Multifractal modelling of floods

Nowadays, an efficient modelling and forecasting of river runoff phenomena remains to be a rather unresolved issue in geophysics, since the river runoff reflects not only the precipitation input but also complex interactions between diverse basin factors and climatic changes that strongly modify this input. Furthermore, all involved processes occur over a wide range of space and time scales. Resulting discharge data are highly irregular, difficult to measure, and even more difficult to model. These complexities lead to a situation when major floods that surprise society are still frequent and essentially harmful. The extreme variability over a wide range scales suggests to proceed to a multifractal analysis of the river runoff This paper reviews the present state of the art of scaling analysis and models of river flow as well as emphasizes some general requirements and challenges to make such modelling more effective. Not only the main multifractal parameters were estimated for daily and monthly river discharges of various catchments during the last century, but also the critical statistical moment order qD. The latter is the exponent of the algebraic fall-off of the discharge statistical distribution. As a consequence, for large enough discharges, the probability of having a discharge 10 times larger will be only 10(-qD) times smaller. Seasonal periodicity is another important feature to be taken into account, which unfortunately have been overlooked in earlier multifractal studies. In particular, we discuss a simple discharge model that is based on stochastic multiplicative cascades with re-ordered singularities to take into account seasonal effects. This opens anew prospective to develop a unified understanding of river basin processes in space and time, in particular for flood forecasting and prediction.