ISSN 0378-1305 Rev. Int. Hél. N° 46 (2018) Mohamed Nia.
REVUE INTERNATIONALE D'HÉLIOTECHNIQUE N° 46 (2018) 46-53
http:\\www.comples.org ___________________________________________________________________________________
TREND IN TEMPERATURE AVERAGE AS A PARAMETER TO QUANTIFY IN CLIMATOLOGY
Mohamed NIA
High school, Ibn Chabira, Bousaada, 28200, M'sila, Algeria
Email : [email protected]
Reçu 02-08-2018, Revu 30-09-2018, en ligne 27-10-2018
Résumé Les mesures des variations de la température de l'air nous donnent des indications sur les activités quotidiennes humaines. Cette étude
montre que les températures moyennes sur plusieurs années sont liées aux modifications climatiques ce qui permet d'introduire les tendances
dans les températures moyennes comme paramètre pour les évaluations climatiques. Ce paramètre est d’une grande importance pour la
compréhension des origines des changements climatiques afin de réduire leurs impacts. Ce travail s’est concentré sur la détection des tendances dans les données de température de huit stations en Algérie sur la période 1973-2015 en utilisant le test statistique de Mann-
Kendall appliqué à un niveau de signification de 5% et l’estimateur de Sen pour connaitre la pente d’une éventuelle tendance. Dans la
plupart des huit stations l’étude a mis en évidence une hausse dans la température moyenne que ce soit la température moyenne mensuelle; la
température moyenne saisonnière ou la température moyenne annuelle.
Abstract Measurements of air temperature variations give indications for human daily activities.
This study shows that seasonal and annual temperature averages along many years are related to climatic modifications. It allows to introduce trends in temperature averages as a parameter for climatic evaluations. This parameter is of importance for the understanding in
climatology of origins, prevision, and evolution in order to reduce impact effects.
This work has focused on detecting trends of temperature data from eight stations in Algeria from 1973 to 2015 using statistical tests such as
Mann-Kendall test applied at a level of 5% of significance (for trend) and Sen’s estimator (for slope of trend). In most of the eight stations the study has brought to light an increase in the temperature average whether monthly average, seasonal average or annual average.
Keywords: climate, parameter, statistical data, trend test, Mann-Kendall, Sen’s estimator.
I. INTRODUCTION
Studies of climate variability are of particular interest in scientific research, water resources, for the economy and for the
people themselves.
Most parts of the world has seen a sharp rise in temperatures which we live today its consequences (floods, ice melt, fires,
droughts, desertification etc.). These phenomena have caused massive population displacement, economic disruption, and in
some cases, famine and even loss of life. It is therefore necessary to explain temperature trend and seek subsequently causes to
take precautions to minimize the dangers that can result in order to be in shelter (Anwer., 2015 ; Cécile., 2007-2008 ; Ceppi et
al. 2012 ; Domroes and El-Tantawi., 2005 ; Fan et al. 2011; Fossou et al. 2015; GIEC., 2007; Xu et al. 2005).
In order to reach our goal of this work and quantify the evolution of temperature series data the use of mathematical statistic
was an indispensable tool. Determination of trend in the temperature series is performed in the mean of Mann-Kendall test and
the slope of a possible trend is determined by the Sen’s slope estimator.
II. DATA AND STUDY AREAS
II.1.Area
In Algeria the northern region is characterized by a Mediterranean climate, with hot, dry and mild summers, rainy
winters, with annual rainfall between 400 mm and 1000 mm. Summer and winter average temperatures are 25°C and 11°C
respectively. Annual precipitation in the highlands and the Saharan Atlas do not exceed 200 mm to 400 mm.
The Sahara is a very windy and arid region, where temperature variations are often considerable; these variations can be
explained by the total absence of humidity. Across the Algerian desert the height of the annual rains is less than 130 mm.
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ISSN 0378-1305 Rev. Int. Hél. N° 46 (2018) Mohamed Nia.
II.2. Data
Data used are the averages of monthly, seasonal and annual temperatures; they have summers provided by the website
(http://meteo-climat-bzh.dyndns.org/mete19-1154-1965-2016.php), table 1.
Table 1 : Characteristics of stations
III. METHODS
III.1. Mann-Kendall test
Mann-Kendall test is a non parametric test for trend detection. The null hypothesis of the test is H0 (no trend), against the
alternative hypothesis Ha (presence of trend) (Esterby., 1993; Goula et al. 2012; Jose and Claudia., 2008 ; Longobardi and
Villani., 2010; Mateescu., 2011; Nasri and Modarres., 2009; Qin et al. 2010; Scherrer et al. 2016). Statistic (Z) of the test is
calculated as follows.
𝑆 = 𝑠𝑔𝑛 𝑥𝑗 − 𝑥𝑖 𝑁𝑗=𝑖+1
𝑁−1𝑖=1 (1)
𝑍 =
(𝑆−1)
𝑣𝑎𝑟 (𝑆) 𝑖𝑓 𝑆 > 0
0 𝑖𝑓 𝑆 = 0(𝑆+1)
𝑣𝑎𝑟 (𝑆) 𝑖𝑓 𝑆 < 0
(2)
where
𝑣𝑎𝑟(𝑆) = 𝑁(𝑁 − 1)(2𝑁 + 5)/18 . (3)
For equal values in the series, var(S) was substituted in the above equation by
𝑣𝑎𝑟 𝑆 = 𝑁 𝑁−1 2𝑁+5 − 𝑡𝑝 𝑡𝑝−1 2𝑡𝑝+5
𝑞𝑝=1
18. (4)
where (tp) denotes the number of equality in the series involving (p) values and (q) is the number of equalities groups. The null
hypothesis is rejected at significance level (α) if 𝑍 > Z 1−
α
2 where Z
1−α
2 is 1 −
α
2 quantile of the standard normal
distribution.
III.2. Sen estimator of the slope
If a linear trend is present in the time series its slope (a) (change per unit time) can be estimated using an non parametric
procedure developed by Sen (1968) (Drápela., Drápelová., 2011; Fossou et al., 2014 ; Gajbhiye et al., 2015; Ghasemi., 2015;
Miro et al., 2006; Partal and Kahya., 2006); this means that the trend may be expressed by a function f(t) such as
𝑓 𝑡 = 𝑎𝑡 + 𝑏 . (5)
In order to obtain the slope (a), the slopes of all data pairs are calculated ; If there are (N) values (xj) in serie we get n = N(N-
1)/2 slope estimates (ai). Sen estimator of the slope is the median of these values (ai). The (n) values (ai) are ranked from
smallest to largest and Sen estimator of the slope is.
𝑎 =
1
2𝑎𝑛+1 𝐼𝑓 𝑛 𝑖𝑠 𝑜𝑑𝑑
1
2 𝑎𝑛
2+
𝑎𝑛+2
2 𝑖𝑓 𝑛 𝑖𝑠 𝑒𝑣𝑒𝑛 .
(6)
IV. RESULT AND DISCUSSION
Statistical values of the Mann-Kendall test applied at 95% significance level for the eight stations are given in table 2; It
showed that an upward trends have existed since 1973 in the monthly average temperatures for all stations except in
December and February.
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Station Biskra Annaba Alger Ghardaïa El Goléa Tamanrasset In-Amenas In-Salah
Longitude 05°43'12"E 07°48'36"E 03°15'E 03°47'24"E 02°52'E 05°26'E 09°38'E 02°27'36"E
Latitude 34°51'N 36°49'12"N 36°43'N 32°22'48"N 30°34'N 22°48'N 28°03'N 27°13'48"N
Elevation 125m 5m 24m 461m 397m 1362m 561m 269m
ISSN 0378-1305 Rev. Int. Hél. N° 46 (2018) Mohamed Nia.
For El-Goléa, Tamanrasset and In-Amenas the upward trend was for 75% of months and the magnitudes of the increase
trend varies from 0.02°C/year to 0.09°C/year and the largest slopes are for El-Goléa and In-Amenas ; for Biskra, Ghardaïa
and In-Salah the increase trend was for 67% of months where the slopes of the upward trends were from
0.04°C/year to 0.09°C/year and the largest slopes are for Ghardaïa and In-Salah; the upward trend detected in
monthly average temperatures for the two coastals stations of Annaba and Algiers was in 58% of months and the
magnitudes of trend where from 0.03°C/year to 0.07°C/year and the highest are for Algiers.
In seasonal average temperatures it was found that El-Goléa, Tamanrasset and In-Amenas were touched by an
increase trend in all seasons with slopes that varied from 0.02°C/year to 0.07°C/year; for the rest of stations the
trend was in 75% of seasons and slopes were from 0.03°C/year to 0.06°C/year ; the largest slopes were for El-
Goléa and Ghardaïa. whereas for average annual temperatures all stations were affected by an upward trends
whose slopes were 0.05°C/year for El-Goléa, Ghardaïa, and In-Amenas; 0.04°C/year for Algiers and 0.03°C/year
for the rest of stations; generally the upward trends are in almost of 1°C/year to 4°C/year on the study period that
spans 43 years. This remarkable temperature increase is related to greenhouse gases; these anthropogenic emissions
are mainly due to carbon dioxide (CO₂) coming in first from the consumption of fossil fuels; the biggest of the gas
emission sources are traffic ( affects most large cities like Algiers, Annaba, Biskra and Guardaia), households,
industry (the steel complex of El Hadjar and asmidal factory that manufactures phosphate and nitrogen fertilizers,
oil and natural gas fields in southern Algeria and the in Algerian-Libyan border), services, agriculture, forestry and
cattle breeding are an important source of methane production, deforestation caused by land use, energy
transformation (Refinery crude, power plants) ( Ministère de l’Aménagement du Territoire et de l’Environnement.,
2001; Ministère de l’Energie et des Mines.,2007).
For January it’s only in 25% of stations where a trend were obseved with 0.04°C/year in El-Goléa and In-Amenas.
Regarding seasonal average temperatures upward trends were manifested in 100% of stations for Summer and
Autumn, in 87.5% of stations for Spring and in 37.5% of stations for winter. The largest slopes were
0.06°C/year in Summer for Ghardaïa and El-Goléa, 0.07°C/year in Autumn for El-Goléa and In-Amenas and
0.06°C/year in Spring for Ghardaïa and El-Goléa.
For annual average temperature all stations studied were affected with an upward trends. Slopes for these
stations were 0.05°C/year in Ghardaïa , El-Goléa and In-Amenas , 0.04°C/year in Algiers and 0.03°C/year in
Biskra, Annaba, Tamanrasset and In-Salah.
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ISSN 0378-1305 Rev. Int. Hél. N° 46 (2018) Mohamed Nia.
49
Figure 1: Largest slopes in the average temperature of March and April
Figure 1 : Trends in the average temperature of March in El-Goléa,
In-Amenas
1970 1975 1980 1985 1990 1995 2000 2005 2010 201517
18
19
20
21
22
23
24
25El-Goléa
Year
Ave
rag
e te
mp
era
ture
in
Ap
ril (°
C)
1970 1975 1980 1985 1990 1995 2000 2005 2010 201514
15
16
17
18
19
20
21
22In-Amenas
Year
Ave
rag
e te
mp
era
ture
in
Ma
rch
(°C
)
1970 1975 1980 1985 1990 1995 2000 2005 2010 201517
18
19
20
21
22
23
24
25
26
27Biskra
Year
Ave
rag
e te
mp
era
ture
in
Ap
ril (°
C)
1970 1975 1980 1985 1990 1995 2000 2005 2010 201517
18
19
20
21
22
23
24
25
26Guardaia
Year
Ave
rag
e te
mp
era
ture
in
Ap
ril (°
C)
ISSN 0378-1305 Rev. Int. Hél. N° 46 (2018) Mohamed Nia.
50
Figure 2: Largest slopes in the average temperature
of May, July and August
1970 1975 1980 1985 1990 1995 2000 2005 2010 201522
23
24
25
26
27
28
29
30
31Biskra
Year
Ave
rag
e te
mp
era
ture
in
Ma
y (
°C
)
1970 1975 1980 1985 1990 1995 2000 2005 2010 201515
16
17
18
19
20
21
22Algiers
Year
Ave
rag
e te
mp
era
ture
in
Ma
y (
°C
)
1970 1975 1980 1985 1990 1995 2000 2005 2010 201530
31
32
33
34
35
36
37Guardaia
Year
Ave
rag
e te
mp
era
ture
in
Ju
ly (
°C
)
1970 1975 1980 1985 1990 1995 2000 2005 2010 201529
30
31
32
33
34
35
36Guardaia
Year
Ave
rag
e te
mp
era
ture
in
Au
gu
st(
°C
)
ISSN 0378-1305 Rev. Int. Hél. N° 46 (2018) Mohamed Nia.
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Figure 3: Largest slopes in the average temperature of September, October and November
1970 1975 1980 1985 1990 1995 2000 2005 2010 201526
27
28
29
30
31
32
33
34In-Amenas
Year
Ave
rag
e te
mp
era
ture
in
Se
pte
mb
er
(°C
)
1970 1975 1980 1985 1990 1995 2000 2005 2010 201531
32
33
34
35
36
37In-Salah
Year
Ave
rag
e te
mp
era
ture
in
Se
pte
mb
er
(°C
)
1970 1975 1980 1985 1990 1995 2000 2005 2010 201518
19
20
21
22
23
24
25
26
27El-Goléa
Year
Ave
rag
e te
mp
era
ture
in
Octo
be
r (°
C)
1970 1975 1980 1985 1990 1995 2000 2005 2010 201513
14
15
16
17
18
19
20In-Amenas
Year
Ave
rag
e te
mp
era
ture
in
No
ve
mb
er
(°C
)
ISSN 0378-1305 Rev. Int. Hél. N° 46 (2018) Mohamed Nia.
Table 2: Trends in average temperature with the values of Mann-Kandall test and Sen’s slope (°C/year).
Figure 1, Figure 2 and Figure 3 illustrate the largest slopes highlighted for the average monthly temperatures and table 2
summarizes the results of the application of statistical tests.
V. CONCLUSION
Measurements of the mean values of air temperatures, whether monthly, seasonal or annual for eight stations in Algeria have
shown upward trends in the period 1973-2015.
This phenomenon could be a result of human activities which are related to industry and agriculture developments.
A temperature average is introduced as a parameter for quantifying climatic evaluations.
This parameter is of importance for the understanding in climatology of origins, prevision, and evolution in order to reduce
impact effects.
Remerciement
Le professeur Pierre MIALHE a bien voulu relire ce travail: MERCI.
_____________________________________________________________________________________________________
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Month Biskra Annaba Alger Ghardaïa El-Goléa Tamanrasset In-Amenas In-Salah
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8 3.44 ; 0.05 2.73 ; 0.04 3.27 ; 0.05 4.56 ; 0.08 4.83 ; 0.07 4.17 ; 0.04 4.34 ; 0.06 3.73 ; 0.04
9 2.02 ; 0.04 3.65 ; 0.07 5.05 ; 0.05 4.25 ; 0.07 3.92 ; 0.07
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Winter 2.18 ; 0.03 1.99 ; 0.02 2.62 ; 0.03
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