Horizontal Gravity in Ocean Ekman transport

Three-dimensional gravity vector field g (=  i g λ + j g φ + k g z ) in geodesy has been greatly simplified to a uniform vertical vector (-g 0 k ) in oceanography with ( λ, φ, z ) the (longitude, latitude, height), ( i , j , k ) the corresponding unit vectors, and g 0  = 9.81 m/s 2 . Recent studies by the author show such simplification incorrect. The horizontal gravity is important in ocean dynamics. Along the same path, the horizontal gravity is included into the classical Ekman layer dynamics with constant eddy viscosity and depth-dependent-only density ρ ( z ) represented by an e-folding near-inertial buoyancy frequency. A new Ekman spiral and in turn a new formula for the Ekman transport are obtained. With the horizontal gravity data from the global static gravity model EIGEN-6C4 and the surface wind stress data from the Comprehensive Ocean-Atmosphere Data Set (COADS), the Ekman transport due to the horizontal gravity is crucial and cannot be neglected.