Power laws in intra-storm temporal rainfall variability

Abstract

During a storm event, rainfall intensity rarely remains uniform but rather shows radical temporal variation. Given the time window w within a storm, the maximum rainfall intensity over w, namely i(w) decreases as w increases. Our analysis of individual storm events using ground measurements of 1-minute temporal resolution reveals that the i(w)-w relationship follows either a single or broken power law. Such scale-invariance is likely associated with known fractal or multi-fractal characteristics of rainfall structure. In broken power-law events, two power-law exponents of beta(m) (at minute time scale) and beta(h) (at hourly time scale) are fitted for segments separated by the characteristic time tau. Mostly beta(m) < beta(h), implying the persistence of high rainfall concentration prior to tau. This reflects the characteristics of convective storms, and the range of beta agrees with the known time span of convective storm duration. The more concentrated storm event exhibits the stronger persistence (a smallerp beta(m)) prior to tau and the faster moisture depletion (a greater beta(h)) thereafter. The knowledge gained from this study provides important implications to the existing design storm formula, often called the Mononobe formula: observed scale-free infra-storm variability is in accordance with this formula while the scaling transition at subhourly time scale explains the known limitations of its practical applications.