Intensity-duration-frequency curves from scaling representations of rainfall

We develop methods to estimate the intensity-duration-frequency (IDF) curves for three rainfall models with local multifractal behavior and varying complexity. The models use the classical notion of exterior and interior process, respectively for the variation of rainfall intensity at (approximately) storm and sub-storm scales. The exterior process is non-scaling and differs in the three models, whereas the interior process is stationary multifractal in all cases. The model based IDF curves are robust, against outliers and can be obtained from only very few years of rainfall data. In an application to a 24-year rainfall record from Florence, Italy, the models closely reproduce the empirical IDF curves and make similar extrapolations for return periods longer than the historical record.