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An innovative method for trend analysis of monthly pan evaporations
Journal of Hydrology 527 (2015) 1123–1129
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Technical Note
An innovative method for trend analysis of monthly pan evaporations Ozgur Kisi ⇑ Canik Basari University, Architecture and Engineering Faculty, Civil Engineering Department, 55080 Samsun, Turkey
a r t i c l e
i n f o
Article history: Received 4 May 2015 Received in revised form 26 May 2015 Accepted 4 June 2015 Available online 14 June 2015 This manuscript was handled by Geoff Syme, Editor-in-Chief Keywords: Trend analysis Innovative method Mann–Kendall Monthly pan evaporation
s u m m a r y Trend analysis of monthly pan evaporations was performed by using recently developed innovative trend analysis (ITA) method. The ITA was applied to the monthly pan evaporation data of six different locations, Adiyaman, Batman, Diyarbakir, Gaziantep, Kilis and Siirt in Turkey. Monthly trends of pan evaporation were also investigated by commonly used non-parametric Mann–Kendall (MK) method. According to the MK method, a significantly decreasing trend was found for the Adiyaman Station while the Diyarbakir and Kilis stations showed significantly increasing trend at the confidence level of 10%. No trend was found for the Batman, Gaziantep and Siirt stations with respect to MK. The ITA results indicated that the low, medium and peak pan evaporation values of the Batman, Gaziantep and Siirt stations had some increasing and decreasing trends although no trend was found for these stations according to the MK test. The main advantages of innovative method are that it is not dependent on any assumption such as serial correlation, non-normality and sample number and trends of low, medium and high data can be easily observed by this method. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction Pan evaporation is very important in estimating water budgeting and modeling crop water response to different weather conditions. It is commonly used as an index of evapotranspiration and for predicting lake and reservoir evaporation. It is also a useful parameter in estimating reference evapotranspiration (Snyder, 1992; Shirsath and Singh, 2010). Trend analysis of pan evaporation is widely relevant to the hydrological community as indicators of hydrological and climate change and is very important for planning regional water resources. Trends of hydrologic variables have been investigated by many researchers using different methodologies (Biswas, 2003; Kahya and Kalayci, 2004; Jonsdottir et al., 2006, 2008; Feidas et al., 2007; Kim and Jain, 2010; Yin et al., 2010; Kliment et al., 2011; Tabari et al., 2011; Jhajharia et al., 2012; Ceribasi et al., 2013; Gebremicael et al., 2013; Gocic and Trajkovic, 2013, 2014; Liu and Zhang, 2013; Kazmierczak et al., 2014). Kahya and Kalayci (2004) investigated the trends of monthly streamflows of Turkey by using Mann–Kendall, Sen’s T, the Spearman’s Rho and Seasonal Kendall methods. Jonsdottir et al. (2006) investigated the long term variability of precipitation, temperature and discharge of Icelandic rivers using MK test. Feidas et al. (2007) examined the trends of annual and seasonal precipitation time series of ⇑ Tel.: +90 362 2801080. E-mail address: [email protected] http://dx.doi.org/10.1016/j.jhydrol.2015.06.009 0022-1694/Ó 2015 Elsevier B.V. All rights reserved.
Greece using MK test and they indicated that annual precipitation generally presents a clear significant decreasing trend for the period 1955–2001, which was determined by the respective decreasing trend in winter precipitation. Jonsdottir et al. (2008) analyzed the trends of annual means of temperature, precipitation and discharge, and of seasonal maximum precipitation at 17, 28 and 10 Icelandic stations, respectively, for the period 1961–2000 by using parametric methods. Kim and Jain (2010) investigated the changes in the seasonality of streamflow in the western United States based on a quantile regression methodology. Tabari et al. (2011) investigated the annual, seasonal and monthly trends of the Penman– Monteith ET0 in the western half of Iran using MK test, the Sen’s slope estimator and the linear regression. On the seasonal scale, they found stronger increasing trends in ET0 data in winter and summer compared with those in autumn and spring. Kliment et al. (2011) used MK trend test for analyzing annual and monthly rainfall–runoff data from Sumava Mountains (Bohemian Forest), the Jeseniky Mountains and the Krugne Mountains (Ore Mountains) in Czech Republic. Jhajharia et al. (2012) used MK test for the trend analysis of Penman–Monteith ET0 over the humid region of northeast (NE) India. During the last 22 years, they found significantly decreasing trends at annual and seasonal time scales for 6 sites in NE India. Gocic and Trajkovic (2013) investigated the annual and seasonal trends of seven meteorological variables of twelve weather stations in Serbia during 1980–2010 by using non-parametric Mann–Kendall and Sen’s methods. Ceribasi et al. (2013) analyzed the relationship among Sakarya River streamflow
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Black Sea
Turkey Diyarbakir Siirt Adiyaman Batman Gaziantep Kilis
Mediterranean Sea Fig. 1. The location of the six stations in Turkey.
Station
Data period
PEmin
PEmax
PEmean
SD
CV
Csx
Adiyaman Batman Diyarbakir Gaziantep Kilis Siirt
1970–2010 1986–2007 1970–2008 1970–2010 1970–2010 1975–2010
0.6 0.4 1.2 1.0 1.2 0.3
13.1 17.2 20.2 12.2 12.7 16.6
5.68 7.12 8.00 6.20 6.74 7.67
2.97 3.49 4.05 2.55 2.56 3.70
1.91 2.04 1.98 2.43 2.64 2.07
0.143 0.620 0.257 0.038 0.139 0.031
and sediment transported with rainfall by applying Mann–Kendall and Spearman Rho trend analysis methods. Gebremicael et al. (2013) used MK and Pettitt tests for examining the trends of Blue Nile flow and sediment load at the outlet of the Upper Blue Nile basin at El Diem station. Test results revealed statistically significant increasing trends of annual stream flow, wet season streamflow and sediment load at confidence level of 5% while the dry season flow indicated significantly decreasing trend. The annual rainfall over the basin, however, showed no significant trends. Gocic and Trajkovic (2014) examined the FAO-56 Penman– Monteith (FAO-56 PM) and adjusted Hargreaves (AHARG) reference evapotranspiration (ET0) trends at monthly, seasonal and annual time scales by using linear regression, Mann–Kendall and Spearman’s Rho tests at the 1% and 5% significance levels. Kazmierczak et al. (2014) examined the trend analysis of annual and seasonal (May–October) rainfall data of Upper Odra Catchment using MK test and a decreasing trend was found in annual precipitation amount in the period 1954–2013, for Legnica and Opole at a significance level above 75%. There are limited studies in the literature that investigate the trends of pan evaporation (Tebakari et al., 2005; Zuo et al., 2006; Liu et al., 2010; Tabari and Marofi, 2010; Talaee et al., 2014). Tebakari et al. (2005) examined the temporal and spatial distribution characteristics of the pan evaporation amount in the Chao Phraya River basin, in the Kingdom of Thailand for the period of 19 years, from 1982 to 2000. They could not find any significant
trend for the pan evaporation data they used. Zuo et al. (2006) analyzed the trends of pan evaporation and environmental factors for China in the last 40 years. They indicated that the long-term pan evaporation trend could not be defined by the change of an environmental factor, such as, it is more logical to attribute the pan evaporation decrease to the global radiation reduction in eastern China than in western China. Liu et al. (2010) investigated the trends of pan evaporation of China using MK test and generally no significant trend was found in pan evaporation data. Tabari and Marofi (2010) used MK test, the Sen’s slope estimator and the linear regression to investigate temporal variations of pan evaporation in Hamedan province in western Iran. They showed that the study area has become warmer and drier over the last 22 years end therefore, crop water requirements were increased. Talaee et al. (2014) examined the trends of the Hargreaves reference evapotranspiration, pan evaporation and pan coefficient series in the west of Iran by using the sequential MK, Kendall and
30
First half of the time series
Table 1 Basic statistics of pan evaporation data of six stations in Turkey.
25 20
Trend 15
No trend
10 5 0
0
5
10
15
20
25
30
Second half of the time series Fig. 2. The innovative trend method proposed by Sen (2012).
Table 2 Geographic characteristics and climatic conditions of the stations used in the study. Station
Adiyaman Batman Diyarbakir Gaziantep Kilis Siirt
Longitude, (E)
38° 41° 40° 37° 37° 41°
0
16 070 130 290 050 560
Latitude, (N)
37° 37° 37° 37° 36° 37°
0
45 530 540 040 430 550
Elevation (m a.s.l.)
679 610 649 854 638 896
De Martonne Index
Climate
14.11 10.40 10.83 12.66 10.90 14.80
Dry, Dry, Dry, Dry, Dry, Dry,
semi-arid semi-arid semi-arid semi-arid semi-arid semi-arid
(semi (semi (semi (semi (semi (semi
desert) desert) desert) desert) desert) desert)
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O. Kisi / Journal of Hydrology 527 (2015) 1123–1129
14
Adiyaman
20
y = -0.0041x + 6.3258
Batman
12
Ep, mm
10
Ep, mm
y = 0.0157x + 5.9247
15
8 6 4
10 5
2 0 1 13 25 37 49 61 73 85 97 109 121 133 145
1 26 51 76 101 126 151 176 201 226 251 276 301
0
Month 25
Diyarbakir
Month 14
y = 0.0159x + 6.1091
15 10
8 6 4
5
2 0 1 23 45 67 89 111 133 155 177 199 221 243 265
210
229
191
172
153
134
96
115
77
58
39
1
20
0
Month 14
Month 20
y = 0.0094x + 5.9574
Kilis
Siirt
12
y = 0.0031x + 7.2708
15
Ep, mm
10
Ep, mm
y = 0.0029x + 5.9415
10
Ep, mm
Ep, mm
Gaziantep
12
20
8 6 4
10 5
2 232
253
211
190
169
148
127
85
106
43
Month
64
1
1 14 27 40 53 66 79 92 105 118 131 144 157
22
0
0
Month
Fig. 3. Time variations and linear trends of PE data for each station.
Spearman tests for the period 1982–2003. In their study, no significant trend was found in the reference evapotranspiration time series, while an upward trend of 16 mm/year was observed in the pan evaporation series. Recently, innovative trend analysis method have been successfully applied in water resources (Sen, 2012, 2014; Haktanir and Citakoglu, 2014; Kisi and Ay, 2014; Ay and Kisi, 2015). Sen proposed a new innovative trend analysis (ITA) technique in 2012 (Sen, 2012). He reported that commonly used MK and Spearman’s rho tests have some restrictive assumptions, such as independent structure of the time series, normality of the distribution, and length of data. Haktanir and Citakoglu (2014) applied ITA method to data of 14 standard duration annual maximum rainfall series. Kisi and Ay (2014) investigated trends of some water quality 2 +3 parameters such as pH, T, EC, Na+, K+, CO2 3 , HCO3 , Cl , SO4 , B and Q recorded at five different stations by ITA and MK. Sen (2014) applied ITA method for temperature data recorded at the Marmara region in Turkey. Ay and Kisi (2015) examined the trend
of monthly total precipation of six different provinces in Turkey by MK and ITA. To the knowledge of the author, there is not any published work in the literature related to application of ITA to pan evaporation. The aim of this study is to investigate the applicability of ITA method which is not dependent on any restrictive assumption as serial correlation, non-normality and sample number to monthly pan evaporations. For this aim, pan evaporation data from six different locations, Adiyaman, Batman, Diyarbakir, Gaziantep, Kilis and Siirt in Turkey were used. Data were also analyzed by commonly used MK trend test and results were presented. 2. Study area and data In the present study, pan evaporation (PE) data of Adiyaman (long. 38° 160 E, lat. 37° 450 N, alt. 679 m), Batman (long. 41° 070 E, lat. 37° 530 N, alt. 610), Diyarbakir (long. 40° 130 E, lat. 37° 540 N, alt. 649 m), Gaziantep (long. 40° 130 E, lat. 37° 540 N, alt.
Table 3 Mann–Kendall test results of the monthly pan evaporations. Station
Data period
Calculated ±Z
Critical ±Z0.90
Critical ±Z0.95
H0 hypothesis a = 10%
H0 hypothesis a = 5%
Trend ± a = 10%
Trend ± a = 5%
Adiyaman Batman Diyarbakir Gaziantep Kilis Siirt
1970–2010 1986–2007 1970–2008 1970–2010 1970–2010 1975–2010
2.072 1.250 4.124 1.344 2.214 0.923
±1.65 ±1.65 ±1.65 ±1.65 ±1.65 ±1.65
±1.96 ±1.96 ±1.96 ±1.96 ±1.96 ±1.96
Reject Accept Reject Accept Reject Accept
Reject Accept Reject Accept Reject Accept
Yes () No Yes (+) No Yes (+) No
Yes () No Yes (+) No Yes (+) No
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Table 4 Spearman Rho test results of the monthly pan evaporations. Station
Data period
Calculated ±Z
Critical ±Z0.90
Critical ±Z0.95
H0 hypothesis a = 10%
H0 hypothesis a = 5%
Trend ± a = 10%
Trend ± a = 5%
Adiyaman Batman Diyarbakir Gaziantep Kilis Siirt
1970–2010 1986–2007 1970–2008 1970–2010 1970–2010 1975–2010
1.875 1.500 4.396 1.545 2.283 0.966
±1.65 ±1.65 ±1.65 ±1.65 ±1.65 ±1.65
±1.96 ±1.96 ±1.96 ±1.96 ±1.96 ±1.96
Reject Accept Reject Accept Reject Accept
Accept Accept Reject Accept Reject Accept
Yes () No Yes (+) No Yes (+) No
No No Yes (+) No Yes (+) No
14
20
(a)
(a)
12
15
PE, mm (1970-1992)
PE, mm (1970-1989)
10
8
6
Trend No trend
4
+5% band -%5 band
2
0
10
Trend No trend +5% band
5
-10% band
-%5 band
+10% band
-10% band +10% band
0
2
4
6
8
10
12
14
0
PE, mm (1990-2010)
0
2
4
6
8
10
12
14
16
18
20
PE, mm (1993-2008) 18
(b) 16
(b)
12
14 10
PE, mm (1970-1989)
PE, mm (1986-1996)
12 10 8
Trend 6
No trend +5% band
4
8
6
Trend No trend
4
-%5 band
+5% band
-10% band
2
-%5 band
+10% band
2
-10% band
0 0
2
4
6
8
10
12
14
16
18
PE, mm (1997-2007) Fig. 4. The results of Sen’s method for (a) Adiyaman and (b) Batman stations.
+10% band 0
0
2
4
6
8
10
12
PE, mm (1990-2010) Fig. 5. The results of Sen’s method for (a) Diyarbakir and (b) Gaziantep stations.
649 m), Kilis (long. 37° 050 E, lat. 36° 430 N, alt. 638 m) and Siirt (long. 41° 560 E, lat. 37° 550 N, alt. 896 m) stations operated by the Turkish Meteorological Organization were used. The stations are located in Southeastern Anatolia Region of Turkey (Fig. 1) where the annual precipitation varies between 400 and 800 mm. The greatest portion of the annual precipitation falls in winter while the wettest months are December and January. Summers in the region are very dry and have high temperatures (Komuscu et al., 1998). Temperatures are ranged between 3.3 °C and
20.5 °C in winter months and ranged between 16.0 °C and 46.8 °C in summer months. Data period and basic statistical properties of the pan evaporation data are provided in Table 1 for each station. In the table, the PEmin, PEmax, PEmean, SD, Cv and Csx indicate the minimum, maximum, mean pan evaporations, standard deviation, variation coefficient and skewness, respectively. The Kilis and Gaziantep data show higher variation than the other stations (see
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O. Kisi / Journal of Hydrology 527 (2015) 1123–1129
Cv values in Table 1). PE data of Batman Station show the highest skewness while the Gaziantep and Siirt data have significantly low skewed distribution (close to normal distribution). Diyarbakir Station has the highest PE values. The basic geographic and climate characteristics of the six station are provided in Table 2. De Martonne aridity indexes are given for each station. The expression of this index developed by (De Martonne, 1926) is
Iar-DM ¼ P=ðT m þ 10Þ
ð1Þ
where P is total annual precipitation and Tm is mean annual temperature. The equation contains the value of 10 °C to produce positive results in regions with negative average annual temperatures, such as mountainous regions or deserts from median latitudes (Lungu et al., 2011). It is clear from Table 2 that all the stations have a dry, semi-arid climate. 3. Innovative trend method In the innovative trend analysis (ITA), first proposed by Sen (2012), time series is divided into two equal parts. Both sub-series are separately sorted in ascending order. The first half
of the time series is located on the X-axis, and the second half of the time series is located on the Y-axis. Fig. 2 clearly shows the innovative method on the Cartesian coordinate system. It is clear from the figure that if investigated data are collected on the 1:1 ideal line, we can say that there is no trend in the time series. If data are located on the upper triangular area of the ideal line (45° line), we can say that there exists an increasing trend in the time series. If data are accumulated in the lower triangular area of the 1:1 line, we can say that there is a decreasing trend in the time series (Sen, 2012, 2014). Thus, trends of low, medium and high values of any engineering hydro-meteorological or hydro-climatic time series can be clearly identified by this method. 4. Mann–Kendall method Mann–Kendall (MK) is a non-parametric trend test which is commonly used in identifying trends in climatological and hydrological time series (Kendall, 1975; Mann, 1945). S test statistics of MK can be given as
S¼
n X i1 X signðxi xj Þ
ð2Þ
i¼2 j¼1
(a)
10
8 9 > < if ðxi xj Þ < 0 then 1 > = signðxi xj Þ ¼ if ðxi xj Þ ¼ 0 then 0 > > : ; if ðxi xj Þ > 0 then 1
8
VarðSÞ ¼
PE, mm (1986-1996)
12
Trend No trend +5% band -%5 band 2
-10% band +10% band
0
0
2
4
6
8
10
12
PE, mm (1997-2008)
(b)
16 14
PE, mm (1975-1992)
Pl
k1 t k ðt k
18
1Þð2t k þ 5Þ
ð4Þ
where n is the number of the data and xi and xj are the sequential data in the time series, tk is the number of ties for the kth value. The second term in Eq. (4) is given for tied censored data. Z, standard test statistics can be computed as
6
4
nðn 1Þð2n þ 5Þ
ð3Þ
8 9 ffiffiffiffiffiffiffiffiffi > if S < 0 then pSþ1 > > > VarðSÞ > > < = Z ¼ if ðxi xj Þ ¼ 0 then 0 > > > > > ffiffiffiffiffiffiffiffiffi > : if ðxi xj Þ > 0 then pS1 ;
ð5Þ
VarðSÞ
Positive Z values indicate upward (increasing) trends while negative Z values reveal downward (decreasing) trends. For testing both increasing and decreasing trends at a significance level, the null hypothesis was rejected for the absolute value of Z greater than Z1a/2, obtained from the standard normal cumulative distribution tables (Partal and Kahya, 2006; Tabari et al., 2011; Sonali and Nagesh Kumar, 2013). Significance levels of a = 10% and 5% were applied in the present study.
12
5. Application and results
10
The time variations and linear trends of PE data are illustrated in Fig. 3 for each station. From the figure, it is observed that the Adiyaman data show decreasing trend while the Batman, Diyarbakir, Gaziantep, Kilis and Siirt stations have increasing trend. Table 3 indicates the MK test results of the six provinces according to the confidence levels of 10% and 5%. It should be noted that pre-whitening was not applied here in order not to lose originality of the PE time series (Sen, 2012; Sang et al., 2014). It is clear from the table that the Adiyaman Station shows decreasing trend while the Batman, Diyarbakir, Gaziantep, Kilis and Siirt stations have increasing trend. Diyarbakir and Kilis stations indicate significantly increasing trends according to the both 10% and 5% confidence levels. Adiyaman Station, however, shows significantly decreasing trends at the both confidence levels. Spearman Rho test results are given in Table 4 for each station according to the confidence levels
8
Trend 6
No trend +5% band
4
-%5 band -10% band
2
+10% band 0
0
2
4
6
8
10
12
14
16
PE, mm (1993-2010) Fig. 6. The results of Sen’s method for (a) Kilis and (b) Siirt stations.
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Table 5 Results of the Mann–Kendall (MK), Spearman Rho and ITA methods for monthly pan evaporations. Station
Mann–Kendall (a = 5% and 10%)
Adiyaman Batman Diyarbakir Gaziantep Kilis Siirt
Yes () No Yes (+) No Yes (+) No
Spearman Rho
ITA method (5% band)
(a = 5% and 10%)
Low
Medium
Peak
Low
Medium
Peak
No and Yes () No Yes (+) No Yes (+) No
Yes Yes Yes Yes Yes Yes
Yes No Yes No Yes Yes
Yes Yes Yes Yes No Yes
No Yes Yes Yes Yes Yes
No No Yes (+) No Yes (+) Yes (+)
Yes () Yes (+) Yes (+) No No No
of 10% and 5%. From the table, it is obvious that the trends are similar to those obtained using the MK method. Comparison of Tables 3 and 4 clearly indicates that the Spearman Rho method gives slightly higher positive trends and lower negative trends than the MK method. According to the Spearman Rho method, for example, Adiyaman Station shows significantly decreasing trend at a confidence level of 10% while it has no trend with respect to MK. The MK and Spearman Rho trend tests resulted inverse trends in the PE time series at the two nearby stations of Adiyaman (with significant negative trend) and Gaziantep (with positive trend). It was reported that inverse trends at two nearby stations may be due to some natural factors and special conditions (Turkes and Sumer, 2004). Different microclimates between the stations mainly associated with local topography and wind circulation may cause this trend difference. The trends of nature and magnitude of the meteorological parameters (e.g., evaporation) may be diversely affected by the local physical geographic (e.g., topography etc.) and atmospheric circulation features (Tabari et al., 2011). The other reason for different trend of these nearby stations may be due to the fact that the Adiyaman Station is near to Ataturk Dam which has the largest reservoir in Turkey and therefore has a humid climate. Urbanization (changes in land uses such as non-agricultural uses of lands, and vegetation cover) may also be another reason for inverse PE trends at these nearby stations. Turkes and Sumer (2004) classified the Adiyaman City as urban (100,000 < Population < 500,000) while the Gaziantep City was classified as large urban (500,000 < Population < 1,000,000). The results of the ITA are provided in Fig. 4 for the Adiyaman and Batman stations. According to the 5% relative band, low PE values (<3 mm) of Adiyaman Station show monotonic increasing trend while they have no trend with respect to 10% relative band. The medium and high PE values (>3 mm and <13 mm) indicate decreasing trend with respect to 5% relative band which they generally do not access 10% relative band limit. Some peak values higher than 13 mm, however, indicate monotonic increasing trend according to the 10% relative band. In Batman Station, low PE values (<4 mm) show significantly decreasing trend while the medium values (>5 mm and <9 mm) have no trend with respect to both relative bands. The high or peak PE values (>9 mm) indicate significantly increasing trend with respect to 10% relative band. Fig. 5 illustrates the monthly PE trends of Diyarbakir and Gaziantep stations. It is clear from the figure that there exists an increasing trend for low, medium and high values of the Diyarbakir Station with respect to 10% relative band. In Gaziantep Station, the low PE values lower than 2 mm show increasing trend while the medium (>3 mm and <8 mm) and medium-high values (>8 mm and <10 mm) generally indicate no trend with respect to 10% relative band. However, some medium (>3 mm and <5 mm) and peak (>10 mm) values show monotonic increasing trend according to the 5% relative band. The results of the ITA of monthly PE data of Kilis and Siirt stations are given in Fig. 6. In Kilis Station, the low (<4 mm) and low-medium (>4 mm and <6.5 mm) PE values show monotonic increasing trend while the medium-high (>6.5 mm and <9 mm) generally indicate no
(+) () (+) (+) (+) (+)
() (+) (+) (+)
ITA method (10% band)
() (+) (+) (+) (+)
() (+) (+) (+) (+)
trend with respect to 10% relative band. However, peak (>9 mm) values show no trend according to the 5% relative band. The low (<2 mm) PE values of Siirt Station show increasing trend while the low-medium (>4 mm and <7 mm) values indicate slightly increasing trend with respect to 10% relative band. The medium (>7 mm and <11 mm) and medium high (>11 mm and <13 mm) PE values show no trend according to the 5% relative band while the peak values indicate increasing trend with respect to 5% relative band. The ITA results of six stations given in Figs. 4–6 are summarized and compared with MK and Spearman Rho in Table 5. It is clear from the table that the ITA, MK and Spearman Rho give similar trend results for the Adiyaman, Diyarbakir and Kilis stations. However, ITA gives some positive or negative trends for the Batman, Gaziantep and Siirt although the MK and Spearman Rho tests indicate no trend for these stations. Especially for the Batman station, the MK and Spearman Rho indicate increasing trend but not significant with respect to 10% and 5% confidence levels. However, significantly decreasing and increasing trends are clearly seen for the low and high PE values in this station (Fig. 4). According to the MK, Spearman Rho and ITA methods, Diyarbakir and Kilis stations have significantly increasing PE trends and these may cause droughts or water stress at these cities in the future. According to the ITA method, Batman Station has also significantly increasing trend in peak PE values after 1997s. Significantly increasing trends imply global warming effect at the location of Diyarbakir, Kilis and Batman stations. 6. Conclusion In this study, trends of monthly pan evaporations were investigated by using an innovative method, Mann–Kendall and Spearman Rho test. Data from Adiyaman, Batman, Diyarbakir, Gaziantep, Kilis and Siirt stations in Turkey were used in the analysis. According to the MK and Spearman Rho methods, the Adiyaman Station showed significantly decreasing trend while the Diyarbakir and Kilis stations had significantly increasing trend at the confidence level of 10%. Batman, Gaziantep and Siirt stations also showed increasing trend but not significant. MK, Spearman Rho and innovative methods provided similar trend results for the Adiyaman, Diyarbakir and Kilis stations. The results of innovative method, however, indicated that the Batman, Gaziantep and Siirt stations had some increasing and decreasing trends for the low, medium and peak pan evaporation values although there was no trend in these stations according to the MK and Spearman Rho tests. The present study revealed that innovative trend analysis method has some advantages in relative to the MK and Spearman Rho methods. One main advantage is that it does not have any assumptions (e.g., serial correlation, non-normality, sample number etc.) as in the MK and Spearman Rho methods. The other main advantage is that the trends of low, medium and high data can be easily identified by innovative method. This new method can provide a priori view to the engineers and can be used in global climate scenarios.
O. Kisi / Journal of Hydrology 527 (2015) 1123–1129
Acknowledgement This study was supported by The Turkish Academy of Sciences (TÜBA). The author would like to thank TÜBA for its support of this study. References Ay, M., Kisi, O., 2015. Investigation of trend analysis of monthly total precipitation by an innovative method. Theoret. Appl. Climatol. 120 (3–4), 617–629. Biswas, S., 2003. Groundwater flow direction and long term trend of water level of nadia district, West Bengal: a statistical analysis by Satyajit Biswas. J. Geol. Soc. India 61, 22–36, Reply. Journal of the Geological Society of India 61(6): 741– 742. Ceribasi, G., Dogan, E., Sonmez, O., 2013. Evaluation of Sakarya River streamflow and sediment transport with rainfall using trend analysis. Fresenius Environ. Bull. 22 (3A), 846–852. De Martonne, E., 1926. Une nouvelle fonction climatologique: L’indice d’aridité. La Meteorologie, 449–458. Feidas, H., Noulopoulou, C., Makrogiannis, T., Bora-Senta, E., 2007. Trend analysis of precipitation time series in Greece and their relationship with circulation using surface and satellite data: 1955–2001. Theoret. Appl. Climatol. 87 (1–4), 155– 177. Gebremicael, T.G., Mohamed, Y.A., Betrie, G.D., van der Zaag, P., Teferi, E., 2013. Trend analysis of runoff and sediment fluxes in the Upper Blue Nile basin: a combined analysis of statistical tests, physically-based models and landuse maps. J. Hydrol. 482, 57–68. Gocic, M., Trajkovic, S., 2013. Analysis of changes in meteorological variables using Mann–Kendall and Sen’s slope estimator statistical tests in Serbia. Global Planet. Change 100, 172–182. Gocic, M., Trajkovic, S., 2014. Analysis of trends in reference evapotranspiration data in a humid climate. Hydrol. Sci. J.–J. Des Sci. Hydrol. 59 (1), 165–180. Haktanir, T., Citakoglu, H., 2014. Trend, independence, stationarity, and homogeneity tests on maximum rainfall series of standard durations recorded in Turkey. J. Hydrol. Eng. 19 (9). Jhajharia, D., Dinpashoh, Y., Kahya, E., Singh, V.P., Fakheri-Fard, A., 2012. Trends in reference evapotranspiration in the humid region of northeast India. Hydrol. Process. 26 (3), 421–435. Jonsdottir, J.F., Jonsson, P., Uvo, C.B., 2006. Trend analysis of Icelandic discharge, precipitation and temperature series. Nord. Hydrol. 37 (4–5), 365–376. Jonsdottir, J.F., Uvo, C.B., Clarke, R.T., 2008. Trend analysis in Icelandic discharge, temperature and precipitation series by parametric methods. Hydrol. Res. 39 (5–6), 425–436. Kahya, E., Kalayci, S., 2004. Trend analysis of streamflow in Turkey. J. Hydrol. 289 (1–4), 128–144. Kazmierczak, B., Kotowski, A., Wdowikowski, M., 2014. Trend analysis of annual and seasonal precipitation amounts in the upper odra catchment. Ochrona Srodowiska 36 (3), 49–54. Kendall, M.G., 1975. Rank Correlation Methods. Charless Griffin, London. Kim, J.S., Jain, S., 2010. High-resolution streamflow trend analysis applicable to annual decision calendars: a western United States case study. Clim. Change 102 (3–4), 699–707.
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Kisi, O., Ay, M., 2014. Comparison of Mann–Kendall and innovative trend method for water quality parameters of the Kizilirmak River, Turkey. J. Hydrol. 513, 362–375. Kliment, Z., Matouskova, M., Ledvinka, O., Kralovec, V., 2011. Trend analysis of rainfall–runoff regimes in selected headwater areas of the Czech Republic. J. Hydrol. Hydromech. 59 (1), 36–50. Komuscu, A.U., Erkan, A., Oz, S., 1998. Possible impacts of climate change on soil moisture availability in the Southeast Anatolia Development Project Region (GAP): an analysis from an agricultural drought perspective. Clim. Change 40 (3–4), 519–545. Liu, X.M., Zhang, D., 2013. Trend analysis of reference evapotranspiration in Northwest China: the roles of changing wind speed and surface air temperature. Hydrol. Process. 27 (26), 3941–3948. Liu, M., Shen, Y.J., Zeng, Y., Liu, C.M., 2010. Trend in pan evaporation and its attribution over the past 50 years in China. J. Geog. Sci. 20 (4), 557–568. Lungu, M., Panaitescu, L., Nita, S., 2011. Aridity, climatic risk phenomenon in Dobrudja. Resent Environ. Sustain. Dev. 5 (1), 179–789. Mann, H.B., 1945. Nonparametric tests against trend. Econometrica 13, 245–259. Partal, T., Kahya, E., 2006. Trend analysis in Turkish precipitation data. Hydrol. Process. 20 (9), 2011–2026. Sang, Y.F., Wang, Z.G., Liu, C.M., 2014. Comparison of the MK test and EMD method for trend identification in hydrological time series. J. Hydrol. 510, 293–298. Sen, Z., 2012. Innovative trend analysis methodology. J. Hydrol. Eng. 17 (9), 1042– 1046. Sen, Z., 2014. Trend identification simulation and application. J. Hydrol. Eng. 19 (3), 635–642. Shirsath, P.B., Singh, A.K., 2010. A comparative study of daily pan evaporation estimation using ANN, regression and climate based models. Water Resour. Manage 24 (8), 1571–1581. Snyder, R.L., 1992. Equation for evaporation-pan to evapotranspiration conversions. J. Irrig. Drain. Eng.-Asce 118 (6), 977–980. Sonali, P., Nagesh Kumar, D., 2013. Review of trend detection methods and their application to detect temperature changes in India. J. Hydrol. 476, 212–227. Tabari, H., Marofi, S., 2010. Changes of pan evaporation in the West of Iran. Water Resour. Manage 25 (1), 97–111. Tabari, H., Marofi, S., Aeini, A., Talaee, P.H., Mohammadi, K., 2011. Trend analysis of reference evapotranspiration in the western half of Iran. Agric. For. Meteorol. 151 (2), 128–136. Talaee, P.H., Tabari, H., Abghari, H., 2014. Pan evaporation and reference evapotranspiration trend detection in western Iran with consideration of data persistence. Hydrol. Res. 45 (2), 213–225. Tebakari, T., Yoshitani, J., Suvanpimol, C., 2005. Time-space trend analysis in pan evaporation over Kingdom of Thailand. J. Hydrol. Eng. 10 (3), 205–215. Turkes, M., Sumer, U.M., 2004. Spatial and temporal patterns of trends and variability in diurnal temperature ranges of Turkey. Theoret. Appl. Climatol. 77 (3–4), 195–227. Yin, Y.H., Wu, S.H., Chen, G., Dai, E.F., 2010. Attribution analyses of potential evapotranspiration changes in China since the 1960s. Theoret. Appl. Climatol. 101 (1–2), 19–28. Zuo, H.C., Bao, Y., Mang, C.J., Hu, Y.Q., 2006. An analytic and numerical study on the physical meaning of pan evaporation and its trend in recent 40 years. Chin. J. Geophys.-Chin. Ed. 49 (3), 680–688.
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Technical Note
An innovative method for trend analysis of monthly pan evaporations Ozgur Kisi ⇑ Canik Basari University, Architecture and Engineering Faculty, Civil Engineering Department, 55080 Samsun, Turkey
a r t i c l e
i n f o
Article history: Received 4 May 2015 Received in revised form 26 May 2015 Accepted 4 June 2015 Available online 14 June 2015 This manuscript was handled by Geoff Syme, Editor-in-Chief Keywords: Trend analysis Innovative method Mann–Kendall Monthly pan evaporation
s u m m a r y Trend analysis of monthly pan evaporations was performed by using recently developed innovative trend analysis (ITA) method. The ITA was applied to the monthly pan evaporation data of six different locations, Adiyaman, Batman, Diyarbakir, Gaziantep, Kilis and Siirt in Turkey. Monthly trends of pan evaporation were also investigated by commonly used non-parametric Mann–Kendall (MK) method. According to the MK method, a significantly decreasing trend was found for the Adiyaman Station while the Diyarbakir and Kilis stations showed significantly increasing trend at the confidence level of 10%. No trend was found for the Batman, Gaziantep and Siirt stations with respect to MK. The ITA results indicated that the low, medium and peak pan evaporation values of the Batman, Gaziantep and Siirt stations had some increasing and decreasing trends although no trend was found for these stations according to the MK test. The main advantages of innovative method are that it is not dependent on any assumption such as serial correlation, non-normality and sample number and trends of low, medium and high data can be easily observed by this method. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction Pan evaporation is very important in estimating water budgeting and modeling crop water response to different weather conditions. It is commonly used as an index of evapotranspiration and for predicting lake and reservoir evaporation. It is also a useful parameter in estimating reference evapotranspiration (Snyder, 1992; Shirsath and Singh, 2010). Trend analysis of pan evaporation is widely relevant to the hydrological community as indicators of hydrological and climate change and is very important for planning regional water resources. Trends of hydrologic variables have been investigated by many researchers using different methodologies (Biswas, 2003; Kahya and Kalayci, 2004; Jonsdottir et al., 2006, 2008; Feidas et al., 2007; Kim and Jain, 2010; Yin et al., 2010; Kliment et al., 2011; Tabari et al., 2011; Jhajharia et al., 2012; Ceribasi et al., 2013; Gebremicael et al., 2013; Gocic and Trajkovic, 2013, 2014; Liu and Zhang, 2013; Kazmierczak et al., 2014). Kahya and Kalayci (2004) investigated the trends of monthly streamflows of Turkey by using Mann–Kendall, Sen’s T, the Spearman’s Rho and Seasonal Kendall methods. Jonsdottir et al. (2006) investigated the long term variability of precipitation, temperature and discharge of Icelandic rivers using MK test. Feidas et al. (2007) examined the trends of annual and seasonal precipitation time series of ⇑ Tel.: +90 362 2801080. E-mail address: [email protected] http://dx.doi.org/10.1016/j.jhydrol.2015.06.009 0022-1694/Ó 2015 Elsevier B.V. All rights reserved.
Greece using MK test and they indicated that annual precipitation generally presents a clear significant decreasing trend for the period 1955–2001, which was determined by the respective decreasing trend in winter precipitation. Jonsdottir et al. (2008) analyzed the trends of annual means of temperature, precipitation and discharge, and of seasonal maximum precipitation at 17, 28 and 10 Icelandic stations, respectively, for the period 1961–2000 by using parametric methods. Kim and Jain (2010) investigated the changes in the seasonality of streamflow in the western United States based on a quantile regression methodology. Tabari et al. (2011) investigated the annual, seasonal and monthly trends of the Penman– Monteith ET0 in the western half of Iran using MK test, the Sen’s slope estimator and the linear regression. On the seasonal scale, they found stronger increasing trends in ET0 data in winter and summer compared with those in autumn and spring. Kliment et al. (2011) used MK trend test for analyzing annual and monthly rainfall–runoff data from Sumava Mountains (Bohemian Forest), the Jeseniky Mountains and the Krugne Mountains (Ore Mountains) in Czech Republic. Jhajharia et al. (2012) used MK test for the trend analysis of Penman–Monteith ET0 over the humid region of northeast (NE) India. During the last 22 years, they found significantly decreasing trends at annual and seasonal time scales for 6 sites in NE India. Gocic and Trajkovic (2013) investigated the annual and seasonal trends of seven meteorological variables of twelve weather stations in Serbia during 1980–2010 by using non-parametric Mann–Kendall and Sen’s methods. Ceribasi et al. (2013) analyzed the relationship among Sakarya River streamflow
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Black Sea
Turkey Diyarbakir Siirt Adiyaman Batman Gaziantep Kilis
Mediterranean Sea Fig. 1. The location of the six stations in Turkey.
Station
Data period
PEmin
PEmax
PEmean
SD
CV
Csx
Adiyaman Batman Diyarbakir Gaziantep Kilis Siirt
1970–2010 1986–2007 1970–2008 1970–2010 1970–2010 1975–2010
0.6 0.4 1.2 1.0 1.2 0.3
13.1 17.2 20.2 12.2 12.7 16.6
5.68 7.12 8.00 6.20 6.74 7.67
2.97 3.49 4.05 2.55 2.56 3.70
1.91 2.04 1.98 2.43 2.64 2.07
0.143 0.620 0.257 0.038 0.139 0.031
and sediment transported with rainfall by applying Mann–Kendall and Spearman Rho trend analysis methods. Gebremicael et al. (2013) used MK and Pettitt tests for examining the trends of Blue Nile flow and sediment load at the outlet of the Upper Blue Nile basin at El Diem station. Test results revealed statistically significant increasing trends of annual stream flow, wet season streamflow and sediment load at confidence level of 5% while the dry season flow indicated significantly decreasing trend. The annual rainfall over the basin, however, showed no significant trends. Gocic and Trajkovic (2014) examined the FAO-56 Penman– Monteith (FAO-56 PM) and adjusted Hargreaves (AHARG) reference evapotranspiration (ET0) trends at monthly, seasonal and annual time scales by using linear regression, Mann–Kendall and Spearman’s Rho tests at the 1% and 5% significance levels. Kazmierczak et al. (2014) examined the trend analysis of annual and seasonal (May–October) rainfall data of Upper Odra Catchment using MK test and a decreasing trend was found in annual precipitation amount in the period 1954–2013, for Legnica and Opole at a significance level above 75%. There are limited studies in the literature that investigate the trends of pan evaporation (Tebakari et al., 2005; Zuo et al., 2006; Liu et al., 2010; Tabari and Marofi, 2010; Talaee et al., 2014). Tebakari et al. (2005) examined the temporal and spatial distribution characteristics of the pan evaporation amount in the Chao Phraya River basin, in the Kingdom of Thailand for the period of 19 years, from 1982 to 2000. They could not find any significant
trend for the pan evaporation data they used. Zuo et al. (2006) analyzed the trends of pan evaporation and environmental factors for China in the last 40 years. They indicated that the long-term pan evaporation trend could not be defined by the change of an environmental factor, such as, it is more logical to attribute the pan evaporation decrease to the global radiation reduction in eastern China than in western China. Liu et al. (2010) investigated the trends of pan evaporation of China using MK test and generally no significant trend was found in pan evaporation data. Tabari and Marofi (2010) used MK test, the Sen’s slope estimator and the linear regression to investigate temporal variations of pan evaporation in Hamedan province in western Iran. They showed that the study area has become warmer and drier over the last 22 years end therefore, crop water requirements were increased. Talaee et al. (2014) examined the trends of the Hargreaves reference evapotranspiration, pan evaporation and pan coefficient series in the west of Iran by using the sequential MK, Kendall and
30
First half of the time series
Table 1 Basic statistics of pan evaporation data of six stations in Turkey.
25 20
Trend 15
No trend
10 5 0
0
5
10
15
20
25
30
Second half of the time series Fig. 2. The innovative trend method proposed by Sen (2012).
Table 2 Geographic characteristics and climatic conditions of the stations used in the study. Station
Adiyaman Batman Diyarbakir Gaziantep Kilis Siirt
Longitude, (E)
38° 41° 40° 37° 37° 41°
0
16 070 130 290 050 560
Latitude, (N)
37° 37° 37° 37° 36° 37°
0
45 530 540 040 430 550
Elevation (m a.s.l.)
679 610 649 854 638 896
De Martonne Index
Climate
14.11 10.40 10.83 12.66 10.90 14.80
Dry, Dry, Dry, Dry, Dry, Dry,
semi-arid semi-arid semi-arid semi-arid semi-arid semi-arid
(semi (semi (semi (semi (semi (semi
desert) desert) desert) desert) desert) desert)
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O. Kisi / Journal of Hydrology 527 (2015) 1123–1129
14
Adiyaman
20
y = -0.0041x + 6.3258
Batman
12
Ep, mm
10
Ep, mm
y = 0.0157x + 5.9247
15
8 6 4
10 5
2 0 1 13 25 37 49 61 73 85 97 109 121 133 145
1 26 51 76 101 126 151 176 201 226 251 276 301
0
Month 25
Diyarbakir
Month 14
y = 0.0159x + 6.1091
15 10
8 6 4
5
2 0 1 23 45 67 89 111 133 155 177 199 221 243 265
210
229
191
172
153
134
96
115
77
58
39
1
20
0
Month 14
Month 20
y = 0.0094x + 5.9574
Kilis
Siirt
12
y = 0.0031x + 7.2708
15
Ep, mm
10
Ep, mm
y = 0.0029x + 5.9415
10
Ep, mm
Ep, mm
Gaziantep
12
20
8 6 4
10 5
2 232
253
211
190
169
148
127
85
106
43
Month
64
1
1 14 27 40 53 66 79 92 105 118 131 144 157
22
0
0
Month
Fig. 3. Time variations and linear trends of PE data for each station.
Spearman tests for the period 1982–2003. In their study, no significant trend was found in the reference evapotranspiration time series, while an upward trend of 16 mm/year was observed in the pan evaporation series. Recently, innovative trend analysis method have been successfully applied in water resources (Sen, 2012, 2014; Haktanir and Citakoglu, 2014; Kisi and Ay, 2014; Ay and Kisi, 2015). Sen proposed a new innovative trend analysis (ITA) technique in 2012 (Sen, 2012). He reported that commonly used MK and Spearman’s rho tests have some restrictive assumptions, such as independent structure of the time series, normality of the distribution, and length of data. Haktanir and Citakoglu (2014) applied ITA method to data of 14 standard duration annual maximum rainfall series. Kisi and Ay (2014) investigated trends of some water quality 2 +3 parameters such as pH, T, EC, Na+, K+, CO2 3 , HCO3 , Cl , SO4 , B and Q recorded at five different stations by ITA and MK. Sen (2014) applied ITA method for temperature data recorded at the Marmara region in Turkey. Ay and Kisi (2015) examined the trend
of monthly total precipation of six different provinces in Turkey by MK and ITA. To the knowledge of the author, there is not any published work in the literature related to application of ITA to pan evaporation. The aim of this study is to investigate the applicability of ITA method which is not dependent on any restrictive assumption as serial correlation, non-normality and sample number to monthly pan evaporations. For this aim, pan evaporation data from six different locations, Adiyaman, Batman, Diyarbakir, Gaziantep, Kilis and Siirt in Turkey were used. Data were also analyzed by commonly used MK trend test and results were presented. 2. Study area and data In the present study, pan evaporation (PE) data of Adiyaman (long. 38° 160 E, lat. 37° 450 N, alt. 679 m), Batman (long. 41° 070 E, lat. 37° 530 N, alt. 610), Diyarbakir (long. 40° 130 E, lat. 37° 540 N, alt. 649 m), Gaziantep (long. 40° 130 E, lat. 37° 540 N, alt.
Table 3 Mann–Kendall test results of the monthly pan evaporations. Station
Data period
Calculated ±Z
Critical ±Z0.90
Critical ±Z0.95
H0 hypothesis a = 10%
H0 hypothesis a = 5%
Trend ± a = 10%
Trend ± a = 5%
Adiyaman Batman Diyarbakir Gaziantep Kilis Siirt
1970–2010 1986–2007 1970–2008 1970–2010 1970–2010 1975–2010
2.072 1.250 4.124 1.344 2.214 0.923
±1.65 ±1.65 ±1.65 ±1.65 ±1.65 ±1.65
±1.96 ±1.96 ±1.96 ±1.96 ±1.96 ±1.96
Reject Accept Reject Accept Reject Accept
Reject Accept Reject Accept Reject Accept
Yes () No Yes (+) No Yes (+) No
Yes () No Yes (+) No Yes (+) No
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Table 4 Spearman Rho test results of the monthly pan evaporations. Station
Data period
Calculated ±Z
Critical ±Z0.90
Critical ±Z0.95
H0 hypothesis a = 10%
H0 hypothesis a = 5%
Trend ± a = 10%
Trend ± a = 5%
Adiyaman Batman Diyarbakir Gaziantep Kilis Siirt
1970–2010 1986–2007 1970–2008 1970–2010 1970–2010 1975–2010
1.875 1.500 4.396 1.545 2.283 0.966
±1.65 ±1.65 ±1.65 ±1.65 ±1.65 ±1.65
±1.96 ±1.96 ±1.96 ±1.96 ±1.96 ±1.96
Reject Accept Reject Accept Reject Accept
Accept Accept Reject Accept Reject Accept
Yes () No Yes (+) No Yes (+) No
No No Yes (+) No Yes (+) No
14
20
(a)
(a)
12
15
PE, mm (1970-1992)
PE, mm (1970-1989)
10
8
6
Trend No trend
4
+5% band -%5 band
2
0
10
Trend No trend +5% band
5
-10% band
-%5 band
+10% band
-10% band +10% band
0
2
4
6
8
10
12
14
0
PE, mm (1990-2010)
0
2
4
6
8
10
12
14
16
18
20
PE, mm (1993-2008) 18
(b) 16
(b)
12
14 10
PE, mm (1970-1989)
PE, mm (1986-1996)
12 10 8
Trend 6
No trend +5% band
4
8
6
Trend No trend
4
-%5 band
+5% band
-10% band
2
-%5 band
+10% band
2
-10% band
0 0
2
4
6
8
10
12
14
16
18
PE, mm (1997-2007) Fig. 4. The results of Sen’s method for (a) Adiyaman and (b) Batman stations.
+10% band 0
0
2
4
6
8
10
12
PE, mm (1990-2010) Fig. 5. The results of Sen’s method for (a) Diyarbakir and (b) Gaziantep stations.
649 m), Kilis (long. 37° 050 E, lat. 36° 430 N, alt. 638 m) and Siirt (long. 41° 560 E, lat. 37° 550 N, alt. 896 m) stations operated by the Turkish Meteorological Organization were used. The stations are located in Southeastern Anatolia Region of Turkey (Fig. 1) where the annual precipitation varies between 400 and 800 mm. The greatest portion of the annual precipitation falls in winter while the wettest months are December and January. Summers in the region are very dry and have high temperatures (Komuscu et al., 1998). Temperatures are ranged between 3.3 °C and
20.5 °C in winter months and ranged between 16.0 °C and 46.8 °C in summer months. Data period and basic statistical properties of the pan evaporation data are provided in Table 1 for each station. In the table, the PEmin, PEmax, PEmean, SD, Cv and Csx indicate the minimum, maximum, mean pan evaporations, standard deviation, variation coefficient and skewness, respectively. The Kilis and Gaziantep data show higher variation than the other stations (see
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O. Kisi / Journal of Hydrology 527 (2015) 1123–1129
Cv values in Table 1). PE data of Batman Station show the highest skewness while the Gaziantep and Siirt data have significantly low skewed distribution (close to normal distribution). Diyarbakir Station has the highest PE values. The basic geographic and climate characteristics of the six station are provided in Table 2. De Martonne aridity indexes are given for each station. The expression of this index developed by (De Martonne, 1926) is
Iar-DM ¼ P=ðT m þ 10Þ
ð1Þ
where P is total annual precipitation and Tm is mean annual temperature. The equation contains the value of 10 °C to produce positive results in regions with negative average annual temperatures, such as mountainous regions or deserts from median latitudes (Lungu et al., 2011). It is clear from Table 2 that all the stations have a dry, semi-arid climate. 3. Innovative trend method In the innovative trend analysis (ITA), first proposed by Sen (2012), time series is divided into two equal parts. Both sub-series are separately sorted in ascending order. The first half
of the time series is located on the X-axis, and the second half of the time series is located on the Y-axis. Fig. 2 clearly shows the innovative method on the Cartesian coordinate system. It is clear from the figure that if investigated data are collected on the 1:1 ideal line, we can say that there is no trend in the time series. If data are located on the upper triangular area of the ideal line (45° line), we can say that there exists an increasing trend in the time series. If data are accumulated in the lower triangular area of the 1:1 line, we can say that there is a decreasing trend in the time series (Sen, 2012, 2014). Thus, trends of low, medium and high values of any engineering hydro-meteorological or hydro-climatic time series can be clearly identified by this method. 4. Mann–Kendall method Mann–Kendall (MK) is a non-parametric trend test which is commonly used in identifying trends in climatological and hydrological time series (Kendall, 1975; Mann, 1945). S test statistics of MK can be given as
S¼
n X i1 X signðxi xj Þ
ð2Þ
i¼2 j¼1
(a)
10
8 9 > < if ðxi xj Þ < 0 then 1 > = signðxi xj Þ ¼ if ðxi xj Þ ¼ 0 then 0 > > : ; if ðxi xj Þ > 0 then 1
8
VarðSÞ ¼
PE, mm (1986-1996)
12
Trend No trend +5% band -%5 band 2
-10% band +10% band
0
0
2
4
6
8
10
12
PE, mm (1997-2008)
(b)
16 14
PE, mm (1975-1992)
Pl
k1 t k ðt k
18
1Þð2t k þ 5Þ
ð4Þ
where n is the number of the data and xi and xj are the sequential data in the time series, tk is the number of ties for the kth value. The second term in Eq. (4) is given for tied censored data. Z, standard test statistics can be computed as
6
4
nðn 1Þð2n þ 5Þ
ð3Þ
8 9 ffiffiffiffiffiffiffiffiffi > if S < 0 then pSþ1 > > > VarðSÞ > > < = Z ¼ if ðxi xj Þ ¼ 0 then 0 > > > > > ffiffiffiffiffiffiffiffiffi > : if ðxi xj Þ > 0 then pS1 ;
ð5Þ
VarðSÞ
Positive Z values indicate upward (increasing) trends while negative Z values reveal downward (decreasing) trends. For testing both increasing and decreasing trends at a significance level, the null hypothesis was rejected for the absolute value of Z greater than Z1a/2, obtained from the standard normal cumulative distribution tables (Partal and Kahya, 2006; Tabari et al., 2011; Sonali and Nagesh Kumar, 2013). Significance levels of a = 10% and 5% were applied in the present study.
12
5. Application and results
10
The time variations and linear trends of PE data are illustrated in Fig. 3 for each station. From the figure, it is observed that the Adiyaman data show decreasing trend while the Batman, Diyarbakir, Gaziantep, Kilis and Siirt stations have increasing trend. Table 3 indicates the MK test results of the six provinces according to the confidence levels of 10% and 5%. It should be noted that pre-whitening was not applied here in order not to lose originality of the PE time series (Sen, 2012; Sang et al., 2014). It is clear from the table that the Adiyaman Station shows decreasing trend while the Batman, Diyarbakir, Gaziantep, Kilis and Siirt stations have increasing trend. Diyarbakir and Kilis stations indicate significantly increasing trends according to the both 10% and 5% confidence levels. Adiyaman Station, however, shows significantly decreasing trends at the both confidence levels. Spearman Rho test results are given in Table 4 for each station according to the confidence levels
8
Trend 6
No trend +5% band
4
-%5 band -10% band
2
+10% band 0
0
2
4
6
8
10
12
14
16
PE, mm (1993-2010) Fig. 6. The results of Sen’s method for (a) Kilis and (b) Siirt stations.
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Table 5 Results of the Mann–Kendall (MK), Spearman Rho and ITA methods for monthly pan evaporations. Station
Mann–Kendall (a = 5% and 10%)
Adiyaman Batman Diyarbakir Gaziantep Kilis Siirt
Yes () No Yes (+) No Yes (+) No
Spearman Rho
ITA method (5% band)
(a = 5% and 10%)
Low
Medium
Peak
Low
Medium
Peak
No and Yes () No Yes (+) No Yes (+) No
Yes Yes Yes Yes Yes Yes
Yes No Yes No Yes Yes
Yes Yes Yes Yes No Yes
No Yes Yes Yes Yes Yes
No No Yes (+) No Yes (+) Yes (+)
Yes () Yes (+) Yes (+) No No No
of 10% and 5%. From the table, it is obvious that the trends are similar to those obtained using the MK method. Comparison of Tables 3 and 4 clearly indicates that the Spearman Rho method gives slightly higher positive trends and lower negative trends than the MK method. According to the Spearman Rho method, for example, Adiyaman Station shows significantly decreasing trend at a confidence level of 10% while it has no trend with respect to MK. The MK and Spearman Rho trend tests resulted inverse trends in the PE time series at the two nearby stations of Adiyaman (with significant negative trend) and Gaziantep (with positive trend). It was reported that inverse trends at two nearby stations may be due to some natural factors and special conditions (Turkes and Sumer, 2004). Different microclimates between the stations mainly associated with local topography and wind circulation may cause this trend difference. The trends of nature and magnitude of the meteorological parameters (e.g., evaporation) may be diversely affected by the local physical geographic (e.g., topography etc.) and atmospheric circulation features (Tabari et al., 2011). The other reason for different trend of these nearby stations may be due to the fact that the Adiyaman Station is near to Ataturk Dam which has the largest reservoir in Turkey and therefore has a humid climate. Urbanization (changes in land uses such as non-agricultural uses of lands, and vegetation cover) may also be another reason for inverse PE trends at these nearby stations. Turkes and Sumer (2004) classified the Adiyaman City as urban (100,000 < Population < 500,000) while the Gaziantep City was classified as large urban (500,000 < Population < 1,000,000). The results of the ITA are provided in Fig. 4 for the Adiyaman and Batman stations. According to the 5% relative band, low PE values (<3 mm) of Adiyaman Station show monotonic increasing trend while they have no trend with respect to 10% relative band. The medium and high PE values (>3 mm and <13 mm) indicate decreasing trend with respect to 5% relative band which they generally do not access 10% relative band limit. Some peak values higher than 13 mm, however, indicate monotonic increasing trend according to the 10% relative band. In Batman Station, low PE values (<4 mm) show significantly decreasing trend while the medium values (>5 mm and <9 mm) have no trend with respect to both relative bands. The high or peak PE values (>9 mm) indicate significantly increasing trend with respect to 10% relative band. Fig. 5 illustrates the monthly PE trends of Diyarbakir and Gaziantep stations. It is clear from the figure that there exists an increasing trend for low, medium and high values of the Diyarbakir Station with respect to 10% relative band. In Gaziantep Station, the low PE values lower than 2 mm show increasing trend while the medium (>3 mm and <8 mm) and medium-high values (>8 mm and <10 mm) generally indicate no trend with respect to 10% relative band. However, some medium (>3 mm and <5 mm) and peak (>10 mm) values show monotonic increasing trend according to the 5% relative band. The results of the ITA of monthly PE data of Kilis and Siirt stations are given in Fig. 6. In Kilis Station, the low (<4 mm) and low-medium (>4 mm and <6.5 mm) PE values show monotonic increasing trend while the medium-high (>6.5 mm and <9 mm) generally indicate no
(+) () (+) (+) (+) (+)
() (+) (+) (+)
ITA method (10% band)
() (+) (+) (+) (+)
() (+) (+) (+) (+)
trend with respect to 10% relative band. However, peak (>9 mm) values show no trend according to the 5% relative band. The low (<2 mm) PE values of Siirt Station show increasing trend while the low-medium (>4 mm and <7 mm) values indicate slightly increasing trend with respect to 10% relative band. The medium (>7 mm and <11 mm) and medium high (>11 mm and <13 mm) PE values show no trend according to the 5% relative band while the peak values indicate increasing trend with respect to 5% relative band. The ITA results of six stations given in Figs. 4–6 are summarized and compared with MK and Spearman Rho in Table 5. It is clear from the table that the ITA, MK and Spearman Rho give similar trend results for the Adiyaman, Diyarbakir and Kilis stations. However, ITA gives some positive or negative trends for the Batman, Gaziantep and Siirt although the MK and Spearman Rho tests indicate no trend for these stations. Especially for the Batman station, the MK and Spearman Rho indicate increasing trend but not significant with respect to 10% and 5% confidence levels. However, significantly decreasing and increasing trends are clearly seen for the low and high PE values in this station (Fig. 4). According to the MK, Spearman Rho and ITA methods, Diyarbakir and Kilis stations have significantly increasing PE trends and these may cause droughts or water stress at these cities in the future. According to the ITA method, Batman Station has also significantly increasing trend in peak PE values after 1997s. Significantly increasing trends imply global warming effect at the location of Diyarbakir, Kilis and Batman stations. 6. Conclusion In this study, trends of monthly pan evaporations were investigated by using an innovative method, Mann–Kendall and Spearman Rho test. Data from Adiyaman, Batman, Diyarbakir, Gaziantep, Kilis and Siirt stations in Turkey were used in the analysis. According to the MK and Spearman Rho methods, the Adiyaman Station showed significantly decreasing trend while the Diyarbakir and Kilis stations had significantly increasing trend at the confidence level of 10%. Batman, Gaziantep and Siirt stations also showed increasing trend but not significant. MK, Spearman Rho and innovative methods provided similar trend results for the Adiyaman, Diyarbakir and Kilis stations. The results of innovative method, however, indicated that the Batman, Gaziantep and Siirt stations had some increasing and decreasing trends for the low, medium and peak pan evaporation values although there was no trend in these stations according to the MK and Spearman Rho tests. The present study revealed that innovative trend analysis method has some advantages in relative to the MK and Spearman Rho methods. One main advantage is that it does not have any assumptions (e.g., serial correlation, non-normality, sample number etc.) as in the MK and Spearman Rho methods. The other main advantage is that the trends of low, medium and high data can be easily identified by innovative method. This new method can provide a priori view to the engineers and can be used in global climate scenarios.
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