Analysis of the Long-Term Variations of the Stream Flow Regime

To achieve accurate investigations of the long-term changes in the SF regime, the statistical analyses should be performed using lengthy periods (i.e. 50 years or more) (Kundzewicz & Robson, 2004; Walling & Fang, 2003).

The long-term variations analyses include an investigation of the changes in the hydrological variables describing the annual SF over the 50-year period from 1961 to 2010 along with testing their changes’ trend. Analyses were performed based on two time scales. The first is yearly and the second is the sub-periodic changes. The sub periods were reached by segmentation of the 50 years into 7 sub-periods via two methods: the direct segmentation and change-point test.

The work also includes an exploration of the variations in the monthly SF regime and the

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For the high and low SF, the assessment was performed with respect to the duration and magnitude as both parameters play an important role to understand the variations of SF regime (Mirabbasi et al., 2012).

Investigation of yearly duration of high SF comprises three levels, danger level, warning level and alert level while investigation of the yearly duration of low SF analysis was conducted at a single level, that when the SF drop below 14.5 m3_{/s, which is around 25%}

of the average SF over the study period.

3.5.2.1 Determination of Representative Hydrological Variables

The long-term variations in SF regime could be explored via SF features like magnitude, rate, frequency, duration, timing and rate of change. These features are generally applied in three circumstances: average, low and high flow. Several hydrological variables can be employed to investigate the variations in the features of SF (Moliere et al., 2009). In this research, the variations in SF were investigated depending on SF rate (discharge), which is the quantity of water passing through an identified location per of time (Poff et al., 1997; Richter, 1996; Yang et al., 2005).

Nine hydrological variables describing SF were selected to investigate the long-term changes of the Selangor River’s SF regime. The variables are mean annual stream flow (SF1), maximum annual stream flow over the sub-period (SF2), minimum annual stream flow over the sub-period (SF3), maximum monthly flow over a single year (SF4), minimum monthly stream flow over a single year (SF5), the deference between maximum and minimum stream flow (RA), SD, coefficient of variation (CV) and the Pluviometric Ratio (PR).

SD and CV are statistical measures of dispersion in a data series around its average; and the CV denotes the ratio of standard deviation to the SF1. The CV is employed in

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matching the amount of dispersion and variation among data series (Albrecher et al., 2010; Boik & Shirvani, 2009).

PR corresponds to the ratio between maximum and minimum SF, and it is indication of seasonal variability. When the PR value is close to 1, seasonal variability is minor, but when the value is above 1, seasonal variability rises directly (Laraque et al., 2007). The mathematical formula for RA and PR are as follow.

RA = SF4 – SF5 PR = SF4/SF5

The values of nine variables were calculated from the Q records at the Rantau Panjang station over a 50-year period from 1961 to 2010. Table 3.3 shows the nine variables and their measurement units.

Table 3.3: Hydrological variables utilized to describe the annual stream flow

# Var. Definition Unit

1 SF1 Mean annual stream flow m3_/s

2 SF2 Maximum annual stream flow over the sub-period m3_/s

3 SF3 Minimum annual stream flow over the sub-period m3_/s

4 SF4 Maximum monthly stream flow over a single year m3_/s

5 SF5 Minimum monthly stream flow over a single year m3_/s

6 RA The deference between maximum and minimum

annual stream flow m

3_/s

7 SD Standard Deviation m3_/s

8 CV Coefficient of variation ratio 9 PR The Pluviometric Ratio ratio

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3.5.2.2 Segmentation of the Study Period

To study and analyze the long-term changes in SF regime over long periods i.e. 50 years, the yearly variations may be not adequate to investigate the trend of long-term variations. For this cause, long periods could be segmented into short sub-periods, such as 7 or 10 years. The short sub-periods are commonly include consecutive years with comparable hydrologic features (Descroix et al., 2012).

The segmentation process could be carried out by many methods such as the Hidden Markov model, the Hubert model and the change-point test. The change-point method is a statistics test employed to find the date(s) at which a big change happens in a data series. The selected dates demonstrate a change in the mean or variance (Beaulieu et al., 2009; Rougé et al., 2012; Villarini et al., 2011). In literature, many approaches have been employed to check for the existence of change points in the data of long periods such as Bayesian inference, moving t-test and Pettit’s test (Descroix et al., 2012; Ma et al., 2008; Rougé et al., 2012; Xiong & Guo, 2004; Zheng et al., 2007).

In this research, the 50-year period from 1961 to 2010 was segmented into seven sub- periods by two techniques. The first is the change points using Pettit’s test, while the second method is direct segmentation method. The first technique entails selecting multiple change-points, as calculated using Pettitt's test. This technique leads to the segmentation of the study period into seven, non-identical sub-periods. The second method is direct segmentation in which the study period was divided into seven identical 7-year sub-periods. The sub-periods obtained in the two ways are presented in Table 3.4.

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Table 3.4: Sub-periods obtained via two segmentation techniques Sub-period No. Segmentation technique Change-point Direct 1 1961-1972 1961-1967 2 1973-1978 1968-1974 3 1979-1986 1975-1981 4 1987-1991 1982-1988 5 1992-1995 1989-1995 6 1996-2004 1996-2002 7 2005-2010 2003-2009