On the Use of Simple Scaling Stochastic (SSS) Framework to the Daily Hydroclimatic Time Series in the Context of Climate Change

Abstract

Climate Change hypothesis pushed the scientific community to question the characteristics of the classical statistics such as mean, variance, standard deviation, covariance, etc. in the hydroclimatic field. Many studies have revealed that the climate has always changed and that these changes are closely related to the Hurst phenomenon detected in long hydroclimatic time series and in stochastic term which is equivalent to a simple scaling behavior of climate variability on the time scale. A new statistical framework taking into account the climatic variability is now applied. Most studies are at annual scale where variability at finer scales is not taken into account. This paper proposes to verify the validity of the new statistical framework at finer time scale: the daily time scale. Twelve (12) daily time series of flows, rainfalls and temperatures with 18,628 observations, each one, were studied. Four different methods, such as Rescaled range Statistic (R/S) method, R/S modified method, Aggregate Variances method and Aggregated Standard Deviation (ASD) were applied to determine the Hurst exponent (H). All methods lead to the conclusion that the investigated time series have a long-term persistence phenomenon. Contrary to annual time series where variability corresponds to a Simple Scaling Stochastic (SSS) process, the daily time series seem to correspond to a process having both a SSS component and a deterministic component.