Trend analysis of streamflow in Turkey

Transcription

1 Journal of Hydrology 289 (2004) Trend analysis of streamflow in Turkey Ercan Kahya a, *, Serdar Kalaycı b a Istanbul Technical University, Civil Engineering Department, Hydraulics Division, Maslak, Istanbul, Turkey b Selçuk University, Civil Engineering Department, Konya, Turkey Received 10 December 2002; revised 27 October 2003; accepted 13 November 2003 Abstract This paper presents trends computed for the 31-year period of monthly streamflows obtained from 26 basins over Turkey. Four non-parametric trend tests (the Sen s T, the Spearman s Rho, the Mann-Kendall, and the Seasonal Kendall which are known as appropriate tools in detecting linear trends of a hydrological time series) are adapted in this study. Moreover, the Van Belle and Hughes basin wide trend test is included in the analysis for the same purpose. Homogeneity of trends in monthly streamflows is also tested using a procedure developed by Van Belle and Hughes. Thus, this study includes a complete application of both the Van Belle and Hughes tests for homogeneity of trends and basin wide trend (originally developed for trend detection in water quality data) on a hydroclimatic variable. As a result, basins located in western Turkey, in general, exhibit downward trend, significant at the 0.05 or lower level, whereas basins located in eastern Turkey show no trend. In most cases, the first four tests provide the same conclusion about trend existence. Use of the Seasonal Kendall, which involves a single overall statistic rather than one statistic for each season, is justified by the homogeneity of trend test. Moreover, some basins located in southern Turkey exhibit a global trend, implying the homogeneity of trends in seasons and stations together, based on the Van Belle and Hughes basin wide trend test. q 2003 Elsevier B.V. All rights reserved. Keywords: Climate change; Mann-Kendall test; Non-parametric tests; Streamflow variability; Trend analysis; Turkey 1. Introduction In general, observational and historical hydroclimatologic data are used in planning and designing water resources projects. There is an implicit assumption, so called stationarity implying timeinvariant statistical characteristics of the time series under consideration, in all water resources engineering works. Such an assumption can no longer be valid * Corresponding author. Tel.: ; fax: addresses: ercan.kahya@itu.edu.tr (E. Kahya); skalayci@selcuk.edu.tr (S. Kalaycı). if the presumed changes in global climate as a result of the increase of greenhouse gases in the atmosphere. This, of course, results in major problems (e.g. dislocation and inefficiencies) in regional water resources management. From a more specific perception, for example, floods are considered as an outcome of stationary, independent and identically distributed random process by hydrologists for a long time. Nevertheless some investigators (i.e. Cayan and Peterson, 1989; Lins and Slack, 1999; Jain and Lall, 2000) have reported evidence of trends (possibly due to anthropogenic influences) and long-term variability of climate /$ - see front matter q 2003 Elsevier B.V. All rights reserved. doi: /j.jhydrol

2 E. Kahya, S. Kalaycı / Journal of Hydrology 289 (2004) Among regional streamflow-trend studies in the world, Zhang et al. (2001) stated that monthly mean streamflow in Canada for most months decreased, with the strongest decrease in summer and autumn months, and there was almost no basin exhibiting upward trend. In contrast, Lettenmaier et al. (1994) presented the upward streamflow trend pattern, at its peak in midwinter, covering most of the United States with the exception of a small number of downtrends concentrated in the Northwest, Florida, and coastal Georgia. Lins and Slack (1999) came to similar conclusion studying streamflow trends calculated for selected quantiles of discharge. Lettenmaier et al. also stressed that the trend in streamflow are not fully parallel to the changes in precipitation and temperature due to a combination of climate and water management effects. However, Burn and Elnur (2002) indicated the similarities in trends and patterns in the hydrological variables and in meteorological variables at chosen locations in Canada, implying the relations between the two groups of variables. All previous studies regarding trends in surface climatic variables in Turkey concentrated on temperature and precipitation patterns. For example, Türkes et al. (1995) used various non-parametric tests to identify abrupt changes and trends in the long-term mean temperature of both individual stations and geographical regions in Turkey during the period They found that climate tended to be warmer in the eastern Anatolia and to be cooler particularly in the Marmara and Mediterranean regions using regional mean temperature series. Türkes (1996) worked with the area-averaged annual rainfall series during the period and pointed out that slightly insignificant decreases were generally observed over Turkey, particularly in the Black Sea and Mediterranean regions. Kadıoğlu (1997) examined trends in the mean annual temperature records during the period in the eighteen stations across Turkey and found insignificant increasing trends in the mean annual temperatures. He also indicated that a regional increase in mean minimum temperatures, which could be attributed to the urban heat island effect, appeared around His results are inconclusive for the existence of long-term trends. In contrast, Tayanç et al. (1997) found statistically significant cooling in mean temperatures mostly in northern Turkey and warming mostly in large urban locations. In the same context, Karaca et al. (1995) showed the urban heat island intensity in İstanbul although it is surrounded by the Black Sea and the Marmara Sea. To stress the importance of trend analysis of hydrologic variables (streamflow as the most attracting variable), in a watershed which is assumed not to be exposed to anthropogenic influences; the following explanations based on the work of Zhang et al. (2001) are presented. Under certain geomorphic conditions, the nature of river reflects the integrated watershed response to climatic forcing. This critical point was previously noted by Cayan and Peterson (1989); Kahya and Dracup (1993) in searching teleconnections between surface hydroclimatic variables and the large-scale atmospheric circulation. Since the geomorphologic evolution of watershed is quite slow in comparison with climate change, the detectable changes in the hydrologic regimes of stable, unregulated watersheds may be considered as the reflection of changes in climate. Consequently hydrologic variables might be used as indicators to detect and monitor climate change. Because of the review of major trend studies covering Turkey and the fact of streamflow being a privileged variable as stated earlier, a study regarding streamflow trend analysis in the geography of Turkey seemed to be an important necessity. The objective of this investigation is to document trend characteristics of Turkish streamflow data for evidence of climate change. 2. Data Monthly mean streamflow records compiled by EIE (General Directorate of Electrical Power Resources Survey and Development Administration) are used in this study. In most hydroclimatologic studies, a completely homogeneous data set has been rarely used. Thus, the common practice in most cases is to put forward reasonable criteria for the condition of homogeneity. For example, Lins (1985) included streamflow stations on watercourses where diversion amounts have been less than 10% of the mean flow and storage capacity amounted less than 10% of the mean annual runoff. In order to comply with the homogeneity condition, a total of 83 streamflow

3 130 E. Kahya, S. Kalaycı / Journal of Hydrology 289 (2004) gauging stations distributed over 26 river basins (Fig. 1) have been selected among more than 300 stations and from where there was no reported regulation or diversion in upstream. This data set is the same as used by Kahya and Karabörk (2001) who confirmed the homogeneity by checking out the data for man-made changes, such as jumps due to relocation of station, regulation or diversion due to the presence of dams or weirs. Table 1 presents the number of selected stations for the analysis among available stations in each basin as well as the basic features of river basins in Turkey. It should be recognized that there is a difficulty associated with differentiating between natural variability and trends. By taking the preceding arguments into consideration, we have not applied a test for homogeneity of streamflow records in this study. The majority of streamflow records include observations of 31 years spanning from 1964 to However, we were obligated to include some shorter records [Station 212 ( ); Station 1003 ( ); Station 1102 ( ); Station 2505 ( ) and Station 2507 ( )] in the analysis for the sake of at least having one data coverage in each basin. Hydroclimatologists are concerned with analysing time series by concentrating on differences in 30-year normals along the whole period of records. This is why the period of 30-year is assumed to be long enough for a valid mean statistic. It also amounts to describing hydroclimatic time series as non-stationary with local periods of stationary (Kite, 1991). The length of data set in our study, mostly 31 years, suffices the minimum required length in searching evidence of climatic change in hydroclimatic time series. Burn and Elnur (2002) stated that the selection of stations in a climate change research is substantial at the initial step and that a minimum record length of 25 years ensures validity of the trend results statistically. For the climatology of Turkey (readers are referred to Türkes (1996) for details); precipitation, the main component of runoff process, displays a considerable temporal and spatial variability in Turkey. Annual rainfall totals, in general, decrease from the coastal belts to the interior. Annual rainfall amount exceeds 1000 mm and reaches to national maximum of 2304 mm on far eastern of the coastline of the Black Sea where rainfall shows almost uniform distribution over time. Along the Mediterranean coast, the precipitation mostly occurs in the winter and the mean annual total of this region is above 800 mm. In the central Anatolia, as a result of being protected from the moisture bearing air masses, the range of mean annual precipitation totals are from 350 to 500 mm. Over the continental southeastern and eastern Anatolia, annual precipitation totals increase from south (400 mm) to north (800 mm). In the Marmara and Aegean Sea regions, annual precipitation totals vary from 600 to 800 mm. The Atlantic Ocean and the Mediterranean Sea are major sources of moist air masses, which cause precipitation during late autumn, winter and early spring over Turkey. These mid-latitude storms from the Atlantic are predominantly governed by the North Atlantic Oscillation (NAO) shown in Cullen and demenocal (2000). Significant relations between the NAO and Turkish surface climatic parameters (precipitation, streamflow, and temperature) have been recently shown by Karabörk et al. (2003). 3. Methodology The first work in this section is to rationalize the use of a group of methodological approaches, successfully applied in other disciplines, in a hydrologic variability study. Tests for trend have been of keen interest in environmental sciences during the final quarter of the last century. Unfortunately many existing water quality data in a region is not amenable to analysis by standard methods. The assumptions of classical parametric methods (i.e. normality, linearity, and independence) are mostly not satisfied by water quality data whose elements sometimes might be missing to some extent or censored (Van Belle and Hughes, 1984). These analysis difficulties motivated some investigators to compare existing trend methods and develop new methods to overcome the mentioned problems. But streamflow data set, compared to water quality data, have less similar problems including the length of records. Therefore it is worthwhile to consider the trend analysis techniques used in water quality studies when examining streamflow data for the same purpose. In the climatic and hydrologic literature, only one non-parametric method (almost always the Mann- Kendall) has been used in similar trend studies.

4 Fig. 1. Locations of streamflow gauging stations used in the study with their basins. Integer in circle indicates the basin identification number. E. Kahya, S. Kalaycı / Journal of Hydrology 289 (2004)

5 132 E. Kahya, S. Kalaycı / Journal of Hydrology 289 (2004) Table 1 Summary of major characteristics of basins in Turkey Basin number Basin name Available stations Selected stations Area of river basin ( 1000 km 2 ) Basin average height (m) Average precipitation (mm/year) Total streamflow (mm/year) 1 Meriç Marmara Susurluk Aegean Gediz Little Menderes Big Menderes West Mediterranean Middle Mediterranean , Burdur Lake Afyon , Sakarya West Black Sea Yesilırmak Kızılırmak Middle Anatolia , East Mediterranean Seyhan Hatay Ceyhan Euphrates , East Black Sea Çoruh Aras , Van Lake , Tigris Total Total Total Average Average Average In order to have more confidence on the existence of trend in a streamflow time series, we have decided to apply five different tests in this study. We assume that the existence of trend in a streamflow station should be approved by at least two methods. Similarly, Yu et al. (1993) utilized three different non-parametric trend tests (the Mann-Kendall, the Seasonal Kendall, and the Sen s T) and the Van Belle and Hughes tests to identify linear trends in water quality data. Alike techniques were applied to search trends in water quality data across a river basin (e.g. Kahya et al., 1998; Kalaycı and Kahya, 1998) and in lake water level data (e.g. Kalaycı et al., 2002) in Turkey. Yu and his collaborators compared the performances of these methods by using the Monte Carlo simulation for each selected sample size, n ¼ 3; 5, 9, and 15 years. For n ¼ 9 and 15, there are no significant differences in relative power between these methods. They came up with the same conclusion of Van Belle and Hughes (1984) that both the Sen s T and the Mann-Kendall (aligned rank methods) are asymptotically more powerful than intrablock methods such as the Seasonal Kendall. Among various widely used techniques, five non-parametric tests are selected to analyze linear trends in streamflow data over Turkey. All tests initially require rank transformation of the original data and then following usual parametric procedures. Brief descriptions of the techniques are briefly presented here. Readers are particularly referred to Van Belle and Hughes (1984); Yu et al. (1993) for the details.

6 E. Kahya, S. Kalaycı / Journal of Hydrology 289 (2004) Techniques for trend detection Sen s T test: This technique is an aligned rank method having procedures (Sen, 1968a,b) that first removes block (season) effect from each datum, then sum the data over blocks, and finally produce a statistic from these sums. The aligned rank test is more powerful than its counterpart (intrablock procedures) and is distribution free and not affected by seasonal fluctuations (Van Belle and Hughes, 1984). The original monthly data at a station are deseasonalized and then converted to the ranks to calculate the test statistic T whose distribution follows Nð0; 1Þ under the null hypothesis of no trend. If ltl. z a ; a trend exists in that station at the a level. Mathematical developments of the test are well given in Sen (1968a); Van Belle and Hughes (1984). Spearman s Rho test: A quick and simple test to determine whether correlation exists between two classifications of the same series of observations is the Spearman s rank correlations test. In this test, there is a significant trend only if the correlation between time steps and streamflow observations are found to be significant. Account of the test statistic z based on r s was not presented here, since it can easily be found in statistical books. For n (sample size).30, the distribution of r s will be normal, so that the normal distribution tables can be used. In thisp ffiffiffiffiffiffiffi case, the test statistic ðr s Þ is computed by z ¼ r s n 2 1: If lzl. z a at a significance level of a; then the null hypothesis of no trend (on the other word, values of observations are identically distributed) is rejected. Mann-Kendall test:this technique, commonly known as the Kendall s tau statistic, has been widely used to test for randomness against trend in climatological time series (Zhang et al., 2001). In this test, the null hypothesis H o states that the deseasonalized data ðx 1 ; ; x n Þ are a sample of n independent and identically distributed random variables (Yu et al., 1993). The alternative hypothesis H 1 of a two-sided test is that the distribution of x k and x j are not identical for all k; j # n with k j: The test statistic S is calculated with Eqs. (1) and (2) which S ¼ Xn21 X n sgnðx j 2 x k Þ ð1þ k¼1 j¼kþ1 8 9 þ1 if ðx j 2 x k Þ. 0 >< >= sgnðx j 2 x k Þ¼ 0 if ðx j 2 x k Þ¼0 >: >; 21 if ðx j 2 x k Þ, 0 ð2þ has mean zero and variance of S; computed by VarðSÞ ¼½nðn21Þð2n þ 5Þ 2 P t tðt 2 1Þð2t þ 5ÞŠ=18; and is asymptotically normal (Hirsch and Slack, 1984), where t is the extent of any given tie and P t denotes the summation over all ties. For the cases that n is larger than 10, the standard normal variate z is computed by using the following equation (Douglas et al., 2000). 8 9 S 2 1 pffiffiffiffiffiffiffiffi if S. 0 >< VarðSÞ >= z ¼ 0 if S ¼ 0 ð3þ S þ 1 >: pffiffiffiffiffiffiffiffi if S, 0 >; VarðSÞ Thus, in a two-sided test for trend, the H o should be accepted if lzl # z a=2 at the a level of significance. A positive value of S indicates an upward trend and a negative value indicates a downward trend. Seasonal Kendall test: This test can be used for time series with seasonal variation and does not require normality of the time series (Hirsch et al., 1982; Yu et al., 1993). This test is intended to assess the randomness of a data set X ¼ðX 1 ; ; X 12 Þ and X i ¼ðx i1 ; ; x in Þ; where X is a matrix of the entire monthly data over n years at a station. The test statistic is a sum of the Mann-Kendall statistic ðs; similar to that in Eq. (1)) computed for each month. The interpretation of the rest of the test is similar to that of the Mann-Kendall test. Sen s estimator of slope: If a linear trend is present, the true slope (change per unit time) can be estimated by using a simple non-parametric procedure developed by Sen (1968b). In computational procedures, the slope estimates of N pairs of data are first computed by Q i ¼ðx j 2 x k Þ=ðj 2 kþ for i ¼ 1; ; N; where x j and x k are data values at times j and k ðj. kþ; respectively. The median of these N values of Q i is Sen s estimator of slope. If there is only one datum in each time period, then N ¼ nðn 2 1Þ=2 where n is the number of time periods. If N is odd, then Sen s estimator is computed by Q median ¼ Q ðnþ1þ=2 and if N

7 134 E. Kahya, S. Kalaycı / Journal of Hydrology 289 (2004) is even, then Sen s estimator is computed by Q median ¼½Q ðnþ=2 þ Q ðnþ2þ=2 Š=2: The detected value of Q median is tested by a two-sided test at the 100(1 2 a) % confidence interval and true slope may be obtained by the non-parametric test Van Belle and Hughes homogeneity of trend test The Sen s T, the Mann-Kendall, the Seasonal Kendall, and the Spearman s Rho tests include an implicit assumption of trend homogeneity between seasons. Using an imaginary data set, Van Belle and Hughes (1984) demonstrated that the overall statistic indicates no trend although a trend is apparent for each season. As a result, an overall trend test at a station leads to an ambiguous conclusion when the trend, in fact, is heterogeneous between seasons. For this purpose, they suggest a preliminary test for homogeneity of trend based on the study of crossclassified data. The overall statistic ðx 2 totalþ is partitioned into two parts as x 2 total ¼ x 2 homogeneousþx 2 trend: The computation of these three chi-square terms mainly involves with a standard normal deviate ðzþ which is based on the Mann-Kendall statistic ðsþ for each season. For homogeneity in seasonal trends at a station, the following statistic is calculated. x 2 homogeneous ¼ x 2 total 2x 2 trend ¼ Xm ðz i Þ 2 2mð ZÞ 2 Z i ¼ i¼1 The values of ðz i Þ and ðzþ are calculated by S i pffiffiffiffiffiffiffiffiffi VarðS i Þ and Z ¼ 1 m ðm ¼ 12 for monthly dataþ X m Z i i¼1 ð5þ ð6þ where S i is the Mann-Kendall statistic for month i: Two possible cases are concerned: (a) if x 2 homogeneous exceeds the a level critical value for the chi-square distribution with ðm 2 1Þ degrees of freedom (df), the null hypothesis of homogeneous seasonal trends over time (referring to trends in the same direction) must be rejected; (b) if x 2 homogeneous does not exceed, then the calculated value for x 2 trend is referred to the chi-square distribution with df ¼ 1 to test for a common trend in all seasons. The chi-square statistics are computed from equations shown in Table 2 (not presented here) of Van Belle and Hughes (1984). The acceptance or rejection of the hypothesis can then be determined by comparing the computed values of x 2 station; x 2 season and x 2 station2season with the a level critical values in the standard chi-square table with ðk 2 1Þ; ðm 2 1Þ and ðk 2 1Þ: ðm 2 1Þ degree of freedom, respectively Van Belle and Hughes trend test for the general case In this section, an alternative approach to those given in the preceding sections is suggested to recourse if one wants to make a basin-wide statement about all possible trend features using a single method. Following to Van Belle and Hughes (1984), the data from several streamflow stations in a basin are combined into a single global trend test. The analysis procedures are similar to analysis of variance except the use of x 2 tests instead of F tests. For making a basin wide statement about trend in a variable, Van Belle and Hughes suggest to combine m seasons of analysis data from k stations for n years in a basin into a single global trend test. For this purpose, the following four questions are of interest: (i) Is the degree of trend homogeneous between seasons?, (ii) Is the degree of trend homogeneous between stations?, (iii) Is there evidence of station-season interaction?, and (iv) What can be supposed about an overall trend within-season trend, within-station trend, or within station-season trend? Partitioning of the overall statistic ðx 2 totalþ is given in Table 2 of Van Belle and Hughes (1984). The analysis procedure involves computing the value of various chi-squares (i.e. x 2 total; x 2 homogeneous; x 2 station; x 2 season; x 2 trend and x 2 station2season) for testing the trend heterogeneity. It will be convenient to present the rest of the analysis procedures when presenting the outcomes of this test in Section Results and discussions 4.1. Trend results The spatial distribution of trends in monthly mean streamflow for the study period is shown in Fig. 2. Basins located in western Turkey (marked as dark

8 E. Kahya, S. Kalaycı / Journal of Hydrology 289 (2004) Table 2 Results of homogeneity of trends between months based on the Van Belle and Hughes Homogeneity of Trend test Basin no Station no x 2 homogeneous x 2 trend * * * * * * þ þ þ * * * * * * * * þ * * * * * * * * * * * * * þ * * * * * * * þ * þ Table 2 (continued) Basin no Station no x 2 homogeneous x 2 trend * * * * * * þ * * * * * * * * þ *, refers to that monthly trends are homogeneous; þ, refers to that monthly trends are heterogeneous; The critical values of x 2 homogeneous and x 2 trend at a ¼ 0.05 level equal to and 3.84, respectively. See the text for notational explanations. grey in Fig. 2) completely display negative trends, suggesting decrease in monthly mean streamflow. Similar findings appear in the west part of southeastern Anatolia region. A small region situated

9 136 E. Kahya, S. Kalaycı / Journal of Hydrology 289 (2004) Fig. 2. Results of trend analysis. Regions with light (dark) grey reveal a significant downward (upward) trend. The remaining regions (shown in white) demonstrate no significant trend.

10 E. Kahya, S. Kalaycı / Journal of Hydrology 289 (2004) mostly on northern Yesilırmak basin (marked as light grey in Fig. 2) displays positive trends, suggesting increase in monthly mean streamflow. In contrast, basins in the middle and eastern Turkey (marked as white in Fig. 2), in general, show no trends. It is noted that all trends detected are significant at the 0.05 level. Among 83 stations, a total number of stations containing positive or negative trend is 56 (56, 47, 61) based on the Mann-Kendall (the Seasonal Kendall, the Spearman s Rho, the Sen s T) test. In general, 47 (5, 3) stations in 19 (4, 3) basins result in the same conclusion based on the four (three, two) tests. Therefore it is readily said that the majority of detected trends in Fig. 2 were confirmed by at least three different tests. However, stations 1335, 1401, 1413 and 1414 in Fig. 1 have a trend confirmed only by one test (mostly by the Seasonal Kendall). Three stations are located in Kızılırmak basin and their trend indications are not as much reliable as the other stations Van Belle and Hughes homogeneity of trend test When analyzing monthly data at a station, the first condition to check out, in fact, should be the homogeneity of monthly trends, which is an implicit assumption in the trend tests. To see the validity of this assumption in the trend results presented in Section 4.1, the procedures of Van Belle and Hughes homogeneity of trend test are applied for individual stations within 26 basins and its outcomes are summarized in Table 2. For example, all computed x 2 homogeneous values of three stations in the East Mediterranean basin (No: 17 in Fig. 1) are less than the critical x 2 (equal to 19.68) with df ¼ at the a ¼ 0:05 significance level (Table 2). Since the x 2 homogeneous values are not significant, the x 2 trend values for the three stations can be compared to the critical x 2 value with df ¼ 1 at the same significance level. As a result, all three stations have x 2 trend larger than x 2 critical (equal to 3.84), thus monthly streamflow trends are homogeneous. In other words, trends in all months have the same direction (downward). Moreover, the four (three) tests confirmed the implied trend in stations 1712 and 1714 (station 1905) in the East Mediterranean basin. In general, if x 2 homogeneous exceeds x 2 critical (with df ¼ 11Þ; the null hypothesis of homogeneous seasonal trends over time (implying that trends in all months have the same direction and magnitude) should be rejected. In this case, the use of the Seasonal Kendall test becomes questionable, but the Mann-Kendall test is suggested to apply for each individual season by considering the effect of positive serial correlation (Zhang et al., 2001; Burn and Elnur, 2002). Table 2 summarizes the results of Van Belle and Hughes homogeneity of trend test for each station. Only 14% of stations (12 out of 83) in the study domain result in heterogeneity in monthly trends. When inspecting the results given in the third column of Table 2, the reliability of the trend indications in Fig. 2 is shown by another approach since seasonal trends in most stations come out to be homogeneous. Fig. 3 shows the outcomes of testing the homogeneity of seasonal trends in graphical fashion and its resemblance to Fig. 2 is fairly obvious. Therefore, the analysis results obtained in Section 4.1 do not need to be revised. This evaluation has been expected, since the indications of both the Mann- Kendall and the Seasonal Kendall tests for monthly streamflow were similar for all stations. In contrast, existing monthly trends are in different directions according to the Van Belle and Hughes Homogeneity of Trend test in few stations (i.e. stations 314, 321, 406, 713 and 1905) although the four non-parametric tests indicated a downward trend for these stations. Therefore, trend testing at these stations is suggested to be carried out separately for each individual month as in Zhang et al. (2001). In the other case, if the value of x 2 homogeneous is less than x 2 critical (with df ¼ 11), then x 2 trend is referred to the table of chi-square distribution with ðdf ¼ 1Þ to demonstrate the possibility of a valid test for a common trend (for all seasons) at a station. The results of this possibility are presented in the fourth column of Table 2, which is completely consistent with the indications of the third column (except for station 1418). Thus, a common trend is present for all seasons in streamflow data, having a significant trend Van Belle and Hughes trend test for the general case In this section, our purpose is to test the homogeneity of trend directions in streamflow at different stations. This test would be easier if no

11 138 E. Kahya, S. Kalaycı / Journal of Hydrology 289 (2004) Fig. 3. Homogeneity of seasonal trends based on the Van Belle and Hughes homogeneity of trend test. Basins with dark grey have homogeneous monthly trends as the opposite for the basins with light grey. Basins with white indicate no trend.

12 E. Kahya, S. Kalaycı / Journal of Hydrology 289 (2004) seasonal cycles are the component of streamflow time series. When seasonality is present in the data set, the four chi-square statistics (i.e. x 2 total; x 2 trend; x 2 station, and x 2 season) are first computed by using equations given by Van Belle and Hughes (1984). Then the values of x 2 station; x 2 season; and x 2 station2season are compared with the relevant critical chi-square values if they are significant. Before taking these three statistics into consideration for the global trend analysis, it will be useful to comment the spatial distributions of stations whose the chi-square statistics are significant (Fig. 4). Fig. 4a reveals a picture of the degree of trends homogeneous between stations. It is meaningless to obtain a conclusion in some basins having only one station (i.e. basins with number of 1, 2, 6, and 11; all shown in white in Fig. 4a) for the statistic x 2 station: This is also true for the next cases in Fig. 4b and c. Basins with the number of 8, 9, 13, 16, 17, and 20 are also marked as those having a significant trend in Fig. 2. Fig. 4b displays the degree of trends between seasons for the combined two situations of all stations in a basin. When comparing this figure with Fig. 3 (corresponding to the single situation of all stations in a basin), the basins with the number of 5, 7, 9, 15, 16, 17, 19, 20, and 21 reflect the homogeneity of seasons for the two distinct cases. Finally, the station-season interaction is evident in most basins as shown in Fig. 4c. In the analysis procedures, the following four cases are examined: (a) When all three statistics (x 2 station; x 2 season; and x 2 station2season) are not significant, then the x 2 trend statistic can be compared to the value of x 2 critical (with df ¼ 1Þ to test for overall or global trend in a basin. In our analysis, this case was only possible for eight basins to be tested, but only four basins (namely, the Mid-Mediterranean, the Mid-Anatolia, the East-Mediterranean, and the Ceyhan) located in southern Turkey reveal a significant global trend. Hence no evidence of trend heterogeneity is found either between seasons or between stations. Therefore the streamflow data could be combined and are said to have decreasing trend over the period (b) When x 2 season is significant (implying heterogeneous seasonal trends), but x 2 station is not (c) significant (implying homogeneity of stations); then different trend direction in each season should be tested (see Van Belle and Hughes (1984) for details). Three basins (No: 8, 13, and 23) shown with light grey in Fig. 5 confirm this condition. The m seasonal statistics are needed to be calculated in these basins. Then each refers to the value of x 2 critical (with df ¼ 1) at the a ¼ 0:05 significance level. In the West Mediterranean basin (No: 8), the statistic ðk p Z 2 j :Þ ðj is the index for season) becomes larger than x 2 critical (with df ¼ 1) ¼ 3.84 for each individual month. This basin has been also previously shown as one of those having significant downward trend and seasonal homogeneity (Figs. 2 and 3). In the West Black Sea basin (No: 13), the statistic is found to be significant for February, May, June, July, August, and December months. However, the western part of this basin was also shown as an area having significant and homogeneous monthly streamflow trends (Figs. 2 and 3). This discrepancy may be due to the effects of dominant statistics belonging to the months when computing the overall test statistic. Finally the Çoruh basin (No: 23) is designated as an area having insignificant trend in which no significant trend previously was detected in Section 4.1. This conclusion is also verified by the present analysis, resulting in insignificant trends for eleven months. When the opposite case to that in (b) occurs, then test for trend at each station is required. The results of this case are depicted in Fig. 5, indicating that trend analysis should be carried out for individual stations in six basins with dark grey (No: 3, 4, 12, 14, 19, and 25). The k station statistics are needed to be computed in these basins. Then each refers to the value of x 2 critical (with df ¼ 1) at the a ¼ 0:05 significance level. In the Gediz and the Big Menderes basins (No: 5 and 7), the statistic ðm p Z 2 1Þ (l is the index for station) is found to be larger than x 2 critical (with df ¼ 1) ¼ 3.84 for each individual station, thus the existence of trend is confirmed. In the Fırat basin (No: 21), the relevant statistics appear to be less than the critical value only for stations 2122 and 2147, thus the remaining five stations reveal

13 140 E. Kahya, S. Kalaycı / Journal of Hydrology 289 (2004) Fig. 4. (a) Spatial distribution of the x 2 station statistic in the Van Belle and Hughes global trend test. In basins with dark grey, the x 2 station statistic is insignificant, referring to the homogeneity of stations. (b) Same as in (a) except for the x 2 season statistic. (c) Same as in (a) except for the x 2 station2season statistic.

14 Fig. 5. Results of the Van Belle and Hughes global trend analysis for streamflow in Turkey for the cases other than in Fig. 6. Basins with light grey have homogeneous stations and heterogeneous seasonal trend whereas basins with dark grey have the reverse conditions. E. Kahya, S. Kalaycı / Journal of Hydrology 289 (2004)

15 142 E. Kahya, S. Kalaycı / Journal of Hydrology 289 (2004) Fig. 6. Results of the Van Belle and Hughes global trend analysis for streamflow in Turkey. Basins with light grey have heterogeneous stations and seasonal trends or significant station-season interaction.

16 E. Kahya, S. Kalaycı / Journal of Hydrology 289 (2004) significant trend. However, only station 1517 indicates significant trend in the Kızılırmak basin (No: 15). In the Hatay and Van Lake basins (No: 19 and 25), one out of two stations (1906 and 2507), results in a significant trend. The whole findings in this analysis phase are completely consistent with those summarised in Fig. 3. (d) When both x 2 station and x 2 season are significant (implying that both stations and seasons are heterogeneous) or x 2 station2season is significant (implying that there is a substantial stationseason interaction), then the only meaningful trend tests can be done for individual stationseason combinations. These tests are carried out by comparing each Z jl statistic with the critical value of standard normal distribution. In this case, Z jl statistic is supposed to be recomputed with inclusion of the correction of continuity (Yu et al., 1993). Fig. 6 displays the final case, in which few basins have heterogeneity in both seasonal and station trends or in station-season interaction. Since the x 2 trend test cannot be done for these basins, meaningful trend tests can be applied for stations in the Aegean Water, the Susurluk, and the Van Lake basins. Consequently the results presented so far are quite convincing on the existence of linear trend in monthly mean streamflow data over Turkey. Although the analyses in Sections 4.1 and 4.2 are mainly based on testing at individual station, their outcomes seem to be consistent with those of the Van Belle and Hughes trend test for the general case in Section 4.3 which reflects a regional testing. However, the following facts should be remembered in evaluating trends in a hydrologic series: (i) there is a difference between natural low frequency variability, such as a phase shift in the NAO and the human-induced climate change and (ii) the multidecadal variability could appear as a trend in a relatively short sample (for example, 30-year). 5. Conclusions The application of trend detection techniques to 26 Turkish basins has resulted in the identification of significant trends appearing in the western and south eastern parts of the country. The direction of trends is, in general, downward. The both aligned (i.e. the Sen s T test) and intrablock (i.e. the Seasonal Kendall) methods produce more or less similar conclusions. The homogeneity of trend directions in multiple streamflow stations and in months is tested by the Van Belle and Hughes method. In fact, the homogeneity of seasonal trends should be tested by this method before the non-parametric tests in Section 3.1, which implicitly assume homogeneous seasonal trends in the time series under consideration, are conducted. This substantial point somehow has been ruled out in germane investigations in the literature. It is shown that this issue did not appear as a problem in the present study. Moreover the Van Belle and Hughes trend test for the general case is first applied to monthly streamflow data as a comprehensive approach for the trend detection purpose. In general, its results seem fairly consistent with those of the individual non-parametric tests. As a common conclusion often made in the relevant previous studies, it would be inappropriate to express that the observed trends in Turkish streamflow pattern have occurred as a consequence of climate change. Moreover, the trend attribution and the relation between the observed streamflow trends and climate change should be addressed in future studies with the inclusion of the influences of precipitation and temperature variables. Physical interpretations for the appearance of trend in a surface hydroclimatologic variable may logically be related to the greenhouse effects, urban heat islands aerosol or a contentious subject of global warming (Balling, 1992). It is wise not to rule out the possibility that this type of inconclusive (due to several inherent reasons) changes in a hydroclimatologic time series is mostly due to natural variability. The presence of trends in Turkish streamflow patterns may be attributed to the observed decreases in rainfall and, to some extent, to increases in temperature. Since there is an increasing attention given to coupling streamflow processes with the atmospheric circulation models, it is essential to investigate the nature of streamflow trends over large domains and how they are related to trends in precipitation and temperature, that have been better

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