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


  • Joan Armengol
  • Sergi Sabater
  • Antoni Vidal
  • Francesc Sabater

Paraules clau:

River discharge, fractal dimension, Hurst exponent, fractional Brownian motion, persistence


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 1 954 to 1 988 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) . 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 dimensiono 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, 1 0.1 and 11.7 months which can be considered an expression of cycles of circa 7 and 1 1 years.