3.2.2 Multi-temporal correlation
The negative values of the multi-temporal components were eliminated
with the help of equivalent substitution. Subsequently, double
cumulative curves were plotted for the multi-temporal components of
runoff and sediment discharge to study their multi-temporal
correlations, detailed evolution, and structural breaks. The double
cumulative curves of the multi-temporal components are shown below.
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Figure 5
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From Figure 5:
(1) Higher goodness of fit is noted in the runoff-sediment discharge
double cumulative curves of the IMF1 and IMF2 components. The
corresponding R2 values are 0.9996 and 0.9995,
respectively. The curve of IMF3 shows structural breaks in 1978, 1989,
2001, and 2005, and that in 2005 was the most prominent. Similarly,
structural breaks were noted in 1994, 1997, and 2001 for the curve of
IMF4, and the most prominent occurred in 2001. Furthermore, the double
cumulative curve of the RES component demonstrated that the runoff and
sediment discharge showed consistent variation macroscopically. In
short, the runoff-sediment discharge double cumulative curves were
different at different time scales. At some time scales, more distinct
structural breaks were present, indicating significant variation in the
runoff-sediment discharge relationship.
(2) The slopes of the trendlines for the multi-temporal components
declined gradually. This suggests that, microscopically, the components
had different amplitudes and fluctuations. Local characteristics of the
runoff and sediment discharge variation became observable only when the
components were analyzed separately. Thus, different slopes were found
for the trendlines of different double cumulative curves and the
runoff-sediment discharge correlations varied at different time scales.
For the IMF1 and IMF2 components, higher goodness of fit was observed in
their double cumulative curves. However, lower goodness of fit was noted
for the curves of the IMF3 and IMF4 components. This indicated that
medium- and high-frequency components exhibited stronger runoff-sediment
discharge correlations, whereas low-frequency ones demonstrated weaker
correlations. Additionally, the RES component reflected the macroscopic
variation of water and sediment systems. Reasonable goodness of fit was
observed for its double cumulative curve, demonstrating a relatively
strong runoff-sediment discharge correlation at the macroscopic scale.
Hence, the characteristics of the macroscopic variations in the runoff
and sediment discharge reflected by the RES component should be examined
to study the runoff-sediment discharge relationship and its evolution.
(3) Overall, some points of structural breaks on the microscopic scale
in the runoff-sediment discharge double cumulative curves of the
multi-temporal components appeared as ordinary points on the macroscopic
scale in the curve of the raw series. Hence, accurate identification of
structural break points is closely related to the time scales employed
during the analysis. When the raw series was examined, characteristics
of the macroscopic scale may bury or neutralize those of the microscopic
scale. Thus, when structural breaks are concerned, more attention should
be paid to the details. For relatively complex raw series, medium-
and/or high-frequency modal components can be utilized to study the
runoff-sediment discharge relationships and their detailed evolution.
Research on runoff-sediment discharge relationships can focus on
relevant short- and/or medium-term observations. When the relationships
show change and information (for example, years), structural breaks have
to be determined and low-frequency components can be employed.