Retracted: True Gravity in Atmospheric Ekman Layer Dynamics

Abstract True gravity is a three‐dimensional vector field, g ( λ , φ , z ) = i g λ + j g φ + k g z , with ( λ , φ , z ) the (longitude, latitude, height) and ( i , j , k ) the corresponding unit vectors. The longitudinal‐latitudinal component of the true gravity, g h = i g λ + j g φ , is neglected completely in meteorology through using the standard gravity (− g 0 k , g 0 = 9.81 m/s 2 ) or the effective gravity [− g ( φ ) K ]. Here, k (or K ) is normal to the Earth spherical (or ellipsoidal) surface. Such simplification of g ( λ , φ , z ) has never been challenged. This study uses the classical atmospheric Ekman layer dynamics as an example to illustrate the importance of g h . The standard gravity (−g 0 k ) 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 ), , causes the Ekman pumping in addition to the geostrophic vorticity ( ). With from the EIGEN‐6C4 static gravity model, and calculated from July sea level pressure ( p ) data from the Comprehensive Ocean‐Atmosphere Data Set, the global mean strength of the Ekman pumping over the world oceans is 3.69 cm s −1 due to g h , which is much larger than 0.33 cm s −1 due to the geostrophic vorticity. It implies the urgency to use the true gravity g ( λ , φ , z ) into atmospheric GCM and weather forecast although the results are obtained from specific density field and gravity model.