In this study, a method is developed which allows to combine gravimetric and geometric data in order to improve the spatial resolution of the resulting mass balance estimate. The so called equivalent ice density of the changing ice volume is estimated within a mathematical inversion model which includes as observations geometric information about the volumetric change of the ice sheet and the resulting gravity change. In the presentation, detailed insights into the mathematical and stochastic procedures will be delivered.
As gravimetric information, monthly GRACE gravity fields are applied. They have a limited spatial resolution of a few 100 km, but allow direct conclusions about the true mass changes across Greenland. The ice volumes are described by a product of ESA’s Climate Change Initiative which is derived from altimetry data. They have a very fine spatial resolution (down to a few km), but are not directly sensitive to the density of the changing ice volumes.
By combining both datasets in a common mathematical model, the advantages of both data types (direct sensitivity to mass vs. high spatial resolution) are used to improve the spatial resolution of mass balance estimates across Greenland. The result will be a map of mass trends which has the same spatial resolution like the input map of geometric changes. At the same time, the high-resolution distribution of surface-mass changes is reasoned in the GRACE gravity fields. The resulting distribution is compared to the results of other studiers regarding the spatial structure of mass changes and the total mass loss.
However, due to limits concerning the computational effort regarding the applied computers, it is only possible to recognize structures which correspond to the applied sampling rate of the grid on which the density distribution is estimated. Furthermore, regularization methods due to near-singularities of the normal equation matrix have to be applied. Along the coasts due to the limited resolution of the input GRACE gravity fields, leakage effects occur in the sense of a physically unreasonable assignment of mass changes to nearby oceanic surfaces. However, those effects can be partly reduced through the here presented combination approach.