Earth rotation deceleration/acceleration due to semidiurnal oceanic/atmospheric tides: Revisited with new calculation

The global oceanic/atmospheric tides exert decelerating/accelerating secular torques on the Earth rotation. We developed new formulations to accurately calculate amounts of two kinds of secular tidal torques. After Melchior, we found that an additional factor 1+k-l = 1.216, which has been formerly neglected, must be multiplied unto the tidal torque integral. By using our refined formulations and the recent oceanic/atmospheric global tide models, we found that: (i) semidiurnal oceanic lunar/solar tides exert decelerating torques of about −4.462×1016/−0.676×1016Nm respectively and (ii) atmospheric S2 tide exerts accelerating torque of 1.55×1015Nm. Former estimates of the atmospheric S2 tidal torque were twice as large as our estimate due to improper consideration of loading effect. We took the load Love number for atmospheric loading effect from Guo et al. (2004). For atmospheric loading of spherical harmonic degree two, the value of k'=−0.6031 is different from that for ocean loading as k'=−0.3052, while the latter is currently used for both cases – ocean/atmospheric loading – without distinction. We discuss (i) the amount of solid Earth tidal dissipation (which has been left most uncertain) and (ii) secular changes of the dynamical state of the Earth-Moon-Sun system. Our estimate of the solid Earth tidal torque is −4.94×1015Nm.