Accurate estimates of terrestrial water storage variations (TWSV) are critical for a variety of applications, e.g., model calibration and climate studies. This study aims to find the added value of river run-off data for regularizing GRACE mascon solution, from which TWSV can be estimated. Most subbasins of the Mississippi Basin show an exponential relationship between run-off and TWSV with moderate to good predictive value. The mean value of the explained variance (R^2) for the models is 0.4, when excluding the Lower Mississippi and Middle Missouri subbasins the mean value increases to 0.5. The Lower Mississippi and Middle Missouri subbasins are the only subbasins with no clear correlation between run-off and storage, most likely due to aquifer depletion.

Since ready-to-used GRACE mascon solutions cannot be modified, the mascon method developed at the Geoscience and Remote Sensing Department of the Delft University of Technology is used in this study. This study proposes modifications to tailor this method to the Mississippi Basin and mass anomalies of hydrological origin. After applying standard Tikhonov regularization, the exponential relationship is used to determine the most probable model outcome for each subbasin, adding a new term to the estimator. The resulting GRACE mascon solutions (Tikhonov and run-off regularized solutions) have a root-mean-square deviation (RMSD) of around 3.5 cm when compared to ready-to-use mascon solutions from the Jet Propulsion Laboratory and Goddard Space Flight Center. The run-off regularized solutions show smaller deviation (on average 7 %) than the Tikhonov regularized solutions with respect to an independent validation data set. The largest difference between the Tikhonov and run-off regularized solutions occur in the dryer subbasins (Platte, Middle, and Upper Missouri, and Upper Mississippi subbasin). These areas show a stronger inter-annual trend in TWSV, these trends are captured better by the run-off regularized solutions. Additional research, co-estimating the regularization bias, shows that the run-off regularized solutions induce less bias into the solutions. This study shows that using run-off data when processing GRACE data could be of added value, especially in semi-humid to arid areas, since the TWSV in these areas is more susceptible to inter-annual variations. ... Read more

The GRACE Follow-On mission is using classical K-Bandranging (KBR) and a new laser-ranging interferometry (LRI) method. The lattergives ranging data two orders of magnitude more accurate compared to theclassical K-Band ranging data (Dahl C et al. 2016). This gives a newopportunity for analyzing KBR noise by defining KBR noise as the differencebetween the KBR and LRI ranging data. In order to get a realization of KBR noise, the KBR andLRI epochs should be aligned and outliers have to be removed. An interpolation on the LRI data to make the LRI epochsaligned with the KBR epochs did not give sufficient results. Therefore only theoverlapping epochs were used as input for the next step of outlier detection, atotal of 2,250,000 epochs. The outlier detection method starts by taking theabsolute difference between the KBR and LRI range-rates. The largestdifferences were investigated where the original range-rate was compared to anestimation of the true value. This ‘true’ value is found by the use of a thirddegree polynomial function through the six range-rates that lie next to thesuspected outlier. The outlier detection method removes LRI range-rates thatdiffer more than 2.0*10^-8 m/s from the estimated true value and KBRrange-rates that differ more than 7.7*10^-7 m/s. 3764 LRI epochs and362 KBR epochs were labelled as outliers. After the outlier detection a histogram was made for theKBR range-rate noise. It was found that in order to get a normal distributionof KBR range-rate noise, the interval had to be in the range of <-3*10^-7 m/s, 3*10^-7m/s>. 59,000 still fell out of this noise range. 54,000 of these pointsformed 10 major clusters together where a subtraction of the KBR and LRIrange-rates did not give a realization of noise, but a trend similar to theoriginal signal and are therefore likely related to a clocking error. These54,000 points were therefore also removed from the dataset. To the remaining KBR range-rate noise values a thresholdof 3  was applied, removing an additional 4972 noisevalues that were larger than 4.03*10^-7 m/s. Finally , an estimation of the PSD of the KBR range-ratenoise  was made and compared to an oldPSD image of December 2008 of  the GRACEmission. The PSD plot of this project shows three peaks between 10^-4Hz and 10^-3 Hz. These peaks are not present in the PSD plot found inliterature of the GRACE mission. Except from the second and the third peak, thePSD values of the KBR range-rate noise of this project were lower, up to twoorders of magnitude in the lower frequency range (around 10^-4 Hz)and one order of magnitude in the higher frequency range (around 10^-1Hz). ... Read more

Climate change causes alterations in large scale mass transport patterns in the ocean, cryosphere and hydrology. The Gravity Recovery and Climate Experiment (GRACE) satellite mission which has been operational in the years 2002-2017 has already improved our understanding of large scale mass transport on Earth, but improvement of data quality is still needed. This will increase the quality of our current estimates of the effects of climate change on one hand and help in the validation and initiation of climate models on the other, which improves the accuracy of future predictions.

Noise in GRACE Level-2 data (monthly gravity field solutions) is caused by various reasons. The measurements themselves are already executed and their quality is fixed but better data processing algorithms and background models can reduce the current noise level. This is also relevant for the GRACE Follow On mission which might have a higher measurement precision. Over the ocean, these GRACE monthly solutions ideally only show mass exchange between continents and ocean and effects of self-attraction and loading. Therefore, the signal over the ocean is expected to consist predominantly of a linear trend and a seasonal variability. For certain oceanic regions this is not the case. In these areas still a signal variance representing interannual differences in the mass-derivative and large residuals with respect to a low-pass filtered signal are observed. This low-pass filtered signal contains only signals of a frequency lower than the semiannual cycle. These signal variance and residuals are unexpected and can be caused by inaccuracies in the currently applied oceanic background models in GRACE data processing.

For various Release 5 and Release 6 monthly solutions the noise variance, signal variance and residuals as aforementioned are estimated. The noise and signal variance are estimated by Variance Component Estimation (VCE). Additionally, numerical experiments are performed to analyze different regularization functionals and set-ups in the VCE. The oceanic regions where the largest signal variance and residuals are observed correlate. These areas are for GRACE Release 5 data the Baltic Sea, Black Sea, Arafura Sea, East Siberian Arctic Shelf, Argentine Basin and Hudson Bay. For GRACE Release 6 data a significant drop of this signal variance and residuals can be observed for the Hudson Bay and East Siberian Arctic Shelf.

Consequently, the oceanic background models for these releases are compared against each other and against the Global Tide and Surge Model (GTSM) which is a 2D hydrological model based on the Delft3D Flexible Mesh software developed by Deltares. For the whole ocean both 3/6-hourly time-series and monthly time-series are analyzed. For the shallow regions up to 200 m, the Black Sea and the Red Sea, GTSM shows significant differences with respect to the current applied oceanic background models. When comparing the oceanic background models of different releases it can be observed that the regions where the signal variance and residuals decreased for GRACE Release 6 with respect to Release 5 correlate to regions where the differences between these models is significant. This indicates that oceanic background models do significantly influence the quality of GRACE monthly solutions over the ocean.

Furthermore, it is investigated whether it can be expected that GTSM will improve the GRACE monthly solutions. For this, monthly time-series of the current applied oceanic background models are added back to the GRACE monthly solutions; consequently, by GTSM computed monthly time-series are removed. Compared to GRACE Release 5 monthly solutions, GTSM shows a reduction in the signal variance and residuals for the Hudson Bay, East Siberian Arctic Shelf, Black Sea, Baltic Sea, North Sea, Arafura Sea and certain parts of the Arctic and Southern ocean. Compared to GRACE Release 6, a reduction in the signal variance and residuals is observed for the East Siberian Arctic Shelf, Black Sea, Baltic Sea, North Sea and Arafura Sea. For these regions it is most expected that GTSM can improve GRACE monthly solutions. Since the quality of monthly solutions over the oceans is clearly influenced by the oceanic background models significant alterations in GRACE monthly solutions are expected for the shallow regions up to 200 m, Black Sea and Red Sea when applying GTSM in the GRACE data processing. Whether these will be improvements or not should be analyzed by implementing GTSM-based 3-hourly time-series in the GRACE data processing to create a new GRACE Level-2 data product. ... Read more

The GRACE mission has provided unprecedented insights into mass redistribution processes in the Earth system. Following a strong call for continuation of the mass observations, the GRACE-Follow On (GRACE-FO) mission was launched in May 2018, leaving a coverage gap of ca. 1 year between GRACE and GRACE-FO. Geopotential solutions derived from data of the Swarm mission (2013-present) are candidate data to potentially bridge this gap, as well as bridge the minor discontinuities in the current GRACE time series. This study aims to validate the sensitivity of the Swarm measurement system to mass rates, by comparing GRACE and Swarm observations of the gravity trend induced by glacial isostatic adjustment (GIA). Studies inverting GIA observations (e.g., relative sea level change, surface deformation, [time variable] gravity) into mantle viscosity estimates suggest relatively high viscosity in the Hudson Bay area. This suggests that the North American GIA-induced gravity trend is linear on a multi-decadal time scale, which means we can extrapolate the GRACE-derived GIA observations into the Swarm time period for this area. We find that the Swarm-derived GIA observations correspond well in amplitude and spatial distribution to GRACE observations and conclude that both systems have a similar sensitivity to gravity trends at spatial scales to which Swarm is sensitive to (ca. 1500 km). We validate our findings via geopotential solutions of GRACE-FO and provide a brief analysis of the benefits of adding Swarm-derived information to the combined GRACE / GRACE-FO time series. ... Read more

By combining the RACMO2.3 RCM output with GRACE non-tidal ocean and atmospheric pressure anomaly as well as geo-center motion corrections from 2003 to 2017, a physics-based model to estimate the vertical displacement of the Greenland surface bedrock is created. This model is able to convert the mass and pressure anomalies into vertical displacement in the spherical harmonic domain with the use of load deformation coefficients based on the PREM earth model. The computed vertical displacement has a weak correlation with the observed displacement as measured by the GNET GNSS station network. Both the computed and observed vertical movement show seasonal signals, however the computed signal has both a lower amplitude and different phase to the observed displacement. This could possibly be explained by the selection of the GNET stations used in the analysis or possibly the implementation of the non-tidal ocean and atmospheric pressure anomaly. Questions regarding the optimization of the processing within the model are discussed but remain open. Recommendations for further research into the complexity of the system and shortcomings of the model are discussed in detail. ... Read more

The Jakobshavn glacier was responsible for approximately 1 mm eustatic sea level rise in the period of 2000 to 2010 [Howat et al. 2011]. As such, the Jakobshavn glacier became one of the largest outlet glaciers in Greenland [Joughin et al. 2004]. Ice flow velocities within the same period reached over 10 km/yr with strong seasonal variation [Howat et al. 2011, Joughin et al. 2012]. More recently from 2011 until 2013, even higher ice flow velocities of at least 15 km/yr were observed [Lemos et al. 2018]. Due to the relatively high ice flow velocities, the ice discharge plays the largest role in the mass balance (MB) of the Jakobshavn glacier. Quantification of the ice discharge from ice flow velocities is however, not a common procedure. Yet the evolution of the ice discharge of single glaciers not only improves understanding of the climate-cryosphere system, but also aids quantification of sea level contribution on a drainage basin scale. To that end, this study embodies an indirect ice discharge estimation of the Jakobshavn glacier over the period of November 2010 until March 2016 using altimetry (CryoSat-2 Level 1b (L1b)) and gravimetry (GRACE Level 2 (L2)) data in combination with a regional climate model (RACMO 2.3p2). By subtraction of the altimetric and gravimetric mass balance estimates from the atmospheric component (i.e. the surface mass balance (SMB)), two ice discharge estimates are obtained. This approach does not suffer from the drawbacks involved when estimating ice discharge from velocity fields directly, which are based on offset tracking. Data gaps for long polar nights and clouds in the visible spectrum and decorrelation in general, when the duration between subsequent images over the same location is long, are thus avoided. This is because offset tracking algorithms require recognisable characteristics in subsequent satellite recordings to determine the velocity, i.e. satellite recordings need to be sufficiently correlated. To derive the mass balance from altimetry data, adequate spatial sampling is desired. To that end, this study applies swath processing to CryoSat-2 L1b data with an adapted waveform sample selection criterion to obtain an unprecedented spatial sampling with about 2 order of magnitude more height observations compared to conventional retracking techniques. As a consequence, elevation changes can be derived at a relatively high spatial resolution (250 m).
The elevations are converted to elevation changes, volume change and mass change using weighted least squares estimations (WLSE), hypsometric averaging and density models, respectively. The GRACE-based mass change estimate is acquired using a point-mass assumption at the location of the Jakobshavn glacier. The known, simulated point mass is then scaled to the observed mass by GRACE. In addition, data weighting of GRACE Stokes' coefficients is attempted using the full noise covariance matrix. Subsequently, a LSE is used to infer the mass balance from the two time series (with and without weighting of the Stokes' coefficients). ... 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