• Baer, F., 1972: An alternate scale representation of atmospheric energy spectra. J. Atmos. Sci., 29, 649663, doi:10.1175/1520-0469(1972)029<0649:AASROA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Baldwin, M. E., and M. S. Wandishin, 2002: Determining the resolved spatial scales of Eta Model precipitation forecasts. 19th Conf. on Weather Analysis and Forecasting/15th Conf. on Numerical Weather Prediction, San Antonio, TX, Amer. Meteor. Soc., 3.2. [Available online at https://ams.confex.com/ams/SLS_WAF_NWP/techprogram/paper_47735.htm.]

  • Bourke, W., 1974: A multi-level spectral model. I. Formulation and hemispheric integrations. Mon. Wea. Rev., 102, 687701, doi:10.1175/1520-0493(1974)102<0687:AMLSMI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bourke, W., B. McAvaney, K. Puri, and R. Thurling, 1977: Global modelling of atmospheric flow by spectral methods. General Circulation Models of the Atmosphere, J. Chang, Ed., Academic Press, 267–324.

    • Crossref
    • Export Citation
  • DelSole, T., and M. K. Tippett, 2015: Laplacian eigenfunctions for climate analysis. J. Climate, 28, 7420–7436, doi:10.1175/JCLI-D-15-0049.1.

    • Crossref
    • Export Citation
  • Dunn, R. J. H., K. M. Willett, P. W. Thorne, E. V. Woolley, I. Durre, A. Dai, D. E. Parker, and R. S. Vose, 2012: HadISD: A quality-controlled global synoptic report database for selected variables at long-term stations from 1973-2011. Climate Past, 8, 16491679, doi:10.5194/cp-8-1649-2012.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dutt, A., and V. Rokhlin, 1993: Fast Fourier transforms for nonequispaced data. SIAM J. Sci. Comput., 14, 1368–1393, doi:10.1137/0914081.

    • Crossref
    • Export Citation
  • ECMWF, 2016: ECMWF IFS documentation—Cy41r2, operational implementation 8 March 2016. Part III: Dynamics and numerical procedures. ECMWF, 31 pp. [Available online at https://www.ecmwf.int/sites/default/files/elibrary/2016/16647-part-iii-dynamics-and-numerical-procedures.pdf.]

  • Gandin, L. S., 1963: Objective Analysis of Geophysical Fields. Israeli Program for Scientific Translations, 242 pp.

  • Hamilton, K., Y. O. Takahashi, and W. Ohfuchi, 2008: Mesoscale spectrum of atmospheric motions investigated in a very fine resolution global general circulation model. J. Geophys. Res., 113, D18110, doi:10.1029/2008JD009785.

    • Search Google Scholar
    • Export Citation
  • Harig, C., K. W. Lewis, A. Plattner, and F. J. Simons, 2015: A suite of software analyzes data on the sphere. Eos, Trans. Amer. Geophys. Union, 96, 110, doi:10.1029/2015EO025851.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hofstra, N., M. Haylock, M. New, P. Jones, and C. Frei, 2008: Comparison of six methods for the interpolation of daily, European climate data. J. Geophys. Res., 113, D21110, doi:10.1029/2008JD010100.

    • Search Google Scholar
    • Export Citation
  • Keiner, J., S. Kunis, and D. Potts, 2009: Using NFFT 3—A software library for various nonequispaced fast Fourier transforms. ACM Trans. Math. Software, 36, 130, doi:10.1145/1555386.1555388.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kunis, S., and D. Potts, 2003: Fast spherical Fourier algorithms. J. Comput. Appl. Math., 161, 7598, doi:10.1016/S0377-0427(03)00546-6.

  • Lovejoy, S., and D. Schertzer, 2013: The Weather and Climate. Cambridge University Press, 475 pp.

  • NCEP, 2016: The Global Forecast System (GFS)—Global Spectral Model (GSM). Tech. Rep., Global Climate and Weather Modeling Branch. [Available online at http://www.emc.ncep.noaa.gov/GFS/doc.php.]

  • Potts, D., G. Steidl, and M. Tasche, 1998: Fast and stable algorithms for discrete spherical Fourier transforms. Linear Algebra Appl., 275–276, 433450, doi:10.1016/S0024-3795(97)10013-1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Saha, S., and Coauthors, 2010: The NCEP Climate Forecast System Reanalysis. Bull. Amer. Meteor. Soc., 91, 10151057, doi:10.1175/2010BAMS3001.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Shen, S. S. P., G. R. North, and K. Y. Kim, 1994: Spectral approach to optimal estimation of the global average temperature. J. Climate, 7, 19992007, doi:10.1175/1520-0442(1994)007<1999:SATOEO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Skamarock, W. C., 2004: Evaluating mesoscale NWP models using kinetic energy spectra. Mon. Wea. Rev., 132, 30193032, doi:10.1175/MWR2830.1.

  • Skamarock, W. C., S.-H. Park, J. B. Klemp, and C. Snyder, 2014: Atmospheric kinetic energy spectra from global high-resolution nonhydrostatic simulations. J. Atmos. Sci., 71, 43694381, doi:10.1175/JAS-D-14-0114.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wedi, N., M. Hamrud, and G. Mozdzynski, 2013: A fast spherical harmonics transform for global NWP and climate models. Mon. Wea. Rev., 141, 34503461, doi:10.1175/MWR-D-13-00016.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wieczorek, M. A., and F. J. Simons, 2005: Localized spectral analysis on the sphere. Geophys. J. Int., 162, 655–675, doi:10.1111/j.1365-246X.2005.02687.x.

    • Crossref
    • Export Citation
  • Wieczorek, M. A., and F. J. Simons, 2007: Minimum-variance multitaper spectral estimation on the sphere. J. Fourier Anal. Appl., 13, 665692, doi:10.1007/s00041-006-6904-1.

    • Crossref
    • Search Google Scholar
    • Export Citation
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Spherical Harmonic Spectral Estimation on Arbitrary Grids

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  • 1 Climate and Ecosystems Science Division, Lawrence Berkeley National Laboratory, Berkeley, California
  • 2 Climate and Ecosystems Science Division, Lawrence Berkeley National Laboratory, Berkeley, and Department of Land, Air, and Water Resources, University of California, Davis, Davis, California
  • 3 Climate and Ecosystems Science Division, Lawrence Berkeley National Laboratory, and Department of Earth and Planetary Science, University of California, Berkeley, Berkeley, California
  • 4 National Center for Atmospheric Research, Boulder, Colorado
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Abstract

This study explores the use of nonuniform fast spherical Fourier transforms on meteorological data that are arbitrarily distributed on the sphere. The applicability of this methodology in the atmospheric sciences is demonstrated by estimating spectral coefficients for nontrivial subsets of reanalysis data on a uniformly spaced latitude–longitude grid, a global cloud resolving model on an icosahedral mesh with 3-km horizontal grid spacing, and for temperature anomalies from arbitrarily distributed weather stations over the United States. A spectral correction technique is developed that can be used in conjunction with the inverse transform to yield data interpolated onto a uniformly spaced grid, with optional triangular truncation, at reduced computational cost compared to other variance conserving interpolation methods, such as kriging or natural spline interpolation. The spectral correction yields information that can be used to deduce gridded observational biases not directly available from other methods.

Denotes content that is immediately available upon publication as open access.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Supplemental information related to this paper is available at the Journals Online website: http://dx.doi.org/10.1175/MWR-D-16-0259.s1.

Corresponding author: Nicholas R. Cavanaugh, nrcavanaugh@lbl.gov

Abstract

This study explores the use of nonuniform fast spherical Fourier transforms on meteorological data that are arbitrarily distributed on the sphere. The applicability of this methodology in the atmospheric sciences is demonstrated by estimating spectral coefficients for nontrivial subsets of reanalysis data on a uniformly spaced latitude–longitude grid, a global cloud resolving model on an icosahedral mesh with 3-km horizontal grid spacing, and for temperature anomalies from arbitrarily distributed weather stations over the United States. A spectral correction technique is developed that can be used in conjunction with the inverse transform to yield data interpolated onto a uniformly spaced grid, with optional triangular truncation, at reduced computational cost compared to other variance conserving interpolation methods, such as kriging or natural spline interpolation. The spectral correction yields information that can be used to deduce gridded observational biases not directly available from other methods.

Denotes content that is immediately available upon publication as open access.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Supplemental information related to this paper is available at the Journals Online website: http://dx.doi.org/10.1175/MWR-D-16-0259.s1.

Corresponding author: Nicholas R. Cavanaugh, nrcavanaugh@lbl.gov

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