General diagnostic equations and regime analysis for the height of the planetary boundary layer

A new general theoretical formula for the planetary boundary-layer height h, which accounts for the joint influence of the Earth's rotation, stratification (stable/neutral and unstable), entrainment and free-flow stability effect, is obtained on the basis of parametrization of the turbulent kinetic energy balance equation. Practically all the basic equilibrium stable/neutral and unstable boundary-layer depth prototypes, corresponding limit cases for h, as well as the transition regimes between them, follow from this general formula as respective asymptotic cases. The explicit dependence of the proportionality coefficient for the limit cases on the governing parameters is determined and corresponding comparison with experimental data is given. The case when the Coriolis effect is neglected is separately considered. Again a new general formula for h and the consequent limit cases is obtained in this case. In agreement with the experimental data the great sensitivity of the stable boundary-layer height to the form of the vertical profile of the buoyancy flux is theoretically confirmed and quantitatively analysed. Special attention is paid also to the important role of the free-flow stability effect not only for stable/neutral, but also for unstable conditions. The significant limiting effect of this factor on the boundary-layer depth is demonstrated for mid-, as well as for high latitudes.