Diagnostic and prognostic equations for the depth of the stably stratified Ekman boundary layer

Refined diagnostic and prognostic equations for the depth of the stably stratified barotropic Ekman boundary later (SBL) are derived employing a recently developed non-local formulation for the eddy viscosity. In well-studied cases of the thoroughly neutral SBL, the nocturnal atmospheric SBL and the oceanic SBL dominantly affected by the static stability in the thermocline, the proposed diagnostic equation reduces to the Rossby-Montgomery, Zilitinkevich and Pollard-Rhines-Thompson equations, respectively. In its general form it is applicable to a range of regimes including long-lived atmospheric SBLs affected by the near-surface buoyancy flux and the static stability in the free atmosphere. Both diagnostic and prognostic SBL depth equations are validated against recent data from atmospheric measurements.