Retracted: True Gravity in Atmospheric Ekman Layer Dynamics. Issue 20 (18th October 2021) - Chu, Peter C.
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 (−g0 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 ), ∂ 2 T / ∂ z 2, causes the Ekman pumping in addition to the geostrophic vorticity ( ζ g ). With ∂ 2 T / ∂ z 2 from the EIGEN‐6C4 static gravity model, and ζ g 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. Plain Language Summary: Meteorologists use the spherical (or ellipsoidal) surfaces represented by latitude ( φ ) and longitude ( λ ) as the horizontal and the direction normal to them represented by height ( z ) as the vertical. It is not correct since the vertical direction is represented by the true gravity g ( λ, φ, z ); and the horizontal surfaces are the equipotential surfaces of g ( λ, φ, z ) such as the geoid surface which is nearest to the Earth spherical (or ellipsoidal) surface ( z = 0). In the ( λ, φ, z ) coordinates, the true gravity g ( λ, φ, z ) has latitudinal and longitudinal components, which are neglected completely in meteorology. This study uses the atmospheric Ekman layer dynamics and the true gravity data from the EIGEN‐6C4 static gravity model as an example to show the importance of using the true gravity g ( λ, φ, z ) in the atmospheric dynamics, weather forecast, and climate change. Key Points: True gravity g ( λ, φ, z ) represents vertical and has latitudinal and longitudinal components Replacement of the standard gravity −g0 k (g0 = 9.81 m s −2 ) by g ( λ, φ, z ) in the classical Ekman layer equation leads to a new solution With data from EIGEN‐6C4 and Comprehensive Ocean‐Atmosphere Data Set, the Ekman pumping velocity is much larger due to g ( λ, φ, z ) than due to geostrophic vorticity