Extrêmes et multifractals en hydrologie : résultats, validations et perspectives

Extremes and multifractals in hydrology: results, validations and prospects. The methods of forecasting extremes are probably at a turning point. The predetermination of the extremes based on more or less sophisticated methods of probability law fitting remain sensitive to sampling uncertainties and errors deriving from the choice of probability law. For floods, hydrologists have developed methods of extrapolation by going beyond the (limited) streamflow time series to include historical data, geomorphological data, paleohydrological data, to include the regional context or by integrating knowledge of the rain rate stream-flow relation (e.g. the Gradex method or simulation methods). Thanks to the development of multifractals, new statistical physics techniques, are now available which permit - over wide ranges of scale - to easily handle extreme variability, intermittency and long range correlations in the hydrometeorological fields. For example, it has been shown that nonlinear cascade interactions over large ranges of scale generally lead to power law probability distributions, very rich in extremes. These developments have stimulated several national (in the framework of RIO2 and PNRH) and international (e.g. DSIG or PUB) projects to which the authors have contributed. It is timely to discuss where we stand.