![]() ![]() ![]() In all the fields of the Earth science such as meteorology, oceanography, and geodesy, the horizontal component of any vector A is on the spherical surface if the polar spherical coordinates are used or on the ellipsoidal surface if the oblate spherical coordinates are used, The polar spherical coordinates (more popular) and oblate spherical coordinates (less popular, see Appendix) are the reference coordinate system used in the Earth science. ![]() The correct approach is to compare the horizontal gravity with the horizontal forces such as the Coriolis force or the horizontal pressure gradient force. Thus, the feasibility to neglect the horizontal gravity components ( g λ, g φ) against the vertical gravity ( g z) needs to be investigated. The horizontal pressure gradient forces are considered important in oceanic motion for any scales. However, similar situation also occurs with the three-dimensional pressure gradient force: the horizontal pressure gradient force is much smaller (5–6 orders of magnitudes) than the vertical pressure gradient force in large-scale oceanic motion. The feasibility of such a practice has never been challenged because the horizontal components ( g λ, g φ) are much smaller (5–6 orders of magnitudes) than the vertical component g z and the deviation of the magnitude of g z to g 0 is also very small. Gravity is greatly simplified in oceanography from a three-dimensional vector field with ( λ, φ, z) being the (longitude, latitude, height) and ( i, j, k) being the corresponding unit vectors with eastward positive for i, northward positive for j, and upward positive (in the Earth radial direction) for k to a vertical vector (−g 0 k) with the uniform gravity g 0 = 9.81 m/s 2. ![]()
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