Introduction - Hydrologic Time Series Analysis: Theory and Practice - page 4

2005; Jha and Peiffer, 2006; Jha, 2010). The “think globally, act locally”
slogan of the late 1980s reminds us of our professional attitudes to and scientific
responsibilities for environment (nature) in general and freshwater resources
in particular, which must not be forgotten. Following holistic and
multidisciplinary approaches as well as using modern concepts and tools/
techniques, water scientists and engineers must make sincere and sustained
efforts to improve their understanding about hydrologic/hydrogeologic
processes and their linkage with our ecosystems; thereby improving both the
process and product. It is worth mentioning that the existing tools and
technologies, irrespective of their sophistication, will not eliminate the need
to reach conclusions and make decisions on the basis of incomplete and
uncertain data, and scientific knowledge (Loucks and van Beek, 2005). In
other words, the importance of professional judgement and that of research,
development and education in the planning and management of water resources
must not be undermined amidst increasing popularity and reliance on new/
emerging tools and technologies in the 21 st century.
1.2 What is Time Series?
The term time series is defined as “a sequence of values collected over time
on a particular variable” (Haan, 1977). A time series can consist of the values
of a variable observed at discrete times, averaged over a given time interval,
or recorded continuously with time. It may consist of only deterministic events,
only stochastic events, or a combination of deterministic and stochastic events.
Generally, a hydrologic time series is composed of a stochastic component
superimposed on a deterministic component (Haan, 1977; Shahin et al., 1993).
The deterministic component can be classified as a trend, a jump, a periodic
component, or a combination of these (Haan, 1977). The time intervals for
most hydrologic time series are hour, day, week, month, season or year. Data
in business, economics, engineering, environment, medicine, earth sciences,
hydrology, climatology, meteorology and other areas are often collected in the
form of time series. Some examples of the general time series are share prices
on successive days, company profits in successive years, and sales figures in
successive weeks/months/years; while the examples of hydrologic time series
are hourly/daily/monthly/annual temperature (air or water) readings,
precipitation in successive days/weeks/months/years, hourly/daily/monthly/
annual evaporation or evapotranspiration readings, hourly/daily/monthly/annual
soil moisture, hourly/daily/weekly/monthly/annual streamflow or river-stage
readings, hourly/daily/weekly/monthly/annual groundwater-level readings,
hourly/daily/weekly/monthly/annual tide-level readings, daily water
consumption in domestic, industrial or agricultural sectors, etc.
Furthermore, the realization of a process is the outcome of an experiment
in which the process is observed, and hence a single time series is known as
a realization (Shahin et al., 1993). The term ensemble denotes a collection of