Boundary-Layer Meteorology

, Volume 124, Issue 3, pp 315–333 | Cite as

SHEBA flux–profile relationships in the stable atmospheric boundary layer

  • Andrey A. GrachevEmail author
  • Edgar L Andreas
  • Christopher W. Fairall
  • Peter S. Guest
  • P. Ola G. Persson
Original Paper


Measurements of atmospheric turbulence made during the Surface Heat Budget of the Arctic Ocean Experiment (SHEBA) are used to examine the profile stability functions of momentum, φ m , and sensible heat, φ h , in the stably stratified boundary layer over the Arctic pack ice. Turbulent fluxes and mean meteorological data that cover different surface conditions and a wide range of stability conditions were continuously measured and reported hourly at five levels on a 20-m main tower for 11 months. The comprehensive dataset collected during SHEBA allows studying φ m and φ h in detail and includes ample data for the very stable case. New parameterizations for φ m (ζ) and φ h (ζ) in stable conditions are proposed to describe the SHEBA data; these cover the entire range of the stability parameter ζ = z/L from neutral to very stable conditions, where L is the Obukhov length and z is the measurement height. In the limit of very strong stability, φ m follows a ζ 1/3 dependence, whereas φ h initially increases with increasing ζ, reaches a maximum at ζ ≈ 10, and then tends to level off with increasing ζ. The effects of self-correlation, which occur in plots of φ m and φ h versus ζ, are reduced by using an independent bin-averaging method instead of conventional averaging.


Arctic Ocean Flux–profile relationships Monin–Obukhov similarity theory SHEBA Experiment Stable boundary layer 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Andreas EL (2002) Parameterizing scalar transfer over snow and ice: a review. J Hydrometeorol 3:417–432CrossRefGoogle Scholar
  2. Andreas EL, Hicks BB (2002) Comments on critical test of the validity of Monin-Obukhov similarity during convective conditions. J Atmos Sci 59:2605–2607CrossRefGoogle Scholar
  3. Andreas EL, Fairall CW, Guest PS, Persson POG (1999) An overview of the SHEBA atmospheric surface flux program. 13th symposium on boundary layers and turbulence. Dallas, TX, Amer Meteorol Soc, Proceedings, pp 550–555Google Scholar
  4. Andreas EL, Claffey KJ, Makshtas AP (2000) Low-level atmospheric jets and inversions over the Western Weddell Sea. Boundary-Layer Meteorol 97:459–486CrossRefGoogle Scholar
  5. Andreas EL, Claffey KJ, Jordan RE, Fairall CW, Guest PS, Persson POG, Grachev AA (2006) Evaluations of the von Kármán constant in the atmospheric surface layer. J Fluid Mech 559: 117–149CrossRefGoogle Scholar
  6. Andreas EL, Guest PS, Persson POG, Fairall CW, Horst TW, Moritz RE, Semmer SR (2002) Near-surface water vapor over sea ice is always near ice saturation. J Geophys Res 107(C10), doi: 10.1029/2000JC000411Google Scholar
  7. Andreas EL, Fairall CW, Grachev AA, Guest PS, Horst TW, Jordan RE, Persson POG (2003) Turbulent transfer coefficients and roughness lengths over sea ice: the SHEBA results. In Seventh conference on polar meteorology and oceanography and joint symposium on high-latitude climate variations, American Meteorological Society. 12–16 May 2003, Hyannis, Massachusetts, AMS Preprint CD-ROMGoogle Scholar
  8. Beljaars ACM, Holtslag AAM (1991) Flux parameterization over land surfaces for atmospheric models. J Appl Meteorol 30(3):327–341CrossRefGoogle Scholar
  9. Businger JA, Wyngaard JC, Izumi Y, Bradley EF (1971) Flux–profile relationships in the atmospheric surface layer. J Atmos Sci 28:181–189CrossRefGoogle Scholar
  10. Carl MD, Tarbell TC, Panofsky HA (1973) Profiles of wind and temperature from towers over homogeneous terrain. J Atmos Sci 30:788–794CrossRefGoogle Scholar
  11. Cheng Y, Brutsaert W (2005) Flux–profile relationships for wind speed and temperature in the stable atmospheric boundary layer. Boundary-Layer Meteorol 114(3):519–538CrossRefGoogle Scholar
  12. Clement RJ (2004) Mass and energy exchange of a plantation forest in Scotland using micrometeorological methods. PhD Thesis, The University of Edinburgh, School of Geosciences, 597 p. ( Scholar
  13. Dyer AJ (1974) A review of flux–profile relationships. Boundary-Layer Meteorol. 7:363–372CrossRefGoogle Scholar
  14. Dyer AJ, Bradley EF (1982) An alternative analysis of flux–gradient relationships at the 1976 ITCE. Boundary-Layer Meteorol 22:3–19CrossRefGoogle Scholar
  15. Dyer AJ, Hicks BB (1970) Flux–gradient relationships in the constant flux layer. Quart J Roy Meteorol Soc 96:715–721CrossRefGoogle Scholar
  16. Forrer J, Rotach MW (1997) On the turbulence structure in the stable boundary layer over the Greenland ice sheet. Boundary-Layer Meteorol 85:111–136CrossRefGoogle Scholar
  17. Garratt JR (1992) The atmospheric boundary layer. Cambridge University Press, Cambridge, 316 ppGoogle Scholar
  18. Grachev AA, Fairall CW, Persson POG, Andreas EL, Guest PS (2002) Stable boundary-layer regimes observed during the SHEBA Experiment. In 15th symposium on boundary layers and turbulence. Wageningen, The Netherlands, Amer. Meteorol. Soc., Proc., 374 – 377Google Scholar
  19. Grachev AA, Fairall CW, Persson POG, Andreas EL, Guest PS, Jordan RE (2003) Turbulence decay in the stable arctic boundary layer. In Seventh conference on polar meteorology and oceanography and joint symposium on high-latitude climate variations. Hyannis, Massachusetts, Amer. Meteorol. Soc., Preprint CD-ROMGoogle Scholar
  20. Grachev AA, Fairall CW, Persson POG, Andreas EL, Guest PS (2005) Stable boundary-layer scaling regimes: The SHEBA data. Boundary-Layer Meteorol 116(2):201–235CrossRefGoogle Scholar
  21. Hartogensis OK, De Bruin HAR (2005) Monin–Obukhov similarity functions of the structure parameter of temperature and turbulent kinetic energy dissipation rate in the stable boundary layer. Boundary-Layer Meteorol 116(2):253–276CrossRefGoogle Scholar
  22. Hicks BB (1978) Comments on ‘The characteristics of turbulent velocity components in the surface layer under convective conditions’. by H. A. Panofsky, et al. Boundary-Layer Meteorol. 15(2):255–258CrossRefGoogle Scholar
  23. Högström U (1988) Non-dimensional wind and temperature profiles in the atmospheric surface layer: a re-evaluation. Boundary-Layer Meteorol 42:55–78CrossRefGoogle Scholar
  24. Holtslag AAM, De Bruin HAR (1988) Applied modeling of the nighttime surface energy balance over land. J Appl Meteorol 27:689–704CrossRefGoogle Scholar
  25. Holtslag AAM, Nieuwstadt FTM (1986) Scaling the atmospheric boundary layer. Boundary-Layer Meteorol 36:201–209CrossRefGoogle Scholar
  26. Horst T (2000) On frequency response corrections for eddy covariance flux measurements. Boundary-Layer Meteorol 94(3):517–520CrossRefGoogle Scholar
  27. Howell JF, Sun J (1999) Surface-layer fluxes in stable conditions. Boundary-Layer Meteorol 90:495–520CrossRefGoogle Scholar
  28. Kader BA, Yaglom AM (1990) Mean fields and fluctuation moments in unstably stratified turbulent boundary layers. J Fluid Mech 212:637–662CrossRefGoogle Scholar
  29. Kaimal JC, Finnigan JJ (1994) Atmospheric boundary layer flows: their structure and measurements. Oxford University Press, New York Oxford, 289 ppGoogle Scholar
  30. King JC (1990) Some measurements of turbulence over an Antarctic shelf. Quart J Roy Meteorol Soc 116:379–400CrossRefGoogle Scholar
  31. Klipp CL, Mahrt L (2004) Flux–gradient relationship, self-correlation and intermittency in the stable boundary layer. Quart J Roy Meteorol Soc 130(601):2087–2103CrossRefGoogle Scholar
  32. Kondo J, Kanechika O, Yasuda N (1978) Heat and momentum transfers under strong stability in the atmospheric surface layer. J Atmos Sci 35:1012–1021CrossRefGoogle Scholar
  33. Kristensen L, Fitzjarrald DR (1984) The effect of line averaging on scalar flux measurements with a sonic anemometer near the surface. J Atmos Oceanic Technol 1(3):138–146CrossRefGoogle Scholar
  34. Mahrt L (1999) Stratified atmospheric boundary layers. Boundary-Layer Meteorol 90:375–396CrossRefGoogle Scholar
  35. Mahrt L, Vickers D (2002) Contrasting vertical structures of nocturnal boundary layers. Boundary-Layer Meteorol 105:351–363CrossRefGoogle Scholar
  36. Mahrt L, Sun J, Blumen W, Delany T, Oncley S (1998) Nocturnal boundary-layer regimes. Boundary-Layer Meteorol 88:255–278CrossRefGoogle Scholar
  37. Massman WJ (2000) A simple method for estimating frequency response corrections for eddy covariance systems. Agric Forest Meteorol 104:185–198CrossRefGoogle Scholar
  38. Monin AS, Obukhov AM (1954) Basic laws of turbulent mixing in the surface layer of the atmosphere. Trudy Geofiz Inst Acad Nauk SSSR 24:163–187Google Scholar
  39. Monin AS, Yaglom AM (1971) Statistical fluid mechanics: mechanics of turbulence, vol 1. MIT Press, Cambridge, Massachusetts, 769 ppGoogle Scholar
  40. Moore CJ (1986) Frequency response corrections for eddy correlation systems. Boundary-Layer Meteorol 37(1–2):17–36CrossRefGoogle Scholar
  41. Nieuwstadt FTM (1984) The turbulent structure of the stable, nocturnal boundary layer. J Atmos Sci 41:2202–2216CrossRefGoogle Scholar
  42. Obukhov AM (1946) Turbulence in an atmosphere with a non-uniform temperature. Trudy Inst Teoret Geofiz Akad Nauk SSSR 1:95–115Google Scholar
  43. Obukhov AM (1971) Turbulence in an atmosphere with a non-uniform temperature. Boundary-Layer Meteorol 2:2–29CrossRefGoogle Scholar
  44. Panofsky HA (1963) Determination of stress from wind and temperature measurements. Quart J Roy Meteorol Soc 89:85–94CrossRefGoogle Scholar
  45. Pahlow M, Parlange MB, Porté-Agel F (2001) On Monin–Obukhov similarity in the stable atmospheric boundary layer. Boundary-Layer Meteorol. 99:225–248CrossRefGoogle Scholar
  46. Paulson CA (1970) The mathematical representation of wind speed and temperature profiles in the unstable atmospheric surface layer. J Appl Meteorol 9:857–861CrossRefGoogle Scholar
  47. Paw UKT, Baldocchi DD, Meyers TP, Wilson KB (2000) Correction of eddy-covariance measurements incorporating both advective effects and density fluxes. Boundary-Layer Meteorol 97(3):487–511CrossRefGoogle Scholar
  48. Persson POG, Fairall CW, Andreas EL, Guest PS, Perovich DK (2002) Measurements near the atmospheric surface flux group tower at SHEBA: near-surface conditions and surface energy budget. J Geophys Res 107(C10):8045, doi: 10.1029/2000JC000705CrossRefGoogle Scholar
  49. Smedman A-S (1988) Observations of a multi-level turbulence structure in a very stable atmospheric boundary layer. Boundary-Layer Meteorol 44:231–253CrossRefGoogle Scholar
  50. Sorbjan Z (1989) Structure of the atmospheric boundary layer. Prentice-Hall, New Jersey, 317 ppGoogle Scholar
  51. Uttal T, 27 co-authors (2002) Surface heat budget of the Arctic ocean. Bull Am Meteorol Soc 83:255–276CrossRefGoogle Scholar
  52. Webb EK (1970) Profile relationships: the log-linear range, and extension to strong stability. Quart J Roy Meteorol Soc 96:67–90CrossRefGoogle Scholar
  53. Wilczak JM, Oncley SP, Stage SA (2001) Sonic anemometer tilt correction algorithms. Boundary-Layer Meteorol 99(1):127–150CrossRefGoogle Scholar
  54. Wilson DK (2001) An alternative function for the wind and temperature gradients in unstable surface layers. Boundary-Layer Meteorol 99:151–158CrossRefGoogle Scholar
  55. Wyngaard JC (1973) On surface-layer turbulence. In: Haugen DA (eds) Workshop on micrometeorology. American Meteorology Society, Boston, Mass, pp 101–149Google Scholar
  56. Wyngaard JC, Coté OR (1972) Cospectral similarity in the atmospheric surface layer. Quart J Roy Meteorol Soc 98:590–603CrossRefGoogle Scholar
  57. Yaglom AM (1977) Comments on wind and temperature flux–profile relationships. Boundary-Layer Meteorol 11:89–102CrossRefGoogle Scholar
  58. Yagüe C, Maqueda G, Rees JM (2001) Characteristics of turbulence in the lower atmosphere at Halley IV Station, Antarctica. Dyn Atmos Ocean 34:205–223CrossRefGoogle Scholar
  59. Yagüe C, Viana S, Maqueda G, Redondo JM (2006) Influence of stability on the flux–profile relationships for wind speed, φm, and temperature, φh, for the stable atmospheric boundary layer. Nonlin Processes Geophys 13(2):185–203CrossRefGoogle Scholar
  60. Zilitinkevich S, Baklanov A (2002) Calculation of the height of the stable boundary layer in practical applications. Boundary-Layer Meteorol 105:389–409CrossRefGoogle Scholar
  61. Zilitinkevich S, Calanca P (2000) An extended similarity-theory for the stably stratified atmospheric surface layer. Quart J Roy Meteorol Soc 126:1913–1923CrossRefGoogle Scholar
  62. Zilitinkevich SS, Chalikov DV (1968) Determining the universal wind-velocity and temperature profiles in the atmospheric boundary layer. Izvestiya Acad Sci USSR Atmos Oceanic Phys 4:165–170(English Edition)Google Scholar
  63. Zilitinkevich S, Mironov DV (1996) A multi-limit formulation for the equilibrium depth of a stably stratified boundary layer. Boundary-Layer Meteorol 81:325–351CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, B.V. 2007

Authors and Affiliations

  • Andrey A. Grachev
    • 1
    • 2
    Email author
  • Edgar L Andreas
    • 3
    • 4
  • Christopher W. Fairall
    • 2
  • Peter S. Guest
    • 5
  • P. Ola G. Persson
    • 1
    • 2
  1. 1.Cooperative Institute for Research in Environmental SciencesUniversity of ColoradoBoulderUSA
  2. 2.NOAA Earth System Research LaboratoryBoulderUSA
  3. 3.U.S. Army Cold Regions Research and Engineering LaboratoryHanoverUSA
  4. 4.NorthWest Research Associates, Inc. (Bellevue Division)LebanonUSA
  5. 5.Naval Postgraduate SchoolMontereyUSA

Personalised recommendations