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mixed low flows. In the analyses presented in this chapter, characteristics of
low flows and temporal changes in their magnitudes were studied separately
for each of the three (annual, winter and summer) time scales.
10.3.3 STP- and LTP-like Serial Structures
The low flow time series could exhibit STP or LTP or no persistence at all. For
the investigation of STP, an AR(1) is assumed and therefore the statistical
significance of the first autocorrelation alone was assessed. Lag-1
autocorrelation values of annual, winter and summer low flow time series are
shown in Fig. 10.7. About 78 (22), 67 (33) and 59 (41) percent of annual,
winter and summer low flow time series were found positively (negatively)
autocorrelated. Thus, positive autocorrelations appear to dominate the low
flow regimes of RHBN stations. Out of the 49 stations, the number of stations
where annual, winter and summer low flow time series were found significantly
autocorrelated at 5% level is 8, 8 and 4, respectively. Though the number of
stations with significant autocorrelations at 5% level is not very large,
autocorrelation for many of the remaining low flow time series was found
marginally significant at 10% level (Fig. 10.7), suggesting that it is important
to consider the effect of serial dependence on trend significance.
Fig. 10.7. Lag-1 autocorrelations of (a) annual, (b) winter and (c) summer 30-day
low flows. For each case considered, upper and lower values of the 90%
confidence interval are shown using horizontal dashes. The autocorrelations
that were found significant at the 5% level are circled for clarity. Station indices
(1 to 49) are the same as shown in Fig. 10.5.
The presence of LTP was investigated by estimating Hurst exponent
H (Hurst, 1951). The 0.5 < H < 1 range corresponds to a persistent process,
0 < H < 0.5 range corresponds to an antipersistent process and H = 0.5
corresponds to a purely independent process in an asymptotic sense. Several
methods have been developed to estimate the Hurst exponent (Taqqu et al.,
1995; Doukhan et al., 2002). However, five selected techniques were applied
in this study: (1) rescaled adjusted range statistic (RARS) (Mielniczuk and
Wojdyllo, 2007), (2) aggregated standard deviation (ASD) (Koutsoyiannis,
2003, 2006), (3) FARIMA ( p , d , q ) modelling approach (Hosking, 1984),
where p and q respectively stand for the number of autoregressive and moving
average parameters assumed here not greater than one and d = H - 0.5 is the
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