• Dhar, O. N., and Farooqui S. M. T. , 1973: A study of rainfalls recorded at the Cherrapunji Observatory. Hydrol. Sci. Bull., 18, 441450, doi:10.1080/02626667309494059.

    • Search Google Scholar
    • Export Citation
  • Doswell, C. A., III, Brooks H. E. , and Maddox R. A. , 1996: Flash flood forecasting: An ingredients-based methodology. Wea. Forecasting, 11, 560581, doi:10.1175/1520-0434(1996)011<0560:FFFAIB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Eagleson, P. S., 1970: Dynamic Hydrology. McGraw-Hill, 200 pp.

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

  • Fraedrich, K., and Ziehmann-Schlumbohm C. , 1994: Predictability experiments with persistence forecasts in a red-noise atmosphere. Quart. J. Roy. Meteor. Soc., 120, 387428, doi:10.1002/qj.49712051608.

    • Search Google Scholar
    • Export Citation
  • Fraedrich, K., Blender R. , and Zhu X. , 2009: Continuum climate variability: Long-term memory, scaling, and 1/f-noise. Int. J. Mod. Phys. B, 23, 54035416, doi:10.1142/S0217979209063729.

    • Search Google Scholar
    • Export Citation
  • Galmarini, S., Steyn D. G. , and Ainslie B. , 2004: The scaling law relating world point-precipitation records to duration. Int. J. Climatol., 24, 533546, doi:10.1002/joc.1022.

    • Search Google Scholar
    • Export Citation
  • Hannachi, A., 2013: Intermittency, autoregression and censoring: A first-order AR model for daily precipitation. Meteor. Appl., doi:10.1002/met.1353, in press.

    • Search Google Scholar
    • Export Citation
  • Hubert, P., Tessier Y. , Lovejoy S. , Schertzer D. , Schmitt F. , Ladoy P. , Carbonnel J. P. , and Violette S. , 1993: Multifractals and extreme rainfall events. Geophys. Res. Lett., 20, 931934, doi:10.1029/93GL01245.

    • Search Google Scholar
    • Export Citation
  • Jennings, A. H., 1950: World’s greatest observed point rainfalls. Mon. Wea. Rev., 78, 45, doi:10.1175/1520-0493(1950)078<0004:WGOPR>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Paulhus, J. L. H., 1965: Indian Ocean and Taiwan rainfalls set new records. Mon. Wea. Rev., 93, 331335, doi:10.1175/1520-0493(1965)093<0331:IOATRS>2.3.CO;2.

    • Search Google Scholar
    • Export Citation
  • World Meteorological Organization, 1986: Manual for estimation of probable maximum precipitation. 2nd ed. Operational Hydrology Rep. 1, WMO 332, 269 pp. [Available online at http://library.wmo.int/pmb_ged/wmo_332.pdf.]

  • World Meteorological Organization, 1994: Guide to hydrological practices. 5th ed. WMO 168, 402 pp. [Available online at ftp://ftp.wmo.int/Documents/MediaPublic/Publications/Guide_to_Hydrological_Practices/WMOENG.pdf.]

  • Zhang, H., Fraedrich K. , Blender R. and Zhu X. , 2013: Precipitation extremes in CMIP5 simulations on different time scales. J. Hydrometeor., 14, 923928, doi:10.1175/JHM-D-12-0181.1.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 6 6 6
Full Text Views 7 7 7
PDF Downloads 4 4 4

World’s Greatest Observed Point Rainfalls: Jennings (1950) Scaling Law

View More View Less
  • 1 Max Planck Institute for Meteorology, and Meteorological Institute, University of Hamburg, KlimaCampus, Hamburg, Germany
  • | 2 Meteorological Institute, University of Hamburg, KlimaCampus, Hamburg, Germany
  • | 3 Key Laboratory of Meteorology Disaster of Ministry of Education, Nanjing University of Information Science and Technology, Nanjing, China
Restricted access

Abstract

The observed relation of worldwide precipitation maxima P versus duration d follows the Jennings scaling law, Pdb, with scaling coefficient b ≈ 0.5. This scaling is demonstrated to hold for single-station rainfall extending over three decades. A conceptual stochastic rainfall model that reveals similar scaling behavior is introduced as a first-order autoregressive process [AR(1)] to represent the lower tropospheric vertical moisture fluxes, whose upward components balance the rainfall while the downward components are truncated and defined as no rain. Estimates of 40-yr ECMWF Re-Analysis (ERA-40) vertical moisture flux autocorrelations (at grids near the rainfall stations) provide estimates for the truncated AR(1). Subjected to maximum depth-duration analysis, the scaling coefficient b ≈ 0.5 is obtained extending for about two orders of magnitude, which is associated with a wide range of vertical moisture flux autocorrelations 0.1 < a < 0.7.

Corresponding author address: Huan Zhang, KlimaCampus, University of Hamburg, Grindelberg 5, 20144 Hamburg, Germany. E-mail: huan.zhang@zmaw.de

Abstract

The observed relation of worldwide precipitation maxima P versus duration d follows the Jennings scaling law, Pdb, with scaling coefficient b ≈ 0.5. This scaling is demonstrated to hold for single-station rainfall extending over three decades. A conceptual stochastic rainfall model that reveals similar scaling behavior is introduced as a first-order autoregressive process [AR(1)] to represent the lower tropospheric vertical moisture fluxes, whose upward components balance the rainfall while the downward components are truncated and defined as no rain. Estimates of 40-yr ECMWF Re-Analysis (ERA-40) vertical moisture flux autocorrelations (at grids near the rainfall stations) provide estimates for the truncated AR(1). Subjected to maximum depth-duration analysis, the scaling coefficient b ≈ 0.5 is obtained extending for about two orders of magnitude, which is associated with a wide range of vertical moisture flux autocorrelations 0.1 < a < 0.7.

Corresponding author address: Huan Zhang, KlimaCampus, University of Hamburg, Grindelberg 5, 20144 Hamburg, Germany. E-mail: huan.zhang@zmaw.de
Save