Boundary-Layer Meteorology

, Volume 127, Issue 2, pp 273–292 | Cite as

A Modelling Study of Flux Imbalance and the Influence of Entrainment in the Convective Boundary Layer

Original Paper


It is frequently observed in field experiments that the eddy covariance heat fluxes are systematically underestimated as compared to the available energy. The flux imbalance problem is investigated using the NCAR’s large-eddy simulation (LES) model imbedded with an online scheme to calculate Reynolds-averaged fluxes. A top–down and a bottom–up tracer are implemented into the LES model to quantify the influence of entrainment and bottom–up diffusion processes on flux imbalance. The results show that the flux imbalance follows a set of universal functions that capture the exponential decreasing dependence on u*/w*, where u* and w* are friction velocity and the convective velocity scale, respectively, and an elliptic relationship to z/zi, where zi is the mixing-layer height. The source location in the boundary layer is an important factor controlling the imbalance magnitude and its horizontal and vertical distributions. The flux imbalance of heat and the bottom–up tracer is tightly related to turbulent coherent structures, whereas for the top–down diffusion, such relations are weak to nonexistent. Our results are broadly consistent with previous studies on the flux imbalance problem, suggesting that the published results are robust and are not artefacts of numerical schemes.


Bottom–up tracer Eddy covariance Entrainment Energy imbalance Large-eddy simulation model Top–down tracer 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Businger JA, Wyngaard JC, Izumi Y and Bradley EF (1971). Flux-profile relationships in the atmospheric surface layer. J Atmos Sci 28: 181–189 CrossRefGoogle Scholar
  2. Davis KJ, Bakwin PS, Yi C, Berger BW, Zhao C, Teclaw RM and Isebrands JG (2003). The annual cycles of CO2 and H2O exchange over a northern mixed forest as observed from a very tall tower. Global Change Biol 9: 1278–1293 CrossRefGoogle Scholar
  3. Deardorff JW (1980). Stratocumulus-capped mixed layers derived from a three-dimensional model. Boundary-Layer Meteorol 18: 495–527 CrossRefGoogle Scholar
  4. Jonker HJJ, Duynkerke PG and Cuijpers JWM (1999). Mesoscale fluctuations in scalars generated by boundary layer convection. J Atmos Sci 56: 801–808 CrossRefGoogle Scholar
  5. Kanda M, Inagaki A, Letzel MO, Raasch S and Watanabe T (2004). LES study of the energy imbalance problem with eddy covariance fluxes. Boundary-Layer Meteorol 110: 381–404 CrossRefGoogle Scholar
  6. Klemp JB and Durran DR (1983). An upper boundary condition permitting internal gravity wave radiation in numerical mesoscale models. Mon Wea Rev 111: 430–444 CrossRefGoogle Scholar
  7. Lee X (1998). On micrometeorological observations of surface-air exchange over tall vegetation. Agric For Meteorol 91: 39–49 CrossRefGoogle Scholar
  8. Lee X and Black TA (1993). Atmospheric turbulence within and above a Douglas-fir stand. Part 2: eddy fluxes of sensible heat and water vapor. BoundaryLayer Meteorol 64: 369–390 CrossRefGoogle Scholar
  9. Leuning R (2004). Measurements of trace gas fluxes in the atmosphere using eddy covariance: WPL corrections revisited. In: Lee, X (eds) Handbook of micrometeorology: a guide for surface flux measurement and analysis, pp 119–132. Kluwer Academic Publishers, Dordrecht Google Scholar
  10. Mahrt L (1998). Flux sampling errors for aircraft and towers. J Atmos Oceanic Tech 15: 416–429 CrossRefGoogle Scholar
  11. Moeng CH (1984). A large-eddy simulation model for the study of planetary boundary-layer turbulence. J Atmos Sci 41: 2052–2062 CrossRefGoogle Scholar
  12. Patton EG, Sullivan PP and Moeng CH (2005). The influence of idealized heterologeneity on wet and dry planetary boundary layers coupled to the land surface. J Atmos Sci 62: 2078–2097 CrossRefGoogle Scholar
  13. Piacsek SA and Williams GP (1970). Conservation properties of convection difference schemes. J Comput Phys 6: 392–405 CrossRefGoogle Scholar
  14. Purnell DK (1976). Solution of the advective equation by upstream interpolation with cubic spline. Mon Wea Rev 104: 42–48 CrossRefGoogle Scholar
  15. Raasch S and Etling D (1998). Modeling deep ocean convection: large eddy simulation in comparison with laboratory experiments. J Phys Oceanogr 28: 1786–1802 CrossRefGoogle Scholar
  16. Raasch S and Schröter M (2001). PALM – a large eddy simulation model performing on massively parallel computers. Meteorol Z 10: 363–372 CrossRefGoogle Scholar
  17. Steinfeld G, Letzel MO, Raasch S, Kanda M and Inagaki A (2007). Spatial representativeness of single tower measurements and the imbalance problem with eddy-covariance fluxes: results of a large-eddy simulation study. Boundary-Layer Meteorol 123: 77–98 CrossRefGoogle Scholar
  18. Sullivan PP, McWilliams JC and Moeng CH (1996). A grid nesting method for large-eddy simulation of planetary boundary-layer flows. Boundary-Layer Meteorol 80: 167–202 CrossRefGoogle Scholar
  19. Twine TE, Kustas WP, Norman JM, Cook DR, Houser PR, Meyers TP, Prueger JH, Starks PJ and Wesely ML (2000). Correcting eddy-covariance flux underestimates over a grassland. Agric For Meteorol 103: 279–300 CrossRefGoogle Scholar
  20. Webb EK, Pearman GI and Leuning R (1980). Correction of flux measurements for density effects due to heat and water vapor transfer. Quart J Roy Meteorol Soc 106: 85–100 CrossRefGoogle Scholar
  21. Wilson K, Goldstein A, Falge E, Aubinet M, Baldocchi D, Berbigier P, Bernhofer C, Ceulemans R, Dolman H, Field C, Grelle A, Ibrom A, Law BE, Kowalski A, Meyers T, Moncrieff J, Monson R, Oechel W, Tenhunen J, Valentini R and Verma S (2002). Energy balance closure at FLUXNET sites. Agric For Meteorol 113: 223–243 CrossRefGoogle Scholar
  22. Wyngaard JC and Brost RA (1984). Top-down and bottom–up diffusion of a scalar in the convective boundary layer. J Atmos Sci 41: 102–112 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.School of Forestry and Environmental StudiesYale UniversityNew HavenUSA
  2. 2.National Center for Atmospheric ResearchBoulderUSA

Personalised recommendations