References
Albertson, J. D., Katul, G. G., and Wiberg, P.: 2001, 'Relative Importance of Local and Regional Controls on Coupled Water, Carbon, and Energy Fluxes', Adv. Water Resour. 24, 1103–1118.
Amiro, B. D.: 1990, 'Comparison of Turbulence Statistics within 3 Boreal Forest Canopies', Boundary-Layer Meteorol. 51, 99–121.
Ayotte, K. W., Finnigan, J. J., and Raupach, M. R.: 1999, 'A Second-Order Closure for Neutrally Stratified Vegetative Canopy Flows', Boundary-Layer Meteorol. 90, 189–216.
Baldocchi, D. D.: 1989, 'Turbulent Transfer in a Deciduous Forest', Tree Phys. 5, 357–377.
Baldocchi, D. D. and Meyers, T. D.: 1988, 'A Spectral and Lag-Correlation Analysis of Turbulence in a Deciduous Forest Canopy', Boundary-Layer Meteorol. 45, 31–58.
Bradshaw, P., Launder, B. E., and Lumley, J. L.: 1991, 'Collaborative Testing of Turbulence Models', J. Fluids Engr.-Trans. ASME 113, 3–4.
Brutsaert, W.: 1982, Evaporation into the Atmosphere: Theory, History, and Applications, Kluwer Academic Publishers, Boston, 299 pp.
Castro F. A., Palma, J. M., and Lopes, A. S.: 2003, 'Simulation of the Askervein Flow. Part 1: Reynolds Averaged Navier-Stokes Equations (K-Epsilon Turbulence Model)', Boundary-Layer Meteorol. 107, 501–530.
Finnigan, J. J.: 2000, 'Turbulence in Plant Canopies', Annu. Rev. Fluid Mech. 32, 519–571.
Garratt, J. R.: 1992, The Atmospheric Boundary Layer, Cambridge University Press, Cambridge, U.K., 316 pp.
Green, S.: 1992, 'Modelling Turbulent Air Flow in a Stand of Widely Spaced Trees', J. Comp. Fluid Dyn. Appl. 5, 294–312.
Horn, H. S., Nathan, R., and Kaplan, S. R.: 2001, 'Long-Distance Dispersal of Tree Seeds by Wind', Ecol. Res. 16, 877–885.
Kaimal, J. C. and Finnigan, J. J.: 1994, Atmospheric Boundary Layer Flows: Their Structure and Measurement, Oxford University Press, New York, 289 pp.
Katul, G. G. and Albertson, J. D.: 1998, 'An Investigation of Higher-Order Closure Models for a Forested Canopy', Boundary-Layer Meteorol. 89, 47–74.
Katul, G. G. and Albertson, J. D.: 1999, 'Modeling CO2 Sources, Sinks, and Fluxes within a Forest Canopy', J. Geophys. Res. (Atmospheres) 104, 6081–6091.
Katul, G. G. and Chang, W. H.: 1999, 'Principal Length Scales in Second-Order Closure Models for Canopy Turbulence', J. Appl. Meteorol. 38, 1631–1643.
Katul, G. G., Geron, C. D., Hsieh, C. I., Vidakovic, B., and Guenther, A. B.: 1998, 'Active Turbulence and Scalar Transport near the Forest-Atmosphere Interface', J. Appl. Meteorol. 37, 1533–1546.
Katul, G. G., Lai, C. T., Schafer, K., Vidakovic, B., Albertson, J. D., Ellsworth, D., and Oren, R.: 2001a, 'Multiscale Analysis of Vegetation Surface Fluxes: from Seconds to Years', Adv. Water Resour. 24, 1119–1132.
Katul, G. G., Leuning, R., Kim, J., Denmead, O. T., Miyata, A., and Harazono, Y.: 2001b, 'Estimating CO2 Source/Sink Distributions within a Rice Canopy Using Higher-Order Closure Model', Boundary-Layer Meteorol. 98, 103–125.
Kelliher, F. M., Lloyd, J., Arneth, A., Byers, J. N., McSeveny, T., Milukova, I., Grigoriev, S., Panfyorov, M., Sogatchev, A., Varlargin, A., Ziegler, W., Bauer, G., and Schulze, E. D.: 1998, 'Evaporation from a Central Siberian Pine Forest', J. Hydrol. 205, 279–296.
Kelliher, F. M., Lloyd, J., Arneth, A., Luhker, B., Byers, J. N., McSeveny, T. M., Milukova, I., Grigoriev, S., Panfyorov, M., Sogatchev, A., Varlargin, A., Ziegler, W., Bauer, G., Wong, S. C., and Schulze, E. D.: 1999, 'Carbon Dioxide Efflux Density from the Floor of a Central Siberian Pine Forest', Agric. For. Meteorol. 94, 217–232.
Kobayashi, M. H., Pereira, J., and Siqueira, M.: 1994, 'Numerical Study of the Turbulent Flow over and in a Model Forest on a 2D Hill', J. Wind Eng. Ind. Aerodyn. 53, 357–374.
Lai, C. T., Katul, G. G., Butnor, J., Siqueira, M., Ellsworth, D., Maier, C., Johnsen, K., McKeand, S., and Oren, R.: 2002, 'Modelling the Limits on the Response of Net Carbon Exchange to Fertilization in a South-Eastern Pine Forest', Plant Cell Environ. 25, 1095–1119.
Lai, C. T., Katul, G. G., Ellsworth, D., and Oren, R.: 2000a, 'Modelling Vegetation-Atmosphere CO2 Exchange by a Coupled Eulerian-Langrangian Approach', Boundary-Layer Meteorol. 95, 91–122.
Lai, C. T., Katul, G. G., Oren, R., Ellsworth, D., and Schafer, K.: 2000b, 'Modeling CO2 and Water Vapor Turbulent Flux Distributions within a Forest Canopy', J. Geophys. Res. (Atmospheres) 105, 26333–26351.
Launder, B. and Spalding, D. B.: 1974, 'The Numerical Computation of Turbulent Flows', Comp. Meth. Appl. Mech. Eng. 3, 269–289.
Launder, B. E.: 1996, 'An Introduction to Single-Point Closure Methodology', in J. Lumley (ed.), Simulation and Modeling of Turbulent Flows, Oxford University Press, New York, pp. 243–311.
Lee, X. H., Shaw, R. H., and Black, T. A.: 1994, 'Modeling the Effect of Mean Pressure-Gradient on the Mean Flow within Forests', Agric. For. Meteorol. 68, 201–212.
Leuning, R., Denmead, O. T., Miyata, A., and Kim, J.: 2000, 'Source/Sink Distributions of Heat, Water Vapour, Carbon Dioxide and Methane in a Rice Canopy Estimated Using Lagrangian Dispersion Analysis', Agric. For. Meteorol. 104, 233–249.
Li, Z. J., Miller, D. R., and Lin, J. D.: 1985, 'A First Order Closure Scheme to Describe Counter-Gradient Momentum Transport in Plant Canopies', Boundary-Layer Meteorol. 33, 77–83.
Liu, J., Black, T. A., and Novak, M. D.: 1996, 'E-Epsilon Modeling of Turbulent Air Flow Downwind of a Model Forest Edge', Boundary-Layer Meteorol. 77, 21–44.
Lumley, J. L.:1992, 'Some Comments on Turbulence', Phys. Fluids A (Fluid Dynamics) 4, 203–211.
Mahrt, L., Lee, X. L., Black, A., Neumann, H., and Staebler, R.: 2000, 'Nocturnal Mixing in a Forest Subcanopy', Agric. For. Meteorol. 101, 67–78.
Massman, W. J.: 1997, 'An Analytical One-Dimensional Model of Momentum Transfer by Vegetation of Arbitrary Structure', Boundary-Layer Meteorol. 83, 407–421.
Massman, W. J. and Weil, J. C.: 1999, 'An Analytical One-Dimensional Second-Order Closure Model of Turbulence Statistics and the Lagrangian Time Scale within and above Plant Canopies of Arbitrary Structure', Boundary-Layer Meteorol. 91, 81–107.
Meyers, T. and Paw U, K. T.: 1986, 'Testing of a Higher-Order Closure-Model for Modeling Air-Flow within and above Plant Canopies', Boundary-Layer Meteorol. 37, 297–311.
Meyers, T. P.: 1987, 'The Sensitivity of Modeled SO2 Fluxes and Profiles to Stomatal and Boundary-Layer Resistances', Water Air Soil Poll. 35, 261–278.
Meyers, T. P. and Baldocchi, D. D.: 1991, 'The Budgets of Turbulent Kinetic-Energy and Reynolds Stress within and above a Deciduous Forest', Agric. For. Meteorol. 53, 207–222.
Meyers, T. P. and Paw U, K. T.: 1987, 'Modeling the Plant Canopy Micrometeorology with Higher-Order Closure Principles', Agric. For. Meteorol. 41, 143–163.
Nathan, R., Katul, G. G., Horn, H., Thomas, S., Oren, R., Avissar, R., Pacala, S., and Levin, S.: 2002, 'Mechanisms of Long-Distance Dispersal of Seeds by Wind', Nature 418, 409–413.
Parlange, M. B. and Brutsaert, W.: 1989, 'Regional Roughness of the Landes Forest and Surface Shear-Stress under Neutral Conditions', Boundary-Layer Meteorol. 48, 69–81.
Paw U, K. T. and Meyers, T. P.: 1989, 'Investigations with a Higher-Order Canopy Turbulence Model into Mean Source-Sink Levels and Bulk Canopy Resistances', Agric. For. Meteorol. 47, 259–271.
Pinard, J. and Wilson, J. D.: 2001, 'First-and Second-Order Closure Models for Wind in a Plant Canopy', J. Appl. Meteorol. 40, 1762–1768.
Poggi, D., Porporato, A., Ridolfi, L., Albertson, J. D., and Katul, G. G.: 2004a, 'The Effect of Vegetation Density on Canopy Sublayer Turbulence', Boundary-Layer Meteorol. 111, 565–587.
Poggi, D., Katul, G. G., and Albertson, J. D.: 2004b, 'A Note on the Contribution of Dispersive Fluxes to Momentum Transfer within Canopies', Boundary-Layer Meteorol. 111, 615–621.
Pope, S. B.: 2000,Turbulent Flows, Cambridge University Press, New York, 771 pp.
Raupach, M. R.: 1989a, 'Applying Lagrangian Fluid Mechanics to Infer Scalar Source Distributions from Concentration Profiles in Plant Canopies', Agric. For. Meteorol. 47, 85–108.
Raupach, M. R.: 1989b, 'A Practical Lagrangian Method for Relating Scalar Concentrations to Source Distributions in Vegetation Canopies', Quart. J. Roy. Meteorol. Soc. 115, 609–632.
Raupach, M. R.: 1991, 'Vegetation-Atmosphere Interaction in Homogeneous and Heterogeneous Terrain-Some Implications of Mixed-Layer Dynamics', Vegetatio 91, 105–120.
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.
Raupach, M. R. and Finnigan, J. J.: 1997, 'The Influence of Topography on Meteorological Variables and Surface-Atmosphere Interactions', J. Hydrol. 190, 182–213.
Raupach, M. R. and Shaw, R. H.: 1982, 'Averaging Procedures for Flow within Vegetation Canopies', Boundary-Layer Meteorol. 22, 79–90.
Raupach, M. R., Finnigan, J. J., and Brunet, Y.: 1996, 'Coherent Eddies and Turbulence in Vegetation Canopies: The Mixing-Layer Analogy', Boundary-Layer Meteorol. 78, 351–382.
Raupach, M. R., Weng, S., Carruthers, D., and Hunt, J. C. R.: 1992, 'Temperature and Humidity Fields and Fluxes over Low Hills', Quart. Roy. Meteorol. Soc. 118, 191–225.
Sanz, C.: 2003, 'A Note on K-Epsilon Modelling of Vegetation Canopy Air-Flow', Boundary-Layer Meteorol. 108, 191–197.
Schulze, E. D., Lloyd, J., Kelliher, J., Wirth, C., Rebmann, C., Luhker, B., Mund, M., Knohl, A., Milyukova, I. M., Schulze, W., Ziegler, W., Varlagin, A. B., Sogachev, A. F., Valentini, R., Dore, S., Grigoriev, S., Kolle, O., Panfyorov, M. I., Tchebakova, N., and Vygodskaya, N. N.: 1999, 'Productivity of Forests in the Eurosiberian Boreal Region and their Potential to Act as a Carbon Sink-A Synthesis', Global Change Biol. 5, 703–722.
Siqueira, M. and Katul, G. G.: 2002, 'Estimating Heat Sources and Fluxes in Thermally Stratified Canopy Flows Using Higher-Order Closure Models', Boundary-Layer Meteorol. 103, 125–142.
Speziale, C. G.: 1996, 'Modeling of Turbulent Transport Equations', in J. Lumley (ed.), Simulation and Modeling of Turbulent Flows, Oxford University Press, New York, pp. 185–242
Stull, R.: 1988, An Introduction to Boundary Layer Meteorology, Kluwer Academic Publishers, Boston, 666 pp.
Tennekes, H. and Lumley, J. L.: 1972, A First Course in Turbulence, Massachusetts Institute of Technology, Boston, 300 pp.
Warsi, Z. U. A.: 1992, Fluid Dynamics: Theoretical and Computational Approaches, CRC Press, London, 683 pp.
Wilson, J. D.: 1988, 'A 2nd-Order Closure Model for Flow through Vegetation', Boundary-Layer Meteorol. 42, 371–392.
Wilson, J. D., Finnigan, J. J., and Raupach, M. R.: 1998, 'A First-Order Closure for Disturbed Plant-Canopy Flows, and its Application to Winds in a Canopy on a Ridge'. Quart.J. Roy. Meteorol. Soc. 124, 705–732.
Wilson, J. D., Ward, D. P., Thurtell, G. W., and Kidd, G. E.: 1982, 'Statistics of Atmospheric Turbulence within and above a Corn Canopy', Boundary-Layer Meteorol. 24, 495–519.
Wilson, N. R. and Shaw, R. H.: 1977, 'A Higher Order Closure Model for Canopy Flows', J. Appl. Meteorol. 16, 1197–1205.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Katul, G.G., Mahrt, L., Poggi, D. et al. ONE- and TWO-Equation Models for Canopy Turbulence. Boundary-Layer Meteorology 113, 81–109 (2004). https://doi.org/10.1023/B:BOUN.0000037333.48760.e5
Issue Date:
DOI: https://doi.org/10.1023/B:BOUN.0000037333.48760.e5