Mercuryʹs global topography and tidal signal from laser altimetry by using a rectangular grid

Laser altimeters on board the MESSENGER and BepiColombo missions will accurately map Mercuryʹs topography including the time-dependent elevation from solar tides, which are predicted to be of order 1 m. The amplitude of solar tides, characterized by the Love number h2, reveals information on the interior structure of Mercury, in particular on the state and the size of the core. Koch et al., [Koch et al., (2008). Planet. Space Sci. 56, 1226–1237] have directly decomposed a global synthetic altimetry record into the time-dependent tidal signal and into a spherical harmonic expansion of the static topography. The precision for h2 depends on the maximum degree l of the expansion which is practically limited because the computation time increases very strongly with l. Here, we show that the computation time to achieve the same precision can be substantially reduced if we describe the static topography in terms of local basis functions defined on a rectangular grid. The subsequent projection of the grid data onto the orthonormal spherical harmonic functions is very rapid. The new method is promising to achieve high precision to test current models of Mercuryʹs interior and additionally delivers a topographic map with approximately 4.7 million grid points.