Abstract
The contribution of upwind sources to measurements of vertical scalar flux density as a function of fetch (‘footprint’) is predicted using a Markovian simulation of fluid particle trajectories. Results suggest that both footprint peak position and magnitude change dramatically with surface roughness, thermal stability and observation levels. Results also indicate that the much used 100 to 1 fetch-to-height ratio grossly underestimates fetch requirements when observations are made above smooth surfaces, in stable conditions or at high observation levels.
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Businger, J. A., Wyngaard, J. C., Izumi, Y. and Bradley, E. F.: 1971, ‘Flux Profile Relationships in the Atmospheric Surface Layer’, J. Atmos. Sci. 25, 1021–1025.
Calder, K. L.: 1952, ‘Some Recent British Work on the Problem of Diffusion in the Lower Atmosphere’, Proc. U.S. Tech. Conf. Air Pollut., McGraw-Hill, New York, pp. 787–792.
Deacon, E. L.: 1949, ‘Vertical Diffusion in the Lowest Layers of the Atmosphere’, Quart. J. Roy. Meteorol. Soc. 75, 89–103.
deBaas, A. F., van Dop, H. and Nieuwstadt, F. T. M.: 1986, ‘An Application of the Langevin Equation for Inhomogeneous Conditions to Dispersion in a Convective Boundary Layer’, Quart. J. Roy. Meteorol. Soc. 112, 165–180.
Dyer, A. J.: 1963, ‘The Adjustment of Profiles and Eddy Fluxes’, Quart. J. Roy. Meteorol. Soc. 89, 276–280.
Dyer, A. J. and Hicks, B. B.: 1970, ‘Flux Gradient Relationships in the Constant Flux Layer’, Quart. J. Roy. Meteorol. Soc. 96, 715–721.
Haugen, D. A.: 1973, ‘Workshop in Micrometeorology’, American Meteorol. Soc., Boston, Massachusetts.
Horst, T. W. and Slinn, G. N.: 1984, ‘Estimates for Pollution Profiles above Finite Area-Sources’, Atmos. Environ. 18, 1339–1346.
Philip, J. R.: 1959, ‘The Theory of Local Advection: 1’, J. Meteorol. 16, 3–22.
Leclerc, M. Y., Thurtell, G. W. and Kidd, G. E.: 1988, ‘Measurements and Langevin Simulations of Mean Tracer Concentration Fields Downwind from a Circular Line Source Inside an Alfalfa Canopy’, Boundary-Layer Meteorol. 43, 287–308.
Rao, K. S., Wyngaard, J. C. and Cote, O. R.: 1974, ‘Local Advection of Momentum, Heat and Moisture in Micrometeorology’, Boundary-Layer Meteorol. 7, 331–348.
Raupach, M. R., Coppin, P. A. and Finnigan, J. J.: 1986, ‘Experiments on Scalar Diffusion within a Plant Canopy Part 2. An Elevated Plane Source’, Boundary-Layer Meteorol. 35, 21–52.
Roberts, O. F. T.: 1923, Proc. Roy. Soc. (London), A104, 640.
Reid, J. D.: 1979, ‘Markov Chain Simulations of Vertical Dispersion in the Neutral Surface Layer for Surface and Elevated Releases’, Boundary-Layer Meteorol. 16, 3–32.
Sawford, B. L.: 1984, ‘Lagrangian Statistical Modelling of Turbulent Dispersion’, Proc. Eighth Int. Clean Air Conf., Melbourne, Clean Air Society of Australia and New Zealand, pp. 17–27.
Sawford, B. L.: 1985, ‘Lagrangian Statistical Simulation of Concentration Mean and Fluctuation Fields’, J. Climate Appl. Meteorol. 24, 1152–1166.
Sawford, B. L.: 1986, ‘Generalized Random Forcing in Random-Walk Turbulent Dispersion Models’, Phy. Fluids 29, 3582–3589.
Sawford, B. L. and Guest, F. M.: 1987, ‘Lagrangian Stochastic Analysis of Flux-Gradient Relationships in the Convective Boundary Layer’, J. Atmos. Sci. 44, 1152–1165.
Schuepp, P. H., Leclerc, M. Y., MacPherson, J. I. and Desjardins, R. L.: 1990, ‘Footprint Prediction of Scalar Fluxes from Analytical Solutions of the Diffusion Equation’, Boundary-Layer Meteorol. 50, 355–373.
Sutton, O. G.: 1953, Micrometeorology: A Study of Physical Processes in the Lowest Layers of the Earth's Atmosphere, McGraw Hill, London.
Tanner, B. D.: 1988, ‘Use Requirements for Bowen Ratio and Eddy Correlation Determination of Evapotranspiration’, Proc. of the 1988 Specialty Conference of the Irrigation and Drainage Division, ASCE Lincoln, Nebraska July 19–21.
Taylor, P. A.: 1970, ‘A Model of Airflow above Changes in Surface Heat Flux, Temperature and Roughness for Neutral and Uns Conditions’, Boundary-Layer Meteorol. 1, 18–39.
Thomson, D. J.: 1984, ‘Random Walk Modelling of Diffusion in Inhomogeneous Turbulence’, Quart. J. Roy. Meteorol. Soc. 110, 1107–1120.
Willis, G. E. and Deardorff, J. W.: 1976, ‘A Laboratory Model of Diffusion into the Convective Planetary Boundary Layer’, Quart. J. Roy. Meteorol. Soc. 102, 427–445.
Wilson, J. D.: 1982, ‘An Approximate Analytical Solution to the Diffusion Equation for Short-Range Dispersion from a Continuous Ground-Level Source’, Boundary-Layer Meteorol. 23, 85–103.
Wilson, J. D., Thurtell, G. W. and Kidd, G. E.: 1981a, ‘Numerical Simulation of Particle Trajectories in Inhomogeneous Turbulence II: Systems with Variable Velocity Scale’, Boundary-Layer Meteorol. 21, 423–441.
Wilson, J. D., Thurtell, G. W. and Kidd, G. E.: 1981b, ‘Numerical Simulation of Particle Trajectories in Inhomogeneous Turbulence, III: Comparison of Predictions with Experimental Data for the Surface Layer’, Boundary-Layer Meteorol. 21, 443–463.
Wilson, J. D., Legg, B. J. and Thomson, D. J.: 1983, ‘Calculation of Particle Trajectory in the Presence of a Gradient in Turbulent Velocity Variance’, Boundary-Layer Meteorol. 27, 163–169.
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Leclerc, M.Y., Thurtell, G.W. Footprint prediction of scalar fluxes using a Markovian analysis. Boundary-Layer Meteorol 52, 247–258 (1990). https://doi.org/10.1007/BF00122089
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DOI: https://doi.org/10.1007/BF00122089