Boundary-Layer Meteorology

, Volume 148, Issue 1, pp 93-109

First online:

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

  • H. RichardsonAffiliated withDepartment of Marine, Earth, and Atmospheric Sciences, North Carolina State University
  • , S. BasuAffiliated withDepartment of Marine, Earth, and Atmospheric Sciences, North Carolina State University Email author 
  • , A. A. M. HoltslagAffiliated withMeteorology and Air Quality Section, Wageningen University

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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.


Boundary-layer height Large-eddy simulation Low-level jet Resistance laws Stable boundary layer