Planetary energy balance for tidal dissipation

Dissipation of tidal energy is expressed here as an integral on the surface of a sphere that encloses the mass of the planet. When developed in constituent form, this surface integral depends linearly on the secondary potential that arises from the tidal disturbance; it can therefore be expressed as the sum of one part due to the body tide and another due to the fluid tides. The body tide part depends only on the anelastic response of the solid earth to the primary potential. The fluid tide part depends mainly on the elastic solid earth response to tidal loading and on the sum of the ocean tide and atmospheric tide mass disturbances. The atmosphere's contribution can be evaluated reliably from published analyses of the observed barometric tide. Tide gage data, on the other hand, do not suffice for a comparably reliable analysis of the observed ocean tide and must therefore be supplemented by dynamical interpolation through numerical integration of Laplace's tidal equations. Dissipation obtained from ocean tide models published during the past 5 years has a range of at least ±15% from the average value. The main cause of this uncertainty is the difficulty of modeling dissipation, but there are other uncertain aspects of existing models, notably the lack of provision for absorption of energy into baroclinic motions and for the anelastic response of the solid earth to tidal loading.