• Ahijevych, D. A., R. E. Carbone, J. D. Tuttle, and S. B. Trier, 2001: Radar data and climatological statistics associated with warm season precipitation episodes over the continental U.S. NCAR Tech. Note TN-4481STR, 81 pp.

  • Carbone, R., J. D. Tuttle, D. A. Ahijevych, and S. B. Trier, 2002: Inferences of predictability associated with warm season precipitation episodes. J. Atmos. Sci., 59 , 20332056.

    • Search Google Scholar
    • Export Citation
  • Crane, R. K., 1990: Space-time structure of rain rate fields. J. Geophys. Res., 95 , 20112020.

  • Douglas, E., and A. P. Barros, 2003: Probable maximum precipitation estimation using multifractals: Application in the eastern United States. J. Hydrometeor., 4 , 10121024.

    • Search Google Scholar
    • Export Citation
  • Farge, M., 1992: Wavelet transforms and their applications to turbulence. Annu. Rev. Fluid Mech., 24 , 395457.

  • Fraedrich, K., and C. Larnder, 1993: Scaling regimes of composite rainfall time series. Tellus, 45A , 289298.

  • Georgakakos, K. P., A. A. Carsteanu, P. L. Sturdevant, and J. A. Cramer, 1994: Observation and analysis of Midwestern rain rates. J. Appl. Meteor., 33 , 14331444.

    • Search Google Scholar
    • Export Citation
  • Gilman, D. L., F. J. Fuglister, and J. M. Mitchell, 1963: On the power spectrum of “red noise.”. J. Atmos. Sci., 20 , 182184.

  • Harris, D., M. Menabde, A. Seed, and G. Austin, 1996: Multifractal characterization for rain fields with a strong orographic influence. J. Geophys. Res., 101 , 2640526414.

    • Search Google Scholar
    • Export Citation
  • Harris, D., E. Foufoula-Georgiou, K. K. Droegemeier, and J. J. Levit, 2001: Multiscale statistical properties of a high-resolution precipitation forecast. J. Hydrometeor., 2 , 406418.

    • Search Google Scholar
    • Export Citation
  • Kestin, T. S., D. J. Karoly, J-I. Yano, and N. A. Rayner, 1998: Time–frequency variability of ENSO and stochastic simulations. J. Climate, 11 , 22582272.

    • Search Google Scholar
    • Export Citation
  • Kreyszig, E., 1967: Advanced Engineering Mathematics. 2d ed. John Wiley, 898 pp.

  • Laing, A. G., and J. M. Fritsch, 1997: The global population of mesoscale convective complexes. Quart. J. Roy. Meteor. Soc., 123 , 389405.

    • Search Google Scholar
    • Export Citation
  • Lau, K-M., and H-Y. Weng, 1995: Climate signal detection using wavelet transform: How to make a time series sing. Bull. Amer. Meteor. Soc., 76 , 23912402.

    • Search Google Scholar
    • Export Citation
  • Lovejoy, S., and B. B. Mandelbrot, 1985: Fractal properties of rain, and a fractal model. Tellus, 37A , 209232.

  • Mallat, S. G., 1999: A Wavelet Tour of Signal Processing. 2d ed. Academic Press, 637 pp.

  • Mandelbrot, B. B., 1974: Intermittent turbulence in self-similar cascades: Divergence of high moments and dimension of the carrier. J. Fluid Mech., 62 , 331358.

    • Search Google Scholar
    • Export Citation
  • Marsan, D., D. Schertzer, and S. Lovejoy, 1996: Causal space-time multifractal processes: Predictability and forecasting of rain fields. J. Geophys. Res., 101 , 2633326346.

    • Search Google Scholar
    • Export Citation
  • Menabde, M., A. Seed, D. Harris, and G. Austin, 1999: Multiaffine random field model of rainfall. Water Resour. Res., 35 , 509514.

  • Moncrieff, M. W., 1992: Organized convective systems: Archetypal dynamical models, mass and momentum flux theory, and parameterization. Quart. J. Roy. Meteor. Soc., 118 , 819850.

    • Search Google Scholar
    • Export Citation
  • Moncrieff, M. W., and C-H. Liu, 2006: Representing convective organization in prediction models by a hybrid strategy. J. Atmos. Sci., in press.

    • Search Google Scholar
    • Export Citation
  • Moncrieff, M. W., C-H. Liu, and H-M. Hsu, 2005: Convective dynamics issues at ∼10 km grid-resolution. Proc. Workshop on Representation of Sub-Grid Processes Using Stochastic-Dynamical Models, ECMWF, 91–105.

  • Morlet, J., G. Arens, I. Fourgeau, and D. Giard, 1982: Wave propagation and sampling theory. Geophysics, 47 , 203236.

  • Naveau, P., and M. W. Moncrieff, 2003: A probabilistic description of convective mass flux and its relation to extreme-value theory. Quart. J. Roy. Meteor. Soc., 129 , 22172232.

    • Search Google Scholar
    • Export Citation
  • Orlanski, I., 1975: A rational subdivision of scales for atmospheric processes. Bull. Amer. Meteor. Soc., 56 , 527530.

  • Schertzer, D., and S. Lovejoy, 1987: Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes. J. Geophys. Res., 92 , 96939714.

    • Search Google Scholar
    • Export Citation
  • Tessier, Y., S. Lovejoy, and D. Schertzer, 1993: Universal multifractals: Theory and observations for rain and cloud. J. Appl. Meteor., 32 , 223250.

    • Search Google Scholar
    • Export Citation
  • Tessier, Y., S. Lovejoy, P. Hubert, D. Schertzer, and S. Pecknold, 1996: Multifractal analysis and modeling of rainfall and river flows and scaling, causal transfer functions. J. Geophys. Res., 101 , 2642726440.

    • Search Google Scholar
    • Export Citation
  • Torrence, C., and G. P. Compo, 1998: A practical guide to wavelet analysis. Bull. Amer. Meteor. Soc., 79 , 6178.

  • Veneziano, D., R. L. Bras, and J. F. Niemann, 1996: Nonlinearity and self-similarity of rainfall in time and a stochastic model. J. Geophys. Res., 101 , 2637126392.

    • Search Google Scholar
    • Export Citation
  • Venugopal, V., and E. Foufoula-Georgiou, 1996: Energy decomposition of rainfall in the time-frequency-scale domain using wavelet packets. J. Hydrol., 187 , 337.

    • Search Google Scholar
    • Export Citation
  • Yano, J-I., R. Blender, C. Zhang, and K. Fraedrich, 2004: 1/f noise and pulse-like events in the tropical atmospheric surface variabilities. Quart. J. Roy. Meteor. Soc., 130 , 16971721.

    • Search Google Scholar
    • Export Citation
  • Zepeda-Arce, J., E. Foufoula-Georgiou, and K. K. Droegemeier, 2000: Space-time organization and its role in validating quantitative precipitation forecasts. J. Geophys. Res., 105 , 1012910146.

    • Search Google Scholar
    • Export Citation
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Multiscale Temporal Variability of Warm-Season Precipitation over North America: Statistical Analysis of Radar Measurements

Hsiao-ming HsuNational Center for Atmospheric Research, Boulder, Colorado

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Mitchell W. MoncrieffNational Center for Atmospheric Research, Boulder, Colorado

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Wen-wen TungNational Center for Atmospheric Research, Boulder, Colorado

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Changhai LiuNational Center for Atmospheric Research, Boulder, Colorado

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Abstract

Directionally averaged time series of precipitation rates for eight warm seasons (1996–2003) over the continental United States derived from Next Generation Weather Radar (NEXRAD) measurements are analyzed using spectral decomposition methods. For the latitudinally averaged data, in addition to previously identified diurnal and semidiurnal cycles, the temporal spectra show cross-scale self-similarity and periodicity. This property is revealed by a power-law scaling with an exponent of −4/3 for the frequency band higher than semidiurnal and −3/4 for the 1–3-day band. For the longitudinally averaged series the scaling exponent for the frequency band higher than semidiurnal changes from −4/3 to −5/3 revealing anisotropic properties.

The dominant periods and propagation speeds display temporal variability on about 1/2, 1, 4, 11, and 25 days. Composite patterns describing periods of <5 days display the eastward propagation characteristic of classical mesoscale convective organization. The lower-frequency (>5 days) patterns propagate westward suggesting the influence of large-scale waves, and both dominant periods and propagation speeds show marked interannual variability. The implied dependence between propagation and mean-flow for <5 days is consistent with the macrophysics of warm-season convective organization, and extends known dynamical mechanisms to a statistical framework.

Corresponding author address: Dr. Hsiao-ming Hsu, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307-3000. Email: hsu@ucar.edu

Abstract

Directionally averaged time series of precipitation rates for eight warm seasons (1996–2003) over the continental United States derived from Next Generation Weather Radar (NEXRAD) measurements are analyzed using spectral decomposition methods. For the latitudinally averaged data, in addition to previously identified diurnal and semidiurnal cycles, the temporal spectra show cross-scale self-similarity and periodicity. This property is revealed by a power-law scaling with an exponent of −4/3 for the frequency band higher than semidiurnal and −3/4 for the 1–3-day band. For the longitudinally averaged series the scaling exponent for the frequency band higher than semidiurnal changes from −4/3 to −5/3 revealing anisotropic properties.

The dominant periods and propagation speeds display temporal variability on about 1/2, 1, 4, 11, and 25 days. Composite patterns describing periods of <5 days display the eastward propagation characteristic of classical mesoscale convective organization. The lower-frequency (>5 days) patterns propagate westward suggesting the influence of large-scale waves, and both dominant periods and propagation speeds show marked interannual variability. The implied dependence between propagation and mean-flow for <5 days is consistent with the macrophysics of warm-season convective organization, and extends known dynamical mechanisms to a statistical framework.

Corresponding author address: Dr. Hsiao-ming Hsu, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307-3000. Email: hsu@ucar.edu

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