Theor Appl Climatol (2010) 101:397–409
DOI 10.1007/s00704-009-0225-7
ORIGINAL PAPER
Statistical properties of the temperature, relative humidity,
and net solar radiation in the Blue Nile-eastern Sudan region
Chong-Yu Xu & Qiang Zhang & M. El Hag El Tahir &
Zengxin Zhang
Received: 11 May 2009 / Accepted: 1 October 2009 / Published online: 25 October 2009
# Springer-Verlag 2009
Abstract This paper presents the results of the first stage
of an ongoing project of evaluating the spatial and
temporal variability of soil water as fundamental factors
for vegetation regeneration in the arid ecosystems in the
Blue Nile-eastern Sudan. The specific aim of the present
study is to understand the temporal and spatial variations
of the major climate variables in the region and discuss
its relevance to regional climate variability and changes.
In this case, we systematically analyze the major climate
variables (maximum and minimum air temperature,
relative humidity, and net solar radiation). To evaluate
the different characteristics of the climate variables,
Mann–Kendall method, two-phase regression scheme,
and wavelet transform technique are used; each method
has its own strength and weakness, and the results of the
three methods complement each other. The results show
that the annual and seasonal maximum temperatures are
increasing significantly. The annual minimum temperaC.-Y. Xu (*) : M. El Hag El Tahir
Department of Geosciences, University of Oslo,
P.O. Box 1047, Blindern,
0316 Oslo, Norway
e-mail: chongyu.xu@geo.uio.no
Q. Zhang
Department of Water Resources and Environment,
Sun Yat-sen University,
Guangzhou 510275, China
C.-Y. Xu
Department of Earth Sciences, Uppsala University,
75236 Uppsala, Sweden
Z. Zhang
Jiangsu Key Laboratory of Forestry Ecological Engineering,
Nanjing Forestry University,
Nanjing 210037, China
ture and minimum temperature in dry seasons are
decreasing. The minimum temperature in rainy season
is increasing with a smaller rate as compared with the
increase of maximum temperature in the season. The
difference between maximum and minimum temperature
is increasing in all the seasons. Net solar radiation in the
region shows a significant increasing trend in all seasons,
which corresponds well with the changes of maximum
temperature. Besides, significant decreasing trends can be
identified for relative humidity in all the seasons.
1 Introduction
Sudan is characterized by tropical climate. Within the
Sudan territory, the climate shifts from arid in the north to
tropical wet and dry in the far southwest. Generally, the
humidity conditions are controlled by two air flows: dry
northeasterly winds from the Arabian Peninsula and moist
southwesterly winds from the Congo River basin. The dry
northeasterly winds predominate in Sudan from January to
March, when there is practically no rainfall across the entire
country except some regions in the northwestern Sudan.
From early April, the moist southwesterly winds prevail in
Sudan, bringing rains and thunderstorms, and in August,
the southwesterly flows extend to the northern limits
around Abu Hamad (http://countrystudies.us/sudan/33.
htm). Delayed arrival of the southwesterly flow and
associated rainfall often inflict great loss of human lives
and economy and causes disastrous results.
Sudan is drained mainly by the Nile River and its two
main tributaries, i.e., the Blue Nile and the White Nile
(Fig. 1). The Nile River is the longest river in the world,
flowing for 6,737 km from its farthest headwaters in central
Africa to the Mediterranean and being the lifeline for
398
C.-Y. Xu et al.
Fig. 1 Map of Sudan and the
study region
Sudan. The Blue Nile flows out of the Ethiopian highlands
to meet the White Nile at Khartoum. In the south of
Khartoum, the British built the Jabal al Auliya Dam in 1937
to store the water of the White Nile with the aim to alleviate
the negative effects of slackening flow from the Blue Nile
in the fall. Actually, much water from the reservoir is used
for irrigation or lost by evaporation. Therefore, although the
drainage area is large, evaporation takes most of the water
from the rivers in this region and thus, the discharge of the
Bahr al Ghazal into the White Nile is small (http://www.
mongabay.com/reference/country_studies/sudan/all.html).
Sudan is suffering from rainfall deficit and water
shortage. The currently well-evidenced global warming is
expected to alter the hydrological cycle, and previous
studies tend to provide more observed evidences for this
viewpoint (e.g., Beniston and Stephenson 2004; Brutsaert
2006; Zhang et al. 2008a). Therefore, exploring the
changing characteristics of extreme temperature, relative
humidity, and net solar radiation of the region is a
prerequisite for a good assessment of the impacts of
climatic changes on regional ecological environment and
agricultural development. Actually, there are a lot of reports
concerning extreme climatic events and hydrological
responses to climate changes and so on (e.g., Zhang et al.
2009). Zhang et al. (2008b) indicated that the warming
processes in the Yellow River basin in China are characterized by a significant increase of extreme low temperature. The extreme high temperature has no significant
change trend. Xu et al. (2006) observed a significant
decreasing trend in both the reference evapotranspiration
and the pan evaporation and attributed this decreasing trend
to a significant decrease in net solar radiation and to a less
extent, to a significant decrease in wind speed over the
Yangtze River basin. Manton et al. (2001) found significant
increases in hot days and warm nights and decreases in cool
days and cold nights since 1961 across Southern Asia and the
South Pacific region. As for climate changes in Sudan, little
work has been done as compared to the rich studies carried out
elsewhere in the world. Elagib and Mansell (2000) analyzed
mean temperature changes during 1941–1996. However,
study of changes of temperature extremes such as maximum
and minimum temperature could be more helpful for better
understanding of the regional responses of Sudan to global
warming. Besides, some scientific problems are still kept
unanswered such as: What are the changing properties of the
major climate variables in eastern Sudan as revealed from the
historical records? What could be the implications of the
changing properties of climate variables for evaporation
changes and regional water resource management? The
answers of these scientific questions will be of great
importance for better understanding of the implications of
land-use change on soil degradation in the region.
As the first stage of an ongoing project of evaluating the
spatial and temporal variability of soil water as fundamental
factors for vegetation regeneration in the arid ecosystems in
the Blue Nile-Eastern Sudan, the objectives of this study
are: (1) to understand the trends of climate variables such as
temperature, relative humidity, and net solar radiation in the
region; (2) to explore abrupt behaviors and periodicity
properties of the regional climate variables; and (3) to
discuss the differences of climate changes of eastern Sudan
with other places of the world.
Statistical properties of the temperature, relative humidity, and net solar radiation in the Blue Nile-eastern Sudan region
399
2 Study area and data
The study area lies between latitudes 10° to 16°N and
longitudes 30° to 35°E (Fig. 2). The area is in the belt of
regular oscillation of the intertropical convergence zone
with a tropical continental climate. Ninety percent of the
annual rainfall is collected during the rainy season (April–
October). The annual rainfall has also large interannual
variability as well as spatial variability. It ranges between
75 mm in the north and above 600 mm in the south (Elhag
2006). The lowest daily mean temperature is 13°C and is
measured in December. The highest mean daily temperature
is 43.8°C and is measured in May. The region is
characterized by low relative humidity especially in winter,
reaching its minimum in March and its maximum in
August, varying between 16% and 77% (Elhag 2006).
The open nature of the area and free movement of the air
accelerates evaporation, whether from the surface or
subsoil. The land use types include agriculture, forests,
and range areas. It exhibits high land cover variability. The
area is bounded by Sennar in the north and Ad’ Damzzeen
in the south and traversed by the Blue Nile.
The data from ten stations in the region (Table 1, Fig. 2)
are extracted from the dataset produced by the National
Climatic Data Center in Asheville, NC. The data are
available via: http://www.cdc.noaa.gov/data/gridded/data.
ncep.reanalysis.surface.html and http://www.cdc.noaa.gov/
data/gridded/data.ncep.reanalysis.surfaceflux.html. The data used in this study are daily maximum and minimum
temperature, relative humidity, and net solar radiation
(difference between downward solar radiation flux and
upward solar radiation flux) covering January 1, 1948 to
December 31, 2006. The downloaded data were checked
for two kinds of potential errors, i.e., outliers and
consistency. The outliers (unusual values might be caused
by misplacement of decimal point, etc.) are checked by
using some threshold values. In this study, outliers were
defined as all those values outside the mean±3 standard
deviation (x 3s). If such a value exists, a close exam on
Table 1 Information of the meteorological stations used in the
study
WMO World Meteorological
Organization, m a.s.l meters
above sea level
Station
WMO code
KHARTOUM
EDUEIM
WAD MEDANI
GEDAREF
SENNAR
ELOBEID
ABUNAAMA
RENK
RASHAD
DAMAZINE
62721
62750
62751
62752
62762
62771
62795
62801
62803
62805
Fig. 2 Study region and the location of the meteorological stations
used in this study
the value is needed by comparing with other stations for the
same day. Stations having sequences of several years of low
values or high values might be caused by change of
instrument and/or change of measurement place, etc. In this
study, double mass plots of one station data against data at
nearby stations were constructed and used to check the
homogeneity and consistency for all the stations one by
one. In the above checks, no remarkable errors were found.
3 Methodology
The methods used in the study include the Mann–Kendall,
wavelet transform, and the two-phase regression scheme.
Each method has its own strength and weakness; the results
of the three methods complement each other as will be
shown in the results section.
The Mann–Kendall trend test (MK; Mann 1945; Kendall
1975) is used to analyze the trends of the climate data. In
Latitude ºN
Longitude ºE
15.60
14.00
14.40
14.03
13.55
13.17
12.73
11.75
11.87
11.78
32.55
32.33
33.48
35.40
33.62
30.23
34.13
32.78
31.05
34.38
Abbreviation
kha
dum
wdm
gdf
snr
obd
abu
rnk
rsh
dzm
Elevation (m a.s.l)
380
380
405
600
420
570
445
380
885
470
400
C.-Y. Xu et al.
this study, the influence of serial correlation in the time
series on the results of MK test has been eliminated by
prewhitening (e.g., Yue et al. 2002; Yue and Wang 2002).
“Prewhitening” is one of the methods used to prevent false
indication of trend, where autocorrelation is removed from
the data by assuming a certain correlation model, usually a
Markovian one (e.g., Von Storch 1995). The 95% confidence interval was used as a threshold to classify the
significance of positive and negative MK trends.
The continuous wavelet transform technique (Farge
1992; Torrence and Compo 1998; Grinsted et al. 2004), as
a tool for analyzing localized variations of power within a
time series, is applied in the current study. More recently,
this method has been applied in studying annual maximum
streamflow series of the Yangtze River basin by the authors
of the present paper (Zhang et al. 2007). The concept and
procedure of the wavelet method were thoroughly
explained and discussed by Torrence and Compo (1998),
and the wavelet software can be found at http://paos.
colorado.edu/research/wavelets/.
Besides, we also use the simple two-phase regression
scheme (Solow 1987; Easterling and Peterson 1995; Vincent
1998; Lund and Reeves 2002) to explore the abrupt changes
and the trend in the subseries. The model is formulated as:
m1 þ a 1 t1 þ "t
Xt ¼
ð1Þ
m2 þ a 2 t2 þ "t
where t1 =[j-n, j-1], t2 =[j, j+n-1], and n may be n=2, 3,...,
<N/2, or may be selected at suitable intervals. The j=n+1,
n+2,..., N–n+1 is the reference time point, and N is the
length of the time series.
The least squares estimates of the trend parameters in
Eq. 1 are:
j1
P
b1 ¼
a
ðt t 1 Þ Xt X 1
t¼jn
j1
P
and
ðt t 1 Þ2
t¼jn
jþn1
P
b2 ¼
a
t¼j
ðt t 2 Þ X t X 2
jþn1
P
ð2Þ
ðt t 2 Þ2
t¼j
In Eq. 2, X 1 and X 2 are the average series values before and
after time j, respectively. t 1 and t 2 are the average time
observations before and after time j, respectively. Least
squares estimates of the location parameters μ1 and μ2 in
Eq. 1 are:
The denominators in Eq. 2 can be explicitly evaluated
as:
ð3Þ
b1 t 1 and m
b2 t 2
b1 ¼ X 1 a
b2 ¼ X 2 a
m
j1
X
ðt t 1 Þ2 ¼
ðj 1Þjðj 2Þ
and
12
ðt t 2 Þ2 ¼
ðn j þ 1Þðn j þ 2Þðn jÞ
12
t¼jn
jþn1
X
t¼j
ð4Þ
Under the null hypothesis of no change points, the
regression parameters during the two phases must equal,
b1 -b
b1 -b
i.e., α1 =α2 and μ1 =μ2. If so, m
m2 and a
a2 should be
close to zero for each subsample divided by j.
Rescaling this to a regression F statistic merely states
that (Lund and Reeves 2002)
Fc ¼
ðSSERed SSEFull Þðn 4Þ
2SSEFull
ð5Þ
In Eq. 5, SSEFull is the “full model” sum of squared errors
computed from
SSEFull ¼
j1
X
b 1 t Þ2 þ
b1 a
ðXt m
t¼jn
jþn1
X
b 2 t Þ2
b2 a
ðXt m
t¼j
ð6Þ
SSERed is the “reduced model” sum of squared errors,
which was formulated as
SSERed ¼
jþn1
X
bRed t Þ2
bRed a
ðXt m
ð7Þ
t¼jn
bRed are estimated under the constraints
bRed and a
where m
bRed and m1 ¼ m2 ¼ m
bRed (Lund and Reeves
a1 ¼ a 2 ¼ a
2002). If a change point is present at time j-1, Fc should be
statistically larger when compared to the threshold value by
F test. The effective degree of freedom after the correction
of dependence and in a normalized distribution for the time
series (Storch and Zwiers 1999; Jiang et al. 2007) can be
estimated by
2n
EffD ¼
INT 1 þ 2
INTP
ðn=2Þ
t¼1
!
ð8Þ
rX ðt Þrt ðt Þ
where INT denotes the integer part of the number. After the
effective degree of freedom is known, the threshold value
(Fth) can be obtained via the F test table (Lund and Reeves
2002). If Fc >Fth, then we can say that the change point is
statistically significant. This method is used to detect
significant change points and linear trends between the
change points in the time series.
Statistical properties of the temperature, relative humidity, and net solar radiation in the Blue Nile-eastern Sudan region
Maximum temperature (oC)
45
401
Minimum temperature (oC)
28
40
Temperature (oC)
Temperature (oC)
26
35
30
24
22
20
18
16
14
12
25
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Time (months)
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Time (months)
Difference between
max. and min. temperature
25
20
15
10
5
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Time (months)
Fig. 3 Long-term monthly mean maximum and minimum temperature and the difference between monthly mean maximum and minimum
temperature at the Khartoum station, Sudan. “+” denotes outlier
4 Results
The study region is dominated by the northeast trade winds
between October and May, which causes the prevailing
aridity. Generally, three seasons can be distinguished: (1)
the cool and dry winter from December to February; (2) the
warm and dry period from March to June; and (3) the warm
and rainy period from July to November. Therefore, we will
anatomize the changing properties of climate variables in
these three seasons.
Table 2 Mann–Kendall trends of temperature variables of the meteorological stations of Sudan
Stations
KHARTOUM
ED_DUEIM
WAD_MEDANI
GEDAREF
SENNAR
EL_OBEID
ABU_NAAMA
RENK
RASHAD
DAMAZINE
Annual max.
temperature
Annual min.
temperature
Difference between max. and
min. temperature
Annual mean max.
temperature
Annual mean min.
temperature
3.93
3.58
2.47
3.41
3.19
3.62
3.36
4.34
3.51
4.18
−2.70
−2.48
−3.42
−2.67
−3.64
−2.36
−3.41
−3.69
−2.24
−3.84
5.06
4.76
4.25
4.76
4.25
5.95
4.13
5.08
5.89
4.17
5.62
5.81
5.25
5.51
5.42
6.23
5.46
6.34
6.55
5.57
−1.59
2.98
2.99
2.07
2.45
−1.43
1.81
2.11
0.58
1.79
Values larger than 1.96 or smaller than −1.96 are significant at >95% confidence level. Annual max./min. temperature is defined as the highest/lowest
daily temperature of the year. Annual mean max./min. temperature is defined as the mean daily max./min. temperature on the annual basis
Values larger than 1.96 or smaller than −1.96 are significant at >95% confidence level. Warm rainy season is from July to November, cool dry season is from December to February, and warm dry
season is from March to June
5.88
6.53
6.44
6.35
−0.57
0.32
−1.96
0.95
3.90
4.68
6.13
4.01
7.41
8.23
8.48
7.62
ABU_NAAMA
RENK
RASHAD
DAMAZINE
4.53
4.73
4.85
3.09
3.09
4.69
5.44
3.30
4.99
6.60
7.16
5.11
−2.71
−2.28
−2.99
−2.52
6.53
6.96
6.70
6.82
−3.71
−1.73
−1.90
−0.11
−1.43
−4.03
4.86
5.28
5.26
6.55
5.88
5.88
4.65
4.77
4.28
4.49
4.20
5.80
7.07
7.62
7.11
7.30
7.45
7.96
KHARTOUM
ED_DUEIM
WAD_MEDANI
GEDAREF
SENNAR
EL_OBEID
3.77
5.06
4.95
4.25
5.24
4.57
3.23
2.79
2.82
3.25
2.75
3.93
3.89
5.80
5.26
5.57
5.43
5.83
−2.69
−1.96
−2.01
−2.31
−2.31
−3.89
Seasonal
mean max.
temperature
in warm dry
season
Difference between
seasonal mean max.
and min.
temperature in cool
dry season
Seasonal
mean min.
temperature
in cool dry
season
Seasonal
mean max.
temperature
in cool dry
season
Difference between
seasonal mean max.
and min. temperature
in warm rainy season
Seasonal
mean min.
temperature
in warm rainy
season
Seasonal
mean max.
temperature
in warm rainy
season
Stations
Table 3 Mann–Kendall trends of seasonal mean temperature variables of the meteorological stations of Sudan
For illustrative purpose, the Khartoum station is used to
demonstrate the mean seasonal properties of the climate
variables. Figure 3 is the boxplot of monthly mean
maximum and minimum temperature and the associated
difference between the maximum and minimum temperature at the Khartoum station. Comparing boxplot medians is
like a visual hypothesis test, analogous to the t test used for
means. Figure 3 illustrates that the higher monthly mean
maximum temperature occurs in April, May, and June, and
lower monthly mean maximum temperature can be observed in January, February, and December. Larger interquartile ranges of monthly mean maximum temperature can
be detected in July, August, September, and October,
showing larger maximum temperature variability in these
months. Figure 3 also indicates a negative skew of monthly
mean maximum temperature in June to October, showing a
higher probability of higher maximum temperature in these
months. Different changing properties are observed in terms
of monthly mean minimum temperature (upper right panel
of Fig. 3). Higher monthly mean minimum temperature is
observed in May to October. Larger variability of monthly
mean minimum temperature is found in January, February,
and December and smaller variability in April to November, which is contrary to that of the monthly mean
maximum temperature (upper left panel of Fig. 3). Lower
panel of Fig. 3 shows monthly variability of the difference
between maximum and minimum temperature. It can be
seen that larger difference is identified in months from
January to May and from September to December. Smaller
difference is found in months from June to August.
Besides, lower panel of Fig. 3 also shows larger variability
of temperature difference in months from May to September. Thus, larger variability of monthly mean maximum
temperature and larger temperature difference mainly occur
in warm seasons. On the contrary, smaller variability is
found mainly in the cool season. However, changing
magnitude of monthly mean minimum temperature is larger
in the cool season when compared to the warm seasons.
Table 2 displays MK results of temperature variables. It
can be seen from Table 2 that all stations in Sudan
considered in this study show a significant increasing
annual maximum temperature, but show a significant
decreasing annual minimum temperature. Therefore, the
difference between the annual maximum and minimum
temperature is in significant increasing trend. Similarly,
annual mean daily maximum temperature (column 5) is in
significant increasing trends. However, annual mean daily
minimum temperature (column 6) shows different changing
characteristics. Eight out of ten stations show increasing
trends in annual mean daily minimum temperature, of
which five are significant at >95% confidence level. Two
Seasonal
mean min.
temperature
in warm dry
season
4.1 Temperature changes in Khartoum station
5.96
5.42
5.07
6.56
5.32
6.45
C.-Y. Xu et al.
Difference between
seasonal mean max.
and min. temperature
in warm dry season
402
Statistical properties of the temperature, relative humidity, and net solar radiation in the Blue Nile-eastern Sudan region
Maximum temperature
256
Time scale (months)
Fig. 4 Abrupt changes and linear trends estimation of areal
average monthly mean maximum temperature variations of
the study region by using the
two-phase regression scheme
method. The upper panel shows
change points on different time
scales; and lower panel shows
linear trends of time intervals
separated by change points.
Dashed lines show decreasing
trend after the change point, and
solid lines indicate increasing
trend after the change point.
Thick solid and dashed lines
denote significant change points
403
64
16
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
Time (years)
maximum temperature shows a significant increasing trend,
however, the seasonal mean minimum temperature in these
two seasons is decreasing, and it is particularly the case in
the cool dry season. All these facts cause the temperature
differences between seasonal mean maximum and mini-
Period (years)
out of ten stations show decreasing trends but are not
significant at >95% confidence level. Different changing
properties are found in the seasonal changes of the
temperature variables when compared to annual variations
(Table 3). The seasonal mean maximum temperature in all
seasons show significant increasing trends. However, the
seasonal mean minimum temperature shows different
changing characteristics in different seasons; significant
increasing trends are found in the warm rainy season, and
opposite are true in the cool dry season; both increase and
decrease trends are found in the warm dry season, but most
of them are not significant. In the warm rainy season, both
seasonal mean maximum and minimum temperatures show
a significant increasing trend, however, larger magnitude
increases of seasonal mean maximum temperature than
seasonal mean minimum temperature in the season cause a
significant increase in temperature difference between
seasonal mean maximum and minimum temperature. In
the cool dry and warm dry seasons, the seasonal mean
0.25
0.5
1
2
4
8
16
1950
1960
1970
1980
Time (years)
1990
2000
Fig. 5 Wavelet transform of areal average monthly mean maximum temperature of the study region. The thick black contour
designates the 95% confidence level against red noise and the cone
of influence (COI) where edge effects might distort the picture is
shown as a U-shaped line
404
C.-Y. Xu et al.
Minimum temperature
256
Time scale (months)
Fig. 6 Abrupt changes and
trends estimation of areal
average monthly mean minimum temperature variations of
the study region by using the
two-phase regression scheme
method. The upper panel shows
change points on different time
scales; and lower panel shows
linear trends of time intervals
separated by change points.
Dashed lines show decreasing
trend after the change point, and
solid lines indicate increasing
trend after the change point.
Thick solid and dashed lines
denote significant change points
64
16
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
Time (years)
mum temperature in cool dry and warm dry seasons have
significant increasing trends.
4.2 Changing properties of areal average temperature
wavelet transform method. The former method analyzes
abrupt behaviors and linear trends of subseries. The wavelet
transform method is used to implement the time–frequency
analysis of the climate variable series and also the
The changing properties of areal average temperature are
analyzed by using the two-phase regression scheme and the
90
0.25
0.5
1
2
4
8
16
1950
Relative humidity (%)
Period (years)
80
1960
1970
1980
Time (years)
1990
2000
Fig. 7 Wavelet transform of areal average monthly mean minimum
temperature of Sudan. The thick black contour designates the 95%
confidence level against red noise and the COI where edge effects
might distort the picture is shown as a U-shaped line
70
60
50
40
30
20
10
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Time (months)
Fig. 8 Long-term monthly average relative humidity at the Khartoum
station, Sudan. “+” denotes outlier
Statistical properties of the temperature, relative humidity, and net solar radiation in the Blue Nile-eastern Sudan region
405
Table 4 Mann–Kendall trends of seasonal mean relative humidity at the meteorological stations of Sudan
Stations
KHARTOUM
ED_DUEIM
WAD_MEDANI
GEDAREF
SENNAR
EL_OBEID
ABU_NAAMA
RENK
RASHAD
DAMAZINE
Annual mean
relative humidity
Seasonal mean relative
humidity in cool dry season
Seasonal mean relative
humidity in warm dry season
Seasonal mean relative humidity
in warm rainy season
−7.97
−8.15
−7.92
−7.40
−7.91
−8.47
−7.47
−8.34
−8.61
−7.20
−5.71
−5.59
−5.34
−4.83
−5.25
−6.64
−5.08
−5.58
−6.43
−4.75
−6.59
−7.08
−7.02
−6.86
−7.21
−7.37
−7.12
−7.59
−7.84
−7.04
−6.98
−7.40
−7.04
−6.78
−7.16
−8.05
−6.87
−7.71
−8.39
−6.77
Values larger than 1.96 or smaller than −1.96 are significant at >95% confidence level. Warm rainy season is from July to November, cool dry
season is from December to February, and warm dry season is from March to June
Relative humidity (%)
Time scale (months)
Fig. 9 Abrupt changes and
trends estimation of areal
average relative humidity variations of the study region by
using the two-phase regression
scheme method. The upper
panel shows change points on
different time scales; and lower
panel shows linear trends of
time intervals separated by
change points. Dashed lines
show decreasing trend after the
change point, and solid lines
indicate increasing trend after
the change point. Thick solid
and dashed lines denote
significant change points
256
64
16
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
Time (years)
4.3 Changes of relative humidity in Khartoum station
Figure 8 shows that higher relative humidity is observed
mainly during July and October, and this period is also the
warm rainy season in eastern Sudan. Boxplot of relative
humidity during June and November shows a positive skew
of relative humidity, indicating a higher probability of
lower relative humidity of these months. The larger
interquartile values of relative humidity during May and
October show a larger variability of relative humidity
changes in these months when compared to other months.
More outlier values (denoted by +signals) also show larger
changing magnitudes of relative humidity. Table 4 displays
MK results of the seasonal relative humidity changes at the
ten stations of Sudan. MK results indicate that the annual
mean relative humidity and relative humidity in all the
seasons are in significant decreasing trends at >95%
confidence level.
4.4 Changing properties of areal average relative humidity
0.25
0.5
1
2
4
8
16
1950
1960
1970
1980
Time (years)
1990
2000
Fig. 10 Wavelet transform of areal average relative humidity of the
study region. The thick black contour designates the 95% confidence
level against red noise and the COI where edge effects might distort
the picture is shown as a U-shaped line
decrease dominates the changes of areal average relative
humidity. On time scales of >64 months, the areal average
relative humidity increases during 1980 and 1990. Besides,
simpler changing patterns are also identified after 1980.
Figure 10 indicates simple periodicity properties of areal
average relative humidity of the study region. The 1-year
period is significant and dominant throughout the time
interval considered which implies no significant alterations
within the periodicity of relative humidity of eastern Sudan.
4.5 Changes of net solar radiation
Figure 11 shows the statistical properties of the mean
monthly net solar radiation in Khartoum station. Obviously,
higher net solar radiation is observed during February and
May, and this period corresponds well with the warm dry
season of Sudan. The lowest net solar radiation corresponds
well to the warm rainy season (July–November) and the
cool winter (December–January). Larger variability of net
260
240
Net shortwave radiation (W/m2)
periodicity properties. Figure 4 illustrates different abrupt
behaviors at different time scales. Generally, the areal
average monthly mean maximum temperature of the study
region is dominated by increasing trends which are
interrupted by short-term decreasing trends. Before 1960s,
the areal average monthly mean maximum temperature is
characterized mainly by decreasing trends and is featured
by increasing trends after 1960s. This general increasing
trend after 1960s is interrupted by short-term decreasing
trend during mid-1990s. Upper panel of Fig. 4 shows that
the decrease of areal average monthly mean maximum
temperature occurs on the time scale of >64 months. As for
the periods of variations of areal average monthly mean
maximum temperature (Fig. 5), the periodicity is characterized by a 1-year period. It should be noted here that the
1-year band disappears from 1970 to 2000, showing a
decreasing wavelet spectrum power. In this time interval,
the half-year period component appears, showing higher
frequency fluctuations. Figure 6 shows that the areal
average monthly mean minimum temperature is dominated
by an increasing trend except the time interval of 1960–
1965 which is characterized by decreasing areal average
monthly mean minimum temperature. Lower panel of
Fig. 6 also shows a smaller-magnitude increase of areal
average monthly mean minimum temperature after 1990
when compared to that before 1990. Similarly, a 1-year
period is dominant throughout the whole study period.
Some significant bands distribute sporadically along the
half- and quarter-year periods (Fig. 7).
C.-Y. Xu et al.
Period (years)
406
220
200
180
160
140
120
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Months
Distinctly remarkable changes can be observed in the areal
average relative humidity of eastern Sudan (Fig. 9). A sharp
Fig. 11 Long-term monthly average net solar radiation at the
Khartoum station, Sudan. “+” denotes outlier
Statistical properties of the temperature, relative humidity, and net solar radiation in the Blue Nile-eastern Sudan region
407
Table 5 Mann–Kendall trends of net solar radiation of the meteorological stations of Sudan
Station name
KHARTOUM
ED_DUEIM
WAD_MEDANI
GEDAREF
SENNAR
EL_OBEID
ABU_NAAMA
RENK
RASHAD
DAMAZINE
Mean net solar radiation in rainy
season
Mean net solar radiation in cool dry
season
4.99
4.37
3.17
4.61
4.30
3.86
4.78
3.54
3.54
4.78
6.19
6.38
2.62
5.71
5.55
6.61
5.79
6.32
6.32
5.79
Mean net solar radiation in warm dry
season
5.77
5.45
6.99
7.03
5.41
5.60
5.51
5.16
5.16
5.51
Values larger than 1.96 or smaller than −1.96 are significant at >95% confidence level. Warm rainy season is from July to November, cool dry
season is from December to February, and warm dry season is from March to June
solar radiation occurs in April to August. MK results
indicate that a significant increasing trend is found in all the
seasons and stations (Table 5), which is consistent with the
increasing trends found for the annual and seasonal
maximum temperature (Table 3, columns 2, 5, and 8).
4.6 Changing properties of areal average net solar radiation
Figure 12 shows different abrupt behaviors at different time
scales. In general, the areal average net solar radiation is
dominated by an increasing trend when the whole period
from 1948 to 2005 is concerned. This general increasing
trend is interrupted by short-term decreasing trends in
1950s and around 1990. The changes also show a large
fluctuation in short periods with a jump in middle 1950s
and a drop in earlier 1970s. Upper panel of Fig. 12 shows
that the decrease of areal average monthly mean net solar
radiation occurs on larger time scales of >64 months. The
changes of net solar radiation show a clear similarity with
the changes of maximum temperature (Fig. 4). Wavelet
transform results indicate a significant 1-year period except
in the period of earlier 1950s (Fig. 13).
5 Discussions
The global temperature increase has exerted tremendous
influences on hydrological cycle, human health, energy
management, and agricultural production (e.g., Karl and
Easterling 1999). Therefore, temperature changes have
been drawing considerable concerns among scholars (e.g.,
Elagib and Mansell 2000). It should be noted here that the
temperature changes are different from region to region.
Bonsal et al. (2001) found great regional and seasonal
differences in the spatial and temporal variability of
extreme temperature in Canada for the period of 1950–
1998, indicating significant warmer summer and spring
periods and slight warmer winters (Founda et al. 2004).
Manton et al. (2001) found significant increases in hot days
and warm nights and decreases in cool days and cold nights
since 1961 across the Southern Asia and South Pacific
region.
In China, Zhai and Pan (2003) showed that the number
of hot days (over 35°C) displays a slight decreasing trend,
while the number of frost days (below 0°C) exhibits a
significant decreasing trend. Zhang et al. (2008b) studied
the changing properties of extreme temperature of the
Yellow River basin, China, indicating that the annual
warming trend in the Yellow River basin mainly results
from the increase in winter minimum temperature. The
maximum temperature in the Yellow River basin is
increasing, but is not significant at >95% confidence level.
The current study reveals different changing characteristics of warming process of Sudan. The annual maximum
temperature is in significant increasing trend; however, the
annual minimum temperature is in decreasing trend, and it
is particularly the case in the cool dry season. Thus, the
difference between the annual maximum and minimum
temperature is significantly increasing. Seasonal differences
can be found in terms of minimum temperature changes.
Significant decreasing minimum temperature mainly occurs
in the cool dry season. Two out of ten stations show
significant decreasing minimum temperature in the warm
dry season. What is confirmed is the significant increasing
difference between maximum and minimum temperature.
The increasing magnitude of maximum temperature in the
dry seasons is smaller than in the rainy season. These
changing properties of temperature may be attributed to
changes of net solar radiation. Our analysis results indicate
that the net solar radiation is significantly increasing in all
408
C.-Y. Xu et al.
256
Time scales (months)
Fig. 12 Abrupt changes and
trends estimation of areal
average net solar radiation variations of the study region by
using the two-phase regression
scheme method. The upper
panel shows change points on
different time scales; and lower
panel shows linear trends of
time intervals separated by
change points. Dashed lines
show decreasing trend after the
change point, and solid lines
indicate increasing trend after
the change point. Thick solid
and dashed lines denote
significant change points
128
64
32
16
8
1950
1960
Period (years)
seasons and stations, which is consistent with the changing
properties of maximum temperature in the region. Our
results indicate a significant decreasing trend in relative
humidity, particularly after mid-1960s. Elagib and Mansell
(2000) draw the general conclusions based on more cited
references (e.g., Perry 1986; Walsh et al. 1988; Elagib and
Alvi 1996) that a marked progressive deterioration of
0.25
0.5
1
2
4
8
16
1950
1970
1980
1990
2000
rainfall has occurred since mid-1960s with culmination in
mid-1980s. The changing properties of precipitation
reported by aforementioned scholars are in good agreement
with those of relative humidity found in this study, which
indicates that there exist good relations between precipitation and relative humidity in the study region.
6 Conclusions
1960
1970
1980
Time (years)
1990
2000
Fig. 13 Wavelet transform of areal average net solar radiation of the
study region. The thick black contour designates the 95% confidence
level against red noise and the COI where edge effects might distort
the picture is shown as a U-shaped line
In this study, we systematically analyzed the major
climate variables of maximum and minimum temperature, relative humidity, and net solar radiation with the
aim to explore the statistical properties of these
variables in eastern Sudan. We obtained the following
conclusions:
1) In eastern Sudan, the annual and seasonal maximum
temperatures are increasing significantly. The increasing magnitude of the maximum temperature in
the rainy season is larger than that in the dry
Statistical properties of the temperature, relative humidity, and net solar radiation in the Blue Nile-eastern Sudan region
seasons. Decreasing trends can be observed in the
annual and dry seasons' minimum temperature. The
minimum temperature in the rainy season is increasing
but the rate of the increase is smaller than that of the
maximum temperature in the same season. Consequently, the difference between annual maximum and
minimum temperature is increasing in all the seasons.
2) There is a decreasing trend in relative humidity in
eastern Sudan, particularly after mid-1960s, which is
in agreement with precipitation changes as reported in
earlier study.
3) The net solar radiation in the region is significantly
increasing in all seasons and stations, which corresponds
well with the changing properties of the maximum
temperature.
4) Our analysis results also indicate a consistent 1-year
period variation within these climate variables we
studied. These results suggest that the climate regime
variations of eastern Sudan, to a larger degree, are
controlled by global climate signal.
Acknowledgments This work is financially supported by The
Research Council of Norway with project number 171783 (FRIMUF)
and by the “985 Project” (grant no. 37000-3171315).
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