This paper examines the effect of basal topography and strength on the grounding-line position, flux and stability of rapidly-sliding ice streams. It does so by supposing that the buoyancy of the ice stream is small, and of the same order as the longitudinal stress gradient. Making this scaling assumption makes the role of the basal gradient and accumulation rate explicit in the lowest order expression for the ice flux at the grounding line and also provides the transcendental equation for the grounding-line position. It also introduces into the stability condition terms in the basal curvature and accumulation-rate gradient. These expressions revert to well-established expressions in circumstances in which the thickness gradient is large at the grounding line, a result which is shown to be the consequence of the non-linearity of the flow. The behaviour of the grounding-line flux is illustrated for a range of bed topographies and strengths. We show that, when bed topography at a horizontal scale of several tens of ice thicknesses is present, the grounding-line flux and stability have more complex dependencies on bed gradient than that associated with the 'marine ice-sheet instability hypothesis', and that unstable grounding-line positions can occur on prograde beds as well as stable positions on retrograde beds.

The dynamics of a marine ice sheet's grounding lines determine the rate of ice discharge from the grounded part of ice sheet into surrounding oceans. In many locations in West Antarctica ice flows into ice shelves through ice streams experiencing low driving stress. However, existing simple theories of marine ice sheets are developed under the assumption of high basal and driving stress. Here we analyze the grounding line behavior of marine ice streams experiencing low basal shear and driving stress. We find that in this regime, the ice flux at the grounding line is a complex function of the geometry of the ice-stream bed, net accumulation rate and gradient of the net accumulation rate. Our analysis shows that the stability of distinct steady states is determined by the same parameters, suggesting a more complex (in)stability criterion than what is commonly referred to within the context of the 'marine ice-sheet instability hypothesis'. We also determine characteristic timescales (e-folding time) of ice-sheet configurations perturbed from their steady states. These timescales can be used to determine whether particular configurations can be considered in isolation from other components of the climate system or whether their effects and feedbacks between the ice sheet and the rest of the climate system have to be taken into account.

This paper develops a model of the synthetic aperture, interferometric satellite radar altimeter echo power, and echo cross-product. The model uses the smallness of the satellite pitch and roll angles, and the limited range of satellite altitude to provide a semianalytical echo model, whose numerical dimensions are limited to two in the synthetic aperture case or three in the interferometric case at large roll angles, making its application to extensive data practical. By not implementing the synthetic beam formation, it is demonstrated that the model recovers the conventional case of a pulse-limited altimeter. A theoretical description of the fluctuations in the multilooked, interferometric cross-product, and the synthetic aperture and pulse-limited powers is given by extending the model to describe correlations between individual looks in each case. The model offers the potential to retrieve ocean-surface parameters from synthetic aperture and pulse-limited altimeter data simultaneously, with obvious application to the new generation of altimeters onboard CryoSat-2, Sentinel-3, and Sentinel-6 during the transition to operational synthetic aperture radar altimetry.

Arctic sea surface height (SSH) is poorly observed by radar altimeters due to the poor coverage of the polar oceans provided by conventional altimeter missions and because large areas are perpetually covered by sea ice, requiring specialized data processing. We utilize SSH estimates from both the ice-covered and ice-free ocean to present monthly estimates of Arctic Dynamic Ocean Topography (DOT) from radar altimetry south of 81.5 degrees N and combine this with GRACE ocean mass to estimate steric height. Our SSH and steric height estimates show good agreement with tide gauge records and geopotential height derived from Ice-Tethered Profilers. The large seasonal cycle of Arctic SSH (amplitude similar to 5 cm) is dominated by seasonal steric height variation associated with seasonal freshwater fluxes, and peaks in October-November. Overall, the annual mean steric height increased by 2.2 +/- 1.4 cm between 2003 and 2012 before falling to circa 2003 levels between 2012 and 2014 due to large reductions on the Siberian shelf seas. The total secular change in SSH between 2003 and 2014 is then dominated by a 2.1 +/- 0.7 cm increase in ocean mass. We estimate that by 2010, the Beaufort Gyre had accumulated 4600 km(3) of freshwater relative to the 2003-2006 mean. Doming of Arctic DOT in the Beaufort Sea is revealed by Empirical Orthogonal Function analysis to be concurrent with regional reductions in the Siberian Arctic. We estimate that the Siberian shelf seas lost similar to 180 km(3) of freshwater between 2003 and 2014, associated with an increase in annual mean salinity of 0.15 psu yr(-1). Finally, ocean storage flux estimates from altimetry agree well with high-resolution model results, demonstrating the potential for altimetry to elucidate the Arctic hydrological cycle.

This is the author accepted manuscript. The final version is available from The International Glaciological Society via http://dx.doi.org/10.3189/2015JoG14J123

Changes in Arctic sea ice volume affect regional heat and freshwater budgets and patterns of atmospheric circulation at lower latitudes. Despite a well-documented decline in summer Arctic sea ice extent by about 40% since the late 1970s, it has been difficult to quantify trends in sea ice volume because detailed thickness observations have been lacking. Here we present an assessment of the changes in Northern Hemisphere sea ice thickness and volume using five years of CryoSat-2 measurements. Between autumn 2010 and 2012, there was a 14% reduction in Arctic sea ice volume, in keeping with the long-term decline in extent. However, we observe 33% and 25% more ice in autumn 2013 and 2014, respectively, relative to the 2010–2012 seasonal mean, which offset earlier losses. This increase was caused by the retention of thick sea ice northwest of Greenland during 2013 which, in turn, was associated with a 5% drop in the number of days on which melting occurred—conditions more typical of the late 1990s. In contrast, springtime Arctic sea ice volume has remained stable. The sharp increase in sea ice volume after just one cool summer suggests that Arctic sea ice may be more resilient than has been previously considered. Changes in Arctic sea ice volume are difficult to quantify. Five years of satellite data reveal a reduction in autumn sea ice volume in 2010–2012, but a sharp increase in 2013 and 2014, suggesting that ice volume can recover quickly.

Density profiles in the upper 10–14 m of snow have been measured along a 500 km traverse across the Greenland ice sheet, using a neutron scattering technique. Repeat measurements, over periods ranging from a few days to 5 years, allow strain rates to be determined as a function of depth. Very large strain rates are observed in the surface layer of snow over summer periods. In the underlying multiyear snow, strain rate decreases with decreasing porosity. However, once this effect has been removed, the effect of increasing overburden pressure is counteracted by increasing strength of the material. There are fluctuations in strain rate associated with the annual layering, which indicate that winter and summer snow have different strengths. Based on these observations, we derive a new densification equation which includes the effect of snow density and snow type, and the effect of temperature, described by an Arrhenius expression with activation energy of the order of 110 kJ mol−1 and an exponential prefactor determined simply by the temperature history of the snow. For multiyear snow and meteorological conditions that do not vary from year to year, our equation reduces to a form similar to the Herron and Langway equation for first‐stage densification. Using the new equation, we calculate the sensitivity of compaction rate to short‐term fluctuations in temperature and accumulation as 0.11–0.20 m a−1 K−1 and 0.33–0.95 m a−1(meters water equivalent)−1, respectively, and discuss the consequent uncertainty in satellite measurements of the long‐term elevation trend in this area of the Greenland ice sheet.

The most effective way of determining the rate of elevation change of the Earth's large ice sheets using radar altimeters is to examine the difference in the elevation measured on ascending and descending orbits. This crossover difference has a static and time-varying component, and by isolating the time-varying part, one can construct a time series of the ice sheet elevation change. The static component of the crossover difference arises as a result of an anisotropic dependence of the extinction coefficient on the angle between the radar polarization and wind-induced features of the firn. Here, the static crossover difference observed by CryoSat-2 over the Antarctic ice sheet is examined, and a simple model is developed to explain the observed pattern. There is an excellent agreement between the modeled results and the observations, calling into question the results of previous studies of the same phenomenon with different radar altimeters.

This letter describes the retrieval of the pitch of the CryoSat-2 satellite from the full bit rate (FBR) SAR mode data that are collected over the ocean by the SAR/Interferometric Radar Altimeter (SIRAL). Starting with the FBR SAR mode data, we form beams at the forward and backward look angles with respect to the nadir direction. If the satellite is flying pitched, the asymmetrical weighting of the echo power in the forward-looking and backward-looking beams that resulted from the along-track antenna gain pattern is used to measure the pitch of the satellite. The method depends on accurate knowledge of the orbit and the altimeter echoes only. In consequence, we are able to compare the results with the contemporaneous pitch value that is measured by the onboard star trackers, and particularly, we are able to determine a bias in the star tracker pitch measurements. We find that the star trackers' pitch measurements are biased, with a constant offset of 0.055 ° ± 0.0073 °. Because the star tracker attitude is used to inform the onboard control system, this bias implies that CryoSat-2 is flying nose up, with an average pitch of about 0.055 °.

We use 3 years of Cryosat-2 radar altimeter data to develop the first comprehensive assessment of Antarctic ice sheet elevation change. This new data set provides near-continuous (96%) coverage of the entire continent, extending to within 215 km of the South Pole and leading to a fivefold increase in the sampling of coastal regions where the vast majority of all ice losses occur. Between 2010 and 2013, West Antarctica, East Antarctica, and the Antarctic Peninsula changed in mass by -134 +/- 27, -3 +/- 36, and -23 +/- 18 Gt yr(-1), respectively. In West Antarctica, signals of imbalance are present in areas that were poorly surveyed by past missions, contributing additional losses that bring altimeter observations closer to estimates based on other geodetic techniques. However, the average rate of ice thinning in West Antarctica has also continued to rise, and mass losses from this sector are now 31% greater than over the period 2005-2010.

We use satellite observations to show that, between 1992 and 2011, the Pine Island Glacier hinge line retreated at a rate of 0.950.09 km yr(-1) despite a progressive steepening and shoaling of the glacier surface and bedrock slopes, respectively, which ought to impede retreat. The retreat has remained constant because the glacier terminus has thinned at an accelerating rate of 0.530.15 m yr(-2), with comparable changes upstream. This acceleration is consistent with an intensification of ocean-driven melting in the cavity beneath the floating section of the glacier. The pattern of hinge-line retreat meanders and is concentrated in isolated regions until ice becomes locally buoyant. Because the glacier-ocean system does not appear to have reached a position of relative stability, the lower limit of sea level projections may be too conservative.

This paper describes the calibration of the CryoSat-2 interferometer, whose principal purpose is to accurately measure the height of the Antarctic and Greenland ice sheets. A sequence of CryoSat-2 data acquisitions over the tropical and midlatitude oceans were obtained between June and September 2010, from the SIRAL "A" and redundant SIRAL "B" radars operating in their "SARIN" mode, during a sequence of satellite rolls between -0.6° and 0.4°. Using the arrival angle of the echo relative to the interferometer baseline, the attitude of the satellite determined by the star trackers, and estimates of the ocean surface across-track slope from the EGM08 geoid, we determined the errors in the interferometer estimate of surface slope as functions of the roll angle and ocean surface waveheight. These were found to be in close agreement with the theoretical description. The scale factor of the interferometric measurement of angle was determined to be 0.973 ± 0.002. We estimate the accuracy of the across-track slope measurement of the interferometer by applying this scale factor to the measured phase. In applying this scale factor to the measurements, the across-track slope of the marine geoid was obtained with an accuracy of 26 μrad at 10 km and 10 μrad at 1000 km. We conclude that the instrument performance considerably exceeds that needed for the accurate determination of height over the sloping surfaces of the continental ice sheets. The results also demonstrate that CryoSat-2 provides the first observations of the instantaneous vector gradient of the ocean surface, and that the normal-incidence interferometric configuration has a greater potential for the measurement of the ocean across-track slope than has been previously recognized.

Satellite records show a decline in ice extent over more than three decades, with a record minimum in September 2012. Results from the Pan‐Arctic Ice‐Ocean Modelling and Assimilation system (PIOMAS) suggest that the decline in extent has been accompanied by a decline in volume, but this has not been confirmed by data. Using new data from the European Space Agency CryoSat‐2 (CS‐2) mission, validated with in situ data, we generate estimates of ice volume for the winters of 2010/11 and 2011/12. We compare these data with current estimates from PIOMAS and earlier (2003–8) estimates from the National Aeronautics and Space Administration ICESat mission. Between the ICESat and CryoSat‐2 periods, the autumn volume declined by 4291 km 3 and the winter volume by 1479 km 3 . This exceeds the decline in ice volume in the central Arctic from the PIOMAS model of 2644 km 3 in the autumn, but is less than the 2091 km 3 in winter, between the two time periods.

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An increasing amount of freshwater has been stored in the Arctic Ocean over the past few decades. Satellite measurements of sea surface height reveal a spin-up of the Beaufort Gyre in the western Arctic that is associated with changes in the wind field, and is estimated to have led to the additional storage of about 8,000 km3 of freshwater. The Arctic Ocean’s freshwater budget comprises contributions from river runoff, precipitation, evaporation, sea-ice and exchanges with the North Pacific and Atlantic1. More than 70,000 km3 of freshwater2 are stored in the upper layer of the Arctic Ocean, leading to low salinities in upper-layer Arctic sea water, separated by a strong halocline from warm, saline water beneath. Spatially and temporally limited observations show that the Arctic Ocean’s freshwater content has increased over the past few decades, predominantly in the west3,4,5. Models suggest that wind-driven convergence drives freshwater accumulation6. Here we use continuous satellite measurements between 1995 and 2010 to show that the dome in sea surface height associated with the western Arctic Beaufort Gyre has been steepening, indicating spin-up of the gyre. We find that the trend in wind field curl—a measure of spatial gradients in the wind that lead to water convergence or divergence—exhibits a corresponding spatial pattern, suggesting that wind-driven convergence controls freshwater variability. We estimate an increase in freshwater storage of 8,000±2,000 km3 in the western Arctic Ocean, in line with hydrographic observations4,5, and conclude that a reversal in the wind field could lead to a spin-down of the Beaufort Gyre, and release of this freshwater to the Arctic Ocean.