A comparative study on the parametrization of a time-variable geopotential model from GRACE monthly solutions

The gravity field of the Earth is time-dependent due to several types of mass variations which take place on different time scales. Usually, the time-variability of the gravitational potential of the Earth is expressed by the monthly determination of a static geopotential model based on data from gravity field missions. In this paper, the variability of the potential is parameterized by a functional approach which contains a polynomial trend and periodic contributions. The respective parameters are estimated based on the monthly solutions derived from the GRACE and GRACE-FO gravity field mission up to a maximum degree of expansion n max = 96 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n_\text {max}=96$$\end{document} . As a preliminary data analysis, a Fourier analysis is performed on selected potential coefficients from the available monthly solutions of the GFZ. The indicated frequency components are then used to formulate a time-dependent analytical approach to describe each Stokes coefficient's temporal behaviour. Different approaches are presented that include both polynomial and periodic components. The respective parameters for modelling the temporal variability of the coefficients are estimated in a Gauss-Markov model and tested for significance by statistical methods. Extensive comparative numerical studies are carried out between the newly generated model variants and the existing monthly GRACE, GRACE-FO and the existing time dependent EIGEN-6S4 solutions. The numerical comparisons make it clear that estimated models based on all available monthly solutions describe the essential periods very well, but such monthly events that deviate strongly from the mean behaviour of the signal show less precision in the space domain. Models that are estimated based on fourteen consecutive monthly solutions, covering one selected year, represent the amplitudes much more precise. The statements made apply to four initial data used, which are filtered to varying degrees. In particular, DDK2, DDK5 and DDK8, as well as unfiltered coefficients were used. For all the model approaches used, it can be seen that the potential coefficients contain up to about n approximate to 40 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\approx 40$$\end{document} in case of DDK5 periodically signals with annual, semi-annual or quarterly, as well as Luna nodal periods and do not vary significantly beyond that degree. Only an offset can be estimated significantly for all Stokes coefficients.