Temporal variation of tidal parameters
Geophysics
Final Report Abstract
The locally inhomogeneous component of the gravitational field of the Sun, the Moon, and other celestial bodies is called tidal field. Gravimeters installed on Earth’s surface move in the tidal field because of Earth’s rotation about its spin axis and the Earth and other celestial bodies movement on their orbits and measure a time varying signal. The measured amplitude of the tidal gravity signal exceeds the signal expected on a rotating rigid sphere of the size of the Earth by about 16 per cent and is shifted in phase. The rheology and structure of the Earth’s body as well as the tide driven motion of water in the oceans and air in the atmosphere contribute to this additional response. It is given by the admittance of the Earth in terms of the ratio of the measured gravity signal with respect to the signal, which would be measured on a rigid Earth without oceans and atmosphere. Tidal analysis of gravimeter data infers parameters, the so-called gravimetric factor and phase that quantify Earth’s admittance at different frequencies. Recent studies have shown that, if tidal analysis is run as a moving window analysis (MWA), the tidal parameters in individual time windows vary systematically with time. These variations appear to express not a scatter in the results caused by noise, but rather a temporal variation of Earth’s admittance to the tidal forcing. A seasonally varying admittance of the oceans and radiation driven gravity variation in the atmosphere as well as deficiencies of the analysis model have been discussed as potential cause of these variations. In work package 1 we investigated the hypothesis that time-variable ocean loading is the origin of globally observed annual variations of the M2 tidal parameters in time series recorded by superconducting gravimeters. We suppose that non-linear, time-stepping, hydro-dynamic modeling of Earth’s oceans has the potential to quantify observed temporal variations of tidal admittance, and investigated five advanced models. All available models take into account barotropic and baroclinic tides and incorporate tidal as well as meteorological forcing. They differ in various properties like the spatial resolution and incorporation of measured data. Loading was calculated individually for globally distributed gravity stations using up-to-date Green’s functions. The loading time series was added to predicted tides on a seismological earth model including an updated model for the core resonance. We analyzed the resulting synthetic observation curve in a traditional approach just as the real observations by MWA. As a result, three of the five ocean models produce annual variations of the M2 tidal parameters that resemble the observed variations in terms of period and magnitude (10−4 for the gravimetric factor and 0.01◦ for the phase at the Central European stations). We conclude that ocean loading is a plausible source for the time-varying tidal admittance as observed in gravimetric time series, although the current ocean models do not yet describe the annual variation of the M2 amplitude accurately enough to quantify the relationship statistically, or to correct gravity data a-priori with the corresponding loading time series. Work package 2 has a focus on deficiencies of the a-priori wave grouping model used in traditional analysis approaches. Such deficiencies would be due to a frequency dependence of tidal admittance not well captured by the analysis model, which also may comprise an a-priori assumed ratio of tidal parameters for different spherical degree, as is used in traditional analysis programs. To further investigate the causes of temporal tidal parameter variations it is necessary to isolate the parameters of the so-called radiation tides, to handle tidal harmonics of different degree separately and to allow for variations on smaller frequency bands than would be allowed by the widely used Rayleigh criterion for wave grouping. We implement a robust approach to tidal analysis, by adding a model constraint to the objective function with respect to a reference model. In this way we can use free inversion parameters per each tidal harmonic. In an iterative procedure we update the reference model based on the parameters which receive the strongest constraints from the gravity data. Wave grouping in the reference model hence is data driven and allows for a detailed structure in the model where supported by the data. The local tidal model derived from 11.5 years of data recorded at Black Forest Observatory (BFO, Schiltach) then is used as the a-priori analysis model in a moving window analysis. By this we reduce the amplitude of temporal variations in the diurnal tidal band by up to a factor of seven. The remaining distribution of parameters about the mean comes closer to a normal distribution. In the half-diurnal band, significant temporal variations on semi-annual and annual time scales remain, giving evidence to ocean loading effects as supposed in WP 1. The new approach provides the necessary basis for further investigations of time varying tidal admittance and their causes.
Publications
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A catalogue of gravimetric factor and phase variations for twelve wave groups. KIT Scientific Working Papers, 101. Karlsruhe Institute of Technology (KIT).
E. Schroth, T. Forbriger, M. Westerhaus
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Analysis of temporal variations of gravimetric tidal
parameters. Dissertation. Karlsruher Institut für Technologie (KIT).
E. Schroth
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Eterna - Programs for tidal analysis and prediction. Karlsruhe Institute of Technology.
H.-G. Wenzel
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RIGTID. Karlsruhe Institute of Technology.
W. Zürn, R. Broucke, P. Muller
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Reduction of apparent temporal variations of tidal parameters by a proper local response model. J. Geod., 97, 82. (doi: 10.1007/s00190-023-01770-w)
A. Ciesielski, T. Forbriger, W. Zürn, A. Rietbrock
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Regularization in tidal analysis and the application of the local response model in moving window analysis.
Adam Ciesielski
