Atmospheric acceleration and Earth-expansion deceleration of the Earth rotation

Previous studies suggest that tidal friction gives rise to the secular deceleration of the Earth rotation by a quantity of about 2.25 ms/cy. Here we just consider additional contributions to the secular Earth rotation deceleration. Atmospheric solar semi-diurnal tide has a small amplitude and certain amount of phase lead. This periodic global air-mass excess distribution exerts a quasi-constant torque to accelerate the Earth's spin rotation. Using an updated atmospheric tide model, we re-estimate the amounts of this atmospheric acceleration torque and corresponding energy input, of which the associated change rate in LOD (length of day) is −0.1 ms/cy. In another aspect, evidences from space-geodesy and sea level rise observations suggest that Earth expands at a rate of 0.35 mm/yr in recent decades, which gives rise to the increase of LOD at rate of 1.0 ms/cy. Hence, if the previous estimate due to the tidal friction is correct, the secular Earth rotation deceleration due to tidal friction and Earth expansion should be 3.15 ms/cy.