Controls on ERS altimeter measurements over ice sheets: Footprint-scale topography, backscatter fluctuations, and the dependence of microwave penetration depth on satellite orientation

We consider the reliability of radar altimeter measurements of ice sheet elevation and snowpack properties in the presence of surface undulations. We demonstrate that over ice sheets the common practice of averaging echoes by aligning the first return from the surface at the origin can result in a redistribution of power to later times in the average echo, mimicking the effects of microwave penetration into the snowpack. Algorithms that assume the topography affects the radar echo shape in the same way that waves affect altimeter echoes over the ocean will therefore lead to biased estimates of elevation. This assumption will also cause errors in the retrieval of echo-shape parameters intended to quantify the penetration of the microwave pulse into the snowpack. Using numerical simulations, we estimate the errors in retrievals of extinction coefficient, surface backscatter, and volume backscatter for various undulating topographies. In the flatter portions of the Antarctic plateau, useful estimates of these parameters may be recovered by averaging altimeter echoes recorded by the European Remote Sensing satellite (ERS-1). By numerical deconvolution of the average echoes we resolve the depths in the snowpack at which temporal changes and satellite travel-direction effects occur, both of which have the potential to corrupt measurements of ice sheet elevation change. The temporal changes are isolated in the surface-backscatter cross section, while directional effects are confined to the extinction coefficient and are stable from year to year. This allows the removal of the directional effect from measurement of ice-sheet elevation change

The impact of weather and climate variability upon estimates of ice-sheet mass balance from satellite radar altimeters

Satellite radar altimeters are being used to measure ice sheet mass balance by detecting changes in surface elevation. Climate variability may cause errors in these measurements by altering the structure of the snow and the penetration of the radar pulse. Three parameters describe the microwave penetration and scattering; the surface backscatter σ°surf, the volume backscatter σ°vol, the extinction coefficient ke, These parameters were measured in Antarctica using ERS-1 altimeter data and compared with satellite radiometer data, glaciological observations, and a scattering model, to determine the sensitivity of the radar echo to the snow structure. Echo distortion, caused by topographic undulations, limits the accuracy of σ°surf, σ°vol, and ke. In flatter regions though, the retrieval shows that reflections at layer interfaces beneath the surface generally account for most of the backscatter. Surface reflection can cause 60% of the backscatter in low accumulation regions prone to surface crusts. Only about 1% of the total backscatter arises from volume scattering by snow grains, although this mechanism controls the magnitude of ke. Only σ°surf changes on monthly timescales, through changes in the roughness and density of the surface snow. However, because of an anisotropy in snow structure in windy regions, ke and σ°vol depend upon the direction of travel of the satellite, which may vary between measurements. The sensitivity of ke and σ°vol to changes in accumulation rate, temperature and density is investigated, and used to calculate the errors in the mass balance which might be expected for measurement intervals of many years, and also to map accumulation rates on the plateau. By changing the rate of snow compaction, the meteorological boundary conditions can also alter the average density of the ice sheets, causing further errors in the mass balance measurement. A numerical model of time-variant snow densification was used to calculate the errors from this source. Overall, it is concluded that satellite radar altimeters are probably capable of reducing the present uncertainties in ice-sheet mass balance, but it will be essential to accompany each measurement with investigations into the climate during the measurement interval, and the preceding decades, to be certain. Similarly, it will be essential to monitor the scattering behaviour of the snow throughout each measurement

Exploring the use of transformation group priors and the method of maximum relative entropy for Bayesian glaciological inversions

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

Flow speed within the Antarctic ice sheet and its controls inferred from satellite observations

Accurate dynamical models of the Antarctic ice sheet with carefully specified initial conditions and well-calibrated rheological parameters are needed to forecast global sea level. By adapting an inverse method previously used in electric impedance tomography, we infer present-day flow speeds within the ice sheet. This inversion uses satellite observations of surface velocity, snow accumulation rate, and rate of change of surface elevation to estimate the basal drag coefficient and an ice stiffness parameter that influences viscosity. We represent interior ice motion using a vertically integrated approximation to incompressible Stokes flow. This model represents vertical shearing within the ice and membrane stresses caused by horizontal stretching and shearing. Combining observations and model, we recover marked geographical variations in the basal drag coefficient. Relative changes in basal shear stress are smaller. No simple sliding law adequately represents basal shear stress as a function of sliding speed. Low basal shear stress predominates in central East Antarctica, where thick insulating ice allows liquid water at the base to lubricate sliding. Higher shear stress occurs in coastal East Antarctica, where a frozen bed is more likely. Examining Thwaites glacier in more detail shows that the slowest sliding often coincides with elevated basal topography. Differences between our results and a similar adjoint-based inversion suggest that inversion or regularization methods can influence recovered parameters for slow sliding and finer scales; on broader scales we recover a similar pattern of low basal drag underneath major ice streams and extensive regions in East Antarctica that move by basal sliding

The sensitivity of West Antarctica to the submarine melting feedback

We use an ice sheet model with realistic initial conditions to forecast how the Amundsen Sea sector of West Antarctica responds to recently observed rates of submarine melting. In these simulations, we isolate the effects of a positive feedback, driven by submarine melt in new ocean cavities flooded during retreat, by allowing the present climate, calving front and melting beneath existing ice shelves to persist over the 21st century. Even without additional forcing from changes in climate, ice shelf collapse, or ice cliff collapse, the model predicts slow, sustained retreat of West Antarctica, driven by the marine ice sheet instability and current levels of ocean-driven melting. When observed rates of melting are included in new subglacial ocean cavities, the simulated sea level contribution increases, and for sufficiently intense melting it accelerates over time. Conditional Bayesian probabilities for sea level contributions can be derived but will require improved predictions of ocean heat delivery

A comparative study of participatory and household risk assessments and an investigation into the impact of a participatory risk assessment to effect change: case study: Section D, Sweet Home farm, Cape Town

Includes bibliographical references (leaves 68-80).This research aimed to compare the respective contributions of Participatory Action Research (PAR) and household surveys to inform understanding of informal settlement risks and the impact/influence of PAR to effect change. Urban risks in Section D of Sweet Home Farm informal settlement in the City of Cape Town were examined through the lenses of community risk assessment (CRA) and household survey methodologies conducted sixteen months apart. The results described a risk profile for the study site, which was similar to that of many of Cape Town's informal settlements. However, there was more concern over chronic "everyday" threats, such as the disposal of solid waste and crime, rather than fire and flood, which are prioritised by the City. This stressed the need for risk assessments at the local level

Representing grounding line migration in synchronous coupling between a marine ice sheet model and a z-coordinate ocean model

Synchronous coupling is developed between an ice sheet model and a z-coordinate ocean model (the MITgcm). A previously-developed scheme to allow continuous vertical movement of the ice-ocean interface of a floating ice shelf (“vertical coupling”) is built upon to allow continuous movement of the grounding line, or point of floatation of the ice sheet (“horizontal coupling”). Horizontal coupling is implemented through the maintenance of a thin layer of ocean ( ∼ 1 m) under grounded ice, which is inflated into the real ocean as the ice ungrounds. This is accomplished through a modification of the ocean model’s nonlinear free surface evolution in a manner akin to a hydrological model in the presence of steep bathymetry. The coupled model is applied to a number of idealized geometries and shown to successfully represent ocean-forced marine ice sheet retreat while maintaining a continuous ocean circulation

Highly variable friction and slip observed at Antarctic ice stream bed

The slip of glaciers over the underlying bed is the dominant mechanism governing the migration of ice from land into the oceans, with accelerating slip contributing to sea-level rise. Yet glacier slip remains poorly understood, and observational constraints are sparse. Here we use passive seismic observations to measure both frictional shear stress and slip at the bed of the Rutford Ice Stream in Antarctica using 100,000 repetitive stick-slip icequakes. We find that basal shear stresses and slip rates vary from 10$^4$ to 10$^7$ Pa and 0.2 to 1.5 m per day, respectively. Friction and slip vary temporally over the order of hours, and spatially over 10s of metres, due to corresponding variations in effective normal stress and ice–bed interface material. Our findings suggest that the bed is substantially more complex than currently assumed in ice stream models and that basal effective normal stresses may be significantly higher than previously thought. Our observations can provide constraints on the basal boundary conditions for ice-dynamics models. This is critical for constraining the primary contribution of ice mass loss in Antarctica and hence for reducing uncertainty in sea-level rise projections

Snow densification and recent accumulation along the iSTAR traverse, Pine Island Glacier, Antarctica

Neutron probe measurements of snow density from 22 sites in the Pine Island Glacier basin have been used to determine mean annual accumulation using an automatic annual-layer identification routine. A mean density profile which can be used to convert radar two-way-travel times to depth has been derived, and the effect of annual fluctuations in density on estimates of the depth of radar reflectors is shown to be insignificant, except very near the surface. Vertical densification rates have been derived from the neutron probe density profiles and from deeper firn core density profiles available at 9 of the sites. These rates are consistent with the rates predicted by the Herron and Langway model for stage 1 densification (by grain-boundary sliding, grain growth and intracrystalline deformation) and stage 2 densification (predominantly by sintering), except in a transition zone extending from ≈8 to ≈13 m from the surface in which 10–14% of the compaction occurs. Profiles of volumetric strain rate at each site show that in this transition zone the rates are consistent with the Arthern densification model. Comparison of the vertical densification rates and volumetric strain rates indicates that the expected relation to mean annual accumulation breaks down at high accumulation rates even when corrections are made for horizontal ice velocity divergence