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.
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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.
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
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.
Brutsaert, W.: 1975b, ‘The Roughness Length for Water Vapor, Sensible Heat, and other Scalars’, J.Atmos. Sci. 32, 2028–2031.
Brutsaert, W.: 1975c, ‘Comments on Surface Roughness Parameters and the Height of Dense Vegetation’, J.Meteorol. Soc. Japan 53, 96–97.
Chamberlain, A. C.: 1966, ‘Transport of Gases to and from Grass and Grass-Like Surfaces’, Proc.Roy. Soc. London A290, 236–265.
Chamberlain, A. C.: 1974, ‘Mass Transfer to Bean Leaves’, Boundary-Layer Meteorol. 6, 447–486.
Cionco, R. M.: 1965, ‘A Mathematical Model for Air Flow in a Vegetative Canopy’, J.Appl. Meteorol. 4, 517–522.
Cionco, R. M.: 1972, ‘A Wind-Profile Index for Canopy Flow’, Boundary-Layer Meteorol. 3, 255–263.
Corino, E. R. and Brodkey, R. S.: 1969, ‘A Visual Investigation of the Walt Region in Turbulent Flow, J. Fluid Mech. 37, 1–30.
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.
Denmead, O. T.: 1964, ‘Evaporation Sources and Apparent Diffusivities in a Forest Canopy’, J.Appl. Meteorol. 3, 383–389.
Denmead, O. T.: 1976, ‘Temperature Cereals, in Vegetation and the Atmosphere (J. L. Monteith, Ed.), Vol. 2 Case Studies, 1–31, Academic Press, London.
Garratt, J. R.: 1978, ‘Transfer Characteristics for a Heterogeneous Surface of Large Aerodynamic Roughness’, Quart. J. Roy. Meteorol. Soc., 104, 495–502.
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.
Goudriaan, J.: 1977, Crop Micrometeorology: a Simulation Study, Pudoc, Centre for Agric. Publishing and Documentation, Wageningen, Netherlands, 249 pp.
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.
Inoue, E.: 1963, ‘On the Turbulent Structure of Airflow Within Crop Canopies’. J. Meteorol. Soc. Japan 41, 317–326.
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.
Kondo, J.: 1971, ‘Relationship Between the Roughness Coefficient and Other Aerodynamic Parameters’. J. Meteorol. Soc. Japan 49, 121–124.
Kondo, J.: 1972, ‘On a Product of Mixing Length and Coefficient of Momentum Absorption Within Plant Canopies’, J. Meteorol. Soc. Japan 50, 487–488.
Kondo, J. and Akashi, S.: 1976, ‘Numerical Studies of the Two-Dimensional Flow in Horizontally Homogeneous Canopy Layers’, Boundary-Layer Meteorol. 10, 255–272.
Landsberg, J. J. and James, G. B.: 1971, ‘Wind Profiles in Plant canopies: Studies on an Analytical Model’, J. Appl. Ecol. 8, 729–741.
Landsberg, J. J. and Powell, D. B. B.: 1973, ‘Surface Exchange Characteristics of Leaves Subject to Mutual Interference’, Agric. Meteorol. 13, 169.
Landsberg, J. J. and Thom, A. S.: 1971, ‘Aerodynamic Properties of a Plant of Complex Structure’, Quart. J. Roy. Meteorol. Soc. 97, 565–570.
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.
Lemon, E., Allen, L. H. Jr., and Mueller, L.: 1970, ‘Carbon Dioxide Exchange of a Tropical Rain Forest’, Part II. Bioscience 20, 1054–1059.
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.
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.
Monteith, J. L.: 1973, Principles of Environmental Physics, Elsevier Publ. Co., Inc., N.Y., 241 pp.
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.
Oliver, H. R.: 1975, ‘Ventilation in a Forest’, Agric. Meteor. 14, 347–355.
Owen, P. R. and Thomson, W. R.: 1963, ‘Heat Transfer Across Rough Surfaces’, J. Fluid Mech. 15, 321–334.
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.
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.
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.
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.
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.
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.
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.
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.
Saito, T.: 1964, On the Wind Profile within Plant Communities, Bull. Nation. Inst. Agric. Sci. Japan (Nogyo Gijutsu Kenkyusho Hokoku) A 11, 67–73.
Schlichting, H.: 1960, Boundary Layer Theory (transl. by J. Kestin), 4th Ed., McGraw-Hill, N.Y.
Schuepp, P. H.: 1972, ‘Studies of Forced-convection Heat and Mass Transfer of Fluttering Realistic Leaf Models’, Boundary-Layer Meteorol. 2, 263–274.
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.
Shaw, R. H.: 1977, ‘Secondary Wind Speed Maxima Inside Plant Canopies’, J. Appl. Meteorol. 16, 514–521.
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.
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.
Shreffler, J. H.: 1976, ‘A Model for the Transfer of Gaseous Pollutants to a Vegetational Surface’, J. Appl. Meteorol. 15, 744–746.
Stewart, D. W.: ‘A Simulation of Net Photosynthesis of Field Corn’, Ph.D. Thesis., Cornell University, Ithaca, N.Y., 1970.
Thom, A. S.: 1971, ‘Momentum Absorption by Vegetation’, Quart. J. Roy. Meteorol. Soc. 97, 414–428.
Thom, A. S.: 1972, ‘Momentum, Mass and Heat Exchange of Vegetation’, Quart. J. Roy. Meteorol. Soc. 98, 124–134.
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.
Thorpe, M. R. and Butler, D. R.: 1977, ‘Heat Transfer Coefficients for Leaves on Orchard Apple Trees’, Boundary-Layer Meteorol. 12, 61–73.
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.
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.
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.
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.
Watson, G. N.: 1966, A treatise on the Theory of Bessel functions, 2nd ed., 804 pp. Cambridge University Press, Cambridge.
Wigley, G. and Clark, J. A.: 1974, ‘Heat Transfer Coefficients for Constant Energy Flux Models of Broad Leaves’, Boundary-Layer Meteorol. 7, 139-150
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.
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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
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DOI: https://doi.org/10.1007/BF02220492