Boundary-Layer Meteorology

, Volume 88, Issue 3, pp 479–504

Unsteadiness as a cause of non-equality of eddy diffusivities for heat and vapour at the base of an advective inversion

  • K. G. McNaughton
  • J. Laubach


This paper examines the effect of non-stationarity of the wind on similarity of the eddy diffusivities for heat and vapour within a stable layer at the bottom of an internal boundary layer formed downwind of a dry-to-wet transition. First, we present some experimental data taken above a rice crop downwind of very extensive dry range lands at Warrawidgee, NSW, Australia. These data establish that periods of higher wind speed were associated with periods of higher saturation deficit in the canopy of the rice crop, and lower Bowen ratio. It is shown that Bowen ratios calculated for 30-second sub-intervals varied three-fold within a single 20-minute averaging period. Thus periods of higher wind speed corresponded to periods of higher moisture flux and smaller sensible heat flux.

An idealized situation is then analysed theoretically. It is assumed that the time scale of the slow variations of the wind is long compared with the surface-layer time scale and that fetch is sufficient that the air near the ground is in continuous equilibrium with the surface. Using a two-scale Reynolds decomposition of the fluctuating wind and scalar variables into active and inactive components, it is shown that unsteadiness can lead to an eddy diffusivity for saturation deficit, calculated as the ratio of average flux to average gradient, that is larger than that for total energy calculated in a similar way. Using this ratio to calculate the ratio of diffusivities for temperature and humidity, KT/Kq, it is found that the latter can be much larger than one if the Bowen ratio is small and negative. Despite this, assuming KT = Kq and using the Bowen ratio method to calculate surface energy fluxes will usually incur only minor errors.

Advection Advective inversion Eddy diffusivity Internal boundary layer Monin- Obukhov similarity Unsteadiness 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bink, N. J.: 1996a, 'The Structure of the Atmospheric Surface Layer Subject to Local Advection', PhD Thesis, Wageningen Agricultural University, 206 pp.Google Scholar
  2. Bink, N. J.: 1996b, 'The Ratio of Eddy Diffusivities for Heat and Water Vapour under Conditions of Local Advection', Phys. Chem. Earth. 21, 119-122.Google Scholar
  3. Blad, B. L. and Rosenberg, N. E.: 1974, 'Lysimetretric Calibration for the Bowen Ratio-Energy-Balance Method for Evapotranspiration Estimation in the Central Great Plain', J. Appl. Meteorol. 13, 227-236.Google Scholar
  4. Bradshaw, P.: 1967, '“Inactive” motion and pressure fluctuations in turbulent boundary layers', J. Fluid Mech. 30, 241-258.Google Scholar
  5. De Bruin, H. A. R., Bink, N. J., and Kroon, L. J. M.: 1991, 'Fluxes in the Surface Layer under Advective Conditions', in Schmugge, T. J. and André, J. (eds.), Land Surface Evaporation: Measurement and Parameterization, Springer-Verlag, New York, pp. 157-169.Google Scholar
  6. De Bruin, H. A. R., Kohsiek, W., and Van den Hurk, B. J. J. M.: 1993, 'A Verification of Some Methods to Determine the Fluxes of Momentum, Sensible Heat and Water Vapour using Standard Deviation and Structure Parameter of Scalar Meteorological Quantities', Boundary-Layer Meteorol. 63, 231-257.Google Scholar
  7. Denmead, O. T. and Bradley, E. F.: 1985, 'Flux-Gradient Relationships in a Forest Canopy', in Hutchison, B. A. and Hicks, B. B. (eds.), The Forest-Atmosphere Interaction, Reidel, Dordrecht, pp. 421-442.Google Scholar
  8. Denmead, O. T. and Bradley, E. F.: 1987, 'On Scalar Transport in Plant Canopies', Irrig. Sci. 8, 131-149.Google Scholar
  9. Dias, N. L. and Brutsaert, W.: 1996, 'Similarity of Scalars under Stable Conditions', Boundary-Layer Meteorol. 80, 355-373.Google Scholar
  10. Garratt, J. R.: 1990, 'The Internal Boundary Layer - A Review', Boundary-Layer Meteorol. 50, 171-203.Google Scholar
  11. Kaimal, J. C. and Finnigan, J. J.: 1994, Atmospheric Boundary Layer Flows, Oxford University Press, New York. 289 pp.Google Scholar
  12. Katul, G. G., Albertson, J. D., Cheng-I Hseih, C. P. S., Sigmon, J. T., Parlange, M. B., and Knoerr, K. R.: 1996, 'The “Inactive” Eddy Motion and the Large-Scale Turbulent Pressure Fluctuations in the Dynamic Sublayer', J. Atmos. Sci. 53, 2512-2524.Google Scholar
  13. Kroon, L. J. M. and Bink, N. J.: 1996, 'Conditional Statistics of Vertical Heat Fluxes in Local Advection Conditions', Boundary-Layer Meteorol. 80, 49-78.Google Scholar
  14. Kroon, L. J. M. and De Bruin, H. A. R.: 1995, 'The Crau Field Experiment: Turbulent Exchange in the Surface Layer Under Conditions of Strong Local Advection', J. Hydrol. 166, 327-351.Google Scholar
  15. Lang, A. R. G., McNaughton, K. G., Chen Fazu, Bradley, E. F., and Ohtaki, E.: 1983, 'Inequalities of Eddy Transfer Coefficients for Vertical Transport of Sensible and Latent Heats during Advective Inversions', Boundary-Layer Meteorol. 25, 25-41.Google Scholar
  16. McNaughton, K. G.: 1976, 'Evaporation and Advection I: Evaporation from Extensive Homogeneous Surfaces', Quart. J. Roy. Meteorol. Soc. 102, 181-191.Google Scholar
  17. McNaughton, K. G. and Jarvis, P. G.: 1983, 'Predicting the Effects of Vegetation Changes on Transpiration and Evaporation', in Kozlowski, T. T. (ed.), Water Deficits and Plant Growth, Academic Press, New York, pp. 1-47.Google Scholar
  18. Motha, R. P., Verma, S. B., and Rosenberg, N. J.: 1979, 'Exchange Coefficients Under Sensible Heat Advection Determined by Eddy Correlation', Agric. Meteorol. 20, 273-280.Google Scholar
  19. Priestley, C. H. B. and Taylor, R. J.: 1972, 'On the Assessment of Surface Heat Flux and Evaporation Using Large-Scale Parameters', Mon. Wea. Rev. 100, 81-92.Google Scholar
  20. Rao, K. S., Wyngaard, J. C., and Coté, O. R.: 1974, 'Local Advection of Momentum, Heat, and Moisture in Micrometeorology', Boundary-Layer Meteorol. 7, 331-348.Google Scholar
  21. Rider, N. E., Philip, J. R., and Bradley, E. F.: 1963, 'The Horizontal Transport of Heat and Moisture - A Micrometeorological Study', Quart. J. Roy. Meteorol. Soc. 89, 507-531.Google Scholar
  22. Stearns, C. R.: 1971, 'The Effect of Time-Variable Fluxes on Mean Wind and Temperature Structure', Boundary-Layer Meteorol. 1, 389-398.Google Scholar
  23. Swinbank, W. C. and Dyer, A. J.: 1967, 'An Experimental Study in Micro-Meteorology', Quart. J. Roy. Meteorol. Soc. 93, 494-500.Google Scholar
  24. Timofeev, M. P.: 1954, 'Change in the Meteorological Regime on Irrigation', Acad. Sci. (USSR) Bull. Geophys. 2, 108-113.Google Scholar
  25. Townsend, A. A.: 1961, 'Equilibrium Layers and Wall Turbulence', J. Fluid Mech. 11, 97-120.Google Scholar
  26. Verma, S. B., Rosenberg, N. J., and Blad, B. L.: 1978, 'Turbulent Exchange Coefficients for Sensible Heat and Water Vapour Under Advective Conditions', J. Appl. Meteorol. 17, 330-338.Google Scholar
  27. Wyngaard, J. C. and Brost, R. A.: 1984, 'Top-Down and Bottom-Up Diffusion of a Scalar in the Convective Boundary Layer', J. Atmos. Sci. 41, 102-112.Google Scholar
  28. Wyngaard, J. C., Pennell, W. T., Lenschow, D. H., and LeMone, M. A.: 1978, 'The Temperature-Humidity Covariance Budget in the Convective Boundary Layer', J. Atmos. Sci. 35, 47-58.Google Scholar

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • K. G. McNaughton
  • J. Laubach

There are no affiliations available

Personalised recommendations