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By ‘Noah Effect’ we designate the observation that extreme precipitation can be very extreme indeed, and by ‘Joseph Effect’ the finding that a long period of unusual (high or low) precipitation can be extremely long. Current models of statistical hydrology cannot account for either effect and must be superseded. As a replacement, ‘self‐similar’ models appear very promising. They account particularly well for the remarkable empirical observations of Harold Edwin Hurst. The present paper introduces and summarizes a series of investigations on self‐similar operational hydrology.