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series. The turning point test and the Kendall's rank correlation test were
applied for detecting trends, whereas the correlogram technique was used to
detect the periodicity. The harmonic analysis was done for identifying
significant harmonics. The series was then tested for stationarity and the
dependent part of the stochastic component was found to be expressed well by
the second-order autoregressive model. Therefore, the developed model
superimposed a periodic-deterministic process and a stochastic component.
The adequacy of fit was judged by the insignificant correlation and the normal
distribution of obtained residuals. It was concluded that the developed periodic-
stochastic model can be used for representing the time-based structure of the
irrigation requirement time series for paddy crops.
Wu et al. (1997) evaluated the efficacy of the time series analysis technique
to predict average water content in the soil profile and the water content at
different soil depths from the measurements made at a single depth. The
volumetric water content of a Zimmerman fine sand in Princeton, MN was
measured by TDR at six depths during the early 1993 growing season. The
time series made up of hourly measurements of soil water content was first-
order differenced to obtain stationarity. The differenced data were used to
conduct analyses in the frequency domain to evaluate the coherence and
cross-amplitude between two soil water content time series and were
subsequently fitted to the autoregressive moving average models to obtain
coefficients for the transfer function models in the time domain. The transfer
function models were then used to predict water contents at 50, 75 and 100 cm
depths and the average water content in the top 100-cm soil profile from the
measured water content at 25-cm depth. Overall, the predictions were
reasonable, with an increased accuracy as the separation distance from the 25-
cm depth decreased.
6.6 Concluding Remarks
Time series analysis has been used in a variety of fields in the past, such as
hydrology, climatology, geology, ocean engineering, seismology, etc. In this
chapter, however, the studies related to only hydrologic and climatologic time
series have been reviewed. It is clear from this review that precipitation and
streamflow are major hydrologic variables followed by temperature and surface
water quality, which attracted the attention of researchers from different parts
of the world for applying time series analysis techniques. The application of
standard statistical tests and the evaluation of some statistical tests has been a
major focus of applied research in this area. Comparatively, less number of
studies is reported wherein a new approach is developed or an existing approach
is modified to improve overall efficiency of some time series analysis
techniques. Furthermore, no study is reported to date which covers all aspects
(i.e., basic properties) of hydrologic/hydrogeologic time series analysis. Trend
detection by Kendall or seasonal Kendall test has been a major focus of most
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