Abstract
We propose an analytical model for the so-called footprint of scalar fluxes in the atmospheric boundary layer. It is the generalization of formulations already given in the literature, which allows to account for thermal stability. Our model is only marginally more complicated than these, and it is therefore simple enough to be applicable for a routine footprint analysis within long-term measurements. The mathematical framework of our model is a stationary gradient diffusion formulation with height-independent crosswind dispersion. It uses the solution of the resulting two-dimensional advection – diffusion equation for power law profiles of the mean wind velocity and the eddy diffusivity. To find the adjoint Monin–Obukhov similarity profile, we propose two different approaches, a purely analytical one and a simplenumerical error minimalization.
Similar content being viewed by others
References
Businger, J. A.: 1986, ‘Evaluation of the Accuracy with which Dry Deposition Can Be Measured with Current Micrometeorological Techniques’ J. Climate 25, 1100-1124.
Calder, K. L.: 1952, ‘Some Recent British Work on the Problem of Diffusion in the Lower Atmosphere, Proceedings of the U.S. Technology Conference on Air Pollution, McGraw-Hill, New York, pp. 787-792.
Dyer, A. J.: 1974, ‘A Review of Flux-Profile Relationships’ Boundary-Layer Meteorol. 7, 363-372.
Haenel, H. D. andGrünhage, L.: 1999, ‘Footprint Analysis: A Closed Analytical Solution Based on Height-Dependent Profiles of Wind Speed and Eddy Diffusivity’ Boundary-Layer Meteorol. 93, 395-409.
Horst, T. W. andWeil, J. C.: 1992, ‘Footprint Estimation for Scalar Flux Measurements in the Atmospheric Surface Layer’ Boundary-Layer Meteorol. 59, 279-296.
Horst, T. W. andWeil, J. C.: 1994, ‘How Far Is Far Enough?: The Fetch Requirements of Micrometeorological Measurement of Surface Fluxes’ J. Atmos. Oceanic Tech. 11, 1018-1025 (corrigenda in J. Atmos. Oceanic Tech. 12, 447).
Huang, C. H.: 1979, ‘A Theory of Dispersion in Turbulent Shear Flow’ Atmos. Environ. 13, 453-463.
Leclerc, M. Y. andThurtell, G. W.: 1990, ‘Footprint Prediction of Scalar Fluxes Using a Markovian Analysis’ Boundary-Layer Meteorol. 52, 247-258.
Lin, J. S. andHildemann, L. M.: 1996, ‘Analytical Solutions of the Atmospheric Diffusion Equation with Multiple Sources and Height-Dependent Wind Speed and Eddy Diffusivities’ Atmos. Environ. 30, 239-254.
Pasquill, F.: 1974, Atmospheric Diffusion, 2nd ed., J. Wiley & Sons, New York, 437 pp.
Paulson, C. A.: 1970, ‘The Mathematical Representation ofWind Speed and Temperature Profiles in the Instable Atmospheric Surface Layer’ J. Appl. Meteorol. 9, 857-861.
Schmid, H. P.: 1994, ‘Source Areas for Scalar and Scalar Fluxes’ Boundary-Layer Meteorol. 67, 293-318.
Schuepp, P. H.,Leclerc, M. Y.,MacPherson, J. I., andDesjardins, R. L.: 1990, ‘Footprint Prediction of Scalar Fluxes from Analytical Solutions of the Diffusion Equation’ Boundary-Layer Meteorol. 50, 355-373.
Stull, R. B.: 1988, An Introduction to Boundary Layer Meteorology, Kluwer Academic Publishers, Dordrecht, 666 pp.
van Ulden, A. P.: 1978, ‘Simple Estimates for Vertical Diffusion from Sources near the Ground’ Atmos. Environ. 12, 2125-2129.
Wienhold, F. G.,Welling, M., andHarris, G. W.: 1995, ‘Micrometeorological Measurement and Source Region Analysis of Nitrous Oxide Fluxes from an Agricultural Soil, Atmos. Environ. 29, 2219-2227.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kormann, R., Meixner, F.X. An Analytical Footprint Model For Non-Neutral Stratification. Boundary-Layer Meteorology 99, 207–224 (2001). https://doi.org/10.1023/A:1018991015119
Issue Date:
DOI: https://doi.org/10.1023/A:1018991015119