Skip to main content
SpringerLink
Log in

Aerodynamic Variables in the Bulk Formulation of Turbulent Fluxes

  • Published:
Boundary-Layer Meteorology Aims and scope Submit manuscript

Abstract

Aerodynamic variables are required to apply Monin–Obukhov similarity theory in the bulk formulation of surface fluxes. In the literature, these aerodynamic variables are commonly misinterpreted. In this paper, we review the concept of the aerodynamic variable, its connection to surface-layer similarity theory and how and why the aerodynamic variable is replaced with other variables.

Observed mean variables below the surface layer, such as the surface radiation temperature, or the air temperature at canopy height, are often used in place of the extrapolated aerodynamic variables in the bulk formula, requiring empirical relationships between aerodynamic and observed variables, or requiring empirical adjustments of bulk resistances. The present study examines the validity of these relationshi Experiment (CODE). The results indicate that using a measured substitute for an aerodynamic variable can lead to significant errors in estimates of turbulent surface fluxes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • André, J. C. and Mahrt, L.: 1982, 'The Nocturnal Surface Inversion and Influence of Clear-Air Radiative Cooling', J. Atmos. Sci. 39, 864–878.

    Google Scholar 

  • Beljaars, A. C. M. and Holtslag, A. A. M.: 1991, 'Flux Parameterization Over Land Surfaces for Atmospheric Models', J. Appl. Meteorol. 30, 327–341.

    Google Scholar 

  • Bosveld, F. C.: 1997, 'Derivation of Fluxes from Profiles Over a Moderately Homogeneous Forest', Boundary-Layer Meteorol. 84, 289–327.

    Google Scholar 

  • Brost, R. A. and Wyngaard, J. C.: 1978, 'A Model Study of the Stably Stratified Planetary Boundary Layer', J. Atmos. Sci. 35, 1427–1440.

    Google Scholar 

  • Brutsaert, W. H.: 1982, Evaporation into the Atmosphere. D. Reidel, Dordrecht, 299 pp.

    Google Scholar 

  • Brutsaert, W. and Sugita, M.: 1996, 'Sensible Heat Transfer Parameterization for Surfaces with Anisothermal Dense Vegetation', J. Atmos. Sci. 53, 209–216.

    Google Scholar 

  • Businger, J. A., Wyngaard, J. C., Izumi, Y., and Bradley, E. F.: 1971, 'Flux Profile Relationships in the Atmospheric Surface Layer', J. Atmos. Sci. 28, 181–189.

    Google Scholar 

  • den Hartog, G., Mickle, R. E., Neumann, H. H., Arnold, J., Deary, J., and Beavan, A.: 1992, Final documentation report on vineyard measurements for the San Joaquin Valley Air Pollution Study Agency, Contract 91–2.

  • Dyer, A. J.: 1974, 'A Review of Flux-Profile Relationships', Boundary-Layer Meteorol. 7, 363–372.

    Google Scholar 

  • Fazu, Chen and Schwerdtfeger, P.: 1989, 'Flux-Gradient Relationships for Momentum and Heat Over a Rough Natural Surface', Quart. J. Roy. Meteorol. Soc. 115, 335–352.

    Google Scholar 

  • Fleagle, R. G. and Businger, J. A.: 1980, An Introduction to Atmospheric Physics, Academic Press, 432 pp.

  • Garratt, J. R.: 1978a, 'Flux Profile Relations Above Tall Vegetation', Quart. J. Roy. Meteorol. Soc. 104, 199–211.

    Google Scholar 

  • Garratt, J. R.: 1978b, 'Transfer Characteristics for a Heterogeneous Surface of Large Aerodynamic Roughness', Quart. J. Roy. Meteorol. Soc. 104, 491–502.

    Google Scholar 

  • Garratt, J. R.: 1980, 'Surface Influence Upon Vertical Profiles in the Atmospheric Near-Surface Layer', Quart. J. Roy. Meteorol. Soc. 106, 803–819.

    Google Scholar 

  • Garratt, J. R.: 1992, The Atmospheric Boundary Layer, Cambridge University Press, 316 pp.

  • Garratt, J. R. and Hicks, B. B.: 1973, 'Momentum, Heat and Water Vapor Transfer to and from Natural and Artificial Surfaces', Quart. J. Roy. Meteorol. Soc. 99, 680–687.

    Google Scholar 

  • Garratt, J. R. and Francey, R. J.: 1978, 'Bulk Characteristics of Heat Transfer in the Unstable, Baroclinic Atmospheric Boundary Layer', Boundary-Layer Meteorol. 15, 399–421.

    Google Scholar 

  • Grantz, D.: 1992, Biophysical measurements to support CODE-91, The California Ozone Deposition Experiment, June–August, 1991.

  • Högström, U.: 1988, 'Non-Dimensional Wind and Temperature Profiles in the Atmospheric Surface Layer: A Re-evaluation', Boundary-Layer Meteorol. 42, 55–78.

    Google Scholar 

  • Hopwood, W. P.: 1996, 'Observations and Parameterization of Momentum Transfer in Heterogeneous Terrain Consisting of Regularly Spaced Obstacles', Boundary-Layer Meteorol. 81, 217–243.

    Google Scholar 

  • Howell, J. F. and Sun, J.: 1999, 'Surface-Layer Fluxes in Stable Conditions', Boundary-Layer Meteorol. 90, 495–520.

    Google Scholar 

  • Huband, N. D. S. and Monteith, J. L.: 1986, 'Radiative Surface Temperature and Energy Balance of a Wheat Canopy, Part I: Comparison of Radiative and Aerodynamic Canopy Temperature', Boundary-Layer Meteorol. 36, 1–17.

    Google Scholar 

  • Kaimal, J. C. and Finnigan, J. J.: 1994, Atmospheric Boundary Layer Flows, Oxford University Press, 289 pp.

  • Kohsiek, W., De Bruin, H. A. R., The, H., and Van Den Hurk, B.: 1993, 'Estimation of the Sensible Heat Flux of a Semi-Arid Using Surface Radiative Temperature Measurements', Boundary-Layer Meteorol. 63, 213–230.

    Google Scholar 

  • Kubota, A. and Sugita, M.: 1994, 'Radiometrically Determined Skin Temperature and Scalar Roughness to Estimate Surface Heat Flux. Part I: Parameterization of Radiometric Scalar Roughness', Boundary-Layer Meteorol. 69, 397–416.

    Google Scholar 

  • Kustas, W. P., Choudhury, B. J., Moran, M. S., Reginato, R. J., Jackson, R. D., Gay, L. W., and Weaver, H. L.: 1989, 'Determination of Sensible Heat Flux Over Sparse Canopy Using Thermal Infrared Data', Agric. For. Meteorol. 44, 197–216.

    Google Scholar 

  • Kustas, W. P., Choudhury, B. J., Inoue, Y., Pinter, P. J., Moran, M. S., Jackson, R. D., and Reginato, R. J.: 1990, 'Ground and Aircraft Infrared Observations Over a Partially-Vegetated Area', Int. J. Remote Sens. 11, 409–427.

    Google Scholar 

  • Kustas, W. P. and Humes, K. S.: 1996, 'Sensible Heat Flux from Remotely-Sensed Data at Different Resolutions', in J. B. Stewart, E. T. Engman, R. A. Feddes, and Y. Kerr (eds.), Scaling Up in Hydrology Using Remote Sensing, Ch. 8, John Wiley and Sons, London, pp. 127–145.

    Google Scholar 

  • Lhomme, J.-P., Monteny, B., Amadou, M., Chehbouni, A., and Troufleau, D.: 1994, 'Determination of Sensible Heat Flux Over Sahelian Fallow Savannah Using Infra-Red Thermometry', J. Fluid Mech. 68, 93–106.

    Google Scholar 

  • Mahrt, L., Sun, J., MacPherson, J. I., Jensen, N. O., and Desjardins, R.L.: 1997, 'Formulation of Surface Heat Flux: Application to BOREAS', J. Geophys. Res. 102, 29,641–29,649.

    Google Scholar 

  • Mahrt, L.: 1996, 'The Bulk Aerodynamic Formulation Over Heterogeneous Surfaces', Boundary-Layer Meteorol. 78, 87–119.

    Google Scholar 

  • Massman, W. J., Pederson, J., Delany, A., Grantz, D., den Hartog, G., Neumann, H. H., Oncley, S. P., Pearson, Jr., R., and Shaw, R. H.: 1994, 'An Evaluation of the Regional Acid Deposition Model Surface Module for Ozone Uptake at Three Sites in the San Joaquin Valley of California', J. Geophys. Res. 99, 8281–8294.

    Google Scholar 

  • Monin, A. S. and Obukhov, A. M.: 1954, 'Basic Laws of Turbulent Mixing in the Atmosphere near the Ground', Tr. Akad. Nauk SSSR Geofiz. Inst. 24(15), 163–187.

    Google Scholar 

  • Monteith, J. L.: 1963, in L. T. Evans (ed.), Environmental Control of Plant Growth, Academic Press, New York, pp. 95–112.

    Google Scholar 

  • Mulhearn, P. J., Finnigan, J. J.: 1978, 'Turbulent Flow Over a Very Rough, Random Surface', Boundary-Layer Meteorol. 15, 109–132.

    Google Scholar 

  • Norman, J. M., Kustas, W. P. and Humes, K. S.: 1995, 'A Two-Source Approach for Estimating Soil Vegetation Energy Fluxes from Observations of Directional Radiometric Surface Temperature', Agric. For. Meteorol. 77, 263–293.

    Google Scholar 

  • Norman, J. M. and Becker, F.: 1995, 'Terminology in Thermal Infrared Remote Sensing of Natural Surfaces', Agric. For. Meteorol. 77, 153–166.

    Google Scholar 

  • Owen, P. R. and Thomson, W. R.: 1963, 'Heat Transfer Across Rough Surfaces', J. Fluid Mech. 15, 321–334.

    Google Scholar 

  • Paulson, C. A.: 1970, 'The Mathematical Representation of Wind Speed and Temperature Profiles in the Unstable Atmospheric Surface Layer', J. Appl. Meteorol. 9, 857–861.

    Google Scholar 

  • Pederson, J. R., Mahrt, W. J., Delany, A., Oncley, S., Den Hartog, G., Neumann, H. H., Mickle, R. E., Shaw, R. H., Paw U, K. T., Grantz, D. A., MacPherson, J. I., Desjardins, R., Schuepp, P. H., Pearson Jr., R., and Arcado, T. E.: 1995, 'California Ozone Deposition Experiment: Methods, Results, and Opportunities', Atmos. Environ. 29, 3115–3132.

    Google Scholar 

  • Qualls, R. J. and Brutsaert, W.: 1995, 'The Effect of Vegetation Density on the Parameterization of Scalar Roughness to Estimate Spatially Distributed Sensible Heat Fluxes', Water Resour. Res. 32, 645–652.

    Google Scholar 

  • Raupach, M. R., Thom, A. S., and Edwards, I.: 1980, 'A Wind-Tunnel Study of Turbulent Flow Close to Regularly Arrayed Rough Surfaces', Boundary-Layer Meteorol. 18, 373–397.

    Google Scholar 

  • Shuttleworth, W. J. and Wallace, J. S.: 1985, 'Evaporation from Sparse Crops — An Energy Combination Theory', Quart. J. Roy. Meteorol. Soc. 111, 839–855.

    Google Scholar 

  • Shuttleworth, W. J.: 1989, 'Micrometeorology of Temperate and Tropical Forest', Phil. Trans. Roy. Soc. Lond. B324, 299–334.

    Google Scholar 

  • Stewart, J. B., Kustas, W. P., Humes, K. S., Nichols, W. D., Moran, M. S., and De Bruin, H. A. R.: 1994, 'Sensible Heat Flux-Radiometric Surface Temperature Relationship for Eight Semiarid Areas', J. Appl. Meteorol. 33, 1110–1117.

    Google Scholar 

  • Stewart, J. B.: 1995, 'Turbulent Surface Fluxes Derived from Radiometric Surface Temperature of Sparse Prairie Grass', J. Geophys. Res. 33, 25,429–25,433.

    Google Scholar 

  • Sugita, M. and Kubota, A.: 1994, 'Radiometrically Determined Skin Temperature and Scalar Roughness to Estimate Surface Heat Flux Part II: Performance of Parameterized Scalar Roughness for the Determination of Sensible Heat', Boundary-Layer Meteorol. 70, 1–12.

    Google Scholar 

  • Sugita, M. and Brutsaert, W. H.: 1990, 'Regional Surface Fluxes from Remotely Sensed Skin Temperature and Lower Boundary Layer Measurements', Water Resour. Res. 26, 2937–2944.

    Google Scholar 

  • Sun, Jielun and Mahrt, L.: 1995a, 'Determination of Surface Fluxes from the Surface Radiative Temperature', J. Atmos. Sci. 52, 1096–1106.

    Google Scholar 

  • Sun, Jielun and Mahrt, L.: 1995b, 'Relationship of the Heat Flux to Microscale Temperature Variations: Application to BOREAS', Boundary-Layer Meteorol. 76, 291–301.

    Google Scholar 

  • Thom, A. S., Stewart, J. B., Oliver, H. R., and Gash, J. H. C.: 1975, 'Comparison of Aerodynamic and Energy Budget Estimates of Fluxes Over a Pine Forest', Quart. J. Roy. Meteorol. Soc. 101, 93–105.

    Google Scholar 

  • Wieringa, J.: 1993, 'Representative Roughness Parameters for Homogeneous Terrain', Boundary-Layer Meteorol. 63, 323–363.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Center for Atmospheric Research, USA

    Jielun Sun

  2. USDA Forest Service, Fort Collins, CO, 80526, U.S.A.

    William Massman

  3. Department of Botany and Plant Sciences, Air Pollution Research Center, University of California, Riverside, Kearney Agricultural Center, Parlier, CA, 93648, U.S.A.

    David A Grantz

Authors
  1. Jielun Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. William Massman
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. David A Grantz
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sun, J., Massman, W. & Grantz, D.A. Aerodynamic Variables in the Bulk Formulation of Turbulent Fluxes. Boundary-Layer Meteorology 91, 109–125 (1999). https://doi.org/10.1023/A:1001838832436

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1001838832436

Search

Navigation