Atmospheric torque on the Earth and comparison with atmospheric angular momentum variations

Abstract

The purpose of this paper is to compute atmospheric torques on the Earth, including the oceans, with an emphasis on the equatorial components. This dynamic approach is an alternative method to the classical budget‐based angular momentum method for viewing atmospheric effects on Earth's orientation in space. The expression of the total torque interaction between the atmosphere and the Earth is derived from the angular momentum balance equation. Such a torque is composed of three parts due to pressure, gravitation, and friction. Each of these torque components is evaluated numerically by a semi‐analytical approach involving spherical harmonic approximations, and their orders of magnitude are intercompared. For the equatorial components the pressure and gravitational torques have far larger amplitudes than that of the friction torque; these two major torques have the same order of magnitude but opposite signs, and the value of the sum of the torques is shown to be close to the equatorial components of the atmospheric angular momentum time derivative s, as would be expected in a consistent model‐based analysis system. The correlation between the two time series is shown to be very good at low frequency and decrease slowly with increasing frequency. The correlation is still significant (≥ 0.7) up to 0.5 cycle per day, but the correlation coefficient reduces to 0.5 at the diurnal frequency band, indicating the difficulty of calculating rapidly changing model‐based torques within an atmospheric analysis system.