Abstract
This paper completes the construction of a two-layer model for the energy balance of sparse canopies begun by Van den Hurk and McNaughton (1994). The model is based on the Lagrangian theory of Raupach (1989). In the earlier work, we showed that the average effect of the near-field component of the scalar concentration profile can be represented by a ‘near-field’ resistor. Here we calculate values for the upper and lower ‘far-field’ resistors using Raupach's expression for the far-field diffusivity and his empirical descriptions of the profiles of vertical velocity variance and Lagrangian integral time scale (Raupach, 1988). The boundary-layer resistance for the foliage of the overstorey canopy is also reassessed. Calculations are carried out for a range of possible canopies. Representative values are chosen for use where a detailed description of the vegetation is unavailable.
The resistors of the new model are compared with those of earlier two-layer models. The new ‘far-field’ resistors are smaller than the corresponding ‘aerodynamic’ resistors of the earlier models of Shuttleworth and Wallace (1985) and Choudhury and Monteith (1988) while the new boundary-layer resistor can be somewhat larger, depending on the choices made in the calculation. We could not find experimental data on canopy energy balances suitable for deciding which model is best. Instead, we have attempted to verify the model using measurements of surface temperature and calculated values of the ‘excess’ resistance, but the results are not definitive. A major conclusion is that turbulent transport near the ground beneath an overstorey canopy is poorly known and therefore is poorly represented in all models. Another conclusion is that current models for the excess resistance are inadequate.
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References
Bache, D. H.: 1986, ‘On the Theory of Gaseous Transport to Plant Canopies’,Atmos. Envir. 20, 1379–1388.
Beljaars, A. C. M. and Holtslag, A. A. M.: 1991, ‘Flux Parameterizations over Land Surfaces for Atmospheric Models’,J. Appl. Meteorol. 30, 327–341.
Chamberlain, A. C.: 1966, ‘Transfer of Gasses To and From Grass and Grass-Like Surfaces’,Proc. Roy. Soc. A 290, 236–290.
Chen, J.: 1984, ‘Uncoupled Multi-Layer Model for the Transfer of Sensible and Latent Heat Flux Densities from Vegetation’,Boundary-Layer Meteorol. 28, 213–226.
Chen, J.-M., Ibbetson, A., and Milford, J. R.: 1988a, ‘Boundary-Layer Resistances of Artificial Leaves in Turbulent Air I: Leaves Parallel to the Mean Flow’,Boundary-Layer Meteorol. 45, 137–156.
Chen, J.-M., Ibbetson, A., and Milford, J. R.: 1988b, ‘Boundary-Layer Resistances of Artificial Leaves in Turbulent Air II: Leaves Inclined to the Mean Flow’,Boundary-Layer Meteorol. 45, 371–390.
Choudhury, B. J. and Monteith, J. L.: 1988, ‘A Four-Layer Model for the Heat Budget of Homogeneous Land Surfaces’,Quart. J. R. Meteorol. Soc. 114, 373–398.
Cionco, R. M.: 1972, ‘A Wind Profile Index for Canopy Flow’,Boundary-Layer Meteorol. 3, 255–263.
Cionco, R. M.: 1978, ‘Analysis for Canopy Index Values for Various Canopy Densities’,Boundary-Layer Meteorol. 15, 81–93.
Cowan, I. R.: 1968, ‘Mass, Heat and Momentum Exchange Between Stands of Plants and their Atmospheric Environment’,Quart. J. R. Meteorol. Soc. 94, 523–544.
Denmead, O. T. and Bradley, E. F.: 1985, ‘Flux-Gradient Relationships in a Forest Canopy’, in: B. A. Hutchison and B. B. Hicks (eds.),The Forest Atmosphere Interaction. Reidel, Dordrecht, pp. 421–442.
Dolman, A. J. and Wallace, J. S.: 1991, ‘Lagrangian andK-Theory Approaches in Modelling Evaporation from Sparse Canopies’,Quart. J. R. Meteorol. Soc. 117, 1325–1340.
Garratt, J. R. and Hicks, B. B.: 1973, ‘Momentum, Heat and Water Vapour Transfer to and from Natural and Artificial Surfaces’,Quart. J. R. Meteorol. Soc. 99, 680–687.
Garratt, J. R.: 1978, ‘Transfer Characteristics for a Heterogeneous Surface of Large Aerodynamic Roughness’,Quart. J. R. Meteorol. Soc. 104, 491–502.
Green, S. R.: 1992, ‘Modelling Turbulent Air Flow in a Stand of Widely Spaced Trees’,PHOENICS J. Comp. Fluid Dynam. 5, 294–312.
Ham, J. M. and Heilman, J. L.: 1991, ‘Aerodynamic and Surface Resistances Affecting Energy Transport in a Sparse Crop’,Agric. For. Meteorol. 53, 267–284.
Heilman, J. L. and Kanemasu, E. T.: 1976, ‘An Evaluation of a Resistance Form of the Energy Balance to Estimate Evapotranspiration’,Agronomy J. 68, 607–611.
Hicks, B. B., Hyson, P., and Moore, C. J.: 1975, ‘A Study of Eddy Fluxes over a Forest’,J. Appl. Meteorol. 14, 58–66.
Huband, N. D. S. and Monteith, J. L.: 1986a, ‘Radiative Surface Temperature and Energy Balance of a Wheat Canopy I. Comparison of Radiative and Aerodynamic Canopy Temperature’,Boundary-Layer Meteorol. 36, 1–17.
Huband, N. D. S. and Monteith, J. L.: 1986, ‘Radiative Surface Temperature and Energy Balance of a Wheat Canopy II. Estimating Fluxes of Sensible and Latent Heat’,Boundary-Layer Meteorol. 36, 107–116.
Jones, H. G.: 1992,Plants and Microclimate: A Quantitative Approach to Environmental Plant Physiology. 2nd Edition. Cambridge University Press. 428 pp.
Kreith, F.: 1973,Principles of Heat Transfer. Intertext Educational, New York, 656 pp.
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.
Meyers, T. P. and Paw U, K. T.: 1987, ‘Modelling the Plant Canopy Micrometeorology with Higher-Order Closure Principles’,Agric. For. Meteorol. 41, 143–163.
Monteith, J. L.: 1963, ‘Evaporation and Environment’, in: G. E. Fogg (ed.),The State and Movement of Water in Living Organisms. Cambridge University Press, Cambridge, pp. 205–234. (Society for Experimental Biology Symposium No 19).
Owen, P. R. and Thompson, W. R.: 1963, ‘Heat Transfer Across Rough Surfaces’,J. Fluid Mechanics 15, 321–334.
Pereira, A. R. and Shaw, R. H.: 1980, ‘A Numerical Experiment on the Mean Wind Structure Inside Canopies of Vegetation’,Agric. For. Meteorol. 22, 303–3198.
Philip, J. R.: 1964, ‘Sources and Transfer Processes in the Air Layers Occupied by Vegetation’,J. Appl. Meteorol. 3, 390–395.
Raupach, M. R.: 1988, ‘Canopy Transport Processes’, in: O. T. Denmead and W. L. Steffan (eds.),Flow and Transport in the Natural Environment: Advances and Applications. Springer-Verlag, Berlin, pp. 95–127.
Raupach, M. R.: 1989a, ‘A Practical Lagrangian Method for Relating Concentrations to Source Distributions in Vegetation Canopies’,Quart. J. R. Meteorol. Soc. 115, 609–632.
Raupach, M. R.: 1989b, ‘Applying Lagrangian Fluid Mechanics to Infer Scalar Source Distributions from Concentration Profiles in Plant Canopies’,Agric. For. Meteorol. 47, 85–108.
Raupach, M. R.: 1989c, ‘Stand Overstorey Processes’,Phil. Trans. R. Soc. Lond. B 324, 175–190.
Raupach, M. R.: 1992, ‘Drag and Drag Partition on Rough Surfaces’,Boundary-Layer Meteorol. 60, 375–395.
Raupach, M. R. and Thom, A. S.: 1981, ‘Turbulence in and Above Plant Canopies’,Ann. Rev. Fluid Mech. 13, 97–129.
Shuttleworth, W. J. and Gurney, R. J.: 1990, ‘The theoretical Relationship Between Foliage Temperature and Canopy Resistance in Sparse Crops’,Quart. J. R. Meteorol. Soc. 116, 497–519.
Shuttleworth, J. W. and Wallace, J. S.: 1985, ‘Evaporation from Sparse Crops — An Energy Combination Theory’,Quart. J. R. Meteorol. Soc. 111, 839–855.
Thom, A. S.: 1972, ‘Momentum, Mass and Heat Exchange of Vegetation’,Quart. J. R. Meteorol. Soc. 98, 124–134.
Van den Hurk, B. J. J. M. and McNaughton, K. G.: 1994, ‘A Two-Layer Model for Describing the Energy Balance of a Plant Canopy Based on Lagrangian Principles’,J. Hydrol. (In press).
Waggoner, P. E. and Reifsnyder, W. E.: 1968, ‘Simulation of the Temperature, Humidity and Evaporation Profiles in a Leaf Canopy’,J. Appl. Meteorol. 7, 400–409.
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McNaughton, K.G., Van Den Hurk, B.J.J.M. 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 (1995). https://doi.org/10.1007/BF00712121
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DOI: https://doi.org/10.1007/BF00712121