Boundary-Layer Meteorology

, Volume 165, Issue 2, pp 371–384 | Cite as

An Analytical Formulation of the Monin–Obukhov Stability Parameter in the Atmospheric Surface Layer Under Unstable Conditions

  • Piyush Srivastava
  • Maithili Sharan
Notes and Comments


A non-iterative analytical scheme is developed for unstable stratification that parametrizes the Monin–Obukhov stability parameter \(\zeta \) (\({=}z{/}L\), where z is the height above the ground and L is the Obukhov length) in terms of bulk Richardson number (\(Ri_B\)) within the framework of Businger–Dyer type similarity functions. The proposed scheme is valid for a wide range of roughness lengths of heat and momentum. The absolute relative error in the transfer coefficients of heat and momentum is found to be less than 1.5% as compared to those obtained from an iterative scheme for Businger–Dyer type similarity functions. An attempt has been made to extend this scheme to incorporate the similarity functions having a theoretically consistent free convection limit. Further, the performance of the scheme is evaluated using observational data from two different sites. The proposed scheme is simple, non-iterative and relatively more accurate compared to the schemes reported in the literature and can be used as a potential alternative to iterative schemes used in numerical models of the atmosphere.


Bulk Richardson number Monin–Obukhov similarity theory Parametrization schemes Stability parameter Transfer coefficients 



The authors thank the UK Met Office for provision of the Cardington measurements and National Center for Atmospheric Research (NCAR) for CASES-99 observations. This work is partially supported by the Ministry of Earth Sciences, Government of India under the CTCZ program, JC Bose Fellowship to MS from DST-SERB, Govt of India and SRF to PS from University Grant Commission. The authors thank the reviewers for their valuable comments and suggestions.

Supplementary material

10546_2017_273_MOESM1_ESM.docx (184 kb)
Supplementary material 1 (docx 183 KB)


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© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Centre for Atmospheric SciencesIndian Institute of Technology DelhiHauz KhasIndia

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