On Self-Similar Traffic Modeling of Water Resources in Arid Regions

Abstract

This paper reviews earlier work claiming that water-resource inputs closely follow a self-similar model, which is a manifestation of the more general multi-fractal behavior. Such claims have been repeatedly verified for wet terrains, but are still to be tested for arid regions. The paper presents a tutorial introduction to the concepts and phenomena of self similarity and multi-fractality for water-resource inputs. It also discusses the important implications of these phenomena for water consumption and storage. While conservative water consumption is an all-time virtue, it must be stressed and strictly imposed during periods of water shortages or droughts, which are more likely to be extended than to be brief. Periods of heavy rainfalls and floods should be optimally utilized to improve existing water storage levels. A mandatory policy for water conservation is strongly advocated by this paper, which contributes a scientific confirmation for the intuitively observed self-similarity phenomenon in arid regions. The paper presents a pilot and pioneering statistical study of a rainfall data set in a desert arid region. This study clearly indicates that this data set has a multi-fractal behavior, and that a mono-fractal model does not suit it. To the best of our knowledge, this result is the first published decisive confirmation for the self-similarity and multifractality phenomenon for rainfall data in arid regions.