The Ebinur lake basin, Tien Shan, China, was described in the early 20th century as the ‘Green Labyrinth’. This relatively productive area supports agriculture and stands in contrast to the regional aridity. Glacier melt runoff is an important source of water for this arid region and has played a significant role in its economic development. However, over the past 40 years the ecology and environment of the region have seriously degenerated due to human activity and climate change. To investigate changes in glacier water supply, measurements from two reference glaciers were performed and used to validate satellite data and historical data for glaciers in the water catchment. Variability in regional glacier total area and volume over the past 40 years was reconstructed from historical documents, aerial photographs and remote-sensing data. Our investigations of 446 glaciers showed that from 1964 to 2004 the total glacier area decreased by 14.7% (0.4% a–1), corresponding to an estimated volume change of 20.5%. During this period, the most dramatic decrease in glacier area corresponded to a rapid rise in temperature. This reduction in glacier area is accelerating and impacting the future sustainability of the region’s water resources.

This paper addresses the causes of the prevailing meteorological conditions observed over an Antarctic blue-ice area and their effect on the surface mass balance. Over blue-ice areas, net accumulation is zero and ablation occurs mainly through sublimation. Sublimation rates are much higher than over adjacent snowfields. The meteorological conditions favourable for high sublimation rates (warm, dry and gusty) are due to the specific orographic setting of this blue-ice area, with usually a steep upwind mountainous slope causing strong adiabatic heating. Diabatic warming due to radiation, and entrainment of warm air from aloft into the boundary layer augment the warming. The prevailing warm, dry conditions explain roughly 50% of the difference in sublimation, and the different characteristics of blue ice (mainly its lower albedo) the other 50%. Most of the annual sublimation (∼70%) takes place during the short summer (mainly in daytime), with winter ablation being restricted to occasional warm, dry föhn-like events. The additional moisture is effectively removed by entrainment and horizontal advection, which are maximum over the blue-ice area. Low-frequency turbulent motions induced by the upwind mountains enhance the vertical turbulent transports. Strong gusts and high peak wind speeds over blue-ice areas cause high potential snowdrift transports, which can easily remove the total precipitation, thereby maintaining zero accumulation.

The formulation of a physical problem in terms of a variational (or action) principle conveys significant advantages for the analytical formulation and numerical solution of that problem. One such problem is ice-sheet dynamics as described by non-Newtonian Stokes flow, for which the variational principle can be interpreted as stating that a measure of heat dissipation, due to internal deformation and boundary friction, plus the rate of loss of total potential energy is minimized under the constraint of incompressible flow. By carrying out low-aspect-ratio approximations to the Stokes flow problem within this variational principle, we obtain approximate dynamical equations and boundary conditions that are internally consistent and preserve the analytical structure of the full Stokes system. This also allows us to define an action principle for the popular first-order or ‘Blatter–Pattyn’ shallow-ice approximation that is distinct from the action principle for the Stokes problem yet preserves its most important properties and elucidates various details about this approximation. Further approximations within this new action functional yield the standard zero-order shallow-ice and shallow-shelf approximations, with their own action principles and boundary conditions. We emphasize the specification of boundary conditions, which are problematic to derive and implement consistently in approximate models but whose formulation is greatly simplified in a variational setting.

Dust deposition to snow can have regionally important climatic and hydrologic impacts resulting from direct reduction of surface albedo and indirectly from the initiation of snow albedo feedbacks. Modeling the radiative impacts of dust deposited in snow requires knowledge of the optical properties of both components. Here we present an inversion technique to retrieve the effective optical properties of dust deposited in mountain snow cover from measurements of hemispherical dust reflectance and particle size distributions using radiative transfer modeling. First, modeled reflectance is produced from single scattering properties modeled with Mie theory for a specified grain size distribution over a range of values for the imaginary part of the complex refractive index (k = 0.00001–0.1). Then, a multi-step look-up table process is employed to retrieve kλ and single scattering optical properties by matching measured to modeled reflectance across the shortwave and near infrared. The real part of the complex refractive index, n, for dust aerosols ranges between 1.5 and 1.6 and a sensitivity analysis shows the method is relatively insensitive to the choice of n within this range, 1.525 was used here. Using the values retrieved by this method to update dust optical properties in a snow + aerosol radiative transfer model reduces errors in springtime albedo modeling by 50–70%.

Automatic c-axes analyzers have been developed over the past few years, leading to a large improvement in the data available for analysis of ice crystal texture. Such an increase in the quality and quantity of data allows for stricter statistical estimates. The current textural parameters, i.e. fabric (crystallographic orientations) and microstructure (grain-boundary networks), are presented. These parameters define the state of the polycrystal and give information about the deformation undergone by the ice. To reflect the findings from automatic measurements, some parameter definitions are updated and new parameters are proposed. Moreover, a MATLAB® toolbox has been developed to extract all the textural parameters. This toolbox, which can be downloaded online, is briefly described.

Spatial evolution of supraglacial debris cover on mountain glaciers is a largely unmonitored and poorly understood phenomenon that directly affects glacier melt. Supraglacial debris cover for 93 glaciers in the Karakoram, northern Pakistan, was mapped from Landsat imagery acquired in 1977, 1998, 2009 and 2014. Surge-type glaciers occupy 41% of the study area and were considered separately. The time series of debris-covered surface area change shows a mean value of zero or near-zero change for both surging and non-surging glaciers. An increase in debris-covered area is often associated with negative regional mass balances. We extend this logic to suggest that the stable regional mass balances in the Karakoram explain the zero or near-zero change in debris-covered area. This coupling of trends combined with our 37 year time series of data suggests the Karakoram anomaly extends further back in time than previously known.

Cerro Charquini, Bolivia (Cordillera Real, 5392 ma.s.l.) was selected as a site to reconstruct glacier recession since the maximum of the Little Ice Age (LIA) in the central Andes. Five glaciers, located on differently exposed slopes, present comprehensive and well-preserved morainic systems attributed to former centuries. The moraines were dated by lichenometry and show a consistent organization on the different slopes. The past geometry of the glaciers was reconstructed using ground topography and aerophotogrammetry. Lichenometric dating shows that the LIA maximum occurred in the second half of the 17th century, after which the glaciers have receded nearly continuously. Over the last decades of the 20th century (1983–97), recession rates increased by a factor of four. On the northern and western slopes, glaciers receded more than on the southern and eastern slopes (by 78% and 65% of their LIA maximum area, respectively). The mean equilibrium-line altitude (ELA) rose by about 160 m between the LIA maximum and 1997. Recession rates were analysed in terms of climatic signal, suggesting that glacier recession since the LIA maximum was mainly due to a change in precipitation and that the 19th century may have been drier. For the 20th century, a temperature rise of about 0.6°C appears to be the main cause of glacier recession. Recent climatic conditions from 1983 to 1997 correspond to a mass deficit of about 1.36m w.e.a–1. If such conditions persist, the small glaciers below 5300ma.s.l. in the Cordillera Real should disappear completely in the near future.

X-ray microtomography has become an essential tool for investigating the mechanical and physical properties of snow, which are tied to its microstructure. To allow a quantitative characterization of the microstructure, the grayscale X-ray attenuation coefficient image has to be segmented into a binary ice/pore image. This step, called binary segmentation, is crucial and affects all subsequent analysis and modeling. Common segmentation methods are based on thresholding. In practice, these methods present some drawbacks and often require time-consuming manual post-processing. Here we present a binary segmentation algorithm based on the minimization of a segmentation energy. This energy is composed of a data fidelity term and a regularization term penalizing large interface area, which is of particular interest for snow where sintering naturally tends to reduce the surface energy. The accuracy of the method is demonstrated on a synthetic image. The method is then successfully applied on microtomographic images of snow and compared to the threshold-based segmentation. The main advantage of the presented approach is that it benefits from local spatial information. Moreover, the effective resolution of the segmented image is clearly defined and can be chosen a priori.

Changes of glaciers and glacial lakes and their causes were examined in the Hengduan Shan from 1990 to 2014, based on Landsat TM/ETM+/OLI images. A total glacier area of 1298.8 ± 62.1 km2 and glacial lake area of 255.8 ± 31.6 km were inventoried in 2014. The area of glaciers declined at an average rate of −0.40 ± 0.26% a−1, while glacial lakes expanded at average rate of +0.12 ± 0.03% a−1 over the past 24 years. These changes probably resulted from an observable temperature increase and slight precipitation increase. A ‘corridor-barrier’ effect formed by the longitudinal range–gorge terrain may have had major impacts on the distributions and changes of glaciers and glacial lakes. The Ningjing-Yunling Shan, where glaciers and glacial lakes are sparsely distributed, are an important geographic transition line in the Hengduan Shan because of the barrier effect of the mountain ranges against moisture from the southwest. In contrast, between the south and north, there were small differences with respect to the distributions and changes of glaciers and glacial lakes, owing to a north–south corridor effect for water and heat transport and diffusion through the longitudinal gorges in the Hengduan Shan.

Resistive stresses and velocities at depth are calculated along the Byrd Station Strain Network, Antarctica, using field data. There are found to be large longitudinal variations in basal drag and this result is little affected by errors in the input data or by uncertainties in the constitutive relation for ice. Basal drag varies by a factor of about 2 along the strain network, and is usually equal to the driving stress to within 10–20%. Sites of high drag are not always correlated with basal topographic highs, indicating that some process such as basal water drainage is involved in controlling the friction at the bed. Basal sliding velocities are very sensitive to errors in measured surface velocities and the rate factor in Glen’s flow law. As a result, calculated sliding velocities are much less reliable than deep stresses, and need to be interpreted with caution.

Brine volume of sea ice is a function of the salinity and temperature of the ice, and it is related to its strength. This paper gives three equations which can be used to compute the brine volume for three temperature ranges from −0.5° to −22.9°C. A less accurate equation covering the total range is also presented.

We present a technique that modifies and extends down-hole target methods to provide absolute measures of uncertainty in radar-reflector depth of origin. We use ice-core profiles to model wave propagation and reflection, and then cross-correlate the model results with radio-echo sounding (RES) data to identify the depth of reflector events. Stacked traces recorded with RES near the EPICA drill site in Dronning Maud Land, Antarctica, provide reference radargrams, and dielectric properties along the deep ice core form the input data to a forward model of wave propagation that produces synthetic radargrams. Cross-correlations between synthetic and RES radargrams identify differences in propagation wave speed. They are attributed to uncertainties in pure-ice permittivity and are used for calibration. Removing conductivity peaks results in the disappearance of related synthetic reflections and enables the unambiguous relation of electric signatures to RES features. We find that (i) density measurements with g-attenuation or dielectric profiling are too noisy below the firn–ice transition to allow clear identification of reflections, (ii) single conductivity peaks less than 0.5 m wide cause the majority of prominent reflections beyond a travel time of about 10 µs (~900m depth) and (iii) some closely spaced conductivity peaks within a range of 1–2m cannot be resolved within the RES or synthetic data. Our results provide a depth accuracy to allow synchronization of age–depth profiles of ice cores by RES, modeling of isochronous internal structures, and determination of wave speed and of pure-ice properties. The technique successfully operates with dielectric profiling and electrical conductivity measurements, suggesting that it can be applied at other ice cores and drill sites.

In order to apportion the dust sources of mountain glaciers in western China, the Sr-Nd isotopic compositions of insoluble particles were determined in snow samples collected from 13 sites. The combined plot of 87Sr/86Sr and εNd(0) demonstrates a distinctive geographic pattern over western China, which can be classified into three regions from north to south. Samples from the Altai mountains show the lowest 87Sr/86Sr ratio and the highest εNd(0) value, similar to the data of deserts in the north of China such as the Gurbantunggut desert. Samples from the southern Tibetan Plateau (TP) and Himalaya show the highest 87Sr/86Sr and lowest εNd(0) values, resembling the local and regional dust sources found in the southern TP and Himalaya-India region. Samples from the Tien Shan and northern Tibetan Plateau exhibit intermediate 87Sr/86Sr and εNd(0) values, similar to the data reported for the northern margin of the TP (NM_TP). However, three sampling sites, JMYZ (Jiemayangzong) located in the Himalaya and ZD (Zadang) and YL (Yulong) located in the southeast TP, presented distinctive Sr-Nd isotopic signatures typical of the NM_TP, suggesting potential long-range and high-altitude dust transport across the TP.

“Sliding velocity” and “friction law” are precisely defined. Different scales for tackling glacier dynamics are introduced. The energy balance in the melting-refreezing process is clarified. The validity of a Glen body as a model for ice rheology is discussed. The assumed model for subglacial water is a very slightly pervious ice, and a not absolutely watertight ice-bedrock interface, owing to glacial striae and rock joints. Then autonomous hydraulic regimes and cavities at water vapour pressure have a negligible influence on the drag, and only the interconnected regime has to be considered.

A more rigorous treatment of Weertman’s model (independent knobs) gives quite different numerical factors. In general a term increasing with Terzaghi’s effective pressure N has to be added to the drag. The double-valued friction law found by Weertman is shown to have been an error.

Kamb’s relations for the model with a vanishing microrelief are considerably simplified. His conjectural solution cannot be extended to slopes actually found in the microrelief.

The author’s (Lliboutry, 1968) treatment is unsatisfactory and includes an error. With a model consisting of irregular bumps of similar length, a new friction law is given. The pertinent measure of the bedrock roughness is then the shadowing function, not the spectral power density.

In the empirical study of jökulhlaups, the peak discharge, Qmax, and water volume drained by the ice-dammed lake during the floods, Vt, appear to follow a power-law relation , where K are b are constants determined from field data. First identified by Clague and Mathews (1973), this relation is a useful reference for predicting flood magnitude, but its physical origin remains unclear. Here, we develop the theory that connects it to contemporary models for simulating the flood hydrograph. We explain how the function Qmax = f(Vt) arises from Nye’s (1976) theory of time-dependent water flow in a subglacial channel coupled to a lake, and we describe how discharge–volume data record the (monotonically increasing) form of this function so long as the lake is not emptied in the floods. The Grímsvötn jökulhlaups present an example where, because of partial draining of the lake, agreement between the model-derived f and data is excellent. It is documented that other lake systems drain completely, but we explain how the exponent b ≈ 2/3 observed for them collectively is due primarily to a scaling effect related to their size, modified by other factors such as the flood initiation process.

We use a simple numerical model to test whether surface water influx to the bed of the interior Greenland ice sheet has the potential to cause significant subglacial channel growth similar to that observed near the ice-sheet margin and at alpine glaciers. We examine the effects on channel growth from (1) rapid supraglacial lake drainage events and (2) sustained water input into moulins. By assuming that all drainage occurs through subglacial channels and by prescribing favorable pressure conditions at the domain inlet, the model can provide upper bounds on channel growth. Our results indicate that R-channels do not grow significantly within the limited period of high pressure associated with lake drainage events. Subsequent channel growth only occurs with sustained pressures above overburden. Rapid closure of channels at low pressures suggests channels in the interior are unlikely to draw significant quantities of water from nearby distributed networks. These results indicate that other drainage mechanisms such as turbulent sheets or linked-cavity networks are likely to be of greater importance for interior subglacial drainage than the growth of channels.

Western Kunlun Mountain (WKM) glaciers show balanced or even slightly positive mass budgets in the early 21st century, and this is anomalous in a global context of glacier reduction. However, it is unknown whether the stability prevails at longer time scales because mass budgets have been unavailable before 2000. Here topographical maps, Shuttle Radar Topography Mission and Landsat data are used to examine the area and surface elevation changes of glaciers on the WKM since the 1970s. Heterogeneous glacier behaviors are observed not only in the changes of length and area, but also in the spatial distribution of surface elevation changes. However, on average, glacier area and elevation changes are not significant. Glaciers reduce in the area by 0.07 ± 0.1% a−1 from the 1970s to 2016. Averaged glacier mass loss is −0.06 ± 0.13 m w.e. a−1 from the 1970s to 1999. These findings show that the WKM glacier anomaly extends back at least to the 1970s.

Field observations, aerial photographs and satellite images are used to reconstruct the past surges of Lowell Glacier, Yukon, Canada, since 1948 based on the timing of terminus advances. A total of five surges occurred over this time, each with a duration of ~1–2 years. The time between successive surges ranged from 12 to 20 years, and appears to have been shortening over time. The relatively short advance and quiescent phases of Lowell Glacier, together with rapid increases in velocity during surges, suggest that the surging is controlled by a hydrological switch. The 2009–10 surge saw ablation area velocities increase by up to two orders of magnitude from quiescent velocities, and the terminus increase in area by 5.1 km2 and in length by up to 2.85 km. This change in area was the smallest since 1948, and follows the trend of decreasing surge extents over time. This decrease is likely driven by a strongly negative surface mass balance of Lowell Glacier since at least the 1970s, and means that the current town site of Haines Junction is very unlikely to be flooded by damming caused by any future advances of the glacier under the current climate regime.

Shearing of subglacial till has been invoked widely as a mechanism of glacier motion and sediment transport, but standard indicators for determining shear strain from the geologic record are not adequate for estimating the very high strains required of the bed-deformation model. Here we describe a laboratory study of mixing between shearing granular layers that allows an upper limit to be placed on bed shear strain in the vicinity of till contacts. Owing to random vertical motions of particles induced by shearing, mixing can be modeled as a linearly diffusive process, and so can be characterized with a single mixing coefficient, D. Ring-shear experiments with equigranular beads and lithologically distinct tills provide the value of D, although in experiments with till D decreases systematically with strain to a minimum value of 0.0045 mm2. Kinetic gas theory provides an estimate of the dimensionless mixing coefficient which is within an order of magnitude of laboratory values. Knowing the minimum value of D, the distribution of index lithologies measured across till contacts in the geologic record can be used to estimate the maximum shear strain that has occurred across till contacts. Application of this technique to the contact between the Des Moines and Superior Lobe tills in east-central Minnesota, U.S.A., indicates that shear strain did not exceed 15 000 at the depth of the contact.

The occurrence of isolated ice- or snow-covered summits is reviewed. Their existence appears in the first place to be a function of their breadth in relation to the altitude of the firn line on adjacent glaciers; other factors remain to be discussed. Light may thus be thrown on questions of past glaciation of rounded summits in critical areas, and notably on the amount of precipitation then prevailing.