Comments on “horizontal gravity disturbance vector in atmospheric dynamics” by Peter C. Chu

In a recent paper [Chu (2023; Chu23)], the author formulated the equations governing atmospheric motion in a spheroidal coordinate system. Since the mass distribution of the Earth is not exactly spheroidal, the true gravity is not vertical in that coordinate system. Chu23 compared the magnitude of the static horizontal component of gravity in that system to those of the dynamically active forces and concluded that the horizontal components of gravity should not be neglected. In recent papers by the authors [Chang and Wolfe (2022; CW22) and Stewart and McWilliams (2022; CW22)], we explained that the actual interpretation of the approximation made in atmospheric and oceanic modeling is not neglecting the horizontal component of the true gravity, but is a geometrical approximation, approximating nearly spheroidal geopotential surfaces with bumps on which the true gravity is vertical by exactly spheroidal surfaces. We showed that under such an interpretation, the errors due to the geometrical approximation are small. Chu23 claimed that CW22 and SM22 erroneously neglected the gravity perturbations in their analyses. Here, we explain further the differences between these approaches, in the process showing that the criticisms of Chu23 on CW22 and SM22 are invalid, further supporting our conclusion that the horizontal component of the true gravity is not relevant in ocean and atmospheric dynamics. Physically, the reason why horizontal gravity is irrelevant in the coordinate system used by Chu23 is that it is balanced by a static horizontal pressure gradient force.