On the concept of similar storms and their parameterization via scaling

Empirical evidence suggests that statistical properties of storm rainfall within a homogeneous season have a well-structured dependence on storm duration. For example, the mean and standard deviation of total storm depth increase with duration each according to a power law with the same exponent; the lag-one correlation coefficient of hourly rainfall depths increases with duration; and the decay rate of the autocorrelation function of hourly rainfall depths decreases with duration. Motivated by the first observation, a simple scaling model for rainfall intensity within a storm was hypothesized and was shown both analytically and empirically that such a model can explain reasonably well the observed statistical structure in the interior of storms providing thus an efficient parameterization of storms of varying durations and total depths. This simple scaling model is also consistent with, and provides a theoretical basis for, the concept of mass curves (normalized cumulative storm depth vs. normalized cumulative time since the beginning of a storm) which are extensively used in hydrologic design.