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Footprint Analysis: A Closed Analytical Solution Based On Height-Dependent Profiles Of Wind Speed And Eddy Viscosity

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Abstract

Based on the theoretical background of existing models for the crosswind-integrated footprint, a new model is presented, which, in contrast to the existing models, describes the normalized footprint by a closed analytical formula. This was made possible by using well-known power profiles for wind speed and eddy viscosity instead of Monin–Obukhov based profiles at a certain stage of model development. However, the major difference between the new model and the existing models is that the so-called shape parameter of vertical plume dispersion, a function of upwind distance in the existing models, is set constant in the new model in order to circumvent a formal inconsistency found in the derivation of the existing models. Due to this inconsistency, the existing models do not generally satisfy the fundamental condition that the cumulative normalized footprint must approach unity for the upwind distance tending towards infinity.

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Authors and Affiliations

  1. Institute for Plant Ecology, University of Giessen, Heinrich-Buff-Ring 38, D-35392, Giessen, Germany

    H.-D. Haenel & L. Grünhage

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  1. H.-D. Haenel
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  2. L. Grünhage
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Haenel, HD., Grünhage, L. Footprint Analysis: A Closed Analytical Solution Based On Height-Dependent Profiles Of Wind Speed And Eddy Viscosity. Boundary-Layer Meteorology 93, 395–409 (1999). https://doi.org/10.1023/A:1002023724634

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