Why We Can Approximate Spheroidal Geopotential Surfaces as Spherical but Can't Approximate True Geopotential Surfaces as Spheroidal in Atmospheric and Oceanic Modeling

 Horizontal pressure gradient error is negligible in approximating spheroidal geopotential surfaces as spherical.  Horizontal pressure gradient error is nonnegligible gravity disturbance vector in approximating true geopotential surfaces as spheroidal.  Horizontal gravity disturbance vector should be included in any analytical and numerical atmospheric and oceanic models.