Boundary-Layer Meteorology

, Volume 112, Issue 3, pp 503–523 | Cite as

A Simple Parameterisation for Flux Footprint Predictions

  • N. Kljun
  • P. Calanca
  • M. W. Rotach
  • H. P. Schmid


Flux footprint functions estimate the location and relative importance of passive scalar sources influencing flux measurements at a given receptor height. These footprint estimates strongly vary in size, depending on receptor height, atmospheric stability, and surface roughness. Reliable footprint calculations from, e.g., Lagrangian stochastic models or large-eddy simulations are computationally expensive and cannot readily be computed for long-term observational programs. To facilitate more accessible footprint estimates, a scaling procedure is introduced for flux footprint functions over a range of stratifications from convective to stable, and receptor heights ranging from near the surface to the middle of the boundary layer. It is shown that, when applying this scaling procedure, footprint estimates collapse to an ensemble of similar curves. A simple parameterisation for the scaled footprint estimates is presented. This parameterisation accounts for the influence of the roughness length on the footprint and allows for a quick but precise algebraic footprint estimation.

Boundary-layer scaling Boundary-layer stability Fetch Flux footprint Lagrangian stochastic particle dispersion model Parameterisation 


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  1. de Haan, P. and Rotach, M. W.: 1998, ‘A Novel Approach to Atmospheric Dispersion Modelling: The Puff-Particle Model (PPM)’, Quart. J. Roy. Meteorol. Soc. 124, 2771–2792.Google Scholar
  2. Hanna, S. R., Chang, J. C., and Strimaitis, D. G.: 1993, ‘Hazardous Gas Model Evaluation with Field Observations’, Atmos. Environ. 27A, 2265–2281.Google Scholar
  3. Horst, T. W. and Weil, J. C.: 1992, ‘Footprint Estimation for Scalar Flux Measurements in the Atmospheric Surface Layer’, Boundary-Layer Meteorol. 59, 279–296.CrossRefGoogle Scholar
  4. Horst, T. W. and Weil, J. C.: 1994, ‘How Far is Far Enough?: The Fetch Requirements for Micrometeorological Measurement of Surface Fluxes’, J. Atmos. Ocean. Tech. 11, 1018–1025.Google Scholar
  5. Hsieh, C. I., Katul, G., and Chi, T.: 2000, ‘An Approximate Analytical Model for Footprint Estimation of Scalar Fluxes in Thermally Stratified Atmospheric Flows’, Adv. Water Resour. 23, 765–772.CrossRefGoogle Scholar
  6. Kljun, N., Kormann, R., Rotach, M. W., and Meixner, F. X.: 2003, ‘Comparison of the Lagrangian Footprint Model LPDM-B with an Analytical Footprint Model'. Boundary-Layer Meteorol. 106, 349–355.CrossRefGoogle Scholar
  7. Kljun, N., Rotach, M. W., and Schmid, H. P.: 2002, ‘A 3D Backward Lagrangian Footprint Model for a Wide Range of Boundary Layer Stratifications’, Boundary-Layer Meteorol. 103, 205–226.CrossRefGoogle Scholar
  8. Kormann, R. and Meixner, F. X.: 2001, ‘An Analytical Footprint Model for Non-Neutral Stratification’, Boundary-Layer Meteorol. 99, 207–224.CrossRefGoogle Scholar
  9. Miyake, M.: 1965, Transformation of the Atmospheric Boundary Layer over Inhomogeneous Surfaces, Sci. Rep. 5R-6, University of Washington, Seattle, U.S.A.Google Scholar
  10. Raupach, M. R., Antonia, R. A., and Rajagopalan, S.: 1991, ‘Rough-Wall Turbulent Boundary Layers’, Appl. Mech. Rev. 44, 1–25.Google Scholar
  11. Rotach, M. W.: 2001a, ‘Simulation of Urban-Scale Dispersion Using a Lagrangian Stochastic Dispersion Model’, Boundary-Layer Meteorol. 99, 379–410.CrossRefGoogle Scholar
  12. Rotach, M. W.: 2001b, ‘Urban-Scale Dispersion Modeling Taking into Account the Turbulence and Flow Characteristics of the Roughness Sublayer’, in 3rd International Symposium on Environmental Hydraulics, Tempe, AZ.Google Scholar
  13. Rotach, M. W., Gryning. S.-E., and Tassone, C.: 1996, ‘A Two-Dimensional Lagrangian Stochastic Dispersion Model for Daytime Conditions’, Quart. J. Roy. Meteorol. Soc. 122, 367–389.CrossRefGoogle Scholar
  14. Schmid, H. P.: 1994, ‘Source Areas for Scalars and Scalar Fluxes’, Boundary-Layer Meteorol. 67, 293–318.CrossRefGoogle Scholar
  15. Schmid, H. P.: 2002, ‘Footprint Modeling for Vegetation Atmosphere Exchange Studies: A Review and Perspective’, Agric. For. Meteorol. 113, 159–184.CrossRefGoogle Scholar
  16. Stull, R. B.: 1988, An Introduction to Boundary Layer Meteorology, Kluwer Academic Publishers, Dordrecht, 666 pp.Google Scholar
  17. Van Ulden, A. P.: 1978, ‘Simple Estimates for Vertical Diffusion from Sources near the Ground’, Atmos. Environ. 12, 2125–2129.Google Scholar
  18. Weil, J. C. and Horst, T. W.: 1992, ‘Footprint Estimates for Atmospheric Flux Measurements in the Convective Boundary Layer’, in S. Schartz and W. Slinn (eds.), Precipitation Scavening and Atmosphere-Surface Exchange, Vol. 2, pp. 717–728.Google Scholar
  19. Wilson, J. D. and Swaters, G. E.: 1991, ‘The Source Area Influencing aMeasurement in the Planetary Boundary Layer: The “Footprint” and the “Distribution of Contact Distance” ’, Boundary-Layer Meteorol. 55, 25–46.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • N. Kljun
    • 1
  • P. Calanca
    • 2
  • M. W. Rotach
    • 3
  • H. P. Schmid
    • 4
  1. 1.Institute for Atmospheric and Climate Science ETHZurichSwitzerland
  2. 2.Swiss Federal Research Station for Agroecology and AgricultureZurichSwitzerland
  3. 3.Institute for Atmospheric and Climate Science ETHZurichSwitzerland
  4. 4.Department of GeographyBloomingtonU.S.A.

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