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 ≊ 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 maximumdepth-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. © 2013 American Meteorological Society.