Ernst J. O. Schrama

A Reconciled Estimate of Ice-Sheet Mass Balance

Warming and Melting Mass loss from the ice sheets of Greenland and Antarctica account for a large fraction of global sea-level rise. Part of this loss is because of the effects of warmer air temperatures, and another because of the rising ocean temperatures to which they are being exposed. Joughin et al. (p. 1172) review how ocean-ice interactions are impacting ice sheets and discuss the possible ways that exposure of floating ice shelves and grounded ice margins are subject to the influences of warming ocean currents. Estimates of the mass balance of the ice sheets of Greenland and Antarctica have differed greatly—in some cases, not even agreeing about whether there is a net loss or a net gain—making it more difficult to project accurately future sea-level change. Shepherd et al. (p. 1183) combined data sets produced by satellite altimetry, interferometry, and gravimetry to construct a more robust ice-sheet mass balance for the period between 1992 and 2011. All major regions of the two ice sheets appear to be losing mass, except for East Antarctica. All told, mass loss from the polar ice sheets is contributing about 0.6 millimeters per year (roughly 20% of the total) to the current rate of global sea-level rise. The mass balance of the polar ice sheets is estimated by combining the results of existing independent techniques. We combined an ensemble of satellite altimetry, interferometry, and gravimetry data sets using common geographical regions, time intervals, and models of surface mass balance and glacial isostatic adjustment to estimate the mass balance of Earth’s polar ice sheets. We find that there is good agreement between different satellite methods—especially in Greenland and West Antarctica—and that combining satellite data sets leads to greater certainty. Between 1992 and 2011, the ice sheets of Greenland, East Antarctica, West Antarctica, and the Antarctic Peninsula changed in mass by –142 ± 49, +14 ± 43, –65 ± 26, and –20 ± 14 gigatonnes year−1, respectively. Since 1992, the polar ice sheets have contributed, on average, 0.59 ± 0.20 millimeter year−1 to the rate of global sea-level rise.

Partitioning recent Greenland mass loss

GRACE and Movement Together Recent measurements of the rate of mass loss from the Greenland ice sheet vary approximately by a factor of three. Resolving these discrepancies is essential for determining the current mass balance of the ice sheet and to project sea level rise in the future. Van den Broeke et al. (p. 984) obtained consistent estimates from two independent methods, one based on observations of ice movement combined with model calculations and the other on remote gravity measurements made by the GRACE (Gravity Recovery and Climate Experiment) satellites. The combination of these approaches also resolves the separate contributions of surface processes and of ice dynamics, the two major routes of ice mass loss. The major components of decay contributing to mass loss from the Greenland Ice Sheet can be quantified. Mass budget calculations, validated with satellite gravity observations [from the Gravity Recovery and Climate Experiment (GRACE) satellites], enable us to quantify the individual components of recent Greenland mass loss. The total 2000–2008 mass loss of ~1500 gigatons, equivalent to 0.46 millimeters per year of global sea level rise, is equally split between surface processes (runoff and precipitation) and ice dynamics. Without the moderating effects of increased snowfall and refreezing, post-1996 Greenland ice sheet mass losses would have been 100% higher. Since 2006, high summer melt rates have increased Greenland ice sheet mass loss to 273 gigatons per year (0.75 millimeters per year of equivalent sea level rise). The seasonal cycle in surface mass balance fully accounts for detrended GRACE mass variations, confirming insignificant subannual variation in ice sheet discharge.

GRACE observes small‐scale mass loss in Greenland

Using satellite gravity data between February 2003 and January 2008, we examine changes in Greenlands mass distribution on a regional scale. During this period, Greenland lost mass at a mean rate of 179 ± 25 Gt/yr, equivalent to a global mean sea level change of 0.5 ± 0.1 mm/yr. Rates increase over time, suggesting an acceleration of the mass loss, driven by mass loss during summer. The largest mass losses occurred along the southeastern and northwestern coast in the summers of 2005 and 2007, when the ice sheet lost 279 Gt and 328 Gt of ice respectively within 2 months. In 2007, a strong mass loss is observed during summer at elevations above 2000 m, for the first time since the start of the observations.

A preliminary tidal analysis of TOPEX/POSEIDON altimetry

Approximately 12 months of data from the TOPEX/POSEIDON satellite altimeter mission are analyzed for the major short-period oceanic tides. A harmonic analysis is performed on data captured within bins defined on a deep-ocean grid, which, owing to tidal aliasing considerations, must have a relatively coarse spatial resolution. Our analysis is in terms of corrections to the Schwiderski and Cartwright-Ray models, and it confirms many of the Schwiderski differences previously reported by Cartwright and Ray. Our differences with respect to the Geosat-based Cartwright and Ray model form a sectorial pattern in M2 with high/low differences separated roughly 180° in longitude. We suggest that these sectorial errors were most likely induced by Geosats relatively large orbit error. Comparisons to independent data validate the improved TOPEX/POSEIDON solutions; in situ “ground truth” shows M2 RMS differences of 4.10cm (Schwiderski), 3.86cm (Cartwright and Ray), 2.63cm (this paper). Global rates of energy dissipation confirm earlier estimates for M2, and show improved agreement with satellite tracking studies for K1 and S2. These preliminary exercises confirm that TOPEX/POSEIDON should result in a new generation of improved global tidal models.

Surface mass redistribution inversion from global GPS deformation and Gravity Recovery and Climate Experiment (GRACE) gravity data

Monitoring hydrological redistributions through their integrated gravitational effect is the primary aim of the Gravity Recovery and Climate Experiment (GRACE) mission. Time?variable gravity data from GRACE can be uniquely inverted to hydrology, since mass transfers located at or near the Earths surface are much larger on shorter timescales than those taking place within the deeper Earth and because one can remove the contribution of atmospheric masses from air pressure data. Yet it has been proposed that at larger scales this may be achieved independently by measuring and inverting the elastic loading associated with redistributing masses, e.g., with the global network of the International GPS Service (IGS). This is particularly interesting as long as GRACE monthly gravity solutions do not (yet) match the targeted baseline accuracies at the lower spherical harmonic degrees. In this contribution (1) we describe and investigate an inversion technique which can deal jointly with GPS data and monthly GRACE solutions. (2) Previous studies with GPS data have used least squares estimators and impose solution constraints through low?degree spherical harmonic series truncation. Here we introduce a physically motivated regularization method that guarantees a stable inversion up to higher degrees, while seeking to avoid spatial aliasing. (3) We apply this technique to GPS data provided by the IGS service covering recent years. We can show that after removing the contribution ascribed to atmospheric pressure loading, estimated annual variations of continental?scale mass redistribution exhibit pattern similar to those observed with GRACE and predicted by a global hydrology model, although systematic differences appear to be present. (4) We compute what the relative contribution of GRACE and GPS would be in a joint inversion: Using current error estimates, GPS could contribute with up to 60% to degree 2 till 4 spherical harmonic coefficients and up to 30% for higher?degree coefficients.

A preliminary evaluation of ocean topography from the TOPEX/POSEIDON mission

We have analyzed 50 ten-day cycles of TOPEX/POSEIDON (T/P) altimeter data to evaluate the ocean dynamic topography and its temporal variations. We have employed data from both the U.S. and French altimeters along with the NASA precision orbits in this analysis. Errors in the diurnal and semidiurnal components of the Cartwright-Ray tide model have been significantly reduced using a correction developed from T/P altimeter data by Schrama and Ray (this issue). A hybrid geoid model formed from a combination of JGM-2 and OSU91A was employed, as well as a geoid model based solely on OSU91 A. The long wavelengths of the mean dynamic topography show considerable improvement over previous missions based on comparisons to historical hydrographic data, although geoid error still corrupts the dynamic topography for wavelengths shorter than 2500 km. The RMS variability is similar to previous results from Geosat, with background “noise” approaching 3 cm RMS. The computed annual and semiannual variations are also similar to previous Geosat results, although the hemispheric distribution of the annual heating cycle is much better represented in the T/P results. They also compare reasonably well with the Levitus hydrographic compilation in the northern hemisphere, although the T/P variations generally have larger amplitudes. Ten-day average maps of variations in sea level compare well with simultaneous measurements at ocean tide gauges, with RMS differences of less than 4 cm and correlations greater than 0.6 for most of the island gauges. Time-longitude plots of these sea level variations at different latitudes in the Pacific clearly show the presence of equatorial Kelvin waves and Rossby waves, with the wave speeds agreeing well with theoretical and observed values. Measurement of variations in global sea level over cycles 2–51 have an RMS variability of 6.3 mm and a rate of change of −3.5±8 mm/yr, the uncertainty primarily due to insufficient averaging of the interannual and periodic sea level variations. With several more years of data and accurate monitoring of the altimeter drift at the calibration sites, T/P has the potential for providing a precise (±1 mm/yr) estimate of the rate of global sea level rise. These results show that the accuracy of the T/P measurements of sea level has dramatically improved over previous missions, with estimated time variable errors of 4 cm or less (1σ). Although geographically correlated orbit errors have also been reduced to the few centimeter level, further improvement in determinations of the mean dynamic topography will be difficult to obtain until a more accurate model of the marine geoid is available.

Signal and noise in Gravity Recovery and Climate Experiment (GRACE) observed surface mass variations

The Gravity Recovery and Climate Experiment (GRACE) product used for this study consists of 43 monthly potential coefficient sets released by the GRACE science team which are used to generate surface mass thickness grids expressed as equivalent water heights (EQWHs). We optimized both the smoothing radius and the level of approximation by empirical orthogonal functions (EOFs) and found that 6.25° and three modes are able to describe more than 73.5% of the variance. The EQWHs obtained by the EOF method describe all known variations in the continental hydrology, present?day ice sheet melting, and global isostatic adjustment. To assess the quality of the estimated grids, we constructed degree error spectra of EQWHs. We conclude that a significant part of the errors in GRACE can be explained by a scaling factor of 0.85 relative to degree error estimates provided by the GGM02C gravity model but that the present?day errors in the GRACE data are a factor 2 to 5 larger than forecasted by tide model differences and atmospheric pressure differences. Comparison to a network of 59 International GNSS Service (IGS) stations confined the filter parameter settings to three EOF modes and 5° or 6.25° smoothing radius. Residuals that remain after the EOF method do exhibit S2 aliasing errors and a semiannual continental hydrology signal contained in the Global Land Data Assimilation Systems (GLDAS) model. Further analysis of the residual EOF signal revealed alternating track correlation patterns that are partially explained by the GRACE covariance matrix and the handling of nuisance parameters in the GRACE data processing.

Improved accuracy of GRACE gravity solutions through empirical orthogonal function filtering of spherical harmonics

One of the major problems one has to deal with when working with Gravity Recovery and Climate Experiment (GRACE) data is the increasing error spectrum at higher degrees in the provided Stokes coefficients, appearing as unphysical North?South striping patterns in the maps of equivalent water height (EWH). This phenomenon is commonly suppressed by application of a Gaussian smoothing filter, which unfortunately causes loss of signal and leakage between basins. In this paper we show how a significant amount of the striping can be removed by making use of the temporal characteristics of the error spectrum. The Stokes coefficients are decomposed using empirical orthogonal function analysis and the individual modes are tested for temporal noisiness. After filtering, maps of EWH are largely free of striping. Tests on simulated EWH estimates show that our filtering technique has a marginal effect on the predicted geophysical signal.

Revisiting Greenland ice sheet mass loss observed by GRACE

In this paper we discuss a new method for determining mass time series for 16 hydrological basins representing the Greenland system (GS) whereby we rely on Gravity Recovery and Climate Experiment (GRACE) mission data. In the same analysis we also considered observed mass changes over Ellesmere Island, Baffin Island, Iceland, and Svalbard (EBIS). The summed contribution of the complete system yields a mass loss rate and acceleration of ?252 ± 28 Gt/yr and ?22 ± 4 Gt/yr2 between March 2003 and February 2010 where the error margins follow from two glacial isostatic adjustment (GIA) models and three processing centers providing GRACE monthly potential coefficient sets. We describe the relation between mass losses in the GS and the EBIS region and found that the uncertainties in all areas are correlated. The summed contribution of Ellesmere Island, Baffin Island, Iceland, and Svalbard yields a mass loss rate of ?51 ± 17 Gt/yr and an acceleration of ?13 ± 3 Gt/yr2 between March 2003 and February 2010. The new regional basin reconstruction method shows that the mass loss within the southeastern basins in the GS has slowed down since 2007, while mass loss in western basins increased showing a progression to the north of Greenland.

A mascon approach to assess ice sheet and glacier mass balances and their uncertainties from GRACE data

The purpose of this paper is to assess the mass changes of the Greenland Ice Sheet (GrIS), Ice Sheets over Antarctica, and Land glaciers and Ice Caps with a global mascon method that yields monthly mass variations at 10,242 mascons. Input for this method are level 2 data from the Gravity Recovery and Climate Experiment (GRACE) system collected between February 2003 and June 2013 to which a number of corrections are made. With glacial isostatic adjustment (GIA) corrections from an ensemble of models based on different ice histories and rheologic Earth model parameters, we find for Greenland a mass loss of −278 ± 19 Gt/yr. Whereas the mass balances for the GrIS appear to be less sensitive to GIA modeling uncertainties, this is not the case with the mass balance of Antarctica. Ice history models for Antarctica were recently improved, and updated historic ice height data sets and GPS time series have been used to generate new GIA models. We investigated the effect of two new GIA models for Antarctica and found −92 ± 26 Gt/yr which is half of what is obtained with ICE-5G-based GIA models, where the largest GIA model differences occur on East Antarctica. The mass balance of land glaciers and ice caps currently stands at −162 ± 10 Gt/yr. With the help of new GIA models for Antarctica, we assess the mass contribution to the mean sea level at 1.47 ± 0.09 mm/yr or 532 ± 34Gt/yr which is roughly half of the global sea level rise signal obtained from tide gauges and satellite altimetry.