Abstract

This study is intended to determine potential trends in annual rainfall series with the parametric Student’s t test and the nonparametric Mann–Kendall, Spearman’s rho, and Sneyers tests. The study includes a trend analysis of annual rainfall data from 47 rain gauges, mostly located at rural sites, in the Aegean region of Turkey. The chi-square and Kolmogorov–Smirnov tests showed that the null hypothesis of normality for the majority of the data (45 out of 47 stations) is acceptable. Moreover, the serial independence assumption, based on the lag-1 sample autocorrelations, is rejected in 14 datasets. The parametric Student’s t test detected significant downward trends at 15 rain gauge stations; 14 of them were also confirmed by the three nonparametric tests and by the trend-free version of the Mann–Kendall test. The results of the Sneyers test revealed that the approximate start years of significant downward trends were in the early 1970s and, sometimes, in the early 1980s. Moreover, the testing found that the normalized slopes of linear downward trends were significantly dependent on the station’s longitude, which meant that the farther the station was located from the coast, the smaller the decreasing trend in annual rainfall was. Additional studies carried out on the normalized regional data and on the 5-yr running means showed that a considerable portion of the detected downward trends were mainly due to interactions of the particular start and end times of a large number of stations with interdecadal fluctuations and the dry conditions over the Mediterranean region during the last 25–30 years.

1. Introduction

Most climate change studies rely on detecting significant trends in the records of hydrometeorological variables, such as relative humidity, rainfall, and air temperature. Rainfall is an important ingredient of the hydrological cycle because the water resources system is affected by variations in rainfall. Decreasing trends in rainfall carry great importance in water resources engineering because they may indicate decreases in the total surface water and/or the river flows of a basin. Cigizoglu et al. (2005) used both parametric and nonparametric trend tests on maximum, mean, and low flow data for western Turkey and showed that there is a decreasing trend in the mean and low flows in that region. In his paper, Ozkul (2009) studied two river basins (Gediz and Büyük Menderes) in the Aegean region of Turkey. The simulation results of his study showed a 20% drop-off in total surface water by 2030, with additional reductions in surface water estimated to be 35% by 2050 and 50% by 2100. In addition, increasing evapotranspiration (up to 10% and 54% by 2030 and 2100, respectively) of potential crops will strongly increase the water demand for the region. The modeled decrease in amount of potential surface water in the basins will lead to critical water stress problems among water users, primarily in the domestic, industrial, and agricultural sectors (Ozkul 2009). These motives point out the importance of the rainfall trends in the region.

Over the last 20 years, a considerable effort has been made by many scientists to investigate the influence of climate change on the characteristics of rain events in different areas of the world (e.g., Lettenmaier et al. 1994; Zhang et al. 2000; Jung et al. 2002; Penalba and Vargas 2004; Taschetto and England 2009; De Lima et al. 2010; Wang et al. 2013). A limited number of previous works have analyzed rainfall trends in Turkey, and a few of them involve the Aegean region. Toros et al. (1994) studied seasonal and annual rainfall in western Turkey with observations from 1930 to 1992. They determined a decreasing trend in annual rainfall after 1982 and discussed that it was proof simply of an oscillation in rainfall. Türkeş (1996) utilized data through 1993 to study the annual and seasonal trends of rainfall at 91 Turkish stations, most of which were located in urban sites, and found that the annual rainfall series showed a slightly decreasing trend. The majority of the detected trends appeared to have arisen after sudden decreases over the last 20–25 years. Utilizing almost the same data, Partal and Kahya (2006) found that most of the annual rainfall series showed decreasing trends in the change per year slopes from −0.133 to −0.562 mm month−1 (from −1.596 to −6.744 mm yr−1) in western and southern Turkey. According to the Sneyers test, Partal and Kahya (2006) have also shown that the beginning years of these downward trends were generally between 1945 and 1955. Finally, Türkeş and Erlat (2003) investigated the relations between the North Atlantic Oscillation (NAO) indices and the normalized rainfall using 78 data series in Turkey. They found a negative correlation between the rainfall series and NAO indices. The authors have detected significant downward trends in annual data in 7 out of 11 stations in the Aegean region and determined that the observed trends toward drier conditions are based on the rising trends in the NAO indices.

Since the study area is a part of the Mediterranean region (MR), and because of its proximity to Greece, a few additional studies are included to compare the trends in rainfall over Greece and the MR. Similar to the results reported by Türkeş (1996), significant decreasing trends in winter and annual rainfall in northern and eastern Greece, as well as in its mountainous western regions, have been detected (Xoplaki et al. 2000). Xoplaki et al. (2004) claimed that the long-term changes in Atlantic variability govern Mediterranean rainfall. Thus, decreasing trends in precipitation may have been associated with the intensification of the Azores high that produces the dry conditions over the Mediterranean region. Feidas et al. (2007) investigated the trends of annual and seasonal rainfall in Greece by utilizing data from 22 stations located between 35°00′–40°51′N latitudes and 19°55′–28°05′E longitudes for the period 1955–2001 and combining them with satellite data during the period 1980–2001. Based on the parametric and nonparametric (namely the Sneyers) tests, the authors have detected significant downward trends, especially in winter precipitation and in annual data, in almost half of the stations, with start times changing in the 1974–84 period. The downward trends in the last 25 years seemed to be caused more by dry conditions rather than by a regular downward trend. The authors have also studied the relationship between rainfall variability and atmospheric circulation indices, such as the NAO index (NAOI) and the Mediterranean Oscillation index (MOI). These analyses indicated that the temporal pattern of rainfall in Greece was mainly due to temporal changes in atmospheric circulation; hence, recent rainfall trends might be explained by the coupled patterns of variability in the NAOI and the MOI. The authors, finally, concluded that the observed trends toward drier conditions in Greece might be based on a rising trend in both the NAOI and MOI pattern during the last few decades. Krichak and Alpert (2005) claimed that the decrease of rainfall in the Mediterranean region during the last two decades was mainly created by the positive trend in the eastern Atlantic–western Russian pattern caused by the upward trend in the NAOI. Similarly, Seidel et al. (2008) reported that rainfall decrease across the Mediterranean region may have been a result of a poleward shift of the subtropical highs toward the Mediterranean basin as a part of the Hadley cell’s continuing expansion due to global warming.

There are two authorized rain gauge networks in Turkey. The State Meteorological Works Authority of Turkey (DMI) network was founded in the late 1920s, and a great number of climatological variables are measured at its sites, which are often located in urban areas (cities and towns). The State Hydraulic Works Authority of Turkey (DSI) was founded in the late 1950s to collect additional air temperature, pan evaporation, rainfall, and streamflow data, especially in rural areas and river basins; the results will be utilized in water resources development projects that are planned for the near future.

Although there were a limited number of studies related to the temporal and spatial variation of rainfall data in Turkey (e.g., Toros et al. 1994; Türkeş 1996; Türkeş and Erlat 2003; Partal and Kahya 2006; Ozkul 2009), most of them did not cover the recent datasets or the datasets from the DSI rain gauge network. Some of them did not include the crucial effect of serial correlation on nonparametric trend tests. Additionally, only a few of them have been concerned with the trend slopes and with the approximate dates of abrupt changes (or trends) in annual and seasonal rainfall volumes.

Hence, the main objectives of this study, which is partially based on the work carried out by Ciftlik (2012), were to 1) determine the significant trends and slopes of a presumable linear trend in annual total rainfall recorded at sites mostly located in rural areas with more recent data; 2) identify the abrupt and/or monotonic secular changes in recent annual rainfall patterns on a station and regional basis; 3) evaluate the spatial variation of trends with respect to some geographic variables, such as the latitudes, longitudes, and altitudes of the stations; and 4) compare findings of previous studies carried out with long-term data in the same region and stations that are most often located in densely urbanized sites.

2. Data

The study area covers nearly one-eighth of the Anatolian Peninsula (of Turkey) and is located approximately within the latitudes 36°00′–40°00′N and the longitudes 26°00′–31°00′E (Fig. 1). The region has a Mediterranean climate with annual mean precipitations ranging from 450 to 1200 mm yr−1 (Asikoglu and Benzeden 2014). This work examines 47 rainfall datasets from the Aegean region (western Anatolia). The record lengths are in the range of 32–45 years, with an average length of 40 years. The data were obtained from the DSI and have annual resolutions. Table 1 displays various geographical and at-site statistical characteristics of the stations. The topographical map in Fig. 2 shows the elevations of the stations.

Fig. 1.

Study area and locations of the rain gauge stations (the downward-oriented arrows represent a negative trend).

Fig. 1.

Study area and locations of the rain gauge stations (the downward-oriented arrows represent a negative trend).

Table 1.

Basic statistics and information of annual rainfall series from 1961 to 2005 in the Aegean region. In the bottom row, R indicates regionally averaged data.

Basic statistics and information of annual rainfall series from 1961 to 2005 in the Aegean region. In the bottom row, R indicates regionally averaged data.
Basic statistics and information of annual rainfall series from 1961 to 2005 in the Aegean region. In the bottom row, R indicates regionally averaged data.
Fig. 2.

Topographic map of the region with locations of the rain gauge stations.

Fig. 2.

Topographic map of the region with locations of the rain gauge stations.

To reduce the sampling errors on a regional scale, a regional time series of 41 years in length is developed by averaging the data from 26 stations in the period 1965–2005. The bottom row in Table 1 shows the sample statistics of the regionally averaged data.

3. Methodology

a. Normality and independence testing

Various time series analysis methods depend on the basic assumption that the observed data were sampled from a normal distribution (Madansky 1988; USEPA 1996; Thode 2002). This assumption is quite important, especially for parametric trend tests (Machiwal and Kumar Jha 2012). If parametric trend detection methods are to be used, it may be necessary to determine if the distribution of the data is nearly normal. The assumption of normality can be measured by statistical and/or graphical methods. Some of the well-known statistical methods used to evaluate normality include the Kolmogorov–Smirnov (KS), the Anderson–Darling, the chi-square goodness-of-fit, the Shapiro–Wilk, and the Cramer–von Mises tests. In this study, the normality of the data is checked with the KS and the chi-square tests.

In trend analysis, the recorded data are generally assumed to be serially independent. A positive autocorrelation can increase the number of false positive results, which can complicate the identification of a significant trend (Yue et al. 2002a,b). One method of characterizing a serial correlation in a series over time is the autocorrelation function. The population autocorrelation function ρ(k) may be estimated by sample autocorrelation function r(k). The first-order (lag 1) autocorrelation (for k = 1) of a discrete time series of size N is given by

 
formula

where , , is the arithmetic mean of the first N − 1 records, and is the arithmetic mean of the next N − 1 records. The lag-1 sample autocorrelation given in Eq. (1) measures the correlation between successive records and is called the autocorrelation coefficient or the serial correlation coefficient. The sample autocorrelation function serves two purposes. First, it can detect the serial dependence (or randomness) in a dataset. Second, if the values in the dataset are not random, then it helps the researcher choose an appropriate time series model (Haan 2002).

b. Trend detection

The assumption of a linear trend has been widely used in testing the significance of a monotonic secular variation with time in the observed data. However, this assumption is only an approximation for the unknown secular trend pattern, which may be linear or nonlinear, depending on various external factors that control the total variation of the process. In any case, however, the slope of a linear trend, which represents the change per unit time, is a good measure for the average rate of temporal variation in the period of record.

Occasionally, a simple moving-average filter of order m, where m ranges from 5 to 15, is applied to the data to reduce the effects of nonsystematic (high frequency) components and to see the systematic (low frequency) variation better. However, the averaging of m adjacent items eliminates some of the total variation. Hopefully, the smoothed-out variation is random (high frequency) rather than a portion of the systematic (low frequency) variation (McCuen 2003). A hypothetical model (often a polynomial of order p) is then fitted to the smoothed data in order to identify the temporal patterns of trend or the cyclic variations in the dataset.

Some disadvantages of smoothing are 1) m − 1 items of the dataset are lost, which is a serious limitation for small datasets especially when m selected is large; 2) the choice of m is often subjective; and 3) if the smoothing interval m is not selected properly, it is possible to eliminate some of the systematic variation too (McCuen 2003).

Trend detection methods generally test the null hypothesis H0 (there is no significant trend) against H1, the alternative hypothesis. In practice, parametric and nonparametric testing methods are used for this purpose.

Many approaches in the literature on hydrological and hydrometeorological data use both parametric and nonparametric trend detection methods. In parametric trend-testing procedures, it is crucial to adopt an underlying probability distribution function for the observed data (typically a normal distribution) in which the data series are considered to be serially independent. According to the central limit theorem, the time series (such as the annual total rainfall, which is calculated by aggregating seasonal measurements for each year) are expected to be a new random variable with a distribution close to normal, regardless of the population distribution of random events and a weaker serial dependence structure than that of the original series (Haan 2002). In nonparametric testing procedures, fewer assumptions about the observed data are required. However, many nonparametric techniques still rely on independence assumptions. Therefore, more advanced procedures must be used, especially for seasonal (hourly, daily, monthly, etc.) time series (Kundzewicz and Robson 2000).

1) The parametric student’s test

The parametric Student’s t test takes simple linear regression into consideration. The correlation coefficient r is calculated from the observed data. The test statistic for H0: E(r) = ρ = 0 is

 
formula

and follows the Student’s t distribution with υ = N − 2 degrees of freedom (Haan 2002). In a two-sided test, H0 is tested in the decision phase against H1: E(r) = ρ ≠ 0 at a selected significance level α. The null hypothesis (there is no trend) is rejected if the absolute value of the t statistic is greater than the critical value tα/2,υ (Onoz and Bayazıt 2003).

The slope of a simple linear trend is estimated by

 
formula

where and are the standard deviations of the observed annual rainfall Xt and of the time steps t, respectively.

As with the index procedures applied for the regional analysis of annual and seasonal datasets in a given region (see, e.g., Douglas et al. 2000; Partal and Kahya 2006), a nondimensional slope for each index rainfall dataset can be estimated simply by dividing by the mean :

 
formula

To some extent, is expected to be less sensitive to the spatial variation of annual mean rainfall over the region. Thus, the variation of with the locations (latitude, longitude, and altitude) of the stations would be more meaningful.

2) The Mann–Kendall trend test

The traditional form of the Mann–Kendall (MK) test summarized in the following has been widely used for testing H0 (there is no trend) against H1 (there is a significant trend) in the sample dataset (Kendall 1975). This test uses the order statistic S, which is estimated by calculating the total number of scores for which Xi > Xj and the total number of scores for which Xi < Xj for i > j, denoted by P and M, respectively:

 
formula

For a sample size of N > 10, the sampling distribution of the transformed variable Z in Eq. (6) is asymptotically normal with a mean of zero and the variance given by Eq. (7) (Kendall 1975; Douglas et al. 2000):

 
formula

and

 
formula

where nj is the number of ties for the ith record (the score at which Xi = Xj; Hirsch et al. 1991; Salas 1993). When the absolute value of the calculated Z statistic is greater than Zα/2, the null hypothesis should be rejected. Furthermore, the sign of S shows the direction of the trend.

3) Spearman’s rho trend test

The Spearman’s rho (SR) test (Spearman’s rank correlation test) detects whether a correlation is present between two classifications of the same time series of observed data. The trend is found to be significant if there is a significant correlation between the time steps (i = 1, 2, …, N) and the ranks R(Xi) of the observed data. Spearman’s rank correlation coefficient ρs is computed by

 
formula

The distribution of ρs is asymptotically normal with the mean E(ρs) = 0 and the variance Var(ρs) = 1/(N − 1) for sample sizes N > 30. The standardized test statistic Zs is then computed by the following:

 
formula

The null hypothesis (there is no trend) is rejected at significance level α if the absolute value of the Zs statistic is greater than Zα/2.

4) Sneyers (sequential Mann–Kendall) test

Sneyers (1990) developed a nonparametric test procedure that is a sequential version of the Mann–Kendall rank statistic for detecting the potential trend turning points (start and end times) in a time series approximately.

In the time series (X1, X2, …, Xi, …, XN) for each datum, the comparison of Xi > Xj (for i > j) is made and the number of the case is counted ni. Then, the raw test statistic ti is computed from Eq. (10):

 
formula

Under the assumption that the null hypothesis (there is no trend) is valid, the sequential statistics ti are normally distributed with the mean and variance:

 
formula

and

 
formula

The forward values of the normalized test statistic u(ti) are computed by

 
formula

Note that u(t1) = 0, by definition, and u(ti) is the forward curve of the procedure. A similar analysis on the reversed data (starting from the end of the series) is performed in order to construct the backward curve u′(ti) (Liang et al. 2011). If a significant trend does not exist, the curves u(ti) and u′(ti) will intersect several times. But, if a significant trend or an abrupt change occurs at a specific time point t* and continues thereafter, the u(ti) and u′(ti) curves will intersect each other only at the time point t*, approximately.

c. Testing the trend for serially dependent records

Von Storch and Navarra (1995) showed that the presence of a serial correlation (autocorrelation) in the data raises the likelihood of detecting a trend in the MK trend test. Therefore, the null hypothesis (that there is no trend) may possibly be rejected, even if it is, in reality, true (Yue et al. 2003).

Kulkarni and von Storch (1995) recommended removing the autocorrelation component from a series (prewhitening) before applying the Mann–Kendall trend test in order to reduce the influence of autocorrelation on the test results. The MK test was then performed using the prewhitened data to detect a possible trend. Douglas et al. (2000) indicated that the prewhitening (PW) procedure may decrease the possibility of detecting a trend through the use of the MK test. Later, Yue et al. (2002b) studied this problem by conducting simulation techniques wherein a significant trend and a lag-1 autoregressive [AR(1)] process occurred in a data series. They showed that prewhitening an autoregressive process eliminates part of the trend, and therefore, the null hypothesis (of no trend) could be erroneously accepted. To prevent this effect and more effectively decrease the influence of serial correlation, Yue et al. (2002b) proposed a revised prewhitening method called trend-free prewhitening (TFPW). They showed in their study that, for a time series with a linear trend, eliminating the trend beforehand will not affect the autoregressive process. Yue et al. (2002b) demonstrated that 1) the existence of an AR(1) process will not change the slope of the trend, although the existence of a linear trend will contaminate the estimation of serial correlation, and 2) eliminating the trend beforehand will not change the AR(1) process in a time series but will remove the effect of the significant trend on the estimation of a lag-1 autoregressive process (Yue et al. 2003).

The TFPW proposed by Yue et al. (2002b) is applied in the following manner:

  1. The sample series is assumed to have a linear trend and the serial dependence structure of the series could be represented by an AR(1) model. Before performing the trend analysis, each of the values of the data Xt was divided by the mean value of the sample E(Xt) in order to unitize them (Yue et al. 2002b). A robust estimate of the slope of a linear trend is estimated by utilizing the nonparametric procedure, as explained in the studies of Theil (1950) and Sen (1968). The linear trend in the index rainfall series is removed by fitting the linear function 
    formula
  2. If the expected value of the lag-1 autocorrelation coefficient (r1) of a trend-free (detrended) series yt is not significantly different from zero at a selected significance level of α, then the serial independence assumption is accepted. In this case, the MK trend test is directly applied to the observed data. Otherwise, the prewhitening procedure is performed in order to eliminate the AR(1) components from the trend-free (detrended) data as 
    formula
    After conducting the TFPW procedure, the residual series is expected to be serially independent.
  3. The residuals of the AR(1) model and the determined trend βt are combined with simple addition: 
    formula

In this way, the combined series contains a trend and noise. Now the series is no longer affected by serial dependence, and the MK trend test is applied to the random series in order to evaluate the existence of a trend (Yue et al. 2002b).

4. Discussion of the results

a. Validity of the assumptions of normality and serial independence

As shown in the normality column of Table 1, according to the chi-square and KS goodness-of-fit tests, the assumption of normality is rejected only at two stations (stations 31 and 34). Hence, it can be said that the normality assumption of annual rainfall is sufficiently fulfilled in almost the entire region.

To test the approximate serial independence of a given dataset of size N, the lag-1 autocorrelation (r1) estimated from each dataset is checked if it lies within the approximate 95% confidence interval (Salas 1993; Haan 2002). The results of this approximate test procedure are presented in the serial independence column of Table 1. The lag-1 autocorrelations (r1) of those 14 significantly autocorrelated datasets are given in the r1 without prewhitening column of Table 4 (described in greater detail below).

b. Parametric and nonparametric trend tests applied to the original datasets

Considering the fact that the normality assumption was sufficiently satisfied, the Student’s t test, as a parametric one, is applied to each original dataset. Although the least squares estimate of the slope of a linear trend is not as robust as the Theil–Sen estimate, the least squares estimate of dimensional (change per year) slope of a linear trend (mm yr−1), slope of a linear trend in index rainfalls , Student’s t test statistic, and direction of trend (indicated by an upward- or downward-oriented arrow) for the 15 datasets with significant linear trends are presented in the parametric Student’s t test columns of Table 2.

Table 2.

List of the rain gauges that have a trend in annual rainfall series (downward-oriented arrows represent a negative trend). In the second column, the asterisks indicate serially correlated series for α = 0.05 and υ = N − 2, Zα/2 = 1.96, and tα/2,υ ≅ 2.02. In the bottom row, R indicates regionally averaged data.

List of the rain gauges that have a trend in annual rainfall series (downward-oriented arrows represent a negative trend). In the second column, the asterisks indicate serially correlated series for α = 0.05 and υ = N − 2, Zα/2 = 1.96, and tα/2,υ ≅ 2.02. In the bottom row, R indicates regionally averaged data.
List of the rain gauges that have a trend in annual rainfall series (downward-oriented arrows represent a negative trend). In the second column, the asterisks indicate serially correlated series for α = 0.05 and υ = N − 2, Zα/2 = 1.96, and tα/2,υ ≅ 2.02. In the bottom row, R indicates regionally averaged data.

The results of the MK and SR tests, applied to the original datasets, are given in the Mann–Kendall test and Spearman’s rho test columns of Table 2. It can be seen from this table that the null hypothesis, which states there is no trend in the original dataset, is accepted only in one station, while there exist significant downward trends in the other 14 datasets. Because the results of the Student’s t test are confirmed by the two nonparametric tests and the slopes estimated by least squares and Theil–Sen procedure are found very close, a linear trend assumption for the unknown secular variation in the datasets seems logical.

Since there was no evidence for selecting a trend model other than a simple linear one, cross correlations between the at-site estimates of trend slopes and the geographical variables (latitudes, longitudes, and altitudes of the stations) are investigated. The same analyses are performed for the dimensionless slopes (i.e., trend slopes of annual index rainfalls). It is found that there were no significant cross correlations between the original (the change per year; mm yr−1) slopes and the spatial explanatory variables. Nevertheless, the dimensionless slopes were found to be significantly correlated with the station longitudes as r = 0.71 (Fig. 3), which means that the absolute magnitude of the dimensionless downward trend decreases as the longitude increases over the entire northern half of the region. The reason why the slope is more significantly correlated with geographical coordinates can be attributed to the fact that it is a local parameter scaled by the mean rainfall at each site individually and is almost independent of the spatial distribution of annual mean rainfall.

Fig. 3.

The change of the trends along the longitudes.

Fig. 3.

The change of the trends along the longitudes.

The sequential MK test procedure developed by Sneyers (1990) is applied to 14 original datasets with significant trends in order to explore approximate start and/or end years of monotonic trend development. The Sneyers test results are given in Table 3. The results revealed that there were significant downward trends in annual rainfall datasets recorded at 14 stations, most of which were located in the northern half of the Aegean region with starting years in the early 1970s or, occasionally, in the early 1980s.

Table 3.

Trend start years according to the Sneyers test.

Trend start years according to the Sneyers test.
Trend start years according to the Sneyers test.

c. The MK test applied to PW data

The MK test with conventional PW and TFPW was also applied to the 14 significantly correlated datasets (Table 4), considering the fact that the nonparametric MK test is less powerful than a simpler related test when the data are serially correlated. Note that Table 4 contains the MK test results of seven stations (depicted by an asterisk in Table 2) with prewhitening as well as the test results of the seven additional stations that were found to be significantly serially correlated (see Table 1) but had no significant trends in their original datasets. The slope of a linear trend, as estimated by the nonparametric procedure developed by Theil (1950) and Sen (1968), is utilized in detrending the sample series with zero mean. The test results presented in Table 4 apparently show that the MK test with conventional prewhitening misses the significant trends in six out of seven datasets because of positive serial correlations, as was expected. However, the results of the MK test with trend-free prewhitening given in the trend-free prewhitening columns of Table 4 are consistent with the results of the three tests given in Table 2. Also, it can be seen from the trend-free prewhitening columns of Table 4 that the lag-1 autocorrelations of the detrended datasets were considerably reduced compared to the autocorrelations of the original datasets.

Table 4.

Trend analysis of autocorrelated data (Zα/2 = 1.96 for α = 0.05; downward-oriented arrows represent a negative trend). In the bottom row, R indicates regionally averaged data.

Trend analysis of autocorrelated data (Zα/2 = 1.96 for α = 0.05; downward-oriented arrows represent a negative trend). In the bottom row, R indicates regionally averaged data.
Trend analysis of autocorrelated data (Zα/2 = 1.96 for α = 0.05; downward-oriented arrows represent a negative trend). In the bottom row, R indicates regionally averaged data.

In summary, either the standard applications of Student’s t, MK, and SR tests or the TFPW form of the MK test detected significant downward trends in the annual rainfall of 14 stations that were mostly located in the northern half of the Aegean region (Fig. 1).

d. Regional data and the effect of interdecadal variations on trends

The regional data are developed, as explained in section 2, to reduce the sampling and systematic errors on a regional scale. This time series is normalized by the regional overall mean, = 738.3 mm yr−1. Summary sample statistics and test results that are related to the normality and serial independence of the regionally averaged data are given in the last row of Table 1, whereas the results of parametric and nonparametric tests are in the last rows of Tables 2 and 4. As expected, the regional data are sufficiently close to normal and have a slightly significant serial dependence. According to the Student’s t test, there exists a linear decreasing trend with a normalized slope β′ = −0.005 in the regional data at a significance level (type I error) of 5%. However, the nonparametric tests did not identify a significant trend in the regional time series. The u(ti) and u′(ti) curves of the Sneyers test presented in Fig. 4 detect a weak decreasing trend beginning in 1966, although the two curves become very close in the years 1969, 1978, and 1980. Therefore, the start and end times of a systematic change in regional data are unclear, as one could be in the late 1960s and the other in the early 1980s.

Fig. 4.

The forward curve u(t) (solid) and the backward curve u′(t) (dashed–dotted) of the Sneyers test for annual rainfalls in the Aegean region of Turkey as percentages of the mean in the period 1965–2005.

Fig. 4.

The forward curve u(t) (solid) and the backward curve u′(t) (dashed–dotted) of the Sneyers test for annual rainfalls in the Aegean region of Turkey as percentages of the mean in the period 1965–2005.

Furthermore, the possibility that the particular start and end years for the various stations could interact badly with a possible interdecadal fluctuation in annual rainfall and therefore yield a trend that is an artifact of how the start and end time lines up with the fluctuation is assessed as follows. A 5-yr high-frequency moving-average filter (smoothing) is applied to the normalized regional data in order to partly remove random (nonsystematic) variations, which may mask the systematic variations (such as a trend and/or an interdecadal cyclic fluctuation). Finally, a seventh-order polynomial curve is fitted to the 5-yr running means, specifically to observe the start times of the recession limbs of interdecadal fluctuations (Fig. 5). The figure shows that the annual rainfall over the study area had two wet epochs on the decadal time scale: one from 1965 to 1969 and the second from 1978 to 1983. Comparatively, one considerably short dry epoch is from 1970 to 1977, and the second dry epoch persisted from 1984 to 1995. Then, a close-to-normal period (1996–2005) followed. All these wet and dry spells are the basic characteristics of interdecadal variations in annual rainfall time series, which can be better interpolated from the time series plot of the 5-yr running means and from the seventh-order polynomial curve fitted to the normalized data. The recession limb of either curve in the first period starts approximately in the late 1960s, while the second recession starts in the early 1980s. Note that the start years of a decrease in annual rainfall in most of the stations with significant trends primarily interact with the start years of recession limbs of interdecadal fluctuations. Moreover, the u(t) curve in Fig. 4 shows a similar interdecadal fluctuation, indicating that any trend test could be infected by a significant interdecadal variation in the sample time series and may lead to false decisions.

Fig. 5.

Interannual variations of the normalized regional annual rainfall (dashed line), 5-yr running means (thin line), and seventh-order polynomial curve (thick line) fitted to the regional data representative to the secular trends and/or interdecadal oscillations.

Fig. 5.

Interannual variations of the normalized regional annual rainfall (dashed line), 5-yr running means (thin line), and seventh-order polynomial curve (thick line) fitted to the regional data representative to the secular trends and/or interdecadal oscillations.

As result, the decreasing trends detected through parametric and/or nonparametric tests were, most probably, caused mainly by interdecadal variation in the annual rainfall process and by the dry conditions that have occurred during the last 2–3 decades throughout the Mediterranean region.

5. Conclusions

An overall evaluation of the test results [namely, the Student’s t, the MK (with and without prewhitening), the SR, and the Sneyers tests] revealed that a significant decrease is apparent in annual rainfall totals, especially over the northern half of the Aegean region of Turkey. Significant decreases in annual rainfall mostly began in the early 1970s and, in some stations, in the early 1980s, then continued thereafter. This finding is solidly confirmed by the findings of other studies related to the temporal variability of rainfall over Turkey (Toros et al. 1994; Türkeş 1996; Partal and Kahya 2006), over Greece (Xoplaki et al. 2000, 2004; Feidas et al. 2007), and over the Mediterranean region (Krichak and Alpert 2005; Seidel et al. 2008).

The results of this study showed that the least squares estimates of the slopes may be as efficient as the Theil–Sen robust estimates in detecting monotonic trends in annual data, provided that the normality assumption is fulfilled. As a result, either of the slopes can be utilized in determining the magnitude and the direction of a significant linear trend, especially when the results of the parametric and the nonparametric tests confirm each other. Furthermore, as shown in this paper, at-site values of the normalized slopes significantly correlated with station longitudes and may give rise to evaluations of the geographical variation of recently developing trends over the related area.

Although the external factors that control rainfall variations (i.e., the occurrence of relevant synoptic systems, large-scale atmospheric oscillations, and global temperature) were not investigated in this paper and may mask long-term annual rainfall trend patterns, we expect the findings to be similar to those given by Feidas et al. (2007) for Greece. In this paper, we have shown that the start and end years of a significant change in annual time series could interact badly with a possible interdecadal fluctuation and may produce a trend that, in fact, is an artificial one. In such circumstances, the result of any trend-testing procedure could be misleading. As a result, the significant decrease in annual rainfall across the northern half of the Aegean region of Turkey is quite probably produced by the dry conditions during the last two decades rather than by a systematic downward trend.

Acknowledgments

We are grateful to E. Benzeden for his valuable comments and suggestions and to E. Eris for delivering the maps.

REFERENCES

REFERENCES
Asikoglu
,
O. L.
, and
E.
Benzeden
,
2014
:
Simple generalization approach for intensity–duration–frequency relationships
.
Hydrol. Processes
,
28
,
1114
1123
, doi:.
Ciftlik
,
D.
,
2012
: Trend analysis of annual rainfall observed in DSI stations in Aegean region. MSc. thesis, Dept. of Civil Engineering, Ege University, 74 pp.
Cigizoglu
,
H. K.
,
M.
Bayazit
, and
B.
Onoz
,
2005
:
Trends in the maximum, mean, and low flows of Turkish rivers
.
J. Hydrometeor.
,
6
,
280
290
, doi:.
De Lima
,
M. I. P.
,
S. C. P.
Carvalho
,
J. L. M. P.
de Lima
, and
M. F. E. S.
Coelho
,
2010
:
Trends in rainfall: Analysis of long annual and monthly time series from mainland Portugal
.
Adv. Geosci.
,
25
,
155
160
, doi:.
Douglas
,
E. M.
,
R. M.
Vogel
, and
C. N.
Kroll
,
2000
:
Trends of floods and low flows in the United States: Impact of spatial correlation
.
J. Hydrol.
,
240
,
90
105
, doi:.
Feidas
,
H.
,
Ch.
Noulopoulou
,
T.
Makrogiannis
, and
E.
Bora-Senta
,
2007
:
Trend analysis of precipitation time series in Greece and their relationship with circulation using surface and satellite data: 1955–2001
.
Theor. Appl. Climatol.
,
87
,
155
177
, doi:.
Haan
,
C. T.
,
2002
:
Statistical Methods in Hydrology
. 2nd ed. Iowa State Press, 496 pp.
Hirsch
,
R. M.
,
R. B.
Alexander
, and
R. A.
Smith
,
1991
:
Selection of methods for the detection and estimation of trends in water quality
.
Water Resour. Res.
,
27
,
803
813
, doi:.
Jung
,
H. S.
,
Y. E.
Choi
,
J. H.
Oh
, and
G. H.
Lim
,
2002
:
Recent trends in temperature and precipitation over South Korea
.
Int. J. Climatol.
,
22
,
1327
1337
, doi:.
Kendall
,
M. G.
,
1975
:
Rank Correlation Methods
. Charles Griffin, 135 pp.
Krichak
,
S. O.
, and
P.
Alpert
,
2005
:
Signatures of NAO in the atmospheric circulation during wet winter months over the Mediterranean region
.
Theor. Appl. Climatol.
,
82
,
27
39
, doi:.
Kulkarni
,
A.
, and
H.
von Storch
,
1995
:
Monte Carlo experiments on the effect of serial correlation on the Mann–Kendall test of trends
.
Meteor. Z.
,
4
,
82
85
.
Kundzewicz
,
Z. W.
, and
A.
Robson
, Eds.,
2000
: Detecting trend and other changes in hydrological data. WCDMP-45, WMO/TD 1013, World Climate Programme–Water, WMO/UNESCO, Geneva, Switzerland, 157 pp.
Lettenmaier
,
D. P.
,
E. F.
Wood
, and
J. R.
Wallis
,
1994
:
Hydro-climatological trends in the continental United States
.
J. Climate
,
7
,
586
607
, doi:.
Liang
,
L.
,
L.
Li
, and
Q.
Liu
,
2011
:
Precipitation variability in northeast China from 1961 to 2008
.
J. Hydrol.
,
404
,
67
76
, doi:.
Machiwal
,
D.
, and
M.
Kumar Jha
,
2012
: Methods for testing normality of hydrologic time series. Hydrologic Time Series Analysis: Theory and Practice, Springer, 32–50.
Madansky
,
A.
,
1988
:
Prescriptions for Working Statisticians.
Springer-Verlag, 295 pp.
McCuen
,
R. H.
,
2003
: Modeling Hydrologic Change: Statistical Methods. Lewis Publishers, 433 pp.
Onoz
,
B.
, and
M.
Bayazıt
,
2003
:
The power of statistical tests for trend detection
.
Turk. J. Eng. Environ. Sci.
,
27
,
247
251
.
Ozkul
,
S.
,
2009
:
Assessment of climate change effects in Aegean river basins: The case of Gediz and Buyuk Menderes basins
.
Climatic Change
,
97
,
253
283
, doi:.
Partal
,
T.
, and
E.
Kahya
,
2006
:
Trend analysis in Turkish precipitation data
.
Hydrol. Processes
,
20
,
2011
2026
, doi:.
Penalba
,
O. C.
, and
W. M.
Vargas
,
2004
:
Interdecadal and interannual variations of annual and extreme precipitation over central-northeastern Argentina
.
Int. J. Climatol.
,
24
,
1565
1580
, doi:.
Salas
,
J. D.
,
1993
: Analysis and modeling of hydrologic time series. Handbook of Hydrology, D. R. Maidment, Ed., McGraw-Hill, 19.1–19.72.
Seidel
,
D. J.
,
Q.
Fu
,
W. J.
Randel
, and
T. J.
Reichler
,
2008
:
Widening of the tropical belt in a changing climate
.
Nat. Geosci.
,
1
,
21
24
, doi:.
Sen
,
P. K.
,
1968
:
Estimates of the regression coefficient based on Kendall’s Tao
.
J. Amer. Stat. Assoc.
,
63
,
1379
1389
, doi:.
Sneyers
,
R.
,
1990
: On the statistical analysis of series of observations. World Meteorological Organization Tech. Note 143, 192 pp.
Taschetto
,
A. S.
, and
M. H.
England
,
2009
:
El Niño Modoki impacts on Australian rainfall
.
J. Climate
,
22
,
3167
3174
, doi:.
Theil
,
H.
,
1950
: A rank-invariant method of linear and polynomial regression analysis. Proc. K. Ned. Akad. Wet.,53, 386–392, 512–525, 1397–1412.
Thode
,
H. C.
,
2002
:
Testing for Normality.
Marcel Dekker, 368 pp.
Toros
,
H. D.
,
A.
Deniz
, and
H.
Karan
,
1994
: Statistical analysis of western Anatolia precipitation (in Turkish). Proc. National Hydrometeorology Symp., Istanbul, Turkey, Istanbul Technical University,
185
209
.
Türkeş
,
M.
,
1996
:
Spatial and temporal analysis of annual rainfall variations in Turkey
.
Int. J. Climatol.
,
16
,
1057
1076
, doi:.
Türkeş
,
M.
, and
E.
Erlat
,
2003
:
Precipitation changes and variability in Turkey linked to the North Atlantic Oscillation during the period 1930–2000
.
Int. J. Climatol.
,
23
,
1771
1796
, doi:.
USEPA
,
1996
: Guidance for data quality assessment: Practical methods for data analysis. EPA QA/G-9, U.S. Environmental Protection Agency, 180 pp.
von Storch
,
H.
, and
A.
Navarra
,
1995
: Analysis of Climate Variability. Springer, 352 pp.
Wang
,
S.
,
X.
Zhang
,
Z.
Liu
, and
D.
Wang
,
2013
:
Trend analysis of precipitation in the Jinsha River basin in China
.
J. Hydrometeor.
,
14
,
290
303
, doi:.
Xoplaki
,
E.
,
J.
Luterbacher
,
R.
Burkardt
,
I.
Patrikas
, and
P.
Maheras
,
2000
:
Connection between the large-scale 500
hPa geopotential height fields precipitation over Greece during winter time
.
Climate Res.
,
14
,
129
126
, doi:.
Xoplaki
,
E.
,
J. F.
Gonzalez-Rauco
,
J.
Luterbacher
, and
H.
Wenner
,
2004
:
Wet season Mediterranean precipitation variability: Influence of large-scale dynamics and trends
.
Climate Dyn.
,
23
,
63
78
, doi:.
Yue
,
S.
,
P.
Pilon
, and
G.
Cavadias
,
2002a
:
Power of the Mann–Kendall and Spearman’s rho tests for detection monotonic trends in hydrological series
.
J. Hydrol.
,
259
,
254
271
, doi:.
Yue
,
S.
,
P.
Pilon
,
B.
Phinney
, and
G.
Cavadias
,
2002b
:
The influence of autocorrelation on the ability to detect trend in hydrological series
.
Hydrol. Processes
,
16
,
1807
1829
, doi:.
Yue
,
S.
,
P.
Pilon
, and
B.
Phinney
,
2003
:
Canadian stream flow trend detection: Impacts of serial and cross-correlation
.
Hydrol. Sci. J.
,
48
,
51
63
, doi:.
Zhang
,
X.
,
L. A.
Vincent
,
W. D.
Hogg
, and
A.
Niitsoo
,
2000
:
Temperature and precipitation trends in Canada during the 20th century
.
Atmos.–Ocean
,
38
,
395
429
, doi:.