• Augier, P., , and E. Lindborg, 2013: A new formulation of the spectral energy budget of the atmosphere, with application to two high-resolution general circulation models. J. Atmos. Sci., 70, 22932308, doi:10.1175/JAS-D-12-0281.1.

    • Search Google Scholar
    • Export Citation
  • Bacmeister, J. T., , S. D. Eckermann, , P. A. Newman, , L. Lait, , K. R. Chan, , M. Loewenstein, , M. H. Proffitt, , and B. L. Gary, 1996: Stratospheric horizontal wavenumber spectra of winds, potential temperature, and atmospheric tracers observed by high-altitude aircraft. J. Geophys. Res., 101, 94419470, doi:10.1029/95JD03835.

    • Search Google Scholar
    • Export Citation
  • Bierdel, L., , P. Friederichs, , and S. Bentzien, 2012: Spatial kinetic energy spectra in the convection-permitting limited-area NWP model COSMO-DE. Meteor. Z., 21, 245258, doi:10.1127/0941-2948/2012/0319.

    • Search Google Scholar
    • Export Citation
  • Blažica, V., , N. Žagar, , B. Strajnar, , and J. Cedilnik, 2013: Rotational and divergent kinetic energy in the mesoscale model ALADIN. Tellus, 65A, 18918, doi:10.3402/tellusa.v65i0.18918.

    • Search Google Scholar
    • Export Citation
  • Boer, G., , and T. Shepherd, 1983: Large-scale two-dimensional turbulence in the atmosphere. J. Atmos. Sci., 40, 164184, doi:10.1175/1520-0469(1983)040<0164:LSTDTI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Brune, S., , and E. Becker, 2013: Indications of stratified turbulence in a mechanistic GCM. J. Atmos. Sci., 70, 231247, doi:10.1175/JAS-D-12-025.1.

    • Search Google Scholar
    • Export Citation
  • Bühler, O., , J. Callies, , and R. Ferrari, 2014: Wave–vortex decomposition of one-dimensional ship-track data. J. Fluid Mech., 756, 10071026, doi:10.1017/jfm.2014.488.

    • Search Google Scholar
    • Export Citation
  • Burgess, B. H., , A. R. Erler, , and T. G. Shepherd, 2013: The troposphere-to-stratosphere transition in kinetic energy spectra and nonlinear spectral fluxes as seen in ECMWF analyses. J. Atmos. Sci., 70, 669687, doi:10.1175/JAS-D-12-0129.1.

    • Search Google Scholar
    • Export Citation
  • Callies, J., , R. Ferrari, , and O. Bühler, 2014: Transition from geostrophic turbulence to inertia–gravity waves in the atmospheric energy spectrum. Proc. Natl. Acad. Sci. USA, 111, 17 03317 038, doi:10.1073/pnas.1410772111.

    • Search Google Scholar
    • Export Citation
  • Charney, J. G., 1971: Geostrophic turbulence. J. Atmos. Sci., 28, 10871095, doi:10.1175/1520-0469(1971)028<1087:GT>2.0.CO;2.

  • Cho, J. Y. N., , and E. Lindborg, 2001: Horizontal velocity structure functions in the upper troposphere and lower stratosphere: 1. Observations. J. Geophys. Res., 106, 10 22310 232, doi:10.1029/2000JD900814.

    • Search Google Scholar
    • Export Citation
  • Cho, J. Y. N., , R. E. Newell, , and J. D. Barrick, 1999: Horizontal wavenumber spectra of winds, temperature, and trace gases during the Pacific Exploratory Missions: 2. Gravity waves, quasi-two-dimensional turbulence, and vortical modes. J. Geophys. Res., 104, 16 29716 308, doi:10.1029/1999JD900068.

    • Search Google Scholar
    • Export Citation
  • Dewan, E., 1997: Saturated-cascade similitude theory of gravity wave spectra. J. Geophys. Res., 102, 29 79929 817, doi:10.1029/97JD02151.

    • Search Google Scholar
    • Export Citation
  • Errico, R. M., 1985: Spectra computed from a limited area grid. Mon. Wea. Rev., 113, 15541562, doi:10.1175/1520-0493(1985)113<1554:SCFALA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Frehlich, R., , and R. Sharman, 2008: The use of structure functions and spectra from numerical model output to determine effective model resolution. Mon. Wea. Rev., 136, 15371553, doi:10.1175/2007MWR2250.1.

    • Search Google Scholar
    • Export Citation
  • Gage, K. S., 1979: Evidence for a k−5/3 law inertial range in mesoscale two-dimensional turbulence. J. Atmos. Sci., 36, 19501954, doi:10.1175/1520-0469(1979)036<1950:EFALIR>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Gage, K. S., , and G. D. Nastrom, 1985: On the spectrum of atmospheric velocity fluctuations seen by MST/ST radar and their interpretation. Radio Sci., 20, 13391347, doi:10.1029/RS020i006p01339.

    • Search Google Scholar
    • Export Citation
  • Gkioulekas, E., , and K. K. Tung, 2006: Recent developments in understanding two-dimensional turbulence and the Nastrom–Gage spectrum. J. Low Temp. Phys., 145, 2557, doi:10.1007/s10909-006-9239-z.

    • Search Google Scholar
    • Export Citation
  • Hamilton, K., , Y. O. Takahasi, , 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
  • Koshyk, J. N., , and K. Hamilton, 2001: The horizontal kinetic energy spectrum and spectral budget simulated by a high-resolution troposphere–stratosphere–mesosphere GCM. J. Atmos. Sci., 58, 329348, doi:10.1175/1520-0469(2001)058<0329:THKESA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Koshyk, J. N., , B. A. Boville, , K. Hamilton, , E. Manzini, , and K. Shibata, 1999: Kinetic energy spectrum of horizontal motions in middle-atmosphere models. J. Geophys. Res., 104, 27 17727 190, doi:10.1029/1999JD900814.

    • Search Google Scholar
    • Export Citation
  • Lilly, D. K., 1983: Stratified turbulence and the mesoscale variability of the atmosphere. J. Atmos. Sci., 40, 749761, doi:10.1175/1520-0469(1983)040<0749:STATMV>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Lindborg, E., 1999: Can the atmospheric kinetic energy spectrum be explained by two-dimensional turbulence? J. Fluid Mech., 388, 259288, doi:10.1017/S0022112099004851.

    • Search Google Scholar
    • Export Citation
  • Lindborg, E., 2006: The energy cascade in a strongly stratified fluid. J. Fluid Mech., 550, 207242, doi:10.1017/S0022112005008128.

  • Lindborg, E., 2007: Horizontal wavenumber spectra of vertical vorticity and horizontal divergence in the upper troposphere and lower stratosphere. J. Atmos. Sci., 64, 10171025, doi:10.1175/JAS3864.1.

    • Search Google Scholar
    • Export Citation
  • Lindborg, E., 2015: A Helmholtz decomposition of structure functions and spectra calculated from aircraft data. J. Fluid Mech., 762, R4, doi:10.1017/jfm.2014.685.

    • Search Google Scholar
    • Export Citation
  • Marenco, A., and et al. , 1998: Measurement of ozone and water vapor by Airbus in-service aircraft: The MOZAIC airborne program, an overview. J. Geophys. Res., 103, 25 63125 642, doi:10.1029/98JD00977.

    • Search Google Scholar
    • Export Citation
  • Nastrom, G. D., , and K. S. Gage, 1985: A climatology of atmospheric wavenumber spectra of wind and temperature observed by commercial aircraft. J. Atmos. Sci., 42, 950960, doi:10.1175/1520-0469(1985)042<0950:ACOAWS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Nastrom, G. D., , K. S. Gage, , and W. Jasperson, 1984: Kinetic energy spectrum of large- and mesoscale atmospheric processes. Nature, 310, 3638, doi:10.1038/310036a0.

    • Search Google Scholar
    • Export Citation
  • Ricard, D., , C. Lac, , S. Riette, , R. Legrand, , and A. Mary, 2013: Kinetic energy spectra characteristics of two convection-permitting limited-area models AROME and Meso-NH. Quart. J. Roy. Meteor. Soc., 139, 13271341, doi:10.1002/qj.2025.

    • Search Google Scholar
    • Export Citation
  • Selz, T., , and G. C. Craig, 2015: Upscale error growth in a high-resolution simulation of a summertime weather event over Europe. Mon. Wea. Rev., 143, 813827, doi:10.1175/MWR-D-14-00140.1.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Skamarock, W. C., , J. B. Klemp, , M. G. Duda, , L. D. Fowler, , S.-H. Park, , and T. Ringler, 2012: A multiscale nonhydrostatic atmospheric model using centroidal Voronoi tesselations and C-grid staggering. Mon. Wea. Rev., 140, 30903105, doi:10.1175/MWR-D-11-00215.1.

    • Search Google Scholar
    • Export Citation
  • 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.

    • Search Google Scholar
    • Export Citation
  • VanZandt, T. E., 1982: A universal spectrum of buoyancy waves in the atmosphere. Geophys. Res. Lett., 9, 575578, doi:10.1029/GL009i005p00575.

    • Search Google Scholar
    • Export Citation
  • Vincent, R. A., , and S. D. Eckermann, 1990: VHF radar observations of mesoscale motions in the atmosphere: Evidence for gravity wave Doppler shifting. Radio Sci., 25, 10191037, doi:10.1029/RS025i005p01019.

    • Search Google Scholar
    • Export Citation
  • Waite, M. L., , and C. Snyder, 2013: Mesoscale energy spectra of moist baroclinic waves. J. Atmos. Sci., 70, 12421256, doi:10.1175/JAS-D-11-0347.1.

    • Search Google Scholar
    • Export Citation
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Accuracy of Rotational and Divergent Kinetic Energy Spectra Diagnosed from Flight-Track Winds

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  • 1 Meteorologisches Institut, Ludwig-Maximilians-Universität, Munich, Germany
  • | 2 National Center for Atmospheric Research, Boulder, Colorado
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Abstract

Under assumptions of horizontal homogeneity and isotropy, one may derive relations between rotational or divergent kinetic energy spectra and velocities along one-dimensional tracks, such as might be measured by aircraft. Two recent studies, differing in details of their implementation, have applied these relations to the Measurement of Ozone and Water Vapor by Airbus In-Service Aircraft (MOZAIC) dataset and reached different conclusions with regard to the mesoscale ratio of divergent to rotational kinetic energy. In this study the accuracy of the method is assessed using global atmospheric simulations performed with the Model for Prediction Across Scales, where the exact decomposition of the horizontal winds into divergent and rotational components may be easily computed. For data from the global simulations, the two approaches yield similar and very accurate results. Errors are largest for the divergent component on synoptic scales, which is shown to be related to a very dominant rotational mode. The errors are, in particular, sufficiently small so that the mesoscale ratio of divergent to rotational kinetic energy can be derived correctly. The proposed technique thus provides a strong observational check of model results with existing large commercial aircraft datasets. The results do, however, show a significant dependence on the height and latitude ranges considered, and the disparate conclusions drawn from previous applications to MOZAIC data may result from the use of different subsets of the data.

The National Center for Atmospheric Research is sponsored by the National Science Foundation.

Corresponding author address: Lotte Bierdel, Meteorologisches Institut, Theresienstrasse 37, 80333 Munich, Germany. E-mail: lotte.bierdel@lmu.de

Abstract

Under assumptions of horizontal homogeneity and isotropy, one may derive relations between rotational or divergent kinetic energy spectra and velocities along one-dimensional tracks, such as might be measured by aircraft. Two recent studies, differing in details of their implementation, have applied these relations to the Measurement of Ozone and Water Vapor by Airbus In-Service Aircraft (MOZAIC) dataset and reached different conclusions with regard to the mesoscale ratio of divergent to rotational kinetic energy. In this study the accuracy of the method is assessed using global atmospheric simulations performed with the Model for Prediction Across Scales, where the exact decomposition of the horizontal winds into divergent and rotational components may be easily computed. For data from the global simulations, the two approaches yield similar and very accurate results. Errors are largest for the divergent component on synoptic scales, which is shown to be related to a very dominant rotational mode. The errors are, in particular, sufficiently small so that the mesoscale ratio of divergent to rotational kinetic energy can be derived correctly. The proposed technique thus provides a strong observational check of model results with existing large commercial aircraft datasets. The results do, however, show a significant dependence on the height and latitude ranges considered, and the disparate conclusions drawn from previous applications to MOZAIC data may result from the use of different subsets of the data.

The National Center for Atmospheric Research is sponsored by the National Science Foundation.

Corresponding author address: Lotte Bierdel, Meteorologisches Institut, Theresienstrasse 37, 80333 Munich, Germany. E-mail: lotte.bierdel@lmu.de
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