Skip to main content
Log in

Heat and mass transfer to and from surfaces with dense vegetation or similar permeable roughness

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

Abstract

A differential equation is obtained to describe the concentration of passive admixtures (water vapor, sensible heat, pollutants, CO2, etc.) of turbulent flow inside a dense and uniform vegetational canopy. The profiles of eddy diffusivity, wind speed and shear stress are assumed to be exponential decay functions of depth below the top of the canopy. This equation is solved for the case of a vegetation with constant concentration of the admixture at the foliage surfaces. The solution is used to formulate bulk mass or heat transfer coefficients, which can be applied to practical problems involving surfaces covered with a vegetation or with similar porous or fibrous roughness elements. The results are shown to be consistent with experimental data presented by Chamberlain (1966), Garratt and Hicks (1973) and Garratt (1978). Calculations with the model illustrate that, as compared to its behavior over surfaces with bluff roughness elements, ln(z 0/z 0c ) (wherez 0 is the momentum roughness andz 0c , the scalar roughness) for permeable roughness elements is relatively insensitive tou * and practically independent ofz 0.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Abramowitz, M. and Stegun, I. A. (Eds.): 1964, ‘Handbook of Mathematical Functions’, National Bureau of Standards Applied Math. Ser. 55, Washington, D.C., 1046 pp.

  • Bache, D. H. and Unsworth, M. H.: 1977, ‘Some Aerodynamic Features of a Cotton Canopy’, Quart. J. Roy. Meteorol. Soc. 103, 121–134.

    Article  Google Scholar 

  • Brown, K. W. and Covey, W.: 1966, ‘The Energy-Budget Evaluation of the Micro-Meteorological Transfer Processes Within a Cornfield’, Agric. Meteorol. 3, 73–96

    Article  Google Scholar 

  • Brutsaert, W.: 1975a, ‘A Theory for Local Evaporation (or Heat Transfer) from Rough and Smooth Surfaces at Ground Level’, Water Resources Res. 11, 543–550.

    Article  Google Scholar 

  • Brutsaert, W.: 1975b, ‘The Roughness Length for Water Vapor, Sensible Heat, and other Scalars’, J.Atmos. Sci. 32, 2028–2031.

    Article  Google Scholar 

  • Brutsaert, W.: 1975c, ‘Comments on Surface Roughness Parameters and the Height of Dense Vegetation’, J.Meteorol. Soc. Japan 53, 96–97.

    Google Scholar 

  • Chamberlain, A. C.: 1966, ‘Transport of Gases to and from Grass and Grass-Like Surfaces’, Proc.Roy. Soc. London A290, 236–265.

    Article  Google Scholar 

  • Chamberlain, A. C.: 1974, ‘Mass Transfer to Bean Leaves’, Boundary-Layer Meteorol. 6, 447–486.

    Article  Google Scholar 

  • Cionco, R. M.: 1965, ‘A Mathematical Model for Air Flow in a Vegetative Canopy’, J.Appl. Meteorol. 4, 517–522.

    Article  Google Scholar 

  • Cionco, R. M.: 1972, ‘A Wind-Profile Index for Canopy Flow’, Boundary-Layer Meteorol. 3, 255–263.

    Article  Google Scholar 

  • Corino, E. R. and Brodkey, R. S.: 1969, ‘A Visual Investigation of the Walt Region in Turbulent Flow, J. Fluid Mech. 37, 1–30.

    Article  Google Scholar 

  • Cowan, I. R.: 1968, ‘Mass, Heat and Momentum Exchange Between Stands of Plants and their Atmospheric Environment’, Quart. J. Ray. Meteorol. Soc. 94, 523–544.

    Article  Google Scholar 

  • Denmead, O. T.: 1964, ‘Evaporation Sources and Apparent Diffusivities in a Forest Canopy’, J.Appl. Meteorol. 3, 383–389.

    Article  Google Scholar 

  • Denmead, O. T.: 1976, ‘Temperature Cereals, in Vegetation and the Atmosphere (J. L. Monteith, Ed.), Vol. 2 Case Studies, 1–31, Academic Press, London.

    Google Scholar 

  • Garratt, J. R.: 1978, ‘Transfer Characteristics for a Heterogeneous Surface of Large Aerodynamic Roughness’, Quart. J. Roy. Meteorol. Soc., 104, 495–502.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Goudriaan, J.: 1977, Crop Micrometeorology: a Simulation Study, Pudoc, Centre for Agric. Publishing and Documentation, Wageningen, Netherlands, 249 pp.

    Google Scholar 

  • Impens, I. I.: 1973, ‘Daytime Distribution of Energy Sinks and Sources and Transfer Processes Within a Sunflower Canopy’, in Plant Response to Climatic Factors, Proc. Uppsala Syrup. 1970 (Ecology and Conservation, 5), Unesco.

    Google Scholar 

  • Inoue, E.: 1963, ‘On the Turbulent Structure of Airflow Within Crop Canopies’. J. Meteorol. Soc. Japan 41, 317–326.

    Google Scholar 

  • Inoue, K., Uchijima, Z., Horie, T., and Iwakiri, S.: 1975, ‘Studies of Energy and Gas Exchange Within Crop Canopies (10). Structure of Turbulence in Rice Crop’. J. A gric. Meteorol. (Nogyo Kisho) Japan 31, 71–82.

    Google Scholar 

  • Kondo, J.: 1971, ‘Relationship Between the Roughness Coefficient and Other Aerodynamic Parameters’. J. Meteorol. Soc. Japan 49, 121–124.

    Google Scholar 

  • Kondo, J.: 1972, ‘On a Product of Mixing Length and Coefficient of Momentum Absorption Within Plant Canopies’, J. Meteorol. Soc. Japan 50, 487–488.

    Google Scholar 

  • Kondo, J. and Akashi, S.: 1976, ‘Numerical Studies of the Two-Dimensional Flow in Horizontally Homogeneous Canopy Layers’, Boundary-Layer Meteorol. 10, 255–272.

    Article  Google Scholar 

  • Landsberg, J. J. and James, G. B.: 1971, ‘Wind Profiles in Plant canopies: Studies on an Analytical Model’, J. Appl. Ecol. 8, 729–741.

    Article  Google Scholar 

  • Landsberg, J. J. and Powell, D. B. B.: 1973, ‘Surface Exchange Characteristics of Leaves Subject to Mutual Interference’, Agric. Meteorol. 13, 169.

    Article  Google Scholar 

  • Landsberg, J. J. and Thom, A. S.: 1971, ‘Aerodynamic Properties of a Plant of Complex Structure’, Quart. J. Roy. Meteorol. Soc. 97, 565–570.

    Article  Google Scholar 

  • Lemon, E.: 1965, ‘Micrometeorology and the Physiology of Plants in their Natural Environment’. In Plant Physiology (F. C. Steward, Ed.), 4A, 203–227, Acad. Press, N.Y.

    Google Scholar 

  • Lemon, E., Allen, L. H. Jr., and Mueller, L.: 1970, ‘Carbon Dioxide Exchange of a Tropical Rain Forest’, Part II. Bioscience 20, 1054–1059.

    Article  Google Scholar 

  • Merlivat, L: 1978, ‘The Dependence of Bulk Evaporation Coefficients on Air-Water Interfacial Conditions as Determined by the Isotopic Method’, J. Geophys. Res. (Oceans and Atmos.) in press.

    Google Scholar 

  • Meroney, R. N.: 1970, ‘Wind Tunnel Studies of the Air Flow and Gaseous Plume Diffusion in the Leading Edge and Downstream Regions of a Model Forest, Atmosph. Envir. 4, 597–614.

    Article  Google Scholar 

  • Monteith, J. L.: 1973, Principles of Environmental Physics, Elsevier Publ. Co., Inc., N.Y., 241 pp.

    Google Scholar 

  • Murphy, C. E. and Knoerr, K. R.: 1975, ‘The Evaporation of Intercepted Rainfall from a Forest Stand: An Analysis by Simulation’, Water Resour. Res. 11, 273–280.

    Article  Google Scholar 

  • Oliver, H. R.: 1975, ‘Ventilation in a Forest’, Agric. Meteor. 14, 347–355.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Parkhurst, D. F. and Pearman, G. I.: 1974, ‘Convective Heat Transfer from a Semi-Infinite Flat Plate to Periodic Flow at Various Angles of Incidence’, Agric. Meteorol. 13, 383–393.

    Article  Google Scholar 

  • Parkhurst, D. F., Duncan, P. R., Gates, D. M., and Kreith, F.: 1968, ‘Wind-tunnel Modelling of Convection of Heat Between Air and Broad Leaves of Plants’, Agric. Meteorol. 5, 33–47.

    Article  Google Scholar 

  • Parlange, J.-Y., Waggoner, P. E. and Heichel, G. H.: 1971, ‘Boundary Layer Resistance and Temperature Distribution on Still and Flapping Leaves’, Plant Phys. 48, 437–442.

    Article  Google Scholar 

  • Parlange, J.-Y. and Waggoner, P. E.: 1972, ‘Boundary Layer Resistance and Temperature Distribution on Still and Flapping Leaves. 2. Field Experiments’, Plant Phys. 50, 60–63.

    Article  Google Scholar 

  • Pearman, G. I., Weaver, H. L., and Tanner, C. B.: ‘Boundary Layer Heat Transfer Coefficients under Field Conditions’, Agric. Meteorol. 10, 83–92.

  • Plate, E. J. and Quraishi, A. A.: 1965, ‘Modeling of Velocity Distributions Inside and Above Tall Crops’, J. Appl. Meteorol. 4, 400–408.

    Article  Google Scholar 

  • Rauner, Ju. L: 1976, Deciduous forests. Ch. 8 in ‘Vegetation and the Atmosphere’ (J. L. Monteith, Ed.) Vol. 2 Case Studies, 241–264, Academic Press, London.

    Google Scholar 

  • Ripley, E. A. and Redmann, R. E.: 1976, Grassland, Ch. 12 in Vegetation and the atmosphere (J. L. Monteith, Ed.) Vol. 2, Case Studies, 349–398, Academic Press, London.

    Google Scholar 

  • Saito, T.: 1962, On Estimation of Transpiration and Eddy-transfer Coefficient with Plant Communities by Energy Balance Method, J. Agric. Meteorol. (Nogyo Kisho), Japan, 17, 101–105.

    Google Scholar 

  • Saito, T.: 1964, On the Wind Profile within Plant Communities, Bull. Nation. Inst. Agric. Sci. Japan (Nogyo Gijutsu Kenkyusho Hokoku) A 11, 67–73.

    Google Scholar 

  • Schlichting, H.: 1960, Boundary Layer Theory (transl. by J. Kestin), 4th Ed., McGraw-Hill, N.Y.

    Google Scholar 

  • Schuepp, P. H.: 1972, ‘Studies of Forced-convection Heat and Mass Transfer of Fluttering Realistic Leaf Models’, Boundary-Layer Meteorol. 2, 263–274.

    Article  Google Scholar 

  • Seginer, I., Mulhearn, P. J., Bradley, E. F., and Finnigan, J. J.: 1976, ‘Turbulent Flow in a Model Plant Canopy’, Boundary-Laydr Meteorol. 10, 423–453.

    Google Scholar 

  • Shaw, R. H.: 1977, ‘Secondary Wind Speed Maxima Inside Plant Canopies’, J. Appl. Meteorol. 16, 514–521.

    Article  Google Scholar 

  • Shaw, R. H.: DenHartog, G., King, K. M., and Thurtell, G. W.: 1974, ‘Measurements of Mean Wind Flow and Three-dimensional Turbulence Intensity within a Mature Corn Canopy’, Agric. Meteorol. 13, 419–425.

    Article  Google Scholar 

  • Shawcroft, R. W., Lemon, E. R., Allen, L. H. Jr., Stewart, D. W., and Jensen, S. E.: 1974, ‘The Soil-plant-atmosphere Model and Some of its Predictions, Agric. Meteorol. 14, 287–307.

    Article  Google Scholar 

  • Shreffler, J. H.: 1976, ‘A Model for the Transfer of Gaseous Pollutants to a Vegetational Surface’, J. Appl. Meteorol. 15, 744–746.

    Article  Google Scholar 

  • Stewart, D. W.: ‘A Simulation of Net Photosynthesis of Field Corn’, Ph.D. Thesis., Cornell University, Ithaca, N.Y., 1970.

    Google Scholar 

  • Thom, A. S.: 1971, ‘Momentum Absorption by Vegetation’, Quart. J. Roy. Meteorol. Soc. 97, 414–428.

    Article  Google Scholar 

  • Thom, A. S.: 1972, ‘Momentum, Mass and Heat Exchange of Vegetation’, Quart. J. Roy. Meteorol. Soc. 98, 124–134.

    Article  Google Scholar 

  • Thorn, A. S.: 1975, ‘Momentum, Mass and Heat Exchange of Plant Communities. Ch. 3 in Vegetation and the Atmosphere (J. L. Monteith, Ed.), Vol. 1 Principles, 57–109, Academic Press, London.

    Google Scholar 

  • Thorpe, M. R. and Butler, D. R.: 1977, ‘Heat Transfer Coefficients for Leaves on Orchard Apple Trees’, Boundary-Layer Meteorol. 12, 61–73.

    Article  Google Scholar 

  • Uchijima, Z.: 1972, ‘Studies on the Micro-climate within Plant Communities. (1) On the Turbulent Transfer Coefficient within Plant Layer’, J. Agric. Meteorol. (Nogyo Kisho) Japan 18, 1–9.

    Article  Google Scholar 

  • Uchijima, Z.: 1966, ‘Micrometeorological Evaluation of Integral Exchange Coefficient at Foliage Surfaces and Source Strengths within a Corn Canopy’, Bull. Nation. Inst. Agric. Sci. Japan (Nogyo Giiutsu Kenkyusho Hokoku) A13, 81–93.

    Google Scholar 

  • Uchijima, Z., Udagawa, T., Horie, T., and Kobayashi, K.: 1970, ‘Studies of Energy and Gas Exchange Within Crop Canopies (8). Turbulent Transfer Coefficient and Foliage Exchange Velocity within a Corn Canopy’, J. Agric. Meteorol. (Nogyo Kisho) Japan 25, 215–227.

    Article  Google Scholar 

  • Uchijima, Z. and Wright, J. L.: 1964, ‘An Experimental Study of Air Flow in a Corn Plant-air Layer’, Bull. Nation. Inst. Agric. Sci. Japan (Nogyo Giiutsu Kenkyusho Hokoku ) A11, 19–66.

    Google Scholar 

  • Watson, G. N.: 1966, A treatise on the Theory of Bessel functions, 2nd ed., 804 pp. Cambridge University Press, Cambridge.

    Google Scholar 

  • Wigley, G. and Clark, J. A.: 1974, ‘Heat Transfer Coefficients for Constant Energy Flux Models of Broad Leaves’, Boundary-Layer Meteorol. 7, 139-150

    Article  Google Scholar 

  • Wright, J. L. and Brown, K. W.: 1967, ‘Comparison of Momentum and Energy Balance Methods of Computing Vertical Transfer within a Crop’, Agronomy Your 59, 427–432.

  • Yaglom, A. M. and Kader, B. A.: 1974, ‘Heat and Mass Transfer Between a Rough Wall and Turbulent Fluid Flow at High Reynolds and Péclet Numbers’, Z Fluid Mech. 62, 601–623.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Brutsaert, W. Heat and mass transfer to and from surfaces with dense vegetation or similar permeable roughness. Boundary-Layer Meteorol 16, 365–388 (1979). https://doi.org/10.1007/BF02220492

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02220492

Keywords

Navigation