Fractal Methods in Hydrology

Virtually all areas of hydrology have been deeply influenced by the concepts of fractality and scale invariance. The roots of scale invariance in hydrology can be traced to the early work of Robert E. Horton, R. L. Shreve and J. T. Hack on the topology and metric properties of river networks and of Henry Hurst on river flow. These early developments uncovered symmetries and laws that only later were recognized as manifestations of scale invariance. Lucien Le Cam, who in the early 1960s pioneered the use of multiscale pulse models of rainfall, provided renewed impetus to the scale-based models. Fractal approaches in hydrology have become more rigorous and widespread since Benoît Mandelbrot systematized fractal geometry and discovered multifractal measures. Professor Veneziano and collaborators have a longstanding interest in the area of scale-invariant methods, including the construction of scale-invariant processes, their properties and the inference of scale invariance from data. They have applied these methods to several areas of hydrology, including rainfall and rainfall extremes, fluvial erosion topography and flow through random porous media.