Climate variables that control the annual cycle of the surface energy and mass balance on Zhadang glacier in the central Tibetan Plateau were examined over a 2 year period using a physically based energy-balance model forced by routine meteorological data. The modelled results agree with measured values of albedo, incoming longwave radiation, surface temperature and surface level of the glacier. For the whole observation period, the radiation component dominated (82%) the total surface energy heat fluxes. This was followed by turbulent sensible (10%) and latent heat (6%) fluxes. Subsurface heat flux represented a very minor proportion (2%) of the total heat flux. The sensitivity of specific mass balance was examined by perturbations of temperature (±1 K), relative humidity (±20%) and precipitation (±20%). The results indicate that the specific mass balance is more sensitive to changes in precipitation than to other variables. The main seasonal variations in the energy balance were in the two radiation components (net shortwave radiation and net longwave radiation) and these controlled whether surface melting occurred. A dramatic difference in summer mass balance between 2010 and 2011 indicates that the glacier surface mass balance was closely related to precipitation seasonality and form (proportion of snowfall and rainfall).

Recent snow accumulation rate is a key quantity for ice-core and mass-balance studies. Several accumulation measurement methods (stake farm, fin core, snow-radar profiling, surface morphology, remote sensing) were used, compared and integrated at eight sites along a transect from Terra Nova Bay to Dome C, East Antarctica, to provide information about the spatial and temporal variability of snow accumulation. Thirty-nine cores were dated by identifying tritium/b marker levels (1965_66) and non-sea-salt (nss) SO42_ spikes of the Tambora (Indonesia) volcanic event (1816) in order to provide information on temporal variability. Cores were linked by snow radar and global positioning system surveys to provide detailed information on spatial variability in snow accumulation. Stake-farm and ice-core accumulation rates are observed to differ significantly, but isochrones (snow radar) correlate well with ice-core derived accumulation. The accumulation/ablation pattern from stake measurements suggests that the annual local noise (metre scale) in snow accumulation can approach 2 years of ablation and more than four times the average annual accumulation, with no accumulation or ablation for a 5 year period in up to 40% of cases. The spatial variability of snow accumulation at the kilometre scale is one order of magnitude higher than temporal variability at the multi-decadal/secular scale. Stake measurements and firn cores at Dome C confirm an approximate 30% increase in accumulation over the last two centuries, with respect to the average over the last 5000 years

We have obtained common offset, common midpoint (CMP) and borehole vertical (VRP) ground-penetrating radar profiles close to the margin of Falljökull, a small, steep temperate valley glacier situated in southeast Iceland. Velocity analysis of CMP and VRP surveys provided a four-layered velocity model. This model was verified by comparison between the depths of englacial reflectors and water channels seen in borehole video, and from the depths of boreholes drilled to the bed. In the absence of sediment within the glacier ice, radar velocity is inversely proportional to water content. Using mixture models developed by Paren and Looyenga, the variation of water content with depth was determined from the radar velocity profile. At the glacier surface the calculated water content is 0.23–0.34% (velocity 0.166 m ns−1), which rises sharply to 3.0–4.1% (velocity 0.149 m ns−1) at 28 m depth, interpreted to be the level of the piezometric surface. Below the piezometric surface the water content drops slowly to 2.4–3.3% (velocity 0.152 m ns−1) until ∼102 m depth where it falls to 0.09–0.14% (velocity 0.167 m ns−1). The water content of the ice then remains low to the glacier bed at about 112 m. These results suggest storage of a substantial volume of water within the glacier ice, which has significant implications for glacier hydrology, ice rheology and interpretations of both radar and seismic surveys.

Discriminating between glacier variations due to natural climate variability and those due to true climate change is crucial for the interpretation and attribution of past glacier changes, and for the expectations of future changes. We explore this issue for the well-documented glaciers of Mount Baker in the Cascades Mountains of Washington State, USA, using glacier histories, glacier modeling, weather data and numerical weather model output. We find that natural variability alone is capable of producing kilometer-scale excursions in glacier length on multi-decadal and centennial timescales. Such changes are similar in magnitude to those attributed to a global Little Ice Age. The null hypothesis, that no climate change is required to explain the glacier fluctuations in this setting, cannot be rejected. These results for Mount Baker glaciers are also consistent with an earlier study analyzing individual glaciers in Scandinavia and the Alps. The principle that long-timescale fluctuations of glacier length can be driven by short-timescale fluctuations in climate reflects a robust and fundamental property of stochastically forced physical systems with memory. It is very likely that this principle also applies to other Alpine glaciers and that it therefore complicates interpretations of the relationship between glacier and climate history. However, the amplitude and timescale of the length fluctuations depends on the details of the particular glacier geometry and climatic setting, and this remains largely unevaluated for most glaciers.

Gornersee, Switzerland, is an ice-marginal lake, which drains almost every year, subglacially, within a few days. We present an analysis of the lake outburst events between 1950 and 2005, as well as results of detailed field investigations related to the lake drainage in 2004 and 2005. The latter include measurements of lake geometry, water pressure in nearby boreholes and glacier surface motion. A distributed temperature-index melt model coupled to a linear-reservoir runoff model is used to calculate hourly discharge from the catchment of Gornergletscher in order to distinguish between the melt/precipitation component and the outburst component of the discharge hydrograph. In this way, drainage volume and timing are determined. From 1950 there is a clear trend for the outburst flood to occur earlier in the melt season, but there is no trend in lake discharge volumes. Peak discharges from the lake lie significantly below the values obtained using the empirical relation proposed by Clague and Mathews (1973). The shapes of the 2004 and 2005 lake outflow hydrographs differ substantially, suggesting different drainage mechanisms. From water balance considerations we infer a leakage of the glacier-dammed lake in 2005, starting 1 week prior to the lake outburst. During the drainage events, up to half of the lake water is temporarily stored in the glacial system, causing substantial uplift of the glacier surface.

Marine ice sheets with mechanics described by the shallow-ice approximation by definition do not couple mechanically with the shelf. Such ice sheets are known to have neutral equilibria. We consider the implications of this for their dynamics and in particular for mechanisms which promote marine ice-sheet retreat. The removal of ice-shelf buttressing leading to enhanced flow in grounded ice is discounted as a significant influence on mechanical grounds. Sea-level rise leading to reduced effective pressures under ice streams is shown to be a feasible mechanism for producing postglacial West Antarctic ice-sheet retreat but is inconsistent with borehole evidence. Warming thins the ice sheet by reducing the average viscosity but does not lead to grounding-line retreat. Internal oscillations either specified or generated via a MacAyeal–Payne thermal mechanism promote migration. This is a noise-induced drift phenomenon stemming from the neutral equilibrium property of marine ice sheets. This migration occurs at quite slow rates, but these are sufficiently large to have possibly played a role in the dynamics of the West Antarctic ice sheet after the glacial maximum. Numerical experiments suggest that it is generally true that while significant changes in thickness can be caused by spatially uniform changes, spatial variability coupled with dynamical variability is needed to cause margin movement.

Wind tunnel measurements of snowdrift in a turbulent, logarithmic velocity boundary layer have been made in Davos, Switzerland, using natural snow. Regression analysis gives the drift threshold friction velocity (u*t), assuming an exponential drift profile and a simple drift to friction velocity relationship. Measurements over 15 snow covers show that u*t is influenced more by snow density and particle size than by ambient temperature and humidity, and varies from 0.27 to 0.69 ms–1. Schmidt’s threshold algorithm and a modified version used in SNOWPACK (a snow-cover model) agree well with observations if small bond sizes are assumed. Using particle hydraulic diameters, obtained from image processing, Bagnold’s threshold parameter is 0.18. Roughness lengths (z0) vary between snow covers but are constant until the start of drift. Threshold roughness lengths are proportional to . The influence of macroscopic objects on the roughness length is shown by the lower values measured over the smooth and flat snow surface of the wind tunnel (0.04 ≤ z0 ≤ 0.13 mm), compared to field measurements. Mean drifting-snow grain sizes for mainly new and partly decomposed snow are 100–175 μm, and independent of surface particle size.

Physically based projections of the Greenland ice sheet contribution to future sea-level change are subject to uncertainties of the atmospheric and oceanic climatic forcing and to the formulations within the ice flow model itself. Here a higher-order, three-dimensional thermomechanical ice flow model is used, initialized to the present-day geometry. The forcing comes from a high-resolution regional climate model and from a flowline model applied to four individual marine-terminated glaciers, and results are subsequently extended to the entire ice sheet. The experiments span the next 200 years and consider climate scenario SRES A1B. The surface mass-balance (SMB) scheme is taken either from a regional climate model or from a positive-degree-day (PDD) model using temperature and precipitation anomalies from the underlying climate models. Our model results show that outlet glacier dynamics only account for 6–18% of the sea-level contribution after 200 years, confirming earlier findings that stress the dominant effect of SMB changes. Furthermore, interaction between SMB and ice discharge limits the importance of outlet glacier dynamics with increasing atmospheric forcing. Forcing from the regional climate model produces a 14–31 % higher sea-level contribution compared to a PDD model run with the same parameters as for IPCC AR4.

Rapid thinning and velocity increase on major Greenland outlet glaciers during the last two decades may indicate that these glaciers became unstable as a consequence of the Jakobshavn effect (Hughes, 1986), with terminus retreat leading to increased discharge from the interior and consequent further thinning and retreat. To assess whether recent trends deviate from longer-term behavior, we measured glacier surface elevations and terminus positions for Jakobshavn Isbræ, West Greenland, using historical photographs acquired in 1944, 1953, 1959, 1964 and 1985. These results were combined with data from historical records, aerial photographs, ground surveys, airborne laser altimetry and field mapping of lateral moraines and trimlines, to reconstruct the history of changes since the Little Ice Age (LIA). We identified three periods of rapid thinning since the LIA: 1902–13, 1930–59 and 1999–present. During the first half of the 20th century, the calving front appears to have been grounded and it started to float during the late 1940s. The south and north tributaries exhibit different behavior. For example, the north tributary was thinning between 1959 and 1985 during a period when the calving front was stationary and the south tributary was in balance. The record of intermittent thinning, combined with changes in ice-marginal extent and position of the calving front, together with changes in velocity, imply that the behavior of the lower parts of this glacier represents a complex ice-dynamical response to local climate forcings and interactions with drainage from the interior.

Several authors relate accumulation (or precipitation) at the glacier equilibrium-line altitude (ELA) to summer mean temperature using exponential or power-law functions. I analyze the accumulation–temperature relation at the ELA with a degree-day model using data from the 1992 paper by A. Ohmura and others. The dataset includes estimates at the ELA of winter balance and of ‘winter balance plus summer precipitation’ which represent respectively low and high estimates of annual accumulation, which is seldom measured. The Ohmura dataset only lists summer mean temperature, but I recover monthly temperatures for the whole year for 66 of the glaciers by assuming sinusoidal temperature variation through the year and using annual temperature range from a gridded climatology. Monthly degree-day sums are then estimated from monthly mean temperature and summed to give annual totals so degree-day factors for melting snow at the ELA are obtained. The degree-day factors fall close to those reported in the literature for glacier snowmelt, with averages of 3.5 ± 1.4 and 4.6 ± 1.4 mm d−1 K−1 for low- and high-accumulation estimates on the 66 glaciers. The degree-day model gives a family of accumulation–temperature curves that depend upon the annual temperature range, representing the contrast between maritime and continental climates.

Permafrost existed around and under marginal parts of the southern Laurentide ice sheet during the Last Glacial Maximum. The presence of permafrost was important in determining the extent, form and dynamics of ice lobes and the landforms they produced because of influences on resistance to basal motion and subglacial hydrology. We develop a two-dimensional time-dependent model of permafrost and glacier-ice dynamics along a flowline to examine: (i) the extent to which permafrost survives under an advancing ice lobe and how it influences landform development and hydrology, and (ii) the influence of permafrost on ice motion and surface profile. The model is applied to the Green Bay lobe, which terminated near Madison, Wisconsin, during the Last Glacial Maximum. Simulations of ice advance over permafrost indicate that the bed upstream of the ice-sheet margin was frozen for 60–200 km at the glacial maximum. Permafrost remained for centuries to a few thousand years under advancing ice, and penetrated sufficiently deep (tens of meters) into the underlying aquifer that drainage of basal meltwater became inefficient, likely resulting in water storage beneath the glacier. Our results highlight the influence of permafrost on subglacial conditions, even though uncertainties in boundary conditions such as climate exist.

Information about glacier volume and ice thickness distribution is essential for many glaciological applications, but direct measurements of ice thickness can be difficult and costly. We present a new method that calculates ice thickness via an estimate of ice flux. We solve the familiar continuity equation between adjacent flowlines, which decreases the computational time required compared to a solution on the whole grid. We test the method on Columbia Glacier, a large tidewater glacier in Alaska, USA, and compare calculated and measured ice thicknesses, with favorable results. This shows the potential of this method for estimating ice thickness distribution of glaciers for which only surface data are available. We find that both the mean thickness and volume of Columbia Glacier were approximately halved over the period 1957–2007, from 281 m to 143 m, and from 294 km3 to 134 km3, respectively. Using bedrock slope and considering how waves of thickness change propagate through the glacier, we conduct a brief analysis of the instability of Columbia Glacier, which leads us to conclude that the rapid portion of the retreat may be nearing an end.

The recent dynamic behaviour of Karakoram glaciers is expected to differ from that shown by glaciers in the central and eastern Himalaya because of regional variations in precipitation and temperature trends. However, there are insufficient quantitative data to support or confute such hypotheses. We present velocity data covering the period 1993–2008 for Baltoro Glacier, one of the longest glaciers in the Karakoram. Velocity measurements were made using cross-correlation feature tracking applied to European Remote-sensing Satellite (ERS-1 and -2) and Envisat advanced synthetic aperture radar (ASAR) data, supplemented by differential global positioning system (DGPS) measurements. We find a gradual acceleration of the glacier during the early 2000s, in particular during winter months. Multi-seasonal data reveal a large difference between summer and winter flow characteristics, but only in the upper ablation zone. Summer 2005 was a particularly dynamic period following from the heavy winter snowfall of 2004, indicating the importance of basal meltwater availability for glacier flow. Transverse velocity profiles indicate that Baltoro Glacier undergoes ‘block’ flow across much of the upper ablation zone during the summer, which we interpret as evidence of widespread basal sliding. The DGPS data confirm the rapid increase in flow detected during 2005. Modelled climatic data reveal decreasing summer temperatures and increasing precipitation over the study period, helping to explain the observed dynamic variations and their differences from glaciers elsewhere in the Himalaya.

Subglacial water threatens the stability of a deep ice sheet. The Greenland ice sheet has been the subject of extensive radar surveys under NASA’s PARCA program and others, yet the extent of basal water has not previously been explored in detail. This paper provides a method for recovering basal radar reflection characteristics that yield robust discrimination of subglacial water, using PARCA data, by narrowing the spread of measured echo intensities. Sources of validation are provided, and they support the procedure and its results. The method can be extended to the entire Greenland radar dataset. It is not dependent on details of radar characteristics but relies on sufficient penetration performance, high-fidelity data acquisition and appropriate treatment of signals and interface statistics.

An anomalously slight glacier mass gain during 2000 to the 2010s has recently been reported in the Karakoram region. However, to date, no investigations of the region-wide glacier mass balance in the Karakoram prior to 2000 have been reported, leaving a knowledge gap for assessing glacier responses to climate change. We calculated elevation and mass change using DEMs generated from KH-9 images acquired during 1973–1980 and the 1 arc-second SRTM DEM. We find a slight mass loss of −0.09 ± 0.03 m w.e. a−1 (12 366 km2) for 1973–2000, which is less negative than the global average rate for 1971–2009 (−0.31 ± 0.19 m w.e. a−1). Within the Karakoram, the glacier change patterns are spatially and temporally heterogeneous. In particular, a nearly stable state in the central Karakoram (−0.04 ± 0.05 m w.e. a−1 during the period 1974–2000) implies that the Karakoram anomaly dates back to the 1970s. Combined with the previous studies, we conclude that the Karakoram glaciers as a whole were in a nearly balanced state during the 1970s to the 2010s.

Despite previous studies, glacier–lake interactions and future lake development in the Poiqu River basin, central Himalaya, are still not well understood. We mapped glacial lakes, glaciers, their frontal positions and ice flow from optical remote sensing data, and calculated glacier surface elevation change from digital terrain models. During 1964–2017, the total glacial-lake area increased by ~110%. Glaciers retreated with an average rate of ~1.4 km2 a−1 between 1975 and 2015. Based on rapid area expansion (>150%), and information from previous studies, eight lakes were considered to be potentially dangerous glacial lakes. Corresponding lake-terminating glaciers showed an overall retreat of 6.0 ± 1.4 to 26.6 ± 1.1 m a−1 and accompanying lake expansion. The regional mean glacier elevation change was −0.39 ± 0.13 m a−1 while the glaciers associated with the eight potentially dangerous lakes lowered by −0.71 ± 0.05 m a−1 from 1974 to 2017. The mean ice flow speed of these glaciers was ~10 m a−1 from 2013 to 2017; about double the mean for the entire study area. Analysis of these data along with climate observations suggests that ice melting and calving processes play the dominant role in driving lake enlargement. Modelling of future lake development shows where new lakes might emerge and existing lakes could expand with projected glacial recession.

Debris cover over glaciers greatly affects their rate of ablation and is a sensitive indicator of glacier health. This study focuses on estimation of debris cover over Samudratapu glacier, Chenab basin, Himalaya, using optical remote-sensing data. Remote-sensing image data of IRS-1C LISS-III (September 2001), IRS-P6 AWiFS (September 2004) and Terra ASTER (September 2004) along with Survey of India topographical maps (1963) were used in the study. Supervised classification of topographically corrected reflectance image data was systematically conducted to map six land-cover classes in the glacier terrain: snow, ice, mixed ice and debris, debris, valley rock, and water. An accuracy assessment of the classification was conducted using the ASTER visible/near-infrared data as the reference. The overall accuracies of the glacier-cover maps were found to range from 83.7% to 89.1%, whereas the individual class accuracy of debris-cover mapping was found to range from 82% to 95%. This shows that supervised classification of topographically corrected reflectance data is effective for the extraction of debris cover. In addition, a comparative study of glacier-cover maps generated from remote-sensing data (supervised classification) of September 2001 and September 2004 and Survey of India topographical maps (1963) has highlighted the trends of glacier depletion and recession. The glacier snout receded by about 756 m from 1963 to 2004, and the total glacier area was reduced by 13.7 km2 (from 110 km2 in 1963). Further, glacier retreat is found to be accompanied by a decrease in mixed ice and debris and a marked increase in debris-cover area. The area covered by valley rock is found to increase, confirming an overall decrease in the glacier area. The results from this study demonstrate the applicability of optical remote-sensing data in monitoring glacier terrain, and particularly mapping debris-cover area.

Rapid, local drainage of surface meltwater to the base of the Greenland ice sheet is thought to result in surface velocity variations as far inland as the equilibrium zone (Zwally and others, 2002). Ice-penetrating radar surveys throughout this region allow us to characterize englacial drainage features that appear as vertically stacked diffraction hyperbolae in common-offset profiles. These data are used with a radar-simulation model, which allows for variations in geometry, penetration depth and infill material, to understand the characteristics of these hyperbolae and the likelihood that they are produced by moulins. We find only a moderate correlation between the locations of these possible moulins and supraglacial lakes, indicating that many lakes drain over the surface of the ice sheet, or do not contain sufficient water to reach the bed through moulin formation. We find a strong correlation between moulin location in the ablation region and elevated along-flow tension (due to flow over rough bedrock), which generates surface crevassing and provides an entry point for meltwater. Although theory suggests that moulins may form anywhere on the ice sheet given sufficient meltwater input, our data suggest that they are far more common in the ablation zone than near, or inland from, the equilibrium line.

Field surveys of supraglacial ponds on debris-covered glaciers in the Nepal Himalaya clarify that ice-cliff calving occurs when the fetch exceeds ∼80 m. Thermal undercutting is important for calving processes in glacial lakes, and subaqueous ice melt rates during the melt and freeze seasons are therefore estimated under simple geomorphologic conditions. In particular, we focus on the differences between valley wind-driven water currents in various fetches during the melt season. Our results demonstrate that the subaqueous ice melt rate exceeds the ice-cliff melt rate when the fetch is >20 m and water temperature is 2–4°C. Calculations suggest the onset of calving due to thermal undercutting is controlled by water currents driven by winds at the surface of the lake, which develop with expanding water surface.

As simulations of 21st-century climate start to include components with longer timescales, such as ice sheets, the initial conditions for those components will become critical to the forecast. This paper describes an algorithm for specifying the initial state of an ice-sheet model, given spatially continuous observations of the surface elevation, the velocity at the surface and the thickness of the ice. The algorithm can be viewed as an inverse procedure to solve for the viscosity or the basal drag coefficient. It applies to incompressible Stokes flow over an impenetrable boundary, and is based upon techniques used in electric impedance tomography; in particular, the minimization of a type of cost function proposed by Kohn and Vogelius. The algorithm can be implemented numerically using only the forward solution of the Stokes equations, with no need to develop a separate adjoint model. The only requirement placed upon the numerical Stokes solver is that boundary conditions of Dirichlet, Neumann and Robin types can be implemented. As an illustrative example, the algorithm is applied to shear flow down an impenetrable inclined plane. A fully three-dimensional test case using a commercially available solver for the Stokes equations is also presented.