Boundary-Layer Meteorology

, Volume 134, Issue 2, pp 257–267 | Cite as

Bulk Transfer Relations for the Roughness Sublayer

Article

Abstract

In the roughness sublayer (RSL), Monin–Obukhov surface layer similarity theory fails. This is problematic for atmospheric modelling applications over domains that include rough terrain such as forests or cities, since in these situations numerical models often have the lowest model level located within the RSL. Based on empirical RSL profile functions for momentum and scalar quantities, and scaling the height with the RSL height z*, we derive a simple bulk transfer relation that accounts for RSL effects. To verify the validity of our approach, these relations are employed together with wind speed and temperature profiles measured over boreal forest during the BOREAS experimental campaign to estimate momentum and heat fluxes. It is demonstrated that, when compared with observed flux values, the inclusion of RSL effects in the transfer relations yields a considerable improvement in the estimated fluxes.

Keywords

Atmospheric numerical modelling Roughness sublayer Surface-layer transfer relations 

List of symbols

CD

Drag coefficient for momentum

CH

Drag coefficient for heat

d

Displacement height (m)

h

Canopy height (m)

i

Index indicating momentum (M) or heat (H) transport

k

von Kàrmàn constant

L

Obukhov stability length (m)

Ls

Aerodynamic canopy length scale (m)

u

Wind speed (m s−1)

uh

Wind speed at canopy top (m s−1)

u*

Friction velocity (m s−1)

z

Height above the displacement height (zZd) (m)

z*

Roughness sublayer height above the displacement height (m)

z0

Aerodynamic roughness length (m)

z0H

Roughness length for heat (m)

Z

Height above the ground (m)

Z*

Roughness sublayer height measured from the ground (m)

αi

Coefficient used in the stability functions

δ

Average inter-element spacing (m)

\({\phi}\)

Roughness sublayer profile function

η

Coefficient used in roughness sublayer function

\({\Phi_{M,H}}\)

Surface-layer stability function for momentum, heat

χ

Height scaled with the roughness sublayer height (χ = z/z*)

ζ

Height scaled with the Obukhov length (ζ = z/L)

λ

Coefficient in the approximated roughness sublayer correction

μM,H

Coefficient in the approximated roughness sublayer correction

ν

Coefficient in the approximated roughness sublayer correction

ψM,H

Integrated stability function for momentum, heat

θ

Potential temperature (K)

θ*

Surface-layer temperature scale (K)

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References

  1. Abramowitz M, Stegun IA (1972) Handbook of mathematical functions with formulas, graphs, and mathematical tables, 10th printing. National Bureau of Standards, Washington, p 1046 ppGoogle Scholar
  2. Arya SP (2001) Introduction to micrometeorology, 2nd edition. Academic Press, San Diego, p 420 ppGoogle Scholar
  3. Bartlett PA, McCaughey JH, Lafleur PM, Verseghy DL (2002) A comparison of the mosaic and aggregated canopy frameworks for representing surface heterogeneity in the Canadian boreal forest using CLASS: a soil perspective. J Hydrol 266: 15–39CrossRefGoogle Scholar
  4. Cellier P, Brunet Y (1992) Flux–gradient relationships above tall plant canopies. Agric For Meteorol 58: 93–117CrossRefGoogle Scholar
  5. Dyer AJ (1974) A review of flux-profile relationships. Boundary-Layer Meteorol 7: 363–372CrossRefGoogle Scholar
  6. Garratt JR (1978) Flux profile relations above tall vegetation. Q J Roy Meteorol Soc 104: 199–211CrossRefGoogle Scholar
  7. Garratt JR (1980) Surface influence upon vertical profiles in the atmospheric near-surface layer. Q J Roy Meteorol Soc 106: 803–819CrossRefGoogle Scholar
  8. Garratt JR (1983) Surface influence upon vertical profiles in the nocturnal boundary layer. Boundary-Layer Meteorol 26: 69–80CrossRefGoogle Scholar
  9. Garratt JR (1992) The atmospheric boundary layer. Cambridge University Press, UK, p 316 ppGoogle Scholar
  10. Graefe J (2004) Roughness layer corrections with emphasis on SVAT model applications. Agric For Meteorol 124: 237–251CrossRefGoogle Scholar
  11. Harman IN, Finnigan JJ (2007) A simple unified theory for flow in the canopy and roughness sublayer. Boundary-Layer Meteorol 123: 339–363CrossRefGoogle Scholar
  12. Harman IN, Finnigan JJ (2008) Scalar concentration profiles in the canopy and roughness sublayer. Boundary-Layer Meteorol 129: 323–351CrossRefGoogle Scholar
  13. Högström U, Bergström H, Smedman A-S, Halldin S, Lindroth A (1989) Turbulent exchange above a pine forest, I: fluxes and gradients. Boundary-Layer Meteorol 49: 197–217CrossRefGoogle Scholar
  14. Kaimal JC, Finnigan JJ (1994) Atmospheric boundary layer flows. Oxford University Press, Oxford, p 289 ppGoogle Scholar
  15. Koçak MC (2008) Simple geometry facilitates iterative solution of a nonlinear equation via a special transformation to accelerate convergence to third order. J Comput Appl Math 218: 350–363CrossRefGoogle Scholar
  16. Kuparinen A, Markkanenb T, Riikonenb H, Vesalab T (2007) Modeling air-mediated dispersal of spores, pollen and seeds in forested areas. Ecol Model 208: 177–188CrossRefGoogle Scholar
  17. Luhar A, Venkatram A, Lee S-M (2006) On relationships between urban and rural near-surface meteorology for diffusion applications. Atmos Environ 40: 6541–6553CrossRefGoogle Scholar
  18. Mölder M, Lindroth A (1999) Thermal roughness length of a boreal forest. Agric For Meteorol 98–99: 659–670CrossRefGoogle Scholar
  19. Mölder M, Grelle A, Lindroth A, Halldin S (1999) Flux-profile relationships over a boreal forest—roughness sublayer corrections. Agric For Meteorol 98–99: 645–658CrossRefGoogle Scholar
  20. Neirynck J, Ceulemans R (2008) Bidirectional ammonia exchange above a mixed coniferous forest. Environ Pollut 154: 424–438CrossRefGoogle Scholar
  21. 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
  22. Physick WL, Garratt JR (1995) Incorporation of a high-roughness lower boundary into a mesoscale model for studies of dry deposition over complex terrain. Boundary-Layer Meteorol 74: 55–71CrossRefGoogle Scholar
  23. Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipes in FORTRAN: the art of scientific computing, 2nd edition. Cambridge University Press, UK, p 934 ppGoogle Scholar
  24. Raupach MR, Antonia RA, Rajagopalan S (1991) Rough-wall turbulent boundary layers. Appl Mech Rev 44: 1–25CrossRefGoogle Scholar
  25. Raupach MR, Finnigan JJ, Brunet Y (1996) Coherent eddies and turbulence in vegetation canopies: the mixing layer analogy. Boundary-Layer Meteorol 78: 351–382CrossRefGoogle Scholar
  26. Ricciardelli F, Polimeno S (2006) Some characteristics of the wind flow in the lower urban boundary layer. J Wind Eng Ind Aerodyn 94: 815–832CrossRefGoogle Scholar
  27. Rotach MW (1999) On the influence of the urban roughness sublayer on turbulence and dispersion. Atmos Environ 24–25: 4001–4008CrossRefGoogle Scholar
  28. Sellers PJ, Hall FG, Kelly RD, Black A, Baldocchi D, Berry J, Ryan M, Ranson KJ, Crill PM, Lettenmaier DP, Margolis H, Cihlar J, Newcomer J, Fitzjarrald D, Jarvis PG, Gower ST, Halliwell D, Williams D, Goodison B, Wickland DE, Guertin FE (1997) BOREAS in 1997: experiment overview, scientific results, and future directions. J Geophys Res 102: 28731–28769CrossRefGoogle Scholar
  29. Simpson IJ, Thurtell GW, Neumann HH, Den Hartog G, Edwards GC (1998) The validity of similarity theory in the roughness sublayer above forests. Boundary-Layer Meteorol 87: 69–99CrossRefGoogle Scholar
  30. Verhoef A, McNaughton KG, Jacobs AFG (1997) A parameterization of momentum roughness length and displacement height for a wide range of canopy densities. Hydrol Earth Syst Sci 1: 81–91CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.VITO—Flemish Institute for Technological ResearchMolBelgium

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