Boundary-Layer Meteorology

, Volume 154, Issue 2, pp 207–228 | Cite as

Half-Order Stable Boundary-Layer Parametrization Without the Eddy Viscosity Approach for Use in Numerical Weather Prediction

  • Richard J. ForemanEmail author
  • Stefan Emeis
  • Beatriz Canadillas


A turbulence parametrization for wind speed in the stable boundary layer consisting of a single empirical parameter is proposed without the use of the eddy viscosity concept or turbulent kinetic energy equation. Instead, a drag-coefficient-type formulation as a function of the bulk Richardson number has been found to be able to reproduce observed stable boundary-layer wind speeds as effectively as a model based on the eddy viscosity approach. The advantage of this simpler approach is that the model can, in theory, be modified more easily for certain applications, such as the effects of large-scale wind parks on mesoscale meteorology.


Bulk Richardson number Drag coefficient Eddy viscosity Stable boundary layer Stable boundary-layer parametrization Weather Research and Forecasting model Wind energy 



This work has been funded in consecutive projects (“VERITAS” and “TUFFO”) by the German Ministries of the Environment (BMU) and of Economy and Energy (BMWi) via the PTJ (FKZ 0325060 & 0325304). Sea surface temperature measurements were provided by the German Hydrographic Agency (BSH) and Høvsøre measurements by R. Floors and S.E. Gryning (Tall Wind project, funded by the Danish Government, Sagsnr. 2104–08–0025). Thanks to Johannes Werhahn for technical support. The advice of reviewers is gratefully acknowledged.


  1. Calder K (1966) Concerning the similarity theory of A.S. Monin and A.M. obukhov for the turbulent structure of the thermally stratified surface layer of the atmosphere. Q J R Meteorol Soc 92:141–146CrossRefGoogle Scholar
  2. Coiffier J (2011) Fundamentals of numerical weather prediction. Cambridge University Press, Cambridge 340 ppCrossRefGoogle Scholar
  3. Csanady G (1974) Equilibrium theory of the planetary boundary layer with an inversion lid. Boundary-Layer Meteorol 6:63–79CrossRefGoogle Scholar
  4. Emeis S (2010) A simple analytical wind park model considering atmospheric stability. Wind Energy 13:459–469CrossRefGoogle Scholar
  5. Emeis S (2011) Surface-based remote sensing of the atmospheric boundary layer. Springer, Berlin 174 ppCrossRefGoogle Scholar
  6. Emeis S (2012) Wind Energy Meteorol. Springer, Berlin 196 ppGoogle Scholar
  7. Floors R, Vincent CL, Gryning SE, Peña A, Batchvarova E (2013) The wind profile in the coastal boundary layer: wind lidar measurements and numerical modelling. Boundary-Layer Meteorol 147:469–491CrossRefGoogle Scholar
  8. Foreman RJ, Emeis S (2012a) A method for increasing the turbulent kinetic energy in the Mellor–Yamada–Janjić boundary-layer parametrization. Boundary-Layer Meteorol 145:329–349CrossRefGoogle Scholar
  9. Foreman RJ, Emeis S (2012b) Correlation equation for the marine drag coefficient and wave steepness. Ocean Dyn 62:1323–1333CrossRefGoogle Scholar
  10. Garratt J (1987) The stably stratified internal boundary layer for steady and diurnally varying offshore flow. Boundary-Layer Meteorol 38:369–394CrossRefGoogle Scholar
  11. Hong S (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
  12. Hong S, Pan H (1996) Nonlocal boundary layer vertical diffusion in a medium-range forecast model. Mon Weather Rev 124:2322–2339CrossRefGoogle Scholar
  13. Hong S, Noh Y, Dudhia J (2006) A new vertical diffusion package with an explicit treatment of entrainment processes. Mon Weather Rev 134:2318–2341CrossRefGoogle Scholar
  14. Louis JF (1979) A parametric model of vertical eddy fluxes in the atmosphere. Boundary-Layer Meteorol 17:187–202CrossRefGoogle Scholar
  15. Mellor GL, Yamada T (1982) Development of a turbulence closure model for geophysical fluid problems. Rev Geophys Space Phys 20:851–875CrossRefGoogle Scholar
  16. Nakanishi M (2001) Improvement of the Mellor–Yamada turbulence closure model based on large-eddy simulation data. Boundary-Layer Meteorol 99:349–378CrossRefGoogle Scholar
  17. Neumann T, Nolopp K (2007) Three years operation of far offshore measurements at FINO1. DEWI Mag 30:42–46Google Scholar
  18. Peña A, Floors R, Gryning SE (2014) The Høvsøre tall wind-profile experiment: a description of wind profile observations in the atmospheric boundary layer. Boundary-Layer Meteorol 150:69–89CrossRefGoogle Scholar
  19. Poulos GS, Blumen W, Fritts DC, Lundquist JK, Sun J, Burns SP, Nappo C, Banta R, Newsom R, Cuxart J, Terradellas E, Balsley B, Jensen M (2002) CASES-99: a comprehensive investigation of the stable nocturnal boundary layer. Bull Am Meteorol Soc 83:555–581CrossRefGoogle Scholar
  20. Skamarock WC (2008) A description of the advanced research WRF, version 3. Tech. Report, National Center for Atmospheric ResearchGoogle Scholar
  21. Stull R (1988) An introduction to boundary layer meteorology. Kluwer, Dordrecht, 666 ppGoogle Scholar
  22. Sušelj K, Sood A (2010) Improving the Mellor–Yamada–Janjić parameterization for wind conditions in the marine planetary boundary layer. Boundary-Layer Meteorol 136:301–324CrossRefGoogle Scholar
  23. Svensson G, Holtslag A, Kumar V, Mauritsen T, Steeneveld G, Angevine W, Bazile E, Beljaars A, de Bruijn E, Cheng A et al (2011) Evaluation of the diurnal cycle in the atmospheric boundary layer over land as represented by a variety of single-column models: the second gabls experiment. Boundary-Layer Meteorol 140:177–206CrossRefGoogle Scholar
  24. Tennekes H, Lumley J (1972) A first course in turbulence. MIT Press, Cambridge 300 ppGoogle Scholar
  25. Troen IB, Mahrt L (1986) A simple model of the atmospheric boundary layer; sensitivity to surface evaporation. Boundary-Layer Meteorol 37:129–148CrossRefGoogle Scholar
  26. Wang W, Bruyere C, Duda M, Dudhia J, Gill D, Lin H, Michalakes J, Rizvi S, Zhang X, Beezley J et al (2010) ARW version 3 modeling system users guide. National Center for Atmospheric Research.

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Richard J. Foreman
    • 1
    Email author
  • Stefan Emeis
    • 1
  • Beatriz Canadillas
    • 2
  1. 1.Institute for Meteorology and Climate ResearchKarlsruhe Institute of Technology (KIT)Garmisch-PartenkirchenGermany
  2. 2.DEWI GmbH (German Wind Energy Institute)WilhelmshavenGermany

Personalised recommendations