Validation of geophysical excitation functions by a rigorous combination with Earth orientation parameters and gravity field coefficients

Geophysical excitation functions model the re-distribution of atmospheric, oceanic and hydrologic masses. The change of the mass distribution of the Earth affects polar motion and length of day as well as gravity field coefficients of second degree. As all these quantities are related to the unknown Earth's tensor of inertia, a combined analysis allows to identify inconsistencies between the data and to determine the tensor of inertia. Usually, this physical relation between the Earth rotation parameters, excitation functions and second degree gravity field coefficients which is induced by the tensor of inertia, is not considered. In our study, we rigorously exploit it for the independent mutual validation based on least-squares estimation including variance-covariance component estimation. The functional model is based on the well known linear approximation of the Euler-Liouville equation. The construction of an appropriate stochastic model is hindered in practice due to insufficient knowledge on variances and covariances. Here, the missing stochastic information is determined empirically by analyzing the input data. Improved Earth orientation parameters, second degree gravity field coefficients and improved excitation functions are obtained as estimation results. Furthermore the unknown tensor of inertia is determined. The observation residuals indicate the degree of mutual consistency of the data. We give a short overview of our adjustment model. We present and discuss some results obtained from two different oceanic and atmospheric excitations (NCEP + ECCO and ECMWF + OMCT). The analysis and discussion of the resulting estimated excitation functions is emphasized. The work regarding the mutual validation is performed within the project P9 “Combined analysis and validation of Earth rotation models and observations” of the Research Unit FOR 584 (“Earth rotation and global dynamic processes”) which is funded by the German research funding organization DFG.