Skip to main content
SpringerLink
Log in

Bulk Formulation of the Surface Heat Flux

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

Abstract

An interpretive literature survey examines different approachesfor applying the bulk aerodynamic formulato predict the surface heat flux. The surface heat flux is often predicted in terms of the surface radiation temperature, which is also used to predict the upward longwave radiation and the heat flux into the soil. In models, the thermal roughness length based on the surface radiation temperature (radiometric roughness length) is often specified to be smaller than the roughness length for momentum for a number of distinct reasons. The definition of the radiometric roughness length depends on the way that the surface temperature is measured, the choice of stability functions and displacement height and inclusion of any additional resistances.

Using airborne eddy correlation data collected over eight different sites including bare soil, crops and grassland and several types of forests, the radiometric roughness length is found to vary by orders of magnitude in a manner that is difficult to formulate. Alternatively, we evaluate the approach where the thermal roughness length is equated with the better behaved roughness length for momentum and the corresponding aerodynamic surface temperature is modelled in terms of the surface radiation temperature, solar radiation, and vegetation index. The influence of wind speed and soil moisture on the difference between the aerodynamic and surface radiation temperatures is also examined.

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

  • 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 

  • Blyth, E. M.: 1995, 'Using a Simple SVAT Scheme to Describe the Effect of Scale on Aggregation', Boundary-Layer Meteorol. 72, 267–285.

    Google Scholar 

  • Bosveld, F. C., Holtslag, A. A. M., and Van den Hurk, B. J. J. M.: 1999, 'Interpretation of Crown Radiation Temperatures of a Dense Douglas Fir Forest with Similarity Theory', Boundary-Layer Meteorol. 92, 429–451.

    Google Scholar 

  • Brutsaert,W.: 1979, 'Heat and Mass Transfer to and from Surfaces with Dense Vegetation or Similar Permeable Roughness', Boundary-Layer Meteorol. 16, 365–388.

    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 

  • Chehbouni, A., Lo Seen, D., Njoku, E. G., and Monteny, B. M.: 1996: 'Examination of the Difference between Radiative and Aerodynamic Surface Temperatures over Sparsely Vegetated Surfaces', Remote Sens. Environ. 58, 177–186.

    Google Scholar 

  • Chen, F., Janjic, S., and Mitchell, K.: 1997a, 'Impact of Atmospheric Surface-Layer Parameterizations in the New Land-Surface Scheme of the NCEP Mesoscale Eta Model', Boundary-Layer Meteorol. 85, 391–421.

    Google Scholar 

  • Chen, J., Rich, P., Gower, S., Norman, J., and Plummer, S.: 1997b, 'Leaf Area Index of Boreal Forests: Theory, Techniques and Measurements', J. Geophys. Res. 102, 29,429–29,473.

    Google Scholar 

  • Desjardins, R. L., MacPherson, J. I., Mahrt, L., Schuepp, P. H., Pattey, E., Neumann, H., Baldocchi, D., Wofsy, S., Fitzjarrald, D., McCaughey, H., and Joiner, D. W.: 1997, 'Scaling up Flux Measurements for the Boreal Forest Using Aircraft-Tower Combinations', J. Geophys. Res. 102, 29,125–29,134.

    Google Scholar 

  • Garratt, J. R.: 1978, '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. and Hicks, B. B.: 1973, 'Momentum, Heat and Water Vapour Transfer to and from Natural and Artificial Surfaces', Quart. J. Roy. Meteorol. Soc. 99, 680–687.

    Google Scholar 

  • Garratt, J. R., Hicks, B. B., and Valigura, R. A.: 1993, 'Comments on “The Roughness Length for Heat and Other Vegetation Parameters for a Surface of Short Grass” ', J. Appl. Meteorol. 32, 1301–1303.

    Google Scholar 

  • Holtslag, A. A. M. and Ek, M.: 1996, 'The Simulation of Surface Fluxes and Boundary-Layer Development over the Pine Forest in HAPEX-MOBILHY', J. Appl. Meteorol. 35, 202–213.

    Google Scholar 

  • Huband, N. D. S. and Monteith, J. L.: 1986, 'Radiative Surface Temperature and Energy Balance of a Wheat Canopy, I. Comparison of Radiative and Aerodynamic Canopy Temperature', Boundary-Layer Meteorol. 36, 107–116.

    Google Scholar 

  • Jackson, T. J. and Schmugge, T. J.: 1991, 'Vegetation Effects on the Microwave Emission of Soils', Remote Sens. Environ. 36, 203–212.

    Google Scholar 

  • Jackson, T. J., Le Vine, D. M., Swift, C. T., Schmugge, T. J., and Schiebe, F. R.: 1995, 'Large Area Mapping of Soil Moisture Using the ESTAR Passive Microwave Radiometer in Washita 92', Remote Sens. Environ. 53, 27–37.

    Google Scholar 

  • Jasinski, M. and Crago, R.: 1999, 'Estimation of Vegetation Aerodynamic Roughness of Natural Regions Using Frontal Area Density Determined from Satellite Imagery', Agric. For. Meteorol. 94, 65–77.

    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., Humes, K. S., Norman, J. M., and Moran, M. S.: 1996, 'Single-and Dual-Source Modeling of Surface Energy Fluxes with Radiometric Surface Temperature', J. Appl. Meteorol. 35, 110–121.

    Google Scholar 

  • Lhomme, J.-P., Chehbounni, A., and Monteny, B.: 2000, 'Sensible Heat Flux-Radiometric Surface Temperature Relationship over Sparse Vegetation: Parameterizing B-1', Boundary-Layer Meteorol. 97, 431–457.

    Google Scholar 

  • Lhomme, J.-P., Katerji, N., Perrier, A., and Bertolini, J.-M.: 1988, 'Radiative Surface Temperature and Convective Flux Calculation over Crop Canopies', Boundary-Layer Meteorol. 43, 383–392.

    Google Scholar 

  • Liu, W. T., Katsaros, K., and Businger, J.: 1979, 'Bulk Parameterization of Air-Sea Exchanges of Heat and Water Vapor Including the Molecular Constraints at the Interface', J. Atmos. Sci. 36, 1722–1735.

    Google Scholar 

  • MacPherson, J. I., Dobosy, R., Verma, S., Kustas, W. P., Prueger, J. H., and Williams, A.: 1999, 'Intercomparisons between Flux Aircraft and Towers in SGP97', in Fourteenth Conference on Hydrology, American Meteorological Society, Dallas, pp. 125–128.

    Google Scholar 

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

    Google Scholar 

  • Mahrt, L.: 2000, 'Surface Heterogeneity and Vertical Structure of the Boundary Layer', Boundary-Layer Meteorol. 96, 33–62.

    Google Scholar 

  • Mahrt, L. and Vickers, D.: 2002, 'Contrasting Vertical Structures of Nocturnal Boundary Layers', Boundary-Layer Meteorol. 105, 351–363.

    Google Scholar 

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

    Google Scholar 

  • Mahrt, L., Sun, J., Vickers, D., MacPherson, J. I., Pederson, J. R., and Desjardins, R. L.: 1994, 'Observations of Fluxes and Inland Breezes over a Heterogeneous Surface', J. Atmos. Sci. 51, 2165–2178.

    Google Scholar 

  • Mahrt, L., Vickers, D., Sun, J., and McCaughey, J. H.: 2001, 'Calculation of Area-Averaged Fluxes: Application to BOREAS', J. Appl. Meteorol. 40, 915–920.

    Google Scholar 

  • Malhi, Y.: 1995, 'The Behavior of the Roughness Length for Temperature over Heterogeneous Surfaces', Quart. J. Roy. Meteorol. Soc. 122, 1095–1125.

    Google Scholar 

  • Massman, W.: 1999, 'A Model Study of ? B -1 H for Vegetated Surfaces Using “Localized Near-Field” Lagrangian Theory', J. Hydrol. 223, 27–43.

    Google Scholar 

  • McNaughton, K. G. and Van Den Hurk, B. J. J. M.: 1995, 'A “Lagrangian” Revision of the Resistors in the Two-Layer Model for Calculating the Energy Budget of a Plant Canopy', Boundary-Layer Meteorol. 74, 261–288.

    Google Scholar 

  • Mölder, M. and Kellner, E.: 2002, 'Excess Resistance of Bog Surfaces in Central Sweden', Agric. For. Meteorol. 112, 23–30.

    Google Scholar 

  • Mölder, M. and Lindroth, A.: 1999, 'Thermal Roughness Length of a Boreal Forest', Agric. For. Meteorol. 98-99, 659–670.

    Google Scholar 

  • Nakamura, R. and Mahrt, L.: 2001, 'Roughness Lengths and Similarity Theory for Local and Spatially Averaged Fluxes', Agric. For. Meteorol. 100, 47–61.

    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 Radiometeric Surface Temperature', Agric. For. Meteorol. 77, 263–293.

    Google Scholar 

  • Pagowski, M. and Moore, G. W. K.: 2001, 'A Numerical Study of an Extreme Cold-Air Outbreak over the Laborador Sea: Sea, Ice, Air-Sea Interaction and Development of Polar Lows', Mon. Wea. Rev. 129, 47–72.

    Google Scholar 

  • Poulos, G. S., Blumen, W., Fritts, D., Lundquist, J., Sun, J., Burns, S., Nappo, C., Banta, R., Newsome, R., Cuxart, J., Terradellas, E., Balsley, B., and Jensen, M.: 2002, 'CASES-99: A Comprehensive Investigation of the Stable Nocturnal Boundary Layer', Bull. Amer. Meteorol. Soc. 81, 757–779.

    Google Scholar 

  • Qualls, R. and Yates, D.: 2001, 'Directional Radiometric Temperature Profiles within a Grass Canopy', Adv. Water Resour. 24, 145–155.

    Google Scholar 

  • Raupach, M. R.: 1994, 'Simplified Expressions for Vegetation Roughness Length and Zero-Plane Displacement as Functions of Canopy Height and Area Index', Boundary-Layer Meteorol. 71, 211–216.

    Google Scholar 

  • Raupach, M. R. and Thom, A. S.: 1981, 'Turbulence in and above Plant Canopies', Annu. Rev. Fluid Mech. 13, 97–129.

    Google Scholar 

  • Sellers, P., Hall, F., Margolis, H., Kelly, B., Baldocchi, D., den Hartog, G., Cihlar, F., Ryan, M. G., Goodison, B., Crill, P., Ranson, K. J., Lettenmaier, D., and Wickland, D. E.: 1995, 'The Boreal Ecosystem-Atmosphere Study (BOREAS):An Overview and Early Results from the 1994 Field Year', Bull. Amer. Meteorol. Soc. 76, 1549–1577.

    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 

  • 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 

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

    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 

  • Sun, J.: 1999, 'Diurnal Variation of Thermal Roughness Height over a Grassland', Boundary-Layer Meteorol. 92, 407–427.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • Sun, J., Massman, W., and Grantz, D.: 1999, 'Aerodynamic Variables in the Bulk Formula', Boundary-Layer Meteorol. 91, 109–125.

    Google Scholar 

  • Troufleau, D., Lhomme, J. P., Monteny, B., and Vidal, A.: 1997: 'Sensible Heat Flux and Radiometric Surface Temperature over Sparse Sahelian Vegetation. I. An Experimental Analysis of the ? B -1 Parameter', Boundary-Layer Meteorol. 188, 815–838.

    Google Scholar 

  • Vickers, D. and Mahrt, L.: 1997, 'Quality Control and Flux Sampling Problems for Tower and Aircraft Data', J. Atmos. Oceanic Tech. 14, 512–526.

    Google Scholar 

  • Wieringa, J.: 1993, 'Representative Roughness Parameters for Homogeneous Terrain', Boundary-Layer Meteorol. 63, 323–364.

    Google Scholar 

  • Williams, M., Law, B. E., Anthoni, P. M., and Unsworth, M.: 2001, 'Using a Simulation Model and Ecosystem Flux Data to Examine Carbon-Water Interaction in Ponderosa Pine', Tree Physiol. 21, 287–198.

    Google Scholar 

  • Yang, K., Koike, T. and Yang, D.: 2003, 'Surface Flux Parameterization in the Tibetan Plateau', Boundary-Layer Meteorol. 106, 245–262.

    Google Scholar 

  • Zibognon, M., Crago, R., and Suleiman, A.: 2002, 'Conversion of Radiometric to Aerodynamic Surface Temperature with an Anisothermal Canopy Model', Water Resour. Res. 38, 1–6.

    Google Scholar 

  • Zilitinkevich, S. S.: 1995, 'Non-Local Turbulent Transport: Pollution Dispersion Aspects of coherent Structure of Convective Flow', in H. Power, N. Moussiopoulos, and C. A. Brebbia (eds.), Air Pollution, Vol. 1, Air Pollution Theory and Simulation, Computational Mechanics Publication, Southampton, pp. 53–60.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, OR, 97331, U.S.A

    L. Mahrt & Dean Vickers

Authors
  1. L. Mahrt
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dean Vickers
    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

Mahrt, L., Vickers, D. Bulk Formulation of the Surface Heat Flux. Boundary-Layer Meteorology 110, 357–379 (2004). https://doi.org/10.1023/B:BOUN.0000007244.42320.1e

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:BOUN.0000007244.42320.1e

Search

Navigation