Extension of Spherical Nonparametric Estimators to Nonisotropic Kernels: An Oceanographic Application

K. I. Hodges Environmental Systems Science Centre, University of Reading, Reading, United Kingdom

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Abstract

In a recently published paper, spherical nonparametric estimators were applied to feature-track ensembles to determine a range of statistics for the atmospheric features considered. This approach obviates the types of bias normally introduced with traditional estimators. New spherical isotropic kernels with local support were introduced. In this paper the extension to spherical nonisotropic kernels with local support is introduced, together with a means of obtaining the shape and smoothing parameters in an objective way. The usefulness of spherical nonparametric estimators based on nonisotropic kernels is demonstrated with an application to an oceanographic feature-track ensemble.

Corresponding author address: Dr. K. I. Hodges, Environmental Systems Science Centre, University of Reading, Harry Pitt Building, Whiteknights, P.O. Box 238, Reading RG6 6AL, United Kingdom.

Abstract

In a recently published paper, spherical nonparametric estimators were applied to feature-track ensembles to determine a range of statistics for the atmospheric features considered. This approach obviates the types of bias normally introduced with traditional estimators. New spherical isotropic kernels with local support were introduced. In this paper the extension to spherical nonisotropic kernels with local support is introduced, together with a means of obtaining the shape and smoothing parameters in an objective way. The usefulness of spherical nonparametric estimators based on nonisotropic kernels is demonstrated with an application to an oceanographic feature-track ensemble.

Corresponding author address: Dr. K. I. Hodges, Environmental Systems Science Centre, University of Reading, Harry Pitt Building, Whiteknights, P.O. Box 238, Reading RG6 6AL, United Kingdom.

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  • Abramson, I. S., 1982: On bandwidth variation in kernel estimates: A square root law. Ann. Stat.,10, 1217–1223.

  • Bryan, K., 1969: A numerical method for the study of the circulation of the ocean. J. Comput. Phys.,4, 347–376.

  • Diggle, P. J., and N. I. Fisher, 1985: Sphere: A contouring program for spherical data. Comput. Geosci.,11, 725–766.

  • Fisher, N. I., T. Lewis, and B. J. J. Embleton, 1987: Statistical Analysis of Spherical Data. Cambridge University Press, 329 pp.

  • Härdle, W., 1990: Applied Nonparametric Regression. Cambridge University Press, 333 pp.

  • Hodges, K. I., 1995: Feature tracking on the unit sphere. Mon. Wea. Rev.,123, 3458–3465.

  • ——, 1996: Spherical nonparametric estimators applied to the UGAMP model integration for AMIP. Mon. Wea. Rev.,124, 2914–2932.

  • Jones, M. C., 1993: Simple boundary correction for kernel density estimation. Stat. Comput.,3, 135–146.

  • ——, J. S. Marron, and S. J. Sheather, 1996: A brief survey of bandwidth selection for density estimation. J. Amer. Stat. Assoc.,91, 401–407.

  • Kent, J. T., 1982: The Fisher-Bingham distribution on the sphere. J. Roy. Stat. Soc.,44B, 71–80.

  • Lutjeharms, J. R. E., N. D. Bang, and C. P. Duncan, 1981: Characteristics of the current east and south of Madagascar. Deep-Sea Res.,28A, 879–901.

  • Press, W. H., B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, 1990: Numerical Recipes in C: The Art of Scientific Computing. Cambridge University Press, 735 pp.

  • Saoudi, S., A. Hillion, and F. Ghorbel, 1994: Non-parametric probability density function estimation on a bounded support: Applications to shape classification and speech coding. Appl. Stochastic Models Data Anal.,10, 215–231.

  • Scott, D. W., 1992: Multivariate Density Estimation. John Wiley & Sons, 317 pp.

  • Semtner, A. J., Jr., and R. J. Chervin, 1988: A simulation of the global ocean circulation with resolved eddies. J. Geophys. Res.,93, 15 502–15 522.

  • Silverman, B. W., 1986: Density Estimation for Statistics and Data Analysis. Chapman and Hall, 175 pp.

  • Smith R. D., J. K. Dukowicz, and R. C. Malone, 1992: Parallel ocean general circulation modelling. Physica D,60, 38–61.

  • Wahba, G., and J. Wendelberger, 1980: Some new mathematical methods for variational objective analysis using splines and cross validation. Mon. Wea. Rev.,108, 1122–1143.

  • Wand, M. P., and M. C. Jones, 1993: Comparison of smoothing parameterizations in bivariate kernel density estimation. J. Amer. Stat. Assoc.,88, 520–528.

  • Woodcock, N. H., 1977: Specification of fabric shapes using an eigenvalue method. Bull. Amer. Geol. Soc.,88, 1231–1236.

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