• Ackermann, G. R., 1983: Means and standard deviation of horizontal wind components. J. Climate Appl. Meteor., 22 , 959961.

  • Batschelet, E., 1981: Circular Statistics in Biology. Academic Press, 371 pp.

  • Berkowicz, R., , O. Hertel, , S. E. Larsen, , N. N. Sørensen, , and M. Nielsen, 1997: Modelling traffic pollution in streets. National Environmental Research Institute, Roskilde, Denmark, 52 pp.

    • Search Google Scholar
    • Export Citation
  • Castans, M., , and C. G. Barquero, 1994: A framework for the structure of a low wind speed field. Bound.-Layer Meteor., 69 , 137147.

  • Castans, M., , and C. G. Barquero, 1998: Some comments on the study of low persistence wind. Atmos. Environ., 32 , 253256.

  • Cirillo, M. C., , and A. A. Poli, 1992: An intercomparison of semiempirical diffusion models under low wind speed, stable conditions. Atmos. Environ., 26 , 765774.

    • Search Google Scholar
    • Export Citation
  • Essa, K. S. M., , F. Mubarak, , and S. Abu Khadra, 2005: Comparison of some sigma schemes for estimation of air pollutant dispersion in moderate and low winds. Atmos. Sci. Lett., 6 , 9096.

    • Search Google Scholar
    • Export Citation
  • Essenwanger, O. M., 1986: General Climatology: Elements of Statistical Analysis. World Survey of Climatology Series, Vol. 1B, Elsevier, 441 pp.

    • Search Google Scholar
    • Export Citation
  • Farrugia, P. S., , and A. Micallef, 2004: Derivation of a new measure of angular dispersion for circular variables using a geometrical description. Meteor. J., 7 , 111117.

    • Search Google Scholar
    • Export Citation
  • Farrugia, P. S., , and A. Micallef, 2006: Comparative analysis of estimators for wind direction standard deviation. Meteor. Appl., 13 , 2941.

    • Search Google Scholar
    • Export Citation
  • Fisher, N. I., 1983: Comment on “A method for estimating the standard deviation of wind directions”. J. Climate Appl. Meteor., 22 , 19711972.

    • Search Google Scholar
    • Export Citation
  • Fisher, N. I., 1987: Problems with the current definitions of the standard deviation of wind direction. J. Climate Appl. Meteor., 26 , 15221529.

    • Search Google Scholar
    • Export Citation
  • Fisher, N. I., 1995: Statistical Analysis of Circular Data. Cambridge University Press, 295 pp.

  • Hanna, S. R., 1983: Lateral turbulence intensity and plume meandering during stable conditions. J. Climate Appl. Meteor., 22 , 14241430.

    • Search Google Scholar
    • Export Citation
  • Hertel, O., , and R. Berkowicz, 1989: Modelling pollution from traffic in a street canyon: Evaluation of data and model development. National Environment Research Institute Rep. DMU LUFT-A129, 77 pp.

    • Search Google Scholar
    • Export Citation
  • Hicks, B. B., , D. D. Baldocchi, , T. P. Meyers, , R. P. Hosker, , and D. R. Matt, 1987: A preliminary multiple resistance routine for deriving dry deposition velocities from measured quantities. Water Air Soil Pollut., 36 , 311330.

    • Search Google Scholar
    • Export Citation
  • Ibarra, J. I., 1995: A new approach for the determination of horizontal wind direction fluctuations. J. Appl. Meteor., 34 , 19421949.

  • Irwin, J. S., 1980: Dispersion estimate suggestion 9: Processing of wind data. Internal Rep. II-B-33, Environmental Application Branch, Meteorology and Assessment Division, ESRL, U.S. EPA, 17 pp.

    • Search Google Scholar
    • Export Citation
  • Irwin, J. S., 1983: Estimating plume dispersion—A comparison of several sigma schemes. J. Climate Appl. Meteor., 22 , 92114.

  • Leung, D. Y. C., , and C. H. Liu, 1996: Improved estimators for the standard deviations of horizontal wind fluctuations. Atmos. Environ., 30 , 24572461.

    • Search Google Scholar
    • Export Citation
  • Leung, D. Y. C., , and C. H. Liu, 1998: Comment by Drs Castans and Barquero on the study of low persistence wind: Author’s reply. Atmos. Environ., 32 , 255256.

    • Search Google Scholar
    • Export Citation
  • Mardia, K. V., 1972: Statistics of Directional Data. Academic Press, 387 pp.

  • Mori, Y., 1986: Evaluation of several “single-pass” estimators of the mean and the standard deviation of wind direction. J. Climate Appl. Meteor., 25 , 13871397.

    • Search Google Scholar
    • Export Citation
  • Nelson, E. W., 1984: A simple and accurate method for calculation of the standard deviation of horizontal wind direction. J. Air Pollut. Control Assoc., 34 , 11391140.

    • Search Google Scholar
    • Export Citation
  • Pasquill, F., 1976: Atmospheric dispersion parameters in Gaussian plume modelling: Part II. Possible requirements for change in the Turner workbook values. U.S. EPA Rep. EPA-600/4-760306, 44 pp.

    • Search Google Scholar
    • Export Citation
  • Sharan, M., , A. K. Yadav, , and M. P. Singh, 1995: Comparison of sigma schemes for estimation of air pollutant dispersion in low winds. Atmos. Environ., 29 , 20512059.

    • Search Google Scholar
    • Export Citation
  • Skibin, D., 1984: A simple method for determining the standard deviation of wind direction. J. Atmos. Oceanic Technol., 1 , 101102.

  • Turner, D. B., 1986: Comparison of three methods for calculating the standard deviation of the wind direction. J. Climate Appl. Meteor., 25 , 703707.

    • Search Google Scholar
    • Export Citation
  • Verrall, K. A., , and R. L. Williams, 1982: A method for estimating the standard deviation of wind direction. J. Appl. Meteor., 21 , 19221925.

    • Search Google Scholar
    • Export Citation
  • Verrall, K. A., , and R. L. Williams, 1983: Reply. J. Climate Appl. Meteor., 22 , 1972.

  • Weber, R., 1991: Estimator for the standard deviation of wind direction based on moments of the Cartesian components. J. Appl. Meteor., 30 , 13411353.

    • Search Google Scholar
    • Export Citation
  • Weber, R., 1992: A comparison of different estimators for the standard deviation of wind direction based on persistence. Atmos. Environ., 26 , 983986.

    • Search Google Scholar
    • Export Citation
  • Weber, R., 1997: Estimators for the standard deviation of horizontal wind direction. J. Appl. Meteor., 36 , 14031415.

  • Yadav, A. K., , and M. Sharan, 1996: Statistical evaluation of sigma schemes for estimating dispersion in low wind conditions. Atmos. Environ., 30 , 25952606.

    • Search Google Scholar
    • Export Citation
  • Yamartino, R. J., 1984: A comparison of several “single pass” estimators of the standard deviation of wind direction. J. Climate Appl. Meteor., 23 , 13621366.

    • Search Google Scholar
    • Export Citation
  • Yamartino, R. J., , and G. Wiegand, 1986: Development and evaluation of simple models for the flow, turbulence and pollutant concentration fields within an urban street canyon. Atmos. Environ., 20 , 21372156.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 433 433 28
PDF Downloads 382 382 31

On the Algorithms Used to Compute the Standard Deviation of Wind Direction

View More View Less
  • 1 Faculty of Science, University of Malta, Msida, Malta
© Get Permissions Rent on DeepDyve
Restricted access

Abstract

The standard deviation of wind direction is a very important quantity in meteorology because in addition to being used to determine the dry deposition rate and the atmospheric stability class, it is also employed in the determination of the rate of horizontal diffusion, which in turn determines transport and dispersion of air pollutants. However, the computation of this quantity is rendered difficult by the fact that the horizontal wind direction is a circular variable having a discontinuity at 2π radians, beyond which the wind direction starts again from zero, thus preventing angular subtraction from being a straightforward procedure. In view of such a limitation, this work is meant to provide new mathematical expressions that simplify both the computational and analytical work involved in handling the standard deviation of wind direction. This is achieved by deriving a number of Fourier series and Taylor expansions that can represent the minimum angular distance and its powers. Using these expressions, the relation between two algorithms commonly used to determine the standard deviation of wind direction is analyzed. Furthermore, given that these trigonometric expansions effectively reduce the mathematical complexity involved when dealing with circular statistics, their potential application to solve other problems is discussed.

Corresponding author address: Pierre S. Farrugia, Department of Physics, Faculty of Science, University of Malta, Msida MSD 2080, Malta. Email: pierre-sandre.farrugia@um.edu.mt

Abstract

The standard deviation of wind direction is a very important quantity in meteorology because in addition to being used to determine the dry deposition rate and the atmospheric stability class, it is also employed in the determination of the rate of horizontal diffusion, which in turn determines transport and dispersion of air pollutants. However, the computation of this quantity is rendered difficult by the fact that the horizontal wind direction is a circular variable having a discontinuity at 2π radians, beyond which the wind direction starts again from zero, thus preventing angular subtraction from being a straightforward procedure. In view of such a limitation, this work is meant to provide new mathematical expressions that simplify both the computational and analytical work involved in handling the standard deviation of wind direction. This is achieved by deriving a number of Fourier series and Taylor expansions that can represent the minimum angular distance and its powers. Using these expressions, the relation between two algorithms commonly used to determine the standard deviation of wind direction is analyzed. Furthermore, given that these trigonometric expansions effectively reduce the mathematical complexity involved when dealing with circular statistics, their potential application to solve other problems is discussed.

Corresponding author address: Pierre S. Farrugia, Department of Physics, Faculty of Science, University of Malta, Msida MSD 2080, Malta. Email: pierre-sandre.farrugia@um.edu.mt

Save