Modelo Multifractal Aplicado al Riego

Abstract

We define the binomial multifractal distribution as an expression of a law of small numbers. We studied a form of evaluation or design of a distribution system in an irrigation district by determining its conduction capacity with the desired flexibility knowing the following parameters: flow, frequency, and irrigation time. The method consists of the approximation of the binomial distribution through the Gaussian, an inverse relation of probability, two estimations of Gaussian parameters, and the application of the multifractal distribution. We present the mathematical reformulation of Boltzmann relation in the statistical mechanics, which gives origin to the multifractal model. In particular, we illustrate its application in the problems of irrigation, pointing out that it is also possible to apply it to multifractal models: variogram, exponential, gamma, and Gaussian.