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Footprint prediction of scalar fluxes from analytical solutions of the diffusion equation

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Abstract

The use of analytical solutions of the diffusion equation for ‘footprint prediction’ is explored. Quantitative information about the ‘footprint’, i.e., the upwind area most likely to affect a downwind flux measurement at a given height z, is essential when flux measurements from different platforms, particularly airborne ones, are compared. Analytical predictions are evaluated against numerical Lagrangian trajectory simulations which are detailed in a companion paper (Leclerc and Thurtell, 1990). For neutral stability, the structurally simple solutions proposed by Gash (1986) are shown to be capable of satisfactory approximation to numerical simulations over a wide range of heights, zero displacements and roughness lengths. Until more sophisticated practical solutions become available, it is suggested that apparent limitations in the validity of some assumptions underlying the Gash solutions for the case of very large surface roughness (forests) and tentative application of the solutions to cases of small thermal instability be dealt with by semi-empirical adjustment of the ratio of horizontal wind to friction velocity. An upper limit of validity of these solutions for z has yet to be established.

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Authors and Affiliations

  1. Dept. of Renewable Resources, Macdonald College of McGill University, H9X 1CO, Ste. Anne-de-Bellevue, Qué., Canada

    P. H. Schuepp

  2. Dept. of Soil Sci. and Biomet., Utah State University, Logan, USA

    M. Y. Leclerc

  3. National Aeronautical Establishment of the National Research Council of Canada, Canada

    J. I. MacPherson

  4. Land Resource Research Centre, Agriculture Canada, Ottawa, Canada

    R. L. Desjardins

Authors
  1. P. H. Schuepp
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  2. M. Y. Leclerc
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  3. J. I. MacPherson
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  4. R. L. Desjardins
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Schuepp, P.H., Leclerc, M.Y., MacPherson, J.I. et al. Footprint prediction of scalar fluxes from analytical solutions of the diffusion equation. Boundary-Layer Meteorol 50, 355–373 (1990). https://doi.org/10.1007/BF00120530

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