Potential of Multifractals for Water Resources Planners

The natural variability of water resources and the augmenting demand for water leads mankind to strongly interfere with the hydrologic cycle in attempts too ensure that water will be available in adequate quantity and quality, with a proper distribution in space and time. So, engineers will be often concerned with ambitious plans of flood control. Runoff predictions, such as the estimates of peak flows that are associated with a particular exceedence probability, form the basis for the design of most civil engineering works. Since river runoff phenomena reflect many complex interactions at different scales between diverse basin factors as well as meteorological and climatic fluctuations, that strongly modify the precipitation input, the prediction of a maximum expected water flow remain a rather unsolved issue. Indeed, as hydrologists often observed it, the probabilistic distribution of runoff is skew; however its mathematical form is far from being known, in particular its tails. As a consequence, the insufficient spillway capacity remains worldwide the second commonest cause of dam failure (after the foundation failure). Present communication demonstrates how the multifractal framework overcomes some present difficulties in the flood predictions within space and time domains. Moreover, our multifractal results reflect crucial changes in river regimes after dam construction, that may have drastic consequences for the spillway capacity. To consolidate our results, we use few millions of flow measurements at very different hydrological locations all over the World. The time-scale of the data ranges from a day to several centuries.