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

Abstract

The observed relation of worldwide precipitation maxima P versus duration d follows the Jennings scaling law, P ' d b , 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.

World's greatest rainfall intensities observed by satellites

“…Maxima rainfall intensities for larger than 0.25° × 0.25° resolutions show that rainfall declines as the spatial scale becomes coarser although not by a factor of two or three (as it is between 1 m 2 and 625 km 2 ), but rather than by a factor ranging between ∼2 (for short durations) and ∼1.1 (for long durations). When the Jennings law is compared between gauges and 1° × 1° cells, the difference is never greater than 5 times, which is less than those reported by a numerical model (Zhang et al , ). The fact that extreme rainfall intensity from gauges can be two to three times greater than measurements from satellites can be explained by the poor ability of satellites to capture extreme events characterized by short‐term but heavy rainfall intensity rates.…”

“…As noted by Field and Shutts (), several studies have suggested that the distribution of rainfall responds to the local concentration of water and energy. Such phenomenon seems to follow a fractal‐type attenuation process as the spatial scale decreases and, as shown by Zhang et al (), the Jennings law is not the exception.…”

“…This precipitation–duration relationship follows a power law R ≈ aD b where the precipitation intensity R is in mm and the duration D in minutes. The b exponent usually ranges between 0.4 for historical records observed by single rain gauges and it gets close to 0.5 for a worldwide compilation of the maximum observed rainfall over a given time scale (Zhang et al , ). Recent studies have provided probabilistic (Galmarini et al ) and stochastic (Zhang et al , ) explanations of such scaling law at the rain gauge point scale.…”

“…The b exponent usually ranges between 0.4 for historical records observed by single rain gauges and it gets close to 0.5 for a worldwide compilation of the maximum observed rainfall over a given time scale (Zhang et al , ). Recent studies have provided probabilistic (Galmarini et al ) and stochastic (Zhang et al , ) explanations of such scaling law at the rain gauge point scale. It is however unknown how that relationship behaves for larger spatial scales in comparison to the conventional ∼1 m 2 footprint of a typical rain gauge.…”

“…A. Breña-Naranjo, A. Pedrozo-Acuña and M. A. Rico-Ramirez ( Zhang et al, 2013). The fact that extreme rainfall intensity from gauges can be two to three times greater than measurements from satellites can be explained by the poor ability of satellites to capture extreme events characterized by short-term but heavy rainfall intensity rates.…”