Distributions of microcanonical cascade weights of rainfall at small timescales

Empirical frequency distributions of multiplicative cascade weights, or breakdown coefficients, at small timescales are analyzed for 5-min precipitation time series from four gauges in Germany. It is shown that histograms of the weights, W, are strongly deformed by the recording precision of rainfall amounts. A randomization procedure is proposed to statistically remove the artifacts due to precision errors in the original series. Evolution of the probability distributions of W from beta-like for large timescales to combined beta-normal distribution with a pronounced peak at W ≈ 0.5 for small timescales is observed. A new 3N-B distribution built from 3 separate normal, N, distributions and one beta, B, distribution is proposed for reproduction of the empirical histograms of W at small timescales. Parameters of the 3N-B distributions are fitted for all gauges and analyzed timescales. Microcanonical cascades models with a generator based on 3N-B distributions are developed and their performance at disaggregating precipitation at 1280-min intervals down to 5-min intervals is evaluated.