Editorial Type:
Article
Article Type:
Research Article

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

Huan Zhang Max Planck Institute for Meteorology, and Meteorological Institute, University of Hamburg, KlimaCampus, Hamburg, Germany

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Klaus Fraedrich Max Planck Institute for Meteorology, and Meteorological Institute, University of Hamburg, KlimaCampus, Hamburg, Germany

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Xiuhua Zhu Meteorological Institute, University of Hamburg, KlimaCampus, Hamburg, Germany

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Richard Blender Meteorological Institute, University of Hamburg, KlimaCampus, Hamburg, Germany

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Ling Zhang Key Laboratory of Meteorology Disaster of Ministry of Education, Nanjing University of Information Science and Technology, Nanjing, China

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Print Publication:
01 Dec 2013
DOI:
https://doi.org/10.1175/JHM-D-13-074.1
Page(s):
1952–1957
Restricted access

Abstract

The observed relation of worldwide precipitation maxima P versus duration d follows the Jennings scaling law, P ≈ db, 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, P ≈ db, 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
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Journal of Hydrometeorology

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