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.

[1]  Witold F. Krajewski,et al.  Recent advances in rainfall modeling, estimation, and forecasting (95RG00338) , 1995 .

[2]  Scale Similarity for Random Fields , 1969 .

[3]  Novikov,et al.  Infinitely divisible distributions in turbulence. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[4]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[5]  B. Mandelbrot,et al.  Fractal properties of rain, and a fractal model , 1985 .

[6]  Shigeo Kida,et al.  Log-Stable Distribution and Intermittency of Turbulence , 1991 .

[7]  Merab Menabde,et al.  Multifractal characterization of rain fields with a strong orographic influence , 1996 .

[8]  D. Schertzer,et al.  New Uncertainty Concepts in Hydrology and Water Resources: Multifractals and rain , 1995 .

[9]  Anthony B. Davis,et al.  Multifractal characterizations of nonstationarity and intermittency in geophysical fields: Observed, retrieved, or simulated , 1994 .

[10]  D. Lavallée.  Multifractal analysis and simulation techniques and turbulent fields , 1991 .

[11]  Jensen,et al.  Erratum: Fractal measures and their singularities: The characterization of strange sets , 1986, Physical review. A, General physics.

[12]  Shaun Lovejoy,et al.  Generalized Scale Invariance in the Atmosphere and Fractal Models of Rain , 1985 .

[13]  D. Schertzer,et al.  Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes , 1987 .

[14]  Edward C. Waymire,et al.  A statistical analysis of mesoscale rainfall as a random cascade , 1993 .

[15]  Thomas M. Over,et al.  Statistical Analysis of Mesoscale Rainfall: Dependence of a Random Cascade Generator on Large-Scale Forcing , 1994 .