Multifractal Runoff Process and Influence of a Seasonal Periodicity

Nowadays, an efficient modeling and forecasting of river runoff phenomena remains to be a rather unresolved issue in geophysics, since the gauged river runoff reflects not only the precipitation input but also complex interactions between various basin factors and climatic changes that strongly modify this input. For present communication we use more then 1500 river runoff gauges located in six rather different hydrological zones of Russia. The time-scale of these monthly data-records is varying for different stations from several years to several centuries. First we intended to use standard Universal Multifractal methods in order to define the multi-scaling properties of this huge (i.e., more then a million data in total) hydrological database. Unfortunately, a S-shape behavior was systematically presented in the results, whereas scaling ideas would support a straight-line behavior. Since the river runoff phenomena for this part of Russia are strongly influenced by a snow-melting period, we consider that this very strong seasonal periodicity of the data may be responsible for the scale-braking behavior. Indeed, one of the important constraints of multifractal fields, such as the translation invariance, may have been easily destroyed. In order to illustrate this idea, we propose a very simplified multifractal model of river basin. This model helps not only to model a runoff process influenced by a seasonal periodicity, but also adequately reproduces changes in scaling regimes, i.e. the S-shape behavior observed in Nature.