Trends of Extreme Precipitation Events in Serbia Under the Global Warming

Abstract

This paper examines extreme precipitation events (EXPEs) and their trends based on daily precipitation values observed at 14 stations in Serbia for the period 1961–2020. The following EXPEs were investigated: RR10mm (heavy precipitation days), RR20mm (very heavy precipitation days), Rx1day (highest 1-day precipitation amount), Rx3day (highest 3-day precipitation amount), Rx5day (highest 5-day precipitation amount), R95p (very wet days) and R99p (extremely wet days). A positive trend for all EXPEs was dominant in Serbia from 1961 to 2020. All annual Rx1day time series show a positive trend, which is significant at 12 out of 14 stations. The highest values of all EXPEs were observed in 2014, when the annual precipitation totals were the highest at almost all stations in Serbia. To examine the potential influence of global warming, the mean values of the EXPEs were calculated for two periods: 1961–1990 and 1991–2020. In the second period, higher values were determined for all EXPEs than in the first period. The large-scale variability modes, such as the North Atlantic Oscillation (NAO), the East Atlantic Oscillation (EA), and the East Atlantic–West Russia (EAWR) pattern, were correlated with the EXPEs. A negative correlation was found between the EXPEs and the NAO and the EAWR, and a positive correlation between the EXPEs and the EA pattern. For future research, the contribution of high-resolution data will be examined.

1. Introduction

According to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC) [1], it is likely that the frequency and intensity of heavy precipitation events have increased on a global scale in most land regions. Extreme precipitation events will occur more frequently as a result of climate change [2,3]. In their comprehensive analysis of extreme precipitation and its proportion of the global land area, Li et al. [4] pointed to an increasing trend on a global scale. Zeder and Fisher [5] pointed out that short- and long-lasting extreme precipitation events have become more intense in the Central European region. They detected a significant scaling signal with the Northern Hemisphere temperature anomalies for the annual maximum and most seasonal maximum single- and multi-day precipitation events. The increase in extreme precipitation can lead to severe natural disasters such as floods [6] and landslides [7].

Earlier studies on extreme precipitation in Serbia dealt with a smaller number of indices, a shorter time period, and a selected area of Serbia. Unkašević and Tošić [8] analyzed the maximum daily precipitation values at ten stations in the period from 1949 to 2007 and pointed out that the wettest day of the year produces 41.3 mm of precipitation, which is on average 6.3% of the total annual precipitation in Serbia. Malinović-Milićević et al. [9] analyzed the indices of extreme precipitation for seven stations from 1966 to 2013 in Vojvodina (northern Serbia) and concluded that the positive annual trends are influenced by the significant increase in the intensity and frequency of extreme precipitation in autumn. Tošić et al. [10] investigated the extreme daily precipitation in Serbia using data from 16 stations in the period 1961–2014. They found that the total annual precipitation for 2014 was the highest in the period 1961–2014 at almost all stations in Serbia, resulting in the most catastrophic floods in Serbia’s recent history. Bezdan et al. [11] investigated the impact of climate change on extreme precipitation events and the associated flood risk by examining the Rx3day in spring in the past (1971–2019) and in the future (2020–2100) for nine stations in Vojvodina, northern Serbia. They found that Rx3day with a ten-year return period is likely to increase by 19% to 33% in the future, depending on the location. In their study on future changes in extreme precipitation using regional climate simulation data from the EBU-POM model under the SRES-A1B scenario, Erić et al. [12] found that climate change has a significant impact on extreme precipitation in central Serbia.

Large-scale variability modes such as the North Atlantic Oscillation (NAO), the El Niño–Southern Oscillation (ENSO), and the Atlantic Multidecadal Variability (AMV) modulate precipitation extremes through changes in environmental conditions or embedded storms [1]. In our study, the potential influence of the NAO, the East Atlantic Oscillation (EA), and the East Atlantic–West Russia (EAWR) pattern on extreme precipitation events is investigated, as these large-scale variability modes have the greatest influence on climate variables in Serbia [13] and have not been considered in the previous studies on extreme precipitation in Serbia.

The aim of our study is to analyze the trends of extreme precipitation events on both an annual and seasonal basis for 14 stations distributed across Serbia by applying the modified Mann–Kendall test for the first time. Previous studies identified an increase in extreme precipitation in Northern Europe and a decrease in extreme precipitation in Southern Europe [14]. Considering the fact that Serbia is located between Central and Southern Europe, the contribution of this work is a detailed analysis of annual and seasonal trends in this part of Europe, where such an analysis has been lacking so far. The influence of global warming is investigated by comparing the results for two climate periods—1961–1990 and 1991–2020—as the analysis was performed only for temperature in Serbia [15]. Materials and methods are presented in Section 2. The results obtained for extreme precipitation events are analyzed in Section 3. The last section is dedicated to discussion and conclusions.

2. Materials and Methods

2.1. Study Area and Data

The study area is Serbia, which is located in south-eastern Europe, on the Balkan Peninsula. The climate in Serbia varies spatially from a temperate continental climate in the northern part to a continental climate in the central part and a modified Mediterranean climate in the southern part [16]. The precipitation regime in Serbia is continental, i.e., the highest monthly precipitation is measured at most stations in June and in Zaječar and Niš in the south-eastern part of Serbia in May [17]. The lowest monthly precipitation is observed for all stations in February [17].

Extreme precipitation events (EXPEs) were analyzed on the basis of daily precipitation recorded at 14 stations across Serbia from 1961 to 2020. The location of the meteorological stations with the corresponding geographical coordinates is shown in Figure 1 and Table 1. The data without break used in this work was provided by the Serbian Meteorological Service, which technically and critically controlled these measurements. Monthly values of teleconnection indices (North Atlantic Oscillation—NAO, East Atlantic—EA, and East Atlantic–West Russia—EAWR pattern) were obtained from the Climate Prediction Center of the National Oceanic and Atmospheric Administration, http://www.cpc.ncep.noaa.gov/data/teledoc/telecontents.shtml (accessed on 21 March 2024), for the period 1961–2020.

2.2. Methods

2.2.1. Climate Indices

The Expert Team on Climate Change Detection and Indices (ETCCDI) has developed a set of 27 indices based on daily temperature and precipitation that are commonly used in climate change analysis [18,19,20]. From this list, 7 indices are selected and presented in Table 2. This selection was made because these indices represent extreme precipitation events the best. The temporal characteristics of the following EXPEs were investigated: RR10mm (heavy precipitation days), RR20mm (very heavy precipitation days), Rx1day (highest 1-day precipitation amount), Rx3day (highest 3-day precipitation amount), Rx5day (highest 5-day precipitation amount), R95p (very wet days), and R99p (extremely wet days). The EXPEs were analyzed on an annual and seasonal basis and for two reference periods 1961–1990 and 1991–2020. According to [21], Rx1day and Rx5day represent extreme precipitation of moderate duration or more persistent events that often have a severe impact on society.

2.2.2. The Modified Mann–Kendall (MMK) Test

The Mann–Kendall (MK) test [22,23] is a non-parametric statistical method designed to detect monotonic trends in a time series. MK is suitable for analyzing datasets with outliers, non-linear trends, and non-normally distributed values. The MK method is based on the correlation between the ranks of time series values and their chronological order. The null hypothesis assumes that the observations are independent and identically distributed (no trend), and the alternative hypothesis suggests the presence of a monotonic trend (upward or downward).

The test utilizes statistics

(1)$\mathrm{S}={\sum }_{i=1}^{n-1}{\sum }_{j=i+1}^n\mathrm{s}\mathrm{g}\mathrm{n}\left(x_j-x_i\right),$

where $x_i$ and $x_j$ are the data values in the time series $x_1,x_2,\dots ,x_n,$ $n$ is the total number of data points, and $\mathrm{s}\mathrm{g}\mathrm{n}\left(·\right)$ denotes the sign function, defined as

(2)$\mathrm{s}\mathrm{g}\mathrm{n}\left(x_j-x_i\right)=\left\{\begin{array}{c}1 \mathrm{i}\mathrm{f} x_j>x_i\\ 0 \mathrm{i}\mathrm{f} x_j=x_i\\ -1 \mathrm{i}\mathrm{f} x_j<x_i\end{array}\right.,$

Assuming the data are independent and identically distributed under the null hypothesis, the S statistics has a mean zero (E(S) = 0), and its variance is given by

(3)$\mathrm{V}\mathrm{a}\mathrm{r}\left(\mathrm{S}\right)={\displaystyle \frac{1}{18}}\left[n\left(n-1\right)\left(2n+5\right)-{\sum }_{p=1}^q{t}_{\mathrm{p}}\left(t_p-1\right)\left(2t_{\mathrm{p}}+5\right)\right],$

where $q$ represents the number of tied groups, and $t_{\mathrm{p}}$ is the number of observations in the $p$-th group. The test statistic ${\mathrm{Z}}_{\mathrm{S}}$, which follows a normal distribution, is computed as

(4)${\mathrm{Z}}_{\mathrm{S}}=\left\{\begin{array}{c}{\displaystyle \frac{\mathrm{S}-1}{\sqrt{\mathrm{V}\mathrm{a}\mathrm{r}\left(\mathrm{S}\right)}}} \mathrm{i}\mathrm{f} \mathrm{S}>0\\ 0 \mathrm{i}\mathrm{f} \mathrm{S}=0\\ {\displaystyle \frac{\mathrm{S}+1}{\sqrt{\mathrm{V}\mathrm{a}\mathrm{r}\left(\mathrm{S}\right)}}} \mathrm{i}\mathrm{f} \mathrm{S}<0\end{array}\right.,$

A positive ${\mathrm{Z}}_{\mathrm{S}}$ value indicates an upward trend, while a negative ${\mathrm{Z}}_{\mathrm{S}}$ value indicates a downward trend. To assess significance, the $p$-value ($\mathrm{p}\mathrm{v}$) is computed as

(5)$\mathrm{p}\mathrm{v}=2\min \left(\mathrm{\varnothing }\left({\mathrm{Z}}_{\mathrm{S}}\right),1-\mathrm{\varnothing }\left({\mathrm{Z}}_{\mathrm{S}}\right)\right),$

where min( ) represents the minimum of the two arguments and ∅( ) is the cumulative distribution function of the standard normal distribution. The null hypothesis is rejected if the p-value of the standardized test statistic Z_S is less than the chosen significance level α.

The Mann–Kendall nonparametric test has been widely used to analyze trends in hydro-meteorological time series [24,25]. However, climate data often display autocorrelation, and to ensure accurate outcomes, serial correlation must be removed before applying the MK test. Yue and Wang [26] introduced the Modified Mann–Kendall (MMK) test, which incorporates a correction factor into the variance formula. The MMK test adjusts the variance using a correction factor $n/n^{\ast },$ where $n$ represents the actual sample size (the number of observations in the original time series), and $n^{\ast }$ is the effective number of independent observations. The corrected variance is calculated as

(6)${\mathrm{V}\mathrm{a}\mathrm{r}}^{\ast }\left(\mathrm{S}\right)=\mathrm{V}\mathrm{a}\mathrm{r}\left(\mathrm{S}\right){\displaystyle \frac{n}{{ n}^{\ast }}},$

where $\mathrm{V}\mathrm{a}\mathrm{r}\left(\mathrm{S}\right)$ is given by Equation (3). The correction factor is expressed as [27]

(7)${\displaystyle \frac{n}{{ n}^{\ast }}}=1+2{\sum }_{k=1}^{n-1}\left(1-{\displaystyle \frac{k}{n}}\right){\rho }_k,$

where ${\mathsf{\rho }}_k$ is the population serial correlation coefficient, and k represents the time interval between correlated pairs ${(x}_{\mathrm{t}},x_{t+k})$. The coefficient ${\mathsf{\rho }}_k$ can be represented by the sample lag-k serial correlation coefficient calculated as [28]

(8)$r_k={\displaystyle \frac{\frac{1}{n-k}\sum _{t=1}^{n-k}\left(x_t-\overline{x}\right)\left(x_{t+k}-\overline{x}\right)}{\frac{1}{n}\sum _{t=1}^n{\left(x_t-\overline{x}\right)}^2}},$

where $\overline{x}=\left({\displaystyle \frac{1}{n}}\right){\sum }_{t=1}^n{x}_t$ is the sample mean.

Using the corrected variance ${\mathrm{V}\mathrm{a}\mathrm{r}}^{\ast }\left(\mathrm{S}\right)$ from Equation (6), the MMK test statistic ${\mathrm{Z}}_{\mathrm{S}}$ is calculated by replacing $\mathrm{V}\mathrm{a}\mathrm{r}\left(\mathrm{S}\right)$ with ${\mathrm{V}\mathrm{a}\mathrm{r}}^{\ast }\left(\mathrm{S}\right)$ in Equation (4). The MMK test proved to be effective in removing the influence of correlation, providing more accurate and reliable trend analyses. It has been recently employed for the analysis of hydrological data [25,29].

2.2.3. Sen’s Slope Estimator

The Mann–Kendall test is used to identify the existence of significant trends in time series, while Sen’s slope method [30] quantifies the magnitude of the trend. To calculate Sen’s slope, first for each pair of data values $x_i$ and $x_j$ observed at times $i$ and $j$ (j > i), the slope $Q_{i,j}$ of the line that connects $x_i$ and $x_j$ is calculated as

(9)${\mathrm{Q}}_{i,j}={\displaystyle \frac{x_j-x_i}{j-i}}, i=1, 2,\dots ,n-1, j=i+1, i+2,\dots ,n.$

For a time series with $n$ data points, the maximum number of pairs ($x_i$, $x_j$), j > i is $N={\displaystyle \frac{n\left(n-1\right)}{2}}$, and the Sen’s slope estimator is obtained as the median ${\mathrm{Q}}_{\mathrm{med}}$ of all the $N$ values of ${\mathrm{Q}}_{i,j}$. The sign of ${\mathrm{Q}}_{\mathrm{med}}$ indicates the data trend (a positive sign indicates an upward trend; a negative sign indicates a downward trend), and its value indicates the magnitude of the trend. Sen’s slope estimator has been widely used in the analysis of hydro-meteorological time series [31,32]. All calculations are performed using open-source software [33,34].

2.3. Large-Scale Teleconnection Patterns

The main driver of mean and extreme precipitation variability in the North Atlantic-European region is the NAO, which is characterized by two centers of action over Iceland and the Azores [35]. In [36], it was pointed out that extreme precipitation over Northern (Southern) Europe is correlated (anti-correlated) with the NAO. The EA is recognized as a secondary mode of variability in the North Atlantic-European region [37]. It has been shown that a combination of NAO and EA can more accurately describe the variability of both winter and summer climates [38]. The EAWR pattern is associated with negative geopotential height anomalies over the area north of the Caspian Sea and positive geopotential height anomalies over Western Europe and Northern China [39]. They reported that the relationship between precipitation and EAWR pattern showed opposite polarities in Western Europe and the Middle East. In Serbia, positive precipitation anomalies were observed when the EAWR pattern was in the negative phase [40].

3. Results

3.1. Annual Analysis

3.1.1. Precipitation Indices

The annual mean values of RR10mm and RR20mm, averaged over 14 stations in Serbia, are shown in Figure 2. The maximum value of RR10mm (34.2 days) was recorded in 2014, while the minimum value of 10.7 days was recorded in Serbia in 2000. The trend of RR10mm is positive, but not significant at the 5% significance level. The maximum value of RR20mm was also observed in 2014 with 14.3 days, the minimum value of 2.9 days occurred in 1990, followed by 3.1 days in 2000. The maximum values of RR10mm and RR20mm in 2014 are due to the highest total annual precipitation measured at almost all stations in Serbia in the period 1961–2014 [10]. The lowest value of RR10mm was observed in 2000, when the lowest precipitation amounts were recorded in Serbia [17].

The mean values of the highest 1-, 3- and 5-day precipitation, averaged over 14 stations in Serbia, are shown in Figure 3. The highest mean values of RX1day, RX3day, and RX5day were measured in 2014 with 76.4 mm, 119.0 mm, and 130.1 mm, respectively. The lowest values of RX1day (29.6 mm) and RX3day (40.4 mm) were observed in 2000. The lowest value of RX5day, 49.6 mm, was measured in 1990, followed by 50.2 mm in 2000.

It is interesting to note that more than 200 mm of precipitation fell in 72 h in western Serbia from 14–16 May 2014, resulting in the most catastrophic flooding in Serbia’s recent history [10]. In the same year, eastern Serbia was affected by heavy rainfall from September 15 to 17, with a 3-day maximum sum of 188.8 mm measured in Negotin [10].

The mean values of R95p and R99p, averaged over 14 stations in Serbia, are shown in Figure 4. The highest values of R95p (30.1) and R99p (9.8) were observed in 2014, while the lowest value of R95 (8.8) was recorded in 2000, and the lowest value of R99p (1.2) in 1990, followed by 1.5 in 2000.

Table 3 shows the mean values of EXPEs for the two periods 1961–1991 and 1991–2020, calculated for 14 stations in Serbia. The mean values of RR10mm ranged between 15.8 in Zrenjanin and 30.2 in Zlatibor in western Serbia in the period 1961–1990 and between 16.5 (Zrenjanin) and 34.4 (Zlatibor) in the period 1991–2020. The RR20mm values ranged between 5.1 (Zrenjanin) and 10.3 (Zlatibor) in the first period and between 5.1 (Zrenjanin) and 11.2 (Zlatibor) in the second period. The minimum value of the highest 1-day precipitation of 35.5 mm was recorded in Niš, while the maximum value of 51.3 mm was observed in Zlatibor from 1961 to 1990. It is interesting to note that the highest value of Rx1day was measured in Negotin (52.5 mm) in eastern Serbia in the period 1991–2020. The mean value of the highest 3-day precipitation of 51.8 mm was observed in Sremska Mitrovica in the first period and 55.3 mm in Zrenjanin in the second period. The highest value of 74.3 mm for Rx3day was recorded in Loznica and 87.9 mm for Rx5day in the second period. The lowest value for Rx5day was measured in Niš from 1961 to 1991 (52.8 mm) and from 1991 to 2020 (58.0 mm). The mean value of R95p was 17 in the first period and 18.5 in the second period, with the highest increase from 15.1 to 21.3 in Novi Sad (Table 3). The mean value of R99p was 3.3 in the first period and 4.1 in the second period, with the greatest difference between 2.3 and 4.9 in Novi Sad.

3.1.2. Trend Analysis

The Modified Mann–Kendall test (MMK) and the Sen slope method were used to examine the possible trends and their magnitudes in the EXPEs. As shown in Figure 2, Figure 3 and Figure 4, there is an increase in all EXPEs in Serbia from 1961 to 2020. The annual values of Sen’s slope estimators for seven indices and all meteorological stations are shown in Table 4. A positive trend can be observed for most stations. The only exception is a negative trend for RX3day and RX5day in Belgrade and RX5day in Veliko Gradište. A significant positive trend is observed for RX1day at 12 of 14 stations, for RX5day at 10 stations, for RX3day and RR20mm at 9 stations, for RR10mm and R99p at 8 stations, and for R95p at 6 stations (Table 4). A positive trend with a significance level of 5% can be observed for all precipitation indices considered in Sombor, Novi Sad, Loznica, Smederevska Palanka, and Zlatibor.

3.1.3. Relationship with Teleconnection Indices

According to [41], atmospheric circulation explains most of the spatial and temporal variability in precipitation from the global and hemispheric to the regional scale. A possible influence of the large-scale circulation patterns—the NAO, EA, and EAWR—on extreme precipitation events in Serbia is investigated. A correlation coefficient of EXPEs and NAO is shown in Table 5. In Serbia, there was a negative correlation between the NAO and RR10mm, RR20mm and R95p. The highest 1-, 3- and 5-day precipitation amounts are positively correlated with the NAO (Table 5). Half of all stations show a positive, and the other half a negative correlation between R99p and NAO. A significant negative correlation is observed between the NAO and RR10mm (−0.2578) for Belgrade, RR20mm (−0.2927) for Loznica, and RX1day (−0.2855) for Sombor (Table 5).

In Serbia, there was a positive correlation between the EA and the EXPE (Table 6). In [15], a significant positive influence of the EA on temperature indices was found on the basis of gridded data in Serbia. The positive phase of the EA is associated with the transport of warm air over Serbia [13]. Due to the expected warming, warmer air can hold more moisture, and more extreme precipitation is expected. All stations show a positive correlation for RR20mm, RX1day, RX5day, and R99p (Table 6). It is found that the EA has a stronger influence on the EXPEs in Serbia than the NAO. For example, six stations have a significant correlation between R99p and EA, four stations for RX1day, three stations for RX3day and R95p, two stations for RR20mm and RX5day, and one station for RR10mm. The EAWR has a negative influence on the EXPEs in Serbia (Table 7). A significant correlation between the EAWR and R95p is found for seven stations, for six stations for RR20mm, for five stations for RR10mm and R99p, for three stations for RX1day, and for two stations for RX3day (Table 7).

Figure 5 shows the correlation between RR20mm, RX1day, and R99p with the EA (left column) and EAWR (right column) patterns. An opposite relationship is observed for the EA and EAWR pattern with the selected EXPEs.

There is a more significant relationship between RR20mm and EAWR than for EA (Figure 5a,b). Similar but opposite values are found for RX1day (Figure 5c,d). The EA has a significant influence on R99p in eastern and central Serbia (Figure 5e), while EAWR has a significant influence from northern to southern Serbia (Figure 5f).

3.2. Seasonal Analysis

The time series of the EXPEs were analyzed, and the sign of trend coefficients for all seasons are shown in Table 8. Most stations show a positive trend of RR10mm in autumn (13 stations, of which 5 are significant). There are 10 stations with a positive trend of RR10mm in winter, 9 stations in spring, and 8 stations in summer. All 14 stations show an increase of RR20mm, RX1day, RX3day, RX5day, and R99p in autumn and of RX1day and R99p in spring. A positive trend for RX1day is observed for 13 stations in summer and 8 stations in winter. RX3day and RX5day show a similar number of stations with a corresponding trend: 8 in winter, 10 and 11 in spring, and 11 and 12 in summer, respectively. The most consistent pattern for all EXPEs was observed in autumn. Only one station, Niš, located in southeastern Serbia, shows a negative trend for RR10mm and R95p in autumn. Our results agree with those of [42], who analyzed RX5day among several climate indices for 10 stations in Serbia from 1961 to 2010 and found a statistically significant increase only in autumn. Our results are in accordance with [43], who found the strongest upward trend in the northern region of Southern Europe in autumn when analyzing extreme precipitation trends in Europe from 1950 to 2008. In spring, a negative trend is recorded at five stations (Kragujevac, Negotin, SP, Zaječar, Zrenjanin) for RR10mm and R95p, at four stations (Kraljevo, Negotin, Smederevska Palanka, Veliko Gradište) for RX3day, and at three stations (Negotin, Veliko Gradište, Zrenjanin) for RX5day, with the stations located mainly in central and eastern Serbia.

Figure 6 shows trend coefficients of RR20mm, RX1day, and R99p during the summer (left column) and winter (right column). In summer, it is most often the case that one station (Niš for RX1day and R99p, Sremska Mitrovica for RR20mm, shown in Figure 6) or two stations (Belgade and Niš for RX3day, Kragujevac and Niš for RX5day) show a negative trend. In addition, four stations (Kraljevo, Loznica, Sremska Mitrovica, Veliko Gradište) show a negative trend for R95p, and six stations (Kragujevac, Kraljevo, Loznica, Sombor, Sremska Mitrovica, Veliko Gradište) for RR10mm in summer (Table 8).

A more coherent trend pattern of selected indices is observed in summer, compared to winter (Figure 6). The highest number of stations with a negative trend is observed in the winter season (Table 8). In particular, the following stations show a negative trend: Sremska Mitrovica, Zrenjanin, Belgrade, Kraljevo, Veliko Gradište, and Zlatibor, mainly in central Serbia.

Hamouda and Pasquero [36] found an overall increasing trend in both the frequency and intensity of extreme precipitation in all seasons except winter using the EOBS dataset in the period 1979–2008. Fischer and Knutti [44] pointed out that the intensification of heavy precipitation is confirmed in the observed records in many regions of the world, as the model predictions were made decades ago.

4. Discussion and Conclusions

Extreme precipitation events (RR10mm, RR20mm, Rx1day, Rx3day, Rx5day, R95p, and R99p) were analyzed using data from 14 stations in Serbia. An increase in the area-averaged values of all extreme events considered during the period 1961–2020 was observed. A significant positive trend of RX1day was found at 12 out of 14 stations. Only two stations (Negotin and Niš) in the east and southeast of Serbia showed a non-significant positive trend, as these stations recorded the smallest increase in precipitation. In their previous study on extreme precipitation measured at 16 stations in the period 1961–2014 in Serbia [10], a non-significant positive trend was found for the number of days with at least 10 and 20 mm of precipitation, the annual daily maximum of precipitation, the precipitation sum over three and five consecutive days, and the annual total amount of precipitation. Unkašević and Tošić [8] determined an increase in very intense precipitation (RR20 and R95p) over almost all of Serbia until the end of the twentieth century and beyond. The results obtained for the seasonal values of the EXPEs show seasonal differences in trend direction. The most consistent pattern of positive trends was observed in autumn. An increase in EXPEs prevailed in spring, and a negative trend was observed mainly at stations in central and eastern Serbia. In summer, a positive trend was recorded at the majority of stations. A high value of Rx1day (116.6 mm) was measured in Novi Sad in the summer of 2018. High temperatures and a very unstable atmosphere favored strong convection and caused high rainfall, which led to flooding in the city due to surfaces and limited drainage systems [45]. In Serbia, with a moderate continental climate [16], intensive local heating in summer leads to heavy precipitation. In addition, due to a warmer Mediterranean Sea and enhanced moisture transport, more precipitation extremes can be expected in Central Europe [46]. A positive trend was mostly observed during the winter season, while negative trends were observed in central and northern Serbia. An increase in the frequency of extreme precipitation changes in northern Europe and a decrease in southern Europe was found in winter [43]. According to [47], the role of large-scale processes and local mechanisms leading to extreme precipitation differs in cold and warm seasons.

The mean values of the EXPEs were calculated over two 30-year periods (1961–1990 and 1991–2020). Higher values of all EXPEs were obtained in the second period, 1991–2020. The lowest values of RR10mm and RR20mm were measured in Zrenjanin (northern Serbia), and the highest in Zlatibor (western Serbia). This agrees with [17], who found that northern Serbia receives less than 600 mm of precipitation annually, while the western and southwestern areas are the rainiest regions in Serbia. The minimum values of Rx1day and Rx5day were recorded in Niš (southern Serbia), while the maximum value of Rx1day was recorded in Zlatibor (western Serbia) from 1961 to 1990 and in Negotin (eastern Serbia) from 1991 to 2020. It is interesting to note that the highest 1-day precipitation in eastern Serbia occurred during the period 1991–2020, which is caused by synoptic situations characterized by cyclone activity over the Black Sea and local topography [48]. The highest values of Rx3day and Rx5day were observed in Loznica (western Serbia). The greatest amounts of precipitation were recorded in western Serbia (Zlatibor and Loznica), influenced by the air intrusion from the west and the local topography [8]. Unkašević and Tošić [8] also pointed out that the greatest average precipitation in summer was recorded in western Serbia, caused by cold fronts, showers, and thunderstorms in cold air masses from the west, while in winter, precipitation was caused by cyclone activity from the western Mediterranean.

The highest values of all EXPEs were observed in 2014, when the annual precipitation totals were highest at almost all stations in Serbia. According to [49], the occurrence of extreme precipitation on the same day at least at two stations indicates the role of large-scale atmospheric circulations rather than local effects. In [1], it was pointed out that large-scale atmospheric circulation patterns are important drivers of local and regional extremes. Many studies confirm the influence of the NAO on precipitation [36,50,51]. In our study, a negative correlation between the NAO and the EXPEs was found for all stations (Table 5). This is consistent with previous studies on the influence of the NAO on precipitation in Serbia [52]. A stronger influence of EAWR and EA than NAO on EXPEs in Serbia was registered (Table 6 and Table 7). It was found that the EAWR is negatively, and the EA mainly positively, correlated with the EXPEs. The strongest influence of the EA was observed in central Serbia, from Loznica in the west to Zaječar in the east of Serbia. In addition, a significant correlation between the EA and RX1day, RX3day, RX5day, R95p, and R99p was observed for Novi Sad in the north. A strong negative influence of the EAWR was found for RR20mm, RX1day, RX3day, R95p, and R99p in northern Serbia. In addition, a significant negative correlation was found between the EAWR and RR10mm and R95p for stations in central and southern Serbia and for RX1day and RX3day in Zaječar in eastern Serbia. Our results agree with [40], who concluded that precipitation over Serbia and the Balkans depends on the EAWR phase, but not on the NAO and EA phase, which leads to an excess of precipitation over Serbia in the negative EAWR phase. In 2014, when the highest values of all EXPEs were observed, the annual NAO index was −0.0867, the EA index was 0.7367, and the EAWR index was −0.3841. The positive phase of the EA, which is associated with the transport of warm air over Serbia, and negative values of the NAO and EAWR indices favored an excess of precipitation in Serbia. With a warming climate and a higher temperature in the Mediterranean, increased moisture transport is to be expected, which will lead to more extreme precipitation in Serbia.

For future plans, a contribution to increasing the resolution using gridded data for Serbia should be investigated. We also plan to analyze the extreme precipitation events for future scenarios of the 21st century.

Author Contributions

Conceptualization, I.T. and T.S.; methodology, I.T. and V.D.; software, A.S.A.d.S.; validation, S.P., I.L. and M.T.; formal analysis, A.S.A.d.S. and L.F.; investigation, I.T. and S.P.; data curation, I.L. and M.T.; writing—original draft preparation, I.T., S.P., T.S. and B.S.; writing—review and editing, I.T., S.P., T.S., B.S. and V.D.; visualization, L.F., I.L. and M.T.; supervision, V.D.; project administration, I.T.; funding acquisition, I.T., T.S. and B.S. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data presented in this study are available from the authors upon request.

Acknowledgments

A.S.A.d.S., T.S., and B.S. acknowledge the support of Brazilian agencies CAPES and CNPq (grants No 308782/2022-4 and 309499/2022-4). I.T., L.F., M.T., I.L., S.P., and V.D. acknowledge the support of the Ministry of Science, Technological Development and Innovation of the Republic of Serbia, grant No. 451-03-136/2025-03/200162. The authors are very grateful to the anonymous reviewers for their constructive suggestions that led to the improvement of the paper.

Conflicts of Interest

The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

Footnotes

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Figures and Tables

Figure 1 Location of meteorological stations in Serbia and position of Serbia in Europe.

Figure 2 Extreme precipitation events: (a) RR10mm; (b) RR20mm, calculated as an areal average over Serbia (blue line). The straight line represents linear regression; the uncertainty is shaded.

Figure 3 Extreme precipitation events: (a) RX1day; (b) RX3day; (c) RX5day, calculated as an areal average over Serbia (blue line). The straight line represents linear regression; the uncertainty is shaded.

Figure 4 Extreme precipitation events: (a) R95p; (b) R99p, calculated as an areal average over Serbia (blue line). The straight line represents linear regression; the uncertainty is shaded.

Figure 5 Correlation coefficient between RR20mm (a,b), RX1day (c,d), and R99p (e,f) with the EA (left) and the EAWR pattern (right).

Figure 6 Trend coefficient for RR20mm (a,b), RX1day (c,d), and R99p (e,f) in summer (left) and winter (right). Coefficients greater than 1.96 or less than −1.96 indicate a trend that is significant at the 5% level.

Table 1

Abbreviation (Abb) of meteorological stations with their latitude, longitude, and altitude (m).

Abb	Station	Latitude	Longitude	Altitude (m)
SO	Sombor	45°47′	19°05′	88
ZR	Zrenjanin	45°24′	20°21′	80
NS	Novi Sad	45°20′	19°51′	84
SM	Sremska Mitrovica	44°58′	19°38′	82
BG	Belgrade	44°48′	20°28′	132
VG	Veliko Gradište	44°45′	21°31′	82
LO	Loznica	44°33′	19°14′	121
SP	Smederevska Palanka	44°22′	20°57′	121
NE	Negotin	44°13′	22°31′	42
KG	Kragujevac	44°02′	20°56′	185
ZA	Zaječar	43°53′	22°17′	144
KV	Kraljevo	43°44′	20°41′	215
ZL	Zlatibor	43°39′	19°41′	1085
NI	Niš	43°20′	21°54′	202

Table 2

Acronym (Acr), descriptive name of the temperature indices based on daily precipitation (RR), and definition.

Acr	Descriptive Name	Definition
R10mm	Heavy precipitation days	Number of days where RR (daily precipitation) ≥ 10 mm
R20mm	Very heavy precipitation days	Number of days where RR ≥ 20 mm
RX1day	Highest 1-day precipitation amount	The maximum 1-day values for period j
RX3day	Highest 3-day precipitation amount	The maximum 3-day values for period j
RX5day	Highest 5-day precipitation amount	The maximum 5-day values for period j
R95p	Very wet days	Number of days where RR (RR ≥ 1) ≥ 95th percentile
R99p	Extremely wet days	Number of days where RR (RR ≥ 1) ≥ 99th percentile

Table 3

Mean values for RR10mm, RR20mm, Rx1day, Rx3day, Rx5day, R95p, and R99p at 14 stations in Serbia during two periods: 1961–1991 (61-90) and 1991–2020 (91-20).

Abb	RR10mm		RR20mm		RX1day		RX3day		RX5day		R95p		R99p
	61-90	91-20	61-90	91-20	61-90	91-20	61-90	91-20	61-90	91-20	61-90	91-20	61-90	91-20
SO	16.2	18.3	4.1	5.8	38.8	43.4	53.2	59.3	59.6	69.6	16.8	19.1	3.1	4.1
ZR	15.8	16.5	3.8	5.1	37.6	44.3	54.2	55.3	61.9	62.6	17.4	18.2	3.2	4.1
NS	17.4	23.2	4.4	7.3	38.2	52.0	52.3	69.2	58.9	78.4	15.1	21.3	2.3	4.9
SM	18.7	18.2	4.5	5.2	36.7	41.7	51.8	57.7	58.6	65.9	18.3	17.9	3.3	4.0
BG	20.5	21.8	6.0	6.8	43.1	46.3	62.9	64.6	73.2	75.6	17.3	18.9	3.4	3.9
VG	20.4	20.0	5.3	6.1	43.2	50.4	65.4	68.4	73.4	75.6	18.4	18.1	3.2	4.1
LO	27.5	28.6	8.4	9.9	45.3	52.4	65.8	74.3	76.5	87.9	17.2	19.1	3.2	4.1
SP	18.6	19.9	4.8	5.9	44.6	43.5	60.2	61.3	66.5	70.5	17.6	18.7	3.2	4.1
NE	19.4	20.5	6.1	6.8	45.8	52.5	69.0	73.7	78.9	81.3	17.9	18.6	3.3	4.0
KG	19.7	20.1	5.0	5.7	40.0	44.5	58.7	60.0	67.3	68.0	17.6	18.1	3.3	3.9
ZA	19.1	19.4	4.8	5.3	39.0	40.1	54.4	54.9	64.5	64.8	17.9	18.2	3.5	3.8
KV	23.9	23.4	6.9	7.8	40.9	44.8	65.6	63.9	75.0	77.7	18.4	17.8	3.1	4.1
ZL	30.2	34.4	10.3	11.2	51.3	49.4	74.3	71.5	83.0	85.4	17.0	19.1	3.0	4.2
NI	17.9	18.5	4.3	4.7	35.5	39.1	52.8	55.8	58.0	61.9	17.9	18.5	3.2	4.0

Table 4

Sen’s slope estimator for seven precipitation indices at 14 stations (listed in Table 1) in Serbia during the period 1961–2020.

Abb	RR10mm	RR20mm	RX1day	RX3day	RX5day	R95p	R99p
SO	0.0351 1	0.0435	0.1036	0.2000	0.2173	0.0400	0.0286
ZR	0	0.0400	0.1911	0.0750	0.0619	0	0.0213
NS	0.1235	0.0714	0.4586	0.4899	0.5131	0.1429	0.0555
SM	0	0.0088	0.1726	0.1956	0.1690	0	0.0198
BG	0.0286	0	0.1016	−0.0212	−0.0604	0	0
VG	0.0222	0	0.1632	0.0141	−0.0237	0	0
LO	0.0588	0.0435	0.2122	0.3508	0.3889	0.0619	0.0294
SP	0.0588	0.0417	0.1029	0.1131	0.1434	0.0659	0.0400
NE	0.0364	0	0.0910	0.1914	0.1747	0	0
KG	0	0	0.1520	0.0548	0.0577	0.0267	0
ZA	0	0	0.1336	0.1750	0.2084	0	0
KV	0	0.0400	0.1785	0.0789	0.2326	0	0.0192
ZL	0.1163	0.0400	0.1446	0.1000	0.2474	0.0769	0.0241
NI	0.0286	0.0215	0.0600	0.0595	0.1051	0.0286	0.0238

¹ Coefficients that are significant at the 5% level are indicated in bold.

Table 5

Correlation between EXPEs and NAO for 14 stations in Serbia during the period 1961–2020.

Abb	RR10mm	RR20mm	RX1day	RX3day	RX5day	R95p	R99p
SO	−0.0011	−0.0714	−0.2855	−0.2480	−0.2181	−0.0509	−0.1011
ZR	−0.2284	−0.1222	−0.0169	−0.0080	0.0162	−0.2180	−0.2022
NS	−0.0808	−0.0392	0.2173	0.1668	0.1495	−0.0762	−0.0544
SR	−0.0908	0.1442	0.0777	0.0122	0.0499	−0.1013	0.0909
BG	−0.2578	−0.0182	0.2191	0.1341	0.1276	−0.2068	0.0420
VG	−0.1254	0.0493	−0.0097	−0.0356	−0.0034	−0.1261	0.1143
LO	−0.1631	−0.2927	0.0934	0.0262	0.0383	−0.1604	−0.1018
SP	−0.0500	0.1011	0.0245	0.0997	0.0583	−0.0028	0.0817
NE	−0.0760	0.0299	0.0920	0.0732	0.0365	−0.0381	0.0779
KG	−0.1683	−0.1293	−0.0048	0.0744	0.0855	−0.1916	−0.1401
ZA	−0.2342	−0.2010	−0.0682	−0.0500	−0.0608	−0.2256	−0.1943
KV	−0.0570	0.0288	−0.0238	0.0256	0.0975	−0.0514	0.1060
ZL	0.0097	−0.1305	0.0208	0.0450	−0.0496	−0.0968	0.0133
NI	−0.1305	−0.0101	−0.0862	−0.0300	−0.1120	−0.1305	−0.0761

Coefficients that are significant at the 5% level are indicated in bold.

Table 6

Correlation between EXPEs and EA pattern for 14 stations in Serbia during the period 1961–2020.

Abb	RR10mm	RR20mm	RX1day	RX3day	RX5day	R95p	R99p
SO	−0.0010	0.2015	0.1200	0.1791	0.1724	0.0308	0.1960
ZR	0.0159	0.1099	0.2202	0.0909	0.0112	−0.0033	0.0380
NS	0.2259	0.2239	0.3280	0.3165	0.3085	0.2617	0.3087
SR	−0.0051	0.0978	0.2256	0.1725	0.1849	−0.0195	0.1681
BG	0.0925	0.0484	0.0872	0.0720	0.0302	0.0884	0.0816
VG	0.0651	0.1710	0.1383	0.0491	0.0193	0.0732	0.1289
LO	0.2807	0.2376	0.3384	0.3579	0.3855	0.3307	0.3439
SP	0.1151	0.2950	0.0569	0.0848	0.0802	0.1396	0.3674
NE	0.1808	0.1011	0.3288	0.2999	0.2022	0.1441	0.1600
KG	0.1495	0.3129	0.2203	0.1028	0.1009	0.1568	0.2780
ZA	0.1112	0.0847	0.2896	0.2337	0.1561	0.0887	0.1559
KV	0.0250	0.2235	0.0848	−0.0925	0.0738	0.0328	0.3031
ZL	0.2235	0.2422	0.0601	−0.0166	0.0763	0.2686	0.2679
NI	0.0986	0.0738	0.0578	0.0918	0.1335	0.0986	0.1928

Coefficients that are significant at the 5% level are indicated in bold.

Table 7

Correlation between EXPEs and EAWR pattern for 14 stations in Serbia during the period 1961–2020.

Abb	RR10mm	RR20mm	RX1day	RX3day	RX5day	R95p	R99p
SO	−0.0625	−0.3202	−0.3716	−0.2927	−0.2295	−0.0724	−0.2943
ZR	−0.1931	−0.2853	−0.1822	−0.0264	0.0127	−0.1675	−0.2983
NS	−0.2249	−0.3245	−0.2527	−0.2519	−0.2223	−0.2591	−0.3857
SR	−0.1909	−0.2026	−0.2636	−0.1452	−0.0367	−0.1883	−0.2260
BG	−0.0827	−0.1329	0.0618	−0.0054	0.0337	−0.1335	−0.1939
VG	−0.2272	−0.2270	−0.1529	−0.0203	−0.0160	−0.2966	−0.1074
LO	−0.2901	−0.1216	−0.0383	−0.1205	−0.0693	−0.3461	−0.0589
SP	−0.3058	−0.4271	−0.0450	−0.1137	−0.1277	−0.3206	−0.3573
NE	−0.2527	−0.1492	−0.2365	−0.2192	−0.1907	−0.1959	−0.1479
KG	−0.1592	−0.3281	−0.0162	0.0770	0.1064	−0.1803	−0.2214
ZA	−0.3133	−0.1368	−0.3783	−0.3039	−0.2316	−0.2905	−0.1066
KV	−0.1462	−0.1975	−0.0643	0.0028	−0.0573	−0.1446	−0.2013
ZL	−0.2924	−0.3606	−0.1814	−0.0934	−0.1297	−0.2581	−0.1749
NI	−0.2937	−0.1871	−0.1716	−0.2110	−0.2158	−0.2937	−0.2545

Coefficients that are significant at the 5% level are indicated in bold.

Table 8

Summary of the seasonal trend analysis of the extreme precipitation indices based on 14 stations in Serbia during the period 1961–2020.

Acr	Spring	Summer	Autumn	Winter
RR10mm	(9+)3; (5−)2	(8+)3; (6−) 1	(13+)5; (1−)	(10+)1; (4−)1
RR20mm	(13+)3	(13+)2; (1−)	(14+)6	(7+); (6−)2
RX1day	(14+)7	(13+)5; (1−)	(14+)11	(8+)2; (6−)2
RX3day	(10+)4; (4−)	(11+)6; (2−)1	(14+)10	(8+)4; (6−)2
RX5day	(11+)4; (3−)	(12+)8; (2−)1	(14+)8	(8+)1; (6−)4
R95p	(9+)2; (5−)1	(9+)2; (4−)	(13+)5; (1−)	(9+)2; (4−)1
R99p	(14+)2	(13+)2; (1−)1	(14+)5	(9+); (5−)2

¹ The sign and number in parentheses indicate the total number of stations with positive or negative trend coefficients. Numbers of stations with positive or negative trend coefficients that are significant at the 5% level are indicated in bold.

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