Bathymetry is the measurement of the water depth similar to underwater topography. Gravity anomaly and vertical gravity gradient are important data used to inverse bathymetry. In this study, we investigate the sensitivities of the gravity anomalies and vertical gravity gradient data to bathymetry inversion. Firstly, the formulas of the gravity anomaly and vertical gravity gradient signals produced by the seabed terrain are derived, and then a series of numerical studies are designed to investigate the sensitivities. The results show that gravity anomalies and vertical gravity gradients have different sensitive bands to bathymetry inversion. Therefore, accuracy requirements for the gravity anomaly and vertical gravity gradient data are different for bathymetry inversion with different spatial resolutions and accuracies. With decreasing resolution, the accuracy requirement of the gravity anomaly gradually decreases, whereas the accuracy requirement of the vertical gravity gradient first decreases and then increases, indicating that the vertical gravity gradient is more sensitive to the short-wavelength signal than the gravity anomaly, especially in the 0–20 km wavelength ranges. In addition, we perform a theoretical analysis that shows that the vertical gravity gradient has a band that is most sensitive to the seafloor topography. This study is capable to provide a reference for the design of future satellites to retrieve the bathymetry. ... Read more

Satellite gravimetry data acquired by the Gravity Recovery and Climate Experiment (GRACE) allows to derive the temporal evolution in ice mass for both the Antarctic Ice Sheet (AIS) and the Greenland Ice Sheet (GIS). Various algorithms have been used in a wide range of studies to generate Gravimetric Mass Balance (GMB) products. Results from different studies may be affected by substantial differences in the processing, including the applied algorithm, the utilised background models and the time period under consideration. This study gives a detailed description of an assessment of the performance of GMB algorithms using actual GRACE monthly solutions for a prescribed period as well as synthetic data sets. The inter-comparison exercise was conducted in the scope of the European Space Agency’s Climate Change Initiative (CCI) project for the AIS and GIS, and was, for the first time, open to everyone. GMB products generated by different groups could be evaluated and directly compared against each other. For the period from 2003-02 to 2013-12, estimated linear trends in ice mass vary between −99 Gt/yr and −108 Gt/yr for the AIS and between −252 Gt/yr and −274 Gt/yr for the GIS, respectively. The spread between the solutions is larger if smaller drainage basins or gridded GMB products are considered. Finally, findings from the exercise formed the basis to select the algorithms used for the GMB product generation within the AIS and GIS CCI project. ... Read more

The aim of this paper is to present an alternative method that can be used to improve existing gravity field models via the application of gradient data from Gravity field and Ocean Circulation Explorer (GOCE). First, the proposed algorithm used to construct the observation equation is presented. Then methods for noise processing in both time and space domains aimed at reducing noises are introduced. As an example, the European Improved Gravity model of the Earth by New techniques (EIGEN5C) is modified with gradient observations over the whole lifetime of the GOCE, leading to a new gravity field model named as EGMGOCE (Earth Gravitational Model of GOCE). The results show that the cumulative geoid difference between EGMGOCE and EGM08 is reduced by 4 centimeters compared with that between EIGEN5C and Earth Gravitational Model 2008 (EGM08) up to 200 degrees. The large geoid differences between EGMGOCE and EIGEN5C mainly exist in Africa, South America, Antarctica and Himalaya, which indicates the contribution from GOCE. Compared to the newest GOCE gravity field model resolved by direct method from European Space Agency (ESA), the cumulative geoid difference is reduced by 7 centimeters up to 200 degrees. ... Read more

We propose a technique to regularize a GRACE-based mass-anomaly time-series in order to (i) quantify the Standard Deviation (SD) of random noise in the data, and (ii) reduce the level of that noise. The proposed regularization functional minimizes the Month-to-month Year-to-year Double Differences (MYDD) of mass anomalies. As such, it does not introduce any bias in the linear trend and the annual component, two of the most common features in GRACE-based mass anomaly time-series. In the context of hydrological and ice sheet studies, the proposed regularization functional can be interpreted as an assumption about the stationarity of climatological conditions. The optimal regularization parameter and noise SD are obtained using Variance Component Estimation. To demonstrate the performance of the proposed technique, we apply it to both synthetic and real data. In the latter case, two geographic areas are considered: the Tonlé Sap basin in Cambodia and Greenland. We show that random noise in the data can be efficiently (1.5–2 times) mitigated in this way, whereas no noticeable bias is introduced. We also discuss various findings that can be made on the basis of the estimated noise SD. We show, among others, that knowledge of noise SD facilitates the analysis of differences between GRACE-based and alternative estimates of mass variations. Moreover, inaccuracies in the latter can also be quantified in this way. For instance, we find that noise in the surface mass anomalies in Greenland estimated using the Regional Climate Model RACMO2.3 is at the level of 2–6 cm equivalent water heights. Furthermore, we find that this noise shows a clear correlation with the amplitude of annual mass variations: it is lowest in the north-west of Greenland and largest in the south. We attribute this noise to limitations in the modelling of the meltwater accumulation and run-off. ... Read more

The mascon approach is a well-known technique to estimate mass anomalies in Greenland using GRACE satellite gravity data. It partitions the area of interest into laterally-homogeneous patches (mascons). An important aspect of the mascon approach is the chosen geometry of mascons. So far, its impact has not been fully understood. In this study, we use a full-scale numerical study and real data analysis to identify the optimal strategy (primarily, the size of the mascons) for the extrac- tion of mass anomalies over the Greenland drainage systems from GRACE monthly solutions. We use ordinary and weighted least-squares techniques to estimate the mascon parameters. The weighted least-squares estimator uses the full noise covari- ance matrices of monthly GRACE models, i.e. is designed to suppress random noise in the estimates. In addition, the zero-order Tikhonov regularization is applied. Four types of quantities of interest, which are associated with di
erent temporal scales, are investigated in this study: monthly mass anomalies, mean mass anomalies per calendar month, inter-annual mass variations, and long-term linear trends. We show that the dominant error sources are random errors and parameterization (model) errors, as well as the bias introduced by the regularization. Errors in long-term lin- ear trend estimates are dominated by parameterization errors, whereas the role of random errors increases with the decreasing temporal scale. The best solutions are Downloaded from https://academic.oup.com/gji/advance-article-abstract/doi/10.1093/gji/ggy242/5040767 by guest on 05 July 2018 2 J. Ran, P. Ditmar and R. Klees obtained when the territory of Greenland is split into at least 23 mascons (the area of each one being 90; 000 km2). The usage of smaller mascons does not worsen the solutions in most cases, which is explained by the application of the regularization. Usage of larger mascons leads in most cases to inferior results due to the impact of parameterization errors. The application of the weighted least-squares estimator noticeably improves the quality of the solutions, with the exception of long-term linear trends estimated at the drainage system scale. In addition, we considered the long-term linear trend estimates integrated over entire Greenland. It is shown that the best results are obtained in that case when no regularization is applied. The results of real GRACE data processing are consistent with those obtained in the numerical study.
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Transient meltwater accumulation in Greenland spans the entire ice layer, down to the ice bed. As such, this process may have a large impact on Greenland ice dynamics and on the future ice sheet evolution. GrIS subglacial hydrology is an area of active research. Unfortunately, it is difficult to validate and calibrate existing subglacial hydrology models because of intrinsic data limitations. Data collected in situ or from aircraft have a very limited spatial or/and temporal coverage, whereas space-borne electromagnetic sensors (both passive and active)
are capable of observing only the near-surface part of the ice layer. With our study, we present the first direct observations of transient meltwater accumulation in Greenland with satellite gravimetry. We estimate total mass
anomalies using GRACE satellite mission data and subtract from them the contributions associated with the Surface Mass Balance (SMB) and the Ice Discharge (ID). The SMB estimates are provided by the Regional Atmospheric
Climate Model v. 2.3 (RACMO 2.3). The signal related to ID is approximated by a linear function fitting the “Total minus SMB” residuals in spring and autumn months. An analysis of seasonal variations in ice flow at 55 outlet glaciers in northwest and southeast Greenland shows that the deviations of ID-related mass anomalies from a linear trend are negligible. By taking the average of seasonal mass variations in 2003–2013, we observe substantial meltwater accumulation in Greenland during summer, with a peak value of 80-120 Gt in July. At the regional
scale, the largest accumulation is observed in the southeast and northwest parts of Greenland: up to about 40 Gt in each region. The extracted signal is not altered substantially when using an alternative snow and firn model called SNOWPACK, which partitions meltwater into refreezing and runoff differently, as compared to RACMO 2.3. Furthermore, the meltwater accumulation signal is present in all of the considered GRACE data product variants and processing schemes, though with somewhat different magnitude and timing. Our study shows that GRACE data are capable of sensing transient meltwater accumulation not only at the scale of entire GrIS, but also at the scale of individual drainage systems. A continuation of research efforts is envisioned in order to further improve the accuracy of the obtained estimates. ... Read more

The Greenland Ice Sheet (GrIS) is currently losing ice mass as the result of changes in the complex ice-climate interactions that have been driven by global climate change. In order to accurately predict future sea level rise, the mechanisms driving the observed mass loss must be better understood. Here, we combine data from the satellite gravimetry mission GRACE, surface mass balance (SMB) output of RACMO 2.3, and ice discharge estimates to analyze the mass budget of Greenland at various temporal and spatial scales. Firstly, in agreement with previous estimates, we find that the rate of mass loss from Greenland observed by GRACE was between −277 and −269 Gt/yr in 2003–2012. This estimate is consistent with the sum of individual contributions: surface mass balance (SMB, around 216 ± 122 Gt/yr) and ice discharge (520 ± 31 Gt/yr), indicating a good performance of the regional climate model. Secondly, we examine the average accelerations of mass anomalies in Greenland over 2003–2012, suggesting that the SMB (−23.3 ± 2.7 Gt/yr2) contributes 75 % to the total acceleration observed by GRACE. The remaining contributions to the mass loss acceleration for entire Greenland are statistically insignificant. Finally and most importantly, this study suggests the existence of a substantial meltwater storage during summer, with a peak value of 80–120 Gt in July. The robustness of this estimate is demonstrated by using both different GRACE-based solutions and different meltwater runoff estimates (namely, RACMO 2.3 and SNOWPACK). Meltwater storage in the ice sheet occurs primarily due to storage in the high-accumulation regions of the southeast (SE) and northwest (NW) parts of Greenland. Analysis of seasonal variations in outlet glacier discharge shows that the contribution of ice discharge to the observed signal is minor (at the level of only a few Gt) and does not explain the intra-annual differences between the total mass and SMB signals. ... Read more

The Greenland ice sheet (GrIS) is currently losing mass, as a result of complex mechanisms of ice-climate interaction that need to be understood for reliable projections of future sea level rise. The thesis focuses on the estimation of mass anomalies in Greenland using data from the GRACE satellite gravity mission. Monthly GRACE gravity field solutions are post-processed using a new variant of the "mascon approach''. Greenland is covered with multiple distinctive "mascons'', assuming the mass anomalies within each one are laterally-homogeneous.

Gravity disturbances at mean satellite altitude are synthesized from the GRACE spherical harmonic coefficients. They are used as pseudo-observations to estimate the mascon mass anomalies using weighted least-squares techniques. No regularization is applied. The full noise covariance matrix of gravity disturbances is propagated from the full noise covariance matrix of spherical harmonic coefficients using the law of covariance propagation. Those matrices represent a complete stochastic description of random noise in the data, provided that it is Gaussian. The inverse noise covariance matrix is used as a weight matrix in the weighted least-squares estimate of the mascon mass anomalies. The limited spectral content of the gravity disturbances is accounted for by applying a low-pass filter to the design matrix providing a spectrally consistent functional model.

Using numerical experiments with simulated signal and data, we demonstrate the importance of the data weighting and of the spectral consistency between the mascon model and the pseudo-observations. The developed methodology is applied to process real GRACE data using CSR RL05 monthly gravity field solutions with full noise covariance matrices. We distinguish five GrIS drainage systems. The obtained mass anomaly estimates per mascon are integrated over individual drainage systems, as well as over entire Greenland. We find that using a weighted least-squares estimator reduces random noise in the estimates by factors ranging from 1.5 to 3.0, depending on the drainage system. Furthermore, we compare the de-trended mascon mass anomaly time-series with similar time-series from the Regional Atmospheric Climate Model (RACMO 2.3), which describes the Surface Mass Balance (SMB). We show that the weighted least-squares estimate reduces the discrepancies between the time-series by 24\%--47\%.

Then, we combine GRACE mass anomaly estimates, SMB model outputs, and ice discharge data to systematically analyze the mass budget of Greenland at various temporal and spatial scales. Among others, we reveal a substantial seasonal meltwater storage, which peaks in July, reaching in total $100 \pm 20$ Gt. Meltwater storage is particularly intense in the northern, northwestern and southeastern drainage systems. An analysis of outlet glacier velocities shows that the contribution of ice discharge to the seasonal mass variations is minor, at a level of only a few Gt. In addition, we propose a simple way to use GRACE data for validating SMB model outputs in winter, based on the fact that ice discharge cannot be negative.

Finally, we use numerical simulations and real data to identify the optimal GRACE data processing strategy (primarily the size of the mascons) for three temporal scales of interest: monthly mass anomalies, mean mass anomalies per calendar month, and long-term linear trends. We show that the two major contributors to the error budgets are random errors and parameterization (model) errors; the latter are caused by a spatial variability of actual mass anomalies within individual mascons. We find that the errors in long-term linear trend estimates are mainly caused by the parameterization errors, and that accurate estimates require small size mascons in combination with the ordinary least-squares estimator. The error budget of mean mass anomalies per calendar month is dominated by the parameterization error when the size of mascons is large and by random errors otherwise. Hence, accurate estimates require mascons of intermediate size in combination with a weighted least-squares estimator. Finally, we find that random errors are the dominant error source in monthly mass anomalies. We advise to use in this case large mascons and a weighted least-squares estimator.

Our new variant of the mascon approach and the results of this thesis can be used in support of future research on GrIS hydrology, glacier dynamics, and surface mass balance, as well as their mutual interactions. ... Read more

We present an improved mascon approach to transform monthly spherical harmonic solutions based on GRACE satellite data into mass anomaly estimates in Greenland. The GRACE-based spherical harmonic coefficients are used to synthesize gravity anomalies at satellite altitude, which are then inverted into mass anomalies per mascon. The limited spectral content of the gravity anomalies is properly accounted for by applying a low-pass filter as part of the inversion procedure to make the functional model spectrally consistent with the data. The full error covariance matrices of the monthly GRACE solutions are properly propagated using the law of covariance propagation. Using numerical experiments, we demonstrate the importance of a proper data weighting and of the spectral consistency between functional model and data. The developed methodology is applied to process real GRACE level-2 data (CSR RL05). The obtained mass anomaly estimates are integrated over five drainage systems, as well as over entire Greenland. We find that the statistically optimal data weighting reduces random noise by 35–69%, depending on the drainage system. The obtained mass anomaly time-series are de-trended to eliminate the contribution of ice discharge and are compared with de-trended surface mass balance (SMB) time-series computed with the Regional Atmospheric Climate Model (RACMO 2.3). We show that when using a statistically optimal data weighting in GRACE data processing, the discrepancies between GRACE-based estimates of SMB and modelled SMB are reduced by 24–47%. ... Read more