Self-similar random fields and rainfall simulation

The theory of self-similar random fields is applied to the statistical description and simulation of rainfall. Fluctuations in rainfields measured by a high resolution weather radar covering a 15 km square are shown to satisfy the condition of self-similarity. The probability density function of the logarithm of the breakdown coefficients (defined as the ratio of two field means, each computed at different resolutions) of the rainfall fluctuation field generally belongs to the class of infinitely divisible distributions. The theoretical framework for scaling self-similar fields is presented and related to results from alternate frameworks, presented in the literature. A simple procedure for the parameterization and modeling of the experimentally measured probability density function is presented. The obtained generator is then used for rainfall simulation by multiplicative cascades. Simulated results exhibit a good statistical and visual agreement with the measured data.