Improving Stable Boundary-Layer Height Estimation Using a Stability-Dependent Critical Bulk Richardson Number

For many decades, attempts have been made to find the universal value of the critical bulk Richardson number ( $Ri_{Bc}$ ; defined over the entire stable boundary layer). By analyzing an extensive large-eddy simulation database and various published wind-tunnel data, we show that $Ri_{Bc}$ is not a constant, rather it strongly depends on bulk atmospheric stability. A (qualitatively) similar dependency, based on the well-known resistance laws, was reported by Melgarejo and Deardorff (J Atmos Sci 31:1324–1333, 1974) about forty years ago. To the best of our knowledge, this result has largely been ignored. Based on data analysis, we find that the stability-dependent $Ri_{Bc}$ estimates boundary-layer height more accurately than the conventional constant $Ri_{Bc}$ approach. Furthermore, our results indicate that the common practice of setting $Ri_{Bc}$ as a constant in numerical modelling studies implicitly constrains the bulk stability of the simulated boundary layer. The proposed stability-dependent $Ri_{Bc}$ does not suffer from such an inappropriate constraint.