A new set of barotropic free oscillations of the World Ocean is computed with explicit consideration of dissipative terms and the full ocean loading and self-attraction effect (LSA). This set contains free oscillations that did not appear in the spectra of previous studies. Furthermore, the expansion towards longer periods (165 hours) yields new global planetary modes. Altogether 169 free oscillations are computed with periods longer than 7.7 hours. Of these, 71 are gravitational modes, 92 are topographically controlled vorticity modes, and 6 are planetary vorticity modes. The influence of the LSA is investigated for all three kinds of modes with respect to changes in the periods and in the spatial structure of the sea surface elevation and the horizontal mass transports. In particular, for modes in the semi-diurnal and diurnal period range, the parameterization of the LSA is analyzed. For the free oscillations in the period range from 9 to 40 hours the corresponding adjoint solutions are computed and used to synthesize semidiurnal and diurnal tides of second degree. Since these free oscillations are determined with and without consideration of the full LSA-effect, this study allows for a detailed analysis of the LSA on the dynamics of ocean tides, e.g. an physical explanation is given for the induced phase delay computed by ocean tide models. Further, the synthesis gives a spectral composition of certain well known tidal features and pairs of free oscillations are identified, diminishing their contribution either on a global or local scale. Further, semidiurnal and diurnal tidal solutions of a tidal model with assimilation of data are integrated in the procedure of synthesizing tides. This approach shifts the expansion coefficients of each free oscillation in the synthesis of various tidal constituents towards more realistic values and a first attempt is made to improve the eigenfrequencies of the free oscillations through linear least square fits

Here’s a concise author biography for Dr. Malte Müller, whose work includes the monograph A Large Spectrum of Free Oscillations … including the full world ocean loading and self-attraction effects:

🧑‍🔬 Dr. Malte Müller

• Dr. Müller earned his PhD in 2008 from the University of Hamburg, studying within the International Max Planck Research School for Maritime Affairs (Google Sites).

• His doctoral dissertation led to the publication A large spectrum of free oscillations of the World Ocean… including the full ocean loading and self-attraction effects as part of the Hamburg Studies on Maritime Affairs series by Springer in 2008 (Google Sites).

• He was a postdoctoral researcher (2009–2012) at the University of Victoria (Canada), supported by a DFG fellowship, working on ocean circulation modeling and the dynamics of free oscillations (Google Sites).

• From 2012–2013, he served as a research associate at the University of Victoria and University of Michigan, focusing on HYCOM tide modeling (Google Sites).

• Since 2013, he is affiliated with the Norwegian Meteorological Institute, where he advanced to Research Professor (Forsker 1183) in 2018, and concurrently serves as an Associate Professor since 2019 in the Department of Geosciences at the University of Oslo (Google Sites).

🔬 Research Interests & Projects

His research centers on:

• Earth’s free oscillations, ocean tidal loading, and self-attraction effects.

• Dynamic interactions among tides, gravity, and ocean dynamics.

• He has contributed to projects such as:

  • DFG ocean-earth system modeling (2005–2009) investigating Earth's rotation, surface deformation, and gravitational parameters

  • Ocean and Arctic forecasting initiatives like SALIENSEAS, TWEX, and Copernicus AMS Forecasting Centre

  • K‑12 to climate service implementation in the European Arctic (Google Sites, Google Sites)

📚 Selected Publications

• Müller, M. (2008). A large spectrum of free oscillations of the World Ocean including the full ocean loading and self‑attraction effects. Hamburg Studies on Maritime Affairs, Springer Berlin (Google Sites).

• Müller, M. (2008). “The free oscillations of the global ocean”, in High Performance Computing on Vector Systems, published by Springer Berlin alongside contributions from colleagues in tidal modeling research (Google Sites).

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