ABSTRACT
Stochastic simulation models of rain storm events in space and time attempt to reproduce the statistical properties of the event across a range of temporal and spatial scales. Two of the most advanced modeling concepts are: i) stochastic representation of the physical process of rainstorm temporal and spatial evolution and ii) scale-invariance or self-similarity of the spatial rainfall field. The stochastic approach defines the arrival of the rain cells within a rain storm by a point cluster process[7] represented by one of two common models, the Neyman-Scott process or the Bartlett-Lewis process. The former uses a Poisson distribution for the cluster centers, a random number of cells and a distribution of the distance of cell from the cluster center. The latter assumes a Poisson process for arrival of storms, and distributions for the number of cells per storm, intercell intervals, duration and intensity within a cell. For each characteristic, a statistical distribution must be assumed and numerous parameters identified. Alternatively, scale-invariant models[8] exploit the properties of multiplicative random cascades developed in turbulence theory. Observations of rainfall fields suggest that there are certain spatial and temporal properties that behave similarly over a range of scales differing only by a scale parameter. Thus a hierarchy of attributes (e.g., rainfall intensity) can be developed such that larger areas of lower intensity have embedded within them smaller areas of higher intensity and these in turn have even smaller areas of yet higher intensities. Applications of these models are design storms for engineering and water resources and continuous time hydrologic modeling.
