True gravity is a three-dimensional vector, g = igλ+jgφ+kgz, with (λ, φ, z) the (longitude, latitude, height) and (i, j, k) the corresponding unit vectors. The vertical direction is along g, not along k, which is normal to the Earth spherical (or ellipsoidal) surface (called deflected-vertical). Correspondingly, the spherical (or ellipsoidal) surfaces are not horizontal surfaces (called deflected-horizontal surfaces). In the (λ, φ, z) coordinates, the true gravity g has longitudinal-latitudinal component, gh = igλ+jgφ, but it is neglected completely in meteorology through using the standard gravity (-g0k, g0 = 9.81 m/s2) instead. Such simplification on the true gravity g has never been challenged. This study uses the atmospheric Ekman layer as an example to illustrate the importance of gh. The standard gravity (-g0k) is replaced by the true gravity g in the classical atmospheric Ekman layer equation with a constant eddy viscosity (K) and a height-dependent-only density ρ(z) represented by an e-folding stratification. New formulas for the Ekman spiral and Ekman pumping are obtained. The second derivative of the gravity disturbance (T) versus z, also causes the Ekman pumping, , in addition to the geostrophic vorticity with DE the Ekman layer thickness and f the Coriolis parameter. With data from the EIGEN-6C4 static gravity model, the global mean strength of the Ekman pumping due to the true gravity is found to be 4.0 cm s-1. Such evidently large value implies the urgency to include the true gravity g into the atmospheric dynamics.

Geopotential in meteorology is the same as gravity potential in geodesy but with the opposite sign. Meteorologists don’t use the true geopotential (Φ) associated with the true gravity g = igλ+jgφ+kgz, but use the normal geopotential (ΦN) with the normal gravity [-g(φ,z)K], or the standard geopotential (Φ0) with the standard gravity (-g0k, g0 = 9.81 m/s2). Here, (λ, φ, z) are the (longitude, latitude, altitude) with (i, j, k/K) the corresponding unit vectors with k/K normal to the Earth spherical/ellipsoidal surface. In meteorology, difference between Φ0 and ΦN is considered minor but between Φ0 and Φ has not been identified. This study uses two publicly available datasets: (a) ICGEM EIGEN-6C4 and (b) NCEP/NCAR Reanalysis long term mean data to obtain true geopotential Φ and standard geopotential Φ0 for the troposphere (1000 - 100 hPa) and in turn to compute the nondimensional B and C numbers, representing the importance of the latitudinal-longitudinal gradient of disturbing geopotential (Φ-Φ0) versus the pressure gradient force and the Coriolis force. The B number varies from 0.4176 (maximum) at 850 hPa to 0.1630 (minimum) at 200 hPa. The C number varies from 0.6168 (maximum) at 1,000 hPa to 0.1573 (minimum) at 200 hPa. These values show the importance to use the true geopotential Φ in meteorology. A new equation for the geostrophic wind is also presented.

Two related issues in oceanography are addressed: (1) the unit vector (k) normal to the Earth spherical/ellipsoidal surface is not vertical (called deflected-vertical) since the vertical is in the direction of the true gravity, g = igλ+jgφ+kgz, with (λ, φ, z) the (longitude, latitude, depth) and (i, j, k) the corresponding unit vectors; and (2) the true gravity g is replaced by the standard gravity (-g0k, g0 = 9.81 m/s2). In the spherical/ellipsoidal coordinate (λ, φ, z) and local coordinate (x, y, z), the z-direction is along k (positive upward). The spherical/ellipsoidal surface and (x, y) plane are perpendicular to k, and therefore they are not horizontal (called deflected-horizontal) since the horizontal surfaces are perpendicular to the true gravity g such as the geoid surface. In the vertical-deflected coordinates, the true gravity g has deflected-horizontal component, gh = igλ+jgφ (or = igx+jgy), which is neglected completely in oceanography. This study uses the classic ocean circulation theories to illustrate the importance of gh in the vertical-deflected coordinates. The standard gravity (-g0k) is replaced by the true gravity g in the existing equations for geostrophic current, thermal wind relation, and Sverdrup-Stommel-Munk wind driven circulation to obtain updated formulas. The proposed non-dimensional (C, D, F) numbers are calculated from four publicly available datasets to prove that gh cannot be neglected against the Coriolis force, density gradient forcing, and wind stress curl.