The scaling of temporal rainfall

The scaling analysis of temporal rainfall produces very different results if one uses the entire rainfall record inclusive of rainstorms and dry interstorm periods (continuous analysis) or only intrastorm data (within‐storm analysis). We show that the continuous results reflect mainly the alternation of dry and wet periods and that the rain support is not fractal. Therefore, the continuous results are spurious. This conclusion is significant since continuous analysis is the most popular scaling analysis method for rainfall. The literature on within‐storm analysis is much more limited, and standard methods do not exist. We develop such methods and show how their bias can be corrected and the accuracy maximized. The results from within‐storm analysis show higher intermittency (higher‐intensity fluctuations) than continuous analysis. This result has important implications on downscaling and the evaluation of rainfall extremes. Frequently used multifractal models for rainfall are of the log‐Levy (“universal”) type. A key parameter of those models is the stability index 0 < α ≤ 2, with α = 2 corresponding to lognormal models. To account for the alternation of dry and wet periods (also inside the storms), one can add a “beta component,” obtaining beta‐log‐Levy and beta‐lognormal models. By using simulations with α = 2, we show that standard estimators of α are negatively biased and that the hypothesis of beta‐lognormal multifractality inside the storms is statistically acceptable.