Comparisons and possible combinations of time-wise and space-wise approaches for satellite gravity missions data processing

Dedicated satellite gravity missions, such as GOCE, GRACE and GRACE-FO, have been providing essential data for many geodetic and geophysical studies and applications. In the next future, new missions exploiting technological advances and innovative observation principles will be proposed, thus requiring numerical simulations to assess their performances in recovering information on the Earth gravity field. This is typically done by simulating the satellite orbits and propagating the instrumental noise to the error covariance matrix of the spherical harmonic coefficients. Of course, this propagation also depends on the processing techniques. Among them, approaches based on time-wise strategies are devised to directly map the time series of observations to spherical harmonic coefficients, while the approaches based on space-wise strategies are focused on the location of observations estimating the coefficients by some local analysis. In this work we compare a time-wise approach with a space-wise approach for the data analysis of possible future gradiometry missions, for example those based on quantum technology and based on the satellite tracking concept (pair or double pair of satellites, such as NGGM/MAGIC). The time-wise approach basically works in the Fourier transform domain, thus making the simulation very efficient from the computational point of view at the cost of some simplifications, e.g., in the data regularity and in the orbit repetition period. The time-wise approach permits a formal error propagation of realistic instrumental noise power spectral densities. On the other hand, the space-wise approach is focused on projecting the observed gravity information onto a spherical grid and then solving the boundary value problem to estimate the spherical harmonic coefficients. In estimating the grid values, the space-wise approach directly works in the space domain where a collocation method on local patches of data can be exploited for adapting the estimation to the local/regional characteristics of the gravity field. Differently from the time-wise approach, a formal error propagation from the instrumental noise power spectral densities is not feasible, e.g., for the limitations in modelling the error cross-correlation of grid nodes estimated from different data patches. Therefore, the overall error assessment relies on a Monte Carlo simulation. In this study, several numerical simulations are presented to emphasize the pros and cons of the two methods, as well as possible combination strategies to be exploited in studies of the time-variable models of the Earth gravity field.