Complex Love Numbers in the Diurnal and Semidiurnal Tidal Bands Determined From Satellite Tracking and Altimetry

New tidal solutions from laser tracking of eight geodetic satellites and from a constellation of radar altimeters are combined to determine the complex Love number 𝒌2 for four lunar tidal constituents in the diurnal and semidiurnal bands. The tidal solutions for each data type must account for inconsistent prior Love numbers; the altimetry community has historically used elastic Love numbers. Use of the complex Love numbers recommended by current international conventions results in a small (order 4%) discrepancy between altimeter and tracking solutions for the degree-2 prograde spherical harmonics; this points to an anelastic Earth model that is too dissipative, with a phase lag slightly too large. Our estimated phase lag for 𝒌2 varies slightly across the tidal bands, from 0.228◦±0.024◦ for O1 to a smaller 0.178◦±0.020◦ for M2, with corresponding tidal 𝑸 rising from 250 to 320. Results for N2 and Q1 are consistent, but with much larger uncertainties. There is some interdependence on the values adopted for other Love and loading numbers, which we account for. A possibly important systematic error arises from seawater density, needed to relate
ocean tidal elevations to gravitational Stokes coefficients. A constant mean density of 1035 kg m−3 is used, but allowance for spatial variations in ocean density may be necessary.