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ORIGINAL PAPER
Annual and seasonal variability of precipitationin Vojvodina, Serbia
Ivana Tošić & Ivana Hrnjak & Milivoj B. Gavrilov &
Miroslava Unkašević & Slobodan B. Marković & Tin Lukić
Received: 14 November 2012 /Accepted: 28 August 2013# Springer-Verlag Wien 2013
Abstract Annual and seasonal variability of precipitationobserved at 92 stations in Vojvodina (Serbia) were analyzedduring the period 1946–2006. The rainfall series were exam-ined by means of the empirical orthogonal functions (EOF).The first set of singular vectors explains from 68.8 % (insummer) to 81.8 % (in winter) of the total variance. Thetemporal variability of the time series associated with themain EOF configurations (the principal components, PCs)was examined using the Mann–Kendall test and the spectralanalysis. The time series of PC1 revealed decreasing trend inthe winter and spring precipitation and increasing trend in theautumn, summer, and annual precipitation. The relationshipsbetween the first PC and circulation patterns, such as theNorth Atlantic Oscillation (NAO), the East Atlantic (EA)pattern, and East Atlantic/West Russia pattern, were alsoinvestigated. The PC1, displaying temporal behavior ofthe first mode, demonstrated evident correspondence withthe NAO index in analysis of the annual, winter, andautumn precipitation. Power spectra of the PC1 showstatistically significant oscillations of about 3.3 yearsfor the spring precipitation and about 8 and 15 years for thewinter precipitation. Comparisons with spectral analysis ofauthors for some regions in Europe, most of them in theMediterranean domain, show that similar periodicities aredetected.
1 Introduction
The spatial and temporal variability of precipitation is impor-tant from both the scientific and practical point of view.Analysis of spatial–temporal variability of the precipitationhas received considerable attention. A number of authors fo-cused on the regional changes in precipitation (e.g., von Storchet al. 1993; Hurrell 1995; Reljin et al. 2001; Tomozeiu et al.2002; Zveryaev 2004; Tošić 2004; Nastos and Zerefos 2010).Several others considered global distribution of precipitationand its variability (e.g., Diaz et al. 1989; Dai andWigley 2000).Most of the aforementioned studies are based on analysis of thewinter or annual precipitation. Zveryaev and Allan (2010) haveanalyzed summer rainfall in Europe and determined the spatialand temporal variability using empirical orthogonal functionsanalysis.
This paper investigates the spatial and temporal variabilityof the annual and seasonal precipitation in Vojvodina, Serbia(Fig. 1a). The Vojvodina Province is in the northern part ofSerbia, which covers an area of 21.533 km2. It is located in thePannonian Plain of Central Europe. The Vojvodina region isdivided by the Danube and Tisa rivers into: Bačka in thenorthwest, Banat in the east, and Syrmia (Srem) in the south-west. This region is a relatively flat area with two mountains:Vršac Mountains (with a peak of 641 m) in SE Banat andFruška Gora Mountain (with a peak of 539 m) in northernSrem. It has a population of about two million. The region isvery important for agriculture, so that a better comprehensionof precipitation behavior is a key factor to this sector.
Dividing Vojvodina into four subregions: Bačka, NorthBanat, South Banat, and Srem, Gavrilov et al. (2013, in prepa-ration) found that the precipitation trends were with all threemark (positive, negative, and zero), but theyweremostly positivefor all subregions and seasons aswell as for thewholeVojvodina.
The outline of the paper is as follows: after the Introduction,Section 2 describes the data and methods used in the study. In
I. Tošić (*) :M. UnkaševićFaculty of Physics, Institute of Meteorology, University of Belgrade,11000 Belgrade, Dobračina 16, Serbiae-mail: [email protected]
I. Hrnjak :M. B. Gavrilov : S. B. Marković : T. LukićFaculty of Sciences, Department of Geography, Tourism and HotelManagement, University of Novi Sad, Trg Dositeja Obradovića 3,21000 Novi Sad, Serbia
Theor Appl ClimatolDOI 10.1007/s00704-013-1007-9
Fig. 1 Geographical location of a Serbia in Europe and b the meteorological stations in Vojvodina (northern Serbia)
I. Tošić et al.
Section 3, the results of the spatial variability provided by theempirical orthogonal functions (EOF) analysis are presented.Section 4 contains the results obtained using the trend analysisand spectral analysis. In addition, links between the first PCand circulation patterns are examined. The conclusions arepresented in Section 5.
2 Data and methods used
2.1 Data used
In the present work, an analysis of the monthly precipitation inVojvodina during the period 1946–2006, recorded at 92 sta-tions without gaps was done. The locations of stations areshown in Fig. 1b. Most of the stations which are analyzed inthis study are with altitude between 80 and 100 m. Only onestation, Ležimir, is at 200 m. Measurements were performedevery day without a break using the same types of instru-ments. The technical and critical control of these measure-ments was realized by the Serbian Meteorological Service.
The homogeneity of the annual precipitation series wasexamined according to Alexandersson (1986). This relative testis based upon the assumption that the ratio between precipita-tion amounts at the station being tested (test station) and thereference series is fairly constant in time. The correlation coef-ficients between the candidate stations and the reference sta-tions were above 0.7 because of the relatively low and uniformterrain of Vojvodina. The homogeneity analysis showed thatthe precipitation time series for 92 stations are homogeneous.
To assess the links between variability of precipitation andatmospheric circulation, we used indices of the major tele-connection patterns that have been described by Barnston andLivezey (1987). In our analysis along with links to the NorthAtlantic Oscillation (NAO;Hurrell 1995), we examined links tosuch teleconnections as the East Atlantic (EA) pattern and theEast Atlantic/West Russia (EA/WR) pattern. The EA pattern issimilar to the NAO and characterized by a meridionale dipoleof two anomaly centers, but the EA action centers are displacedsoutheastward relative to those of the NAO pattern. The EA/WR pattern is one of three prominent teleconnection patternsthat affect Eurasia throughout the year. The positive phase isassociated with positive height anomalies located over Europeand northern China, and negative height anomalies located overthe central North Atlantic and north of the Caspian Sea. Theindex values were taken from the NOAA Climate PredictionCenter Website http://www.cpc.ncep.noaa.gov/data/teledoc/.The data cover the period from 1950 to 2006.
2.1.1 Climate characteristics
The climate of Vojvodina is moderate continental, with coldwinters and hot, humid summers. The maximum precipitation
occurs in June, while minimum is in February. The mean ofthe annual and seasonal precipitation sums during the period1946–2006 are shown in Fig. 2. The minimum annual precip-itation totals is registered over northern Vojvodina (around540 mm/year), while the maximum of 660 mm is measured inSWVojvodina (Fig. 2a). The winter (Fig. 2b), spring (Fig. 2c),and autumn (Fig. 2e) precipitations are between 120 and160 mm, while summer precipitation totals (Fig. 2d) are from180 mm in northern Vojvodina to 220 mm in SE and SWVojvodina. Spatial precipitation patterns are mostly influencedby orography, i.e., by Vršac Mountains near Vršac in SEVojvodina and Fruška Gora Mountain in SW Vojvodina.
2.2 The empirical orthogonal functions method
The EOF has been used in meteorology since the work ofLorenz (1956). One of the main purposes of EOF is to reducethe number of variables to be studied while retaining most ofthe information contained in the original set of variables inorder to understand and interpret the structure of the data. Inthis analysis, the covariance matrix approach (Wilks 1995;Venegas 2001) was used.
The data matrix F, that consists of M rows (spatial points)and N columns (temporal samples) of the standardized data asfollows:
F ¼x1 1ð Þ x1 2ð Þ ⋯ x1 Nð Þx2 1ð Þ x2 2ð Þ ⋯ x2 Nð Þ⋯ ⋯ ⋯ ⋯
xM 1ð Þ xM 2ð Þ ⋯ xM Nð Þ
26643775: ð1Þ
is used to derive the spatial covariance matrix RFF by multi-plying matrix F by its transpose F ′
RFF ¼ F� F0: ð2Þ
The matrix product RFF is symetric and square, even ifF itself is not square. Then, the covariance matrix isdecomposed into matricesΛ and E
RFF�E ¼ E�Λ; ð3Þ
where, Λ =M ×M is diagonal matrix containing the eigen-values λ k of RFF. The square matrix E has dimension M ×M . Its column vectors are the eigenvectors ofRFF correspond-ing to eigenvalues. Each eigenvector represents the spatialEOF pattern, i.e., the empirical orthogonal functions. Theeffective dimension of matrix E is M ×K , where K are themodes of the EOF decomposition. The time evolution of theK th EOF is given by the time series Ak (t ), which is obtainedprojecting the original data series onto eigenvector and
Annual and seasonal variability of precipitation in Vojvodina, Serbia
summing over all locations. In matrix notation, matrix A isobtained by multiplying matrices E ′ and F
A ¼ E0 � F: ð4Þ
The rows in matrixA are time series of length N . They arecalled the Principal components or PCs.
The main variability modes of the annual and seasonalprecipitation in Vojvodina (Serbia) are identified with this
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I. Tošić et al.
technique. We did not rotate the EOFs, because a rotation ofthe EOFs show similar patterns retaining the basic structuresof the unrotated. It is commonly assumed that this indicatesthat the patterns are representative in themselves (see, forexample, Mo and Ghill 1987; Fraedrich et al. 1993).
2.3 The autocorrelation spectral analysis
Spectral analysis of discrete meteorological data sequencesplays an important role in data analysis, interpretation, andsearches for periodicities. Time series analysis methods aim toexamine temporal sequences of data in terms of its frequencycontent. In this study, the power spectra of annual and season-al standardized anomalies were analyzed using the autocorre-lation spectral analysis (ASA) (Blackman and Tukey 1958;WMO 1966). The ASA is obtained by applying the discreteFourier transform algorithm to the correlation functions esti-mated from time series, and taking the classical Hammingwindow (WMO 1966) as smoothing function. The averagingoperation of raw spectral estimate is necessary in order toobtain a consistent estimate of the spectrum in terms of discreteestimates.
If we have N terms of a series x i, we compute the serialcovariances C τ for all lags τ =0 to τ =m (where m <N )according to:
Cτ ¼ 1
N−τ
XN−τ
i¼1
xi−x� �
xiþτ−x� �
; ð5Þ
where x is the mean of all x i in the series. Raw spectralestimates Sk, k =0,1,2…,m–1, m are then obtained directlyfrom these Cτ values by the equations:
bS0 ¼ 1
2mC0 þ Cmð Þ þ 1
m
Xm−1τ¼1
Cτ ; ð6Þ
bSk ¼ C0
mþ 2
m
Xm−1τ¼1
Cτcosπkτm
� �þ 1
mCm −1ð Þk ; ð7Þ
bSm ¼ 1
2mC0 þ −1ð ÞmCm½ � þ 1
m
Xm−1τ¼1
−1ð ÞτCτ : ð8Þ
The first of these equations is used to compute bS0 , and
Eq. (8) is used to compute the last spectral estimate bSm . Allthe interveningm −1 spectral estimates are computed from themiddle equation by setting k in the cosine argument tosuccesive integral values k =1, 2,…, m –1.
Final spectral estimates, Sk , are then computed bysmoothing the raw estimates with three-term weightedaverages. In the Hamming method, the smoothing formulaeare:
S0 ¼ 1
2bS0 þ bS1� �
; ð9Þ
Sk ¼ 1
4bSk−1 þ 2bSk þ bSkþ1
� �; ð10Þ
Sm ¼ 1
2bSm−1 þ bSm� �
; ð11Þ
where k in (10) is set equal to 1, 2, …, m −1.In order to determine the significant peaks in the calculated
spectra, the theoretical curve (null continuum) along with its
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Fig. 3 Eigenvalues of the annualprecipitation with the error bar
Table 1 Explained variances (in percent) of the first EOF pattern of theannual and seasonal precipitation
EOF pattern Annual Winter Spring Summer Autumn
EOF1 73.0 85.4 69.3 68.8 81.8
Annual and seasonal variability of precipitation in Vojvodina, Serbia
associated 95 % confidence level has been fitted asdescribed in WMO (1966). Following Tukey (1950),
the ratio between the spectral estimate and the nullcontinuum (“white” or Markov “red noise”) for any spectral
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I. Tošić et al.
component follows a Chi-square distribution (χ2) divided bythe degrees of freedom
ν ¼2N−
m
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where N is the record length analyzed andm the maximum lagconsidered in the computation of the correlation function. Thus,if we fix a confidence limit of say 95 %, and compute theprobability point for the χ2 distribution at this percentage, theempirical spectral component will be significant if the ratio of
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Fig. 5 Time series of the first EOF (PC1) for the a annual, b winter, c spring, d summer, and e autumn precipitation with their trend and the NAO index(NAOI); r is the correlation coefficient
Annual and seasonal variability of precipitation in Vojvodina, Serbia
the power associated with a peak in the spectrum to the localpower level of the null continuum is greater than this probabil-ity point.
2.4 Trend
The presence or absence of trend in individual rainfall serieshas been determined using the Mann–Kendall rank statistic τ(Kendall and Stuart 1961). This is defined as:
τ ¼ 4X
ni
N N−1ð Þ−1; ð13Þ
where ni is the number of values larger than the i th value inthe series subsequent to its position in the series of N values.To apply this statistic to evaluate significance (WMO 1966), acomparison is made with:
τð Þt ¼ �tg
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4N þ 10
9N N−1ð Þ
s; ð14Þ
where t g is the desired probability point of the standardGaussian distribution for a two-sided test. Linear trend hasbeen determined by conventional least squares regressionanalysis. In trend evaluation, the 5 % level of significancehas been taken for the rejection of the null hypothesis of notrend for individual sets of data.
3 Spatial patterns of annual and seasonal precipitation
The anomalymatrix of the annual and seasonal precipitation iscomputed by subtracting from each monthly and seasonalvalue the respective monthly and seasonal long-term meanfor the period 1946–2006. In this way, the annual cycle wasremoved from all time series. The patterns provided by theEOF method show the main spatial features of annual andseasonal precipitation, while their coefficient time series(PCs) describe the dominant variability in the dataset. Severalcriteria have been suggested for deciding how many EOFs toretain in order to separate signal from noise (Jolliffe 1986;Preisendorfer 1988), but a clear-cut number of EOFs is rare. Inthis study, the simple scree test of Cattell (1966) was adopted.The scree plot of the present analysis (Fig. 3) contains onebreak of the slope at the second EOF. In addition, the samplingerrors of the EOFs estimated (North et al. 1982) are shown bythe error bar in Fig. 3; degeneracy occurs when the differencesbetween nearby eigenvalues are less than the sampling error.From Fig. 3, it can be seen that only the first leading EOFrepresent the signal.
The variances explained by the first EOF for the annual andseasonal precipitation anomalies are presented in Table 1. Thefirst set of EOFs explains from 68.8 % (in summer) to 85.4 %
(in winter) of the total variance. The high explained varianceis due to flat and relatively uniform terrain of Vojvodina. Thespatial structure of EOF1 for the annual and seasonal precip-itation (Fig. 4) is characterized by a homogeneous positivevalue over the whole region indicating that a large-scaleprocess could be responsible for the precipitation variability.Its highest values are concentrated over SW Vojvodina, exceptduring the winter with the maximum value over NEVojvodina.This similarity of EOF1 with the mean field (Fig. 2) reflects thefact that the variance turns out to be maximal when the meanfield is larger, as expected for precipitation.
4 Temporal variability of the annual and seasonalprecipitation
The time variability of the annual and seasonal precipitation isinvestigated analyzing the trend and power spectra of the PC1of precipitation. Time series of the PC1 and the NAO indexare shown in Fig. 5. Trend coefficients for the annual andseasonal PC1 are presented in Table 2. It is found that the trendof PC1 for the annual precipitation is a slightly negative(Fig. 5a; Table 2). The highest value of PC1 corresponds tothe year of 1999; in July 1999, heavy rainfall and floodingoccurred in Serbia (Unkašević et al. 2004). A decrease ofprecipitation existed during the winter (significant at the 5 %level, Fig. 5b) and spring (Fig. 5c). The minimum value of PC1,registered in 2000 (Unkašević et al. 2004), is evident during thesummer season (Fig. 5d), which is reflected on the annualprecipitation. According to Table 2, there is an increase ofprecipitation during the summer and autumn (significant at the5 % level, Fig. 5e). It is obtained that the trends of NAO indexare significant and opposite to the PC1 trend, except for thesummer and autumn seasons (not shown).
Table 3 Annual and seasonal correlation coefficients between PC1 andNAO index, EA/WR index, and EA index
PC1 Annual Winter Spring Summer Autumn
NAO index −0.2682 −0.5166 −0.1283 0.1660 −0.3271EA/WR index −0.1372 −0.5179 −0.1693 0.1091 −0.3523EA index −0.1568 −0.1938 −0.2065 −0.1639 −0.2181
Coefficients that are significant at the 1 and 5 % significance levels arepresented in italics and bold, respectively
Table 2 Trend coefficients for the annual and seasonal PC1
PC Annual Winter Spring Summer Autumn
PC1 −0.0010 −0.0222 −0.0066 0.0052 0.0152
Coefficients that are significant at the 5 % significance levels arepresented in italics
I. Tošić et al.
To investigate the relationship between precipitation andthe dominant patterns of atmospheric variability (such asthe NAO, the EA, and the EA/WR), we performed the corre-lation between teleconnection indices and PC1. The signifi-cance level of the correlation coefficient is computed bytransforming the correlation to create a t statistic having
N -2 degrees of freedom. The obtained results are shown inTable 3. The PC1, displaying temporal behavior of the firstmode, demonstrates evident correspondence with the NAOindex in analysis of the annual, winter, and autumn precipita-tion. During the winter, the first EOFmode of the precipitationin Vojvodina is strongly linked to the NAO (Table 3). The
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Fig. 6 The power spectra of the first EOF (PC1) for the: a annual, b winter, c spring, d summer, and e autumn precipitation. The 95% confidence level(T95) is denoted by the dotted line , the null continuum (“white noise”) is denoted by the dashed line
Annual and seasonal variability of precipitation in Vojvodina, Serbia
negative relationship between NAO and precipitation wasexpected according to previous results obtained for Serbiaand Montenegro by Tošić (2004). The correlation betweenthe first PC and the NAO index is negative and significant(−0.5166). That means the positive phase of the NAO resultsin decreased intraseasonal fluctuations and deficient precipi-tation over Vojvodina (Fig. 5b). During the autumn, the firstEOFmode of seasonal mean precipitation is strongly linked tothe autumn NAO (−0.3271). More negative values of theNAO after 1985 contributed to increased precipitation inVojvodina (Fig. 5e). Peaks of the cross-correlation betweenthe precipitation and NAO index during the winter and au-tumn are detected at the zero time lag (not shown). Thesignificant correlation (at the 1 % level of significance) isobserved between the EA/WR index and PC1 for the winterand autumn precipitation (Table 3). No significant correlationshave been found between the EA index and PC1 (Table 3).
Many authors found significant correlation between theprecipitation amounts and NAO in Europe during the winter(Hurrell 1995; Tomozeiu et al. 2002; Tošić 2004; Zveryaev2004). During the summer season, Zveryaev and Allan (2010)found that the first EOF mode of European precipitation isassociated with the North Atlantic Oscillation. The significantcorrelation between the PC1 and NAO during the summer hasnot been identified in this study.
The power spectra of the annual and seasonal precipitationare shown in Fig. 6. The theoretical curve (null continuum)along with its associated 95 % confidence level is also repre-sented in Fig. 6. In all cases, the null continuum is “whitenoise”, since the lag-one autocorrelation coefficients do notdiffer significantly from zero (WMO 1966). Significant oscil-lations of 3.3 years, and about 8.6 and 15 years of PC1 duringthe spring and winter are observed, respectively.
The presence of the 8-year peaks in PC1 confirm theimportance of considering the NAO index with the oscilla-tions of about 6–10 (Hurrell and van Loon 1995) in explainingprecipitation variability over Vojvodina during the winter.These facts are in agreement with those derived by Tošićand Unkašević (2005), who found significant peak of 8 yearswhen analyzing precipitation in Belgrade (Serbia) during theperiod 1889–2000. The periodicity of 3.3 years in springprecipitation is coincident with periodicities of 3–4 years inthe spring rainfall for Barcelona obtained by Lana andBurgueño (2000). Gajić-Čapka (1994) analyzing annual pre-cipitation found the periods of 3.6 and 3.7 years for threedifferent climate regions of Croatia.
The presence of the Quasi-biennial oscillation confirmed inspectral analysis for some regions in Europe (e.g., MaherasandVafiadis 1991; Gajić-Čapka 1994; Rodriguez-Puebla et al.1998; Lana and Burgueño 2000; Garcia et al. 2002; Tošić andUnkašević 2005), have not been found for PC1. Longeroscillations of about 15 years in winter PC1 are expectedaccording to previous results obtained for Belgrade by Tošić
and Unkašević (2005). Lana and Burgueño (2000) detectedperiodicities of 16 years in the winter series for Barcelona.
5 Conclusions
An analysis of the annual and seasonal precipitation variabilityover Vojvodina (Serbia) was carried out using the EOF analysis,trend, and the spectral analysis. For this purpose, monthlyprecipitation amounts from 92 stations in Vojvodina duringthe period 1946–2006 were analyzed. The first EOF patternfor the annual and seasonal precipitation is characterized bya homogeneous positive value over the whole region withhigher values over the mountains. The first set of EOFsexplains from 68.8 % (in summer) to 85.4 % (in winter) ofthe total variance. The similarity of EOF1 with the mean fieldis confirmed.
The time series associated with the first EOF pattern (PC1)reveals decreasing trend in the winter precipitation amounts.All of the analyses conducted were coherent in demonstratingthat winter precipitation in Vojvodina is influenced by theNAO. An intensification of the positive phase of the NAOcould be one of the causes of the observed decrease in winterprecipitation in Vojvodina. We did not find significant corre-lations between this mode and known teleconnection patternsduring the summer.
The power spectra of the precipitation PC1 show statisti-cally significant oscillations of 3.3 years during the spring,and about 8.6 and 15 years during the winter. Our findings areconsistent with the quasiperiodic oscillations reported in otherstudies on fluctuations of European precipitation.
It is expected that the decrease of the precipitation duringthe winter and spring in Vojvodina will contribute to theslightly reduction of the annual precipitation.We consider thatthe results of this regional study could contribute to a betterunderstanding of the spatial and temporal variability in south-eastern Europe, a region not always covered in Europeanstudies.
Acknowledgments This study was supported by the Serbian Ministryof Science, Education and Technological Development, under grants no.176013 and 176020.
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Annual and seasonal variability of precipitation in Vojvodina, Serbia
