The Surface Expression of Deep Columnar Flows

Studies of the Earth's secular variation have blossomed in recent decades, due to the availability of brand‐new satellite data. In particular, flow inversions at the core surface that incorporate the effects of rapid rotation a priori have been able to provide new insight into flows with time scales as short as a few years. These models have been mostly developed in a cylindrical representation, while core inversion methods are based on a spherical surface representation of the flow. This technical brief links band‐limited expressions for the flow coefficients in a cylindrical representation and those in a spherical surface representation, and demonstrates that these also remain band‐limited, with equal degrees of freedom. Correct regularity conditions on the stream function ensure a regular representation of these flows on the spherical surface. A triangular truncation rule for the cylindrical representation that is applicable for “isotropic resolution” is also presented. The equations we derive will be of use in future data‐assimilation work employing this cylindrical flow representation, and may prove helpful for conventional core‐inversion strategies.