Estimates of point-cloud positional accuracies in terrestrial laser scanning (TLS) datasets are currently limited to rudimentary combinations of GPS position error and manufacturer precision specifications. However, rigorous error propagation techniques can be applied to the three-dimensional TLS points and potentially integrated into software visualization and analysis products. Beyond the immediate value of qualitatively observing the distribution of expected TLS errors within a point cloud, rigorously estimated point errors can be further propagated to quantify expected errors in derived products such as point-to-point distance measurements, best-fit planes or volume computations. We review TLS error sources, detail their propagation through a rigid registration and illustrate the application of estimated TLS point errors to propagated snow volume uncertainties for a large and small TLS dataset. The resulting volume errors are of negligible size compared to the volume magnitudes, in no case exceeding 0.007% of the computed snow volume. For a dataset generating a large snow volume, the method of surface representation (e.g. grid or triangulated mesh) was more influential than the estimated TLS point errors on volume uncertainty. This suggests the random errors inherent in TLS measurement techniques are not a limiting factor in achievable snow volume accuracies.

Observations show that glaciers around the world are in retreat and losing mass. Internationally coordinated for over a century, glacier monitoring activities provide an unprecedented dataset of glacier observations from ground, air and space. Glacier studies generally select specific parts of these datasets to obtain optimal assessments of the mass-balance data relating to the impact that glaciers exercise on global sea-level fluctuations or on regional runoff. In this study we provide an overview and analysis of the main observational datasets compiled by the World Glacier Monitoring Service (WGMS). The dataset on glacier front variations (∼42 000 since 1600) delivers clear evidence that centennial glacier retreat is a global phenomenon. Intermittent readvance periods at regional and decadal scale are normally restricted to a subsample of glaciers and have not come close to achieving the maximum positions of the Little Ice Age (or Holocene). Glaciological and geodetic observations (∼5200 since 1850) show that the rates of early 21st-century mass loss are without precedent on a global scale, at least for the time period observed and probably also for recorded history, as indicated also in reconstructions from written and illustrated documents. This strong imbalance implies that glaciers in many regions will very likely suffer further ice loss, even if climate remains stable.

Large numbers of small valley glaciers on Svalbard were thicker and more extensive during the Little Ice Age (LIA), demonstrated by prominent ice-cored moraines up to several kilometres beyond present-day margins. The majority of these glaciers have since experienced a long period of strongly negative mass balance during the 20th century and are now largely frozen to their beds, indicating they are likely to have undergone a thermal transition from a polythermal to a cold-based regime. We present evidence for such a switch by reconstructing the former flow dynamics and thermal regime of Tellbreen, a small cold-based valley glacier in central Spitsbergen, based on its basal sequence and glaciological structures. Within the basal sequence, the underlying matrix-supported diamict is interpreted as saturated subglacial traction till which has frozen at the bed, indicating that the thermal switch has resulted in a cessation of subglacial sediment deformation due to freezing of the former deforming layer. This is overlain by debris-poor dispersed facies ice, interpreted to have formed through strain-induced metamorphism of englacial ice. The sequential development of structures includes arcuate fracture traces, interpreted as shear planes formed in a compressive/transpressive stress regime; and fracture traces, interpreted as healed extensional crevasses. The formation of these sediment/ice facies and structures is indicative of dynamic, warm-based flow, most likely during the LIA when the glacier was significantly thicker.

Ice-sheet models can be used to forecast ice losses from Antarctica and Greenland, but to fully quantify the risks associated with sea-level rise, probabilistic forecasts are needed. These require estimates of the probability density function (PDF) for various model parameters (e.g. the basal drag coefficient and ice viscosity). To infer such parameters from satellite observations it is common to use inverse methods. Two related approaches are in use: (1) minimization of a cost function that describes the misfit to the observations, often accompanied by explicit or implicit regularization, or (2) use of Bayes’ theorem to update prior assumptions about the probability of parameters. Both approaches have much in common and questions of regularization often map onto implicit choices of prior probabilities that are made explicit in the Bayesian framework. In both approaches questions can arise that seem to demand subjective input. One way to specify prior PDFs more objectively is by deriving transformation group priors that are invariant to symmetries of the problem, and then maximizing relative entropy, subject to any additional constraints. Here we investigate the application of these methods to the derivation of priors for a Bayesian approach to an idealized glaciological inverse problem.

The observable microstructures in ice are the result of many dynamic and competing processes. These processes are influenced by climate variables in the firn. Layers deposited in different climate regimes may show variations in fabric which can persist deep into the ice sheet; fabric may ‘remember’ these past climate regimes. We model the evolution of fabric variations below the firn–ice transition and show that the addition of shear to compressive-stress regimes preserves the modeled fabric variations longer than compression-only regimes, because shear drives a positive feedback between crystal rotation and deformation. Even without shear, the modeled ice retains memory of the fabric variation for 200 ka in typical polar ice-sheet conditions. Our model shows that temperature affects how long the fabric variation is preserved, but only affects the strain-integrated fabric evolution profile when comparing results straddling the thermal-activation-energy threshold (∼−10°C). Even at high temperatures, migration recrystallization does not eliminate the modeled fabric’s memory under most conditions. High levels of nearest-neighbor interactions will, however, eliminate the modeled fabric’s memory more quickly than low levels of nearest-neighbor interactions. Ultimately, our model predicts that fabrics will retain memory of past climatic variations when subject to a wide variety of conditions found in polar ice sheets.

To better understand the risk of disasters due to glacial lake outburst floods (GLOFs), we synthetically analyze the spatial distribution and evolution of moraine-dammed lakes and potentially dangerous glacial lakes (PDGLs) in the Chinese Himalaya. Our county-based assessment of GLOF disaster risk combines PDGL outburst hazard, regional exposure, vulnerability of exposed elements and adaptation capability (risk management) using the analytic hierarchy process. We synthetically analyze the disaster risk using the weighted comprehensive method. Remote-sensing data show there are 329 moraine-dammed lakes (>0.02 km2; total area 125.43 km2) in the Chinese Himalaya, of which 116 (total area 49.49 km2) are identified as PDGLs. The zones at highest risk of GLOF disaster are mainly located in Nyalam, Tingri, Dinggyê, Lhozhag, Kangmar and Zhongba, in the mid-eastern Himalaya. Lowest-risk zones are located in the eastern Himalaya. On the county scale, Lhozhag and Lhunze have the highest hazard degrees and exposure, while Zhongba and Zando have the highest degree of vulnerability and lowest adaptation capacity. Our regionalization results for GLOF disaster risk are consistent with the distribution of historical disaster sites across the Chinese Himalaya.

We analyzed the dielectric spectra (0.1 Hz–1 MHz) of 49 firn and ice samples from ice sheets and glaciers to better understand how differing ice formation and evolution affect electrical properties. The dielectric relaxation of ice is well known and its characteristic frequency increases with the concentration of soluble impurities in the ice lattice. We found that meteoric ice and firn generally possess two such relaxations, indicating distinct crystal populations or zonation. Typically, one population is consistent with that of relatively pure ice, and the other is significantly more impure. However, high temperatures (e.g. temperate ice), long residence times (e.g. ancient ice from Mullins Glacier, Antarctica) or anomalously high impurity concentrations favor the development of a single relaxation. These relationships suggest that annealing causes two dielectrically distinct populations to merge into one population. The dielectric response of temperate ice samples indicates increasing purity with increasing depth, suggesting ongoing rejection of impurities from the lattice. Separately, subglacially (lake) frozen samples from the Vostok (Antarctica) 5G ice core possess a single relaxation whose variable characteristic frequency likely reflects the composition of the source water. We conclude that multi-frequency methods are essential to dielectric discrimination between different types of glacier ice.

The impact of climate change on the variability of local discharge was investigated in a glacierized high mountain catchment located in the source area of the Ürümqi river, northwest China. We used past climate records to drive a hydrological model to simulate the discharge from 2000 to 2008. The model was then used to project future discharge variations for the period 2041–60, based on a regionally downscaled climate-change scenario combined with three stages of glacier coverage (i.e. compared to the glacier coverage in 2008): unchanged glacier size (100% glacierized), recession of half the glacier area (50% glacierized) and complete disappearance of glaciers (0% glacierized). In each scenario, snowmelt will begin half a month earlier and the discharge will increase in May. For the 100% glacierized scenario, the discharge will increase by 66 ± 35% in a smaller (3.34 km2) and more glaciated (50%) catchment and 33 ± 20% in a larger (28.90 km2) and proportionally less glaciated (18%) catchment. If the glacier area reduces by half, the discharge will decrease by 8 ± 5% and 9 ± 6%, respectively. Once the glacier disappears, the discharge will decrease by 58 ± 20% and 40 ± 13%, respectively. Together, the results indicate that a warming climate and the resulting glacier shrinkage will cause significant changes in the volume and timing of runoff.

In this study we present 19 new or re-analysed series of glacier-wide seasonal mass balance for the Swiss Alps based on direct measurements. The records partly start around 1920 and continue until today. Previously unpublished and unevaluated observations of point winter and annual balance are compiled from various sources and archives. These highly valuable datasets have not yet been consistently evaluated and were thus unavailable to the scientific community. Using distributed modelling for spatial interpolation and extrapolation and homogenization of the point measurements, we infer continuous series of area-averaged mass balance. The results are validated against independent decadal ice volume changes from photogrammetric surveys. Six of the new seasonal series cover 60 years and more and add a substantial amount of information on the variations of regional glacier mass change. This will strengthen the worldwide collection of glacier monitoring data, especially for the data-sparse period before the 1980s. We compare our results to existing long-term series and present an updated assessment of mass-balance variability and glacier sensitivity throughout the European Alps.

Glacier volume and ice thickness distribution are important variables for water resource management in Norway and the assessment of future glacier changes. We present a detailed assessment of thickness distribution and total glacier volume for mainland Norway based on data and modelling. Glacier outlines from a Landsat-derived inventory from 1999 to 2006 covering an area of 2692 ± 81 km2 were used as input. We compiled a rich set of ice thickness observations collected over the past 30 years. Altogether, interpolated ice thickness measurements were available for 870 km2 (32%) of the current glacier area of Norway, with a total ice volume of 134 ± 23 km3. Results indicate that mean ice thickness is similar for all larger ice caps, and weakly correlates with their total area. Ice thickness data were used to calibrate a physically based distributed model for estimating the ice thickness of unmeasured glaciers. The results were also used to calibrate volume–area scaling relations. The calibrated total volume estimates for all Norwegian glaciers ranged from 257 to 300 km3.

The continued use of the positive degree-day (PDD) method to predict ice-sheet melt is generally favoured over surface energy-balance methods partly due to the computational efficiency of the algorithm and the requirement of only one input variable (temperature). In this paper, we revisit some of the assumptions governing the application of the PDD method. Using hourly temperature data from the GC-Net network we test the assumption that monthly PDD total (PDDM) can be represented by a Gaussian distribution with fixed standard deviation of monthly temperature (σM). The results presented here show that the common assumption of fixed σM does not hold, and that σM may be represented more accurately as a quadratic function of average monthly temperature. For Greenland, the mean absolute error in predicting PDDM using our methodology is 3.9°C d, representing a significant improvement on current methods (7.8°C d, when σM = 4.5°C). Over a range of glaciated settings, our method reproduces PDDM, on average, to within 1.5–8.5°C d, compared to 4.4–15.7°C d when σM = 4.5°C. The improvement arises because we capture the systematic reduction in temperature variance that is observed over melting snow and ice, when surface temperatures cannot warm above 0°C.

This study shows how a new generation of terrestrial laser scanners can be used to investigate glacier surface ablation and other elements of glacial hydrodynamics at exceptionally high spatial and temporal resolution. The study area is an Alpine valley glacier, Haut Glacier d’Arolla, Switzerland. Here we use an ultra-long-range lidar RIEGL VZ-6000 scanner, having a laser specifically designed for measurement of snow- and ice-cover surfaces. We focus on two timescales: seasonal and daily. Our results show that a near-infrared scanning laser system can provide high-precision elevation change and ablation data from long ranges, and over relatively large sections of the glacier surface. We use it to quantify spatial variations in the patterns of surface melt at the seasonal scale, as controlled by both aspect and differential debris cover. At the daily scale, we quantify the effects of ogive-related differences in ice surface debris content on spatial patterns of ablation. Daily scale measurements point to possible hydraulic jacking of the glacier associated with short-term water pressure rises. This latter demonstration shows that this type of lidar may be used to address subglacial hydrologic questions, in addition to motion and ablation measurements.

Understanding physical processes in near-zero accumulation areas can help us to better understand polar ice-core records, particularly during periods when accumulation rates were lower than today. We report measurements from a 5 m firn core from the Allan Hills, Antarctica, which include physical properties using computer tomography, stable isotope ratios δD and δ18O, and 210Pb activity. The core shows a highly metamorphosed firn with homogeneous and stable structure, but with discrete layers near the surface. The observed firn structure is caused by a combination of unique depositional and post-depositional processes. The irregular δD and δ18O signal does not follow the stratigraphic sequence and implies post-depositional modification caused by microscopic pressure gradients in the firn that can result from either forced ventilation over rough surfaces in the presence of wind or alternating temperature-gradients between the firn and the atmosphere. Our results also indicate impact snow deposition under high winds and with a high initial density and air exchange between the atmosphere and the snowpack.210Pb activity below 0.3 m falls below the detection limit, implying that most of the core is more than 100 years old. We conclude that the Allan Hills record provides a unique opportunity to investigate important processes that would have affected ice-core records from glacial periods.

The Greenland ice sheet is experiencing dramatic melt that is likely to continue with rapid Arctic warming. However, the proportion of meltwater stored before reaching the global ocean remains difficult to quantify. We use NASA MODIS surface reflectance data to estimate river discharge from two West Greenland rivers – the Watson River near Kangerlussuaq and the Naujat Kuat River near Nuuk – over the summers of 2000–12. By comparison with in situ river discharge observations, ‘inundation–discharge’ relations were constructed for both rivers. MODIS-based total annual discharges agree well with total discharge estimated from in situ observations (86% of summer discharge in 2009 to 96% in 2011 at the Watson River, and 106% of total discharge in 2011 to 104% in 2012 at the Naujat Kuat River). We find, however, that a time-lapse camera, deployed at the Watson River in summer 2012, better captures the variations in observed discharge, benefiting from fewer data gaps due to clouds. The MODIS-derived estimates indicate that summer discharge has not significantly increased over the last decade, despite a strong warming trend. Also, meltwater runoff estimates derived from the regional climate model RACMO2/GR for the drainage basins are higher than our reconstructions of river discharge. These results provide indirect evidence for a considerable component of water storage within the glacio-hydrological system.

Snow avalanches are gravity-driven flows consisting of hard snow/ice particles. Depending on the snow quality, particularly temperature, avalanches exhibit different flow regimes, varying from dense flowing avalanches to highly disperse, mixed flowing-powder avalanches. In this paper we investigate how particle interactions lead to streamwise density variations, and therefore an understanding of why avalanches exhibit different flow types. A basic feature of our model is to distinguish between the velocity of the avalanche in the mean, downslope direction and the velocity fluctuations around the mean, associated with random particle movements. The mechanical energy associated with the velocity fluctuations is not entirely kinetic, as particle movements in the slope-perpendicular direction are inhibited by the hard boundary at the bottom giving rise to a change in flow height and therefore change in flow density. However, this volume expansion cannot occur without raising the center of mass of the particle ensemble, i.e. an acceleration, which, in turn, exerts a pressure on the bottom, the so-called dispersive pressure. As soon as the volume no longer expands, the dispersive pressure vanishes and the pressure returns to the hydrostatic pressure. Different streamwise density distributions, and therefore different avalanche flow regimes, are possible.

Discharge from marine-terminating outlet glaciers accounts for up to half the recent mass loss from the Greenland ice sheet, yet the causal factors are not fully understood. Here we assess the factors controlling the behaviour of Humboldt Glacier (HG), allowing us to evaluate the influence of basal topography on outlet glacier response to external forcing since part of HG’s terminus occupies a large overdeepening. HG’s retreat accelerated dramatically after 1999, coinciding with summer atmospheric warming of up to 0.19°C a–1 and sea-ice decline. Retreat was an order of magnitude greater in the northern section of the terminus, underlain by a major basal trough, than in the southern section, where the bedrock is comparatively shallow. Velocity change following retreat was spatially non-uniform, potentially due to a pinning point near HG’s northern lateral margin. Consistent with observations, numerical modelling demonstrates an order-of-magnitude greater sensitivity to sea-ice buttressing and crevasse depth (used as a proxy for atmospheric warming) in the northern section. The trough extends up to 72 km inland, so it is likely to facilitate sustained retreat and ice loss from HG during the 21st century.

To understand the dynamics of ice shelves, a knowledge of their internal and basal structure is very important. As the capacity to perform local surveys is limited, remote sensing provides an opportunity to obtain the relevant information. We must prove, however, that the relevant information can be obtained from remote sensing of the surface. That is the aim of this study. The Jelbart Ice Shelf, Antarctica, exhibits a variety of surface structures appearing as stripe-like features in radar imagery. We performed an airborne geophysical survey across these features and compared the results to TerraSAR-X imagery. We find that the stripe-like structures indicate surface troughs coinciding with the location of basal channels and crevasse-like features, revealed by radio-echo sounding. HH and VV polarizations do not show different magnitude. In surface troughs, the local accumulation rate is larger than at the flat surface. Viscoelastic modelling is used to gain an understanding of the surface undulations and their origin. The surface displacement, computed with a Maxwell model, matches the observed surface reasonably well. Our simulations show that the surface troughs develop over decadal to centennial timescales.

Repeated measurements of density profiles and surface elevation along a 515 km traverse of the Greenland ice sheet are used to determine elevation change rates and the error in determining mass-balance trends from these rates which arises from short-term fluctuations in mass input, compaction and surface density. Mean values of this error, averaged over 100 km sections of the traverse, decrease with time from the start of observations in 2004, with a half-time of ∼4 years. After 7 years the mean error is less than the ice equivalent mass imbalance.

In this study we compare the anisotropic flow relations for polycrystalline ice of Azuma and Goto-Azuma (1996), Thorsteinsson (2002), Placidi and others (2010) and Budd and others (2013). Observations from the Dome Summit South (DSS) ice-coring site at Law Dome, East Antarctica, are used to model the vertical distribution of deviatoric stress components at the borehole site. The flow relations in which the anisotropic rheology is parameterized by a scalar function, so that the strain-rate and deviatoric stress tensor components are collinear, provide simple shear and vertical compression deviatoric stress profiles that are most consistent with laboratory observations of tertiary creep in combined stress configurations. Those flow relations where (1) the anisotropy is derived from the magnitude of applied stresses resolved onto the basal planes of individual grains and (2) the macroscopic deformation is obtained via homogenization of individual grain responses provide stress estimates less consistent with laboratory observations. This is most evident in combined simple shear and vertical compression flow regimes where shear is dominant. Our results highlight the difficulties associated with developing flow relations which incorporate a physically based description of microdeformation processes. In particular, this requires that all relevant microdeformation, recrystallization and recovery processes are adequately parameterized.

We investigated the evolution of two major rifts cutting across Mertz Glacier Tongue, East Antarctica, using a combination of satellite images and 60 day sets of GPS data from two stations deployed either side of the western rift in 2007. The eastern rift began to open in the early 1990s, and the western rift initiated in 2002 in conjunction with the collision of a large iceberg with the tongue. Velocity time series derived from the 2007 GPS data exhibited strong variations at tidal periods modulated by sea-surface height and sea-surface slope and reproduced here with a conceptually simple model. We found that opening of the western rift in 2002 leads to a dramatic change in behavior of the tongue as the large range in velocity (700–2400 m a−1) observed in 2000 was largely reduced (1075–1225 m a−1) in 2007. Opening of the western rift decoupled the glacier from the transverse loading on the tongue driven by east–west tidal circulation. This loading previously induced time-varying lateral drag, which caused the large velocity range. Our results suggest changes in the mechanical behavior of an ice tongue impact the dynamics of the outlet glacier system and should be considered in longer-term mass-balance evaluations.