Analysis of mass variations in Greenland by a novel variant of the mascon approach

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.