Probabilistic description of rainfall intensity at multiple time scales

The probabilistic description of the average rainfall intensity over a certain time scale in relationship with the time scale length has theoretical interest, in understanding the behaviour of the rainfall process, and practical interest in constructing relationships between intensity, time scale (sometimes called “duration”) and return period (or “frequency”). To study these relationships, the principle of maximum entropy can serve as a sound theoretical background. Using a long rainfall dataset from Athens, Greece, and time scales ranging from 1 hour to 1 year, we study statistical properties such as (a) probability dry and its relationship with rainfall intensity and time scale, (b) marginal probability distribution function of rainfall intensity, with emphasis on the tails, and its variation with time scale (c) dependence structure of rainfall intensity with reference to time scale, and (d) statistical properties that are invariant or scaling with time scale. The study concludes with a discussion of the usefulness of these analyses in hydrological design.