Acta geographica Slovenica, 58-1, 2018, 7–25
ASSESSING AVERAGE ANNUAL AIR
TEMPERATURE TRENDS USING THE
MANN–KENDALL TEST IN KOSOVO
Milivoj B. Gavrilov, Slobodan B. Marković, Natalija Janc, Milena Nikolić,
Aleksandar Valjarević, Blaž Komac, Matija Zorn, Milan Punišić†, Nikola Bačević
Temperatures were confirmed to rise in Kosovo in the last decades.
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Assessing average annual air temperature trends using the Mann–Kendall test in Kosovo
DOI: https://doi.org/10.3986/AGS.1309
UDC: 911.2:551.524(497.115)
COBISS: 1.01
Assessing average annual air temperature trends using the Mann–Kendall test
in Kosovo
ABSTRACT: The annual trends of surface mean monthly air temperature and monthly extreme temper-
atures were analyzed from ten meteorological stations in Kosovo. The data refer to observation periods
between 1949 and 1999 for four stations, and observation periods between 1965 and 1999 for the remain-
ing six stations. Trends were analyzed for nine time series. Positive trends were found in six series, and
negative trends were found in three series. After an assessment of these trends using the Mann–Kendall
test, positive trends were confirmed in four series, a negative trend was confirmed in one series, and in
one series there was no trend, whereas trends were characterized as slightly positive in two time series and
slightly negative in one series.
Key wORDS: air temperature trends, climate change, Mann–Kendall test, Kosovo
Oce na tren dov pov preč nih let nih tem pe ra tur zra ka na Koso vu z upo ra bo
Mann-Ken dal lo ve ga testa
POVZeTeK: V ra zi ska vi so bili ana li zi ra ni let ni tren di pov preč nih in ekstrem nih meseč nih tem pe ra tur
zraka, izmer je nih na dese tih meteo ro loš kih posta jah na Koso vu. Podat ki se pri šti rih posta jah nana ša jo
na opazo val no obdob je 1949–1999, pri preo sta lih šestih posta jah pa na opa zo val no obdob je 1965–1999.
Tren di so bili ana li zi ra ni za devet časov nih nizov. Pozi tiv ni tren di so bili ugo tov lje ni v še stih nizih, nega -
tiv ni pa v treh. Po oce ni teh tren dov z upo ra bo Mann-Ken dal lo ve ga testa so bili pozi tiv ni tren di potr je ni
v šti rih nizih, nega tiv ni trend je bil potr jen v enem nizu, v enem nizu tren da ni bilo, rah lo pozi tiv ni tren -
di so bili potrjeni v dveh časov nih nizih in rah lo nega tiv ni v enem nizu.
KLJUČNe BeSeDe: tren di tem pe ra tur zra ka, pod neb ne spre mem be, Mann-Ken dal lov test, Koso vo
Milivoj B. Gavrilov, Slobodan B. Marković, Nikola Bačević
Department of Geography, Tourism and Hotel Management,
Faculty of Sciences, University of Novi Sad
gavrilov.milivoj@gmail.com, slobodan.markovic@dgt.uns.ac.rs,
nikolabacevic@yahoo.com
Natalija Janc
natalijanc@earthlink.net
Milena Nikolić
Belgrade Business School, Higher education Institution for Applied Studies
milenan80@yahoo.com
Aleksandar Valjarević
Mathematical Institute of the Serbian Academy of Sciences and Arts
valjarkosmos@yahoo.com
Blaž Komac, Matija Zorn
Anton Melik Geographical Institute, Research Centre of the Slovenian
Academy of Sciences and Arts
blaz@zrc-sazu.si, matija.zorn@zrc-sazu.si
8
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Milan Punišić
Ministry of Natural Resources, Mining and Spatial Planning
The paper was submitted for publication on November 11th, 2014.
Ured niš tvo je pris pe vek pre je lo 11. no vem bra 2014.
Acta geographica Slovenica, 58-1, 2018
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Assessing average annual air temperature trends using the Mann–Kendall test in Kosovo
10
1 Introduction
According to the Intergovernmental Panel on Climate Change (IPCC 2007) report, the average global sur-
face air temperature of the world has increased by 0.7 °C in the last hundred years. Klein Tank et al. (2002)
showed that trends in average temperature increased in the period between 1946 and 1999 in europe. This
increase in global and regional temperature varies seasonally and regionally. In europe the trends are high-
er in central and north-eastern areas and in mountainous regions, whereas lower trends are found in the
Mediterranean region and temperatures are increasing higher in winter than summer (all during the peri-
od from 1977 to 2000; Alcamo et al. 2007).
Historically, the climate of Kosovo has generally been analyzed as part of the climate of Serbia and
yugoslavia. Using extreme temperatures at fifteen meteorological stations in Serbia, Unkašević and Tošić (2013)
suggested that the climate in the region warmed up between 1949 and 2009. Analyzing data between 1949
and 2007, Unkašević and Tošić (2009a) found that a slow decrease in summer temperatures until 1975 was
followed by a temperature increase lasting until 2007. In addition to these papers, other recent works address-
ing the climate in Serbia with and without Kosovo have been published (Jovanović etal. 2002; Gburčik etal. 2006;
Đorđević 2008; Unkašević and Tošić 2009b; Gavrilov etal. 2010; 2013; Pavlović Berdon 2012; Hrnjak etal. 2014;
Tošić et al. 2014; Gavrilov et al. 2015; 2016). In addition, the weather and climate of Kosovo were investi-
gated in the work of Sokolović et al. (1984).
This study focuses on average annual air temperature trends in Kosovo from 1949 to 1999 and from 1965
to 1999. The first period contains nearly two thirty-year-climate cycles, and the second contains more than
one thirty-year-climate cycle. Therefore the results are proper indicators for recent climate change.
2 Area and data
2.1 Study area
Kosovo is located in the southwestern part of the Balkan Peninsula and covers an area of 10,887km2 (Figure 1).
Its geomorphological characteristics and geographical location divide it into two regions; Kosovo proper in
the east is a plateau with a relatively consistent elevation, and Metohija in the west is a hilly area bordered by
high mountains. The climate of Kosovo is moderate continental with cold winters and warm summers, with
a great range of extreme temperatures and a non-uniform distribution of rainfall. The average annual air tem-
perature is 10.8 °C, and the annual amount of precipitation between 1949 and 1999 was 669 mm (Internet 1).
2.2 Data
This work contains an analysis of surface air temperature trends obtained from ten meteorological sta-
tions. The locations of the stations are presented in Figure 1, and their main parameters are given in Table 1
Table 1: List of meteorological stations and their geographical coordinates and elevations.
Number Meteorological station Elevation (m) Latitude (°N) Longitude (°E)
Stations operated from 1949 to 1999
1 Kosovska Mitrovica 510 42° 53' 20° 52'
2 Peć 498 42° 40' 20° 18'
3 Prizren 402 42° 13' 20° 44'
4 Priština 573 42° 39' 21° 09'
Stations operated from 1965 to 1999
5 Istok 465 42° 47' 20° 30'
6 Skivijane 415 42° 28' 20° 21'
7 Suva Reka 420 42° 21' 20° 49'
8 Gnjilane 520 42° 28' 21° 29'
9 Uroševac 580 42° 23' 21° 10'
10 Dragaš 1060 42° 04' 20° 39'
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in accordance with the Republic Hydrometeorological Service of Serbia. Meteorological stations were divid-
ed into two groups, depending on the periods in which they were first established and operational. The
first group consists of four stations that operated from 1949 to 1999, and the second group consists of the
remaining six stations, which operated from 1965 to 1999. Nine of the stations have a relatively uniform
elevation, varying between 402 m and 580 m, whereas the Dragaš station has an elevation of 1,060 m (in
this paper it is referred to as a mountain station).
In order to obtain trends, we used three data sets: monthly mean temperatures, monthly maximum
temperatures, and monthly minimum temperatures for all stations. From the monthly temperatures, the
average annual mean temperatures, average annual maximum temperatures, and average annual minimum
temperatures were calculated. Finally, from these three types of average annual temperatures, new data
sets were derived, marked as: T, Tx, and Tn, respectively, for trend calculations for Kosovo (K) over two peri-
ods: 1949–1999 (P1) from four stations (Kosovska Mitrovica, Peć, Prizren, and Priština) and 1965–1999 (P2)
Acta geographica Slovenica, 58-1, 2018
11
Figure 1: Kosovo.
43° 15'
20° 00'
43° 15'
21° 45'
42° 00'
21° 45'
42° 00'
20° 00'
Projection UTM FUSe 34
Meteorological station
Border line
Rivers
Contour line
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Assessing average annual air temperature trends using the Mann–Kendall test in Kosovo
from five stations (Istok, Skivijane, Suva Reka, Gnjilane, and Uroševac); whereas Dragaš (D) was treated
as a special data set because it is a mountain station, with data available for the period from 1965 to 1999 (P2).
each of these data sets is marked with an acronym consisting of the abbreviation for the territory/station,
period, and type of temperature. In total, all nine data sets (time series) were used for trend calculation (Table 2).
Table 2: List of nine time series to calculate air temperatures trends.
Territory/station 1949–1999 (P1) 1965–1999 (P2)
K-P1-T K-P2-T
Kosovo (K) K-P1-Tx K-P2-Tx
K-P1-Tn K-P2-Tn
– D-P2-T
Dragaš (D) – D-P2-Tx
– D-P2-Tn
Before the previous calculation, the homogeneity of the temperature data was examined according to
the Alexandersson (1986) test. The test showed that the time series are not non-homogeneous for a signif-
icance level of 5%.
3 Methods
Temperature trends were analyzed for nine time series using two statistical approaches: calculation of the
linear temperature trend equation and application of the Mann–Kendall test.
The first approach was to calculate the tendency (trend) equation of temperature using linear inter-
polation of the average annual temperatures (wibig and Glowicki 2002). This method was used to determine
the sign of the temperature trends and the trend magnitude (Gavrilov et al. 2015; 2016) as the difference
in temperatures between the beginning and end of both periods P1 and P2.
The second statistical approach used the Mann–Kendall test (Kendall 1975; Gilbert 1987) to indicate
statistically significant trends. The Mann–Kendall test is widely used in analysis of climatologic time series;
for example, temperature and precipitation (Karmeshu 2012), extreme temperatures (wibig and Glowicki 2002),
hail (e.g., Gavrilov et al. 2010, 2013), aridity (Hrnjak et al. 2014), evapotranspiration (Tabari et al. 2011),
and atmospheric deposition (Drapela and Drapelova 2011), and also in hydrological time series (yue and
wang 2004) and other geophysical time series, such as soil freezing and thawing (Sinha and Cherkauer 2007)
because it is simple and robust, and it can cope with missing values and values below the detection limit.
In using the Mann–Kendall test to define statistically significant trends, two hypotheses were tested:
the null hypothesis, H0, that there is no trend in the time series, and the alternative hypothesis, Ha, that
there is a trend in the time series for a given significance level. Probability p in percent (Karmeshu 2012;
Gavrilov et al. 2016) was calculated to determine the level of confidence in the hypothesis. If the computed
value p is lower than the chosen significance level α (e.g., α = 5 %), the H0 (there is no trend) should be reject-
ed, and the Ha (there is a significant trend) should be accepted; and if p is greater than the significance level
α then the H0 is accepted (or cannot be rejected). For calculating probability p and hypothesis testing, XLSTAT
statistical analysis software was employed (Internet 2).
It is considered that accepting the Ha indicates that a trend is statistically significant. On the other hand,
acceptance of the H0 implies that there is no trend (no change), whereas often in practice the trend equa-
tion indicates the opposite; that is, that there is a trend. Therefore, to reduce the contradictions in analyzing
the temperature trends between two independent statistical approaches – the trend equation and the
Mann–Kendall test – the modified interpretation of the Mann–Kendall test will be offered. Moreover, this
interpretation makes it possible to obtain more diverse results.
It is quite clear that, with decreasing probability p, statistical confidence in the H0 decreases and con-
fidence in the Ha increases, and vice versa. Because probability p takes values between 0% and 100%, for
the purposes of this study a modified interpretation of the Mann–Kendall test was introduced and four
levels of confidence were defined (Gavrilov et al. 2015; 2016). when the computed probability p is: (1) less
or equal to 5%, the trend is significantly positive/negative; (2) greater than 5% and less than or equal to 30%,
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the trend is moderately positive/negative; (3) greater than 30% and less than or equal to 50%, the trend is
slightly positive/negative; and (4) greater than 50%, there is no trend. As can be seen, in cases (1) and (4)
both interpretations of the Mann–Kendall test have the same meaning; namely, that there is a significant
trend and that there is no trend. Differences occur in cases (2) and (3), where the Mann–Kendall test claims
there is no trend, and the modified Mann–Kendall test allows a trend with reduced levels of confidence.
4 Results and discussion
4.1 The values of trends
By applying both statistical approaches to each of the nine time series in Table 2, nine cases are obtained (Table 3).
Table 3: The trend equation y, the trend magnitude Δy, and probability p of the confidences for all time series.
Time series Trend equation Δy (°C) p (%)
K-P1-T y = -0.006 x + 10.97 0.3 25
K-P1-Tx y = 0.013 x + 23.50 –0.7 17
K-P1-Tn y = 0.012 x – 1.40 –0.6 4.5
K-P2-T y = 0.021 x + 10.31 –0.7 1
K-P2-Tx y = 0.024 x + 23.42 –0.8 2
K-P2-Tn y = 0.011 x – 2.17 –0.4 24
D-P2-T y = -0.003 x + 8.31 0.1 89
D-P2-Tx y = 0.070 x + 20.41 –2.5 1
D-P2-Tn y = -0.047 x – 1.76 1.7 1
In Table 3 the first column is the time series; the second column is the linear trend equation, where y is
the average annual value of the temperature in °C and x is the time in years; Δy is the trend magnitude in
°C; and p is the probability in percent, α = 5% is the significance level (it is the same in all cases).
4.2 Evaluation of trends
In strictly formal terms, as evidenced by the trend equations in Table 3, in all cases some trends can be observed.
However, not all trends have the same sign, magnitude, and probability. To obtain the final evaluation of
temperature trends, values from Table 3, Figures 2–4, and the results of hypothesis testing were used.
Figure 2 and the trend equations for the time series K-P1-T, K-P1-Tx, and K-P1-Tn show that the trends
are negative once and positive twice, respectively. Mann–Kendall test will prove whether these statements
are true. Because the probabilities p are greater than the significance level, α = 5%, the H0 cannot be reject-
ed in the first two cases. The risk of rejecting the H0 while it is true are 25% and 17%, respectively. Because
the p in K-P1-Tn is lower than the significance level, the H0 should be rejected and the Ha should be accept-
ed. The statement that there is a trend is correct with a probability greater than 95%. In accordance with
the modified Mann–Kendall test, these three trends are characterized as moderately negative, moderate-
ly positive, and significantly positive, respectively.
Figure 3 and the trend equations for the time series K-P2-T, K-P2-Tx, and K-P2-Tn show that the trends
are positive in all cases. Mann–Kendall test will prove whether these statements are true. Because the prob-
abilities p in K-P2-T and K-P2-Tx are lower than the significance level, α = 5%, the H0 should be rejected
and the Ha should be accepted in both cases. The statement that there are trends is correct with a proba-
bility greater than 98%. Because the p in K-P2-Tn is greater than the significance level, the H0 cannot be
rejected. The risk of rejecting the H0 while it is true is 24%. In accordance with the modified Mann–Kendall
test, these cases are characterized as significantly positive twice and moderately positive once, respectively.
Figure 4 and the trend equations for the time series D-P2-T, D-P2-Tx, and D-P2-Tn show that the trends
are negative, positive, and negative, respectively. Mann–Kendall test will prove whether these statements are
true. Because probability p in D-P2-T is greater than the significance level, α = 5%, the H0 cannot be rejected.
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02468
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Tx(°C)
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–
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Acta geographica Slovenica, 58-1, 2018
The risk of rejecting the H0 while it is true is 89%. Because the probabilities p in D-P2-Tx and D-P2-Tn
are lower than the significance level, the H0 should be rejected and the Ha should be accepted in both cases.
The statement that there are trends is correct with a probability greater than 99%. Now, the trends are char-
acterized as no trend, significantly positive, and significantly negative, respectively. It should be noted that
in the case D-P2-T the Δy is equal to the standard error of the temperature measurement, and so it is also
considered no trend.
5 Conclusions
The main results of the analysis of temperature trends in Kosovo are shown in Table 4.
Table 4: The main results of the analysis of trends.
Time series Trend equation Modified Mann–Kendall test
K-P1-T Negative trend Negative moderate trend
K-P1-Tx Positive trend Positive moderate trend
K-P1-Tn Positive trend Positive significant trend
K-P2-T Positive trend Positive significant trend
K-P2-Tx Positive trend Positive significant trend
K-P2-Tn Positive trend Positive moderate trend
D-P2-T Negative trend No trend
D-P2-Tx Positive trend Positive significant trend
DP-2-Tn Negative trend Negative significant trend
Based on the trend equations, positive trends were found in six and negative trends were found in three
time series. After applying the Mann–Kendall test, significantly positive trends were confirmed in four
time series, a moderately positive trend was found in two time series, and a significantly negative trend, mod-
erately negative trend, and no trend were found in a single case each.
From the results presented above, it is very difficult to derive an overall general rule, but some con-
clusions can be drawn. First, positive temperature trends dominate. All of them could be explained by the
effects of global warming on Kosovo. This impact is most evident in the case of representative time series
K-P2-T, which covers the 1980s and 1990s, when the effect of global warming was first detected in the
region (Gavrilov et al. 2016). On the other hand, the representative case K-P1-T was also influenced by
global warming, but no positive trend was noted. This can be explained by impacts from the 1960s and 1970s,
when there were no signs of global warming (Hardy 2006).
In the case of the Dragaš mountain station, the results were very diverse. There, all three trends were
found: positive, negative, and no trend. This case, as well as a detailed explanation of other cases, requires
additional research.
In spite of the limited meteorological data available, the results presented provide insight into the climate
dynamics of the region.
ACKNOwLeDGeMeNTS: This study was supported by the Serbian Ministry of Science, education and
Technological Development, under grant nos. 176020 and III 44006. The authors are grateful for the sup-
port of Ivana Tošić, Ph.D. The authors sincerely appreciate the efforts of Valentina Janc in improving this
manuscript.
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