Geostrophic Drag Law in Conventionally Neutral Atmospheric Boundary Layer: Simplified Parametrization and Numerical Validation

Abstract

This study investigates the parameterization of the geostrophic drag law (GDL) for conventionally neutral atmospheric boundary layers (CNBLs). Utilizing large eddy simulations, we confirm that in CNBLs capped by a potential temperature inversion, the boundary-layer height scales as \(u_*/\sqrt{N f}\), where \(u_*\) represents the friction velocity, N the free-atmosphere Brunt–Väisälä frequency, and f the Coriolis parameter. Additionally, we confirm that the wind gradients normalized by the Brunt–Väisälä frequency have universal profiles above the surface layer. Leveraging these physical insights, we derived analytical expressions for the GDL coefficients A and B, correcting the earlier form of Zilitinkevich and Esau (Q J R Meteorol Soc 131:1863–1892, 2005). These expressions for A and B have been validated numerically, ensuring their accuracy in representing the geostrophic drag coefficient \(u_*/G\) (G is the geostrophic wind speed) and the cross-isobaric angle. This work extends the range for which the GDL has been validated up to \(u_*/G =[0.019, 0.047]\). This further supports the application of GDL to CNBLs over a broader range of \(u_*/G\), which is useful for meteorological applications such as wind energy.