Converting measurements of ice-sheet surface elevation change to mass change requires measurements of accumulation and knowledge of the evolution of the density profile in the firn. Most firn-densification models are tuned using measured depth–density profiles, a method which is based on an assumption that the density profile in the firn is invariant through time. Here we present continuous measurements of firn-compaction rates in 12 boreholes near the South Pole over a 2 year period. To our knowledge, these are the first continuous measurements of firn compaction on the Antarctic plateau. We use the data to derive a new firn-densification algorithm framed as a constitutive relationship. We also compare our measurements to compaction rates predicted by several existing firn-densification models. Results indicate that an activation energy of 60 kJ mol−1, a value within the range used by current models, best predicts the seasonal cycle in compaction rates on the Antarctic plateau. Our results suggest models can predict firn-compaction rates with at best 7% uncertainty and cumulative firn compaction on a 2 year timescale with at best 8% uncertainty.

Crary Ice Rise formed after the Ross Ice Shelf re-grounded ~1 kyr BP. We present new ice-penetrating radar data from two systems operating at center frequencies of 7 and 750 MHz that confirm the ice rise is composed of a former ice shelf buried by subsequent accumulation. Stacks of englacial diffraction hyperbolas are present almost everywhere across the central ice rise and extend up to ~350 m above the bed. In many cases, bed reflections beneath the diffraction hyperbolas are obscured for distances up to 1 km. Waveform modeling indicates that the diffraction hyperbolas are likely caused by marine ice deposits in former basal crevasses and rifts. The in-filling of rifts and basal crevasses may have strengthened the connection between the ice rise and the surrounding ice shelf, which could have influenced local and regional ice dynamics. Three internal reflection horizons mark the upper limit of disturbed ice and diffraction hyperbolas in different sections of the ice rise, indicating at least three stages of flow stabilization across the ice rise. A surface lineation visible in MODIS imagery corresponds spatially to deepening and strong deformation of these layers, consistent with the characteristics of former grounding lines observed elsewhere in Antarctica.

Radar sounding is a powerful geophysical approach for characterizing the subsurface conditions of terrestrial and planetary ice masses at local to global scales. As a result, a wide array of orbital, airborne, ground-based, and in situ instruments, platforms and data analysis approaches for radioglaciology have been developed, applied or proposed. Terrestrially, airborne radar sounding has been used in glaciology to observe ice thickness, basal topography and englacial layers for five decades. More recently, radar sounding data have also been exploited to estimate the extent and configuration of subglacial water, the geometry of subglacial bedforms and the subglacial and englacial thermal states of ice sheets. Planetary radar sounders have observed, or are planned to observe, the subsurfaces and near-surfaces of Mars, Earth's Moon, comets and the icy moons of Jupiter. In this review paper, and the thematic issue of the Annals of Glaciology on ‘Five decades of radioglaciology’ to which it belongs, we present recent advances in the fields of radar systems, missions, signal processing, data analysis, modeling and scientific interpretation. Our review presents progress in these fields since the last radio-glaciological Annals of Glaciology issue of 2014, the context of their history and future prospects.

Accumulation rates and their spatio-temporal variability are important boundary conditions for ice-flow models. The depths of radar-detected internal layers can be used to infer the spatial variability of accumulation rates. Here we infer accumulation rates from three radar layers (26, 35 and 41 ka old) in the Vostok Subglacial Lake region using two methods: (1) the local-layer approximation (LLA) and (2) a combination of steady-state flowband modeling and formal inverse methods. The LLA assumes that the strain-rate history of a particle traveling through the ice sheet can be approximated by the vertical strain-rate profile at the current position of the particle, which we further assume is uniform. The flowband model, however, can account for upstream strain-rate gradients. We use the LLA to map accumulation rates over a 150 km × 350 km area, and we apply the flowband model along four flowbands. The LLA accumulation-rate map shows higher values in the northwestern corner of our study area and lower values near the downstream shoreline of the lake. These features are also present but less distinct in the flowband accumulation-rate profiles. The LLA-inferred accumulation-rate patterns over the three time periods are all similar, suggesting that the regional pattern did not change significantly between the start of the Holocene and the last ~20 ka of the last Glacial Period. However, the accumulation-rate profiles inferred from the flowband model suggest changes during that period of up to 1 cma–1 or ~50% of the inferred values.

Using a Monte Carlo (MC) method, we determine the accumulation-rate profile along a flowband, the influx of ice into the upstream end of the flowband and the age of an internal layer. The data comprise the depth profile of the internal layer, a few velocity measurements at the surface and the average accumulation at one location. The data in our example were collected at Taylor Mouth, a flank site off Taylor Dome, Antarctica. We present three alternative formulations of this inverse problem. Depending on the formulation used, this particular inverse problem can have up to four solutions, each corresponding to a different spatial accumulation-rate pattern. This study demonstrates the ability of a MC method to find several solutions to this inverse problem, and how to use a Metropolis algorithm to determine the probability distribution of each of these different solutions. The only disadvantage of the MC method is that it is computationally more expensive than other inverse methods, such as the Gradient method.

When an ice-flow model is constrained by data that exist over only a section of an ice sheet, it is computationally advantageous to limit the model domain to only that section. For example, a limited domain near an ice-core site might cross an ice divide, and have no termini. Accurately calculating ice-sheet evolution in response to spatial and temporal variations in climate and ice flow depends on accurately calculating the transient ice flux crossing the limited-domain boundaries. In the absence of information from outside the limited domain, this is an ill-posed problem. Boundary conditions based only on information from inside the limited domain can produce ice-sheet evolution incompatible with the full ice sheet within which we suppose it to exist. We use impulse-response functions to provide boundary values that are informed by the external ice sheet, without conventionally 'nesting' the limited domain in a full ice-sheet model. Evolution within a limited domain can then be consistent with evolution of boundary conditions is designed for future use in affected the limited domain can be inferred from the full ice sheet. Our treatment of limited-domain an inverse problem in which external changes that data from within the limited domain.

The spatial pattern of accumulation rate can be inferred from internal layers in glaciers and ice sheets. Non-dimensional analysis determines where finite strain can be neglected (‘shallow-layer approximation’) or approximated with a local one-dimensional flow model (‘local-layer approximation’), and where gradients in strain rate along particle paths must be included (‘deep layers’). We develop a general geophysical inverse procedure to infer the spatial pattern of accumulation rate along a steady-state flowband, using measured topography of the ice-sheet surface, bed and a ‘deep layer’. A variety of thermomechanical ice-flow models can be used in the forward problem to calculate surface topography and ice velocity, which are used to calculate particle paths and internal-layer shapes. An objective tolerance criterion prevents over-fitting the data. After making site-specific simplifications in the thermomechanical flow algorithm, we find the accumulation rate along a flowband through Taylor Mouth, a flank site on Taylor Dome, Antarctica, using a layer at approximately 100 m depth, or 20% of the ice thickness. Accumulation rate correlates with ice-surface curvature. At this site, gradients along flow paths critically impact inference of both the accumulation pattern, and the depth-age relation in a 100 m core.

The mean, trend and variability of net snow accumulation in firn cores are often used to validate model output, develop remote-sensing algorithms and quantify ice-sheet surface mass balance. Thus, accurately defining uncertainties associated with these in situ measurements is critical. In this study, we apply statistical simulation methods to quantify the uncertainty in firn-core accumulation data due to the uncertainty in depth–age scales. The methods are applied to a suite of firn cores from central West Antarctica. The results show that uncertainty in depth–age scales can give rise to spurious trends in accumulation that are the same order of magnitude as accumulation trends reported in West Antarctica. The depth–age scale uncertainties also significantly increase the apparent interannual accumulation variability, so these uncertainties must first be accounted for before using firn-core data to assess such processes as small-spatial-scale variability. Better quantification of error in accumulation will improve our ability to meaningfully compare firn-core data across different regions of the ice sheet, and provide appropriate targets for calibration and/or validation of model output and remote-sensing data.