Seasonality of Taylor\u2019s law of fluctuation scaling in all-India daily rainfall

Abstract

Here we show that the variance over time of all-India daily rainfall (AIR) can be related to the mean over time of AIR by a seasonally varying power law. Outside of the peak monsoon months of July and August, AIR variance increases in proportion to a positive power of mean daily rainfall. During July and August, monthly averages of AIR show little association with the corresponding variances. This power-law relationship of temporal variance to temporal mean is known in biological sciences as Taylor’s law (TL) and in physical sciences as fluctuation scaling. We explain the seasonal variation in TL qualitatively by independent and identically distributed random sampling. Accounting for day-to-day correlation in AIR is sufficient to match quantitatively the observed power-law behavior. Our findings provide a quantitative month-specific assessment of the variability of AIR that could prove useful for the design of crop insurance and social safety nets for the large fraction of the population of the Indian subcontinent that depends on rainfed agriculture.