the effects of softening on nearshore erosion of a cohesive shoreline abstract a study designed to measure spatial and temporal variation in the shear strength of the surface of a till substrate in the nearshore was carried out on the south shore of lake ontario canada the primary goal was to determine whether softening or reduction in shear strength occurred during the study period and the significance of this as a control on the overall rate of vertical lowering of the cohesive profile characteristics of the nearshore environment and the substrate were determined through the collection of till shear strength measurements substrate cores and surficial sediment thickness along a 300 m long underwater profile changes in shear strength were monitored over a four month period in experimental plots in water depths of 1 6 3 5 and 4 75 m together with measurements of bed erosion softening of the till was evident from cores which showed a rapid increase in strength and corresponding decrease in moisture content to a depth of about 0 1 m below the till surface after which they became constant shear strength of the exposed till surface decreased during periods of low wave activity and similar results were found in laboratory experiments periods of high wave activity resulted in the removal of a layer of softened material thus exposing harder underlying till the results suggest that erosion during a storm is related to the thickness of the softened layer that develops during non storm periods because of the steep increase in strength with depth below the till surface maximum erosion during a storm is generally

response of glacial landscapes to spatial variations in rock uplift rate 1 the response of glaciated landscapes to rapid rock uplift driven by tectonic convergence is an important often neglected aspect of proposed interactions between plate tectonic processes and climate change rivers typically respond to more rapid rock uplift in part through increasing channel gradients in contrast the glacial buzzsaw hypothesis suggests that glaciers can erode as quickly as the fastest rock uplift rates 6 10 mm yr without any increase in mean elevations however it has not been established how this is achieved we examined moving window maps swath and longitudinal profiles hillslope relief and hypsometry for glacierized and formerly glacierized basins in areas of spatially variable rock uplift rate in the southern alps new zealand and around nanga parbat pakistan to determine whether glaciers have a specific response to rapid rock uplift the response of these glaciated landscapes to rapid rock uplift 6 10 mm yr comprises 1 modest steepening of the longitudinal profiles in smaller glaciated basins 2 maintenance of shallow downvalley slopes in larger glaciated basins 30 km2 southern alps 100 km2 nanga parbat 3 development of tall headwalls and 4 steepening of the basin as a whole dominated by hillslope lengthening around nanga parbat headwalls several kilometers high constitute 50 of the basin relief at rapid rock uplift rates although glaciers can incise the valley floor swiftly they cannot prevent headwalls from reaching exceptional heights the associated increase in mean distance between cirque heads i e a decrease in drainage density causes regional mean elevation to rise with increasing rock uplift rate however this is much less than the changes in elevation expected in unglaciated ranges

the effect of the subglacial water pressure on the sliding velocity of a glacier in an idealized numerical model in order to interpret observed short term variations of the sliding velocity of a glacier the effect of a variable subglacial water pressure on the sliding velocity has been studied using an idealized numerical model in particular the transient stages of growing or shrinking water filled cavities at the ice bedrock interface were analysed it was found that the sliding velocity was larger when cavities were growing than when they had reached the steady state size for a given water pressure the smallest sliding velocities occurred while cavities were shrinking when cavitation is substantial a small drop of water pressure below the steady state value e g by 0 5 bar can temporarily cause backward sliding a limiting water pressure at which sliding becomes unstable is derived the consequences of more realistic assumptions than those of the model are discussed

positive degree day factors for ablation on the greenland ice sheet studied by energy balance modelling ice ablation is related to air temperature by the positive degree day factor variations of the positive degree day factor in west greenland are studied using an energy balance model to simulate ablation under different conditions degree day factors for simulated and measured ice ablation at nordbogletscher and qaman rssup sermia agree well with values around 8 mm d 1 c 1 degree day factors for snow are less than half those for ice energy balance modelling shows that degree day factors vary with summer mean temperature surface albedo and turbulence but there is only evidence of large positive degree day factors at lower temperatures and with low albedo 0 3 the greatest effect of albedo variations 0 3 0 7 is at lower temperatures while variations in turbulence have greater effect at higher temperatures current models may underestimate runoff from the greenland ice sheet by several tenths because they use a degree day factor for melting ice that is too small for the colder parts of the ice sheet i e the upper ablation area and the northerly margin

numerical simulations of glacial valley longitudinal profile evolution glaciers shape alpine landscapes they broaden valley bottoms enhance local valley relief generate multiple steps overdeepen valley floors and cause tributary valleys to hang these distinctive glacial signatures result from 10 4 10 5 yr of erosion during which swings in climate drive advances and retreats of alpine glaciers we use a numerical model of glacial erosion to explore the development of the longitudinal profiles of glaciated valleys the model is driven by the past 400 k y of variable climate because both sliding speed which dictates abrasion rate and water pressure fluctuations which strongly modulate quarrying rate should peak at the equilibrium line altitude ela we expect the locus of most rapid erosion to follow the transient ela simulations of a single glacial valley show rapid flattening of the longitudinal profile inclusion of a tributary glacier creates a step immediately downvalley of the tributary junction that persists over multiple glaciations and commonly leaves the tributary valley hanging steps and overdeepenings result from an increase in ice discharge immediately below the tributary junction which is accommodated primarily by increased ice thickness and hence sliding rate the size of the step increases with the ratio of tributary to trunk ice discharge while the height of a hanging valley reflects the difference in the time integrated ice discharge in tributary and trunk valleys and therefore increases as the discharge ratio decreases

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

glacial cirque formation in northern scandinavia passglaciaren is a small cirque glacier in the kebnekaise massif northern sweden it is frozen to its bed over more than 70 of its area and under present climatic conditions has little effect on cirque formation more favourable conditions for cirque glacier erosion during the holocene are of short duration assuming similar conditions during previous interglacials it is suggested that forms such as the passglaciaren cirque developed mainly during the initial phases of glacials when they were part of networks of large valley glaciers or of a small warm based mountain centred ice sheet passglaciaren has been examined in order to evaluate its erosive capacity and its association with the subglacial cirque morphology the methods used are radar surveys and direct ice temperature measurements erosion is restricted to a small section of the glacier bed at present resulting in only partial deepening of the cirque and erosion of the backwall in cold arid regions with extensive permafrost small cirque glaciers are largely frozen to the bed and therefore cannot contribute significantly to cirque formation in such regions glacial erosion by larger temperate glaciers is more likely to be the major cause of cirque excavation

positive feedbacks associated with erosion of glacial cirques and overdeepenings the principal points of water input to a glacier are the bergschrund in cirques and crevasse fields lower on the glacier crevasse fields commonly occur over convexities at the heads of overdeepenings in glacier beds the amplitude of subglacial water pressure fluctuations is large just down glacier from these points of water input erosion by quarrying is likely in such areas erosion is thus inferred to be localized on the headwalls of cirques and overdeepenings in the case of overdeepenings this leads to a positive feedback process in which a perturbation in the bed causes crevassing at the surface resulting in erosional forces that accentuate the perturbation when subglacial water flows up an adverse bed slope leading out of a cirque or overdeepening much of the viscous energy dissipated is used to warm the water to keep it at the pressure melting temperature as the ice thins and the pressure decreases in such situations subglacial conduits are maintained by high water pressures rather than by melting of conduit walls in the limit water pressures apparently become so high that water is forced out along the ice bed interface and the conduits collapse the products of erosion are then no longer flushed out and a protective till layer accumulates by limiting erosion on such adverse bed slopes this till layer controls the geometry of these overdeepened basins

allometry and cirque evolution a deductive analysis of the processes responsible for cirque formation leads to a model that describes cirque development through time in this model cirque volumes increase as the third power of time although observed variations in cirque size also reflect pre glacial erosion as well as the average rate of surface recession lowering the deductive findings are extended via analysis of 23 cirques from a part of the sangre de cristo mountains south central colorado the assumption that glacier occupance times are proportionately adjusted to topoclimatic situation leads to the conclusion that average rates of cirque erosion exhibit at least a fourfold possibly as much as an order of magnitude range within a given massif the notion that cirque development rates depend on bed rock resistance is supported by a statistically significant inverse relationship between estimated erosion coefficients and average bed rock joint spacing allometric analysis of a 15 cirque subsample the cirques were chosen because they exhibit similar erosion susceptibility lends credence to the hypothesis that headwall recession has been more rapid than cirque floor lowering within the study area however allometric enlargement cannot by itself account for observed values for the ratio cirque length cirque depth the results imply that pre glacial topography strongly influences observed variability in glacial morphometry

numerical modeling of glacial erosion and headwall processes in alpine valleys abstract how rock relief is developed by glacial erosion in alpine landscapes is a key question in understanding the controls on mountain range topography any generation of relief by glaciers at the highest elevations in mountain ranges can affect the distribution of precipitation in alpine landscapes creating feedbacks between glacier mass balance and glacial erosion relief production at high elevation mountain crests is addressed using a numerical model that incorporates glacier dynamics and subglacial erosion as well as relevant hillslope processes blowing snow from a valley bounding plateau and avalanching onto the accumulation zone of the glacier is included in the model furthermore temperature dependent frost cracking is used as a proxy for headwall backwearing the parameterization of subglacial erosion produces about 500 m of erosion over the 400 ka of each numerical simulation in steady and varying climate scenarios valley floors flatten as headwalls increase in height and retreat headward over time headwall slopes increase in simulations in which quarrying is explicitly incorporated rates of quarrying are high near the base of the headwall increasing headwall length and slope as a result of valley floor lowering high rates of subglacial erosion and production of headwall relief also result when elastic flexural uplift occurs in response to mass unloading small overdeepenings form at the base of the headwall in steady climate simulations when the glacier is small at the end of the model run while the final profiles are relatively insensitive to the erosion rule used quarrying is most effective near the head of the glacier whereas rates of abrasion reflect the instantaneous pattern of integrated ice discharge or ice flux in simulations in which cirques are formed the equilibrium line altitude is hundreds of meters above the cirque floor however the time averaged horizontal position of the equilibrium line corresponds well with the downvalley position of the cirques

holocene rockwall retreat in svalbard a triple rate evolution volumetric calculations of slope deposits direct measurements of rockwall retreat and chronological control based on lichenometry provide a wide range of rockwall retreat rates in svalbard 0 1580 mm ka 1 that appears consistent with previous evaluations from other arctic areas in northwest and central spitsbergen 79 n a triple rate rockwall retreat is suggested for the last two millennia very slow biogenic flaking 2 mm ka 1 moderate retreat due to frost shattering 100 ka 1 and rapid retreat associated with post glacial stress relaxation c 1000 mm ka 1 examination of the distribution of various processes indicates that the holocene retreat of most rockwalls has not exceeded one or two metres bedrock conditions appear to be the main control on retreat rates the massiveness of igneous and metamorphic outcrops widespread in arctic shield areas largely accounts for the slowness of rockwall retreat which on these lithologies is primarily due to chemical and biological processes more rapid rates are usually associated with stress relaxation following glacial surges or with local frost susceptibility of bedrock often where faulting has induced high joint density at such sites rockwall retreat rates are of the same order of magnitude as those reported from alpine areas 1000 3000 mm ka 1 where both bedrock weakening due to tectonic stresses and the greater height of steep rockwalls account for the more rapid rockwall retreat rate 1997 by john wiley sons ltd

geomorphic limits to climate induced increases in topographic relief recognition of the potential for strong dynamic coupling between atmospheric and tectonic processes has sparked intense cross disciplinary investigation and debate on the question of whether tectonics have driven long term climate change or vice versa it has been proposed that climate change might have driven the uplift of mountain summits through an isostatic response to valley incision because isostasy acts to compensate mean elevations the debate hinges on the question of whether climate change can significantly increase topographic relief or more precisely increase the volume of missing mass between summits and ridges here we show that in tectonically active mountain ranges geomorphic constraints allow only a relatively small increase in topographic relief in response to climate change thus although climate change may cause significant increases in denudation rates potentially establishing an important feedback between surficial and crustal processes neither fluvial nor glacial erosion is likely to induce significant isostatic peak uplift

stress gradient coupling in glacier flow ii longitudinal averaging of the flow response to small perturbations in ice thickness and surface slope as a result of the coupling effects of longitudinal stress gradients the perturbations u in glacier flow velocity that result from longitudinally varying perturbations in ice thickness h and surface slope are determined by a weighted longitudinal average of h h and where h and are influence coefficients that control the size of the contributions made by local h and to the flow increment in the longitudinal average the values of h and depend on effects of longitudinal stress and velocity gradients in the unperturbed datum state if the datum state is an inclined slab in simple shear flow the longitudinal averaging solution for the flow perturbation is essentially that obtained previously kamb and echelmeyer 1985 with equivalent values for the longitudinal coupling length l and with h n l and n where n is the flow law exponent calculation of the influence coefficients from flow data for blue glacier washington indicates that in practice differs little from n whereas h can differ considerably from n 1 the weighting function in the longitudinal averaging integral which is the green s function for the longitudinal coupling equation for flow perturbations can be approximated by an asymmetric exponential whose asymmetry depends on two asymmetry parameters and where is the longitudinal gradient of l dl dx the asymmetric exponential has different coupling lengths l and l for the influences from up stream and from down stream on a given point of observation if is in the range 1 5 2 2 as expected for flow perturbations in glaciers or ice sheets in which the ice flux is not a strongly varying function of the longitudinal coordinate x then when dl dx 0 the down stream coupling length l is longer than the up stream coupling length l and vice versa when dl dx 0 flow thickness and slope perturbation data for blue glacier obtained by comparing the glacier in 1957 58 and 1977 78 require longitudinal averaging for reasonable interpretation analyzed on the basis of the longitudinal coupling theory with 4l 1 6 km up stream decreasing toward the terminus the data indicate n to be about 2 5 if interpreted on the basis of a response factor 0 85 derived theoretically by echelmeyer unpublished for the flow response to thickness perturbations in a channel of finite width the data contain an apparent indication that the flow response to slope perturbations is distinctly smaller in relation to the response to thickness perturbations than is expected on a theoretical basis i e h n n 1 for a slab this probably indicates that the effective l is longer than can be tested directly with the available data set owing to its limited range in x

erosion rate of a younger dryas cirque glacier at krakenes western norway an erosion rate of 0 5 to 0 6 mm a 1 is deduced for a younger dryas cirque glacier the erosion period of 700 a was determined from the laminated glaciolacustrine sediments in a small lake just outside the end moraine of the cirque and radiocarbon dates obtained below and above these sediments the volume of eroded bedrock was calculated from measurements of the deposited sediments of which the end moraine the glaciofluvial delta and the glaciolacustrine sediments are most important with a constant erosion rate the cirque could have formed in 83 to 125 000 a

features of glacial valley profiles simply explained 1 glacial occupation of alpine valleys results in a distinct signature in the long valley profile including steepening of the profile in the headwaters flattening at lower elevations and a step in the profile at the convergence of headwater tributaries we present analytic results for glacial erosion patterns by making the following assumptions 1 the initial profile is linear 2 the width of the valley is uniform 3 the annual mass balance varies linearly with elevation 4 the glacier at any time is quasi steady 5 the erosion rate is proportional to ice discharge per unit valley width and 6 glacial erosion rates far exceed fluvial erosion rates a steady glacier under these conditions would erode a parabolic divot in the longitudinal valley profile with its maximum depth coinciding with the down valley position of the equilibrium line altitude ela the calculated flattening of the valley floor down valley of the ela and the steepening of it up valley captures the essence of the glacial signature when a reasonable probability distribution of elas is allowed the predicted erosion peaks at 30 40 of the down valley distance to the glacial limit and the pattern merges smoothly with the steeper fluvial profile downstream of the glacial limit profiles of mass balance that are capped at a maximum value produce shorter glaciers and a slight asymmetry in the expected erosion pattern only when we mimic the tributaries of glacial headwaters by specifying a valley width distribution do we obtain the upper step observed in many valley profiles

pb isotopes a multi function tool for assessing tectonothermal events and crust mantle recycling at late archaean convergent margins abstract lead isotopes are a powerful tool in studying archaean granitoids and continental growth because 207pb is a sensitive indicator of involvement of lead from old archaean crustal sources this paper aims to demonstrate the significance and promote the use of lead isotopes by reviewing the theory concepts and traditions for interpretations of pb isotope data as well as by introducing a global model based on crust mantle recycling for discriminating late archaean convergent margin settings of granitoids case plots of k feldspar and whole rock data of ca 2 7 ga granitoids from several archaean cratons show that lead isotope systematics when interpreted in the correct geological context can be used for resolving many questions on crustal evolution from magmatic and tectonothermal history of individual intrusions to large scale tectonics and supercontinent correlations

a numerical model of landform development by glacial erosion the jagged peaks knife edged ridges and steep sided valleys of alpine landscapes are well known products of glaciation yet little is known about how the dynamics of ice flow and glacial erosion give rise to such landforms by linking a finite element model for ice flow through a valley with a model for glacial erosion we have simulated the gradual evolution of one of the most striking of glacial landforms the u shaped valley incorporating realistic glacier sliding laws and spatial variations in rock resistance our simulations illustrate how ice flow erosion patterns and topography interact in the long term evolution of glacial landforms in addition our results indicate for the first time that the formation of a steady state u shaped valley takes approximately 105 years

the response of two icelandic glaciers to climatic warming computed with a degree day glacier mass balance model coupled to a dynamic glacier model a degree day glacier mass balance model is coupled to a dynamic glacier model for temperate glaciers the model is calibrated for two outlet glaciers from the hofsjokull ice cap in central iceland it is forced with a climate scenario that has recently been defined for the nordic countries for the purpose of outlining the hydrological consequences of future greenhouse warming the scenario for iceland specifies a warming rate of 0 25 c per decade in mid summer and 0 35 c per decade in mid winter with a sinusoidal variation through the year the volume of the glaciers is predicted to decrease by approximately 40 over the next century and the glaciers essentially disappear during the next 200 years runoff from the area that is presently covered by the glaciers is predicted to increase by approximately 0 5 m a 1 30 years from now due to the reduction in the volume of the glaciers the runoff increase reaches a flat maximum of 0 5 2 0 m a 1 100 150 years from now and levels off after that the predicted runoff increase leads to a significant increase in the discharge of rivers fed by meltwater from the outlet glaciers of the ice cap and may have important consequences for the operation and planning of hydroelectric power plants in iceland

pleistocene relief production in laramide mountain ranges western united states gently sloped summits and ridges collectively referred to as summit flats are abundant in many laramide ranges in the western united states the erosion rate of summit flats is 10 m m y on the basis of the concentrations of cosmogenic radionuclides because erosion rates in valleys between summit flats are an order of magnitude faster relief within these ranges is currently increasing by about 100 m m y if summit flat erosion is slower than rock uplift driven by the isostatic response to valley erosion then this relief production could result in increased summit elevations the mean depth of material eroded from a smooth surface fit to existing summit flats varies from 280 to 340 m in four laramide ranges based on geographic information system gis analyses of digital elevation models this erosion would result in a maximum of 250 300 m of rock uplift assuming airy isostasy however because the laramide ranges examined here are narrow relative to the flexural wavelength of the lithosphere erosionally driven rock uplift is limited to 50 100 m over the past several million years summit erosion would approximately offset this rock uplift therefore we conclude that summit elevations have remained essentially constant even though several hundred meters of relief has been produced on the basis of valley and summit erosion rates and the average depth of erosion we estimate that relief production in laramide ranges began at ca 3 ma we hypothesize that this relief production was climatically driven and was associated with the onset or enhancement of alpine glaciation in these ranges

short term velocity variations and basal coupling near a bergschrund storglaciaren sweden distance measurements using an automated electronic distance measurement system in the north cirque of storglaciaren sweden during the summer of 1989 revealed a diurnal variation in glacier speed amplitude and timing of the diurnal cycle correlate well with the timing and intensity of the diurnal temperature cycle indicating that speed responds to variations in daily melt with a lag of approximately 4 h one 2 d period of non diurnal velocity variations corresponded with a large rainfall event finite element modeling suggests that these velocity variations must be closely related to water inputs in the cirque rather than to longitudinal coupling with lower parts of the glacier

time scale for adjustment of glaciers to changes in mass balance the length of time tm over which a glacier responds to a prior change in climate is investigated with reference to the linearized theory of kinematic waves and to results from numerical models we show the following tm may in general be estimated by a volume time scale describing the time required for a step change in mass balance to supply the volume difference between the initial and final steady states the factor f in the classical estimate of m l u where i is glacier length and u is terminus velocity has a simple geometrical interpretation ft is the ratio of thickness change averaged over the full length i to the change at the terminus although both u and f relate to dynamic processes local to the terminus zone the ratio f u and therefore tm are insensitive to details of the terminus dynamics in contrast to conclusions derived from some simplified kinematic wave models a more robust estimate of tm independent of terminus dynamics is given by tm h b where h is a thickness scale for the glacier and b is the mass balance rate negative at the terminus we suggest that tm for mountain glaciers can be substantially less than the 1o2 103 years commonly considered to be theoretically expected

combined measurements of subglacial water pressure and surface velocity of findelengletscher switzerland conclusions about drainage system and sliding mechanism interpretation des mesures de pression dans les forages et des vitesses superficielles la comparaison avec les modeles suggere que l on a neglige le frottement du aux debris dans les modeles et qu il n existe jamais de chenaux cylindriques rectilignes