The status of the world's public-domain digital topography of the land and ice

There has been no reasonably comprehensive survey of what digital, elevation models of the Earth's land surface exist in the public‐domain. We have performed a survey of these data, and we report on the coverage and cost of the data we have established. To qualify for inclusion in our coverage, we required the data to be available to the general public, obtainable from a specific, identified institution, and to have a determined cost. We have established that at 100 m resolution coverage exists of most of the the developed world. In the United States and Australia, the data are available at cost, at around 3000 km^{2} £^{-1}. In the remaining countries, the data are available from mapping agencies with varying commercial pricing strategies. The total cost of the data we have identified is £ 1,688,312. For much of the world we are unable to confirm the existence of such data, and our experience is that in these regions it will prove difficult to obtain digital, elevation data, if, indeed, it exists at all

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

Inland thinning of the Amundsen Sea sector, West Antarctica

[1] Together with the Pine Island glacier (PIG), the Thwaites (TG) and Smith (SG) glaciers are the principal drainage systems of the Amundsen Sea (AS) sector of Western Antarctica. Here we use satellite radar altimetry and interferometry to show that a rapid thinning of ice has occurred within the fastest flowing sections of all AS outlet glaciers. The pattern of thinning extends to distances greater than 150 km inland. Between 1991 and 2001, the TG and SG thinned by more than 25 and 45 m at their grounding lines, and a total of 154 +/- 16 km(3) of ice (or 0.43 mm of eustatic sea level rise) was lost from the AS sector glaciers to the ocean. We show that the thickness changes may have caused the PIG, TG, and SG to retreat inland by over 8, 4, and 7 km respectively, in line with independent estimates of grounding line migration

Bed topography and marine ice-sheet stability

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

Grounding line stability in a regime of low driving and basal stresses

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 accoun

Spatial and temporal evolution of Pine Island Glacier thinning, 1995-2006

We use ERS-2 and ENVISAT satellite radar altimetry to examine spatial and temporal changes in the rate of thinning of the Pine Island Glacier, West Antarctica, during the period 1995 to 2006. We show that the pattern of thinning has both accelerated and spread inland to encompass tributaries flowing into the central trunk of the glacier. Within the 5,400 km(2) central trunk, the average rate of volume loss quadrupled from 2.6 +/- 0.3 km(3) yr(-1) in 1995 to 10.1 +/- 0.3 km(3) yr(-1) in 2006. The region of lightly grounded ice at the glacier terminus is extending upstream, and the changes inland are consistent with the effects of a prolonged disturbance to the ice flow, such as the effects of ocean- driven melting. If the acceleration continues at its present rate, the main trunk of PIG will be afloat within some 100 years, six times sooner than anticipated. Citation: Wingham, D.J., D.W. Wallis, and A. Shepherd (2009), Spatial and temporal evolution of Pine Island Glacier thinning, 1995-2006, Geophys. Res. Lett., 36, L17501, doi: 10.1029/2009GL039126

Arctic sea surface height variability and change from satellite radar altimetry and GRACE, 2003–2014

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°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 ∼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 km3 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 ∼180 km3 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

Western Arctic Ocean freshwater storage increased by wind-driven spin-up of the Beaufort Gyre

The Arctic Ocean’s freshwater budget comprises contributions from river runoff, precipitation, evaporation, sea-ice and exchanges with the North Pacific and Atlantic. More than 70,000km3 of freshwater 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 west. Models suggest that wind-driven convergence drives freshwater accumulation. 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±2,000km3 in the western Arctic Ocean, in line with hydrographic observations, 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

Slepian functions and their use in signal estimation and spectral analysis

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are "spatiospectrally" concentrated, i.e. "localized" in both domains at the same time. Here, we give a theoretical overview of one particular approach to this "concentration" problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and on the surface of a sphere.Comment: Submitted to the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verla