Geology Reference
In-Depth Information
is a widely used approach in image processing (to assess phase shift of signals) and
earth science. Cross-correlation is a traditional approach to measure the similarity of
two signals or data series. The goal of applying this approach in modeling is to
determine whether the two signals or time series are correlated or not correlated.
This information could be used to select major and effective input series to make a
reliable model before actual modeling. If the cross-correlation value of two input
series is very high, one of the series could be redundant and could be eliminated
from the model. Cross-correlations also help to identify time series which are
leading indicators of other series or how much one signal is predicted to change in
relation the other. The cross-correlation test of two time-series data sets involves
calculations of the correlation coef
cient by time-shifting (particularly in case of
rainfall-runoff modeling) one data set relative to the other data set. Each shift is
called a
In other words it is the sampling period of the two time-series data
sets. Another distinct advantage of cross-correlation is that we could know the
cyclic nature of the original time series.
“
lag.
”
3.7 Conclusions
The objective of this chapter was to give key ideas underlying the data selection
techniques that have been used in the case studies included in this topic. We
describe theoretical consideration and mathematical background of the approaches
such as Gamma Test, Delta Test, AIC, BIC, PCA, and CA, along with a brief
insight into their distinctive advantages and disadvantages. Many published
examples cited effectively use these approaches in different dimensions of science
and technology. Traditional means of data selection such as data splitting approa-
ches and cross-correlation approaches are explained. In the next chapter we shall
describe the state-of-the-art data-based models that are used in conjunction with the
above-mentioned data selection methods for reliable modeling of hydrological
processes.
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