Retracted: True Gravity in Atmospheric Ekman Layer Dynamics

Abstract

AbstractTrue gravity is a three‐dimensional vector field, g(λ, φ, z) = igλ + jgφ + kgz, with (λ, φ, z) the (longitude, latitude, height) and (i, j, k) the corresponding unit vectors. The longitudinal‐latitudinal component of the true gravity, gh = igλ+jgφ, is neglected completely in meteorology through using the standard gravity (−g0k, g0 = 9.81 m/s2) 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 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), , 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 gh, 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.