MULTIFRACTAL ANALYSIS AND MODELING OF RAINFALL AND RIVER FLOWS AND SCALING, CAUSAL TRANSFER-FUNCTIONS

River flows have been known to be scaling for over 40 years and scalin g notions have developed rapidly since the 1980s. Using the framework of universal multifractals and time series of rainfall and river runof f for 30 French catchments (basin sizes of 40 km(2) to 200 km(2)) from 1 day to 30 years, we quantify types and extent of the scaling regime s. For both flow and rain series, we observed a scale break at roughly 16 days, which we associate with the ''synoptic maximum''; the time s cale of structures of planetary spatial extent. For the two scaling re gimes in both series, we estimate the universal multifractal parameter s as well as the critical exponents associated with multifractal phase transitions. Using these exponents, we perform (causal) multifractal time series simulations and show how a simple (linear) scaling transfe r function can be used to relate the low-frequency rainfall series to the corresponding river flow series. The high-frequency regime require s nonlinear transforms.