Analysis of Intermittency in Aircraft Measurements of Velocity, Temperature and Atmospheric Tracers using Wavelet Transforms

  • Julio T. Bacmeister
  • Stephen D. Eckermann
  • Lynn Sparling
  • K. Roland Chan
  • Max Loewenstein
  • Michael H. Proffitt
Part of the NATO ASI Series book series (volume 50)


Wavelet transforms of geophysical data are a promising new technique which may extend traditional analyses employing Fourier transforms. Here we will employ wavelet transforms to examine velocity, potential temperature, and trace gas mixing ratio measurements from high-altitude ER-2 aircraft (altitude≈20 km). Probability density functions and quantities similar to structure functions are calculated from wavelet transforms. This analysis reveals differences between the variability of meteorological quantities such as velocity and potential temperature, and that of passive atmospheric tracers. Our analysis suggests that trace gas variability contains intermittent episodes of high variability, while velocity and temperature fluctuations are more uniformly distributed. We propose a simple model consisting of two sets of variability with different degrees of “roughness” and continuity. This “bi-fractal” model is used to interpret structure functions obtained for velocity and N2O. Finally, we show a case of gravity wave-tracer filament interaction in the ER-2 data. We argue that such interactions may increase cross-isentropic mixing of trace gases by gravity waves.


Structure Function Gravity Wave Potential Temperature Zonal Velocity Haar Wavelet 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Aurell, E., U. Frisch, J. Lutsko, and M. Vergassola, On the multifractal properties of the energy dissipation derived from turbulence data. J. Fluid Mech., 238, 467–486, 1992.CrossRefGoogle Scholar
  2. Bacmeister, J. T., S. D. Eckermann, P. A. Newman, L. R. Lait, K. R. Chan, M. Loewen- stein, M. H. Proffitt and B. L. Gary, Stratospheric horizontal wavenumber spectra of winds, potential temperature and atmospheric tracers observed by high-altitude aircraft. J. Geophys. Res., 101, 9441–9470, 1996.CrossRefGoogle Scholar
  3. Daubechies, I., Orthonormal bases of compactly supported wavelets, Comm. Pure Appl. Google Scholar
  4. Math., 41, 909-996, 1988. Daubechies, I., Ten lectures on wavelets, 357 pp., CBMS-61, SIAM, Philadelphia, 1992. Davis, A., A. Marshak, W. Wiscombe and R. Cahalan, Multifractal characterizations of nonstationarity and intermittency in geophysical fields: Observed, retrieved, or simulated, J. Geophys. Res., 99, 8055-8072, 1994.Google Scholar
  5. Frisch, U., Turbulence: the legacy of A. N. Kolmogorov, 296 pp., Cambridge Univ. Press., New York, 1995.Google Scholar
  6. Gardner, C. S., C. A. Hostetler, and S. J. Franke, Gravity wave models for the horizontal wave number spectra of atmospheric velocity and density perturbations, J. Geophys. Res., 98, 1035–1049, 1993a.CrossRefGoogle Scholar
  7. Katul, G. G., M. B. Parlange, C. R. Chu, Intermittency, local isotropy, and non-gaussian statistics in atmospheric surface layer turbulence, Phys. Fluids, 6, 2480–2492, 1994.CrossRefGoogle Scholar
  8. Lilly, D. K., Stratified turbulence and the mesoscale variability of the atmosphere. J. Atmos. Sci., 40, 749–761, 1983.CrossRefGoogle Scholar
  9. Lilly, D. K., and P. F. Lester, Waves and turbulence in the stratosphere, J. Atmos. Sci., 31, 800–812, 1974.CrossRefGoogle Scholar
  10. Loewenstein, M., J. R. Podolske, K. R. Chan, and S. E. Strahan, Nitrous Oxide as a dynamical tracer in the 1987 Airborne Antarctic Ozone Experiment.,/. Geophys. Res., 94, 11,589-11, 598, 1989.Google Scholar
  11. Mallat, S. G., A theory for multiresolution signal decomposition: The wavelet representation, IEEE Trans. Pattern Anal. Machine Intell.11, 674–693, 1989.CrossRefGoogle Scholar
  12. Marsch, E., and C. Y. Tu, Non-Gaussian probability distributions of solar wind fluctuations, Ann. Geophysicae, 12, 1127–1138, 1994.CrossRefGoogle Scholar
  13. Meneveau, C., and K. R. Sreenivasan, The multifractal nature of turbulent energy dissipation, J. Fluid Mech., 224, 429–484, 1991.CrossRefGoogle Scholar
  14. Murphy, D., Time offsets and power spectra of the ER-2 data set from the 1987 Airborne Antarctic Ozone Experiment, J. Geophys. Res., 94, 16737–16748, 1989.Google Scholar
  15. Nastrom, G. D., W. H. Jasperson, and K. S. Gage Horizontal spectra of atmospheric tracers measured during the Global Atmospheric Sampling Program. J. Geophys. Res., 91, 13201–13209, 1986CrossRefGoogle Scholar
  16. Pierrehumbert, R. T., Tracer microstructure in the large-eddy dominated regime, in Chaos applied to fluid mixing, ed. H. Aref, M. S. El Naschie; Pergamon/Elsevier, 347-365, 1995. Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN, 2nd ed., 963 pp. Cambrige University Press, Cambridge, UK, 1992.Google Scholar
  17. Proffitt, M. H., M. J. Steinkamp, J. A. Powell, R. J. McLaughlin, O. A. Mills, A. L. Schmeltekopf, T. L. Thompson, A. F. Tuck, T. Tyler, R. H. Winkler, and K. R. Chan, In situ ozone measurements within the 1987 ozone hole from a high-altitude ER-2 aircraft, J. Geophys. Res., 94, 16547-16556, 1989.Google Scholar
  18. Reid, S. J., G. Vaughan, N. J. Mitchell, I. T. Pritchard, H. J. Smit, T. S. Jorgensen, C. Varostos, and H. de Becker, Distribution of ozone laminae and the possible influence of inertia-gravity waves, Geophys. Res. Lett., 21, 1479–1482, 1994.CrossRefGoogle Scholar
  19. Scott, S. G., T. P. Bui, K.R. Chan, and S.W. Bowen, The meteorological measurement system on the NASA ER-2 aircraft, J. Atmos. Ocean. Tech., 7, 525–540, 1990.CrossRefGoogle Scholar
  20. Waugh, D. W., and R. A. Plumb, Contour advection with surgery: A technique for investigating fine scale structure in tracer transport, J. Atmos. Sci., 51, 530–540, 1994.CrossRefGoogle Scholar
  21. Yamada, M., and K. Ohkitani, Orthonormal wavelet analysis of turbulence, Fluid. Dyn. Res., 8, 101–115, 1991.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Julio T. Bacmeister
    • 1
  • Stephen D. Eckermann
    • 2
  • Lynn Sparling
    • 3
  • K. Roland Chan
    • 4
  • Max Loewenstein
    • 4
  • Michael H. Proffitt
    • 5
  1. 1.Naval Research LaboratoryWashington DCUSA
  2. 2.Computational Physics, Inc.FairfaxUSA
  3. 3.Hughes STXLanhamUSA
  4. 4.NASA Ames Research CenterMoffet FieldUSA
  5. 5.CIRES University of ColoradoBoulderUSA

Personalised recommendations