Empirical evidence suggests that statistical properties of storm rainfall at a location and within a homogeneous season have a well-structured dependence on storm duration. To explain this dependence, a simple scaling model for rainfall intensity within a storm was hypothesized. It was shown both analytically and empirically that such a model can explain reasonably well the observed statistical structure in the interior of storms, thus providing an efficient parametrization 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 versus normalized cumulative time since the beginning of a storm) which are extensively used in hydrologic design. In contrast, popular stationary models of rainfall intensity are shown unable to capture the duration dependent statistical structure of storm depths and are also inconsistent with the concept of mass curves.