Introduction - Hydrologic Time Series Analysis: Theory and Practice - page 9

types of hydrologic data (Haan, 1977). Weekly cycles may be present in the
water-use data of domestic, industrial, or agricultural sectors; many times the
water-use time series contain both annual and weekly periodicities (Haan,
1977). In order to identify and quantify the periodicity in a hydrologic or
climatologic time series, the time scale should be considered less than a year
(i.e., month or six-month). The periodicity effect is not discernible in an
annual time series, and hence half-annual or monthly time series normally
encountered in hydrology can be used for analyzing the periodicity.
Lastly, the phenomenon of 'persistence' is highly relevant to the hydrologic
time series, which means that the successive members of a time series are
linked in some dependent manner (Shahin et al., 1993). In other words,
'persistence' denotes the tendency for the magnitude of an event to be dependent
on the magnitude of previous event(s), i.e., a memory effect. For example, the
tendency for low streamflows to follow low streamflows and that for high
streamflows to follow high streamflows. Thus, 'persistence' can be considered
synonymous with autocorrelation (O'Connel, 1977). Hurst (1951, 1957) was
the first person to describe 'persistence' comprehensively in his studies on a
reservoir design across the Nile River. The phenomenon was defined in terms
of a parameter called “Hurst's coefficient”, the average value of which is
approximately 0.73 for very large samples. However, its theoretical value for
an independent Gaussian process to which hydrologic series are assimilated
should be 0.5 (Capodaglio and Moisello, 1990). If the theoretical and the
observed values of Hurst's coefficient do not correspond, it is known as
“Hurst's phenomenon”. All the stochastic models that have been proposed to
represent hydrologic time series have attempted to include the persistence
phenomenon. However, with the time series records commonly available in
hydrology, it is virtually impossible to identify any long-term persistence in
the hydrologic time series (Capodaglio and Moisello, 1990). Chapter 4 deals
with various methods/tests used for identifying the above characteristics of a
time series.
1.7 Time Series Analysis vis-a-vis Hydrology
In early days, the application of statistics in hydrology was restricted to only
surface water problems, especially for analyzing the hydrologic extremes
such as floods and droughts. However, during the past three decades or so, the
application of statistics in hydrology has expanded considerably to encompass
the problems of both surface water and groundwater systems, including
atmospheric systems. With such a broad domain coupled with the rapid
advancement in computer and data management technologies, statistics has
emerged as a powerful tool for analyzing hydrologic problems. Particularly,
time series analysis has become a major tool in hydrology in the era of
information technology. Today, besides the basic statistical analysis of
hydrologic time series, the applications of time series analysis in hydrological