Analysis of precipitation and drought data in Serbia over the period 1980–2010

Journal of Hydrology 494 (2013) 32–42

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Analysis of precipitation and drought data in Serbia over the period 1980–2010 Milan Gocic ⇑, Slavisa Trajkovic Faculty of Civil Engineering and Architecture, University of Nis, A. Medvedeva 14, 18 000 Nis, Serbia

a r t i c l e

i n f o

Article history: Received 21 December 2012 Received in revised form 31 March 2013 Accepted 28 April 2013 Available online 6 May 2013 This manuscript was handled by Andras Bardossy, Editor-in-Chief, with the assistance of Purna Chandra Nayak, Associate Editor Keywords: Trend analysis Precipitation Drought Statistical tests Serbia

s u m m a r y Precipitation and Standardised Precipitation Index (SPI) trends were analyzed by using linear regression, Mann–Kendall and Spearman’s Rho tests at the 5% significance level. For this purpose, meteorological data from 12 synoptic stations in Serbia over the period 1980–2010 were used. Two main drought periods were detected (1987–1994 and 2000–2003), while the extremely dry year was recorded in 2000 at all stations. The monthly analysis of precipitation series suggests that all stations had a decreasing trend in February and September, while both increasing and decreasing trends were found in other months. On the seasonal scale, there were the increasing trends in autumn and winter precipitation series, while on the annual scale the most of the stations had no significant trends. Besides, the decreasing trend was found at the Belgrade and Kragujevac stations, while the other stations had the increasing trend for the SPI-12 series. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction Drought is a natural phenomena on whose occurrence varies in frequency, severity and duration. Moreover, drought is both a hazard and a disaster (Paulo et al., 2012). It can be classified as meteorological, agricultural, hydrological or socio-economic drought. There were numerous studies on drought (Moreira et al., 2008; Paulo and Pereira, 2008; Shahid, 2008; Khalili et al., 2011; Mishra and Singh, 2010; Tabari et al., 2012) and a variety of indices for describing drought have been developed. Trends in drought occurrence frequency or its duration can be explained through the changes in precipitation (Hisdal et al., 2001). Precipitation is one of the most important meteorological variables which can impact the occurrence of drought or flood. Analysis of precipitation and drought data yields important information which can be used to improve water management strategies, protect the environment, plan agricultural production or in general, impact economic development of a certain region. In recent years, a plethora of scientists worldwide have compared and analyzed the precipitation trends (Gemmer et al., 2004; Partal and Kahya, 2006; Liu et al., 2008; Oguntunde et al., 2011; Tabari and Hosseinzadeh Talaee, 2011; Tabari et al., 2012). ⇑ Corresponding author. Tel.: +381 64 1479423; fax: +381 18 588200. E-mail address: [email protected] (M. Gocic). 0022-1694/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jhydrol.2013.04.044

In Europe, Brunnetti et al. (2001) analyzed trends in daily intensity of precipitation during the period 1951–1996 and detected the significant positive trend in northern Italy. Tolika and Maheras (2005) studied the wet periods for the entire Greek region. They showed that the longest wet periods are observed in Western Greece and in Crete, while stations in the Central and South Aegean area had the shortest wet periods. In Bulgaria, Koleva and Alexandrov (2008) analyzed the long-term variations in precipitation and concluded that the last century can be divided into several wet and dry periods with duration of 10–15 years. Niedz´wiedz´ et al. (2009) discussed the patterns of monthly and annual precipitation variability at seven weather stations in east central Europe during the period 1851–2007. They also identified the dry period in the 1980s and the first half of the 1990s. Ruiz Sinoga et al. (2011) observed the temporal variability of precipitation in southern Spain to detect trends and cycles and noted the general decreasing trend in seasonal precipitation. Furthermore, there have been a number of precipitation studies and reports for different periods and locations in Serbia. For example, Tosic (2004) investigated spatial and temporal variability of winter and summer precipitation at 30 stations for the period 1951–2000, while Unkasevic and Tosic (2011) statistically analyzed the daily precipitation over Serbia during the period 1949–2007. Besides, Tosic and Unkasevic (2005) and Djordjevic (2008) studied precipitation trend in Belgrade to provide informa-

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tion on climate variability. However, a comprehensive analysis of trends and variability in precipitation series over Serbia as presented here is still lacking. The objectives of this study are: (1) to research variability in precipitation on monthly, seasonal and annual time series by using the linear regression, Mann–Kendall and Spearman’s Rho methods; (2) to consider the impact of serial correlation in detecting trends; and (3) to investigate the drought in Serbia between 1980 and 2010.

2. Materials and methods

Table 1 Geographical descriptions of the synoptic stations used in the study. Station name 1. Belgrade 2. Dimitrovgrad 3. Kragujevac 4. Kraljevo 5. Loznica 6. Negotin 7. Nis 8. Novi Sad 9. Palic 10. Sombor 11. Vranje 12. Zlatibor

Longitude (E) 0

20°28 22°450 20°560 20°420 19°140 22°330 21°540 19°510 19°460 19°050 21°550 19°430

Latitude (N) 0

44°48 43°010 44°020 43°430 44°330 44°140 43°200 45°200 46°060 45°470 42°330 43°440

Elevation (m a.s.l.) 132 450 185 215 121 42 204 86 102 87 432 1028

2.1. Study area and data collection The study area was Serbia which is located in the central part of the Balkan Peninsula with an area of 88.407 km2. Its central and southern areas consist of highlands and mountains, while the northern part is mainly flat. The climate of the country is temperate continental, with a gradual transition between the four seasons of the year. Series of monthly precipitation data were collected from 12 synoptic stations from Serbia (Fig. 1) for the period 1980–2010 and were obtained from Republic Hydrometeorological Service of Serbia (http://www.hidmet.gov.rs/). The geographical description of the selected synoptic stations is given in Table 1. The precipitation datasets were investigated for randomness, homogeneity and absence of trends. The autocorrelation analysis was applied to the precipitation monthly time series of each station. The quality of precipitation data were controlled with double-mass curve analysis (Kohler, 1949).

Table 2 Drought classification of SPI. Drought class

SPI value

Non-drought Near normal Moderate Severe/extreme

SPI P 0 1 < SPI < 0 1.5 < SPI 6 1 SPI 6 1.5

2.2. Aridity index An aridity index is a numerical indicator of the degree of dryness of the climate at a given location. A number of aridity indices have been proposed. In this study, the UNEP index (UNEP, 1992) was used. According to the ratio of precipitation (P) and potential evapotranspiration (PET), regions were classified from hyper-arid to humid. PET was estimated from the FAO-56 Penman–Monteith (FAO-56 PM) equation, which is the standard equation for estimating reference evapotranspiration (ET0). It calculates ET0 as (Allen et al., 1998):

ET0 ¼

900 0:408  D  ðRn  GÞ þ c  Tþ273  U 2  VPD D þ c  ð1 þ 0:34  U 2 Þ

ð1Þ

where ET0 = reference evapotranspiration (mm day1); D = slope of the saturation vapor pressure function (kPa °C1); Rn = net radiation (MJ m2 day1); G = soil heat flux density (MJ m2 day1); c = psychometric constant (kPa °C1); T = mean air temperature (°C); U2 = average 24-h wind speed at 2 m height (m s1); and VPD = vapor pressure deficit (kPa). The locations were then classified as hyper-arid (P=PET 6 0:05), arid (0:05 < P=PET 6 0:2), semi-arid (0:2 < P=PET 6 0:5), sub-humid (0:5 < P=PET 6 0:65) or humid (P/PET > 0.65). 2.3. Rainfall variability index Rainfall variability index (d) is calculated as:

di ¼ ðPi  lÞ=r

ð2Þ

where di = rainfall variability index for year i, Pi = annual rainfall for year i, l and r are the mean annual rainfall and standard deviation for the period between 1980 and 2010. A drought year occurs if the d is negative. According to WMO (1975), rainfall time series can be classified into different climatic regimes:

P < l  2  r —extreme dry

Fig. 1. Spatial distribution of the 12 synoptic stations in Serbia map.

l  2  r < P < l  r —dry l  r < P < l þ r —normal P > l þ r —wet

ð3Þ

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M. Gocic, S. Trajkovic / Journal of Hydrology 494 (2013) 32–42

2.4. Drought indices Drought indices are used for drought identification and description of its intensity. There have been a number of drought indices

such as Standardised Precipitation Index, Standardised Precipitation Evapotranspiration Index, Palmer Drought Severity Index, and Reconnaissance Drought Index. In this study, the Standardised Precipitation Index is applied, because of its good characteristics in

Table 3 Statistical parameters of monthly precipitation time series at twelve synoptic stations during the period 1980–2010. Station name

Min (mm)

Max (mm)

Mean (mm)

Standard deviation (mm)

CV (%)

Skewness

Kurtosis

Belgrade Dimitrovgrad Kragujevac Kraljevo Loznica Negotin Nis Novi Sad Palic Sombor Vranje Zlatibor

0.3 1.3 1.4 2.1 1.8 0.0 2.7 0.0 1.2 0.5 0.0 4.7

262.5 174.3 305.0 194.0 240.2 187.5 201.1 237.4 243.3 240.0 155.2 238.0

60.064 53.602 53.649 62.279 71.496 52.249 49.247 55.748 48.592 51.211 48.828 84.858

12.504 10.223 10.086 9.749 13.075 11.049 8.308 15.586 13.966 11.639 10.736 12.362

64.34 63.50 65.82 60.14 58.32 72.24 61.16 68.23 68.48 68.28 62.47 49.02

1.68 2.11 2.79 3.40 2.24 1.97 2.77 2.68 1.96 2.03 0.48 4.35

2.00 2.70 3.92 5.11 2.93 2.46 3.88 3.71 2.45 2.56 0.37 7.10

Note: CV – coefficient of variation.

Fig. 2. Annual precipitation time series at the 12 synoptic stations.

Table 4 Aridity index, annual precipitation and reference evapotranspiration estimated using FAO-56 Penman–Monteith equation. Station name

Precipitation (mm/year)

ET0 (mm day1)

Aridity index

Climate

Belgrade Dimitrovgrad Kragujevac Kraljevo Loznica Negotin Nis Novi Sad Palic Sombor Vranje Zlatibor

720.768 643.224 643.788 747.348 857.952 626.988 590.964 668.976 583.104 614.532 585.936 1018.296

2.501 2.416 2.134 2.184 2.054 2.258 2.292 2.363 2.405 2.320 2.552 1.975

0.790 0.729 0.827 0.938 1.144 0.761 0.706 0.776 0.664 0.726 0.629 1.413

Humid Humid Humid Humid Humid Humid Humid Humid Humid Humid Sub-humid Humid

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M. Gocic, S. Trajkovic / Journal of Hydrology 494 (2013) 32–42

Fig. 3. Annual rainfall variability indices for the 12 synoptic stations.

drought identification and prediction of drought class transitions (Moreira et al., 2008; Paulo and Pereira, 2008; Tabari et al., 2012). 2.4.1. Standardised Precipitation Index The Standardised Precipitation Index (SPI) was developed by McKee et al. (1993, 1995) to quantify the precipitation deficit for multiple time scales (1, 3, 6, 12, 24, 48 months). This versatility allows the SPI to monitor short term water supplies, which are important for agricultural production, and long term water resources, such as ground water supplies, steam-flow and reservoir levels. It depends only on precipitation. Calculating the SPI for a certain time period at any place requires a long sequence of monthly data for the quantity of precipitation, at least 30 – annual sequence (Hayes et al., 1999; Seiler et al., 2002). Mathematically speaking, SPI is based on the cumulative probability of some precipitation appearing at the observation post. Research has shown that precipitation is subject to the law of gamma distribution (Thom, 1958, 1966; Edwards and McKee, 1997). One whole period of observation at one meteorological station is used for the purpose of determining the parameters of scaling and the forms of precipitation probability density function:

gðxÞ ¼

x 1 xa1  eb ; ba  CðaÞ

x>0

ð4Þ

where a = form parameter; b = scale parameter; x = precipitation quantity; C(a) = gamma function defined by the following statement:

CðaÞ ¼

Z

1

ya1 ey dy

ð5Þ

0

Parameters a and b are determined by the method of maximum probability for a multiyear data sequence, i.e.:

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! 1 4A apro ¼ 1þ 1þ 4A 3 Pn lnðxi Þ A ¼ lnðxsr Þ  i¼1 n bpro ¼

xsr

apro

ð6Þ

ð7Þ ð8Þ

where xsr = mean value of precipitation quantity; n = precipitation measurement number; xi = quantity of precipitation in a sequence of data.

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Fig. 3. (continued)

The obtained parameters are further applied to the determination of a cumulative probability of certain precipitation for a specific time period in a temporal scale of all the observed precipitation. The cumulative probability can be presented as:

GðxÞ ¼

Z 0

x

gðxÞdx ¼

1 bpro Cðapro Þ apro

Z 0

x

xapro 1 e

b x

pro

dx

ð9Þ

Since the gamma function has not been defined for x = 0, and the precipitation may amount to zero, the cumulative probability becomes:

HðxÞ ¼ q þ ð1  qÞGðxÞ

ð10Þ

where q = probability that the quantity of precipitation equals zero, which is calculated using the following equation:

Fig. 4. Distribution in percentage of extremely dry, dry, normal and wet years for the 12 synoptic stations during the period 1980–2010.

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M. Gocic, S. Trajkovic / Journal of Hydrology 494 (2013) 32–42

Pereira, 2008; Raziei et al., 2009; Mishra and Singh, 2010; Tabari et al., 2012). 2.5. Statistical methods Many statistical techniques (parametric or non-parametric) have been developed to detect trends within time series such as linear regression, Spearman’s Rho test, Mann–Kendall test, Sen’s slope estimator, and Bayesian procedure. In this study, the Mann–Kendall and Spearman’s Rho tests were used to analyze the precipitation trends, while the linear regression was used to calculate magnitude of trends. Fig. 5. Lag-1 serial correlation coefficient for the precipitation at the synoptic stations.

2.5.1. Mann–Kendall trend test The Mann–Kendall test statistic S (Mann, 1945; Kendall, 1975) is calculated by using

S¼

Table 5 Lag-1 serial correlation coefficients for seasonal precipitation data.

n1 X n X

sgnðxj  xi Þ

ð14Þ

i¼1 j¼iþ1

Station name

Spring

Summer

Autumn

Winter

Belgrade Dimitrovgrad Kragujevac Kraljevo Loznica Negotin Nis Novi Sad Palic Sombor Vranje Zlatibor

0.061 0.092 0.063 0.280 0.249 0.107 0.219 0.278 0.055 0.218 0.090 0.072

0.261 0.098 0.069 0.342 0.073 0.007 0.182 0.001 0.099 0.038 0.005 0.052

0.140 0.127 0.160 0.180 0.070 0.029 0.133 0.040 0.047 0.035 0.223 0.067

0.242 0.037 0.257 0.154 0.137 0.355 0.170 0.080 0.080 0.013 0.013 0.114

where n is the number of data points, xi and xj are the data values in time series i and j (j > i), respectively and sgn(xj  xi) is the sign function determined as:

8 > < þ1; if if sgnðxj  xi Þ ¼ 0; > : 1; if

8   2 > 1 tþc2 t <  t  1þdc0 þc 0 < HðxÞ 6 0:5 2 3 ; 1 tþd2 t þd3 t   SPI ¼ 2 > : þ t  c0 þc1 tþc2 2 t 3 ; 0:5 < HðxÞ 6 1:0 1þd tþd t þd t 1

2

ð12Þ

3

where t is determined as

8 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 > 0 < HðxÞ 6 0:5 < ln ðHðxÞÞ 2; t ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > : ln 1 2 ; 0:5 < HðxÞ 6 1:0 ð1HðxÞÞ

ð16Þ

nðn  1Þð2n þ 5Þ 

and c0, c1, c2, d1, d2 and d3 are coefficients whose values are:

Pm

i¼1 t i ðt i

 1Þð2ti þ 5Þ

18

ð17Þ

where m is the number of tied groups and ti denotes the number of ties of extent i. A tied group is a set of sample data having the same value. In the absence of ties between the observations, the variance is computed as:

r2 ðSÞ ¼

nðn  1Þð2n þ 5Þ 18

ð18Þ

The standard normal test statistic ZS is computed as:

8 S1 pffiffiffiffiffiffiffiffi ; if > > < r2 ðSÞ Z S ¼ 0; if > > : pSþ1 ffiffiffiffiffiffiffiffi ; if 2 r ðSÞ

ð13Þ

ð15Þ

xj  x i < 0

lðSÞ ¼ 0

ð11Þ

where m = number which signified how many times the precipitation was zero in a temporal sequence of data; n = precipitation observation number in a sequence of data. The calculation of the SPI is performed on the basis of next equation (Abramowitz and Stegun, 1965; Bordi et al., 2001; Lloyd-Hughes and Saunders, 2002):

xj  x i ¼ 0

In cases where the sample size n > 10, the mean and variance are given by

r2 ðSÞ ¼ q ¼ m=n

xj  xi > 0

S>0 S¼0 S<0

ð19Þ

Positive values of ZS indicate increasing trends while the negative ZS show decreasing trends. Testing of trends is done at a specific a significance level. In this study, the significance level of a = 0.05 was used. At the 5% significance level, the null hypothesis of no trend is rejected if |ZS| > 1.96.

c0 ¼ 2:515517; c1 ¼ 0:802853; c2 ¼ 0:010328; d1 ¼ 1:432788; d2 ¼ 0:189269; d3 ¼ 0:001308: The SPI severity drought classes are presented in Table 2 that grouped the severe and extremely severe drought classes for modeling purposes since transitions referring to the extremely severe droughts are much less frequent than for other classes (Moreira et al., 2008).The SPI on shorter time scales (for example, 3 and 6 months) describes drought events affecting agricultural practices. In this study, the SPI at 12-month time scale was selected and analyzed because it is more suitable for water resources management purposes in a certain region and more appropriate for identifying the persistence of dry periods (Bonaccorso et al., 2003; Paulo and

2.5.2. Spearman’s Rho test Spearman’s Rho test is non-parametric method commonly used to verify the absence of trends. Its statistic D and the standardized test statistic ZD are expressed as follows (Lehmann, 1975; Sneyers, 1990):

D¼1

ZD ¼ D

6

Pn

i¼1 ðRðX i Þ  nðn2  1Þ

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n2 1  D2

iÞ2

ð20Þ

ð21Þ

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M. Gocic, S. Trajkovic / Journal of Hydrology 494 (2013) 32–42

Table 6 Results of the statistical tests for the monthly precipitation over the period 1980–2010. Station name

Test

Month February

March

April

May

July

August

September

Belgrade

ZS ZD b (mm/month)

1.633 1.557 0.711

1.071 0.951 0.620

0.119 0.173 0.030

0.765 0.854 0.346

1.156 1.298 1.264

0.255 0.321 0.428

1.377 1.294 0.890

0.850 0.654 0.333

0.663 0.711 0.486

0.612 0.554 0.408

Dimitrovgrad

ZS ZD b (mm/month)

1.411 1.483 0.675

2.142* 2.065* 0.738

0.731 0.571 0.098

0.051 0.086 0.153

0.510 0.451 0.394

0.850 1.046 1.131

0.289 0.351 0.365

0.136 0.028 0.813

1.529 1.848 0.922

1.987* 2.371* 1.678

Kragujevac

ZS ZD b (mm/month)

0.799 0.606 0.063

1.089 0.985 0.334

0.850 0.694 0.196

0.391 0.262 0.203

1.190 1.129 0.763

1.207 1.325 0.901

1.666 1.709 0.837

0.731 0.938 0.052

1.156 1.051 0.698

Kraljevo

ZS ZD b (mm/month)

0.238 0.412 0.490

0.969 1.068 0.267

0.272 0.246 0.145

0.119 0.055 0.316

0.493 0.622 0.649

1.020 0.973 0.821

0.001 0.050 0.075

0.986 0.840 0.635

Loznica

ZS ZD b (mm/month)

1.802 2.002 0.885

0.629 0.731 0.131

1.665 1.830 1.089

1.632 1.624 0.730

0.255 0.386 0.460

0.238 0.180 0.523

0.289 0.269 0.088

Negotin

ZS ZD b (mm/month)

1.564 1.634 0.782

0.102 0.117 0.222

0.578 0.792 0.528

0.357 0.415 0.030

2.906* 3.431* 1.647

0.714 0.585 0.518

Nis

ZS ZD b (mm/month)

0.765 0.729 0.372

0.799 0.847 0.513

0.102 0.169 0.062

1.989* 2.280* 0.758

0.782 0.786 0.420

Novi Sad

ZS ZD b (mm/month)

1.241 1.259 0.564

1.156 0.957 0.108

0.051 0.077 0.033

0.969 0.897 0.083

Palic

ZS ZD b (mm/month)

0.952 0.985 0.501

0.799 0.897 0.387

0.289 0.094 0.141

Sombor

ZS ZD b (mm/month)

1.361 1.295 0.730

0.612 0.698 0.167

Vranje

ZS ZD b (mm/month)

0.544 0.477 0.360

Zlatibor

ZS ZD b (mm/month)

0.187 0.316 0.657

January

June

October

November

December

0.001 0.064 0.259

0.850 1.033 0.403

0.901 0.886 0.269

0.799 0.664 0.236

0.935 0.938 0.618

0.051 0.003 0.222

0.323 0.168 0.313

0.289 0.395 0.010

1.513 1.652 1.138

0.493 0.624 0.342

0.001 0.088 0.037

0.289 0.266 0.869

0.340 0.409 0.525

1.258 1.065 1.278

0.527 0.356 0.258

1.224 1.229 1.199

0.051 0.025 0.116

0.255 0.275 0.424

0.714 0.813 0.551

0.442 0.495 0.628

0.119 0.177 0.078

0.986 0.973 1.083

0.901 0.780 0.503

0.544 0.623 0.064

0.340 0.333 0.097

0.374 0.535 0.186

1.122 1.258 1.132

0.816 0.636 0.229

0.255 0.404 0.195

1.462 1.281 0.549

0.493 0.556 0.418

0.833 0.814 0.762

0.272 0.178 0.306

1.224 1.069 0.804

1.088 1.111 0.962

0.918 0.971 1.023

0.408 0.388 0.294

0.578 0.698 0.028

1.274 1.410 1.033

1.020 1.127 1.049

0.051 0.208 0.075

0.034 0.026 0.117

1.139 1.073 0.694

0.527 0.421 0.222

1.105 1.205 0.810

0.289 0.299 0.343

0.001 0.029 0.086

0.629 0.713 0.322

0.391 0.424 0.298

1.003 0.995 1.595

0.578 0.554 0.508

0.918 0.966 0.559

1.139 1.096 0.954

0.340 0.420 0.200

0.680 0.643 0.476

0.629 0.492 0.146

0.493 0.549 0.077

0.612 0.808 0.241

0.102 0.193 0.106

0.102 0.069 0.012

0.306 0.272 0.140

0.714 0.696 0.567

0.170 0.248 0.305

1.139 1.356 0.732

0.935 0.958 0.779

0.850 0.599 0.195

0.544 0.605 0.404

1.666 1.621 0.819

1.343 1.224 1.086

0.136 0.265 0.180

0.187 0.201 0.064

0.085 0.088 0.220

0.034 0.015 0.114

0.272 0.228 0.138

0.884 1.097 1.162

0.714 0.694 0.778

0.901 0.820 0.550

0.918 0.885 0.713

ZS: Mann–Kendall test, ZD: Spearman’s Rho test, b: Slope of linear regression. Bold characters represent trends identified by 2 statistical methods together. Statistically significant trends at the 5% significance level.

*

where R(Xi) is the rank of ith observation Xj in the time series and n is the length of the time series. Positive values of ZD indicate increasing trends while negative ZD show decreasing trends. At the 5% significance level, the null hypothesis of no trend is rejected if |ZD| > 2.08.

lag-1 serial correlation coefficient of sample data xi (designated by r1) computes as (Kendall and Stuart, 1968; Salas et al., 1980)

1

2.5.3. Linear regression method A linear regression method is one of methods which are used to estimate a slope. The slope indicates the mean temporal change of the studied variable. Positive values of the slope show increasing trends, while negative values of the slope indicate decreasing trends. A linear regression line has an equation of the form

y ¼ a þ bx

ð22Þ

where x = the explanatory variable, y = the dependent variable, b = the slope of the line and a = the intercept. 2.5.4. Serial autocorrelation test To remove serial correlation from the series, von Storch and Navarra (1995) suggested to pre-whiten the series before applying the Mann–Kendall and Spearman’s Rho tests. The

r1 ¼ n1

lðxi Þ ¼

Pn1 i¼1

ðxi  lðxi ÞÞ  ðxiþ1  lðxi ÞÞ Pn 2 i¼1 ðxi  lðxi ÞÞ

1 n

n 1X xi n i¼1

ð23Þ

ð24Þ

where l(xi) is the mean of sample data and n is the sample size. For the two-sided test, Salas et al. (1980) recommended that the 95% significance level for r1 can be computed by

pffiffiffiffiffiffiffiffiffiffiffiffi 1  1:96  n  2 r1 ð95%Þ ¼ n1 where n is the sample size.

ð25Þ

M. Gocic, S. Trajkovic / Journal of Hydrology 494 (2013) 32–42

39

Fig. 6. Variations of monthly precipitation in stations with the significant trends during the study period.

3. Results and discussion

is sub-humid because of the highest ET0, minimum of the annual precipitation and the highest value of the temperature difference.

3.1. Summary of statistical parameters 3.3. Rainfall variability Statistical parameters of monthly precipitation time series at twelve synoptic stations during the period 1980–2010 are summarized in Table 3. The mean monthly precipitation is ranged from 48.6 to 84.9 mm. Besides, it is evident that two stations in the south (Nis and Vranje) had the lowest mean monthly precipitation. The highest coefficient of variation (CV) of the precipitation values was observed at Negotin station located in the east Serbia at the rate of 72.24%, while the lowest CV of 49.02% was found at Zlatibor. Time series of annual precipitation at the 12 synoptic stations are shown in Fig. 2. The results indicated that the annual precipitation had high variations during the observed period. The highest precipitation of 1282.3 mm was detected in 1999 at the Zlatibor station, which was caused by cold fronts, showers and thunderstorms in cold air masses from the west (Unkasevic and Tosic, 2011). The lowest precipitation of 247.1 mm was detected in 2000 at the Palic station. The results also showed that the main amount of precipitation fell in the regions along the greatest rivers, such as the Danube (Belgrade, Novi Sad), the Sava (Loznica) and the Velika Morava (Kragujevac, Kraljevo) which was in line with the analysis reported in Unkasevic and Tosic (2011).

Annual rainfall variability indices for the observed synoptic stations are presented in Fig. 3, while the percentage distribution of the extremely dry, dry, normal and wet years during the period 1980–2010 is given in Fig. 4. There were two main periods which were characterized by long and severe droughts, namely 1987– 1994 and 2000–2003. This result is in line with the results indicated by Niedz´wiedz´ et al. (2009). According to Gocic and Trajkovic (2013), change from positive to negative direction was detected in the time series of precipitation in 1986 for all the stations. During the first period, the drought years were approximately 55% of the total years. The second period is characterized by approximately 50% of the drought years, but it had an extremely dry year. The 2000 year was the driest year during the observed period when all of the stations had the precipitation below the annual mean precipitation and the annual precipitation ranged from 247.1 mm at the Palic station to 848.7 mm at the Zlatibor station. Furthermore, it should be noted that there were two dry years, 1984 and 2008. These 2 years were characterized by approximately 60% negative values of the annual rainfall variability index. 3.4. Analysis of precipitation

3.2. Aridity index The estimated UNEP aridity index for the 12 synoptic stations is given in Table 4. The FAO-56 PM equation as a part of the model based on service-oriented paradigm (Gocic and Trajkovic, 2010, 2011) is used for estimating ET0. The results indicated that the aridity index ranged from 0.629 at the Vranje station to 1.413 at the Zlatibor station. The Vranje station is sub-humid, while all other stations are humid. The upper limit for sub-humid climate is 0.65 but Vranje had a slightly lower value. The Vranje station

The serial correlation coefficient can improve the verification of the independence of precipitation time series. If the time series are completely random, the autocorrelation function will be zero for all lags other than zero. In this study, to accept the hypothesis H0: r1 = 0 (that there is no correlation between two consecutive observations and there is no persistence in the time series), the value of r1 should fall between 0.385 and 0.318. Autocorrelation plot for the precipitation at the 12 synoptic stations is presented in Fig. 5. As shown, the precipitation had both positive and negative serial correlations. The highest and at the

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M. Gocic, S. Trajkovic / Journal of Hydrology 494 (2013) 32–42

Table 7 Results of the statistical tests for seasonal and annual precipitation over the period 1980–2010. Station

Test

Belgrade

ZS 1.343 ZD 1.483 b (mm/year) 0.497

Spring

Summer Autumn Winter Annual 0.476 0.203 0.244

1.003 0.899 0.320

0.136 0.284 0.184

0.085 0.155 0.355

Dimitrovgrad ZS 0.573 ZD 0.540 b (mm/year) 0.058

0.612 0.696 0.240

1.806 2.060* 0.609

1.274 1.387 0.427

1.292 1.467 3.154

Kragujevac

ZS 1.173 1.103 ZD b (mm/year) 0.230

0.765 0.854 0.466

1.407 1.375 0.414

0.272 0.461 0.115

0.051 0.038 0.193

Kraljevo

ZS ZD b (mm/year)

0.306 0.033 0.167

0.238 0.239 0.089

0.816 0.759 0.190

0.408 0.403 0.145

0.068 0.017 0.042

Loznica

ZS 0.001 0.081 ZD b (mm/year) 0.086

0.646 0.663 0.342

1.241 1.280 0.578

1.802 2.004 0.577

1.870 2.079* 5.479

Negotin

ZS ZD b (mm/year)

1.972* 2.277* 0.638

0.136 0.091 0.041

0.935 0.796 0.243

1.122 1.714 0.512

0.340 0.331 1.005

Nis

ZS ZD b (mm/year)

0.357 0.349 0.061

0.538 0.571 0.202

0.816 0.763 0.414

0.714 0.853 0.242

0.544 1.349 2.366

Novi Sad

ZS ZD b (mm/year)

0.612 0.167 0.116

0.417 0.513 0.358

2.532* 2.312* 0.804

0.612 0.667 0.269

1.802 1.767 5.743

Palic

ZS ZD b (mm/year)

1.054 1.129 0.289

0.748 0.862 0.193

1.513 1.495 0.503

0.527 0.538 0.211

1.802 2.095* 4.788

Sombor

ZS ZD b (mm/year)

0.578 0.012 0.157

1.615 1.546 0.717

1.172 1.177 0.414

0.868 0.833 0.253

1.989* 2.119* 5.643

Vranje

ZS ZD b (mm/year)

0.357 0.437 0.069

0.382 0.344 0.170

1.394 1.306 0.403

0.544 0.681 0.195

1.309 1.240 2.480

Zlatibor

ZS ZD b (mm/year)

0.578 0.810 0.244

0.068 0.080 0.218

1.479 1.958 0.643

0.731 0.731 0.187

1.207 1.437 3.863

ZS: Mann–Kendall test, ZD: Spearman’s Rho test, b: Slope of linear regression. Bold characters represent trends identified by 2 statistical methods together. Statistically significant trends at the 5% significance level.

*

same time the significant serial correlation of 0.355 was obtained at the Nis station, while the lowest serial correlation of 0.210 was detected at the Novi Sad station. The existence of the positive serial correlation increases the possibility of the Mann–Kendall and Spearman’s Rho tests to reject the null hypothesis of no trend while it is true. A statistically significant trend ZS = 2.102 was detected only at the Nis station before eliminating the effect of serial correlation. After removing lag-1 serial correlation effect an insignificant trend of ZS = 0.357 was obtained. Lag-1 serial correlation coefficients for seasonal precipitation data at the observed stations during the period 1980–2010 are presented in Table 5. As shown, a negative serial correlation was found in the spring, summer, autumn and winter series at 83.3%, 83.3%, 75% and 33.3% of the stations, respectively. The significant serial correlation was not detected. Trends of precipitation are considered statistically at the 5% significance level using the Mann–Kendall test, the Spearman’s Rho test and the linear regression. When a significant trend is identified by two statistical methods, the trend is presented in bold character in the table. The results of the statistical tests for the monthly precipitation series over the period 1980–2010 are summarized in Table 6. As

shown, only the Negotin station had the significant decreasing trend in May with a slope of 1.647 mm/month. The significant increasing trend was detected at the Dimitrovgrad station in February (0.738 mm/month) and October (1.678 mm/month) and at the Nis station in April with a slope of 0.758 mm/month. The magnitudes of the significant trends in the monthly precipitation series for the above mentioned stations are presented in Fig. 6. The results also suggest that all stations exhibited increasing trend in February and September, while both increasing and decreasing trends were obtained in the other months. Seasonal and annual trends of precipitation obtained by statistical methods are given in Table 7. According to these results, the significant increasing trend in annual precipitation series was detected at Sombor station with the slope of 5.643 mm/year, while the other stations had no significant trends. Besides, only Belgrade and Kragujevac had the decreasing trend with the slope of 0.355 mm/year and 0.193 mm/year, respectively. On annual level, precipitation quantities are increasing, with the highest increase in winter. This result is in line with the results indicated by Djordjevic (2008). On the seasonal scale, there were the increasing trends in autumn and winter precipitation series. The decreasing precipitation trend was found in the spring and autumn series at 35% and 42% of the stations, respectively. However, the significant increasing trends were found only at Negotin in spring and at Novi Sad in autumn. The similar results have been previously suggested by several authors (Tosic, 2004; Djordjevic, 2008). According to Gocic and Trajkovic (2013), the insignificant trends in summer and winter precipitation series were caused by the increasing trends in both annual and seasonal minimum and maximum air temperatures’ series and the significant decreasing of the relative humidity series. 3.5. Analysis of SPI-12 Time series of SPI-12 at the 12 synoptic stations during the period 1980–2010 are shown in Fig. 7. The characteristics of droughts at 12-month time scale are presented in Table 8. It should be noted that the most severe drought of nine stations occurred in 2000. Besides, the most severe drought year was 1990 at Zlatibor station and 1993 at Kraljevo station, while the Loznica station had the lowest SPI-12 of 3.56 in 1984. The number of drought years during the observed period at the stations is presented in this table. According to the results, the total drought years were ranged between 3 (at Palic station) and 6 (at Kraljevo, Nis and Zlatibor stations). Lag-1 serial correlation coefficient for the SPI-12 at the observed synoptic stations is illustrated in Fig. 8. The highest and at the same time the significant positive serial correlation coefficient of 0.341 was detected at the Nis station. On the other hand, the highest negative value of 0.006 was observed at the Kragujevac station, while the lowest negative value of 0.237 was found at the Novi Sad station. The results of the Mann–Kendall and Spearman’s Rho tests for the SPI-12 series are presented in Fig. 9. The decreasing trend was found at the Belgrade and Kragujevac stations, while the other stations had the increasing trend. Although no significant trend was detected in the SPI-12 series of the observed stations, it can be determined that the northern regions of Serbia have become drier during the period 1980–2010. This will impact on agriculture and water supply. 4. Conclusions The main objective of this work was to study the monthly, seasonal and annual precipitation trends and drought behavior in Ser-

M. Gocic, S. Trajkovic / Journal of Hydrology 494 (2013) 32–42

41

Fig. 7. Time series of SPI-12 at the 12 synoptic stations. Table 8 Characteristics of droughts at 12-month time scale. Station name

Belgrade Dimitrovgrad Kragujevac Kraljevo Loznica Negotin Nis Novi Sad Palic Sombor Vranje Zlatibor

The most severe drought

Number of drought years during the observed period

SPI

Year

Moderate

Severe/extreme

Total

2.75 3.11 2.49 2.29 3.56 2.34 2.26 2.84 3.10 3.02 2.47 2.37

2000 2000 2000 1993 1984 2000 2000 2000 2000 2000 2000 1990

3 2 1 3 2 2 3 3 2 2 3 2

2 3 3 3 2 3 3 1 1 2 2 4

5 5 4 6 4 5 6 4 3 4 5 6

Fig. 9. Mann–Kendall test (ZS) and Spearman’s Rho test (ZD) for the SPI-12 series.

Fig. 8. Lag-1 serial correlation coefficient for the SPI-12 at the 12 synoptic stations.

bia between 1980 and 2010. In order to achieve this, monthly precipitation data from 12 Serbian synoptic stations were analyzed using the Mann–Kendall test, the Spearman’s Rho test and the lin-

ear regression after eliminating the effect of significant lag-1 serial correlation from the time series. Besides, aridity and annual rainfall variability indices were estimated. According to these results, two main drought periods were detected (1987–1994 and 2000–2003), while the extremely dry year was 2000 at all of the stations.

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The monthly analysis of precipitation series suggests that all stations had decreasing trend in February and September, while both increasing and decreasing trends were found in other months. On the seasonal scale, there were the increasing trends in autumn and winter precipitation series, while on the annual scale the most of the stations had no significant trends. In general, no significant trend was detected in the SPI-12 series at the 5% significance level. The lowest SPI-12 index of 3.561 was detected in 1984 at the Loznica station. The analyzed results of precipitation and SPI-12 series can be helpful for planning the efficient use of water resources, hydroelectric and agricultural production. Further research in analyzing the spatial variation of precipitation trends and the relationship with the climate change is recommended. Moreover, the future work will be oriented into developing an information system for monitoring and early drought warning. Acknowledgements The work is supported by the Ministry of Education, Science and Technological Development, Republic of Serbia (Grant No. TR37003). We would like to thank anonymous referees for their valuable comments and their constructive suggestions that helped us improve the final version of the article. References Abramowitz, M., Stegun, I.A., 1965. Handbook of Mathematical Functions. Dover Publications, New York. Allen, R.G., Pereira, L.S., Raes, D., Smith, M., 1998. Crop Evapotranspiration. Guidelines for Computing Crop Water Requirements. FAO Irrigation and Drainage Paper 56, Roma, Italy. Bordi, I., Frigio, S., Parenti, P., Speranza, A., Sutera, A., 2001. The analysis of the Standardized Precipitation Index in the Mediterranean area: large-scale patterns. Ann. Geofis. 44 (5–6), 965–978. Bonaccorso, B., Bordi, I., Cancelliere, A., Rossi, G., Sutera, A., 2003. Spatial variability of drought: an analysis of the SPI in Sicily. Water Resour. Manage. 17 (4), 273– 296. Brunnetti, M., Buffoni, L., Maugeri, M., Nanni, T., 2001. Trends in daily intensity of precipitation in Italy from 1951 to 1996. Int. J. Climatol. 21 (3), 299–316. Djordjevic, S.V., 2008. Temperature and precipitation trends in Belgrade and indicators of changing extremes for Serbia. Geogr. Pannon. 12 (2), 62–68. Edwards, D.C., McKee, T.B., 1997. Characteristics of 20th century drought in the United States at multiple scales. Atmospheric Science Paper No. 634, 1–30. Gemmer, M., Becker, S., Jiang, T., 2004. Observed monthly precipitation trends in China 1951–2002. Theoret. Appl. Climatol. 77 (1–2), 39–45. Gocic, M., Trajkovic, S., 2010. Software for estimating reference evapotranspiration using limited weather data. Comput. Electron. Agric. 71 (2), 158–162. Gocic, M., Trajkovic, S., 2011. Service-oriented approach for modeling and estimating reference evapotranspiration. Comput. Electron. Agric. 79 (2), 153– 158. 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. Hayes, M., Svoboda, M.D., Wilhite, D.A., Vayarkho, O.V., 1999. Monitoring the 1996 drought using the Standardized Precipitation Index. Bull. Am. Meteorol. Soc. 80 (3), 429–438. Hisdal, H., Stahl, K., Tallaksen, L.M., Demuth, S., 2001. Have streamflow droughts in Europe become more severe or frequent? Int. J. Climatol. 21 (3), 317–333. Kendall, M.G., 1975. Rank Correlation Methods. Griffin, London. Kendall, M.G., Stuart, A., 1968. The Advanced Theory of Statistics: Design and Analysis, and Time-Series, vol. 3. Charles Griffin & Company Limited, London. Khalili, D., Farnoud, T., Jamshidi, H., Kamgar-Haghighi, A.A., Zand-Parsa, S.H., 2011. Comparability analyses of the SPI and RDI meteorological drought indices in different climatic zones. Water Resour. Manage. 25 (6), 1737–1757.

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