Boundary-Layer Meteorology

, Volume 148, Issue 1, pp 93–109 | Cite as

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.


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


  1. Anderson WC, Basu S, Letchford CW (2007) Comparison of dynamic subgrid-scale models for simulations of neutrally buoyant shear-driven atmospheric boundary layer flows. Environ Fluid Mech 7:195–215CrossRefGoogle Scholar
  2. Andreas EL, Claffey KJ, Makshtas AP (2000) Low-level atmospheric jets and inversions over the western Weddell sea. Bound-Layer Meteorol 97:459–486CrossRefGoogle Scholar
  3. Arya S (1975) Buoyancy effects in a horizontal flat-plate boundary layer. J Fluid Mech 68:321–343CrossRefGoogle Scholar
  4. Arya SP (1999) Air pollution meteorology and dispersion. Oxford University Press, New YorkGoogle Scholar
  5. Basu S, Porté-Agel F (2006) Large-eddy simulation of stably stratified atmospheric boundary layer turbulence: a scale-dependent dynamic modeling approach. J Atmos Sci 63:2074–2091CrossRefGoogle Scholar
  6. Basu S, Porté-Agel F, Foufoula-Georgiou E, Vinuesa JF, Pahlow M (2006) Revisiting the local scaling hypothesis in stably stratified atmospheric boundary layer turbulence: an integration of field and laboratory measurements with large-eddy simulations. Bound-Layer Meteorol 119:473–500CrossRefGoogle Scholar
  7. Basu S, Holtslag AAM, van de Wiel BJH, Moene AF, Steeneveld GJ (2008a) An inconvenient “truth” about using sensible heat flux as a surface boundary condition in models under stably stratified regimes. Acta Geophys 56:88–99CrossRefGoogle Scholar
  8. Basu S, Vinuesa JF, Swift A (2008b) Dynamic LES modeling of a diurnal cycle. J Appl Meteorol Climatol 47:1156–1174CrossRefGoogle Scholar
  9. Basu S, Holtslag AAM, Bosveld FC (2011) GABLS3 LES intercomparison study. In: ECMWF/GABLS workshop on “Diurnal cycles and the stable atmospheric boundary layer”, ECMWF, pp 75–82Google Scholar
  10. Brost RA, Wyngaard JC (1978) A model study of the stably stratified planetary boundary layer. J Atmos Sci 35:1427–1440CrossRefGoogle Scholar
  11. Brown AR, Derbyshire SH, Mason PJ (1994) Large-eddy simulation of stable atmospheric boundary layers with a revised stochastic subgrid model. Q J R Meteorol Soc 120:1485–1512CrossRefGoogle Scholar
  12. Clarke RH, Dyer AJ, Brook RR, Reid DG, Troup AJ (1971) The Wangara experiment: boundary layer data. Technical paper no. 19. CSIRO, Division of Atmospheric Physics. Aspendale, Australia, p 362Google Scholar
  13. Esau I, Zilitinkevich S (2010) On the role of the planetary boundary layer depth in the climate system. Adv Sci Res 4:63–69CrossRefGoogle Scholar
  14. Esau IN, Zilitinkevich SS (2006) Universal dependences between turbulent and mean flow parameters instably and neutrally stratified planetary boundary layers. Nonlinear Process Geophys 13:135–144CrossRefGoogle Scholar
  15. García JA, Cancillo ML, Cano JL (2002) A case study of the morning evolution of the convective boundary layer depth. J Appl Meteorol 41:1053–1059Google Scholar
  16. Garratt JR (1992) The atmospheric boundary layer. Cambridge University Press, CambridgeGoogle Scholar
  17. Gryning SE, Batchvarova E (2003) Marine atmospheric boundary-layer height estimated from NWP model output. Int J Environ Pollut 20:147–153Google Scholar
  18. Hanna SR (1969) The thickness of the planetary boundary layer. Atmos Environ 3:519–536CrossRefGoogle Scholar
  19. Heinemann G, Rose L (1990) Surface energy balance, parameterizations of boundary-layer heights and the application of resistance laws near an Antarctic ice shelf front. Bound-Layer Meteorol 51:123–158CrossRefGoogle Scholar
  20. Holtslag AAM, Boville BA (1993) Local versus nonlocal boundary-layer diffusion in a global climate model. J Clim 6:1825–1842CrossRefGoogle Scholar
  21. Holtslag AAM, de Bruijn EIF, Pan HL (1990) A high resolution air mass transformation model for short-range weather forecasting. Mon Weather Rev 118:1561–1575CrossRefGoogle Scholar
  22. Holtslag AAM, Steeneveld GJ, van de Wiel BJH (2007) Role of land surface temperature feedback on model performance for stable boundary layers. Bound-Layer Meteorol 125:361–376CrossRefGoogle Scholar
  23. Hong SY (2010) A new stable boundary-layer mixing scheme and its impact on the simulated East Asian summer monsoon. Q J R Meteorol Soc 136:1481–1496CrossRefGoogle Scholar
  24. Jeričević A, Grisogono B (2006) The critical bulk Richardson number in urban areas: verification and application in numerical weather prediction model. Tellus 58A:19–27Google Scholar
  25. Jiménez MA, Cuxart J (2005) Large-eddy simulations of the stable boundary layer using the standard Kolmogorov theory: range of applicability. Bound-Layer Meteorol 115:241–261CrossRefGoogle Scholar
  26. Kiehl J, Hack J, Bonan G, Boville B, Williamson D, Rasch P (1998) The National Center for Atmospheric Research Community Climate Model: CCM3. J Clim 11(6):1131–1149CrossRefGoogle Scholar
  27. Mahrt L (1981) Modelling the depth of the stable boundary-layer. Bound-Layer Meteorol 21:3–19CrossRefGoogle Scholar
  28. Melgarejo JW, Deardorff JW (1974) Stability functions for the boundary-layer resistance laws based upon observed boundary-layer heights. J Atmos Sci 31:1324–1333CrossRefGoogle Scholar
  29. Nieuwstadt FTM (1984) The turbulent structure of the stable, nocturnal boundary layer. J Atmos Sci 41(14):2202–2216CrossRefGoogle Scholar
  30. Nieuwstadt FTM (1985) A model for the stationary, stable boundary layer. In: Hunt JCR (ed) Turbulence and diffusion in stable environments. Clarendon Press, Oxford, pp 149–179Google Scholar
  31. Ohya Y (2001) Wind-tunnel study of atmospheric stable boundary layers over a rough surface. Bound-Layer Meteorol 98(1):57–82CrossRefGoogle Scholar
  32. Ohya Y, Uchida T (2003) Turbulence structure of stable boundary layers with a near-linear temperature profile. Bound-Layer Meteorol 108(1):19–38CrossRefGoogle Scholar
  33. Ohya Y, Neff D, Meroney R (1997) Turbulence structure in a stratified boundary layer under stable conditions. Bound-Layer Meteorol 83(1):139–161CrossRefGoogle Scholar
  34. Pichugina Y, Banta R (2010) Stable boundary layer depth from high-resolution measurements of the mean wind profile. J Appl Meteorol Climatol 49(1):20–35CrossRefGoogle Scholar
  35. Saiki EM, Moeng CH, Sullivan PP (2000) Large-eddy simulation of the stably stratified planetary boundary layer. Bound-Layer Meteorol 95:1–30CrossRefGoogle Scholar
  36. Seibert P, Beyrich F, Gryning SE, Joffre S, Rasmussen A, Tercier P (1998) Mixing height determination for dispersion modelling, COST action 710-final report, harmonisation of the pre-processing of meteorological data for atmospheric dispersion models, L-2985. European Commission, Luxembourg, EUR 18195 EN (ISBN 92-828-3302-X)Google Scholar
  37. Sørensen JH, Rasmussen A, Svensmark H (1996) Forecast of atmospheric boundary-layer height utilised for ETEX real-time dispersion modelling. Phys Chem Earth 21:435–439CrossRefGoogle Scholar
  38. Steeneveld GJ, van de Wiel BJH, Holtslag AAM (2007) Diagnostic equations for the stable boundary layer height: evaluation and dimensional analysis. J Appl Meteorol Climatol 46(2):212–225CrossRefGoogle Scholar
  39. Stoll R, Porté-Agel F (2008) Large-eddy simulation of the stable atmospheric boundary layer using dynamic models with different averaging schemes. Bound-Layer Meteorol 126(1):1–28CrossRefGoogle Scholar
  40. Stull RB (1988) An introduction to boundary layer meteorology. Kluwer Academic Publishers, DordrechtCrossRefGoogle Scholar
  41. Troen I, Mahrt L (1986) A simple model of the atmospheric boundary layer; sensitivity to surface evaporation. Bound-Layer Meteorol 37:129–148CrossRefGoogle Scholar
  42. Vickers D, Mahrt L (2004) Evaluating formulations of stable boundary layer height. J Appl Meteorol 43: 1736–1749Google Scholar
  43. Vinuesa JF, Basu S, Galmarini S (2007) The diurnal evolution of \(^{222}\) Rn and its progeny in the atmospheric boundary layer during the Wangara experiment. Atmos Chem Phys 7:5003–5019CrossRefGoogle Scholar
  44. Vogelezang DHP, Holtslag AAM (1996) Evaluation and model impacts of alternative boundary-layer height formulations. Bound-Layer Meteorol 81:245–269CrossRefGoogle Scholar
  45. van de Wiel BJH, Moene AF, Jonker HJJ, Baas P, Basu S, Donda JMM, Sun J, Holtslag AAM (2012) The minimum wind speed for sustainable turbulence in the nocturnal boundary layer. J Atmos Sci 69:3116–3127CrossRefGoogle Scholar
  46. Yamada T (1976) On the similarity functions A, B and C of the planetary boundary layer. J Atmos Sci 33:781–793CrossRefGoogle Scholar
  47. Zilitinkevich S, Baklanov A (2002) Calculation of the height of the stable boundary layer in practical applications. Bound-Layer Meteorol 105:389–409Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Marine, Earth, and Atmospheric SciencesNorth Carolina State UniversityRaleighUSA
  2. 2.Meteorology and Air Quality SectionWageningen UniversityWageningenThe Netherlands

Personalised recommendations