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hydrological homogeneous regions or on the basis of Canadian climatic regions
and their plausible subdivisions such as those studied in Plummer et al. (2006)
and Mladjic et al. (2011).
10.4 Concluding Remarks
In this chapter, a framework of trend analysis is outlined and importance of
various fundamental items (like the distributional assumptions and type of
trend model, assumptions about the serial structure of the hydrological time
series and the influence of cross correlations) is discussed for performing a
sound and comprehensive analysis of trends in a given watershed/region. The
influence of serial dependence on the performance of the MK test is studied
through Monte Carlo simulations by generating and testing time series of
known serial structures of type AR(1) and FARIMA in order to establish
general benchmarks. This is followed by a case study on analysis of observed
annual, winter and summer 30-day low flows at selected stations, with longer
records, included in the Canadian RHBN in order to explore sensitivity of
trend significance to STP- and LTP-like serial structures. The choice of 30-
day low flows is made, assuming that longer duration low flow indicators are
more likely to reflect the influence of basin storage in terms of persistence
compared to those of short duration and high flow indicators. For the analysis
of observed low flows, the MMK1 and MK-BBS tests to address the influence
of STP on trend significance and the MKS and ALRT tests to address the
influence of LTP on trend significance were used. For comparison purposes,
the original MK test was applied assuming no serial dependence within
observations. The results of simulated and observed data suggest considerable
influence of serial dependence on trend significance; it means it is very less
likely to find significant trends in the presence of STP- and LTP-like serial
structures. The implication of this finding is that the MK test, if applied with
the independence assumption, will suggest trends more (less) frequently if
positive (negative) autocorrelations prevail in a hydrological gauging network.
For example, the results of simulations suggest that in the presence of a strong
LTP, there are more than 50% (60%) chances that the original MK test would
suggest a significant trend for a sample of size 50 (100), given that there is no
trend with the LTP assumption.
The above discussion and results of simulated and observed low flow
data suggest that it is important to systematically investigate and take into
consideration the influence of serial dependence on trend significance.
However, having recognized the role of STP- and LTP-like serial structures
on trend significance, the risk is that it is very likely that an investigator would
end up misdiagnosing a weak to moderate LTP as STP or no persistence at all.
This is due to the large uncertainty associated with the Hurst exponent estimated
from small size samples. In addition, this exponent also appears to be sensitive
to the method of estimation. Thus, longer observational records as well as
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