Precipitation and Standardised Precipitation Index trends were analyzed by using linear regression, Mann-Kendall and Spearmans Rho tests at the 5 significance level. For this purpose, meteorological data were used from 12 synoptic stations in Serbia over the period 1980-2010. Two main drought periods were detected (1987-1994 and 2000-2003), while the extremely dry year was 2000 at all stations. 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 the 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.
Trend analysis; Precipitation; Drought; Statistical tests; Serbia
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Drought is a natural phenomena which occurrences varying in frequency, severity and duration. Moreover, drought is both a hazard and a disaster (Paulo et al., 2012). It can be classified as agricultural, hydrological or socio-economic drought. Numerous studies on drought have frequently been investigated (Moreira et al., 2008; Paulo and Pereira, 2008; Shahid, 2008; Khalili et al., 2011; Tabari et al., 2012) and a variety of indices for describing drought have been developed. Trends in occurring drought or its duration can be explained through changes in precipitation (Hisdal et al., 2001).
Precipitation is one of the most important meteorological variables which can impact the occurrence of drought or floods. Analysis of precipitation and drought data offers important information which can be applied to improve water management strategies, to protect the environment, to plan agricultural production or in general to impact on economic development of a certain region.
In recent years, a plethora of scientists have compared and analyzed the precipitation trends in the worldwide (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). 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) analysed 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. NiedÅºwiedÅº 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 analysed 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 information 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
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.
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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).
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):
where ET0 = reference evapotranspiration (mm day-1); Δ = slope of the saturation vapor pressure function (kPa oC -1); Rn = net radiation (MJ m-2 day-1); G = soil heat flux density (MJ m-2 day-1); γ = psychometric constant (k Pa oC -1); T = mean air temperature (oC); U2 = average 24-hour wind speed at 2 m height (m s-1); and VPD = vapor pressure deficit (kPa).
The locations were then classified as hyper-arid (), arid (), semi-arid (), sub-humid () or humid ().
2.3. Rainfall variability index
Rainfall variability index (δ) is calculated as:
where δi = rainfall variability index for year i, Pi = annual rainfall for year i, µ and σ are the mean annual rainfall and standard deviation for the period between 1980 and 2010. A drought year occurs if the δ is negative.
According to WMO (1975), rainfall time series can be classified into different climatic regimes:
- extreme dry
- dry (3)
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, Reconnaissance Drought Index. In this study, the Standardised Precipitation Index is applied, because of its good characteristics in 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; Thom, 1966). 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:
where = form parameter; β = scale parameter; x = precipitation quantity; = gamma function defined by the following statement:
Parameters and β are determined by the method of maximum probability for a multiyear data sequence, i.e.:
where xsr = mean value of precipitation quantity; n = precipitation measurement number; xi = quantity of precipitation in a sequence of data.
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:
Since the gamma function has not been defined for x = 0, and the precipitation may amount to zero, the cumulative probability becomes:
where q = probability that the quantity of precipitation equals zero, which is calculated using the following equation:
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.
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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):
where t is determined as
and c0, c1, c2, d1, d2 and d3 are coefficients whose values are:
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, 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.
2.5.1. Mann-Kendall trend test
The Mann-Kendall test statistic S (Mann, 1945; Kendall, 1975) is calculated by using
where n is the number of data points, xi and xj are the data values in time series i and j (), respectively and is the sign function determined as:
In cases where the sample size, the mean and variance are given by
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:
The standard normal test statistic ZS is computed as:
Positive values of ZS indicate increasing trends while the negative ZS show decreasing trends.
Testing of trends is done at a specific α significance level. In this study, the significance level of was used. At the 5 % significance level, the null hypothesis of no trend is rejected if
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
(Lehmen, 1975; Sneyers, 1990):
where 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.
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
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 lag-1 serial correlation coefficient of sample data xi (designated by r1) computes as (Kendall and Stuart, 1968; Salas et al., 1980)
where is the mean of sample data and n is the sample size.
3. Results and discussion
3.1. Summary of statistical parameters
Statistical parameters of monthly precipitation time series at twelve synoptic stations during the period 1980-2010 are summarized in Table 2. 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 Figure 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.
3.2. Aridity index
The estimated UNEP aridity index for the 12 synoptic stations is given in Table 3. 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. As shown, the Vranje station is sub-humid, while all other stations are humid. The results also indicated that the aridity index ranged from 0.629 at the Vranje station to 1.413 at the Zlatibor station.
3.3. Rainfall variability
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 NiedÅºwiedÅº 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. That was 2000th year 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.
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).
3.4. Analysis of precipitation
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.
3.4.1. Serial correlation of the precipitation
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 existence of positive serial correlation increases the possibility to reject the null hypothesis of no trend while it is true. On the contrary, the negative serial correlation will decrease the possibility of rejecting the null hypothesis.
The highest serial correlation of 0.36 was obtained at the Nis station, while the lowest serial correlation of -0.27 was detected at the Sombor station.
3.4.2. Monthly analysis
The results of the statistical tests for the monthly precipitation series over the period 1980-2010 are summarized in Table 4. As shown, only the Negotin station had the significant decreasing trend in May, while the significant increasing trend was detected at the Dimitrovgrad station in February and October and at the Nis station in April.
The results also suggest that all stations exhibited decreasing trend in February and September, while both increasing and decreasing trends were obtained in the other months.
3.4.3. Seasonal and annual analysis
Seasonal and annual trends of precipitation obtained by statistical methods are given in Table 5.
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 reasons for 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. 6. The lowest SPI index of -3.561 was detected in 1984 at the Loznica station. The results also indicated that the extremely dry year was 2000 at all of the stations.
Lag-1 serial correlation coefficient for the SPI-12 at the observed synoptic stations is illustrated in Fig. 7. The highest positive serial correlation coefficient of 0.345 was detected at the Nis station. On the other hand, the highest negative value of -0.007 was observed at the Kragujevac station, while the lowest negative value of -0.273 was found at the Novi Sad station. Moreover, the significant serial correlation was found at the Nis, Palic, Novi Sad and Sombor stations.
The results of the Mann-Kendall and Spearman's Rho tests for the SPI-12 series are presented in Fig. 8. The decreasing trend was found at the Belgrade and Kragujevac stations, while the other stations had the increasing trend. No significant trend was detected in the SPI-12 series.
The main objective of this work was to study the monthly, seasonal and annual precipitation trends and drought behavior in Serbia between 1980 and 2010. In order to achieve this, monthly precipitation data from 12 Serbian synoptic stations were analysed using the Mann-Kendall test, the Spearman's Rho test and the linear 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.
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 the 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.
The work is supported by the Ministry of Education, Science and Technological Development, Republic of Serbia (Grant No. TR37003).