Martin Horwath

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.

A high‐resolution record of Greenland mass balance

We map recent Greenland Ice Sheet elevation change at high spatial (5 km) and temporal (monthly) resolution using CryoSat-2 altimetry. After correcting for the impact of changing snowpack properties associated with unprecedented surface melting in 2012, we find good agreement (3 cm/yr bias) with airborne measurements. With the aid of regional climate and firn modeling, we compute high spatial and temporal resolution records of Greenland mass evolution, which correlate (R = 0.96) with monthly satellite gravimetry and reveal glacier dynamic imbalance. During 2011–2014, Greenland mass loss averaged 269 ± 51 Gt/yr. Atmospherically driven losses were widespread, with surface melt variability driving large fluctuations in the annual mass deficit. Terminus regions of five dynamically thinning glaciers, which constitute less than 1% of Greenland’s area, contributed more than 12% of the net ice loss. This high-resolution record demonstrates that mass deficits extending over small spatial and temporal scales have made a relatively large contribution to recent ice sheet imbalance.

Quantifying the seasonal"breathing"of the Antarctic ice sheet

[1] One way to estimate the mass balance of an ice sheet is to convert satellite observed surface elevation changes into mass changes. In order to do so, elevation and mass changes due to firn processes must be taken into account. Here, we use a firn densification model to simulate seasonal variations in depth and mass of the Antarctic firn layer, and assess their influence on surface elevation. Forced by the seasonal cycle in temperature and accumulation, a clear seasonal cycle in average firn depth of the Antarctic ice sheet (AIS) is found with an amplitude of 0.026 m, representing a volume oscillation of 340 km3. The phase of this oscillation is rather constant across the AIS: the ice sheet volume increases in austral autumn, winter and spring and quickly decreases in austral summer. Seasonal accumulation differences are the major driver of this annual ‘breathing’, with temperature fluctuations playing a secondary role. The modeled seasonal elevation signal explains 31% of the seasonal elevation signal derived from ENVISAT radar altimetry, with both signals having similar phase.

Mass Variation Signals in GRACE Products and in Crustal Deformations crustal deformation from GPS: A Comparison

Geophysical surface mass variations are reflected both in gravity field variations and in load deformations of the solid Earth . These two signatures may be observed by GRACE and by GPS , respectively. This article reports about a comparison between both. Concerning GPS-derived deformations, a meaningful geophysical interpretation requires both homogeneously processed observations and a stable realization of the terrestrial reference system. Here we use results from a reprocessing of a global GPS network with consistent use of the latest processing and modelling strategies. This reprocessing includes the estimation of low-degree deformation terms. We directly compare them to respective GRACE results and find good agreement. Our main results concern the comparison of site displacement time series obtained from GPS, on the one hand, and from GRACE gravity variations converted to load deformations, on the other hand. We do this comparison both for the GRACE background models of short-term variations and for the final monthly GRACE solutions. For vertical deformations, we find good agreement. In contrast, the agreement is poor for the horizontal directions. The differences between GPS and GRACE contain some components which appear to have large-scale correlated patterns in space and seasonal patterns in time. More detailed analyses indicate that residual errors in the GPS solutions are likely the dominant cause of these differences. Analysing internal deformations of regional subnetworks is a way to circumvent some of the large-scale systematics of the GPS solution. Indeed, regional analyses show reasonable agreement between GPS and GRACE even in the horizontal components. Overall, our results demonstrate the progress and challenges of combining independent satellite geodetic observations within the Global Geodetic Observing System.

Height changes over subglacial Lake Vostok, East Antarctica: Insights from GNSS observations

Height changes of the ice surface above subglacial Lake Vostok, East Antarctica, reflect the integral effect of different processes within the subglacial environment and the ice sheet. Repeated GNSS (Global Navigation Satellite Systems) observations on 56 surface markers in the Lake Vostok region spanning 11 years and continuous GNSS observations at Vostok station over 5 years are used to determine the vertical firn particle movement. Vertical marker velocities are derived with an accuracy of 1 cm/yr or better. Repeated measurements of surface height profiles around Vostok station using kinematic GNSS observations on a snowmobile allow the quantification of surface height changes at 308 crossover points. The height change rate was determined at 1 ± 5 mm/yr, thus indicating a stable ice surface height over the last decade. It is concluded that both the local mass balance of the ice and the lake level of the entire lake have been stable throughout the observation period. The continuous GNSS observations demonstrate that the particle heights vary linearly with time. Nonlinear height changes do not exceed ±1 cm at Vostok station and constrain the magnitude of spatiotemporal lake-level variations. ICESat laser altimetry data confirm that the amplitude of the surface deformations over the lake is restricted to a few centimeters. Assuming the ice sheet to be in steady state over the entire lake, estimates for the surface accumulation, on basal accretion/melt rates and on flux divergence, are derived.

Small-scale spatio-temporal characteristics of accumulation rates in western Dronning Maud Land, Antarctica

Spatio-temporal variations of the recently determined accumulation rate are investigated using ground-penetrating radar (GPR) measurements and firn-core studies. The study area is located on Ritscherflya in western Dronning Maud Land, Antarctica, at an elevation range 1400-1560 m. Accumu- lation rates are derived from internal reflection horizons (IRHs), tracked with GPR, which are connected to a dated firn core. GPR-derived internal layer depths show small relief along a 22 km profile on an ice flowline. Average accumulation rates are about 190 kg m -2 a -1 (1980-2005) with spatial variability (1σ) of 5% along the GPR profile. The interannual variability obtained from four dated firn cores is one order of magnitude higher, showing 1σ standard deviations around 30%. Mean temporal variations of GPR- derived accumulation rates are of the same magnitude or even higher than spatial variations. Temporal differences between 1980-90 and 1990-2005, obtained from two dated IRHs along the GPR profile, indicate temporally non-stationary processes, linked to spatial variations. Comparison with similarly obtained accumulation data from another coastal area in central Dronning Maud Land confirms this observation. Our results contribute to understanding spatio-temporal variations of the accumulation processes, necessary for the validation of satellite data (e.g. altimetry studies and gravity missions such as Gravity Recovery and Climate Experiment (GRACE)).

Subglacial Lake Vostok not expected to discharge water

The question whether Antarcticas largest lake, subglacial Lake Vostok, exchanges water is of interdisciplinary relevance but has been undecided so far. We present the potential pathway, outlet location, and threshold height of subglacial water discharge from this lake based on a quantitative evaluation of the fluid potential. If water left Lake Vostok, it would flow toward Ross Ice Shelf. Discharge would occur first to the east of the southern tip of the lake. At this location the bedrock threshold is 91 ± 23 m higher than the hydrostatic equipotential level of Lake Vostok. It is concluded that Lake Vostok is not likely to reach this level within climatic timescales and that no discharge of liquid water is to be expected. We show that in absence of the ice sheet the Lake Vostok depression would harbor a lake significantly deeper and larger than the present aquifer.

A Data‐Driven Approach for Repairing the Hydrological Catchment Signal Damage Due to Filtering of GRACE Products

One of the major sources of uncertainty in mass change estimates from level 02 grace products comes from the signal degradation due to filtering of noisy gravity field products. Filtering suppresses noise but also changes the signal via attenuation and leakage. Therefore, many methods have been devised to tackle the unavoidable signal loss due to filtering. However, most of these methods lack mathematical analysis that is essential for understanding the cause and effect of filtering. Furthermore, they use hydrological models to compute correction terms, such as leakage, bias or scale factor, for repairing the damage due to filtering. Recently a data-driven method was proposed for improving the filtered grace products, which was shown to be superior to three widely used model based methods. However, the method works efficiently only for catchments above a minimum size. This limitation is due to the usage of a uniform layer approximation for deriving a scale factor, which is used to counter the attenuation of the catchment-confined signal. In this contribution, we avoid this approximation, and therefore the usage of scale factor, which lifts the limitation and provides a better mathematical relation. The new data-driven method is able to restore the signal loss due to filtering independent of the catchment size. We validate the method in a realistic grace-type closed-loop simulation environment and compare it with other popular approaches. We show that for 22 out of 32 catchments (small to large size and located in different climatic zones) the improved data-driven method outperforms other methods.

The evaluation of the geoid–quasigeoid separation and consequences for its implementation

The realization of precise height systems demands to assess the effect and necessity of approximations made to the pure theory. In this context, the formulas for the geoid–quasigeoid separation as presented by Flury and Rummel (J Geod 83:829–847, 2009) and further discussed by Sjöberg (J Geod 84:699–702, 2010) are reinterpreted. Starting from the fully topographically reduced gravity disturbance, a modification of the strict formulation of the downward continuation and the indirect effect according to Sjöberg (2010) is given. In practice any implementation of the formula requires approximations in order to realize the downward continuation of gravity along the plumbline with the help of density assumptions and a topography model. The significance of the individual contributors to a refined approximation, taking into account the indirect effect and the first-order gravity gradient, is elaborated in a numerical simulation for the example of the Himalaya region. Special focus is given on the sensitivity and convergency of the topography-induced terms with respect to the integration radius.