modes of operation of thermo mechanically coupled ice sheets by richard c a hindmarsh geoffrey s boulton grant institute of geology university of edinburgh west mains road edinburgh eh9 3jw scotland u k and kolumban hutter lnstitut fur mechanik technische hochschule oarmstadt hochschulstrasse i 0 6100 oarmstadt federal republic of germany dimensionless lapse rate a dimensionless model of thermo mechanically coupled ice sheets is used to analyse the operation of the system three thermal processes are identified i dissipation having a maximum time scale of thousands of years ii advection having a time scale of tens of thousands of years and iii conduction having a time scale of loo 000 years kinematical processes occur on two time scales i a marginal advective time scale of thousands of years and ii a diffusive time scale of tens of thousands of years dominant in the divide area

full depth englacial vertical ice sheet velocities measured using phase sensitive radar we describe a geophysical technique to measure englacial vertical velocities through to the beds of ice sheets without the need for borehole drilling using a ground based phase sensitive radio echo sounder pres during seven antarctic field seasons we measure the temporal changes in the position of englacial reflectors within ice divides up to 900 m thick on berkner island roosevelt island fletcher promontory and adelaide island recorded changes in reflector positions yield full depth profiles of vertical ice velocity that we use to examine spatial variations in ice flow near the divides we interpret these variations by comparing them to the results of a full stokes simulation of ice divide flow qualitatively validating the model and demonstrating that we are directly detecting an ice dynamical phenomenon called the raymond effect using pres englacial vertical ice velocities can be measured in higher spatial resolution than is possible using instruments installed within the ice we discuss how these measurements could be used with inverse methods to measure ice rheology and to improve ice core dating by incorporating pres measured vertical velocities into age modeling

a numerical study of plane ice sheet flow l ecoulement bidimensionnel stationnaire d une nappe de glace reposant sur le sol est analyse numeriquement au moyen du modele simplifie de morland et hutter la glace se comporte comme un fluide visqueux non lineaire dependant de la temperature la nappe de glace est supposee longue et mince

palaeotemperatures still exist in the greenland ice sheet the temperature distribution through the greenland ice sheet at the dye 3 borehole is a record of the past climatic changes in the arctic the numerical model of the temperature distribution now presented reproduces the observed temperature distribution within 0 03 k and shows that the basal ice is still cooled 5 k by the cold ice age climate the results suggest a mean ice age temperature of 32 2 c which is 12 k colder than the present temperature and a precipitation rate 50 25 of the present rate calculations of a more detailed temperature history through the present inter glacial period reveal evidence of the ad 1920 50 maximum the little ice age and the atlantic period

migration of the siple dome ice divide west antarctica the non linearity of the ice flow law or a local accumulation low over an ice divide can cause isochrones internal layers to be shallower under the divide relative to the flanks forming a divide bump in the internal layer pattern this divide signature is analyzed using ice flow models and inverse techniques to detect and quantify motion of the siple dome ice divide west antarctica the principal feature indicating that migration has occurred is a distinct tilt of the axis of the peaks of the warped internal layers beneath the divide the calculated migration rate is 0 05 0 50 m a 1 toward ice stream d and depends slightly on whether the divide bump is caused by the non linearity of ice flow or by a local accumulation low our calculations also suggest a strong south north accumulation gradient of 5 10 x 10 6 a 1 in a narrow zone north of the divide a consequence of divide migration is that pre holocene ice is thickest about 0 5 km south of the present divide position divide motion indicates that non steady processes possibly associated with activity of the bounding ice streams are affecting the geometry of siple dome the migration rate is sufficiently slow that the divide bump is maintained in the internal layer pattern at all observable depths this suggests that major asynchronous changes in the elevation or position of the bounding ice streams are unlikely over at least the past 10 3 10 4 years

ice divide flow at hans tausen iskappe north greenland from surface movement data surface strain rates around the southeastern dome of hans tausen iskappe in peary land north greenland 82 5 n 27 5 w are determined from global positioning system surveys of a strain net average longitudinal surface strain rate increases towards the dome from 1 4 0 2 x 10 4 a 1 at 5 10 ice thicknesses from the divide to 2 4 1 0 x 10 4 a within 1 ice thickness from the divide analysis of the data shows that the ice cap is presently building up within the strain net with an average rate of 0 04 0 02 m a assuming a uniform thickening the shape factor of the horizontal velocity the ratio between the vertically averaged horizontal velocity and the horizontal surface velocity decreases towards the dome from 0 9 at a distance of 10 ice thicknesses from the dome to 0 5 at the dome based on application of the continuity equation our results indicate that a region with anomalous flow is formed around the dome supporting recent indications reported by vaughan and others 1999 it is not possible from our data to constrain parameters of the flow law because there is no independent estimate of the significant present thickening of the central part of the ice cap and its pattern around the dome

thermo mechanically coupled ice sheet response cold polythermal temperate classical mixture concepts are the appropriate vehicle for describing the dynamics of ice masses containing some water we review and derive respectively the theoretical formulations of cold polythermal and temperate ice masses emphasize the peculiarities of the model equations and point to difficulties that were encountered with the proposed models the focus is both on the adequate physical motivation of the models and the consistency of their mathematical representation

recumbent folding of divide arches in response to unsteady ice divide migration arches in stratigraphic layers directly under a flow divide raymond bumps are predicted by models of steady ice sheet flow and have been observed in several ice domes here we model the evolution of these layers when a formerly stationary divide migrates rapidly to a new position then again becomes stationary leaving the arched layers in a flank position as they are then carried downstream with the flow these abandoned arches can develop into recumbent folds these folds can occur over a wide range of divide migration speeds the shearing flow that produces these recumbent folds also distributes the folded layers over a wide distance downstream from the original divide location if the divide offset is abrupt pre cores or material lines comprising core relative isochrones can be used to quickly identify portions of an abandoned raymond bump that would be overturned at any future ice core site downstream if as appears to be the case in greenland the divide is never stable long enough to produce a mature arch folds of this type would not occur the most likely place to find such folds might be the flank of an ice ridge bounded by unsteady ice streams

the crossover stress anisotropy and the ice flow law at siple dome west antarctica we used observations and modeling of siple dome west antarctica a ridge ice divide to infer the importance of linear deformation mechanisms in ice sheet flow we determined the crossover stress a threshold value of the effective deviatoric stress below which linear flow mechanisms dominate over nonlinear flow mechanisms by combining measurements of ice properties with in situ deformation rate measurements and a finite element ice flow model that accounts for the effects of viscous anisotropy induced by preferred crystal orientation fabric we found that a crossover stress of 0 18 bar produces the best match between predicted and observed deformation rates for siple dome this means that including a linear term in the flow law is necessary but generally the flow is still dominated by the nonlinear glen n 3 term the pattern of flow near the divide at siple dome is also strongly affected by crystal fabric measurements of sonic velocity which is a proxy for vertically oriented crystal fabric suggest that a bed parallel shear band exists several hundred meters above the bed within the ice age ice

deformation in the vicinity of ice divides calculs numeriques aux elements finis de la variation de la vitesse horizontale avec la profondeur au voisinage d une difference de la glace symetrique isotherme et ou glissement sur un lit plat

transient glacier response with a higher order numerical ice flow model in this paper a higher order numerical flowline model is presented which is numerically stable and fast and can cope with very small horizontal grid sizes 10 m the model is compared with the results from blatter and others 1998 on haut glacier d arolla switzerland and with the european ice sheet modelling initiative benchmarks huybrechts and others 1996 results demonstrate that the significant difference between calculated basal drag and driving stress profiles in a fixed geometry disappears when the glacier profile is allowed to react to the surface mass balance conditions and reaches a steady state dynamic experiments show that the mass transfer in higher order models occurs at a different speed in the accumulation and ablation areas and that the front position is more sensitive to migration compared to the shallow ice approximation

on the effects of anisotropic rheology on ice flow internal structure and the age depth relationship at ice divides we use numerical modeling with a full system stokes solver to elucidate the effects of nonlinear rheology and strain induced anisotropy on ice flow at ice divides we find that anisotropic rheology profoundly affects the shape of both isochrone layering and surface topography anisotropic effects cause the formation of a downward curving fold i e a syncline in isochrones in the lower central area beneath the ice divide when the resulting syncline is superimposed on the well known raymond anticline a double peaked raymond bump is formed furthermore to each side of the raymond bump flanking synclines are formed in addition anisotropic effects are found to give rise to a subtle concavity in the surface profile to both sides of the summit the lower center syncline the flanking synclines and the near summit surface concavity have all previously been observed in nature but hitherto no explanation for the genesis of these features has been given we compare modeling results with radiograms collected from fuchs ice piedmont and kealey ice rise antarctica good overall agreement is found in particular we are able to reproduce all observed qualitative features of surface geometry and internal layering by including and only by including the effects of induced nonlinear rheological anisotropy on flow rheological anisotropy has the potential to profoundly affect the age distribution with depth and caution must be exercised when estimating age of ice from ice cores with an isotropic model the occurrence of linear features parallel to the ridge of ice divides often seen in satellite imagery is indicative of long term stability rather than signs of ongoing ice divide migration as previously suggested such ice divides are ideal locations for extracting ice cores

potential for stratigraphic folding near ice sheet centers lack of agreement between the deep portions of the greenland icecore project grip and greenland ice sheet project ii gisp2 ice cores from central greenland suggests that folds may disrupt annual layering even near ice divides we use a simple kinematic flow model to delineate regions where slope disturbances wrinkles introduced into the layering could overturn into recumbent folds and where they would flatten leaving the stratigraphic record intact wrinkles are likely to originate from flow disturbances caused internally by inhomogeneities and anisotropy in the ice rheological properties rather than from residual surface structures sastrugi or from open folds associated with transient flow over bed topography if wrinkles are preferentially created in anisotropic ice under divides where the resolved shear stress in the easy glide direction can be weak and variable then the deep intact climate record at dye 3 may result from its greater distance from the divide alternatively the larger simple shear at dye 3 may rapidly overturn wrinkles so that they are not recognizable as folds the ice core record from siple dome may be intact over a greater fraction of its depth compared to the central greenland records if its flat bedrock precludes fluctuations in the stress orientation near the divide

a flow line model for calculating the surface profile and the velocity strain rate and stress fields in an ice sheet a flow line model is presented for calculating the surface profile and the velocity strain rate and stress fields in an ice sheet with given base elevation profile ice thickness at the dome divide flow law parameters mass balance distribution and convergence divergence conditions along the flow line the model which is based on a quasi similarity hypothesis as regards the horizontal velocity depth profiles accounts for changes along the flow line in the depth distributions of temperature normal stress deviators and possible enhanced flow of deep ice of wisconsin origin a curvilinear coordinate system is applied with horizontal axes along flow lines and surface elevation contours respectively the flow equations are reduced to two differential equations one for the surface elevation profile and the other for a profile function that determines the depth distributions of velocities and strain rates the two equations are coupled through a profile parameter that communicates the influence of velocity profile changes to the surface profile equation it is shown that the variation along the flow line of this parameter should also be considered when deriving flow law parameters from ice sheet flow line data for a symmetric dome explicit expressions are derived for the depth distributions of the vertical velocity strain rates and stresses the strain rate profiles display an inflection about half way down the ice sheet and in the case of isothermal ice have surface values 2 2 times their depth averaged values the depth distribution of the vertical velocity indicates that a relatively thick layer of almost stagnant ice is present at the ice sheet base below a dome

on the effects of divide migration along ridge flow and basal sliding on isochrones near an ice divide 1 radar layer geometry in divide areas is strongly influenced by the operation of the raymond effect which causes upwarping of the layers as a consequence of the nonlinear rheology of ice the detailed geometry of these layers is known to store a record of change in the cryosphere of local thinning and of the age of formation of the divide and has been surmised to provide information about lateral motion of divides such lateral motion can be caused by changes in flanking ice streams and the divide area thereby contains a record of ice stream dynamics it has also been suggested that a large perturbation of divide position will obliterate the cumulative effects of the operation of the raymond mechanism leading to the disappearance of raymond bumps since the raymond effect has a strong influence on the age depth relation in ice cores knowledge of whether its operation is localized leading to strong bump formation or distributed is crucial in the interpretation of ice cores the detailed evolution of ice divide radar layer geometry remains poorly understood employing a full thermomechanically coupled transient model we qualitatively explore the effect of divide migration on radar layer geometry certain qualitative features emerge which can be used to infer history of cryosphere change in particular in areas distant from the usual sites of geological dating there remains uncertainty about the influence of sliding on the operation of the raymond effect under certain conditions the existence of sliding can damp or eliminate the operation of the raymond effect if this is generally true then dating of ice divides may simply be a date for the freezing of the divide bottom we show that sliding does not necessarily eliminate the formation of bumps dates of divide formation are likely to be dates for the location of the ridge at a particular spot raymond bump evolution is weakened by flow along the ridge we explore quantitatively the strength of this effect using a scaling analysis to show that the weakening can efficiently be described by one parameter the ratio of along ridge slope to a measure of the across divide curvature

coupled thermomechanical response of an axisymmetric cold ice sheet this study proposes a detailed model for ice sheets having a radially symmetric geometry governing relations are derived from first principles of physics and the interactive effects of mechanical and thermal energy are taken into account the resulting model is a nonlinear partial differential equation relating the temperature velocity and stress fields boundary conditions of accumulation rate geothermal flux sliding laws and surface temperatures having been specified and the model determines a steady state response in terms of ice sheet profile and internal temperatures velocities and stresses we describe the computational methodology for numerically determining solutions from which one can assess the credibility of the model itself and to the extent that it is credible examine effects such as perturbing of external temperatures accumulation rates and so forth piloting examples illustrate this

distortion of isochronous layers in ice revealed by ground penetrating radar in addition to measuring ice sheet thickness ground penetrating radar can be used to delineate reflections in ice sheets1 2 3 these reflections are generally accepted to result from layers of isochronous deposition of snow and can reveal much about the dynamics of the ice flow here we present ground penetrating radar data from fletcher promontory antarctica which show arches and troughs in isochronous ice layers to a depth of 100 m we demonstrate that the origin of these features can be determined by their growth with depth and many features result from local anomalies in accumulation rate which can be correlated with the ice surface slope one arch appears to be the result of a local anomaly in vertical strain rate its proximity to the ice divide width and growth with depth indicate that this arch is one of a class of features postulated by raymond4 but not previously shown to exist in the field such a feature is an indication of the nonlinear rheology of ice and requires that palaeoclimate records from ice cores extracted from the vicinity of ice divides underlain by similar features should be specifically corrected for such effects on ice flow

mass balance and surface movement of the greenland ice sheet at summit central greenland during the grip deep drilling in central greenland the ice sheet topography and surface movement at summit has been mapped with gps measurements of the surface velocity are presented for a strain net consisting of 13 poles at distances of 25 60 km from the grip site some results are the grip site is located approximately 2 km nw of the topographic summit the surface velocity at the gisp 2 site is 1 7 m yr in the w direction the present mass balance at summit is calculated to be 0 03 0 04 m yr i e close to steady state this result is the best now available for summit a small thinning rate might be a transient response of the greenland ice sheet due to the temperature increase at the wisconsin holocene transition

thermal response of a small ice cap to climatic forcing two dimensional finite element calculations of velocity and temperature fields have been applied to the energy balance of a cross section of barnes ice cap baffin island canada the flow plane currently is cooling near the ice divide and warming near the margin long term simula tions show a net warming trend followed by a cooling trend with a steady state average temperature similar to the present sensitivity studies on an idealized version of the flow plane show that the overall temperature responds less than surface temperature forcing because a negative feed back in temperature advection is substantially larger than a positive feed back in strain heating the response times of the flow plane by itself are somewhat faster but of the same magnitude as response times that would be estimated from one dimensional modeling when bedrock temperature calculations are included response times increase an order of magnitude but these do not substantially affect the short term response

ice flow between the greenland ice core project and greenland ice sheet project 2 boreholes in central greenland the ice flow between the greenland ice core project grip and greenland ice sheet project 2 gisp2 boreholes in the summit region of central greenland is modeled with a steady state finite element model the model calculates the free ice sheet surface and the coupled ice flow and temperature fields along the flow line between the boreholes three dimensional effects are expressed in terms of the divergence of the flow and included in the coupled stress and temperature fields in addition to ice core data several geophysical surface programs have provided data that are used to constrain the model the modeled isochrones resemble the bedrock structure along the flow line but rise at the divide the rise at the divide is not seen in internal layers found by surface radio echo sounding an ice particle originally deposited at the surface moves through different stress and temperature regimes a set of trajectory lines are followed from the surface to the boreholes in order to follow the variation of stress deviators temperature and deformation along with the ice movement these variations along a trajectory line constitute a history of the corresponding ice layer the difference between the history of ice layers found in the grip and gisp2 boreholes is mainly due to the shear stress which is 3 4 times higher for gisp2 ice than for grip ice furthermore the grip ice experiences a nonzero longitudinal stress deviator much longer than the gisp2 ice

nature of radio echo layering in the antarctic ice sheet detected by a two frequency experiment a two frequency radio echo sounding experiment was carried out at dome fuji the second highest dome in east antarctica and along a 1150 km long traverse line from the dome to the coast the goal was to determine the dominant causes of the radio echo internal reflections and to investigate their possible changes with depth ranges and regions from the two frequency 60 mhz and 179 mhz radio echo responses at various sites we distinguished four zones each of the zones is characterized by a dominant cause of radio echo internal reflection as follows in the pd zone changes in dielectric permittivity are mainly due to density fluctuations in the pcof zone changes in dielectric permittivity are mainly due to changes in crystal orientation fabrics and in the ca zone changes in electrical conductivity are mainly due to changes in acidity induced by past volcanic eruptions in each of these three zones the changes occur commonly along isochrones in addition a basal echo free zone the fourth zone was found to appear always below the pcof zone these four zones and their distribution suggested variations of the physical conditions within the ice sheet

spike of pyrosynthetic polycyclic aromatic hydrocarbons associated with an abrupt decrease in δ13c of a terrestrial biomarker at the cretaceous tertiary boundary at caravaca spain the first vertical high resolution record of polycyclic aromatic hydrocarbons pahs of pyrosynthetic origin and the corresponding 13 c profile of a terrestrial biomarker across the cretaceous tertiary k t boundary at caravaca spain reveals the following in comparison with adjacent cretaceous marlstones the first thin horizon 0 to 0 5 cm 0 the k t boundary of the boundary clay layer is 1 enriched as much as 112 to 154 fold in typical pyrosynthetic pahs such as coronene benzo g h i perylene and benzo e pyrene and 2 shows an abrupt 13 c decrease of 1 4 1 8 in terrestrial higher plant derived n c 29 alkane the spike of pyrosynthetic pahs associated with an abrupt decrease in 13 c value of a terrestrial biomarker is interpreted to reflect the prevalence of extensive fires with subsequent 13 c decrease in atmospheric co 2 it is estimated that the geologically instantaneous combustion of 18 24 of the terrestrial above ground biomass would be necessary to account for the measured negative isotopic shift at the k t boundary on the basis of carbon mass balance between terrestrial above ground biomass and atmosphere

a new three dimensional higher order thermomechanical ice sheet model basic sensitivity ice stream development and ice flow across subglacial lakes 1 a new three dimensional thermomechanically coupled ice sheet model is developed contrary to the majority of three dimensional ice sheet models shallow ice approximation higher order stress gradients longitudinal and transverse are accounted for in the force balance equations the horizontal velocity field is determined from the force balance equations in their derivative form elliptical equation using the method presented by pattyn 2000 2002a the model is solved on a regular grid in the horizontal and an irregular grid in the vertical and is numerically stable basic experiments include the european ice sheet modeling initiative eismint benchmarks for largescale ice sheet models and a comparison with the saito blatter ice sheet model including higher order stress gradients saito et al 2003 detailed calculations of ice flow over three dimensional bedrock perturbations showed the validity of the higher order solution the model is capable of simulating the evolution of an ice stream within the ice sheet and shows important aspects of observed ice stream features such as the surface flattening and the importance of side drag the simulation of the ice flow over a subglacial lake results in a flattening of the surface a local velocity increase over the lake and a deviation of the ice flow from the main flow direction features which are also observed at lake vostok antarctica index terms 1827 hydrology glaciology 1863 1863 hydrology snow and ice 1827 3230 mathematical geophysics numerical solutions keywords higher order ice sheet model thermomechanical ice stream subglacial lake citation pattyn f a new three dimensional higher order thermomechanical ice sheet model basic sensitivity ice stream development and ice flow across subglacial lakes j geophys res 108 b8 2382 doi 10 1029 2002jb002329 2003

irregular glacial interstadials recorded in a new greenland ice core the greenland ice sheet offers the most favourable conditions in the northern hemisphere for obtaining high resolution continuous time series of climate related parameters profiles of 18o 16o ratio along three previous deep greenland ice cores1 3 seemed to reveal irregular but well defined episodes of relatively mild climate conditions interstadials during the mid and late parts of the last glaciation but there has been some doubt as to whether the shifts in oxygen isotope ratio were genuine representations of changes in climate rather than artefacts due to disturbed stratification here we present results from a new deep ice core drilled at the summit of the greenland ice sheet where the depositional environ ment and the flow pattern of the ice are close to ideal for core recovery and analysis the results reproduce the previous findings to such a degree that the existence of the interstadial episodes can no longer be in doubt according to a preliminary timescale based on stratigraphic studies the interstadials lasted from 500 to 2 000 years and their irregular occurrence suggests complexity in the behaviour of the north atlantic ocean circulation

sensitivity of the divide position at siple dome west antarctica to boundary forcing a linearized perturbation about a two dimensional vialov nye icesheet profile is used to investigate the sensitivity of the divide position at siple dome west antarctica to small changes in the accumulation pattern and in the elevation of its lateral boundaries at the margins of ice streams c and d relaxation time scales for the icesheet surface and divide position are derived from the perturbation theory for siple dome these time scales are short 450 800 years for surface adjustment and 200 350 years for divide position adjustment these short time scales indicate that siple dome responds quickly to forcing at its boundaries therefore the recent migration of the siple dome divide determined from previous work is probably a response to an ongoing sustained forcing rather than a response to a long past climate event such as the transition from the last glacial maximum to the holocene based on our analysis the inferred rate of migration of the siple dome divide could be attained be

evolution of derwael ice rise in dronning maud land antarctica over the last millennia ice rises situated in the ice shelf belt around antarctica have a spatially confined flow regime with local ice divides beneath the divides ice stratigraphy often develops arches with amplitudes that record the divide s horizontal residence time and surface elevation changes to investigate the evolution of derwael ice rise dronning maud land antarctica we combine radar and gps data from three consecutive surveys with a two dimensional full stokes thermomechanically coupled transient ice flow model we find that the surface mass balance smb is higher on the upwind and lower on the downwind slopes near the crest the smb is anomalously low and causes arches to form in the shallow stratigraphy observable by radar in deeper ice arches are consequently imprinted by both smb and ice rheology raymond effect the data show how arch amplitudes decrease as along ridge slope increases emphasizing that the lateral positioning of radar cross sections is important for the arch interpretation using the model with three rheologies isotropic with n 3 4 5 and anisotropic with n 3 we show that derwael ice rise is close to steady state but is best explained using ice anisotropy and moderate thinning our preferred albeit not unique scenario suggests that the ice divide has existed for at least 5000 years and lowered at approximately 0 03 m a 1 over the last 3400 years independent of the specific thinning scenario our modeling suggests that derwael ice rise has exhibited a local flow regime at least since the mid holocene

a fully three dimensional finite element model applied to velocities on storglaciaren sweden a finite element model that solves the stress balance equations for glacier dynamics in three dimensions has been developed by extending previous flow plane models this model retains all terms of the stress tensor and uses a glen type power law for viscosity calculations in the paper the model is applied to storglaciaren sweden to explore both the glacier s dynamics and the model s characteristics values of the stiffness parameter b of 0 20 0 22 mpa year 1 n were required to match observed strain rates on storglaciaren overall velocities required imposition of a problematically small sliding speed stress fields implied by the model simulation showed that the glacier receives its largest driving force from a high slope zone near the equilibrium line and that a large proportion of the resistive stress comes from lateral drag lateral drag is enhanced on this glacier by being frozen to ts sidewalls and by a turning of the main flow as it comes out of the main or northern cirque

flow at ice divide triple junctions 1 three dimensional full stokes modeling 1 ice domes are either axisymmetric high points along ridges or ridge triple junctions we model time dependent isothermal flow near triple junctions solving the full set of mechanical equations with a nonlinear power law rheology forcing is applied through the boundary conditions which affect flow patterns at outlets where such forcing is purely axisymmetric an axisymmetric dome is formed if a threefold symmetry in the forcing is applied the axisymmetric dome breaks up into three ridges subtending angles of 120 sets of experiments where the forcing was not exactly threefold symmetric by angle or by amplitude caused the triple junction to migrate to a new steady state here in steady state the ridges join the triple junction at nearly 120 but one ridge curves to satisfy the boundary forcing the slope pattern in the immediate dome vicinity depends only on a dimensionless parameter which is a function of the ice consistency the accumulation and the rheological power law index attempts to replicate the topography around summit greenland obtained a good fit with n 3 at a triple junction the dome is really distinct from the surrounding ridges contrary to the highest point of a single ridge divide as a consequence the raymond effect is at its strongest at the dome and weakens considerably over one ice thickness as one moves away from the flow center along the ridges leaving the dome the raymond effect is still present and decreases with the ratio of the flow across and along the ridge in the vicinity of the dome horizontal strain rates vary strongly from uniaxial to biaxial large scale effects represented in our model as fluxes at boundaries seem to be the primary controls on dome position and shape

predicted age depth scales for siple dome and inland wais ice cores in west antarctica geophysical data are used with ice flow models and generalized accumulation histories to estimate age and annual layer thickness versus depth for two anticipated ice core sites in west antarctica siple dome 81 65 s 148 81 w and an inland site on the west antarctic ice sheet wais this modeling experiment predicts that 104 year old ice is at 50 depth and 105 year old ice is at 90 depth at both sites both of these cores could contain climate information through the last glacial cycle with annual resolution through the holocene the predicted similarity in resolution and record length between the two cores suggests that they could be compared in detail to obtain both spatial and temporal information about the paleoclimate and history of the west antarctic ice sheet

a numerical study of anisotropic low reynolds number free surface flow for ice sheet modeling few ice sheet flow models have been developed that solve the complete set of mechanical equations until now these models were limited to isotropic conditions we present here a two dimensional finite difference method capable of solving the equations for the steady flow of a viscous incompressible anisotropic fluid with a free surface under isothermal conditions it is not a standard method especially with respect to the time discretization of the numerical scheme and converges for very low reynolds numbers this method is applied here to the planar flow of anisotropic ice over flat or irregular bedrock with no slip boundary conditions at the ice bedrock interface the results are presented here for newtonian behavior in the vicinity of an ice divide the ice is assumed to be isotropic at the ice sheet surface with continuous and prescribed development of anisotropy with increasing depth going from isotropic to anisotropic situations our results indicate that the free surface becomes flatter and the shear strain rates larger and more concentrated near the bedrock the flow is less sensitive to variations of the bedrock topography in the anisotropic case than in the isotropic case furthermore a new phenomenon appears in the anisotropic case the partial stagnation of ice in the holes of the bedrock these effects have significant consequences when dating the ice the isochrones obtained in the anisotropic case are flatter and the anisotropic ice is more than 10 younger above the bumps and more than 100 older within the holes than for the isotropic ice

multitemporal evaluation of topographic normalization methods on deciduous forest tm data five empirical and nonempirical parametric topographic normalization methods the cosine scs minnaert b correction and c correction methods were applied to multitemporal landsat thematic mapper data bands 1 5 and 7 collected in different periods of the growing season april june and july of a mixed deciduous forest area 340 ha in the northern apennines the effectiveness of the models at removing topographic control preserving internal data variability and consistently normalizing radiance for flat pixels from band to band and image to image was evaluated the entirely empirical b correction outperformed the other considered methods without relying on any photometric function

ice rise stratigraphy reveals changes in surface mass balance over the last millennia in dronning maud land we use ice flow modelling to simulate the englacial stratigraphy of blaskimen island an ice rise in dronning maud land and elucidate the evolution of this data sparse region we apply a thermo mechanically coupled elmer ice model to a profile along flowlines and through the ice rise summit where surface mass balance smb flow velocity and ice stratigraphy were recently measured we conclude that i the ice rise is presently thickening at a rate of 0 5 0 6 m ice equivalent per year m ieq a 1 which is twice an earlier estimate using the field data and the input output method ii present thickening started 20 40 years in the past before which the ice rise was in a steady state iii smb contrast between the upwind and downwind slopes was stronger than the present value by 23 or 0 15 m ieq a 1 prior to 1100 years ago since then this contrast has been decreasing overall we surmise that these smb changes are likely a result of synoptic scale atmospheric changes rather than local atmospheric changes controlled by local ice topography our technique effectively assimilates geophysical data avoiding the complexity of ice flow beneath the ice divide thus it could be applied to other ice rises to elucidate the recent glacial retreat

isothermal flow of an anisotropic ice sheet in the vicinity of an ice divide simulations of glacier flow are commonly based on the assumption that ice has an isotropic viscosity here we examine the plane flow of ice in the special region of an ice divide using a constitutive relation for an anisotropic incompressible viscous body that is orthotropic and transversally isotropic ice is assumed to be isotropic at the ice sheet surface with the continuous development of a vertical single maximum c axis fabric with increasing depth we consider the theoretical case of an isothermal ice sheet over a horizontal bedrock with no slip at the ice bedrock interface the ice sheet surface elevation is imposed and the flow corresponding to the steady state is calculated using a two dimensional finite difference model based on the resolution of a pressure poisson equation in this model all components of the stress and strain rate tensor are calculated the main conclusion is that for a fixed surface elevation the general flow pattern accelerates when the anisotropic behavior of the ice is taken into account due to the greater fluidity with respect to shear stress the downward motion of the ice is faster despite a higher resistance to vertical deformation as a result the dominance of shear strain rate in the flow of polar ice is stronger in the anisotropic case than in the isotropic case the shear stresses are slightly relaxed while the longitudinal stresses are significantly increased in the anisotropic case

past precipitation rates derived from ice core measurements methods and data analysis ice cores in which annual layers can be identified or particular horizons dated provide a record of past precipitation rates if measured layer thicknesses can be corrected for thinning by flow since deposition total strain is usually calculated from steady state flow models because of lack of information about the ice cap s history an assumption of uniform vertical strain rate is valid at best in the upper half of the ice column complex models are needed to take account of uneven bedrock and variations in precipitation rate upstream of the borehole drilling at an ice divide avoids these complications new data analyses suggest that precipitation at camp century has fluctuated by only plus or minus 10 for the past 8500 years whereas at devon island on the opposite side of baffin bay precipitation has been uniform only for the past 1300 years with significantly higher values before that estimation of pre holocene precipitation rates is especially difficult because that ice may have an effective viscosity different from holocene ice three published estimates of pre holocene precipitation at camp century are unreliable the authors did not allow for thinning and their time scales differ appreciably data from three antarctic stations show some inconsistencies measuring concentrations of 10be in ice cores may be an alternative method of determining past precipitation rates

the elevation history of ice streams and the spatial accumulation pattern along the siple coast of west antarctica inferred from ground based radar data from three inter ice stream ridges measurements of the surface and internal layer geometry from ice penetrating radar and global positioning system surveys on three inter ice stream ridges in west antarctica siple dome ridge de and ridge bc are examined with ice flow models to infer 1 the history of the divide position at each site and 2 the spatial pattern of accumulation across the ridges we find that the divide position is most steady at siple dome somewhat steady at ridge de and highly variable at ridge bc data from siple dome and ridge de show evidence for steady northward motion of the ice divide for the past few thousand years the layers beneath ridge bc suggest a 5 km northward shift of the divide position within the past several hundred years assuming the divide shifts are all due to changing elevation of the bounding ice streams we infer the relative elevation history for segments of ice streams b e the northward displacement of the divide for all ridges implies a progressive relative thinning of the ice streams from e to b with most dramatic recent thinning 100 m in 103 years of ice stream b relative to ice stream c analysis of the internal layer pattern across the ridges indicates a south north accumulation gradient with higher accumulation rates on the northern flanks of the ridges in all three cases the inferred accumulation distribution is nearly uniform on the northern flanks decreases sharply within a few ice thicknesses across the divides and then decreases gradually farther to the south the north south decrease is strongest for ridge de and weakest for ridge bc this spatial pattern and the reduction in gradient strength with distance from the amundsen sea is consistent with the hypothesis that storms from the amundsen sea carry moisture first south then west over west antarctica and deposit more snow on the windward side of ridges due to orographic lifting this pattern has been stable for at least the past several thousand years

conditions for a steady ice sheet ice shelf junction abstract 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