To investigate the spatial distribution of the energy- and mass-balance fluxes of a glacier, a two-dimensional mass-balance model was developed and applied to Morteratschgletscher, Switzerland. The model is driven by meteorological input from four synoptic weather stations located in the vicinity of Morteratschgletscher. The model results were compared to observations made on the glacier. The calculated mean specific mass balance is −0.47 m w.e. for 1999, and 0.23 m w.e. for 2000. Net shortwave radiation shows a minimum at around 3350 m a.s.l., due to the effects of shading, slope, aspect, reflection from the slopes, and obstruction of the sky. Ignoring these effects results in a 37% increase in the annual incoming shortwave radiation on the glacier, causing 0.34 m w.e. more ablation. A 1°C change in the air temperature results in a shift of 0.67 m w.e. in the mean specific mass balance, while altering the precipitation by 10% causes a change of 0.17 m w.e.

The automatic weather station (AWS) on the snout of the Vadret da Morteratsch, Switzerland, has delivered a unique 12 year meteorological dataset from the ablation zone of a temperate glacier. This dataset can be used to study multi-annual trends in the character of the surface energy budget. Since 2003 there has been a substantial darkening of the glacier tongue due to the accumulation of mineral and biogenic dust. The typical surface albedo in summer has dropped from 0.32 to 0.15. We have analysed the implications of the lowered albedo for the energy balance and the annual ablation. For the 4 year period 2003–06, the decreased albedo caused an additional removal of about 3.5 m of ice. Calculations with an energy-balance model show that the same increase in ablation is obtained by keeping the ice albedo fixed to 0.32 and increasing the air temperature by 1.7 K. Our analysis confirms that for retreating glaciers the deposition of dust from exposed side moraines on the glacier surface constitutes an important feedback mechanism. The mineral dust stimulates the growth of algae, lowers the surface albedo, enhances the melt rates, and thereby facilitates the further retreat of the glacier snout.

We derive mass changes of the Greenland ice sheet (GIS) for 2003–07 from ICESat laser altimetry and compare them with results for 1992–2002 from ERS radar and airborne laser altimetry. The GIS continued to grow inland and thin at the margins during 2003–07, but surface melting and accelerated flow significantly increased the marginal thinning compared with the 1990s. The net balance changed from a small loss of 7 ± 3 Gt a−1 in the 1990s to 171 ± 4 Gt a−1 for 2003–07, contributing 0.5 mm a−1 to recent global sea-level rise. We divide the derived mass changes into two components: (1) from changes in melting and ice dynamics and (2) from changes in precipitation and accumulation rate. We use our firn compaction model to calculate the elevation changes driven by changes in both temperature and accumulation rate and to calculate the appropriate density to convert the accumulation-driven changes to mass changes. Increased losses from melting and ice dynamics (17–206 Gt a−1) are over seven times larger than increased gains from precipitation (10–35 Gt a−1) during a warming period of ∼2 K (10 a)−1 over the GIS. Above 2000 m elevation, the rate of gain decreased from 44 to 28 Gt a−1, while below 2000 m the rate of loss increased from 51 to 198 Gt a−1. Enhanced thinning below the equilibrium line on outlet glaciers indicates that increased melting has a significant impact on outlet glaciers, as well as accelerating ice flow. Increased thinning at higher elevations appears to be induced by dynamic coupling to thinning at the margins on decadal timescales.

We analyzed the possible controls on the distribution of surge-type glaciers in Svalbard using multivariate logit models including 504 glaciers and a large number of glacial and geological attributes. Specifically we examined the potential effect of geological boundaries, mass-balance conditions and thermal regime on surging. It was found that long glaciers with relatively steep slopes overlying young fine-grained sedimentary lithologies with orientations in a broad arc clockwise from northwest to southeast are most likely to be of surge type. No relation between lithological boundaries and surge potential could be established. Possible explanations for length being conducive to surging are transport-distance-related substrate properties, distance-related attenuation of longitudinal stresses and the possible relation between thermal regime and glacier size. Analysis of glaciers with recorded radioecho sounding reveals that a polythermal regime, accumulation-area ratios close to balance and a large elevation span increase the surge potential. The logit models also enabled us to detect 19 new surge-type glaciers, to reclassify six glaciers as normal and to identify unusual surge-type glaciers. Our model results suggest that a polythermal regime and fine-grained potentially deformable beds are conducive to the surge potential of Svalbard glaciers.

Spatial and temporal variations in aerodynamic roughness length (z0) on Haut Glacier d’Arolla, Switzerland, during the 1993 and 1994 ablation seasons are described, based on measurements of surface microtopography. The validity of the microtopographic z0 measurements is established through comparison with independent vertical wind profile z0 measurements over melting snow, slush and ice. The z0 variations are explained through correlation and regression analyses, using independent measurements of meteorological and surface variables, and parameterizations are developed to calculate z0 variations for use in surface energy-balance melt models. Several independent variables successfully explain snow z0 variation through their correlation with increasing surface roughness, caused by ablation hollow formation, during snowmelt. Non-linear parameterizations based on either accumulated melt or accumulated daily maximum temperatures since the most recent snowfall explain over 80% of snow z0 variation. The z0 following a fresh snowfall on an ice surface is parameterized based on relationships with the underlying ice z0, snow depth and accumulated daily maximum temperatures. None of the independent variables were able to successfully explain ice z0 variation. Although further comparative studies are needed, the results lend strong support to the microtopographic technique of measuring z0 over melting glacier surfaces.

Extensive covers of supraglacial debris are often present in glacier ablation areas, and it is essential to assess exactly how the debris affects glacier melt rates. This paper presents a physically based energy-balance model for the surface of a debris-covered glacier. The model is driven by meteorological variables, and was developed using data collected at Miage glacier, Italy, during the ablation seasons of 2005, 2006 and 2007. The debris surface temperature is numerically estimated by considering the balance of heat fluxes at the air/debris interface, and heat conduction through the debris is calculated in order to estimate melt rates at the debris/ice interface. The predicted hourly debris surface temperatures and debris internal temperatures provide a good fit to temperatures measured on rock-covered Miage glacier (r2 >0.94) and the tephra-covered glacier on Villarrica volcano, Chile (r2 >0.82). The model can also be used to reproduce observed changes in melt rates below debris layers of varying types and thicknesses, an important consideration for the overall mass balance of debris-covered glaciers.

Predictions of marine ice-sheet behaviour require models able to simulate grounding-line migration. We present results of an intercomparison experiment for plan-view marine ice-sheet models. Verification is effected by comparison with approximate analytical solutions for flux across the grounding line using simplified geometrical configurations (no lateral variations, no buttressing effects from lateral drag). Perturbation experiments specifying spatial variation in basal sliding parameters permitted the evolution of curved grounding lines, generating buttressing effects. The experiments showed regions of compression and extensional flow across the grounding line, thereby invalidating the boundary layer theory. Steady-state grounding-line positions were found to be dependent on the level of physical model approximation. Resolving grounding lines requires inclusion of membrane stresses, a sufficiently small grid size (<500 m), or subgrid interpolation of the grounding line. The latter still requires nominal grid sizes of <5 km. For larger grid spacings, appropriate parameterizations for ice flux may be imposed at the grounding line, but the short-time transient behaviour is then incorrect and different from models that do not incorporate grounding-line parameterizations. The numerical error associated with predicting grounding-line motion can be reduced significantly below the errors associated with parameter ignorance and uncertainties in future scenarios.

We investigated area changes in glaciers covering an area of ∼200 km2 in the Tista basin, Sikkim, Eastern Indian Himalaya, between ∼1990 and 2010 using Landsat Thematic Mapper (TM) and Indian Remote-sensing Satellite (IRS) images and related the changes to debris cover, supraglacial lakes and moraine-dam lakes. The glaciers lost an area of 3.3 ± 0.8% between 1989/90 and 2010. More detailed analysis revealed an area loss of 2.00 ± 0.82, 2.56 ± 0.61 and 2.28 ± 2.01 km2 for the periods 1989–97, 1997–2004/05 and 2004–2009/10, respectively. This indicates an accelerated retreat of glaciers after 1997. On further analysis, we observed (1) the formation and expansion of supraglacial lakes on many debris-covered glaciers and (2) the merging of these lakes over time, leading to the development of large moraine-dam lakes. We also observed that debris-covered glaciers with lakes lose a greater area than debris-covered glaciers without lakes and debris-free glaciers. The climatic data for 24 years (1987–2011), measured at the Gangtok meteorological station (1812 m a.s.l.), showed that the region experienced a 1.0°C rise in the summer minimum temperature and a 2.0°C rise in the winter minimum temperature, indicating hotter summers and warmer winters. There was no significant trend in the total annual precipitation. We find that glacier retreat is caused mainly by a temperature increase and that debris-covered glaciers can retreat at a faster rate than debris-free glaciers, if associated with lakes.

Spatial and temporal variations of surface albedo on Haut Glacier d’Arolla, Switzerland, during the 1993 and 1994 ablation seasons are described. Correlation and regression analyses are used to explain the albedo variations in terms of independent meteorological and surface property variables. Parameterizations are developed which allow estimation of albedo variation in surface energy-balance models. Snow albedo is best estimated from accumulated daily maximum temperatures since snowfall. On “deep” snow (≥0.5 cm w.e. depth) a logarithmic function is used, while on “shallow” snow (<0.5 cm w.e. depth) an exponential function is used to enable the albedo to decay to the underlying ice or debris albedo. The transition from “deep” to “shallow” snow is calculated as a function of decreasing snow depth (combined r2 = 0.65). This new parameterization performs better than earlier schemes because accumulated daily maximum temperatures since snowfall correlate strongly with snow grain-size and impurity concentration, the main physical controls on snow albedo. Ice albedo may be parameterized by its relationship to elevation (r2 = 0.28), but this approach results in only a small improvement over the assumption of a constant mean ice albedo.

We use models constrained by remotely sensed data from Pine Island and Thwaites Glaciers, West Antarctica, to infer basal properties that are difficult to observe directly. The results indicate strong basal melting in areas upstream of the grounding lines of both glaciers, where the ice flow is fast and the basal shear stress is large. Farther inland, we find that both glaciers have ‘mixed’ bed conditions, with extensive areas of both bedrock and weak till. In particular, there are weak areas along much of Pine Island Glacier’s main trunk that could prove unstable if it retreats past the band of strong bed just above its current grounding line. In agreement with earlier studies, our forward ice-stream model shows a strong sensitivity to small perturbations in the grounding line position. These results also reveal a large sensitivity to the assumed bed (sliding or deforming) model, with non-linear sliding laws producing substantially greater dynamic response than earlier simulations that assume a linear-viscous till rheology. Finally, comparison indicates that our results using a plastic bed are compatible with the limited observational constraints and theoretical work that suggests an upper bound exists on maximum basal shear stress.

In the low latitudes there is an absence of major thermal seasonality, yet there are three different climate regimes related to global circulation patterns and their seasonal oscillation: the humid inner tropics, the dry subtropics and, intermediate between these two, the outer tropics. For the respective glacier regimes the vertical profiles of specific mass balance (VBPs) are modeled considering vertical gradients of accumulation, air temperature and albedo, the duration of the ablation period and a factor for the ratio between melting and sublimation. The model is first calibrated with data from Hintereisferner, Austrian Alps, and is then applied to tropical conditions. The simulated VBP matches well the measured profiles from Irian jaya and Mount Kenya. Due to lack of field evidence, the subtropical VBP cannot be verified directly. However, application of the respective model versions separately to the humid and dry seasons of the outer-tropical Glaciar Uruashraju, Cordillera Blanca, Peru, provides reasonable results. Glaciers in the humid inner tropics are considered to be most sensitive to variations in air temperature, while dry subtropical glaciers are most sensitive to changes in air humidity. The two seasons of the outer tropics have to be viewed from these different perspectives.

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.

Twenty-seven studies on the thermal conductivity of snow (Keff) have been published since 1886. Combined, they comprise 354 values of Keff, and have been used to derive over 13 regression equation and predicting Keff vs density. Due to large (and largely undocumented) differences in measurement methods and accuracy, sample temperature and snow type, it is not possible to know what part of the variability in this data set is the result of snow microstructure. We present a new data set containing 488 measurements for which the temperature, type and measurement accuracy are known. A quadratic equation,

where ρ is in g cm−3, and Keff is in W m−1K−1, can be fit to the new data (R2 = 0.79). A logarithmic expression,

can also be used. The first regression is better when estimating values beyond the limits of the data; the second when estimating values for low-density snow. Within the data set, snow types resulting from kinetic growth show density-independent behavior. Rounded-grain and wind-blown snow show strong density dependence. The new data set has a higher mean value of density but a lower mean value of thermal conductivity than the old set. This shift is attributed to differences in snow types and sample temperatures in the sets. Using both data sets, we show that there are well-defined limits to the geometric configurations that natural seasonal snow can take.

To assess the potential volume of a glacial lake outburst flood (GLOF) more precisely than in previous studies, we analyze ground survey data and remote-sensing digital elevation models (DEMs) around glacial lakes in the Lunana region, Bhutan. Based on a DEM generated from differential GPS ground surveys, we first evaluate the relative accuracies of DEMs produced by the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) and the Shuttle Radar Topography Mission (SRTM). Root-mean-square errors of the altitudinal difference between these DEMs and ground survey data were 11.0 m for ASTER and 11.3 m for SRTM. These errors are similar to those of previous studies. We show that a topographical classification allows a better estimate of elevation on lakes/ponds, riverbeds and glaciers due to their flat surfaces, while the relative accuracy is worse over moraines and hill slopes due to their narrow ridges and steep slopes. Using the optical satellite images and the ground survey data, we re-evaluate the GLOF volume in 1994 as (17.2 ± 5.3) × 106 m3. We show GLOF-related information such as distance, altitudinal difference and gradient at possible outburst points where the lake level is higher than the neighboring riverbed and/or glacial lake.

Ablation of debris-mantled glaciers in Nepal has resulted in the formation of several potentially unstable moraine-dammed lakes, some of which constitute serious hazards. Ngozumpa Glacier, Khumbu Himal, has undergone significant downwasting in recent decades, and is believed to lie close to the threshold for moraine-dammed lake formation. The debris-mantled ablation area of the glacier is studded with numerous supraglacial lakes, the majority of which occupy closed basins with no perennial connections to the englacial drainage system (“perched lakes”). Perched lakes can undergo rapid growth by subaerial and water-line melting of exposed ice faces, and calving. Subaerial and subaqueous melting beneath thick (>1 m) debris mantles is comparatively insignificant. Although lake expansion can contribute substantially to ablation of the glacier, perched lakes cannot continue to grow indefinitely, but are subject to rapid drainage once a connection is made to englacial conduits. The level of one of the lakes on the Ngozumpa, however, is controlled by the altitude of a spillway through the lateral moraine of the glacier. This lake underwent only limited growth in the period 1998–2000, but is likely to experience monotonic growth ifglacier mass balance continues to be negative.

Based on aerial photographs, topographical maps and the Landsat-5 image data, we have analyzed fluctuations of glaciers in the western Qilian Shan, north-west China, from the Little Ice Age (LIA) to 1990. The areas and volumes of glaciers in the whole considered region decreased 15% and 18%, respectively, from the LIA maximum to 1956. This trend of glacier shrinkage continued and accelerated between 1956 and 1990. These latest decreases in area and volume were about 10% in 34 years. The recent shrinkage may be due either to a combination of higher temperatures and lower precipitation during the period 1956–66, or to continuous warming in the high glacierized mountains from 1956 to 1990. As a consequence, glacier runoff from ice wastage between 1956 and 1990 has increased river runoff by 6.2 km3 in the four river basins under consideration. Besides, the equilibrium-line altitude (ELA) rise estimated from the mean terminus retreat of small glaciers <1 km long is 46 m, which corresponds to a 0.3°C increase of mean temperatures in warm seasons from the LIA to the 1950s.

Cryoconite holes are water-filled holes in the surface of a glacier caused by enhanced ice melt around trapped sediment. Measurements on the ablation zones of four glaciers in Taylor Valley, Antarctica, show that cryoconite holes cover about 4–6% of the ice surface. They typically vary in diameter from 5 to 145 cm, with depths ranging from 4 to 56 cm. In some cases, huge holes form with 5 m depths and 30 m diameters. Unlike cryoconite holes elsewhere, these have ice lids up to 36 cm thick and melt from within each spring. About one-half of the holes are connected to the near-surface hydrologic system and the remainder are isolated. The duration of isolation, estimated from the chloride accumulation in hole waters, commonly shows ages of several years, with one hole of 10 years. The cryoconite holes in the McMurdo Dry Valleys create a near-surface hydrologic system tens of cm below the ice surface. The glacier surface itself is generally frozen and dry. Comparison of water levels between holes a few meters apart shows independent cycles of water storage and release. Most likely, local freeze–thaw effects control water passage and therefore temporary storage. Rough calculations indicate that the holes generate at least 13% of the observed runoff on the one glacier measured. This hydrologic system represents the transition between a melting ice cover with supraglacial streams and one entirely frozen and absent of water.

Recent studies of Himalayan glacier recession indicate that there is wide variability in terminus retreat rate and mass balance in the different sectors of the mountain range, primarily linked to the topography and climate of the region. Variable retreat rates of glacier termini and inadequate supporting field data (e.g. mass balance, ice thickness, velocity, etc.) in the Himalayan glaciers make it difficult to develop a coherent picture of climate change impacts. In this study, the results of a detailed mapping campaign and ground-based measurements of ablation rate, terminus retreat and ice loss are reported for the period 2003–10. In addition, background information from an old glacier map (Survey of India, 1962) was compiled and terminus recession measurements were carried out from 1990 field photographs of Chorabari Glacier, central Himalaya. Our ablation stake network results suggest that the influence of debris cover is significant for Chorabari Glacier mass balance and terminus retreat. The terminus survey finds that the glacier is retreating, but at a lower rate than many other non-debriscovered glaciers in the region. The recession and ablation data (particularly in the upper ablation area at higher altitudes) suggest that the ice volume loss of the glaciers is of greater magnitude than the slow terminus retreat and, if the process continues, the lowermost part of the glacier may reduce to a quasi-stationary position while significant ice loss continues.

Mass-balance and dynamic behaviour of Chhota Shigri glacier, western Himalaya, India, has been investigated between 2002 and 2010 and compared to data collected in 1987-89. During the period 2002-10, the glacier experienced a negative glacier-wide mass balance of -0.67 ± 0.40 m w.e. a-1. Between 2003 and 2010, elevation and ice-flow velocities slowly decreased in the ablation area, leading to a 24-37% reduction in ice fluxes, an expected response of the glacier dynamics to its recent negative mass balances. The reduced ice fluxes are still far larger than the balance fluxes calculated from the 2002-10 average surface mass balances. Therefore, further slowdown, thinning and terminus retreat of Chhota Shigri glacier are expected over the next few years. Conversely, the 2003/04 ice fluxes are in good agreement with ice fluxes calculated assuming that the glacier-wide mass balance is zero. Given the limited velocity change between 1987−89 and 2003/04 and the small terminus change between 1988 and 2010, we suggest that the glacier has experienced a period of near-zero or slightly positive mass balance in the 1990s, before shifting to a strong imbalance in the 21st century. This result challenges the generally accepted idea that glaciers in the Western Himalaya have been shrinking rapidly for the last few decades.

Many glacier snouts in the Himalaya are known to be stagnant and exhibiting low surface gradients, conditions that are conducive to the formation of glacial lakes impounded either by the terminal moraine or by the remnant glacier snout. In this study, we use interferometry and feature-tracking techniques to quantify the extent of stagnation in 20 glaciers across the Everest (Qomolangma; Sagarmatha) region, and subsequently we examine the relationship between local catchment topography and ice dynamics. The results show that only one of the studied glaciers, Kangshung Glacier, is dynamic across its entire surface, with flow rates greater than 40 m a−1 being recorded in high-elevation areas. Twelve other glaciers show some evidence of flow, but are generally characterized by long, stagnant tongues, indicating widespread recession and in situ decay. The remaining seven glaciers show no evidence of flow in any of the available datasets. Hypsometric data suggest that catchment topography plays an important role in controlling glacier flow regimes, with those fed by wide, high-altitude accumulation areas showing the most extensive active ice, and those originating at low elevations exhibiting large areas of stagnant ice. Surface profiles extracted from a SRTM digital elevation model indicate that stagnant snouts are characterized by very low (<2°) surface angles and that down-wasting is the prevalent ablation pattern in the study area.