磁波时域有限差分方法

冰雷达技术已成为目前探测南极冰盖内部结构的主要技术手段.近年发展起来的多极化雷达技术可根据不同方向雷达反射功率的变化推断冰盖内部冰晶组构特征和变化规律,进而推断冰盖内部应力应变历史,这对于理解冰流机制和动力过程以及解释冰盖过去、现在和未来的变化规律具有非常重要的作用.本文从Maxwell方程出发,推导出适于介电常数各向异性的三维电磁波时域有限差分方程,进而建立模型模拟各向异性介质的响应输出及其时空分布特征.模拟结果表明： (1) 电磁波在各向异性介质中传播时,波前面为椭圆形,长轴位于介电常数小的主轴方向; (2) 横向各向异性介质反射波振幅在水平面内具有180°的变化周期.通过对现场常用三种天线装置类型模拟对比分析发现,不同天线类型各向异性层底界面反射波存在“时差”现象,并且时差大小和正负与上下层介电常数差异以及同层各向异性差异有关.在模拟计算的基础上,作者讨论了由于介电常数各向异性导致的“时间延迟”和水平面内振幅“周期性变化”的原因.模拟结果和结论对于南极冰盖冰雷达数据处理和解释工作具有指导意义.     

Studying ice sheet stability using the method of separation of variables

Abstract

Stability of two-dimensional stationary continental and marine ice sheets is studied using perturbations of ice sheet surface elevation and the margin position about a steady-state solution. Ice accumulation rate at the upper surface is specified as a function of elevation and span. Ice is considered as a Newtonian fluid. Linearisation and separation of variables yield a non-homogeneous eigenvalue problem. In case when the margin moves, a necessary condition for the existence of a solution is very restrictive on the functions of the bed profile and accumulation rate. The method of separation of variables is applicable when the margin is assumed to be stationary. Singularity of the perturbation at the margin is treated using the method of matched asymptotic expansions. Numerical experiments show that dependence of accumulation rate on elevation contributes strongly towards ice sheet instability. Bed slope, ice thickness at the grounding line of a marine ice sheet and equilibrium line inclination are the main parameters determining the ice sheet reaction to a surface perturbation.     

Complex kame belt morphology,stratigraphy and architecture

The development of glacier karst at the margins of melting ice sheets produces complex glaciofluvial sediment-landform assemblages that provide information on ice sheet downwasting processes. We present the first combined geomorphological, sedimentological and geophysical investigation of the Brampton Kame Belt, an important glaciofluvial depositional zone at the centre of the last British-Irish Ice Sheet. Ground-penetrating radar (GPR) data allow the broad scale internal architecture of ridges (eskers) and flat-topped hills (ice-walled lake plains) to be determined at four sites. In combination with sediment exposures, these provide information on lateral and vertical variations in accretion styles, depositional boundaries, and grain size changes. Building on existing work on the subject, we propose a refined model for the formation of ice-walled lake plains resulting from the evolution and collapse of major drainage axes into lakes as stable glacier karst develops during deglaciation. The internal structure of esker ridges demonstrates variations in sedimentation that can be linked to differences in ridge morphologies across the kame belt. This includes low energy flow conditions and multiple accretion phases identified within large S-N oriented esker ridges; and fluctuating water pressures, hyperconcentrated flows, and significant deformation within a fragmented SW–NE oriented esker ridge. In combination with updated geomorphological mapping, this work allows us to identify two main styles of drainage within the kame belt: (1) major drainage axes aligned broadly S-N that extend through the entire kame belt and collapsed into a chain of ice-walled lakes; and (2) a series of smaller, fragmented SW–NE aligned esker ridges that represent ice-marginal drainage as the ice sheet receded south-eastwards up the Vale of Eden. Our study demonstrates the importance of integrated geomorphological, sedimentological and geophysical investigations in order to understand complex and polyphase glaciofluvial sediment-landform assemblages. © 2019 John Wiley & Sons, Ltd. © 2019 John Wiley & Sons, Ltd.     

Recent advances in understanding ice sheet dynamics

Glaciers and ice sheets play a dynamic role in Earth's climate system, influencing regional- and global-scale climate and responding to climate change on time scales from years to millennia. They are also an integral part of Earth's landscape in alpine and polar regions, where they are an active agent in isostatic, tectonic, and Earth surface processes. This review paper summarizes recent progress in understanding and modelling ice sheet dynamics, from the microphysical processes of ice deformation in glaciers to continental-scale processes that influence ice dynamics. Based on recent insights and research directions, it can be expected that a new generation of ice sheet models will soon replace the current standard. Improvements that can be foreseen in the near future include: (i) the addition of internally-consistent evolutionary equations for ice crystal fabric (anisotropic flow laws), (ii) more generalized flow laws that include different deformation mechanisms under different stress regimes, (iii) explicit incorporation of the effects of chemical impurities and grain size (dynamic recrystallization) on ice deformation, (iv) higher-order stress solutions to the momentum balance (Stokes' equation) that governs ice sheet flow, and (v) the continued merger of ice sheet models with increasingly complex Earth systems models, which include fully-coupled subglacial hydrological and geological processes. Examples from the Greenland Ice Sheet and Vatnajökull Ice Cap, Iceland are used to illustrate several of these new directions and their importance to glacier dynamics.     

利用CryoSat-2波形数据建立南极Lambert冰川流域DEM

Lambert冰川-Amery冰架系统是南极冰盖最大的冰流系统之一,对南极冰盖物质平衡研究有着重要的作用.数字高程模型(DEM)是进行南极冰盖研究的基础.本文基于CryoSat-2 L1b波形数据,研究建立了Lambert冰川流域高分辨率DEM.测高卫星返回波形在冰盖区域存在变形,需进行波形重跟踪处理.利用交叉点分析方法对重心偏移法(OCOG)、阈值法和β参数法等常用的波形重跟踪方法对不同类型的CryoSat-2波形的适用性进行了研究.最后,利用克里金插值方法建立了500 m分辨率的Lambert冰川流域DEM——LAS DEM (Lambert Glacier-Amery Ice Shelf system DEM).利用ICESat卫星测高数据和GPS地面实测数据对LAS DEM进行精度验证,并与另外两种基于CryoSat-2数据的南极DEM进行了对比.结果表明:LAS DEM的整体精度约为0.295±2.7 m,优于另外两种CryoSat-2 DEM;在冰盖内陆地区,LAS DEM的高程误差在2 m之内;在Amery冰架上,LAS DEM的精度优于1 m.     

Seismic modelling study of a subglacial lake

We characterize the seismic response of Lake Vostok, an Antarctic subglacial lake located at nearly 4 km depth below the ice sheet. This study is relevant for the determination of the location and morphology of subglacial lakes. The characterization requires the design of a methodology based on rock physics and numerical modelling of wave propagation. The methodology involves rock-physics models of the shallow layer (firn), the ice sheet and the lake sediments, numerical simulation of synthetic seismograms, ray tracing, τ–p transforms, and AVA analysis, based on the theoretical reflection coefficients. The modelled reflection seismograms show a set of straight events (refractions through the firn and top-ice layer) and the two reflection events associated with the top and bottom of the lake. Theoretical AVA analysis of these reflections indicates that, at near offsets, the PP-wave anomaly is negative for the ice/water interface and constant for the water/sediment interface. This behaviour is shown by AVA analysis of the synthetic data set. This study shows that subglacial lakes can be identified by using seismic methods. Moreover, the methodology provides a tool for designing suitable seismic surveys.