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A one dimensional wind model for diffusion calculations

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Summary

A simple one dimensional wind model, designed for diffusion calculations in flat environments with obstructions, is proposed. It covers the surface layer and up to a maximum height of 500 m with three levels. The lowest level is the internal boundary layer, in which the influence of the immediate environment is manifest. The second is the surface layer in which the wind profile is characterized by the fetch conditions further upstream. The third is the spiral layer, where the wind turns with height. The actual depth of the surface layer is estimated by the model. In both the surface layer and the internal boundary layer, Monin-Obukhov theory is applied. The spiral layer is represented by a classical Ekman-Taylor solution matched at the top of the surface layer. This conceptual model is then tested with data from a meteorological mast at Garching (near Munich, Germany).

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References

  • Barker, E. H., Baxter, T. L., 1975: A note on the computations of atmospheric surface layer fluxes for use in numerical modeling.J. Appl. Meteor.,14, 620–622.

    Google Scholar 

  • Beljaars, A. C. M., 1982: The derivation of fluxes from profiles in perturbed areas.Bound.-Layer Meteor.,24, 35–55.

    Google Scholar 

  • Beljaars, A. C. M., Holtslag, A. A. M., 1991: Flux parameterization over land surfaces for atmospheric models.J. Appl. Meteor.,30, 327–341.

    Google Scholar 

  • Berggström, H., 1986: A simplified boundary layer wind model for practical application.J. Climate. Appl. Meteor.,25, 813–824.

    Google Scholar 

  • Blackadar, A. K., Tennekes, H., 1968: Asymptotic similarity in the planetary boundary layer.J. Atmos. Sci.,25, 1015–1020.

    Google Scholar 

  • Blom, J., Wartena, L., 1969: The influence of changes in surface roughness on the development of the turbulent boundary layer in the lower layers of the atmosphere.J. Atmos. Sci.,26, 255–265.

    Google Scholar 

  • Brown, R. A., 1974: Analytical methods in planetary boundarylayer modeling. London: Adam Hilger.

    Google Scholar 

  • Businger, J. A., Wyngaard, J. C., Izumi, Y., Bradley, E. F., 1971: Flux profile relationships in the atmospheric surface layer.J. Atmos. Sci.,28, 181–189.

    Google Scholar 

  • Claussen, M., 1991: Estimation of areally-averaged surface fluxes.Bound.-Layer Meteor. 54, 387–410.

    Google Scholar 

  • Deardorff, J. W., 1974: Three-dimensional numerical study of height and mean structure of a heated planetary boundary layer.Bound.-Layer Meteor.,7, 81–106.

    Google Scholar 

  • Daewon, W. Byun, 1990: On the analytical solution of fluxprofile relationships for the atmospheric surface layer.J. Appl. Meteor.,29, 652–657.

    Google Scholar 

  • Daewon, W. Byun, 1991: Determination of similarity functions of the resistance law for the planetary boundary layer using surface layer similarity functions.Bound.-Layer Meteor.,57, 17–48.

    Google Scholar 

  • Davenport, A. G., 1960: Rational for determining design wind velocities.J. Struct. Div. Amer. Soc. Civ. Eng.,86, 39–68.

    Google Scholar 

  • Driedonks, A. G. M., 1982: Models and observations of the growth of the atmospheric boundary layer.Bound.-Layer Meteor.,23, 283–306.

    Google Scholar 

  • Driedonks, A. G. M., Tennekes, H., 1984: Entrainment effects in the well-mixed atmospheric boundary layer.Bound.-Layer Meteor.,30, 75–105.

    Google Scholar 

  • Elliott, W. P., 1958: The growth of the atmospheric internal boundary layer.Trans. Amer. Geophys. Union,39, 1048–1054.

    Google Scholar 

  • Fiedler, F., Panofsky, H. A., 1972: The geostrophic drag coefficient and the “effective” roughness length.Quart. J. Roy. Meteor. Soc.,104, 491–502.

    Google Scholar 

  • Garrett, A. J., 1981: Comparison of observed mixed-layer depths to model estimates using observed temperatures and winds, and MOS forecasts.J. Appl. Meteor.,20, 1277–1283.

    Google Scholar 

  • Goff, J. A., 1965: Saturation pressure of water on the new Kelvin scale. In: Wexler, A. (ed.),Humidity and Moisture, vol. 3, New York: Reinhold Publishing Corporation, pp. 289–292.

    Google Scholar 

  • Gryning, S.E., Batchvarova, E., 1990: Simple models of the daytime boundary layer height. Ninth Symposium on Turbulence and Diffusion. American Meteorological Society. April 30–May 3, 1990, Roskilde, Denmark, pp. 379–382.

  • Haltiner, G. J., Martin, F. L., 1957:Dynamical and Physical Meteorology. New York: McGraw-Hill.

    Google Scholar 

  • Iribane, J. V., Godson, W. L., 1973:Atmospheric Thermodynamics. Geophysics and Astrophysics Monographs, vol. 6, Dordrecht: D. Reidel, p.71.

    Google Scholar 

  • Irwin, J. S., Binkowski, F. S., 1981: Estimation of the Monin-Obukhov scaling length using on-site instrumentation.Atmos. Environ.,15, 1091–1094.

    Google Scholar 

  • Jordan-Engeln, G., Reutter, F., 1976:Formelsammlung zur Numerischen Mathematik mit Fortran IV Programmen. B-I.-Hochschultaschenbücher, Band 106.

  • Lösslein, H., 1979: Das bodennahe Windfeld bei Starkwind und Sturm im Hinblick auf Bauwerksbelastungen. Diplomarbeit für Meteorologie, Ludwig-Maximilians-Universität München.

    Google Scholar 

  • Mahrt, L., 1981: Modelling the depth of the stable boundary layer.Bound.-Layer Meteor.,21, 3–19.

    Google Scholar 

  • Nieuwstadt, F. T. M., 1984: Some aspects of the turbulent stable boundary layer.Bound.-Layer Meteor.,30, 31–55.

    Google Scholar 

  • Panofsky, H. A., Dutton, J. A., 1984:Atmospheric Turbulence. Models and methods for engineering applications. New York: John Wiley & Sons.

    Google Scholar 

  • Panofsky, H., Townsend, A. A., 1964: Changes of terrain roughness and wind profile.Quart. J. Roy. Meteor. Soc.,90, 147–155.

    Google Scholar 

  • Paulson, C. A., 1970: The mathematical representation of wind speed and temperature profiles in the unstable atmospheric surface layer.J. Appl. Meteor.,9, 857–861.

    Google Scholar 

  • Plate, E. J., 1971: Aerodynamic characteristics of atmospheric boundary layers. AEC critical review series, U.S. Atomic Energy Commission.

  • Press, W. H., Flannery, B. P., Teukolsky, S. A., Vetterling, W. T., 1990: Numerical recipes in C. Cambridge: Cambridge University Press, pp. 518–528.

    Google Scholar 

  • Rao, K. S., Wyngaard, J. C., Coté, O. R., 1974: The structure of the two dimensional internal boundary layer over a sudden change in surface roughness.J. Atmos. Sci.,31, 738–746.

    Google Scholar 

  • Rogers, R. R., Yau, M. K., 1989:A Short Course in Cloud Physics. Oxford UK: Pergamon, pp. 16–17.

    Google Scholar 

  • Shir, C. C., 1972: A numerical computation of air flow over a sudden change in surface roughness change.J. Atmos. Sci.,29, 304–310.

    Google Scholar 

  • Smeda, M. S., 1979: Incorporation of planetary boundary-layer processes into numerical forecasting models.Bound.-Layer Meteor.,16, 115–129.

    Google Scholar 

  • Stull, R. B., 1988:An Introduction to Boundary Layer Meteorology. Dordrecht, Holla: Kluwer Academic Publishers, pp. 596–613.

    Google Scholar 

  • Taylor, G. I., 1915: The eddy motion in the atmosphere. Phil. Trans. Roy. Soc., A, 215 (Scientific papers 2, I).

  • Townsend, A. A., 1965: The response of a turbulent boundary layer to abrupt changes in surface conditions.J. Fluid. Mech.,22, 799–822.

    Google Scholar 

  • Van Ulden, A., 1978: Simple estimates for vertical diffusion from sources near the ground.Atmos. Environ.,12, 2125–2129.

    Google Scholar 

  • Van Ulden, A. P., Holtslag, A. A. M., 1985: Estimation of atmospheric boundary layer parameters for diffusion applications.J. Climate Appl. Meteor.,24, 1196–1207.

    Google Scholar 

  • Van Wijk, A. J. M., Beljaars, A. C. M., Holtslag, A. A. M., Turkenburg, W. C., 1990: Diabatic wind speed profiles in coastal regions: Comparison of an internal boundary layer model with observations.Bound.-Layer. Meteor.,51, 49–75.

    Google Scholar 

  • Wieringa, J., 1976: An objective exposure correction method for average wind speeds measured at a sheltered location.Quart. J. Roy. Meteor. Soc.,102, 241–253.

    Google Scholar 

  • Wieringa, J., 1981: Estimation of mesoscale and local-scale roughness for atmospheric transport modeling. 11th Int. Tech. Meeting on Air Pollution Modeling and its Application. New York and London: Plenum. pp. 279–295.

    Google Scholar 

  • Wood, N., Mason, P. J., 1992: The influence of static stability on the effective roughness length for momentum and temperatureQuart. J. Roy Meteor. Soc.,117, 1025–1056.

    Google Scholar 

  • Zilitinkevich, S. S., 1972: On the determination of the height of the Ekman boundary layer.Bound.-Layer Meteor.,3, 141–145.

    Google Scholar 

  • Zoumakis, N. M., Kelessis, A. G., 1991: The dependence of the bulk Richardson number on stability in the surface layer.Bound.-Layer Meteor.,57, 407–414.

    Google Scholar 

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Ulrich, W.C. A one dimensional wind model for diffusion calculations. Meteorl. Atmos. Phys. 52, 69–89 (1993). https://doi.org/10.1007/BF01025754

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