Invalid spheroidal geopotential approximation and non-decomposable centrifugal acceleration from gravity – Reply to: Comments on “Horizontal gravity disturbance vector in atmospheric dynamics” by Chang, Wolfe, Stewart, McWilliams

Abstract

Chang, Wolfe, Stewart, and McWilliams commented on my recent work regarding the horizontal gravity disturbance vector in atmospheric and oceanic dynamics. Their comments are incorrect. They ignored the horizontal pressure gradient error, claimed the validity of the spheroidal geopotential approximation subjectively based only on small metric error, and decomposed gravity into gravitational and centrifugal accelerations, which should never have been done. Here, I explain further why the spheroidal geopotential approximation is invalid and why gravity cannot be decomposed into gravitational and centrifugal accelerations in atmospheric and oceanic dynamics. Physically, the horizontal gravity disturbance vector vanishes in the horizontal momentum equation using the true gravity g_t in the true geopotential coordinates but does occur in the horizontal momentum equation using the true gravity g_t in the spheroidal geopotential coordinates due to the horizontal pressure gradient error in the coordinate transformation. The error of horizontal pressure gradient force in transforming true geopotential to spheroidal geopotential coordinates equals to the horizontal gravity disturbance vector. The spheroidal geopotential approximation claimed by Chang, Wolfe, Stewart, and McWilliams is invalid.