Introduction

In barotropic ocean dynamics the secondary effect of ocean loading and selfattraction (LSA) is known to be an essential part. It is often considered in a simplified manner, because the full LSA-term turns the dynamical equations into an integro-differential equation system that makes consideration of the full effect very time consuming in numerical models. However, a recent review of the LSA-effect recommends that ’most serious applications should use the full integral formulation' [41]. This convolution integral is defined through the so called Green's function of loading and self-attraction. The Green's function are given in terms of spherical harmonics, weighted through the degree-dependent loading Love numbers, which are computed by an earth model considering the features of elasticity and the radial density distribution of the earth [9].

In the application of ocean tide models including the full LSA-effect, the first complete solutions were obtained by [8, 16, 1, 56]. These solutions yield the common result that the main structure of the tidal patterns is preserved when including the LSA-effect, but that the computed tide is generally delayed, and in certain areas significant local modifications are found. Recent analysis of the full LSA-effect and its parameterization in a barotropic ocean model forced by atmospheric wind stress, atmospheric pressure, and tidal forces indicate that there are significant differences in the magnitude of the LSA-term, depending on the time scale of the ocean response [48]. The full consideration of the LSA-effect in circulation models has not been realized so far, but a first investigation of a simplified consideration of the LSA is performed by [50].

For understanding the response behavior of oceanic water masses to atmospheric and tidal forces, knowledge of the barotropic free oscillations is substantial and provides a spectral representation of the LSA-effect in barotropic ocean dynamics. These oscillations consist of gravity and vorticity modes, primarily governed by the gravity of the Earth and by the Coriolis force, respectively. They determine the response of the ocean to tidal forces and are furthermore excited by wind stress and atmospheric pressure.