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 iw decreases as w increases. Our analysis of individual storm events using ground measurements of 1-minute temporal resolution reveals that the iw–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 βm (at minute time scale) and βh (at hourly time scale) are fitted for segments separated by the characteristic time τ. Mostly βm < βh, implying the persistence of high rainfall concentration prior to τ. This reflects the characteristics of convective storms, and the range of τ agrees with the known time span of convective storm duration. The more concentrated storm event exhibits the stronger persistence (a smaller βm) prior to τ and the faster moisture depletion (a greater βh) thereafter. The knowledge gained from this study provides important implications to the existing design storm formula, often called the Mononobe formula: observed scale-free intra-storm variability is in accordance with this formula while the scaling transition at sub-hourly time scale explains the known limitations of its practical applications.