late holocene sea level changes and isostasy in western denmark abstract cores and exposed cliff sections in salt marshes around ho bugt a tidal embayment in the northernmost part of the danish wadden sea were subjected to 14c dating and litho and biostratigraphical analyses to reconstruct paleoenvironmental changes and to establish a late holocene relative sea level history four stages in the late holocene development of ho bugt can be identified 1 groundwater table rise and growth of basal peat from at least 2300 bc to ad 0 2 salt marsh formation 0 to ad 250 3 a freshening phase ad 250 to ad 1600 culminating in the drying out of the marshes and producing a distinct black horizon followed by an aeolian phase with sand deposition and 4 renewed salt marsh deposition ad 1600 to present from 16 calibrated ams radiocarbon ages on fossil plant fragments and 4 calibrated conventional radiocarbon ages on peat we reconstructed a local relative sea level history that shows a steady sea level rise of 4 m since 4000 cal yr bp contrary to suggestions made in the literature the relative sea level record of ho bugt does not contain a late holocene highstand relative sea level changes at ho bugt are controlled by glacio isostatic subsidence and can be duplicated by a glacial isostatic adjustment model in which no water is added to the world s oceans after ca 5000 cal yr bp

regionally differentiated contribution of mountain glaciers and ice caps to future sea level rise the contribution to sea level rise from mountain glaciers and ice caps has grown over the past decades a projection of their melting during the twenty first century based on temperature and precipitation projections from ten climate models suggests that by 2100 these glaciers will lose about 21 of their total global volume

compression behaviour of minerogenic low energy intertidal sediments existing geotechnical approaches that describe volumetric changes in intertidal sediments in response to applied vertical effective stresses are limited by a lack of empirical research into their one dimensional compression behaviour in this paper we address this deficiency by presenting the results of an investigation into the compression behaviour of minerogenic low marsh and tidal flat sediments we have tested samples of these sediment types obtained from greatham creek cowpen marsh tees estuary uk analysis of physical properties and oedometer compression tests demonstrates that contrary to the implicit assumptions of existing models the surface sediments studied are overconsolidated structural variability between samples arises due to sedimentological factors notably variations in organic content we attribute overconsolidation to tidal exposure and falls in groundwater level that permit desiccation and cause capillary suction stresses greater rates of compression with respect to effective stress occur in sediments with higher initial voids ratios and more open unstable initial structures variability in structure decreases with application of higher effective stresses due to the destructuration of the sediments which also creates increased homogeneity of compression behaviour under higher effective stresses we subsequently develop a new conceptual framework to describe compression behaviour in minerogenic intertidal sediments that incorporates overconsolidation we advocate a statistical approach that accounts for structural variability and variations in compression behaviour at effective stresses less than and greater than the yield stress we argue that our conceptual framework is broadly applicable to minerogenic intertidal sediments at different locations and burial depths within holocene stratigraphic sequences providing site specific compression data are collected inter site transfer and application of measured material properties should not be undertaken due to local variations in compression behaviour resulting from varying ecological sedimentological geochemical climatic geomorphic and hydrographic conditions the individual characteristics of different field locations should be carefully considered before the suggested framework is routinely applied

transfer of basal sliding variations to the surface of a linearly viscous glacier on etudie pour une plaque a faces paralleles d epaisseur h et de viscosite lineaire l effet en surface des fluctuations de la vitesse de derapage

holocene relative sea level changes and coastal vegetation history at kentra moss argyll northwest scotland abstract a late holocene fall in relative sea level in northwest scotland from ca 1 3mm yr 1 to ca 1 0 mm yr 1 is interpreted from lithostratigraphic biostratigraphic chronostratigraphic and numerical analyses of fossil tidal marsh and acidic peat bog communities elevated by isostatic uplift pollen diatom and stratigraphic data from contemporary depositional environments are used to define the indicative range 0 2 m and reference water level mean high water of spring tides or highest astronomical tide of thirteen dated sea level index points no holocene intertidal sediments are recorded above 7 7 m od and all sea level index points are younger than ca 4 kyr b p in parts of kentra moss beyond the limit of holocene intertidal clastic sedimentation raised bog communities were established by at least 8 3 kyr b p these age and altitude parameters differ from those interpolated for the main postglacial shoreline but support a regional model in which isostatic uplift continues at present in the kentra moss area

theoretical limitations to englacial velocity calculations to study the dynamics of ice sheets and glaciers velocities at the bed of a glacier must be measured directly or calculated using data gathered from boreholes and surface surveys boreholes to the bed are expensive and time consuming to drill so the determination of basal velocity is almost exclusively by numerical inversion of velocities observed at the surface for non linearly viscous glaciers a perturbation analysis demonstrates that inversions for englacial velocities will magnify measurement errors at an exponential rate with depth the rate at which calculation errors grow is proportional to a lyapunov exponent a measure of information loss which is shown to be a simple linear function of spatial frequency with a coefficient depending on glen s flow law exponent n the coefficient decreases with increasing non linearity demonstrating that inversions with non linearly viscous ice have smaller calculation errors than inversions with linearly viscous ice in both the linear and nonlinear cases the lyapunov exponent and rate of error growth increases with decreasing wavelength which limits velocity calculations at the bed to wavelengths on the order of one ice thickness or greater this limitation is theoretical and cannot be countered by more accurate survey data or special numerical techniques

δ13c and c n as potential coastal palaeoenvironmental indicators in the mersey estuary uk the reconstruction of former environments and ultimately relative sea level changes in coastal and estuarine environments normally utilises a range of microfossil proxies such as diatoms foraminifera and pollen as microfossils are sometimes poorly preserved sparse or absent from coastal sediments this study assesses the potential of using 13c and c n analysis of sedimentary organic matter as an alternative contemporary high inter tidal and sub tidal surface saltmarsh sediments of the mersey estuary uk reveal distinctly different 13c and c n values reflecting the contrasting sources of organic matter in relation to ground elevation within the tidal frame despite decomposition effects the relationship between ground elevation 13c and c n is preserved in the sediment record with a gradual increase in 13c and decrease in c n from supra tidal through to inter tidal and to sub tidal environments holocene variations in 13c and c n are compared with stratigraphical palaeoenvironmental changes inferred from diatom and pollen evidence and show a good correspondence although 13c and c n are not as accurate as microfossil analysis in terms of coastal palaeoenvironmental reconstruction they may be applied successfully in the field of relative sea level reconstruction by helping to verify sea level index points when microfossils are absent

evidence for storegga tsunami run up at the head of nordfjord western norway numerical simulations show that the storegga tsunami 8 150 cal a bp penetrated into fjords and sounds along the norwegian coast because of its large wavelengths of about 600 800 km despite this deposits from the tsunami have not previously been reported from the innermost fjord district probably because suitable sedimentary archives are lacking in the steep fjord landscape here we describe a persistent and well defined depositional unit up to 3 m thick found in a lake sequence at the head of the 106 km long nordfjord which we interpret as a deposit from the storegga tsunami the unit is identified and mapped in seismic profiles as a continuous semi transparent unit which in places cut deeply into the underlying strata in sediment cores the unit consists of grey silt with sub units containing shell or plant fragments gravel and sand clasts and redeposited lake mud radiocarbon ages date the deposit to the time of the storegga tsunami 8 150 cal a bp we estimate a minimum run up of 1 7 5 m for the tsunami based on the inferred elevation of the lake outlet relative to sea level at that time

force budget i theory and numerical methods a practical method is developed for calculating stresses and velocities at depth using field measurements of the geometry and surface velocity of glaciers to do this it is convenient to partition full stresses into lithostatic and resistive components the horizontal gradient in vertically integrated lithostatic stress is the driving stress and it describes the horizontal action of gravity the horizontal resistive stress gradients describe the reactions resistive stresses are simply related to deviatoric stresses and hence to strain rates through a constitutive relation a numerical scheme can be used to calculate stresses and velocities from surface velocities and slope and from ice thickness there is no mathematical requirement that the variations in these quantities be small

late quaternary sea level changes crustal movements and coastal evolution in northumberland uk northumberland lies in the transition between holocene emergence and submerg ence and is thus a critical zone for testing models of isostatic rebound we have collected data from this area to reconstruct relative sea level changes and lateral coastline movements for the last 14000 y these are deposits from tidal marsh back barrier wetland and terrestrial environ ments producing 47 sea level index points from 12 sites there is no unequivocal evidence for late devensian sea levels above present and the reliable sea level index points are restricted between 26 m and 12 5 m relative to present and 9 0 2 5 kyr cal bp analysis of these quantifies differential responses to glacio and hydroisostatic rebound with the northern sites recording a mid holocene sea level maximum ca 2 5 m above present whereas the southern sites show a maximum ca 0 5 m above present these observations show a reasonable fit with the predictions from quantitative models of glacio and hydroisostatic rebound but there is currently no unique solution of earth and ice model parameters that will explain all the sea level observations copyright 2000 john wiley sons ltd

stress gradient coupling in glacier flow i longitudinal averaging of the influence of ice thickness and surface slope for a glacier flowing over a bed of longitudinally varying slope the influence of longitudinal stress gradients on the flow is analyzed by means of a longitudinal flow coupling equation derived from the vertically cross sectionally integrated longitudinal stress equilibrium equation by an extension of an approach originally developed by budd 1968 linearization of the flow coupling equation by treating the flow velocity u vertically averaged ice thickness h and surface slope in terms of small deviations u h and a from overall average datum values u 0 h 0 and 0 results in a differential equation that can be solved by green s function methods giving u x as a function of h x and x x being the longitudinal coordinate the result has the form of a longitudinal averaging integral of the influence of local h x and x on the flow u x u x u0 2l l 0 ln n nh n l exp x x l dx where the integration is over the length l of the glacier the operator specified deviations from the datum state and the term on which it operates which is a function of the integration variable x represents the influence of local h x x and channel shape factor x at longitudinal coordinate x on the flow u at coordinate x the influence being weighted by the influence transfer function exp x x l in the integral the quantity l that appears as the scale length in the exponential weighting function is called the longitudinal coupling length it is determined by rheological parameters via the relationship l 2h n n 3n where n is the flowlaw exponent n the effective longitudinal viscosity and n the effective shear viscosity of the ice profile n is an average of the local effective viscosity n over the ice cross section and n 1 is an average of n 1 that gives strongly increased weight to values near the base theoretically the coupling length l is generally in the range one to three times the ice thickness for valley glaciers and four to ten times for ice sheets for a glacier in surge it is even longer l 12h it is distinctly longer for non linear n 3 than for linear rheology so that the flow coupling effects of longitudinal stress gradients are markedly greater for non linear flow the averaging integral indicates that the longitudinal variations in flow that occur under the influence of sinusoidal longitudinal variations in h or with wavelength are attenuated by the factor 1 1 2 l 2 relative to what they would be without longitudinal coupling the short intermediate and long scales of glacier motion raymond 1980 over which the longitudinal flow variations are strongly partially and little attenuated are for 2l 2l 20l and 20l for practical glacier flow calculations the exponential weighting function can be approximated by a symmetrical triangular averaging window of length 4l called the longitudinal averaging length the traditional rectangular window is a poor approximation because of the exponential weighting the local surface slope has an appreciable though muted effect on the local flow which is clearly seen in field examples contrary to what would result from a rectangular averaging window tested with field data for variegated glacier alaska and blue glacier washington the longitudinal averaging theory is able to account semi quantitatively for the observed longitudinal variations in flow of these glaciers and for the representation of flow in terms of effective surface slope values exceptions occur where the flow is augmented by large contributions from basal sliding in the ice fall and terminal zone of blue glacier and in the reach of surge initiation in variegated glacier the averaging length 4l that gives the best agreement between calculated and observed flow pattern is 2 5 km for variegated glacier and 1 8 km for blue glacier corresponding to l h 2 in both cases if l varies with x but not too rapidly the exponential weighting function remains a fairly good approximation to the exact green s function of the differential equation for longitudinal flow coupling in this approximation l in the averaging integral is l x but is not a function of x effects of longitudinal variation of l are probably important near the glacier terminus and head and near ice falls the longitudinal averaging formulation can also be used to express the local basal shear stress in terms of longitudinal variations in the local stope stress with the mediation of longitudinal stress gradients

global distributions of glacier properties a stochastic scaling paradigm many problems in global climate and earth systems science require knowledge of regional or global scale distributions of glacier properties which includes mass balance ice velocity flux thickness volume and surface area among others with roughly 160 000 glaciers worldwide obtaining information on the global probability distributions of most ice properties is expensive and often infeasible only surface area distributions are relatively easy to measure either by direct observation or remote sensing while other properties are difficult to observe this work shows that scaling relationships from the continuum dynamics of ice can link the distribution of surface areas to the global and regional distributions of any other continuum property some data inventories already exist for constructing reasonable distributions of glacier sizes and this analysis presents theoretical arguments based on glacier network topologies similar in concept to river networks to suggest a power law times an exponential distribution of surface areas in agreement with the data therefore by using existing data or the theoretical distributions of surface areas specific distributions for other glacier properties in any region of the world can be constructed as an example predictions up to a scaling constant are made for the distribution of glacier volumes characteristic thicknesses characteristic velocities and characteristic response times in the alps

late holocene land and sea level changes in the british isles implications for future sea level predictions abstract four decades of palaeosea level research in the british isles have produced a large dataset of age altitude curves of postglacial sea level changes patterns of late holocene relative sea level change reveal the persistent influence of the british irish ice sheet and the larger scandinavian ice sheet on contemporary rates of vertical land movements the shennan and horton 2002 map of late holocene relative land movements has been used in future sea level rise predictions by the united kingdom climate impact programme in their 2002 assessment ukcip02 but has been mistaken for a map of absolute land movements in this paper land motion data for britain are extracted from the shennan and horton 2002 relative sea level data and a new map of crustal land movements is presented which also includes ireland this procedure takes into account the regional 20th century sea level rise 0 14 m and the process of ocean syphoning i e a global fall in sea level of 0 3 mm yr due to gia induced ocean floor lowering and re distribution of ocean mass the calculated land motion rates also depend on the global late holocene ice equivalent sea level change given by the intergovernmental panel on climate change as 0 0 0 2 mm yr accounting for these processes reduces the misfit between geological observations of vertical land motion and those independently derived from gravity aligned global positioning system ag gps measurements and shows that ukcip02 has underestimated land subsidence in southern britain and over estimated land uplift in scotland both by 0 1 0 2 mm yr a best fit between gps and geological estimates of land movements in britain is achieved for a global long term eustatic sea level fall of ca 0 2 mm yr suggesting some global ice expansion in the late holocene rather than melt if this is correct uplift rates in scotland would be lower and subsidence rates in southern britain would be faster by 0 4 0 5 mm yr than estimated by ukcip02 more high quality late holocene relative sea level data are required to quantify vertical land motion as accurately as possible especially near large coastal population centres for input into regional scenarios of future sea level rise

holocene shelf sea evolution offshore northeast england abstract spatial and temporal changes of tidally mixed and stratified water conditions during the holocene are poorly understood and constrained within the north sea region this study investigates the changing tidal conditions at a core site from offshore northeast england through the holocene a continuous holocene sedimentary record in british geological survey vibrocore 54 02 97 54 53 05 n 1 3 88 w water depth 55 m collected from a natural trough in the north sea has been investigated a multiproxy approach including the interpretation of magnetic susceptibility values bulk sedimentological characteristics benthic foraminifera faunal and isotopic data is adopted the chronology of this record is constrained by a total of ten accelerator mass spectrometry 14 c dates obtained from molluscs and mixed benthic foraminiferal samples the age derived from benthic foraminifera and molluscs obtained at the same core depth are statistically the same these results suggest that benthic foraminifera tests do not undergo significant post mortem reworking at this shallow site and that the foraminifera based proxy records are reliable sedimentary characteristics indicate that tidally mixed waters between 11 150 and 5869 calendar cal yr bp affected the core site the core site was bathed by tidally mixed water conditions indicated by the presence of ammonia batavus hofker with stratified conditions and associated frontal systems developing at or close to the core site between 5869 and 2032 cal yr bp based on the presence of stainforthia fusiformis williamson finally species that are indicative of fully stratified water such as bulimina marginata d orbigny hyalinea balthica schroter and s fusiformis record the transition from mixed frontal to stratified conditions at 1158 cal yr bp this site records a faunal change in the last 500 years that may be a consequence of fully stratified conditions and enhanced phytodetritus delivery to the sea floor alternatively supported to some extent by heavy metal concentrations the fauna may be responding to eutrophication of coastal waters through anthropogenic influences

a holocene tsunami deposit in eastern scotland a thin regionally extensive laterally persistent sand layer identified within the holocene coastal sequences of eastern scotland dated to 7000 years bp is suggested to be a tsunami deposit the likely source of the tsunami wave is the earthquake induced second storegga slide on the norwegian continental slope at least 750 km northeast of the deposit

mangrove pollen of indonesia and its suitability as a sea level indicator we investigated the mangroves of southeast sulawesi indonesia to assess their potential as proxies for reconstructing sea level during the holocene initial investigations confirmed that the mangrove species demonstrate zonations parallel to the shoreline and are dominated by the family rhizophoraceae with avicennia heritiera and sonneratia also important constituents of the mangroves we investigated the vertical distributions of pollen assemblages at three sites partial cca analysis demonstrated that at all three sites elevation was a significant control on the distribution of pollen assemblages in surface samples we combined the three contemporary transects to develop a regional transfer function to explain the relationship between the surface assemblages and elevations using the maximum likelihood ml method the developed transfer function indicated mangrove pollen can be used as a precise indicator of past sea levels with an error of 0 22 m the transfer function was applied to two fossil cores from the wakatobi marine national park and evaluated using the modern analogue technique both cores showed similar patterns in changes of palaeo mangrove elevation and had modern analogues in the contemporary training set we conclude that mangrove pollen is a suitable proxy for reconstructing sea level in tropical environments

glaciers dominate eustatic sea level rise in the 21st century ice loss to the sea currently accounts for virtually all of the sea level rise that is not attributable to ocean warming and about 60 of the ice loss is from glaciers and ice caps rather than from the two ice sheets the contribution of these smaller glaciers has accelerated over the past decade in part due to marked thinning and retreat of marine terminating glaciers associated with a dynamic instability that is generally not considered in mass balance and climate modeling this acceleration of glacier melt may cause 0 1 to 0 25 meter of additional sea level rise by 2100

heavy mineral assemblages of the storegga tsunami deposit abstract this study applies heavy mineral analysis to the storegga tsunami deposit across a range of locations whale firth maggie s kettle loch and scatsta voe in shetland scotland the usefulness of this proxy is tested in the identification and characterization of these palaeotsunami units furthermore provenance relationships are established based on the mineralogical content of tsunami deposits and their potential source finally the capability of identifying different phases of tsunami inundation in an 8200 years old tsunami deposit is attempted our results show that overall tsunamigenic samples presented a clear dominance of garnets and amphiboles while whale firth presented a more balanced distribution between these two mineral groups in maggie s kettle loch and scatsta voe the tsunamigenic samples are dominated by amphiboles 90 of transparent heavy minerals focusing on the two dominant heavy minerals garnets and amphiboles and their vertical variation one could observe that garnets mimic the heavy mineral concentration variability higher values at the base and decreasing values to the top this effect of concentration of the heaviest of the heavy minerals assemblage presents similarities with the formation of beach placer deposits in fact based on the heavy mineral vertical variation of the tsunami deposits in maggie s kettle loch scatsta voe and whale firth it is possible to conclude that hornblende most likely amphibole of the assemblage has the lowest concentration factor indicating that its transport process is more efficient and consequently most of its particles eventually may have moved offshore in the backwash phase of the tsunami furthermore the more platy shape of amphiboles also favours a slower deposition the opposite can be observed for garnets which require more energy to be transported i e they are more difficult to entrain by the tsunami waves and tend to be more easily preserved in the formation of a tsunamigenic placer deposit the work presented here is of particular relevance for future high resolution sedimentological studies aiming to distinguish different inundation phases of the storegga tsunami and assess the degree of preservation of these deposits especially considering the specific geomorphological and stratigraphic depositional setting of scotland

the last ice sheet in north west scotland reconstruction and implications recent models of the last scottish ice sheet suggest that nunataks remained above the ice surface in areas peripheral to the main centres of accumulation this proposition has been investigated on 140 mountains over an area of 10 000 km2 in nw scotland outside the limits of the later loch lomond readvance in this area there is evidence for a single high level weathering limit that separates glacially eroded terrain from higher areas of in situ frost debris this limit occurs at altitudes ranging from 425 to 450 m in the outer hebrides to 950 m on the mainland and is best developed on lithologies that resisted breakdown after ice sheet downwastage interpretation of this weathering limit as a periglacial trimline cut by the last ice sheet at its maximum thickness is supported by 1 joint depth and schmidt hammer measurements that indicate significantly more advanced rock breakdown above the weathering limit 2 a much greater representation of gibbsite a pre late devensian weathering product in the clay fraction of soils above the limit 3 cosmogenic isotope dating of the exposure ages of rock outcrops above and below the limit 4 the sharpness of the limit at some sites and its regular decline along former ice flowlines and 5 shear stress calculations based on the inferred altitude and gradient of the former ice surface reconstruction of the ice surface based on trimline evidence indicates that the mainland ice shed lay near or slightly east of the present watershed and descended northwards from 900 m to ca 550 m at the north coast independent dispersion centres fed broad ice streams that occupied major troughs on skye an ice dome 800 m deflected the northwestwards movement of mainland ice but the mountains of rum were over ridden by mainland ice up to an altitude of ca 700 m the outer hebrides supported an independent ice cap that was confluent with mainland ice in the minches extrapolation of the trimline evidence indicates that most reconstructions of ice extent are too conservative and suggests that low gradient ice streams extended across the hebridean shelf offshore wider implications of this research are 1 that blockfields and other periglacial weathering covers are not all of the same age or significance depending on the resistance of different lithologies to frost weathering 2 that the contrasting degree of glacial modification in the western and eastern highlands of scotland may reflect a former cover of predominantly warm based ice in the former and predominantly cold based ice in the latter and 3 that the approach and techniques developed in this study have potential application for constraining ice sheet models not only in areas peripheral to the main centres of ice accumulation in britain and ireland but also in other mountain areas where nunataks protruded through warm based late pleistocene ice masses

regional and global volumes of glaciers derived from statistical upscaling of glacier inventory data 1 very few global scale ice volume estimates are available for mountain glaciers and ice caps although such estimates are crucial for any attempts to project their contribution to sea level rise in the future we present a statistical method for deriving regional and global ice volumes from regional glacier area distributions and volume area scaling using glacier area data from 123 000 glaciers from a recently extended world glacier inventory we compute glacier volumes and their sea level equivalent sle for 19 glacierized regions containing all mountain glaciers and ice caps on earth on the basis of total glacierized area of 741 103 68 103 km2 we estimate a total ice volume of 241 103 29 103 km3 corresponding to 0 60 0 07 m sle of which 32 is due to glaciers in greenland and antarctica apart from the ice sheets however our estimate is sensitive to assumptions on volume area scaling coefficients and glacier area distributions in the regions that are poorly inventoried i e antarctica north america greenland and patagonia this emphasizes the need for more volume observations especially of large glaciers and a more complete world glacier inventory in order to reduce uncertainties and to arrive at firmer volume estimates for all mountain glaciers and ice caps

high resolution numerical modeling of tides in the western atlantic gulf of mexico and caribbean sea during the holocene 1 tidal constituents and datums are computed on a high resolution grid of the northwestern atlantic ocean including the gulf of mexico and the caribbean sea a global model is used to determine tidal parameters on a grid with a nominal resolution of 800 800 the global model includes self attraction and loading drag in shallow marginal seas and internal tide drag in the deep ocean simulations are performed at 1000 year intervals during the holocene 10 000 calibrated years before present 10 ka in combination with changes in bathymetry and coastline location derived from a glacial isostatic adjustment model the global model results are then used to force a regional barotropic tidal model the regional model uses an unstructured finite element grid with very high resolution at the coastline the model results reveal significant variations in tidal constituent amplitudes throughout the holocene in the northwestern atlantic semi diurnal components show a strong amplification at around 9 ka while in the gulf of mexico the response is much more muted variations in diurnal tidal parameters are found to be less significant than semi diurnal parameters throughout the model domain changes in tidal range of great relevance to changes in relative sea level rsl are also investigated throughout the holocene the overall structure is similar to the patterns observed in the m2 tide with peak increases of 200 300 relative to present day being observed along the east coast of the united states from 9 to 8 ka finally the high spatial resolution of the regional model allows for the investigation of tidal changes at spatial scales e g individual bays much smaller than in previous studies

sea level change glacial rebound and mantle viscosity fornorthern europe northwestern europe remains a key region for testing models of glacial isostasy because of the good geological record of crustal response to the glacial unloading since the time of the last glacial maximum models for this rebound and associated sea level change require a detailed knowledge of the ice sheet geometry including the ice thickness through time existing ice sheet reconstructions are strongly model dependent and inversions of sea level data for the mantle response may be a function of the model assumptions thus inverse solutions for the sea level data are sought that include both ice and earth model parameters as unknowns sea level data from fennoscandia the north sea the british isles and the atlantic and english channel coasts have been evaluated and incorporated into the solutions the starting ice sheet for fennoscandia is based on a reconstruction of a model by denton hughes 1981 that is characterized by quasi parabolic cross sections and symmetry about the load centre both global northwestern europe as a whole and regional subsets of the data solutions have been made for earth model parameters and ice height scaling parameters the key results are as follows 1 the response of the upper mantle to the changing ice and water loads is spatially relatively homogenous across scandinavia the north sea and the british isles 2 this response can be adequately modelled by an effective elastic lithosphere of thickness 65 85 km and by an effective upper mantle viscosity from the base of the lithosphere to the 670 km depth seismic discontinuity of about 3 4 1020 pa s the effective lower mantle viscosity is at least an order of magnitude greater 3 the ice thickness over scandinavia at the time of maximum glaciation was only about 2000 m much less than the 3400 m assumed in the denton hughes model 4 the ice profiles are asymmetric about the centre of the ice sheet with those over the western part being consistent with quasi parabolic functions whereas the ice heights over the eastern and southern regions increase much more slowly with distance inwards from the ice margin

patterns of holocene relative sea level change in the north of britain and ireland temporal and spatial patterns of relative sea level rsl change in the north of britain and ireland during the holocene are examined four episodes each defined by marked changes in the rsl trend are identified each episode is marked by a rise to a culminating shoreline followed by a fall episode hrsl 1 dates from the younger dryas to early in the holocene hrsl 2 to hrsl 4 occurred later in the holocene there is extensive evidence for each episode and on this basis the spatial distribution of the altitude data for three culminating shorelines and a shoreline formed at the time of the holocene storegga slide tsunami ca 8110 100 cal bp is analysed ordinary kriging is used to determine the general pattern following which gaussian trend surface analysis is employed recognising that empirical measurements of rsl change can be unevenly distributed spatially a new approach is introduced which enables the developing pattern to be identified the patterns for the most widely occurring shorelines were analysed and found to be similar and common centre and axis models were developed for all shorelines the analyses described provide models of the spatial pattern of holocene rsl change in the area between ca 8100 cal bp and ca 1000 cal bp based on 2262 high resolution shoreline altitude measurements these models fit the data closely no shoreline altitude measurement lying more than 1 70 m or 1 82 m from the predicted value the models disclose a similar pattern to a recently published glacial isostatic adjustment model for present rsl change across the area indicating that the overall spatial pattern of rsl change may not have varied greatly during the last ca 8000 years

diatom based tidal level transfer functions as an aid in reconstructing quaternary history of sea level movements in the uk this research analyses the diatom asssemblages recorded from six uk coastal sites and relates these diatom assemblages to tidal levels the relationship between diatom assemblages and tidal levels is examined statistically in order to develop a diatom based tidal level transfer function the results suggest that there is highly significant correlation between the diatom assemblages and water levels from mean high water of neap tides to highest astronomical tide p 0 01 99 random permutations a weighted average wa transfer function is thus established and the predictive ability of this transfer function is highly satisfactory finally this transfer function is applied successfully to estimate palaeotidal levels from fossil diatom data recorded in late holocene coastal sequences copyright 1999 john wiley sons ltd

theory of lattice boltzmann simulations of glacier flow a lattice boltzmann technique for modeling navier stokes fluid flow is extended to allow steady state simulations of glaciers and other slow flowing solids the technique is based on a statistical mechanical representation of flowing ice as a set of particles populations which translate and collide on a face centered cubic lattice the average trajectories of the populations give the velocities of the ice at any point in the glacier the method has considerable advantages over other techniques including its ability to handle complex realistic geometries without additional complications to the code examples are presented for two dimensional simulations

late devensian and holocene records of relative sea level changes in northwest scotland and their implications for glacio hydro isostatic modelling raised tidal marshes and isolation basins lakes that were once connected to the sea in northwest scotland record changes in relative sea level following deglaciation during the late devensian to the present the kentra to arisaig area which was covered by relatively thick ice c 900 m at the last glacial maximum lgm shows a regression from a marine limit between 36 5 m od and 40 m od at c 15 9 kyr cal bp range 15 6 16 3 kyr cal bp through to an early holocene minimum a range of sites in the same area record a mid holocene maximum indicative of mean sea level c 6 5 m above present the maximum is not a well developed and short duration highstand as predicted by a number of models but is an extended period 8 0 5 0 kyr cal bp with sea level within c 1 m of the maximum sites to the north in kintail show no late devensian record because much of the area lies within the younger dryas ice limit the altitude of the mid holocene maximum in kintail is not well constrained but occurred 7 9 8 1 kyr cal bp further north sites on the applecross peninsula record a late devensian fall in sea level and a holocene maximum for mean sea level no higher than c 3 0 m above present in coigach the furthest north of the new sites and well outside the younger dryas ice limit there is no evidence recorded of late devensian sea levels above present the holocene maximum here was around c 2 5 m above present these observations of sea level change all standardised to change in mean sea level relative to present constrain the glacio hydroisostatic rebound model parameters earth models comprising three mantle layers with lateral viscosity and elastic parameters give a satisfactory description of rebound the parameters h lithosphere thickness 65 km g 6 upper mantle viscosity 4 1020 pa 14c seconds and g lower mantle viscosity 1022 pa 14c seconds give the best overall agreement but discrepancies between observations and predictions remain an increase of 10 in ice thickness north of the great glen compared to the previous optimum ice model provides good agreement for many sites but important discrepancies remain for the northern sites and indicate inadequacies in the model of the british ice sheet several alternative ice models are examined but the various combinations of earth and ice model illustrate the non uniqueness of the solution a combination of more extensive ice limits especially onto the hebridean shelf and west shetland shelf and some changes to ice thicknesses over the mainland should produce a better agreement but the spatial coverage of observations remains a limitation to producing a unique solution the characteristics of the holocene highstand age duration and amplitude at the di erent sites refutes the assumption that globally deglaciation ceased abruptly 7000 yr ago the observations are consistent with an ice model that includes c 3 m of melting over the last 7000 yr 2000 elsevier science ltd all rights reserved

the physical basis of glacier volume area scaling ice volumes are known for only a few of the roughly 160 000 glaciers worldwide but are important components of many climate and sea level studies which require water flux estimates a scaling analysis of the mass and momentum conservation equations shows that glacier volumes can be related by a power law to more easily observed glacier surface areas the relationship requires four closure choices for the scaling behavior of glacier widths slopes side drag and mass balance reasonable closures predict a volume area scaling exponent which is consistent with observations giving a physical and practical basis for estimating ice volumes glacier volume is insensitive to perturbations in the mass balance scaling but changes in average accumulation area ratios reflect significant changes in the scaling of both mass balance and ice volume

exploring holocene palaeogeography in the white ribbon a mesolithic case study from the northumberland coast mesolithic settlement sites preserved on the north east coast of england and in south east scotland drive questions about the relationship between early human settlement and the holocene palaeogeography of doggerland palaeogeographical reconstructions before 8000 years ago have been restricted by a lack of sea level index points and particularly by sparse nearshore geophysical and geological datasets required for such reconstructions this paper presents new high resolution geophysical survey data from northumberland s nearshore white ribbon which provide a foundation for more accurate palaeogeographical reconstructions within which early prehistoric settlement sites can be more readily understood high resolution bathymetry data collected in the nearshore adjacent to the mesolithic house site at howick are integrated with coastal lidar seismic geological and archaeological datasets to underpin palaeogeographical reconstructions the reconstructions illustrate changing coastal landscapes during early holocene sea level rise the data and interpretations provide a source to sea context for understanding the archaeology at important sites such as howick and low hauxley furthermore they provide a basis for enhancing management of at risk coastal prehistoric archaeology and a framework to prospect for and protect further vulnerable nearshore archaeological heritage

glacial rebound and sea level change in the british isles observations of sea levels around the coastline of the british isles for the past 10 000 15 000 years exhibit a major regional variation and provide an important data base for testing models of glacial rebound as well as models of the late devensian ice sheet a high resolution rebound model has been developed which is consistent with both the spatial and temporal patterns of sea level change and which demonstrates that the observations are the result of i the glacio isostatic crustal rebound in response to the unloading of the ice sheet over britain and to a lesser degree of the ice sheet over fennoscandia and ii the rise in sea level from the melting late pleistocene ice sheets including the response of the crust to the water loading the hydro isostatic effect the agreement between model and observations is such that there is no need to invoke vertical crustal movements for great britain and ireland of other than glacio hydro isostatic origin the rebound contributions are important throughout the region and nowhere is it sufficiently small for the sea level change to approximate the eustatic sea level rise the observational data distribution around the periphery as well as from sites near the centre of the former ice sheet is sufficient to permit constraints to be established on both earth model parameters specifying the mantle viscosity and lithospheric thickness and the extent and volume of the ice sheet at the time of the last glaciation preliminary solutions are presented which indicate an upper mantle viscosity of 3 5 1020 pas a lithospheric thickness of about 100 km or less and an ice model that was not confluent with the scandinavian ice sheet during the last glaciation and whose maximum thickness over scotland is unlikely to have exceeded about 1500 m

ice volume and subglacial topography for western canadian glaciers from mass balance fields thinning rates and a bed stress model abstracta method is described to estimate the thickness of glacier ice using information derived from the measured ice extent surface topography surface mass balance and rate of thinning or thickening of the ice column shear stress beneath an ice column is assumed to be simply related to ice thickness and surface slope as for an inclined slab but this calculation is cast as a linear optimization problem so that a smoothness regularization can be applied assignment of bed stress is based on the flow law for ice and a mass balance calculation but must be preceded by delineation of the ice flow drainage basin validation of the method is accomplished by comparing thickness estimates to the known thickness generated by a numerical ice dynamics model once validated the method is used to estimate the subglacial topography for all glaciers in western canada that lie south of 60 n adding the present ice volume of each glacier gives the estimated total volume as 2320 km3 equivalent to 5 8 mm of sea leve

the holocene storegga slide tsunami in the united kingdom all currently known sites in the united kingdom with evidence for the holocene storegga slide tsunami are described information on the altitude distribution stratigraphical context age particle size profile and microfossil characteristics of the deposits is presented the tsunami involved a greater area than previously described reaching a coastline over 600 km long the ubiquitous sand layer which forms the main deposit associated with the event is shown to exhibit a consistent morphology and a particle size profile marked by fining upwards sequences an analysis of new and previously published radiocarbon dates indicates that from evidence in the united kingdom the event took place sometime around 7100 radiocarbon years bp 7900 calibrated years bp a new isobase model for mainland scotland and adjacent areas providing a preliminary estimate of land uplift since the tsunami is presented the model estimates contemporary sea surface level offshore at 14 m below the present day mean high water spring tides tsunami sediment run up is greatest in inlets where it reaches at least 25 m on shetland and at least 5 m along the mainland coastline to the south and run up of the tsunami would have exceeded these values the tsunami sediments identified here are considered particularly valuable as a synchronous marker horizon

late quaternary sea level changes and crustal movements in eastern england and eastern scotland an assessment of models of coastal evolution abstract the most comprehensive records of late quaternary coastal environmental change in eastern england and eastern scotland are obtained from the intercalated semi terrestrial peats and intertidal silts clays and sands that have accumulated in estuaries and coastal lowlands radiocarbon dated sea level index points from sites in north east england are evaluated with reference to first a conceptual model of coastal sedimentary environments and second a model of pollen assemblages in holocene coastal environments analysis of these new data indicates differential crustal uplift within north east england of ca 0 2 mm yr for the last 4000 to 5000 radiocarbon years this pattern of uplift is consistent with models of holocene crustal deformation in scotland and england the uplift is attributable to the combined effects of ice unloading and water loading

late devensian and holocene shorelines of the british isles and north sea from models of glacio hydro isostatic rebound sea level change around the british isles since the time of the last glacial maximum is largely due to of the crustal rebound from the glacial unloading of northern britain and the concomitant melt water loading of the adjacent seas and atlantic ocean minor but not insignificant contributions also result from the rebound caused by the unloading of the distant ice sheets including fennoscandia and north america observations of sea level change for this period constrain the glacio hydro isostatic rebound model parameters describing the effective lithospheric thickness or rigidity and the effective mantle viscosity as well as certain ice sheet characteristics such as the ice thickness at the time of the last glacial maximum the models permit palaeobathymetry and palaeoshorelines to be predicted for the british isles region including the north sea the resulting evolution of the coastlines exhibits a complex behaviour through time one that is quite different from the usual models in which sea level change is assumed to be a function of time only in part this is because of the delayed response of the mantle to the spatially variable and time dependent ice and water loads and in part because the unloading history of the british ice sheet is different from those of the major global ice sheets thus maximum emergence of the north sea occurred after deglaciation had started and lasted for an extended period from about 15 000 to 12 000 radiocarbon years bp during this relative sea level still stand shoreline features could have formed for example along the western edge of the norwegian trough when access to the firths of eastern scotland would have been via a long and shallow marine inlet shoreline retreat across the north sea became relatively rapid after about 10000 years the model predictions for the irish and celtic seas also suggest a complex behaviour with the formation of a wide land bridge between about 20000 and 13 000 years ago the model also suggests that as long as the scottish ice extended across the northern irish sea until about 14 000 years ago there would have been a large freshwater periglacial lake located further south both the predicted sea level height age relations and the shoreline positions are consistent with a large body of observational evidence but some discrepancies occur particularly in northern scotland and ireland where the ice heights may have been somewhat greater than assumed in the model

stress gradient coupling in glacier flow iii exact longitudinal equilibrium equation the vertically integrated exact longitudinal stress equilibrium equation of budd 1970 is developed further in such a way as to yield an equation that gives explicitly and exactly the contributions to the basal shear stress made by surface and bed slope surface curvature longitudinal stress deviators and longitudinal stress gradients in a glacier flowing in plane strain over a bed of longitudinally varying slope with this exact equation questions raised by various approximate forms of the longitudinal equilibrium equation can be answered decisively and the magnitude of errors in the approximations can be estimated to first order in the angle that describes fluctuations in the surface slope from its mean value the exact equilibrium equation reduces to 1 2sin 2 b pghsin 2g t b k where g and t are the well known stress deviator gradient and variational stress terms k is a longitudinal curvature term and b is a basal drag term that contributes a resistance to sliding across basal hills and valleys except for t these terms are expressed in simple form and evaluated for practical situations the bed slope relative to the mean slope is not assumed to be small which allows the effects of bedrock topography to be determined particularly through their appearance in the b term

a multi proxy approach to assessing isolation basin stratigraphy from the lofoten islands norway article i nfo article history received 14 november 2009 available online 24 september 2010 this study takes a comprehensive approach to characterizing the isolation sequence of heimerdalsvatnet a coastal lake in the lofoten islands northern norway we use established methods and explore new techniques to assess changes in marine influence bathymetric and sub bottom profiles were acquired to examine basin wide sedimentation and a 5 8 m sediment core spanning the last 7800 cal yr bp was analyzed we measured magnetic susceptibility bulk organic matter properties molecular biomarkers diatom assemblages and elemental profiles acquired by scanning x ray fluorescence these characteristics of the sediment reflect detailed changes in salinity and water column conditions as the lake was progressively isolated three distinct litho chemo stratigraphic units represent a restricted marine phase 7800 6500 cal yr bp a transitional phase characterized by intermittent marine influence 6500 4900 cal yr bp and complete isolation and freshwater sedimentation 4900 cal yr bp to present although there are uncertainties in the estimate of the threshold elevation of the lake the timing of these phases generally corresponds with previous interpretations of the local relative sea level history this record captures sea level regression following the tapes transgression and supports the interpretation of a subsequent sea level stillstand dated in heimerdalsvatnet from 6500 to 4900 cal yr bp

fluctuations in relative sea level during the past 3000 yr in the onnetoh estuary hokkaido northern japan this paper presents the results of a litho bio and chronostratigraphical study of the evidence for late holocene sea level change palaeoseismicity and coastal evolution at the onnetoh estuary northwest japan alternating peat and mud couplets record evidence for four falls in relative sea level since ca 2500 cal yr bp in the latest instance intertidal mud with a salt tolerant diatom and plant macrofossil flora is abruptly overlain by a freshwater peat containing abundant macrofossil remains of the conifer picea glehnii these stratigraphical changes record an abrupt change from tidal flat to upland with no intermediate transition through saltmarsh in the other three instances the stratigraphy records a more gradual fall in relative sea level as shown by gradational stratigraphical contacts and transitional diatom and plant macrofossil assemblages once established these freshwater peat communities are gradually submerged and become overlain by saltmarsh and then intertidal muds radiocarbon ages and tephra date the emergence events to 2700 1750 gradual 1350 950 gradual 650 300 gradual and ca 400 cal yr bp abrupt these ages are similar to a sequence of emergence events recorded at the akkeshi estuary 70 km to the west of the present study site the three falls in relative sea level may record coseismic or swift post seismic uplift caused by plate boundary subduction earthquakes on the kurile subduction zone the oldest relative sea level fall is correlated with the so called yayoi regression dated to 1500 3000 cal yr bp in other parts of japan copyright 2002 john wiley sons ltd

refining the eustatic sea level curve since the last glacial maximum using far and intermediate field sites the eustatic component of relative sea level change provides a measure of the amount of ice transferred between the continents and oceans during glacial cycles this has been quantified for the period since the last glacial maximum by correcting observed sea level change for the glacio hydro isostatic contributions using realistic ice distribution and earth models during the last glacial maximum lgm the eustatic sea level was 125 5 m lower than the present day equivalent to a land based ice volume of 4 6 4 9 107 km3 evidence for a non uniform rise in eustatic sea level from the lgm to the end of the deglaciation is examined the initial rate of rise from ca 21 to 17 ka was relatively slow with an average rate of ca 6 m ka 1 followed by an average rate of ca 10 m ka 1 for the next 10 ka significant departures from these average rates may have occurred at the time of the younger dryas and possibly also around 14 ka most of the decay of the large ice sheets was completed by 7 ka but 3 5 m of water has been added to the oceans since that time

distributed ice thickness and volume of all glaciers around the globe 1 a new physically based approach for calculating glacier ice thickness distribution and volume is presented and applied to all glaciers and ice caps worldwide combining glacier outlines of the globally complete randolph glacier inventory with terrain elevation models shuttle radar topography mission advanced spaceborne thermal emission and reflection radiometer we use a simple dynamic model to obtain spatially distributed thickness of individual glaciers by inverting their surface topography results are validated against a comprehensive set of thickness observations for 300 glaciers from most glacierized regions of the world for all mountain glaciers and ice caps outside of the antarctic and greenland ice sheets we find a total ice volume of 170 103 21 103 km3 or 0 43 0 06 m of potential sea level rise

on the postglacial isostatic adjustment of the british isles and the shallow viscoelastic structure of the earth summary observations of postglacial relative sea level rsl history at sites beyond the margins of the main accumulations of wu rm wisconsin devensian ice may be invoked to test the accuracy of global models of the glacial isostatic adjustment process the existing database of rsl time series for the british isles forms a continuous network of sites that sample the coasts of scotland england and wales fairly uniformly and which may be especially important in this regard not only are these 14c data for the holocene epoch of very high quality in terms of our knowledge of the coastal environment and relationship to palaeo sea level of each age measurement but they are especially numerous and relate to an island that was itself partly glaciated in the north essentially ice free in the south and located well outboard of the massive ice sheet that covered fennoscandia at the last glacial maximum lgm taken together the time series from 55 distinct locations allow us to perform a fairly stringent test of the recently formulated ice 4g vm2 global model of the isostatic adjustment process even without modification this model has been shown to fit most of the time series in the uk data set rather well in order to satisfy very recently published a priori constraints on the maximum thickness of the scottish ice sheet however we find that the lithospheric thickness the feature of the radial viscoelastic structure to which the rebound data from scotland are most sensitive must be somewhat reduced whereas the assumed thickness of the lithosphere in ice 4g vm2 was near to 120 km best fits to the scottish data require a lithospheric thickness near to 90 km this reduced value for lithospheric thickness agrees exceedingly well with the latest estimates of this earth property based on the inversion of oceanic geoid and topography data as the asymptotic thickness characteristic of the oldest ocean floor this would appear to be the best possible a priori estimate for the thickness of the cratonic lithospheres upon which the largest ice sheets of the late pleistocene are known to have rested we also demonstrate explicitly that inferences of the shallow viscoelastic structure beneath the british isles are strongly influenced by the details of the history of deglaciation at remote locations at antarctica in particular

a holocene alluvial sequence in the lower tyne valley northern britain a record of river response to environmental change palaeoenvironmental investigations have been made of late quaternary sediments infilling the lower tyne valley at scotswood newcastle upon tyne 18 km upstream from the mouth of the river attention has focused on the holocene alluvial sedimentary sequence using sedimentological geochemical and palynological analyses holocene valley floor development from c 7500 bp has been largely dominated by a tendency towards river aggradation with some limited lateral and vertical reworking of sediments four alluvial fills have been identified and dated to 1 c 7500 4800 bp 2 from c 2590 bp up to the early first millennium ad and possibly as late as medieval times 3 between the medieval period and the early seventeenth century and 4 between the seventeenth and nineteenth centuries episodes of incision are dated to c 4800 2590 bp and to the period following the early seventeenth century marked variations in the rates and nature of sedimentation and erosion appear to coincide with rising post glacial

holocene coastal change and geoarchaeology at howick northumberland uk the recent discovery of one of the earliest mesolithic occupation sites in northern britain at howick on the northumberland coast in association with multiperiod archaeological evidence nearby highlights the importance of uk coastal settings as focii of human occupation through the holocene environmental evidence from a nearby river valley 8 15 m of sediment ranging in age from about 12 000 cal bp to the present records local and regional environmental change twenty four radiocarbon dates based on plant macrofossils provide a strong chronological framework calcareous microfossil assemblages foraminifera ostracods have been recovered from the fine grained sediments recording a change from marine through to brackish and eventually freshwater conditions between about 8200 and 6500 cal bp a preliminary pollen study of the core has permitted a reconstruction of the regional vegetation as it responded to climatic amelioration and human influence upon the landscape radiocarbon dating and sedimentological evidence indicates a major hiatus between approximately 11 000 and 8000 years bp including the period of mesolithic occupation represented by a 30 cm layer of coarse sands and sandstone pebbles probably the result of a significant high energy event dated to about 8300 cal bp although not a typical tsunami deposit the age and context suggests that this may be associated with the storegga slide event already well documented along the eastern coast of scotland the sedimentary and biological remains at howick record environmental change over much of the holocene and are compared with other environmental change records from the region to provide an environmental framework for the archaeology of this coastline

postglacial relative sea level observations from ireland and their role in glacial rebound modelling the british isles have been the focus of a number of recent modelling studies owing to the existence of a high quality sea level dataset for this region and the suitability of these data for constraining shallow earth viscosity structure local to regional ice sheet histories and the magnitude timing of global meltwater signals until recently the paucity of both glaciological and relative sea level rsl data from ireland has meant that the majority of these glacial isostatic adjustment gia modelling studies of the british isles region have tended to concentrate on reconstructing ice cover over britain however the recent development of a sea level database for ireland along with emergence of new glaciological data on the spatial extent thickness and deglacial chronology of the irish ice sheet means it is now possible to revisit this region of the british isles here we employ these new data to constrain the evolution of the irish ice sheet we find that in order to reconcile differences between model predictions and rsl evidence a thick spatially extensive ice sheet of 600 700 m over much of north and central ireland is required at the lgm with very rapid deglaciation after 21 k cal yr bp copyright 2007 john wiley sons ltd

the storegga slides evidence from eastern scotland for a possible tsunami abstract the second storegga slide on the continental slope off western norway has been dated at between 8000 and 5000 yrs b p a prominent sand layer in flandrian holocene deposits along the coast of eastern scotland and dated at approximately 7000 yrs b p may have been deposited by a tsunami generated by the slide the altitude and stratigraphy of the layer allow estimates to be made of the magnitude of the earthquake which initiated the slide

glacial rebound of the british isles iii constraints on mantle viscosity summary observations of sea level change since the time of the last glacial maximum provide important constraints on the response of the earth to changes in surface loading on time scales of 103 104 years this response is conveniently described by an effective elastic lithospheric thickness and effective viscosities for one or more mantle layers considerable trade off between the parameters describing these layers can occur and different combinations can give rise to comparable predictions of sea level change in particular the trade off between lithospheric thickness and upper mantle viscosity can be important and for any reasonable value for the lithospheric thickness a corresponding mantle viscosity structure can be found that gives a plausible comparison of sealevel predictions with observations in particular thin lithosphere models will lead to low estimates for the upper mantle viscosity while thick lithosphere models lead to high viscosity values however either solution may represent only a local minimum in the model parameter space and may not correspond to the optimum solution it becomes important therefore that in the inversion of observational data a comprehensive search is conducted throughout the entire model parameter space to ensure that the solution identified does indeed correspond to the optimum solution the sea level data for the british isles lend themselves well to such an inversion because of the relatively high quality of the data the good geographic distribution of the data relative to the former ice sheet and reasonable observational constraints on the dimensions of the former ice sheet and on its retreat furthermore because of the contribution to the sea level signal from the distant ice sheets as well as from the melt water load the observational data base for the region also has some resolving power for the viscosity of the deeper mantle the parameter space explored is defined by up to five mantle layers the lithosphere of effective elastic thickness d and a series of upper mantle layers i 2 4 extending down to depths of 200 400 and 670 km respectively each of viscosity qi and a lower mantle layer of viscosity qlm extending down to the coremantle boundary the range of parameters explored is 30 d i 120 km 3 x loi9 iqi

assessment of temporal changes in coastal sand dune environments using the log hyperbolic grain size method three cores 9 m long recovered from late holocene coastal sand dunes in northumberland north eastern england were examined stratigraphically and dated by the infrared stimulated luminescence irsl method to the time period between the medieval warm period mwp 900 1200 ad and little ice age lia 1550 1800 ad grain size variability and caco 3 content were determined at 10 mm intervals throughout parts of the cores the sahara computer program was used to plot the log hyperbolic distribution lhd of grain size spectra from different stratigraphic levels and estimate the lhd s statistical components core samples plot variously in the depositional and erosional domains of the hyperbolic chi vs xi shape triangle which describes components of sediment sorting depositional and erosional phases discriminated within the lhd s shape triangle cannot readily be resolved from core stratigraphies or correlated between cores irsl dates from single cores show a clustering about the period 1430 1540 between the dated horizons dunes accreted at 0 02 0 05 m year 1 enabling the timing of excursions in and to be estimated these excursions which can be resolved to the subannual level between the dated horizons may be related to deposition by episodic storms or storm surges in the north sea region which is supported by historical documentary evidence this innovative use of the lhd method and its derived statistics can be used successfully to describe temporal trends in coastal depositional environments and identify likely storm events in dune sediment records

glacier volume estimation as an ill posed inversion estimating a glacier s volume by inferring properties at depth e g bed topography or basal slip from properties observed at the surface e g area and slope creates a calculation instability that grows exponentially with the size of the glacier random errors from this inversion instability can overwhelm all other sources of error and can corrupt thickness and volume calculations unless problematic short spatial wavelengths are specifically excluded volume area scaling inherently filters these short wavelengths and automatically eliminates the instability while numerical inversions can also give stable solutions by filtering the correct wavelengths explicitly as is frequently done when regularizing a model each of the scaling and numerical techniques has applications to which it is better suited and there are trade offs in resolution and accuracy but when calculating volume neither the modeling nor the scaling approach offers a fundamental advantage over the other both are significantly limited by the inherently ill posed inversion and even though both provide stable volume solutions neither can give unique solutions

a detailed record of the lower jaramillo polarity transition from a southern hemisphere deep sea sediment core a detailed record of the lower jaramillo reversed to normal polarity transition was obtained from a southern hemisphere deep sea sediment core latitude 35 91 e longitude 59 97 e the record consists of over 850 samples taken across 140 cm of section the transition itself is recorded across approximately 70 cm and is represented by more than 475 specimens from about 160 levels giving intermediate directions the transition is identified by a nearly 180 shift from directions in good agreement with a reversed axial dipole field to those closely aligned with a normal axial dipole field for the core site latitude the inclinations shallow gradually early in the reversal and pass through very steep negative values 80 late in the transition the declinations show little appreciable variation until the inclinations have moved through the near vertical and then slowly approach values in agreement with a normal polarity field an intensity low accompanies the directional change during which the intensity drops to less than 15 of the maximum values observed in this sample interval the intensity fluctuation spans a wider interval than the directional change decreasing prior to any systematic change in the directions and then increasing to pre transition levels by the same depth at which the directions have stabilized the vgp path constructed for this reversal is longitudinally constrained to a certain extent between 140 and 230 for intermediate vgp latitudes and is roughly centered 120 from the site longitude this path is therefore a far sided vgp path in hoffman s 1977 terminology assuming a constant sedimentation rate 67m ma through the jaramillo subchron the duration of the transition is estimated to be 11 200 years to 4 500 years depending on the criteria for the directional change whereas the associated intensity variation occurred over 15 000 to 20 000 years considered together with records of the most recent reversal matuyama brunhes in light of current transitional field models this record strongly suggests that the lower jaramillo transitional field was dominated by different harmonics than the matuyam brunhes transitional field

glacial rebound of the british isles ii a high resolution high precision model summary observations of ice movements across the british isles and of sea level changes around the shorelines during late devensian time after about 25 000 yr bp have been used to establish a high spatial and temporal resolution model for the rebound of great britain and associated sea level change the sea level observations include sites within the margins of the former ice sheet as well as observations outside the glaciated regions such that it has been possible to separate unknown earth model parameters from some ice sheet model parameters in the inversion of the glaciohydro isostatic equations the mantle viscosity profile is approximated by a number of radially symmetric layers representing the lithosphere the upper mantle as two layers from the base of the lithosphere to the phase transition boundary at 400 km the transition zone down to 670 km depth and the lower mantle no evidence is found to support a strong layering in viscosity above 670 km other than the high viscosity lithospheric layer models with a low viscosity zone in the upper mantle or models with a marked higher viscosity in the transition zone are less satisfactory than models in which the viscosity is constant from the base of the lithosphere to the 670 km boundary in contrast a marked increase in viscosity is required across this latter boundary the optimum effective parameters for the mantle beneath great britain are a lithospheric thickness of about 65 km a mantle viscosity above 670 km of about 4 5 lo2 pa s and a viscosity below 670 km greater than 4 x lo2 pas

glacial rebound of the british isles i preliminary model results summary observations of sea level change from localities around the british coastline indicate that major spatial and temporal variations have occurred over the past 15000 10000yr these observations provide a valuable data set for testing models of glacial rebound and for estimating the earth s response to surface loading as well as for placing broad constraints on models of the ice sheet over the northern british isles in late devensian time simple models have been developed to examine the criteria required for a high precision rebound model suitable for an inversion of the observations of sea level change for earth and ice model parameters for such a model to have a precision of better than 1 m these requirements include 1 introduction of the fennoscandian and more distant ice sheets into the model both as contributions to the sea level rise and to the crustal deformation of the associated changing ice and water loads 2 an expansion of the ice and meltwater loads to very high spherical harmonic degree including terms up to about 240 for the water load term 3 the development of higher iteration solutions of the sea level equation in order to model accurately the meltwater load contribution to sea level change 4 the introduction of loading cycles before the attainment of the last glacial maximum for both the british ice sheet and the other major but more distant ice sheets and 5 the introduction of time dependent coastlines during the period of rapid global sea level rise the sea level predictions are strongly dependent on both earth model and ice model parameters but because observations are available from a wide range of locations within and beyond the former ice sheet margins some separation of the two types of parameters is possible for example the models exclude the possibility that a substantial ice load occurred over the north sea between scotland and norway in late devensian time and that the maximum ice thickness over northern great britain is unlikely to have exceeded about 1500 m during the last glacial maximum the earth model parameters that can be resolved are the lithospheric thickness and the upper mantle viscosity a high resolution model incorporating the above model criteria and used to infer ice and earth model parameters from the observations of sea level change is developed in the accom panying paper

an iterative scheme for determining glacier velocities and stresses there are no direct methods to measure the boundary condition at the base of a glacier here we propose a method that works by iteratively changing boundary conditions until a satisfactory fit to surface observations is obtained the method is an accelerated version of one known as kozlov maz ya iteration we apply it to the problem of ice flow through a transverse cross section and show it to be effective by solving the inverse problem for a sequence of synthetic data we also apply the method to two real glaciers athabasca and perito moreno one of which has a known basal velocity distribution

holocene land and sea level changes in great britain analysis of more than 1200 radiocarbon dated samples that constrain relative sea levels in great britain over the past 16 000 yr provides estimates of current land level changes negative of relative sea level change maximum relative land uplift occurs in central and western scotland ca 1 6 mm yr 1 and maximum subsidence is in southwest england ca 1 2 mm yr 1 sediment consolidation arising from autocompaction as the sediment accumulates and from land drainage increases the subsidence in areas with thick sequences of holocene sediments with an average effect equivalent to at least an extra ca 0 2 mm yr 1 land subsidence but more in parts of southeast england 0 5 1 1 mm yr 1 modelled changes in tidal range during the mid to late holocene in eastern england suggest that the calculated rate of land subsidence is overestimated unless such changes are quantified the effect is most significant for large coastal lowlands the fenland and humber ca 0 5 and 0 6 mm yr 1 that were tidal embayments during the mid to late holocene

relative sea level changes glacial isostatic modelling and ice sheet reconstructions from the british isles since the last glacial maximum while contributing 1 m equivalent eustatic sea level rise the british isles ice sheet produced glacio isostatic rebound in northern britain of similar magnitude to eustatic sea level change or global meltwater influx over the last 18 000 years the resulting spatially variable relative sea level changes combine with observations from far field locations to produce a rigorous test for quantitative models of glacial isostatic adjustment local ice sheet history and global meltwater influx after a review of the attributes of relative sea level observations significant for constraining large scale models of the isostatic adjustment process we summarise long records of relative sea level change from the british isles and far field locations we give an overview of different global theoretical models of the isostatic adjustment process before presenting intercomparisons of observed and predicted relative sea levels at sites in the british isles and far field for a range of earth and ice model parameters in order to demonstrate model sensitivity and the resolving power available from using evidence from the british isles for the first time we show a good degree of fit between relative sea level observations and predictions that are based upon global earth and ice model parameters independently derived from analysis of far field data with a terrain corrected model of the british isles ice sheet that includes extensive glaciation of the north sea and western continental shelf that does not assume isostatic equilibrium at the last glacial maximum and keeps to trimline constraints of ice surface elevation we do not attempt to identify a unique solution for the model lithosphere thickness parameter or the local scale detail of the ice model in order to provide a fit for all sites but argue that the next stage should be to incorporate an ice sheet model that is based on quantitative glaciological model simulations we hope that this paper will stimulate this debate and help to integrate research in glacial geomorphology glaciology sea level change earth rheology and quantitative modelling copyright 2006 john wiley sons ltd

flandrian sea level changes in the fenland ii tendencies of sea level movement altitudinal changes and local and regional factors stratigraphic micropalaeontologic and radiocarbon data show that since c 6500 bp the fenland has been influenced by 7 periods of positive sea level tendencies and by 6 periods of negative sea level tendencies despite the numerous problems associated with the reconstruction of past altitudes of sea level the periods of positive sea level tendencies were clearly characterised by a rise in sea level the development of transgressive overlaps and a landward movement of the coastline the periods of negative sea level tendencies were characterised by the development of regressive overlaps a seaward movement of the coastline and a reduced or negative rate of sea level rise the various altitudinal errors do not permit the incontrovertible distinction of periods of falling sea levels all changes within the fenland were not synchronous and local factors influenced the exact nature of each sea level indicator dominant regional and local factors have been identified for different areas and different time periods the chronological and spatial characteristics of the sequences within the fenland are best explained by a palaeocoastline without supratidal barriers controlling sedimentation the data indicate an average crustal subsidence in the fenland of 0 9m 1000 years since c 6500 bp and the pattern of positive and negative tendencies of sea level movement is also seen in the chronologies for north west england and north east scotland

the basal speed of valley glaciers an inverse approach geophysical inverse methods are used to calculate the basal motion of a glacier they are applied to a one dimensional forward model that can be linearized to make the analysis simpler the inverse method finds a solution that fits the data within a given error it selects for smooth solutions to discriminate against unrealistic oscillations the method is applied to a simple model glacier of uniform shape and thickness to test how well a given basal motion field can be reconstructed it shows as expected that optimizing for smoothness lowers maxima and increases minima of the solution a step change in basal velocity is drawn out in the inversion over a distance that is given by the half width of a resolving function this is typically about three times the ice thickness but is also affected by the sampling rate of the data the method is then applied to two glaciers where suitable data are available brown glacier on heard island southern indian ocean and mccall glacier in the brooks range alaska u s a the mccall results agree well with earlier estimates of basal motion