There is no horizontal gravity force in geopotential coordinates.

Abstract

In response to a recent challenge to the longstanding practice in modeling large-scale circulations in the atmosphere and ocean that neglects any horizontal component of Earth's gravity-rotation force, this paper demonstrates that a coordinate transformation into geopotential coordinates has no such horizontal force. This framework should be understood as the justification for and, if warranted, the basis for making further refinements to such geophysical models.