Climatology of Velocity and Temperature Turbulence Statistics Determined from Rawinsonde and ACARS/AMDAR Data

Rod Frehlich Cooperative Institute for Research in Environmental Sciences, University of Colorado, and Research Applications Laboratory, National Center for Atmospheric Research,* Boulder, Colorado

Search for other papers by Rod Frehlich in
Current site
Google Scholar
PubMed
Close
and
Robert Sharman Research Applications Laboratory, National Center for Atmospheric Research, Boulder, Colorado

Search for other papers by Robert Sharman in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

The climatology of the spatial structure functions of velocity and temperature for various altitudes (pressure levels) and latitude bands is constructed from the global rawinsonde network and from Aircraft Communications, Addressing, and Reporting System/Aircraft Meteorological Data Relay (ACARS/AMDAR) data for the tropics and Northern Hemisphere. The ACARS/AMDAR data provide very dense coverage of winds and temperature over common commercial aircraft flight tracks and allow computation of structure functions to scales approaching 1 km, while the inclusion of rawinsonde data provides information on larger scales approaching 10 000 km. When taken together these data extend coverage of the spatial statistics of the atmosphere from previous studies to include larger geographic regions, lower altitudes, and a wider range of spatial scales. Simple empirical fits are used to approximate the structure function behavior as a function of altitude and latitude in the Northern Hemisphere. Results produced for spatial scales less than ∼2000 km are consistent with previous studies using other data sources. Estimates of the vertical and global horizontal structure of turbulence in terms of eddy dissipation rate ϵ and thermal structure constant CT2 are derived from the structure function levels at the smaller scales.

Corresponding author address: Rod Frehlich, CIRES, UCB 216, University of Colorado, Boulder, CO 80309. Email: rgf@cires.colorado.edu

Abstract

The climatology of the spatial structure functions of velocity and temperature for various altitudes (pressure levels) and latitude bands is constructed from the global rawinsonde network and from Aircraft Communications, Addressing, and Reporting System/Aircraft Meteorological Data Relay (ACARS/AMDAR) data for the tropics and Northern Hemisphere. The ACARS/AMDAR data provide very dense coverage of winds and temperature over common commercial aircraft flight tracks and allow computation of structure functions to scales approaching 1 km, while the inclusion of rawinsonde data provides information on larger scales approaching 10 000 km. When taken together these data extend coverage of the spatial statistics of the atmosphere from previous studies to include larger geographic regions, lower altitudes, and a wider range of spatial scales. Simple empirical fits are used to approximate the structure function behavior as a function of altitude and latitude in the Northern Hemisphere. Results produced for spatial scales less than ∼2000 km are consistent with previous studies using other data sources. Estimates of the vertical and global horizontal structure of turbulence in terms of eddy dissipation rate ϵ and thermal structure constant CT2 are derived from the structure function levels at the smaller scales.

Corresponding author address: Rod Frehlich, CIRES, UCB 216, University of Colorado, Boulder, CO 80309. Email: rgf@cires.colorado.edu

Save
  • Ballish, B. A., and V. K. Kumar, 2008: Systematic differences in aircraft and radiosonde temperatures. Bull. Amer. Meteor. Soc., 89 , 16891707.

    • Search Google Scholar
    • Export Citation
  • Balsley, B. B., G. Svensson, and M. Tjernstrom, 2007: On the scale-dependence of the gradient Richardson number in the residual layer. Bound.-Layer Meteor., 127 , 5772.

    • Search Google Scholar
    • Export Citation
  • Barnes, S. L., and D. K. Lilly, 1975: Covariance analysis of severe storm environments. Preprints, Ninth Conf. on Severe Local Storms, Norman, OK, Amer. Meteor. Soc., 301–306.

    • Search Google Scholar
    • Export Citation
  • Bengtsson, L., S. Hagemann, and K. I. Hodges, 2004: Can climate trends be calculated from reanalysis data? J. Geophys. Res., 109 , D11111. doi:10.1029/2004JD004536.

    • Search Google Scholar
    • Export Citation
  • Benjamin, S. G., B. E. Schwartz, and R. E. Cole, 1999: Accuracy of ACARS wind and temperature observations determined by collocation. Wea. Forecasting, 14 , 10321038.

    • Search Google Scholar
    • Export Citation
  • Benton, G. S., and A. B. Kahn, 1958: Spectra of large-scale atmospheric flow at 300 millibars. J. Atmos. Sci., 15 , 404410.

  • Bertin, F., J. Barat, and R. Wilson, 1997: Energy dissipation rates, eddy diffusivity, and the Prandtl number: An in situ experimental approach and its consequences on radar estimate of turbulent parameters. Radio Sci., 32 , 791804.

    • Search Google Scholar
    • Export Citation
  • Buell, C. E., 1960: The structure of two-point wind correlations in the atmosphere. J. Geophys. Res., 65 , 33533366.

  • Charney, J. G., 1971: Geostrophic turbulence. J. Atmos. Sci., 28 , 10871095.

  • Chen, W. Y., 1974: Energy dissipation rates of the free atmospheric turbulence. J. Atmos. Sci., 31 , 22222225.

  • 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 , 1022310232.

    • 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 , 1629716308.

    • Search Google Scholar
    • Export Citation
  • Clayson, C. A., and L. Kantha, 2008: On turbulence and mixing in the free atmosphere inferred from high-resolution soundings. J. Atmos. Oceanic Technol., 25 , 833852.

    • Search Google Scholar
    • Export Citation
  • Cohn, S. A., 1995: Radar measurements of turbulent eddy dissipation rate in the troposphere: A comparison of techniques. J. Atmos. Oceanic Technol., 12 , 8595.

    • Search Google Scholar
    • Export Citation
  • Cot, C., 2001: Equatorial mesoscale wind and temperature fluctuations in the lower atmosphere. J. Geophys. Res., 106 , 15231532.

  • Drüe, C., W. Frey, A. Hoff, and Th Hauf, 2008: Aircraft type-specific errors in AMDAR weather reports from commercial aircraft. Quart. J. Roy. Meteor. Soc., 134 , 229239.

    • Search Google Scholar
    • Export Citation
  • Ellsaesser, H. W., 1969: A climatology of epsilon (atmospheric dissipation). Mon. Wea. Rev., 97 , 415423.

  • Fil, C., and L. Dubus, 2005: Winter climate regimes over the North Atlantic and European region in ERA40 reanalysis and DEMETER seasonal hindcasts. Tellus, 57 , 290307.

    • Search Google Scholar
    • Export Citation
  • Frehlich, R., 2001: Errors for space-based Doppler lidar wind measurements: Definition, performance, and verification. J. Atmos. Oceanic Technol., 18 , 17491772.

    • Search Google Scholar
    • Export Citation
  • Frehlich, R., 2006: Adaptive data assimilation including the effect of spatial variations in observation error. Quart. J. Roy. Meteor. Soc., 132 , 12251257.

    • Search Google Scholar
    • Export Citation
  • Frehlich, R., 2008: Atmospheric turbulence component of the innovation covariance. Quart. J. Roy. Meteor. Soc., 134 , 931940.

  • Frehlich, R., and R. Sharman, 2004: Estimates of turbulence from numerical weather prediction model output with applications to turbulence diagnosis and data assimilation. Mon. Wea. Rev., 132 , 23082324.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Frehlich, R., and N. Kelley, 2008: Measurements of wind and turbulence profiles with scanning Doppler lidar for wind energy applications. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens., 1 , 4247.

    • Search Google Scholar
    • Export Citation
  • Frehlich, R., S. Hannon, and S. Henderson, 1998: Coherent Doppler lidar measurements of wind field statistics. Bound.-Layer Meteor., 86 , 233256.

    • Search Google Scholar
    • Export Citation
  • Frehlich, R., Y. Meillier, M. L. Jensen, B. Balsley, and R. Sharman, 2006: Measurements of boundary layer profiles in an urban environment. J. Appl. Meteor. Climatol., 45 , 821837.

    • Search Google Scholar
    • Export Citation
  • Frisch, U., 1995: Turbulence, the Legacy of A. N. Kolmogorov. Cambridge University Press, 296 pp.

  • Fukao, S., and Coauthors, 1994: Seasonal variability of vertical eddy diffusivity in the middle atmosphere: 1. Three-year observations by the middle and upper atmosphere radar. J. Geophys. Res., 99 , 1897318987.

    • Search Google Scholar
    • Export Citation
  • Gage, K. S., and G. D. Nastrom, 1986: Theoretical interpretation of atmospheric wavenumber spectra of wind and temperature observed by commercial aircraft during GASP. J. Atmos. Sci., 43 , 729740.

    • Search Google Scholar
    • Export Citation
  • Gage, K. S., J. L. Green, and T. E. VanZandt, 1980: Use of Doppler radar for the measurement of atmospheric turbulence parameters from the intensity of clear-air echoes. Radio Sci., 15 , 407416.

    • Search Google Scholar
    • Export Citation
  • Gage, K. S., J. L. Green, and T. E. VanZandt, 1986: Spectrum of atmospheric vertical displacements and spectrum of conservative scalar passive additives due to quasi-horizontal atmospheric motions. J. Geophys. Res., 91 , 1321113216.

    • Search Google Scholar
    • Export Citation
  • Gill, A. E., 1989: Atmosphere-Ocean Dynamics. Academic Press, 662 pp.

  • Gkioulekas, E., and K. K. Tung, 2006: Recent developments in understanding two-dimensional turbulence and the Nastrom-Gage spectrum. Low Temp. Phys., 145 , 2557.

    • Search Google Scholar
    • Export Citation
  • Gomis, D., and S. Alonso, 1988: Structure function responses in a limited area. Mon. Wea. Rev., 116 , 22542264.

  • Grotjahn, R., 1993: Global Atmospheric Circulations. Oxford, 430 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
  • Hocking, W. K., 1996: An assessment of the capabilities and limitations of radars in measurements of atmosphere turbulence. Adv. Space Res., 17 , 3747.

    • Search Google Scholar
    • Export Citation
  • Hoinka, K. P., 1998: Statistics of the global tropopause pressure. Mon. Wea. Rev., 126 , 33033325.

  • Hoskins, B. J., H. H. Hsu, I. N. James, M. Masutani, P. D. Sardeshmukh, and G. H. White, 1989: Diagnostics of the global atmospheric circulation based on ECMWF analyses 1979–1989. Tech. Rep. WCRP-27, WMO/TD-326, 217 pp. [Available from World Meteorological Organization, Case Postale 2300, CH-1211 Geneva 20, Switzerland].

    • Search Google Scholar
    • Export Citation
  • Jaatinen, J., and J. B. Elms, 2000: On the windfinding accuracy of Loran-C, GPS and radar. Väisälä News, 152 , 3033.

  • Jaeger, E. B., and M. Sprenger, 2007: A northern-hemispheric climatology of indices for clear air turbulence in the tropopause region derived from ERA40 re-analysis data. J. Geophys. Res., 112 , D20106. doi:10.1029/2006JD008189.

    • Search Google Scholar
    • Export Citation
  • Jasperson, W. H., G. D. Nastrom, and D. C. Fritts, 1990: Further study of terrain effects on the mesoscale spectrum of atmospheric motions. J. Atmos. Sci., 47 , 979987.

    • Search Google Scholar
    • Export Citation
  • Julian, P. R., and A. K. Cline, 1974: The direct estimation of spatial wavenumber spectra of atmospheric variables. J. Atmos. Sci., 31 , 15261539.

    • Search Google Scholar
    • Export Citation
  • Kalnay, E., 2003: Atmospheric Modeling, Data Assimilation and Predictability. Cambridge University Press, 342 pp.

  • Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc., 77 , 437471.

  • Koch, P., H. Wernli, and H. W. Davies, 2006: An event-based jet-stream climatology and typology. Int. J. Climatol., 26 , 283301.

  • 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.

    • Search Google Scholar
    • Export Citation
  • Lenschow, D. H., J. Mann, and L. Kristensen, 1994: How long is long enough when measuring fluxes and other turbulent statistics? J. Atmos. Oceanic Technol., 11 , 661673.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Lindborg, E., 2005: The effect of rotation on the mesoscale energy cascade in the free atmosphere. Geophys. Res. Lett., 32 , L01809. doi:10.1029/2004GL021319.

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

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

    • Search Google Scholar
    • Export Citation
  • Lindborg, E., and J. Y. N. Cho, 2001: Horizontal velocity structure functions in the upper troposphere and lower stratosphere 2. Theoretical considerations. J. Geophys. Res., 106 , 233241.

    • Search Google Scholar
    • Export Citation
  • Lindborg, E., and G. Brethouwer, 2007: Stratified turbulence forced in rotational and divergent modes. J. Fluid Mech., 586 , 83108.

  • Lorenz, E. N., 1967: The nature and theory of the general circulation of the atmosphere. WMO 218, TP 115, 161 pp.

  • Luers, J. K., 1997: Temperature error of the Väisälä RS90 radiosonde. J. Atmos. Oceanic Technol., 14 , 15201532.

  • Luers, J. K., and R. E. Eskridge, 1998: Use of radiosonde temperature data in climate studies. J. Climate, 11 , 10021019.

  • Maddox, R. A., and T. H. Vonder Haar, 1979: Covariance analyses of satellite-derived mesoscale wind fields. J. Appl. Meteor., 18 , 13271334.

    • Search Google Scholar
    • Export Citation
  • Masciadri, E., and S. Egner, 2006: First seasonal study of optical turbulence with an atmospheric model. Astron. Soc. Pac., 118 , 16041619.

    • Search Google Scholar
    • Export Citation
  • Monin, A. S., and A. M. Yaglom, 1975: Statistical Fluid Mechanics: Mechanics of Turbulence. Vol. 2. MIT Press, 874 pp.

  • Moninger, W. R., R. D. Mamrosh, and P. M. Pauley, 2003: Automated meteorological reports from commercial aircraft. Bull. Amer. Meteor. Soc., 84 , 203216.

    • Search Google Scholar
    • Export Citation
  • Nappo, C. J., 2002: An Introduction to Atmospheric Gravity Waves. Academic Press, 276 pp.

  • Nastrom, G. D., and K. S. Gage, 1985: A climatology at atmospheric wavenumber spectra of wind and temperature observed by commercial aircraft. J. Atmos. Sci., 42 , 950960.

    • Search Google Scholar
    • Export Citation
  • Nastrom, G. D., and F. D. Eaton, 1997: Turbulence eddy dissipation rates from radar observations at 5–20 km at White Sands Missile Range, New Mexico. J. Geophys. Res., 102 , 1949519505.

    • Search Google Scholar
    • Export Citation
  • Nastrom, G. D., and F. D. Eaton, 2005: Seasonal variability of turbulence parameters at 2 to 21 km from MST radar measurements at Vandenberg Air Force Base, California. J. Geophys. Res., 110 , D19110. doi:10.1029/2005JD005782.

    • Search Google Scholar
    • Export Citation
  • Nastrom, G. D., T. E. Van Zandt, and J. M. Warnock, 1997: Vertical wavenumber spectra of wind and temperature from high-resolution balloon soundings over Illinois. J. Geophys. Res., 102 , 66856701.

    • Search Google Scholar
    • Export Citation
  • Ogura, Y., 1952: The structure of two-dimensionally isotropic turbulence. J. Meteor. Soc. Japan, 30 , 5964.

  • Palmen, E., and C. W. Newton, 1969: Atmospheric Circulation Systems. Elsevier, 603 pp.

  • Pauley, P. A., 2002: Telling north from south: An example of an error in automated aircraft data. Wea. Forecasting, 17 , 334336.

  • Peters, M. E., Z. Kuang, and C. C. Walker, 2008: Analysis of atmospheric energy transport in ERA-40 and implications for simple models of the mean tropical circulation. J. Climate, 21 , 52295241.

    • Search Google Scholar
    • Export Citation
  • Press, W. H., B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, 1986: Numerical Recipes: The Art of Scientific Computing. 2nd ed. Cambridge University Press, 963 pp.

    • Search Google Scholar
    • Export Citation
  • Reiter, E. R., and P. F. Lester, 1968: Richardson’s number in the free atmosphere. Arch. Meteor. Geophys. Bioklimatol. Ser. A, 17 , 17.

    • Search Google Scholar
    • Export Citation
  • Riley, J. J., and E. Lindborg, 2008: Stratified turbulence: A possible interpretation of some geophysical turbulence measurements. J. Atmos. Sci., 65 , 24162424.

    • Search Google Scholar
    • Export Citation
  • Satheesan, K., and B. V. Krishna Murthy, 2002: Turbulence parameters in the tropical troposphere and lower stratosphere. J. Geophys. Res., 107 , 4002. doi:10.1029/2000JD000146.

    • Search Google Scholar
    • Export Citation
  • Skamarock, W. A., 2004: Evaluating mesoscale NWP models using kinetic energy spectra. Mon. Wea. Rev., 132 , 30193032.

  • Takahashi, Y. O., K. Hamilton, and W. Ohfuchi, 2006: Explicit global simulation of the mesoscale spectrum of atmospheric motions. Geophys. Res. Lett., 33 , L12812. doi:10.1029/2006GL026429.

    • Search Google Scholar
    • Export Citation
  • Tatarski, V. I., 1967: Wave Propagation in a Turbulent Medium. Dover Publications, 285 pp.

  • Tulloch, R., and K. S. Smith, 2006: A theory for the atmospheric energy spectrum: Depth-limited temperature anomalies at the tropopause. Proc. Natl. Acad. Sci. USA, 103 , 1469014694.

    • Search Google Scholar
    • Export Citation
  • Tulloch, R., and K. S. Smith, 2009: Quasigeostrophic turbulence with explicit surface dynamics: Application to the atmospheric energy spectrum. J. Atmos. Sci., 66 , 450467.

    • Search Google Scholar
    • Export Citation
  • Tung, K. K., and W. W. Orlando, 2003: The k3 and k5/3 energy spectrum of atmospheric turbulence: Quasigeostrophic two-level model simulation. J. Atmos. Sci., 60 , 824835.

    • Search Google Scholar
    • Export Citation
  • Uppala, S. M., and Coauthors, 2005: The ERA-40 Re-Analysis. Quart. J. Roy. Meteor. Soc., 131 , 29613012.

  • Vinnichenko, N. K., and J. A. Dutton, 1969: Empirical studies of atmospheric structure and spectra in the free atmosphere. Radio Sci., 4 , 11151126.

    • Search Google Scholar
    • Export Citation
  • Wolff, J., and R. Sharman, 2008: Climatology of upper-level turbulence over the continental United States. J. Appl. Meteor. Climatol., 47 , 21982214.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 775 379 119
PDF Downloads 339 104 17