Accurate modeling of calving glaciers relies on knowledge of many processes (ice flow, surface/submarine melting, calving, mélange interaction) and glacier-specific factors (air temperature, ocean circulation, precipitation rate, glacier geometry) that remain challenging to assess. Iceberg calving, especially, is important to glacier mass loss and difficult to resolve in currently-available models. Given these challenges facing even the most sophisticated models, there is value in simple, computationally-efficient models that can capture first-order effects. In this study we derive a simple model, extending Nye's perfect plastic approximation to include a yield surface at the calving front. With one climate-related input—either an upstream glacier thinning rate or glacier-wide accumulation—this model is able to simulate the advance and retreat of marine-terminating glaciers on annual to decadal scales. Our model requires knowledge of only two glacier-specific factors: glacier bed topography and basal shear strength, both reasonably constrained by laboratory and field observations. We apply the model to a case study of Columbia Glacier, Alaska and show that, despite its simplicity, the model succeeds in reproducing observed centerline profiles and rates of terminus retreat up to 2007.

To improve our knowledge of glacier area changes in the central Chilean and Argentinean Andes (32°9′S–33°4′S), two new glacier inventories from 1989 to 2013/14 are compared with a reinterpreted inventory from 1955. Comparisons show glacier area retreat of 30 ± 3% since 1955, decreasing from 134 to 94 km2 in 2013/14, whilst the annual rate of area loss showed a small increase (insignificant) between the periods of 1955–1989 and 1989–2013/14. Separate analysis of the 1989 and 2013/14 inventories, including a larger sample, revealed a higher rate of glacier change compared with the smaller samples of these inventories. Additionally, an analysis at ~5 year intervals for six major glaciers (1955–2013) indicates large variability in response times and area loss magnitudes. Glacier Olivares Alfa, for example, lost 63% of its ice area, while the Juncal Norte Glacier lost only 10% (1955–2013). The findings from this study improve our current knowledge base concerning widespread glacier decline in the southern Andes, and furthers monitoring efforts in this poorly described region of the world, a region containing vital water resources for populated areas in South America.

The McMurdo Dry Valleys are a cold, dry polar desert and the alpine glaciers therein exhibit small annual and seasonal mass balances, often <±0.06 m w.e. Typically, winter is the accumulation season, but significant snow storms can occur any time of year occasionally making summer the accumulation season. The yearly equilibrium line altitude is poorly correlated with mass balance because the elevation gradient of mass balance on each glacier can change dramatically from year to year. Most likely, winds redistribute the light snowfall disrupting the normal gradient of increasing mass balance with elevation. Reconstructed cumulative mass balance shows that the glaciers have lost <2 m w.e. over the past half century and area changes show minimal retreat. In most cases these changes are less than the uncertainty and the glaciers are considered in equilibrium. Since 2000, however, the glaciers have lost mass despite relatively stable summer air temperatures suggesting a different mechanism in play. Whether this trend is a harbinger of future changes or a temporary excursion is unclear.

Remote sensing is a powerful method to reconstruct annual mass-balance series over past decades by exploiting archives of available images, as well as to study glaciers in inaccessible regions. We present the application of a methodological framework based only on optical satellite images to retrieve glacier-wide annual mass balances for 30 glaciers in the French Alps. The glacier-wide annual mass balance for the period 1983–2014 was reconstructed by combining changes in glacier volumes computed from remote-sensing derived DEMs with annual measurements of the snow line altitude on satellite images. Data from direct observations on two of the glaciers confirmed the accuracy of the annual mass balances quantified by remote sensing with an average difference of ~0.3 m w.e., within the uncertainty range of the methods. Our results confirm the significant increase in mass loss since the early 2000s, with a difference >1 m w.e. a−1 between the periods 1983–2002 and 2003–14. The region-wide mass balance for the French Alps over the period 1979–2011 was −0.66 ± 0.27 m w.e. a−1, close to that of the European Alps. We also show that changes in glacier surface area or length are not representative of changes in mass balance at the scale of a few decades.

Terrestrial time-lapse photography offers insight into glacial processes through high spatial and temporal resolution imagery. However, oblique camera views complicate measurement in geographic coordinates, and lead to reliance on specific imaging geometries or simplifying assumptions for calculating parameters such as ice velocity. We develop a novel approach that integrates time-lapse imagery with multitemporal DEMs to derive full three-dimensional coordinates for natural features tracked throughout a monoscopic image sequence. This enables daily independent measurement of horizontal (ice flow) and vertical (ice melt) velocities. By combining two terrestrial laser scanner surveys with a 73 days sequence from Sólheimajökull, Iceland, variations in horizontal ice velocity of ~10% were identified over timescales of ~25 days. An overall decrease of ~3.0 m surface elevation showed asynchronous rate changes with the horizontal velocity variations, demonstrating a temporal disconnect between the processes of ice surface lowering and mechanisms of glacier movement. Our software, ‘Pointcatcher’, is freely available for user-friendly interactive processing of general time-lapse sequences and includes Monte Carlo error analysis and uncertainty in projection onto DEM surfaces. It is particularly suited for analysis of challenging oblique glacial imagery, and we discuss good features to track, both for correction of camera motion and for deriving ice velocities.

C band backscatter parameters contain information about the upper snowpack/firn in the dry snow zone. The wide incidence angle diversity of the Advanced Scatterometer (ASCAT) gives unprecedented characterisation of backscatter anisotropy, revealing the backscatter response to climatic forcing. The A (isotropic component) and M2 (bi-sinusoidal azimuth anisotropy) parameters are investigated here, in conjunction with data from atmospheric and snowpack models, to identify the backscatter response to surface forcing parameters (wind speed and persistence, precipitation, surface temperature, density and grain size). The long-term mean A parameter is successfully recreated with a regression using these drivers, indicating strong links between the A parameter and precipitation on long timescales. While the ASCAT time series is too short to determine which factors drive observed trends, factors influencing the seasonal and short timescale variability are revealed. On these timescales, A strongly responds to the propagation of surface temperature cycles/anomalies downward through the firn, via direct modulation of the dielectric constant. The influence of precipitation on A is small at shorter timescales. The M2 parameter is controlled by wind speed and persistence, through modification of monodirectionally-aligned surface roughness. This variability indicates that throughout much of coastal Antarctica, a microwave ‘snapshot’ is generally not representative of longer-term conditions.

Greenland's marine-terminating glaciers may be sensitive to oceanic heat, but the fjord processes controlling delivery of this heat to glacier termini remain poorly constrained. Here we use a three-dimensional numerical model of Kangerdlugssuaq Fjord, East Greenland, to examine controls on fjord/shelf exchange. We find that shelf-forced intermediary circulation can replace up to ~25% of the fjord volume with shelf waters within 10 d, while buoyancy-driven circulation (forced by subglacial runoff from marine-terminating glaciers) exchanges ~10% of the fjord volume over a 10 d period under typical summer conditions. However, while the intermediary circulation generates higher exchange rates between the fjord and shelf, the buoyancy-driven circulation is consistent over time hence more efficient at transporting water along the full length of the fjord. We thus find that buoyancy-driven circulation is the primary conveyor of oceanic heat to glaciers during the melt season. Intermediary circulation will however dominate during winter unless there is sufficient input of fresh water from subglacial melting. Our findings suggest that increasing shelf water temperatures and stronger buoyancy-driven circulation caused the heat available for melting at Kangerdlugssuaq Glacier to increase by ~50% between 1993–2001 and 2002–11, broadly coincident with the onset of rapid retreat at this glacier.

Near-surface air temperature is an important determinant of the surface energy balance of glaciers and is often represented by a constant linear temperature gradients (TGs) in models. Spatio-temporal variability in 2 m air temperature was measured across the debris-covered Miage Glacier, Italy, over an 89 d period during the 2014 ablation season using a network of 19 stations. Air temperature was found to be strongly dependent upon elevation for most stations, even under varying meteorological conditions and at different times of day, and its spatial variability was well explained by a locally derived mean linear TG (MG–TG) of −0.0088°C m−1. However, local temperature depressions occurred over areas of very thin or patchy debris cover. The MG–TG, together with other air TGs, extrapolated from both on- and off-glacier sites, were applied in a distributed energy-balance model. Compared with piecewise air temperature extrapolation from all on-glacier stations, modelled ablation, using the MG–TG, increased by <1%, increasing to >4% using the environmental ‘lapse rate’. Ice melt under thick debris was relatively insensitive to air temperature, while the effects of different temperature extrapolation methods were strongest at high elevation sites of thin and patchy debris cover.

If a series of glacial advances occurs over the same pathway, the moraines that are now present may constitute an incomplete record of the total history. This is because a given advance can destroy the moraine left by a previous one, if the previous advance was less extensive. Gibbons, Megeath and Pierce (GMP) formulated an elegant stochastic model for this process; the key quantity in their analysis is $\bi P(n\vert N)$, the probability that n moraines are preserved after N glacial advances. In their paper, GMP derive a recursion formula satisfied by $\bi P(n\vert N)$, and use this formula to compute values of P for a range of values of n and N. In the present paper, we derive an explicit general answer for $\bi P(n\vert N)$, and show explicit, exact results for the mean value and standard deviation of n. We use these results to develop more insight into the consequences of the GMP model; for example, to a good approximation, 〈n〉 increases as ln(N). We explain how a Bayesian approach can be used to analyze $\bi P(N\vert n)$, the probability that there were N advances, given that we now observe n moraines.