Using the rescaled range analysis for the study of hydrological records: The river Ter as an example

Water discharges into the Ter river have a strong influence on the water chemistry and on the dynamics of benthic cornmunities. For this reason, the temporal pattems followed by monthly runoff from 1954 to 1988 have been studied. From a statistical point of view, discharges show a very regular seasonal cycle, but in practice, climatic events introduce a source of variability on runoffs. To determine whether the series of 420 monthly discharges fluctuates with sorne regularity or at random, a rescaled range analilsis was made. The persistence (H) of the series of discharges was measured by the equation R / S = (T / 2)^H . In fact, H is a measure of the existence of clear trends or periodicities in the records of persistent stocastic processes. An additional measure of the persistence was obtained by means of the relationship D = 2 - H, where D is the local fractal dimension. For comparative reasons, a random series of the same length, mean and standard deviation was generated and analysed in the same way as the Ter discharges were. The results were H = 0.68 and D = 1.38 and H = 0.44 and D = 1.52, for the Ter data and for the random series respectively. These results show that the simulated series is a case of ordinary Brownian motion while the Ter discharges series has an intermediate value of persistence. Because of the value of H in the Ter series, there are periods whose values were estimated by the autocorrelation function and the periodogram of the series. The results show the existence of short fluctuations of 3, 6 and 12 months deterrnining the seasonality of the annual cycle, and large fluctuations with periods of 5.5, 8.6, 10.1 and 11.7 months which can be considered an expression of cycles of circa 7 and 11 years.