Boundary-Layer Meteorology

, Volume 126, Issue 1, pp 29–50 | Cite as

Time Scales in the Unstable Atmospheric Surface Layer

  • Meredith MetzgerEmail author
  • Heather Holmes
Original Paper


Calculation of eddy covariances in the atmospheric surface layer (ASL) requires separating the instantaneous signal into mean and fluctuating components. Since the ASL is not statistically stationary, an inherent ambiguity exists in defining the mean quantities. The present study compares four methods of calculating physically relevant time scales in the unstable ASL that may be used to remove the unsteady mean components of instantaneous time signals, in order to yield local turbulent fluxes that appear to be statistically stationary. The four mean-removal time scales are: (t c ) based on the location of the maximum in the ogive of the heat flux cospectra, (\(\tilde t_{MR}\)) the location of the zero crossing in the multiresolution decomposition of the heat flux, (t *) the ratio of the mixed-layer depth over the convective velocity, and (\(\tilde t\,\)) the convergence time of the vertical velocity and temperature variances. The four time scales are evaluated using high quality, three-dimensional sonic anemometry data acquired at the Surface Layer Turbulence and Environmental Science Test (SLTEST) facility located on the salt flats of Utah’s western desert. Results indicate that \(t_c\approx t_{MR}\) and \(t^*\approx \tilde t\) , with t c achieving values about 2–3 times greater than t *. The sensitivity of the eddy covariances to the mean-removal time scale (given a fixed 4-h averaging period during midday) is also demonstrated.


Atmospheric surface layer Atmospheric turbulence Averaging time Mean removal Time scales 


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  1. Bradshaw P (1967). Inactive’ motion and pressure fluctuations in turbulent boundary layers. J Fluid Mech 30: 241–258 CrossRefGoogle Scholar
  2. Chatwin P and Allen C (1985). A note on time averages in turbulence with reference to geophysical applications. Tellus 37B: 46–49 CrossRefGoogle Scholar
  3. Deardorff J (1970). Convective velocity and temperature scales for the unstable planetary boundary layer and for Rayleigh convection. J Atmos Sci 27: 1211–1213 CrossRefGoogle Scholar
  4. Dias NL, Chamecki M, Kan A and Okawa CMP (2004). A study of spectra, structure and correlation functions and their implications for the stationarity of surface-layer turbulence. Boundary-Layer Meteorol 110: 165–189 CrossRefGoogle Scholar
  5. Fiedler F and Panofsky H (1970). Atmospheric scales and spectral gaps. Bull Amer Meteorol Soc 51: 1114–1119 CrossRefGoogle Scholar
  6. Finnigan JJ, Clement R, Malhi Y, Leuning R and Cleugh HA (2003). A re-evaluation of long-term flux measurement techniques Part I: Averaging and coordinate rotation. Boundary-Layer Meteorol 107: 1–48 CrossRefGoogle Scholar
  7. Garratt J (1992). The atmospheric boundary layer. Cambridge University Press, U.K., 316 pp Google Scholar
  8. Heggem T, Lende R and Lovseth J (1998). Analysis of long time series of coastal wind. J Atmos Sci 55: 2907–2917 CrossRefGoogle Scholar
  9. Holmes H (2007) Times scales in the unstable atmospheric surface layer. Master’s thesis, University of Utah, Salt Lake City, UtahGoogle Scholar
  10. Hommema S and Adrian R (2003). Packet structure of surface eddies in the atmospheric boundary layer. Boundary-Layer Meteorol 106: 147–170 CrossRefGoogle Scholar
  11. Howell J and Mahrt L (1997). Multiresolution flux decomposition. Boundary-Layer Meteorol 83: 117–137 CrossRefGoogle Scholar
  12. Jacobson M (2005). Fundamentals of atmospheric modeling, 2nd edn. Cambridge University Press, U.K., 813 ppGoogle Scholar
  13. Jonker H, Duynkerke P and Cuijpers J (1999). Mesoscale fluctuations in scalars generated by boundary layer convection. J Atmos Sci 56: 801–808 CrossRefGoogle Scholar
  14. Kaimal JC and Finnigan JJ (1994). Atmospheric boundary layer flows. Oxford University Press, U.K., 289 pp Google Scholar
  15. Klewicki JC, Metzger MM, Kelner E and Thurlow EM (1995). Viscous sublayer flow visualizations at R θ≈1500000. Phys Fluids 7(4): 857–863 CrossRefGoogle Scholar
  16. Kunkel G and Marusic I (2006). Study of the near-wall-turbulent region of the high Reynolds number boundary layer using a atmospheric flow. J Fluid Mech 548: 375–402 CrossRefGoogle Scholar
  17. Kunkel K, Walters D and Ely G (1981). Behavior of the temperature structure parameter in a desert basin. J Appl Meteorol 20: 130–136 CrossRefGoogle Scholar
  18. Kurien S, Aivalis K and Sreenivasan K (2001). Anisotropy of small-scale scalar turbulence. J Fluid Mech 448: 279–288 CrossRefGoogle Scholar
  19. Lenschow D and Stankov B (1986). Length scales in the convective boundary layer. J Atmos Sci 43: 1198–1209 CrossRefGoogle Scholar
  20. Lenschow D, Mann J and Kristensen L (1994). How long is long enough when measuring fluxes and other turbulence statistics?. J Atmos Oceanic Tech 11: 661–673 CrossRefGoogle Scholar
  21. Lilly D (1968). Models of cloud-topped mixed layers under a strong inversion. Quart J Roy Meteorol Soci 94: 292–309 CrossRefGoogle Scholar
  22. Liu X and Ohtaki E (1997). An independent method to determine the height of the mixed layer. Boundary-Layer Meteorol 85: 497–504 CrossRefGoogle Scholar
  23. Lumley J and Panofsky H (1964). The structure of atmospheric turbulence. John Wiley and Sons, U.S.A., 239 pp Google Scholar
  24. Malek E (2003). Microclimate of a desert playa: evaluation of annual radiation, energy and water budgets components. Int J Climatol 23: 333–345 CrossRefGoogle Scholar
  25. McMillen R (1988). An eddy correlation technique with extended applicability to non-simple terrain. Boundary-Layer Meteorol 43: 231–245 CrossRefGoogle Scholar
  26. Metzger M (2002) Scalar dispersion in high Reynolds number turbulent boundary layers. Ph.D. thesis, University of Utah, Salt Lake City, UtahGoogle Scholar
  27. Metzger M (2006). Length and time scales of the near-surface axial velocity in a high Reynolds number turbulent boundary layer. Int J Heat Fluid Flow 27: 534–541 Google Scholar
  28. Metzger MM and Klewicki JC (2001). A comparative study of near-wall turbulence in high and low Reynolds number boundary layers. Phys Fluids 13: 692–701 CrossRefGoogle Scholar
  29. Metzger MM, Klewicki JC, Bradshaw K and Sadr R (2001). Scaling the near-wall axial turbulent stress in the zero pressure gradient boundary layer. Phys Fluids 13: 1819–1821 CrossRefGoogle Scholar
  30. Metzger M, Klewicki J and Priyadarshana P (2003). Reynolds number dependencies in the behavior of boundary layer axial stress and scalar transport. In: Smits, JA (eds) Reynolds number scaling in turbulent flows, pp 83–89. Kluwer Academic Publishers, Dordrecht Google Scholar
  31. Moncrieff J, Clement R, Finnigan J and Meyers T (2004). Averaging, detrending, and filtering of eddy covariance time series. In: Lee, X, Massman, W, and Law, B (eds) Handbook of micrometeorology, pp 7–31. Kluwer Academic Publishers, Dordrecht Google Scholar
  32. Metzger M, McKeon B and Holmes H (2007). The near-neutral atmospheric surface layer: turbulence and non-stationarity. Proc Roy Soc London A 365: 859–876 Google Scholar
  33. Moore CJ (1986). Frequency response corrections for eddy correlation systems. Boundary-Layer Meteorol 37: 17–35 CrossRefGoogle Scholar
  34. Priyadarshana P and Klewicki J (2004). Study of the motions contributing to the Reynolds stress in high and low Reynolds number turbulent boundary layers. Phys Fluids 16: 4586–4600 CrossRefGoogle Scholar
  35. Rannik U and Vesala T (1999). Autoregressive filtering versus linear detrending in estimation of fluxes by the eddy covariance method. Boundary-Layer Meteorol 91: 259–280 CrossRefGoogle Scholar
  36. Reynolds O (1895). On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Philos Trans Roy Soc London A 186: 123–164 CrossRefGoogle Scholar
  37. Sakai RK, Fitzjarrald DR and Moore KE (2001). Importance of low-frequency contributions to eddy fluxes observed over rough surfaces. J Appl Meteorol 40: 2178–2192 CrossRefGoogle Scholar
  38. Smedman-Högström A and Högström U (1975). Spectral gap in surface-layer measurements. J Atmos Sci 32: 340–350 CrossRefGoogle Scholar
  39. Sozzi R and Favaron M (1997). Sonic anemometry and thermometry: Theoretical basis and data-processing software. Environ Software 11: 259–270 CrossRefGoogle Scholar
  40. Sreenivasan K, Chambers A and Antonia R (1978). Accuracy of moments of veloctiy and scalar fluctuations in the atmospheric surface layer. Boundary-Layer Meteorol 14: 341–359 CrossRefGoogle Scholar
  41. Stull RB (1988). An introduction to boundary layer meteorology. Kluwer Academic Publishers, Dordrecht Google Scholar
  42. Sun J, Massman W and Grantz D (1999). Aerodynamic variables in the bulk formulation of turbulent fluxes. Boundary-Layer Meteorol 91: 109–125 CrossRefGoogle Scholar
  43. Tennekes H and Lumley JL (1972). A first course in turbulence. The MIT Press, Cambridge, Cambridge, Massachusetts, U.S.A., 300 pp Google Scholar
  44. U.S. Geological Survey (1952–1972) Topographic map numbers. N4037.5-W11145/7.5, N4030-W11145/7.5, 40112-F2–OM-024, 40112-F1-TF-024, N4030-W11200/7.5Google Scholar
  45. Van der Hoven I (1957). Power spectrum of horizontal wind speed in the frequency range from 0.0007 to 900 cycles per hour. J Meteorol 14: 160–164 Google Scholar
  46. Vickers D and Mahrt L (2003). The cospectral gap and turbulent flux calculations. J Atmos Oceanic Tech 20: 660–672 CrossRefGoogle Scholar
  47. Wyngaard J, Coté O and Izumi Y (1971). Local free convection similarity, and the budgets of shear stress and heat flux. J Atmos Sci 28: 1171–1182 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of UtahSalt Lake CityUSA

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