MULTIFRACTAL ANALYSIS OF DAILY RIVER FLOWS INCLUDING EXTREMES FOR BASINS OF 5 TO 2 MILLION SQUARE KILOMETERS, ONE-DAY TO 75 YEARS

Multifractal analysis of the daily river how data from 19 river basins of watershed areas ranging from 5 to 1.8 x 10(6) km(2) from the conti nental USA was performed, This showed that the daily river flow series were multifractal over a range of scales spanning at least 2(3) to 2( 16) days. Although no outer limit to the scaling was found (and for on e series this was as long as 74 years duration) for most of the rivers , there is a break in the scaling regime at a period of about one week which is comparable to the atmosphere's synoptic maximum, the typical lifetime of planetary-scale atmospheric structures. For scales longer than 8 days, the universal multifractal parameters characterizing the infinite hierarchy of scaling exponents were estimated. The parameter values were found to be close to those of (small basin) French rivers studied by Tessier et al. (1996). The multifractal parameters showed no systematic basin-to-basin variability; our results are compatible w ith random variations. The three basic universal multifractal paramete rs are not only robust over wide ranges of time scales, but also over wide ranges in basin size, presumably reflecting the space-time multis caling of both the rainfall and runoff processes. Multifractal process es are generically characterized by first-order multifractal phase tra nsitions: qualitatively different behavior is shown for the extreme ev ents in which the probability distributions display algebraic fall-off s associated with (nonclassical) self-organized critical (SOC) behavio r. Using the observed flow series, the corresponding critical exponent s were estimated. These were used to determine maximum flow volume exp onents and hence to theoretically predict maximum flow volumes over ag gregation periods ranging from 2(3) to 2(16) days. These theoretical p redictions are based on four empirical parameters which are valid over the entire range of aggregation periods and compare favourably with t he standard (GEV) method for predicting the extremes, even though the latter implicitly involve many more parameters: three different expone nts for each aggregation period. While the standard approach is essent ially ad hoc and assumes independent random events and exponential pro bability tails (which, we show, systematically underestimate the extre mes), the multifractal approach is based on the clear physical princip le of scale invariance which (implicitly) involves long-range dependen cies, and which (typically) involves nonclassical algebraic probabilit ies. (C) 1998 Elsevier Science B.V. All rights reserved.