Inversion of Earth\textquoterights changing shape to weigh sea level in static equilibrium with surface mass redistribution

We develop a spectral inversion method for mass redistribution on the Earth\textquoterights surface given geodetic measurements of the solid Earth\textquoterights geometrical shape, using the elastic load Love numbers. First, spectral coefficients are geodetically estimated to some degree. Spatial inversion then finds the continental surface mass distribution that would force geographic variations in relative sea level such that it is self-consistent with an equipotential top surface and the deformed ocean bottom surface and such that the total (ocean plus continental mass) load has the same estimated spectral coefficients. Applying this theory, we calculate the contribution of seasonal interhemispheric (degree 1) mass transfer to variation in global mean sea level and nonsteric static ocean topography, using published GPS results for seasonal degree-1 surface loading from the global IGS network. Our inversion yields ocean-continent mass exchange with annual amplitude (2.92 +/- 0.14) \texttimes 1015 kg and maximum ocean mass on 25 August +/-3 days. After correction for the annual variation in global mean vertical deformation of the ocean floor (0.4 mm amplitude), we find geocentric sea level has an amplitude of 7.6 +/- 0.4 mm, consistent with TOPEX-Poseidon results (minus steric effects). The seasonal variation in sea level at a point strongly depends on location ranging from 3 to 19 mm, the largest being around Antarctica in mid-August. Seasonal gradients in static topography have amplitudes of up to 10 mm over 5000 km, which may be misinterpreted as dynamic topography. Peak continental loads occur at high latitudes in late winter at the water-equivalent level of 100-200 mm.