Introduction - Hydrologic Time Series Analysis: Theory and Practice - page 8

from different samples do not change except due to sampling variations. A
time series is said to be strictly stationary if its statistical properties do not
vary with changes of time origin. A less strict type of stationarity, called weak
stationarity or second-order stationarity , is that in which the first- and second-
order moments depend only on time differences (Chen and Rao, 2002). In
nature, strictly stationary time series does not exist, and weakly stationary
time series is practically considered as stationary time series.
There are many ways by which changes in the hydro-meteorological
series can take place. A change can occur gradually (known as 'trend') or
abruptly (known as 'step change' or 'jump'), or may take more complex form
(Shahin et al., 1993). A 'trend' is defined as “a unidirectional and gradual
change (falling or rising) in the mean value of a variable” (Shahin et al.,
1993). A time series is said to have trends, if there is a significant correlation
(positive or negative) between the observed values and time. Trends and shifts
in a hydrologic time series are usually introduced due to gradual natural or
human-induced changes in the hydrologic environment producing the time
series (Haan, 1977; Salas, 1993). Gradual or natural changes in hydrologic
variables could be caused by a global or regional climate change, which
would be a representative of changes occurring over the study area. Changes
in the observed variables that may not be able to be extrapolated over a study
area could be caused by a gradual urbanization of the area surrounding the
monitoring site, changes in the method of measurement at the monitoring site,
or by moving the monitoring site even a short distance away. 'Step changes'
or 'jumps' in a time series usually result from catastrophic natural events such
as earthquakes, tsunami, cyclones, or large forest fires which quickly and
considerably alter the hydrologic regime of an area. The man-made changes
such as the closure of a new dam, the beginning or termination of groundwater
pumping, or other such developmental activities may also cause jumps in
some hydrologic time series (Haan, 1977). Jumps can be either positive or
negative. The 'jump' or 'step change' is usually noted in the overall record at
a monitoring site, but this information is not always presented with the site's
data series. Thus, the variables that appear to have a trend may actually just
represent a change in climatological or hydrological conditions near the
monitoring site. Under such conditions, the affected climatological data should
be modified so that the values are better representative of the study area as a
whole (Hameed et al., 1997). A key element in this process is the ability to
demonstrate whether a change or trend is present in the climatological data
series and to quantify this trend, if it is present.
'Periodicity' is another characteristic of time series (natural hydrologic
time series), which represents a regular or oscillatory form of movement that
is recurring over a fixed interval of time (Shahin et al., 1993). It generally
occurs due to astronomic cycles such as earth's rotation around the sun (Haan,
1977; Kite, 1989). Annual cycles are often apparent in rainfall,
evapotranspiration, streamflow, groundwater level, soil moisture and other