or manmade cavities in the marginal parts of glaciers (Boulton, 1974; Theakstone, 1979; Anderson et al., 1982), a situation which may not be representative of large areas of the glacier bed. Photographic observations made in boreholes drilled to the glacier bed (Engelhardt et al., 1978) are difficult to extrapolate to wider areas of the interface and may be unrepresentative because basal conditions may be changed by the existence of the borehole. The same may be said of observations made in artificial cavities excavated under the central parts of glaciers (Wold and 0strem, 1979; Vivian, 1980; Hagen, et al., 1983). Important developments in our understanding of subglacial processes have, therefore, come from inference of process from form (Gilbert, 1906; Hallet, 1979a; Walder and Hallet, 1979; Hallet and Anderson, 1981) and from theoretical investigations (Boulton, 1974, 1975; 1979; Hallet, 1979b; 1981), but since it has rarely been possible to test theory against field observation, even the

[1] We use ground-based and satellite observations to detect large diurnal and longer-period variations in the flow of the Greenland Ice Sheet (GrIS) during late summer that are strongly coupled with changes in its surface hydrology. The diurnal signals are associated with periodic changes in surface melting, and the longer-period signals are associated with the episodic drainage of supra-glacial lakes. Ice velocity doubles around 2 hours after peak daily melting and returns approximately to wintertime levels around 12 hours afterwards, demonstrating an intimate link between the surface and basal hydrology. During late summer, the ice sheet accelerates by 35% per positive degree-day of melting. The observed link between surface melting and enhanced flow is typical of Alpine glaciers, which may provide an appropriate analogue for the evolution of the GrIS in a warming climate.

[1] We report the spatial and temporal pattern of sliding on the 7-km-long Bench Glacier, Alaska. Using five continuously recording GPS antennas following motion of the surface ice, distributed at 1 km spacing along the glacier center line, we documented surface ice motion over 50 days during summer 2002. Surface speeds in two previous winters constrain the motion component associated with ice deformation, allowing isolation of the sliding speed history. We observed two speedup events bracketing 2 weeks of steady slow sliding. The first event was not associated with a meteorological trigger, was more subtle than the second, and propagated up-glacier at a rate of several hundred meters per day. The second event coincided with a warm up-valley wind, which triggered considerable melt of the glacier surface. Sliding speeds in this event reached 0.3 m d−1 and began almost simultaneously at all sites in the ablation area. Both the horizontal and vertical displacement time series can be explained by growth and collapse of cavities in the lee of bumps in the bedrock bed. Cavities grow during rapid sliding and decay by viscous creep. We posit that effective pressure, averaged over some large area of the bed, is inversely proportional to the sliding speed. This effective pressure then controls the collapse rate of cavities, whose dimensions are estimated from a plausible, stepped-bed geometry. This model explains well the horizontal and vertical surface displacement history through the first event and beginning of the second event. The vertical record demands a substantial and abrupt drop in water pressure that departs from the posited sliding-effective pressure relationship. We argue that this pressure drop reflects establishment of efficient subglacial drainage, also manifested in a nearly simultaneous step increase in water discharge in the exit stream. The establishment of an efficient conduit system terminates sliding; its maintenance inhibits further sliding over the remainder of the summer.

[1] The influence of hydrologic transience and heterogeneity on basal motion is an often-neglected aspect of numerical ice-flow models. We present a flow-band model of glacier dynamics with a Coulomb friction sliding law that is coupled to a model of the basal drainage system by means of subglacial water pressure. The ice-flow model contains “higher-order” stress gradients from the Stokes flow approximation originally conceived by Blatter (1995). The resulting system of nonlinear equations is solved using a modified Picard iteration that is shown to improve the rate of convergence. A parameterization of lateral shearing is included to account for the effects of three-dimensional geometry. We find that lateral drag has a discernible effect on glacier speed even when glacier width exceeds glacier length. Variations in flow-band width are shown to have a greater influence on flow line speed than either different valley cross-sectional shapes or the presence or absence of glacier sliding along valley walls. Modeled profiles of subglacial water pressure depart significantly from pressures prescribed as a uniform fraction of overburden, thus producing profiles of glacier sliding that are distinctly different from those that would be described by a sliding law controlled by overburden pressures. Simulations of hydraulically driven glacier acceleration highlight the value of including a representation of basal hydrology in models aiming for improved predictive capability of glacier dynamics.

[1] The impact of increasing summer melt on the dynamics and stability of the Greenland Ice Sheet is not fully understood. Mounting evidence suggests seasonal evolution of subglacial drainage mitigates or counteracts the ability of surface runoff to increase basal sliding. Here, we compare subdaily ice velocity and uplift derived from nine Global Positioning System stations in the upper ablation zone in west Greenland to surface melt and supraglacial lake drainage during summer 2007. Starting around day 173, we observe speedups of 6–41% above spring velocity lasting ∼40 days accompanied by sustained surface uplift at most stations, followed by a late summer slowdown. After initial speedup, we see a spatially uniform velocity response across the ablation zone and strong diurnal velocity variations during periods of melting. Most lake drainages were undetectable in the velocity record, and those that were detected only perturbed velocities for ∼1 day, suggesting preexisting drainage systems could efficiently drain large volumes of water. The dynamic response to melt forcing appears to (1) be driven by changes in subglacial storage of water that is delivered in diurnal and episodic pulses, and (2) decrease over the course of the summer, presumably as the subglacial drainage system evolves to greater efficiency. The relationship between hydrology and ice dynamics observed is similar to that observed on mountain glaciers, suggesting that seasonally large water pressures under the ice sheet largely compensate for the greater ice thickness considered here. Thus, increases in summer melting may not guarantee faster seasonal ice flow.

[1] In this paper we present a numerical simulation of the observation that most alpine glaciers have reached peak velocities in the early 1980s followed by nearly exponential decay of velocity in the subsequent decade. We propose that similarity exists between precipitation and associated runoff hydrograph in a river basin on one side and annual mean specific mass balance of the accumulation area of alpine glaciers and ensuing changes in ice flow on the other side. The similarity is expressed in terms of a linear reservoir with fluctuating input where the year to year change of ice velocity is governed by two terms, a fraction of the velocity of the previous year as a recession term and the mean specific balance of the accumulation area of the current year as a driving term. The coefficients of these terms directly relate to the timescale, the mass balance/altitude profile, and the geometric scale of the glacier. The model is well supported by observations in the upper part of the glacier where surface elevation stays constant to within ±5 m over a 30 year period. There is no temporal trend in the agreement between observed and modeled horizontal velocities and no difference between phases of acceleration and phases of deceleration, which means that the model is generally valid for a given altitude on a given glacier.

[1] Glaciohydraulic supercooling is a mechanism for accreting ice and sediment to the base of glaciers. We extend existing models by reworking the Spring-Hutter model for subglacial water flow in tubular conduits to allow for distributed water sheets. Our goal is to determine diagnostic features of supercooling relative to controlling variables. Results focus on along-path water flow under time-varying conditions, with attention to ice accretion in and along subglacial overdeepenings. We contrast simulations with constant recharge to diurnally-varying recharge and expose behavior that cannot be inferred from simple models. For example, locations of simulated ice accretion differ from those found for steady state models, even though total ice accretion remains comparable to field estimates. Downstream accretion influences upstream effective pressures that then modify the hydraulic gradient that drives water flow. This modified gradient tends to inhibit additional accretion by increasing velocity and heat production via viscous dissipation. During diurnal cycles, accretion varies considerably: in daytime, viscous dissipation dominates the heat balance and ice melts. In morning and evening, when flow is rising or falling, viscous dissipation is lower and accretion can proceed. Over nighttime, the largest temperature depressions occur in the subglacial system, but water flux is lowest and accretion rates are negligible. We conclude by inferring that overdeepened glaciers with only clear water flows evolve toward stronger supercooling regimes rather than toward a dynamic equilibrium. Stabilizing feedbacks are unlikely to occur through glacier hydrology alone, and other processes, such as erosion, sedimentation, and sliding, must play an important role.

[1] Current heuristic laws that relate the motion of glaciers due to sliding along the bed to the subglacial water pressure fail to reproduce variations in sliding speed on timescales of specific hydrologic events, such as lake drainage, rainfall, or surging. This may be due to the importance of subglacial cavity evolution and shifts in the glacier stress field, both of which are not accounted for in typical sliding laws. We use multiple time series of surface motion over a 66-day period at Breiðamerkurjokull, Iceland, to infer changes in bed separation and longitudinal force budget. We observe multiple, distinct periods of increased surface motion and uplift corresponding to periods of rainfall and/or increased temperatures. We find consistent hysteresis and lags between motion and variations in both the bed separation and longitudinal stress gradient that we attribute to the redistribution of normal stresses at the bed during cavity growth. Increases in the longitudinal stress gradient suggest a downglacier stress transfer during increased basal motion that is consistent with increased drainage system efficiency toward the terminus. Our results suggest that the transient evolution of the subglacial drainage system and shifts in the glacier stress field are important controls on basal motion.

[1] Glaciers draining westward from the Sierra Nevada divide, California, during the Last Glacial Maximum (LGM) were � 7 times longer than east-draining glaciers. We address the degree to which this difference may be attributed to the topographic asymmetry of the west-tilted Sierran block and the climate asymmetry resulting from orographic modification of Pacific Ocean storms. We simulate kilometer-scale glaciers within the 50 � 50 km Kings Canyon region of the southern Sierra by employing a two-dimensional numerical model that is driven by simple, spatially variable climates and treats ice transport by deformation, sliding, and avalanching. In numerical experiments, we match simulated termini to LGM moraine positions to constrain the parameters of different climate scenarios. The 38-km-long LGM glacier in Kings Canyon was reproduced by a climate specified by an equilibrium line altitude (ELA) of 3170 m, a mass balance gradient of 0.01 m/yr/m, and a maximum positive balance of 2 m/yr. This climate generates much shorter (average � 6 km long) east-draining glaciers that, however, overshoot the LGM moraines by � 1 km. Roughly 97% of the E-W difference in glacier lengths can therefore be attributed to topographic asymmetry alone. A second experiment suggesting a 120-m-higher ELA of 3290 m east of the divide can explain the shorter east-draining glaciers. An experiment in which orographic precipitation is explicitly simulated and melt is prescribed using a positive degree-day algorithm matches both Kings Canyon and the average east-draining glacier length with an LGM climate that was 5.6� C cooler and � 2 times wetter than the modern Sierra Nevada.

With the purpose of improving the ice physics underpinning time–dependent glacier flowline models, three independent approaches for solving longitudinal stresses in glaciers are discussed and verified by application to Haut Glacier d’Arolla. To highlight any shortcomings, the reduced and much utilised driving stress approximation is also applied and compared. Modelled velocity patterns using the three full stress schemes exhibit consistency with one another and good coincidence with observed velocities for the 1991 summer melt season. Furthermore, these stress patterns indicate that longitudinal stresses are significant and of a similar order of magnitude as the basal shear stress components. However, the driving stress approximation yields erratic fluctuations in the stress and velocity fields which are neither realistic in terms of mass continuity nor agree with observations. Basal decoupling experiments indicate a complex relationship between basal velocity and englacial stresses with considerable dampening of any basal perturbation occurring as it is dissipated towards the surface and transferred throughout the ice mass. The driving stress approximation fails to account at all for any such coupling. Experiments to identify the length scale over which longitudinal effects operate indicate that they are significant even up to 10 ice thicknesses. The implication here is that longitudinal stresses play a significant role in determining glacier dynamics on length scales up to at least 2 km and that the predictive power of models of glacier flow based purely on the driving stress approximation is therefore subject to significant limitations. Inclusion of longitudinal stresses overcomes one of the main limitations imposed on such models and, given the potential ease of incorporation of the schemes described here, this deficiency may readily be resolved.

Why study glaciers? some basic concepts mass balance flow of a crystalline material the velocity field in a glacier temperature distribution in polar ice sheets the coupling between a glacier and its bed water flow in and under glaciers - geomorphic implications stress and deformation stress and velocity distribution in an idealized glacier applications of stress and deformation principles to classical problems response of glaciers to changes in mass balance problems.

We used synthetic aperture radar offset tracking to reconstruct a unique record of ice surface velocities for a 3.2 year period (15 January 2017–6 April 2020), for the Palcaraju glacier located above Laguna Palcacocha, Cordillera Blanca, Peru. Correlation and spatial cluster analysis of residuals of linear fits through cumulative velocity time series, revealed that velocity variations were controlled by the intra-annual outer tropical seasonality and inter-annual variation in Sea Surface Temperature Anomalies (SSTA), related to the El Niño Southern Oscillation (ENSO). The seasonal signal was dominant, where it was sensitive to altitude, aspect, and slope. The measured velocity variations are related to the spatial and temporal variability of the glacier’s surface energy and mass balance, meltwater production, and subglacial water pressures. Evaluation of potential ice avalanche initiation areas, using deviations from linear long-term velocity trends, which were not related to intra- or inter-annual velocities, showed no evidence of imminent avalanching ice instabilities for the observation period.

We reconstruct englacial and subglacial drainage at Skalafellsjokull, Iceland, using ground penetrating radar (GPR) common offset surveys, borehole studies and Glacsweb probe data. We find that englacial water is not stored within the glacier (water content ~0-0.3%). Instead, the glacier is mostly impermeable and meltwater is able to pass quickly through the main body of the glacier via crevasses and moulins. Once at the glacier bed, water is stored within a thin (1 m) layer of debris-rich basal ice (2% water content) and the till. The hydraulic potential mapped across the survey area indicates that when water pressures are high (most of the year), water flows parallel to the margin, and emerges 3 km down glacier at an outlet tongue. GPR data indicates that these flow pathways may have formed a series of braided channels. We show that this glacier has a very low water-storage capacity, but an efficient englacial drainage network for transferring water to the glacier bed and, therefore, it has the potential to respond rapidly to changes in melt-water inputs.

We provide a high-resolution map of elevation change rates dh dt at the Juneau Icefield (JIF), southeastern Alaska, in order to quantify its contribution to sea-level rise between 2000 and 2009/2013. We also produce the first high-resolution map of ice speeds at the JIF, which we use to constrain flux and look for acceleration. We calculate dh dt using stacked digital elevation models (DEMs) from the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) instrument and the Shuttle Radar Topography Mission (SRTM), taking into account SRTM C-band penetration via comparison with SRTM X-band elevations. Overall, the JIF is losing mass less rapidly (0.13 0.12mw.e. a) than other Alaskan icefields (0.79mw.e. a). We determine glacier speeds using pixel-tracking on optical image pairs acquired from 2001 to 2010 by ASTER, from radar image pairs acquired between 2007 and 2011 and from radar interferometry in 1995. We detect seasonal speed variations but no interannual acceleration, ruling out dynamics as the cause of the observed thinning. Thinning must therefore be due to the documented warming in the region. Flux measurements confirm this for Mendenhall Glacier, showing that calving constitutes only 2.5–5% of mass loss there.

We present subdaily ice flow measurements at four GPS sites between 36 and 72 km from the margin of a marine‐terminating Greenland outlet glacier spanning the 2009 melt season. Our data show that >35 km from the margin, seasonal and shorter–time scale ice flow variations are controlled by surface melt–induced changes in subglacial hydrology. Following the onset of melting at each site, ice motion increased above background for up to 2 months with resultant up‐glacier migration of both the onset and peak of acceleration. Later in our survey, ice flow at all sites decreased to below background. Multiple 1 to 15 day speedups increased ice motion by up to 40% above background. These events were typically accompanied by uplift and coincided with enhanced surface melt or lake drainage. Our results indicate that the subglacial drainage system evolved through the season with efficient drainage extending to at least 48 km inland during the melt season. While we can explain our observations with reference to evolution of the glacier drainage system, the net effect of the summer speed variations on annual motion is small (∼1%). This, in part, is because the speedups are compensated for by slowdowns beneath background associated with the establishment of an efficient subglacial drainage system. In addition, the speedups are less pronounced in comparison to land‐terminating systems. Our results reveal similarities between the inland ice flow response of Greenland marine‐ and land‐terminating outlet glaciers.

We present results of a detailed investigation of surface motion across the tongue of a polythermal glacier, midre Lovenbreen, Svalbard, during the 1999 summer. Surface velocities in the warm-based upper tongue increased during periods of enhanced surface melting and rainfall events, and force-balance analysis indicates that these velocity variations were locally forced, probably by fluctuations in subglacial water pressure. Surface speed-ups were also observed on the cold-based lower tongue (which acted as a sticky spot, through which there was minimal subglacial drainage for most of the summer), but these were largely non-locally forced by longitudinal coupling to the faster-moving ice up-glacier. On one occasion, however, a large, rapid input of surface water to the glacier reduced the basal drag beneath the cold-based lower tongue, presumably due to hydraulic jacking. This resulted in locally forced enhanced surface velocities across the entire tongue, accompanied by a breaching of the lower tongue and an outburst of subglacially stored water.

We infer the horizontal velocity fields of the ice caps Langjokull and Hofsjokull, central Iceland, using repeat-pass interferometric synthetic aperture radar (InSAR). NASA's uninhabited aerial vehicle synthetic aperture radar (UAVSAR) acquired airborne InSAR data from multiple vantage points during the early melt season in June 2012. We develop a Bayesian approach for inferring three- dimensional velocity fields from multiple InSAR acquisitions. The horizontal components generally agree with available GPS measurements wherever ice motion is well constrained by InSAR observations. We provide evidence that changes in volumetric moisture content near the glacier surface induce phase offsets that obfuscate the vertical component of the surface velocity fields, an effect that could manifest itself on any glacier that experiences surface melt. Spatial patterns in the InSAR-derived horizontal speeds are broadly consistent with the results of a simple viscous flow model, and the directionality of the InSAR-derived horizontal flow field is nearly everywhere consistent with the ice surface gradient. Significant differences between the InSAR-derived horizontal speed and the speed predicted by the viscous flow model suggest that basal slip accounts for more than half the observed outlet glacier flow.

We describe the development of mathematical models of ice sheets, focusing on underlying physics and the minimal components that successful models must contain. Our review describes the basic fluid dynamical ice-flow models currently in use; points out numerous poorly understood thermomechanical feedbacks in ice flow; and describes the current, often poorly constrained, state of models for ice-sheet sliding and subglacial drainage, as well as their role in ice-stream dynamics. We conclude with a survey of marine ice-sheet models, outlining recent developments of self-consistent free-boundary models and ongoing research into three-dimensional marine ice sheets.

Viscous contact problems describe the time evolution of fluid flows in contact with a surface fromwhich they can detach. These problems are of particular importance in glaciology,where they arise in the study of grounding lines and subglacial cavities. In this work, we propose a novel numerical method for solving viscous contact problems based on a mixed formulation with Lagrange multipliers of a variational inequality involving the Stokes equation. The advection equation for evolving the geometry of the domain occupied by the fluid is then solved via a specially-built upwinding scheme, leading to a robust and accurate algorithm for viscous contact problems. We then use this numerical scheme to reconstruct friction laws for glacial sliding with cavitation. We also study the effects of unsteady water pressures on sliding with cavitation.

Understanding water movement through a glacier is fundamental to several critical issues in glaciology, including glacier dynamics, glacier‐induced floods, and the prediction of runoff from glacierized drainage basins. To this end we have synthesized a conceptual model of water movement through a temperate glacier from the surface to the outlet stream. Processes that regulate the rate and distribution of water input at the glacier surface and that regulate water movement from the surface to the bed play important but commonly neglected roles in glacier hydrology. Where a glacier is covered by a layer of porous, permeable firn (the accumulation zone), the flux of water to the glacier interior varies slowly because the firn temporarily stores water and thereby smooths out variations in the supply rate. In the firn‐free ablation zone, in contrast, the flux of water into the glacier depends directly on the rate of surface melt or rainfall and therefore varies greatly in time. Water moves from the surface to the bed through an upward branching arborescent network consisting of both steeply inclined conduits, formed by the enlargement of intergranular veins, and gently inclined conduits, spawned by water flow along the bottoms of near‐surface fractures (crevasses). Englacial drainage conduits deliver water to the glacier bed at a limited number of points, probably a long distance downglacier of where water enters the glacier. Englacial conduits supplied from the accumulation zone are quasi steady state features that convey the slowly varying water flux delivered via the firn. Their size adjusts so that they are usually full of water and flow is pressurized. In contrast, water flow in englacial conduits supplied from the ablation area is pressurized only near times of peak daily flow or during rainstorms; flow is otherwise in an open‐channel configuration. The subglacial drainage system typically consists of several elements that are distinct both morphologically and hydrologically. An upglacier branching, arborescent network of channels incised into the basal ice conveys water rapidly. Much of the water flux to the bed probably enters directly into the arborescent channel network, which covers only a small fraction of the glacier bed. More extensive spatially is a nonarborescent network, which commonly includes cavities (gaps between the glacier sole and bed), channels incised into the bed, and a layer of permeable sediment. The nonarborescent network conveys water slowly and is usually poorly connected to the arborescent system. The arborescent channel network largely collapses during winter but reforms in the spring as the first flush of meltwater to the bed destabilizes the cavities within the nonarborescent network. The volume of water stored by a glacier varies diurnally and seasonally. Small, temperate alpine glaciers seem to attain a maximum seasonal water storage of ∼200 mm of water averaged over the area of the glacier bed, with daily fluctuations of as much as 20–30 mm. The likely storage capacity of subglacial cavities is insufficient to account for estimated stored water volumes, so most water storage may actually occur englacially. Stored water may also be released abruptly and catastrophically in the form of outburst floods.