Journal of Applied Sciences

Year: 2005 | Volume: 5 | Issue: 1 | Page No.: 122-126
DOI: 10.3923/jas.2005.122.126

Determination of Sudden Changes in Time Series of Yesilirmak River-durucasu Water Quality Records

Ahmet Kurunc, Kadri Yurekli and Engin Yurtseven

Abstract: A variety of methods and statistical tests are being used to identify existence of trends in time series of water quality parameters. In this study, it was attempted to identify trends and sudden changes for selected water quality parameters at the Yesilirmak River-Durucasu monitoring station. For this purpose, time series of grouped time periods, which do not exhibit inhomogeneity in median and variance values among years, were constituted for each water quality parameter using graphical methods and non-parametric tests. Considering test results, even though different time periods were observed for each water quality parameter, in general, two sudden changes in time series of most water quality parameters were obtained in 1989 and 1998.

Keywords: trend yesilirmak river, Water quality and non-parametric test

INTRODUCTION

There is an increasing need to assess trends in water quality to provide not only a warning of the rates of water-resource degradation, but also knowledge of causal relationship to effectively manage the water resources. It is important to describe the amount or rate of that change, in terms of changes in some central value of the distribution such as mean or median^[1]. Trend analyses are used to determine whether the concentrations of a water quality parameter have consistently increased or decreased during a particular time period^[1-4].

In this study, water quality monitoring records (time series) in each grouped time period which do not produce visual and statistically important variation in median and variance values among years within each grouped period were examined for trend. Therefore, the study on the trend analysis of Yeşilirmak River-Durucasu water quality data has two aims: (I) by using non-parametric statistical tests, to detect time periods for each water quality parameter which do not exhibit inhomogeneity in median and variance values among years within grouped period but presents inhomogeneity in median and variance values between grouped periods and (ii) to identify trends and sudden changes within and between time series of grouped time periods for each water quality parameter.

MATERIALS AND METHODS

Description of study area and data: The Yeşilirmak Basin is one of the twenty-six major basins in Turkey. The river in the basin originates north of Sivas, flows approximately 519 km and reaches to the Black Sea. The headwaters of the river and most of its tributaries originate in the mountains that form the eastern and southern boundaries of the basin. The major tributaries to the Yeşilirmak River are Kelkit, Cekerek, Corum Cat and Tersakan Streams^[5].

Upstream of Hasan Ugurlu Dam and 33 km downstream of city of Amasya at Durucasu Hydroelectric Power Station of the Yeşilirmak River, there is a monitoring station, where the General Directorate of Electric Power Research Survey and Development Administration (EIE) measures water flow and takes water samples once every month. The geographic coordinate of the water quality monitoring station is 40° 44' 40'' N latitudes and 36° 06' 43'' E longitudes. The drainage area of the monitoring station is about 21,650 km².

Among the water quality parameters measured by EIE at Durucasu monitoring station are water specific conductivity (EC) in μS cm^-1, sodium (Na⁺), potassium (K⁺), calcium+magnesium (Ca²⁺+Mg²⁺), bicarbonates (HCO₃¯), chlorides (Cl¯) and sulfates (SO₄²¯) in mg L^-1. The records for these parameters available for the analysis as presented in this study are on a monthly basis for the period 1984-2001.

In addition to these water quality parameters, calculated Sodium Adsorption Rate (SAR) is also used in this study. The drainage area of the monitoring station is about 21,650 km² (Fig. 1).

Confirmatory data analyses: In this study, nonparametric tests including Kruskal-Wallis (to test median homogeneity) and Bartlett’s statistics (to test variance homogeneity) were used to detect time periods for each water quality parameter which do not exhibit inhomogeneity in median and variance values among years within a grouped period but presents inhomogeneity in median and variance values between grouped periods.

Kruskal-Wallis tests the hypothesis that the different samples in the comparison were drawn from the same distributions or from distributions with the same median. The critical value of the Kruskal-Wallis (KW) can be calculated using the following formula^[6]:

In equation (1); N is the total sample size, n is the sample size of the ith group, k is the number of groups and is the mean rank of the ith group.

Bartlett’s test is used to test if k samples have equal variances. The basic idea for this test is that the natural log of the variance is calculated for each group and then these are averaged. The variances are also averaged across groups. The average of the natural logs of the individual variances is subtracted from the natural log of the average variable. The critical value of the Bartlett’s (B) can be calculated using the following formula^[6]:

In equation (2); is the variance of the ith group and is the pooled variance. The pooled variance, a weighted average of the group variances, is defined as:

For both Kruskal-Wallis and Bartlett’s statistics to test median and variance homogeneity within time series of grouped time periods for each water quality parameter, n is 12 (monthly data) and N is multiplicative of 12 depending on the number of year(s) in a grouped time period since there are 12 water quality records in a year for each parameter. If the P value is 0.05, there is a statistically significant difference among the variances at a 95% confidence interval.

The tested time series of possible time periods were chosen for each water quality parameter considering cumulative graph. If there is a statistically significant difference in median and/or variance values among years in time series of a possible time period decided from cumulative graph, then an appropriate time series of a new time period sequence which do not exhibit inhomogeneity (p>0.05) in median and variance values is selected by removing one or more year of monthly data from beginning or end of the selected possible time period. Therefore, time series of grouped time periods for each water quality parameter were constituted in this study when the time series of each grouped time period for each water quality parameter did not exhibit inhomogeneity in median and variance values among years within grouped period. In addition, existence of statistical difference (p<0.05) in median and/or variance values of time series between grouped time periods in each water quality parameter was tested by Kruskal-Wallis and Bartlett’s statistics, respectively.

Trend analysis: For time series of grouped time periods in each water quality parameter which do not exhibit inhomogeneity in median and variance values among years within grouped period, a nonparametric, Kendall’s tau test can be applied for detecting monotonic trend or change (gradual or sudden). The tau value is a measure of the correlation between the time series and time period. In this report, a trend was considered to be significant if the P value was less than or equal to 0.05 which represents a 95% confidence level. The Kendall correlation coefficient tau is defined as^[7]:

As with other types of correlation coefficients, tau can only take on values between -1 and 1, its sign indicates the sign of the slope of the relationship and the absolute value indicates the strength of the relationship. Unless otherwise noted, all statistical tests were performed at 0.05 (95%) significance level.

RESULTS AND DISCUSSION

Confirmatory data analysis: Statistical test results for Kruskal-Wallis and Bartlett’s test to observe time periods of time series, which do not exhibit inhomogeneity in median and variance values among years within grouped period for all water quality parameters are presented in Table 1. As results of these nonparametric tests within time series of grouped time period, only five time periods for EC (1984-1988, 1989-1991, 1992-1997, 1998 and 1991-2001) and HCO₃¯ (1984, 1985-1988, 1989-1997, 1998 and 1999-2001), four time periods for K⁺ (1984-1988, 1989-1993, 1994-1997 and 1998-2001), SO₄²¯ (1984, 1985-1988, 1989-1990 and 1991-2001), Ca²⁺+Mg²⁺ and SAR (1984-1988, 1989-1997, 1998 and 1999-2001) and two time periods for Na⁺ and Cl¯ (1984-1988 and 1989-2001) of which time series did not exhibit inhomogeneity in both median and variance values were observed. It was really interesting to see that for most of these water quality parameters, the first 5 year (1984-1988) period presented no significant evaluation in the median and variance values. In comparison, the time period of 1998 presented a significant difference from the previous (1984-1997) and following (1999-2001) time periods for most water quality parameters including EC, Ca²⁺+Mg²⁺, HCO₃¯, Cl-and SAR. This may due to considerable high fluctuation in discharge in 1998.

Considering 18-year of time period, Kruskal-Wallis test results showed that there was significant differences in times series of all water quality parameters. This conclusion was also confirmed by Bartlett’s test for Na⁺, K⁺, HCO₃¯ and SAR. There were two unusual cases in nonparametric tests of times series. Even though there was no inhomogeneity in median values among years in time series of 1994-1997 period for K⁺, variance value for 1995 showed a significant difference from median values of other years in time period. Similarly, there was no inhomogeneity in variance values among years in time series of 1989-2001 period for Cl¯ but median value for 1998 showed a significant difference from median values of other years in time period (Table 1).

In order to confirm these results, Kruskal-Wallis and Bartlett’s test were also applied to show inhomogeneity in median and variance values between time series of grouped time periods for each water quality parameter (Table 2). For this reason, time series in a grouped time period for a parameter were compared with the following time series of grouped time period for the same parameter. Kruskal-Wallis and/or Bartlett’s test showed that there were significant differences (inhomogeneity) between time series of grouped time periods for each parameter. Therefore, the grouped time periods for each water quality parameter (Table 1) can be used for the trend analysis.

Trend analysis: Kendall’s tau test results were presented in Table 1 (within time series of grouped time periods) and Table 2 (between time series of grouped time periods). Considering 18-year of time period, Kendall tau test results showed that there was an increased trend in times series of EC, Na⁺, K⁺, Cl¯, SO₄²¯ and SAR whereas not a increased or decreased trend in times series of Ca²⁺+Mg²⁺, HCO₃¯ was observed. For the time series of grouped time periods, which did not exhibit inhomogeneity in median and variance values among years for all water quality parameters, not a significant trend was observed except time series in 1998 for HCO₃¯ (decreased trend) and for SAR (increased trend) (Table 1). Monthly measured values of water quality parameters and their trend lines for the grouped time periods were demonstrated in Fig. 2. The slope of the trend lines for time series of each grouped time period in Fig. 2 represents the magnitude of Kendall’s tau value from Table 1. In some cases, even though there were inhomogeneity in median and/or variance values between two time series of grouped time periods (for EC the time periods of II-III and, IV-V; for K⁺ and SAR the time periods of II-III and III-IV; for Ca²⁺+Mg²⁺ and SO₄²⁺ the time periods of III-IV; for HCO₃-the time periods of III-IV and IV-V), not a significant trend was observed between these data series (Table 2). In general, considering the nonparametric test results for all water quality parameters, the dates of sudden changes were occurred in 1989 and 1998.

Nevertheless, some socio-economic evolution in the Yeşilirmak river basin may explain the dates of changes and tendencies. After nineties, the increase in industrialized and urbanized areas in addition to animal husbandry without any wastewater treatment and the development of roads and airports causes pollution by the runoff and leaching of water-proof areas and degrades the Yeşilirmak river water quality.

Similarly, abusive use of mineral fertilizers, soil degradation and rotation cropping system were very important in the basin and have led to a slight increase in concentration of some water quality parameters.

REFERENCES