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

Ezéchiel Obada

doi:10.11648/j.hyd.20160404.11

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.

Highlights

In the last three decades, climate change has been the subject of intensive scientific research
A stochastic basis for dealing with these shifts and trends is offered by Simple Scaling Stochastic (SSS) processes that are consistent with the assumption of hydroclimatic fluctuations on multiple time scales, a behavior that is none other than the Hurst phenomenon discovered by [5]
Among the disadvantages of range Statistic (R/S) Statistics proposed by Hurst, one can cite its sensitivity to the presence of shortterm persistence (STP)

Summary

Introduction

In the last three decades, climate change has been the subject of intensive scientific research. For [2], the falling and rising local trends can be regarded as climate changes or variations, considered by many as deterministic components in climatic time series According to this author, climate cannot be predicted in deterministic term under change [1,2,3]. A stochastic basis for dealing with these shifts and trends is offered by Simple Scaling Stochastic (SSS) processes that are consistent with the assumption of hydroclimatic fluctuations on multiple time scales, a behavior that is none other than the Hurst phenomenon discovered by [5] Pure randomness, such as in classical statistics, where different variables are identically distributed and independent, is sometimes a useful model, but in most cases it is inadequate [1]. According to [1,2], the fluctuations (i.e. change) in times series can be regarded as a manifestation of Hurst phenomenon

Study Location and Data

Estimation of Hurst Exponent

Aggregated Variance Method

Prediction with SSS

Findings

Conclusion