Diurnal angular momentum budget of the atmosphere and its consequences for Earth's nutation

The three-dimensional diurnal atmospheric angular momentum (AAM) budget is investigated, and its geographical features and meteorological dynamics are explored. It is shown that the diurnal atmospheric torques are associated with mass effect (ellipsoidal torque for the equatorial component and mountain torque for the axial component). It is shown that there is an important difference between the torque and angular momentum approaches on diurnal timescales, with the AAM time derivative generally exceeding the calculated torques. For the retrograde diurnal band, however, which is of interest for Earth nutation, the torque approach predicts much larger AAM changes than those observed. The AAM budget equation is also investigated theoretically, in order to give condition on the torques and AAM in order to verify the equation. Alternatively to the condition proposed by Bell, [1994], a condition on the local torque is shown sufficient to verify the AAM budget equation in the retrograde band, that is, the local torque have to balance the ellipsoidal effect. This condition is shown to be verified qualitatively. However, when separating the AAM budget equation into prograde and retrograde part, this last part become very sensitive to the error on the computation of the local torque. This explains why the torque approach always give one order of magnitude larger than the AAM approach at the retrograde diurnal frequencies.