Improving Stable Boundary-Layer Height Estimation Using a Stability-Dependent Critical Bulk Richardson Number Authors H. Richardson Department of Marine, Earth, and Atmospheric Sciences North Carolina State University S. Basu Department of Marine, Earth, and Atmospheric Sciences North Carolina State University A. A. M. Holtslag Meteorology and Air Quality Section Wageningen University Article

First Online: 21 March 2013 Received: 30 April 2012 Accepted: 23 February 2013 DOI :
10.1007/s10546-013-9812-3

Cite this article as: Richardson, H., Basu, S. & Holtslag, A.A.M. Boundary-Layer Meteorol (2013) 148: 93. doi:10.1007/s10546-013-9812-3
Abstract
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.

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

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