The phase-sensitive radio-echo sounder (pRES) is a powerful new instrument that can measure the depth of internal layers and the glacier bed to millimetre accuracy. We use a stationary 16-antenna pRES array on Store Glacier in West Greenland to measure the three-dimensional orientation of dipping internal reflectors, extending the capabilities of pRES beyond conventional depth sounding. This novel technique portrays the effectiveness of pRES in deriving the orientation of dipping internal layers that may complement profiles obtained through other geophysical surveying methods. Deriving ice vertical strain rates from changes in layer depth as measured by a sequence of pRES observations assumes that the internal reflections come from vertically beneath the antenna. By revealing the orientation of internal reflectors and the potential deviation from nadir of their associated reflections, the use of an antenna array can correct this assumption. While the array configuration was able to resolve the geometry of englacial layers, the same configuration could not be used to accurately image the glacier bed. Here, we use simulations of the performance of different array geometries to identify configurations that can be tailored to study different types of basal geometry for future deployments.

Bed roughness is an important control on ice-stream location and dynamics. The majority of previous bed roughness studies have been based on data derived from radio-echo sounding (RES) transects across Antarctica and Greenland. However, the wide spacing of RES transects means that the links between roughness and flow are poorly constrained. Here, we use Digital Terrain Model/bathymetry data from a well-preserved palaeo-ice stream to investigate basal controls on the behaviour of contemporary ice streams. Artificial transects were set up across the Minch Palaeo-Ice Stream (NW Scotland) to mimic RES flight lines over Institute and Möller Ice Streams (Antarctica). We then explored how different data-resolution, transect orientation and spacing, and different methods, impact roughness measurements. Our results show that fast palaeo-ice flow can occur over a rough, hard bed, not just a smooth, soft bed, as previous work has suggested. Smooth areas of the bed occur over both bedrock and sediment covered regions. Similar trends in bed roughness values were found using Fast Fourier Transform analysis and standard deviation methods. Smoothing of bed roughness results can hide important details. We propose that the typical spacing of RES transects is too wide to capture different landform assemblages and that transect orientation influences bed roughness measurements in both contemporary and palaeo-ice-stream setting.

Despite their high value and importance for various glaciological applications, detailed ice thickness measurements of alpine glaciers are still very limited. Knowledge of bedrock topography is essential for paleoglaciological studies. The Guliya ice cap located on the Tibetan Plateau is one of the highest and largest ice caps in mid-low latitude regions. A detailed ground-penetrating radar (GPR) survey was conducted on the Guliya ice cap in 2015 using 20 and 40 MHz frequency antennas. An empirical Bayesian kriging method was used for ice thickness interpolation and uncertainty assessment. GPR measurements revealed complex basal topography of the Guliya glacier with a maximum thickness of 371.12 ± 13 m. The internal reflections caused by changes in the dielectric properties were registered on the 40 MHz radargrams at the summit and were attributed to density variations. As a result of this fieldwork, one of the largest ice thickness datasets in High Mountain Asia was obtained. Guliya glacier elevation changes were assessed by differencing digital elevation models. The glacier gained mass from 2000 to 2015 with an average rate of 0.270 ± 0.11 m w.e. a−1 at the summit and 0.279 ± 0.11 m w.e. a−1 at the lower elevations.

The MODerate resolution Imaging Spectroradiometer (MODIS) land surface temperature (LST) data have been widely used for air temperature estimation in mountainous regions where station observations are sparse. However, the performance of MODIS LST in high-elevation glacierized areas remains unclear. This study investigates air temperature estimation in glacierized areas based on ground observations at four glaciers across the Tibetan Plateau. Before being used to estimate the air temperature, MODIS LST data are evaluated at two of the glaciers, which indicates that MODIS night-time LST is more reliable than MODIS daytime LST data. Then, linear models based on each of the individual MODIS LST products from two platforms (Terra and Aqua) and two overpasses (night-time and daytime) are built to estimate daily mean, minimum and maximum air temperatures in glacierized areas. Regional glacier surface (RGS) models (mean /-mean-square differences: 3.3, 3.0 and 4.8°C for daily mean, minimum and maximum air temperatures, respectively) show higher accuracy than local non-glacier surface models (mean root-mean-square differences: 4.2, 4.7 and 5.7°C). In addition, the RGS models based on MODIS night-time LST perform better to estimate daily mean, minimum and maximum air temperatures than using temperature lapse rate derived from local stations.

Unlike in most other regions, Karakoram glaciers are either stable or advancing, a phenomenon known as the Karakoram anomaly. Despite studies of glacier surges and the derivation of surface velocity maps, the spatiotemporal variability of glacier dynamics still remains poorly understood, particularly in the Eastern Karakoram Range. We use Advanced Land Observing Satellite/the Phased Array type L-band Synthetic Aperture Radar (ALOS/PALSAR)-1/2 data from 2007 to 2011 and 2014 to 2015 to examine detailed surface velocity patterns of the Siachen, Baltoro, Kundos, Singkhu and Gasherbrum Glaciers. The first three glaciers show considerable velocity variability (20–350 m a−1), with clear seasonal patterns. Although all glaciers, except for Baltoro, flow slowest in 2015, the velocity structures are individual and vary in space and time. In Gasherbrum Glacier, peak surge-phase velocities are seasonally modulated, with maxima in summers 2006 and 2007, suggesting surface melt plays an important role in maintaining the active phase. Given the relatively close proximity of these glaciers, we assume that surface melt timing and rates are comparable. We therefore argue that the observed spatiotemporal and interannual velocity patterns are determined by local and internal mechanisms, including englacial and subglacial hydrology, thermal processes and tributary configuration of each individual glacier.

Satellite images were analyzed to measure the frontal positions and ice speeds of 19 marine-terminating outlet glaciers along the coast of Prudhoe Land, northwestern Greenland from 1987 to 2014. All the studied glaciers retreated over the study period at a rate of between 12 and 200 m a−1, with a median (mean) retreat rate of 30 (40) m a−1. The glacier retreat began in the year ~2000, which coincided with an increase in summer mean air temperature from 1.4 to 5.5 °C between 1996 and 2000 in this region. Ice speed near the front of the studied glaciers ranged between 20 and 1740 m a−1 in 2014, and many of them accelerated in the early 2000s. In general, the faster retreat was observed at the glaciers that experienced greater acceleration, as represented by Tracy Glacier, which experienced a retreat of 200 m a−1 and a velocity increase of 930 m a−1 during the study period. A possible interpretation of this observation is that flow acceleration induced dynamic thinning near the termini, resulting in enhanced calving and rapid retreat of the studied glaciers. We hypothesize that atmospheric warming conditions in the late 1990s triggered glacier retreat in northwestern Greenland since 2000.

Basal depth hoar that forms in Arctic snowpacks often has a low thermal conductivity, strongly contributing to the snowpack thermal insulance and impacting the permafrost thermal regime. At Ward Hunt Island (Canadian high Arctic, 83°05′N, 74°07′W) almost no depth hoar was observed in spring 2016 despite favorable thermal conditions. We hypothesize that depth hoar formation was impeded by the combination of two factors (1) strong winds in fall that formed hard dense wind slabs where water vapor transport was slow and (2) low soil moisture that led to rapid ground cooling with no zero-curtain period, which reduced soil temperature and the temperature gradient in the snowpack. Comparisons with detailed data from the subsequent winter at Ward Hunt and from Bylot Island (73°09′N, 80°00′W) and with data from Barrow and Alert indicate that both high wind speeds after snow onset and low soil moisture are necessary to prevent Arctic depth hoar formation. The role of convection to form depth hoar is discussed. A simple preliminary strategy to parameterize depth hoar thermal conductivity in snow schemes is proposed based on wind speed and soil moisture. Finally, warming-induced vegetation growth and soil moisture increase should reduce depth hoar thermal conductivity, potentially affecting permafrost temperature.

Information about the ice volume stored in glaciers is of high importance for sustainable water management in many arid regions of Central Asia. Several methods to estimate the ice volume exist. However, none of them take the specific characteristics of flat terminus debris-covered glaciers into account. We present a method for deriving spatially-distributed ice thickness for debris-covered dendritic glaciers, which are common not only in Central Tien Shan but also in several other mountain ranges in High Asia. The method relies on automatically generated branch lines, observed surface velocities and surface topographic parameters as basic input. Branch lines were generated using Thiessen polygons and Dijkstra's path algorithm. Ice thicknesses for four debris-covered glaciers – South Inylchek, Kaindy, Tomur and Koxkar glaciers – have been estimated along the branch line network solving the equation of laminar flow. For Koxkar and South Inylchek glaciers, respectively, maximum thicknesses of ~250 and 380 m were estimated. These results differ by ~50 m compared with GPR measurements with an uncertainty for the debris-covered parts of ~40%. Based on geodetic mass balances, we estimate that the investigated glaciers lost between 6 and 28% of their volume from 1975 to the early 2000s.

The Holocene climatic optimum was a period 8–5 kyr ago when annual mean surface temperatures in Greenland were 2–3°C warmer than present-day values. However, this warming left little imprint on commonly used temperature proxies often used to derive the climate forcing for simulations of the past evolution of the Greenland ice sheet. In this study, we investigate the evolution of the Greenland ice sheet through the Holocene when forced by different proxy-derived temperature histories from ice core records, focusing on the effect of sustained higher surface temperatures during the early Holocene. We find that the ice sheet retreats to a minimum volume of ~0.15–1.2 m sea-level equivalent smaller than present in the early or mid-Holocene when forcing an ice-sheet model with temperature reconstructions that contain a climatic optimum, and that the ice sheet has continued to recover from this minimum up to present day. Reconstructions without a warm climatic optimum in the early Holocene result in smaller ice losses continuing throughout the last 10 kyr. For all the simulated ice-sheet histories, the ice sheet is approaching a steady state at the end of the 20th century.

In a series of papers, Bartelt and co-workers developed novel snow-avalanche models in which random kinetic energy (RKE) RK (a.k.a. granular temperature) is a key concept. The earliest models were for a single, constant density layer, using a Voellmy model but with RK-dependent friction parameters. This was then extended to variable density, and finally a suspension layer (powder-snow cloud) was added. The physical basis and mathematical formulation of these models are critically reviewed here, with the following main findings: (i) Key assumptions in the original RKE model differ substantially from established results on dense granular flows; in particular, the effective friction coefficient decreases to zero with velocity in the RKE model. (ii) In the variable-density model, non-canonical interpretation of the energy balance leads to a third-order evolution equation for the flow depth or density, whereas the stated assumptions imply a first-order equation. (iii) The model for the suspension layer neglects gravity and disregards well-established theoretical and experimental results on particulate gravity currents. Some options for improving these aspects are discussed.

Forecasting of glacier mass balance is important for optimal management of hydrological resources, especially where glacial meltwater constitutes a significant portion of stream flow, as is the case for many rivers in Iceland. In this study, a method was developed and applied to forecast the summer mass balance of Brúarjökull glacier in southeast Iceland. In the present study, many variables measured in the basin were evaluated, including glaciological snow accumulation data, various climate indices and meteorological measurements including temperature, humidity and radiation. The most relevant single predictor variables were selected using correlation analysis. The selected variables were used to define a set of potential multivariate linear regression models that were optimized by selecting an ensemble of plausible models showing good fit to calibration data. A mass-balance estimate was calculated as a uniform average across ensemble predictions. The method was evaluated using fivefold cross-validation and the statistical metrics Nash–Sutcliffe efficiency, the ratio of the root mean square error to the std dev. and percent bias. The results showed that the model produces satisfactory predictions when forced with initial condition data available at the beginning of the summer melt season, between 15 June and 1 July, whereas less reliable predictions are produced for longer lead times.

Meltwater is important to understanding glacier health and dynamics. Since melt measurements are uncommon, ice ablation estimates are often based on models including the positive degree day (PDD) model. The PDD estimate is popular since it only requires air temperature as input, but suffers from the lack of physical motivation of an energy-balance model. We present a physics-based alternative to the PDD model that still only takes air/surface temperature as input. The model resembles the PDD model except accounting for time lags in ablation when cold ice needs to be warmed. The model is expressed as a differential equation with a single extra parameter related to the efficiency of heating a near-surface layer of ice. With zero thickness, the model reduces to the PDD model, providing a physical basis for the PDD model. Applying the model to data from Greenland, it improves modestly upon the PDD model, with the main improvement being better prediction of early season melting. This new model is a useful compromise, with some of the physics of more realistic models and the simplicity of a PDD model. The model should improve estimates of meltwater production and help constrain PDD parameters when empirical calibration is challenging.

The climatic condition that prevails at a glacier equilibrium line altitude (ELA) is often parameterized in terms of summer air temperature (T) and annual precipitation (P). This simple parameterization was initially proposed by Hans W:son Ahlmann. The physical background of the relationship between P and T on the equilibrium line, however, has been left unexplained since Ahlmann first questioned the mathematical form of the relationship. This relationship can be explained when the thermal and hydrological processes of the ELA formation are investigated. The present authors studied the energy exchange processes that prevail on the ELA during the melt season. The inclusion of solar radiation brings Ahlmann's hypothesis closer to energy balance, and improves his P/T diagram. By comparing the observed fluxes from the polar through the mid-latitude to the equatorial glaciers, it was found that these glaciers in different climatic regions share important similarities at the ELA. Further, it was found that the classic P/T curve originally proposed by Ahlmann in the early 20th century is a concise expression of the conservation principle of energy and mass at the ELA of glaciers, and takes the form of a polynomial of the fourth order.

Measured elastic stiffnesses of ice polycrystals decrease with increasing temperature due to a decrease in grain boundary stiffness with increasing temperature. In this paper, we represent grain boundaries as imperfectly bonded interfaces, across which traction is continuous, but displacement may be discontinuous. We express the additional compliance due to grain boundaries in terms of a second-rank and a fourth-rank tensor, which quantify the effect on elastic wave velocities of the orientation distribution as well as the normal and shear compliances of the grain boundaries. Measurement of the elastic stiffnesses allows determination of the components of these tensors. Application of the method to resonant ultrasound spectroscopy measurements made on ice polycrystals enables determination of the ratio BN/BS of the normal to shear compliance of the grain boundaries, which are found to be more compliant in shear than in compression. The ratio BN/BS is small at low temperatures, but increases as temperature increases, implying that the normal compliance increases relative to the shear compliance as temperature increases.

Strain rates are fundamental measures of ice flow and are used in a wide variety of glaciological applications including investigations of bed properties, calculations of basal mass balance on ice shelves, and constraints on ice rheological models. However, despite their extensive application, strain rates are calculated using a variety of methods and length scales and the details are often not specified. In this study, we compare the results of nominal and logarithmic strain-rate calculations based on a satellite-derived velocity field of the Antarctic ice sheet generated from Landsat 8 satellite data. Our comparison highlights the differences between the two common approaches in the glaciological literature. We evaluate the errors introduced by each approach and their impacts on the results. We also demonstrate the importance of choosing and specifying a length scale over which strain-rate calculations are made, which can strongly influence other derived quantities such as basal mass balance on ice shelves. Finally, we present strain-rate data products calculated using an approximate viscous length-scale with satellite observations of ice velocity for the Antarctic continent.

A geochemical method to characterize post-depositional melting and elution is demonstrated using inductively coupled plasma mass spectrometry to measure concentrations of dissolved and insoluble fractions of major crustal elements in snow samples collected from March 2006 to January 2010 at Urumqi Glacier No. 1, Tien Shan. Dust from these samples has compositional homogeneity, suggesting that dust has a stable dissolved fraction percentage (DFP, calculated as dissolved/(dissolved + insoluble)%). Calcium has the highest DFP (averaging 61.5 ± 19.4%), followed by Na (30.4 ± 19.6%), Mg (13.2 ± 9.8%), and K (7.9 ± 9.8%). Acid input can affect dissolution of Na and Ca. Taking DFP values of unmelted samples as the reference, the higher DFPs refer to strengthened dissolution from acid input, while the lower ones refer to elution. Based on the DFP difference between unmelted and eluted states, an elution sequence Ca > Na > Mg > K is obtained. Some details such as the beginning and the ending stages of elution can be found by DFP and acid input index, while using ion concentration is not capable of this. Our results reveal that acid input is an important mechanism for DFP changes, that the DFP index can provide an effective assessment of snow elution, and that this will aid in understanding low latitude ice cores.

The critique by Issler and other (2017) of our avalanche dynamics model maintains that we disregard well-established results of particulate gravity flows. Here we show that the arguments of Issler and others (1) violate Newton's laws of motion in the avalanche core and (2) ignore size-dependent drag forces on snow particles (Stokes law) that lead to the formation of avalanche suspension layers. We explain why we cannot amend our model equations to accommodate their suggestions. The goal of our approach is to describe highly non-stationary processes in the avalanche core that lead to a wide range of avalanche flow types and therefore different flow behavior. This is important for practical applications.

The widespread retreat of mountain glaciers is a striking emblem of recent climate change. Yet mass-balance observations indicate that many glaciers are out of equilibrium with current climate, meaning that observed retreats do not show the full response to warming. This is a fundamental consequence of glacier dynamics: mountain glaciers typically have multidecadal response timescales, and so their response lags centennial-scale climate trends. A substantial difference between transient and equilibrium glacier length persists throughout the warming period; we refer to this length difference as ‘disequilibrium’. Forcing idealized glacier geometries with gradual warming shows that the glacier response timescale fundamentally governs the evolution of disequilibrium. Comparing a hierarchy of different glacier models suggests that accurate estimates of ice thickness and climatology, which control the timescale, are more important than higher order ice dynamics for capturing disequilibrium. Current glacier disequilibrium has previously been estimated for a selection of individual glaciers; our idealized modeling shows that sustained disequilibrium is a fundamental response of glacier dynamics, and is robust across a range of glacier geometries. This implies that many mountain glaciers are committed to additional, kilometer-scale retreats, even without further warming. Disequilibrium must also be addressed when calibrating glacier models used for climate reconstructions and projections of retreat in response to future warming.