Statistical Characteristics of Hydrologic Time Series - Hydrologic Time Series Analysis: Theory and Practice - page 14

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Statistical Characteristics of
Hydrologic Time Series
Any hydrologic time series can be appropriately analyzed when knowledge
about the basic statistical characteristics of the data series itself is first
considered. Many time series analysis procedures are based on the assumptions
that the time series possess certain characteristics which, in fact, are not true
(Adeloye and Montaseri, 2002; Helsel and Hirsch, 2002; Rao et al., 2003).
The results of such analyses based on false assumptions may provide incorrect
and unreliable interpretations, or unnecessarily inconclusive. Therefore, it is
essential to know about the common characteristics of hydrologic time series,
which can help in selecting appropriate data analysis procedures for a given
hydrologic time series.
One of the most important tasks while analyzing any time series is to
describe and summarize the time series data in forms, which easily convey
their important characteristics. If we want to know expected chloride
concentration in rainfall at a location or spatial variability of infiltration rate
or expected flood for 100-year recurrence period, then it is required to
understand summary statistics of the underlying hydrologic data series. Key
statistical characteristics often described include: a measure of the central
tendency of the data, a measure of spread or variability, a measure of the
symmetry of the data distribution, and perhaps estimates of extremes such as
some large or small percentile (Snedecor and Cochran, 1980; Upchurch and
Edmonds, 1991). This chapter discusses various methods for analyzing
hydrologic time series data. In this chapter, important statistical characteristics
of hydrologic time series are discussed, together with the salient measures for
evaluating the performance of water resources systems.
It is worth explaining the concept behind two basic terms of statistics
called 'population' and 'sample' in order to refresh the memory of the readers.
According to Helsel and Hirsch (2002), the data about which a statement or
summary is to be made are called 'population' or sometimes 'target population'.
Examples of population might be major ion concentrations in all waters of an