Journal of Hydrology 519 (2014) 3263–3274
Contents lists available at ScienceDirect
Journal of Hydrology
journal homepage: www.elsevier.com/locate/jhydrol
Stationarity of annual flood peaks during 1951–2010 in the Pearl River
basin, China
Qiang Zhang a,b,c,⇑, Xihui Gu a,b,c, Vijay P. Singh d, Mingzhong Xiao a,b,c, Chong-Yu Xu e
a
Department of Water Resources and Environment, Sun Yat-sen University, Guangzhou, China
Key Laboratory of Water Cycle and Water Security in Southern China of Guangdong High Education Institute, Sun Yat-sen University, Guangzhou, China
c
School of Earth Sciences and Engineering, Suzhou University, Anhui 234000, China
d
Department of Biological and Agricultural Engineering and Department of Civil and Environmental Engineering, Texas A&M University, College Station, TX, USA
e
Department of Geosciences, University of Oslo, Oslo, Norway
b
a r t i c l e
i n f o
Article history:
Received 12 February 2014
Received in revised form 28 September
2014
Accepted 9 October 2014
Available online 22 October 2014
This manuscript was handled by Andras
Bardossy, Editor-in-Chief, with the
assistance of Bruno Merz, Associate Editor
Keywords:
Stationarity
Pettitt method
GAMLSS models
Long-term persistence
Pearl River basin
s u m m a r y
The assumption of stationarity of annual peak flood (APF) records at 28 hydrological stations across the
Pearl River basin, China, is tested. Abrupt changes in mean and variance are tested using the Pettitt technique and the Loess method. Trends of APFs are analyzed using the Mann–Kendall method and the Spearman technique. And then the stationarity of the APF series is further investigated by GAMLSS models and
long-term persistence. Results indicate that: (1) abrupt changes in mean and variance have similar influences on the changing properties of APFs, such as stationarity. Abrupt changes in mean and variance are
only field significant in the East River basin; (2) the change points have a considerable impact on the
detection of trends, and these may be attributed to the fact that a abrupt increase or decrease in mean
values will affect the trend variations. Besides, for the APF series being free of change points and trend,
the GAMLSS models also corroborate stationarity of the APF series; (3) the nonstationarity in the Pearl
River basin is mainly due to the existence of the change point. However, the APF series with change
points in mean and/or variance are also characterized by long-term persistence, and thus it is infeasible
to assert that the abrupt behaviors and/or trends of the APF series are the result of human activities or
long-term persistence, especially in the East River basin. Results of this study will provide information
for management of water resources and design of hydraulic facilities in the Pearl River basin in a changing environment.
Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction
The stationarity of flood records pertains to physical processes
associated with flood production, sample properties of the flood
records, statistical procedures that are used to infer distributional
properties of flood series, and temporal changes in the flood peak
distribution (Villarini et al., 2009). However, statistical inferences
and statistical analyses for hydrologic time series have relied heavily on the assumption of stationarity. Statistical models for hydrological time series under stationary conditions should be different
from those under nonstationary conditions. Under the nonstationarity assumption, models should be capable of accounting for the
changes in the parameters of the selected distribution over time
(Cox et al., 2002; Villarini et al., 2010). It is well known that almost
all the rivers worldwide have been influenced by various factors,
⇑ Corresponding author at: Department of Water resources and Environment, Sun
Yat-sen University, Guangzhou, China. Tel./fax: +86 20 84113730.
E-mail address: zhangq68@mail.sysu.edu.cn (Q. Zhang).
http://dx.doi.org/10.1016/j.jhydrol.2014.10.028
0022-1694/Ó 2014 Elsevier B.V. All rights reserved.
such as water reservoirs, human withdrawal of freshwater, and
precipitation changes. Moreover, flood risk, water supply, high
and low flows, and water quality are influenced more or less by
water infrastructure, channel modifications (e.g. Zhang et al.,
2011), drainage works, river morphological change, river training
work and land-cover and land-use changes. Milly et al. (2008)
argued that stationarity is dead and should no longer serve as a
central, default assumption in water-resource risk assessment
and planning. Finding a suitable successor is crucial for human
adaptation to changing climate (Milly et al., 2008).
Hydrological nonstationarity has drawn considerable attention
in recent years. Galloway (2011) asked what do we do now if stationarity is dead and called for research into the assumption of stationarity or nonstationarity of hydrological series and related
implications, development of new approaches, and generation of
sufficient information for planning, design and operation of today’s
projects. With consideration of nonstationarity, Coulibaly and
Baldwin (2005) proposed an optimal dynamic recurrent neural
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Q. Zhang et al. / Journal of Hydrology 519 (2014) 3263–3274
networks approach to directly forecast nonstationary hydrological
time series, and found that they are good alternatives for modeling
the complex dynamics of the hydrological system. Considering
both nonlinearity and nonstationarity, Komorník et al. (2006) compared the performances of several forecast models for monthly and
seasonal flows in the Tatry region and proposed a new regimeswitching model.
Nonstationarity in hydrological variables has been widely recognized. And the most common ways to check whether the hydrological stationarity is valid or not are checking for the presence of
trend or change points (Villarini et al., 2009). Besides, the trend
analysis is often disturbed by the presence of change point, the
trend is analyzed follows the change point analysis in the study,
as suggested by Villarini et al. (2009), and the change point has
been analyzed for both the mean and variance. Furthermore, as
the presence of long-term persistence is often overlooked in analyses of stationarity of hydrological variables (Koutsoyiannis, 2006;
Villarini et al., 2009), whether the behavior observed in the hydrological variables could be better explained in terms of long-term
persistence has also been investigated in this study.
In China the Pearl River is the third largest river in terms of
drainage area and the second largest in terms of streamflow, and
has abundant water resources (e.g. Zhang et al., 2009a). However,
uneven spatial and temporal distribution of water resources, with
80% of the total flow occurring in the flood season, i.e. April–September, negatively affects the effective use of water resource. Further, the Pearl River basin plays a significant role in the socioeconomic development of China as one of the fastest developing
regions in China. The Pearl River basin involves the West River,
the North River, the East River and the rivers within the Pearl River
Delta (PRD), with a total drainage area of 453,690 km2. The PRD is
the integrated delta composed of West River delta, North River
delta, and East River delta. The area of PRD is about 9750 km2,
wherein the West River delta and the North River delta account
for about 93.7% of the total area of the PRD. The hydrological processes are impacted by human activities, such as construction of
water reservoirs, forestation and deforestation. Till today, 36
large-sized water reservoirs with a total storage capacity of 29 billion m3 have been constructed (Dai et al., 2007). Construction of
water reservoirs has heavily influenced hydrological processes of
the Pearl River basin, such as streamflow and sediment load
changes (Zhang et al., 2008, 2012a).
Besides, the precipitation regime of the Pearl River basin has
also been significantly changed, perhaps due to climate change
or climate oscillations, and has altered the hydrological cycle
(Zhang et al., 2009a, 2012b). Analysis of precipitation (Zhang
et al., 2012b) indicates decreasing precipitation mainly in the middle and upper Pearl River basin, but a decreasing number of rainy
days almost over the entire Pearl River basin. Thus, the Pearl River
basin is characterized by increasing precipitation intensity which is
further collaborated by higher occurrences of wet periods with
shorter durations. However, analysis of precipitation extremes
indicates increased precipitation variability and high-intensity
rainfall, though rainy days and low-intensity rainfall have
decreased; the amount of rainfall has changed little but its variability has increased over the time interval divided by change points
(Zhang et al., 2009b). Furthermore, seasonal shifts of precipitation
changes have also been observed (Zhang et al., 2009a), with the
result that winter is getting wetter and summer is getting drier,
though the wetting or drying tendency is subject to different magnitudes. Spatiotemporal alterations of precipitation characteristics
have the potential to alter the hydrological characteristics. And the
precipitation changes may considerably impact the statistics of
hydrological processes, such as mean and variance. Meanwhile,
the changing mean seriously affects the design and management
of hydrosystems (Koutsoyiannis, 2006).
Therefore, for management of water resources and evaluation
and mitigation of risk of flood hazards, it is important to investigate stationarity or nonstationarity of hydrological extremes in
the Pearl River basin and related causes. Little has been reported
on this subject in the Pearl River basin. This constituted the major
motivation of this study. The objective of the study is to analyze
whether the stationarity is dead or not in the Pearl River basin.
The results of this study will provide ground information for design
of hydraulic facilities, management of water resources and evaluation of flood hazards in the Pearl River basin.
2. Data
Annual flood peak (APF) records from 28 hydrological stations
were analyzed. Locations of these stations are shown in Fig. 1.
Information on the data, such as the length of annual flood peak
series and drainage areas of tributaries is given in Table 1. There
are no missing data in the dataset considered in the study. The data
were obtained from the Hydraulic Bureau of Guangdong province
and the quality of the data is firmly controlled before their release.
Hence, we assume that the data are of good quality. However, as
we do not have access to the original data, we cannot rule out
the possibility that changes in the flood peak time series are influenced by data problems, such as changes in the rating curve.
3. Methodologies
3.1. Change point analysis
As a nonparametric test that allows detection of changes in the
mean (median) when the change point time is unknown, the Pettitt
test (Pettitt, 1979) has been suggested by Villarini et al. (2009) to
analyze the change point. This test is based on a version of the
Mann–Whitney statistic for testing whether the two samples
X1, . . . , Xm and Xm+1, . . . , Xn come from the same population. The p
value of test statistic is computed using the limiting distribution
approximated by Pettitt (1979), which is valid for continuous variables (e.g. Villarini et al., 2009). And the 95% confidence level was
used to evaluate the significance of change point in the study. Also
as stated by Villarini et al. (2009), changes in the series variability
can have strong impact, especially on extreme values. Then
changes in variance have also been analyzed in this study, and
changes in variance are tested by using the Pettitt test and applying it on the squared residuals (e.g. Villarini et al., 2009).
Besides, field significance of change point has also been analyzed in the study based on the False Discovery Rate (FDR) method
(Ventura et al., 2004; Wilks, 2006; Renard et al., 2008). Let qi be the
p value being related to the test performed at site i (i = 1, . . . , n), and
q(i) denotes the ith smallest of these p values. Then a FDR probability pFDR is defined as follows (Ventura et al., 2004; Wilks, 2006;
Renard et al., 2008):
pFDR ¼ max fpðiÞ : pðiÞ 6 aði=pÞg
i¼1;...;n
ð1Þ
And field significance at the level of a will be declared if at least
one local test has a p value smaller than pFDR, and the level of 0.05
has been used in the paper. It should be noted that it has been
assumed all local tests are independent, however, the FDR procedure has been reported to be very robust when dependence exists
between sites (Ventura et al., 2004; Wilks, 2006).
3.2. Detection of trends
In the study, the detection of trends was done using the Mann–
Kendall trend (M–K) test method and the Spearman technique, and
both of them are non-parametric trend detection method, being
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Q. Zhang et al. / Journal of Hydrology 519 (2014) 3263–3274
Fig. 1. Locations of hydrological stations and water reservoirs, and detail information of the hydrological data can be referred to Table 1.
Table 1
Information on hydrological data considered in the study.
River basin
Stations
Drainage area (km2)
Length of time series
Mean (m3/s)
Standard deviation
West River
Qianjiang
Dahuangjiangkou
Wuzhou
Gaoyao
Jiangbian
Panjiangqiao
Zhexiang
Chongwei
Sancha
Liuzhou
Pingle
Baise
Xinhe
Nanning
Guigang
Jinji
128938
288544
327006
351535
25116
14492
82480
13045
16280
45413
12159
21720
5791
72656
86333
9103
1951–2010
1951–2010
1951–2010
1951–2010
1951–2010
1951–2010
1951–2009
1951–2010
1951–2010
1951–2010
1951–2010
1951–2010
1951–2010
1951–2010
1951–2010
1951–2010
12103
28083
31540
32073
1120
2331
6953
4164
5603
14919
5231
2336
1341
8136
8551
2459
3.72
3.83
3.83
3.53
2.35
2.58
3.20
1.90
2.66
2.49
2.74
1.94
2.29
3.51
3.29
1.92
North River
Changba
Pingshi
Lishi
Hengshi
Gaodao
Shijiao
6794
3567
7097
34013
9007
38363
1951–2010
1964–2008
1955–2009
1956–1998
1951–2010
1951–2010
1638
1275
2226
8929
3463
9528
2.40
1.70
1.80
2.74
2.44
3.00
East River
Longchuan
Heyuan
Lingxia
Boluo
7699
15750
20557
25325
1954–2009
1951–2010
1956–2009
1951–2010
1647
2589
4004
4797
1.29
1.62
2.10
2.21
Moyang River
Shuangjie
4345
1951–2010
2151
2.60
Qin River
Changle
6645
1951–2010
1953
2.06
less sensitive to outliers than parametric statistics. Without requiring normality or linearity, the rank-based nonparametric M–K test
method has been recommended for general use by the World
Meteorological Organization (Mitchell et al., 1966; Alan et al.,
2003). However, it should be noted here that the results of the
M–K test are affected by serial correlation within the time series
(von Storch and Navarra, 1995; Wang and Swail, 2001; Zhang
et al., 2001; Yue et al., 2003). von Storch and Navarra (1995) sug-
gested eliminating the persistence effect in the hydrometeorological series before the Mann–Kendall analysis. Following Zhang et al.
(2001), a statistically significant trend in streamflow series (x1, x2,
x3, . . . , xn) was detected using the following steps: (1) compute
the lag-1 serial correlation q1; (2) if q1 < 0.1, the M–K test is
applied directly in the detection of trends; otherwise (3) the M–K
test is used in the trend detection for the preprocessed time series,
i.e., x2 q1x1, x3 q1x2, . . ., xn q1xn1. The 95% confidence level was
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Q. Zhang et al. / Journal of Hydrology 519 (2014) 3263–3274
used to evaluate the significance of trends. Similar to the M–K test,
the Spearman technique (Helsel and Hirsch, 1993) is also commonly used for detection of trends.
3.3. GAMLSS model
As providing a flexible choice compared with classical generalized additive models (GAM) (e.g., Hastie and Tibshirani, 1990), the
generalized additive models for location, scale and shape (GAMLSS), proposed by Rigby and Stasinopoulos (2005), have been used
in the study to dynamically capture the evolution of the probability
density functions. And the principle of GAMLSS is that assuming a
parametric distribution for the response variable X, and modeling
the parameters of the distribution as functions of an explanatory
variable (such as time t). Also as the GAMLSS allowing for a general
distribution function, such as highly skewed and/or kurtotic continuous or discrete distributions, it is possible to model both the
location, scale and shape parameters of the distribution of X as linear and/or nonlinear, parametric and/or additive nonparametric
functions of explanatory variables (Rigby and Stasinopoulos,
2005; Stasinopoulos and Rigby, 2007; Villarini et al., 2009).
It is assumed that there are independent random variables Xi,
for i = 1, . . . , n, which are from the distribution function of FX(xi; hi)
with hi = (hi1 ; . . . ; hip ), a vector of p distribution parameters accounting for location, scale, and shape. And the distribution parameters
are related to the design matrix of explanatory variables, ti, by
monotonic link functions gk(), for k = 1, . . . , p. Similar to Villarini
et al. (2009), four commonly-used two-parameter extreme value
functions were used in the study: Gumbel distribution (GU),
Gamma distribution (GA), Lognormal distribution (LOGNO, two
parameters), and Weibull distribution (WEI), and then the stationarity of mean and variance was evaluated. Information on
these four distributions is given in Table 2. Taking time t as the
only explanatory variable, the linear function relating t and parameters h1 (for mean) and h2 (for variance) was constructed as:
g 1 ðhi1 Þ ¼ ti b1
ð2Þ
g 2 ðhi2 Þ ¼ ti b2
ð3Þ
where i = 1, . . . , n, b1 and b2 denote the vectors of coefficients of the
linear models. Besides, the Akaike information criterion (AIC)
(Akaike, 1974) was used to select the distribution function with
the highest goodness-of-fit and the model with the minimum AIC
value was selected. And to further access the performance of the
selected model, the worm plot (Stasinopoulos and Rigby, 2007)
was used to test the goodness of fit of distribution functions as a
visual inspection of diagnostic plots of the residuals. Then, in this
way, the models with different probability distributions, trends in
the parameters, and change points in mean and/or variance have
been compared, and these will provide additional evidence of the
presence (or absence) of abrupt and/or slowly varying changes
(Zhang et al., 2004; Villarini et al., 2009). Analysis in this study
was made using the R-based GAMLSS package (http://cran.
r-project.org/web/packages/gamlss/index.html).
3.4. Long-term persistence
Long-term persistence can induce a statistically significant
trend, even though no trend is present (Koutsoyiannis, 2006;
Villarini et al., 2009). In this study, the Hurst exponent was used
to show long-term persistence effects. If the long-term persistence
does exist, the correlation coefficient, Corr( , ), will asymptotically follow a power function as:
CorrðX t ; X tþk Þ Ck
2H2
for k ! 1
ð4Þ
where Xt is the observed series; k is the lag time; C is a constant; H is
the Hurst exponent, ranging within (0, 1). H = 0.5 indicates no longterm persistence and H > 0.5 long-term persistence. There are several methods available for detection of long-term persistence, such
as aggregated variance method (AVM), differenced variance method
(DTV), R/S method, and also residual regressive method. Montanari
et al. (1999) compared performances of different estimation methods for the H values, indicating that aggregated variance method
performs better. Meanwhile, Montanari et al. (1999) suggested that
differenced variance method should also be considered so that the
impacts of abrupt changes and trends on the estimation of the H
values will be greatly alleviated. In this case, the H values of annual
peak flood series were estimated by the aggregated variance
method for the annual peak flood series without change points or
significant trends; the differenced variance method was used to
estimate the H values of the annual peak flood series with change
points or significant trends.
The distribution of H under the null hypothesis of no memory
was built using the bootstrap approach (Efron and Tibshirani,
1997), since the resampling procedure has the potential to destroy
the memory of the series. The resample procedure was done for
B = 3000 times with replacement and the H value was computed
for each series. Then, the empirical distribution of the B bootstrap
values of H was used to define the p value of the Hurst exponent
computed from the observed series (Villarini et al., 2009).
Table 2
Summary of the four two-parameter distributions considered to model APF series, where h1 for mean value and h2 for variance. (see also Table 2 in Villarini et al., 2009).
Probability density function
Distribution Moments
n h
io
1Þ
1
exp yh
exp ðyh
h2
h2
Gumbel
f Y ðyjh1 ; h2 Þ ¼
Weibull
1 < y < 1, 1 < h1 < 1, h2 > 0
h2
h2 1
f Y ðyjh1 ; h2 Þ ¼ h2 yh1 exp hy1
1
h2
y > 0, h1 > 0, h2 > 0
Gamma
f Y ðyjh1 ; h2 Þ ¼
1
1=h2
ðh22 Þ 2
1 1
h2
2
exp
y
½y=h22 h1 Cð1=h22 Þ
y > 0, h1 > 0, h2 > 0
Lognormal
n
o
2
1
1
1
exp ½logðyÞh
f Y ðyjh1 ; h2 Þ ¼ pffiffiffiffiffiffiffiffi
2 y
2h2
2ph2
y > 0, h1 > 0, h2 > 0
2
E½Y ¼ h1 þ ch2 ffi h1 þ 0:57722h2
Var½Y ¼ p2 h22 =6 ffi 1:64493h22
E½Y ¼ h1 C h12 þ 1
h i2 Var½Y ¼ h21 C h22 þ 1 C h12 þ 1
Conjoint function
h1
h2
Identity
Log
Log
Log
Log
Log
Identity
Identity
E½Y ¼ h1
Var½Y ¼ h22 h21
E½Y ¼ x1=2 eh1
Var½Y ¼ xðx 1Þe2h1 ; where x ¼ expðh22 Þ
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Q. Zhang et al. / Journal of Hydrology 519 (2014) 3263–3274
4.1. Change point analysis
!(
2 x 10
!(
1979
!(
!(
1990
!(
1978
!(
!( 1991
!(!(
!(
1968
1991!(
!(
!(
1990
!(
!(
1991
1987
!(
!(
Change points in mean
105°E
110°E
!(
1971
!(
115°E
!(
!(
!(
!(
!( (!
1999
(!
!
(
!
(
1990
(! !(
!(
(!
!(
!(
!( 1981 !(
!(!(
1968
!(!(
!(
!( 1966
!(
1966!( !( 1966
Change points in variance
Fig. 3. Spatial distribution of change points in the mean and variance of APF series
across the Pearl River basin. Red filled circles denote significant change points at the
95% confidence, blue filled circles denote not significant change points and the
region with a mask denote the change points are field significant in that region. (For
interpretation of the references to color in this figure legend, the reader is referred
to the web version of this article.)
stream to the Xinfengjiang water reservoir and the change points
in variance and mean of APF series for Heyuan are 1966 and
1968 respectively, just few years after the construction of the
Xinfengjiang water reservoir. These three water reservoirs and also
Tiantangshan and Xiangang water reservoirs, with a total water
storage capacity of 1.7428 1010 m3, control the river basins with
a total drainage area of 12,496 km2, accounting for 35.4% of the
total drainage area of the East River basin. Results indicate significant impacts of water reservoirs on fluvial streamflow of the East
River basin (Zhou et al., 2012). The variance of APF series from
these four stations of the East River basin was altered abruptly in
nearly 1966 which is in agreement with the time of construction
of the Xinfengjiang water reservoir. This suggests that the
Xinfengjiang water reservoir, when compared with other water
4
5
(a) Shijiao
4
1
3
0.5
2
x 10
4
(b) Dahuangjiangkou
1970
1980
1990
2000
2010
9000
(c) Heyuan
Q/m 3 /s
1
1960
1950
5000
1960
1970
1980
1990
2000
2010
1980
1990
2000
2010
(d) Changle
5000
2500
0
1950
1960
1970
1980
1990
2000
2010
26°N
(b)
1.5
0
1950
!(
1979
115°E
22°N
The change in variance was modeled by the Loess function
(Cohen, 1999) (Fig. 2). Here, only the Loess-based results of APF
series at four stations are presented, i.e. Shijiao, Dahuangjiangkou,
Heyuan and Changle stations. It can be seen from Fig. 2 that the
variance of APF at the Shijiao station (Fig. 2a) is subject to no evident changes. Increasing trends of variance were identified in the
APF series at the Dahuangjiangkou station (Fig. 2b). A closer look
at Fig. 2b indicated roughly two time intervals characterized by
increased variance, i.e. 1950–1965 and 1980–2000. The variance
of APF series at the Heyuan station (Fig. 2c) generally had a
decreasing trend. It can also be observed from Fig. 2c that the
decrease of variance was sharp during 1950–1970 but relatively
flattened during 1970–2010. Different changing characteristics of
variance of APF at the Changle station are found in Fig. 2d. It can
be seen from the figure that the variance was increasing during
1950–1970 and was decreasing after 1970, which is different from
that at other three stations. Fig. 2a–d evidently vividly indicate
changes in variance of APF. Thus, the Loess function has obvious
advantages in terms of analysis of variance.
Based on the analysis of variance by the Loess function, abrupt
changes in variance and mean of APF series from 28 hydrological
stations were investigated using the Pettitt technique and results
are shown in Fig. 3. It can be observed from the figure that the
mean values of APF series from 10 stations were subject to abrupt
changes and the change points occurred mainly during 1990 and
1968–1987. Furthermore, the field significance tests of change
points in mean for the West River, North River and East River have
also been analyzed and results indicated that the change points in
mean are only field significant in the East River basin. Besides, the
variance values of APF series from 8 stations were subject to abrupt
changes and change points occurred during 1971–1990 (Fig. 3b).
Meanwhile, field significance tests indicate that the change points
in variance are also field significant in the East River basin. In general, abrupt changes in the variance and mean of APF series are
only field significant in the East River basin, and the time when
change points occur for each station are just after the time when
the water reservoir in the upstream was built (Fengshuba water
reservoir was built in 1974, Xinfengjiang water reservoir in 1962
and Baipenzhu water reservoir in 1985, details can be referred to
Chen et al., 2010). Such as the Heyuan station is just located down-
Q/m 3 /s
110°E
26°N
105°E
(a)
22°N
4. Results
0
1950
1960
Time (year)
1970
Time (year)
Fig. 2. Fitting of the Loess function.
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Q. Zhang et al. / Journal of Hydrology 519 (2014) 3263–3274
reservoirs, exercises a dominant influence on APF variations in the
East River basin.
Change points of mean of APF from Sancha, Dahuangjiangkou,
Wuzhou and Gaoyao stations along the mainstream of the West
River basin, occurred approximately in 1990. The APF series of
the West River basin are heavily influenced by the confluences of
tributaries on the upstream of the West River and the factors causing abrupt changes in mean are complicated and blurry. The influence of hydraulic facilities is considerable. However, after the
1990s a few hydraulic facilities have been constructed and their
influence can be ignored. Analysis of precipitation extremes in
the Pearl River basin indicated that the amount of rainfall had
changed little but its variability had increased over the time interval divided by change points. Besides, increased precipitation variability and high-intensity rainfall were observed, although rainy
days and low-intensity rainfall had decreased (Zhang et al.,
2009b). Abrupt changes of precipitation maxima were shifting in
different seasons. However, change points of precipitation maxima
in summer occurred in 1990, 1988 and 1991, which are in line with
changes points of APF series of the West River basin. It should be
noted that floods occur mainly during the summer season. Therefore, it can be tentatively stated that abrupt changes of APF series
of the West River basin are mainly the result of abrupt behavior of
precipitation maxima. However, due to spatiotemporal patterns of
precipitation maxima in the Pearl River basin and the production
and confluence of flood streamflows, the abrupt behavior of APF
series usually does not match that of precipitation maxima. Moreover, human interferences also introduce considerable uncertainty
and cause obscure relations between abrupt changes of APF and
precipitation maxima. This analysis implies abrupt changes of
APF series due to various influencing factors and stationarity
cannot be attained in a changing environment.
4.2. Trend analysis
Trend is another factor resulting in nonstationarity. Before
trend detection, autocorrelation analysis was done first (Villarini
et al., 2009), which indicated no significant serial effects (some
case studies are shown in Fig. 4). Without considering the influences of change points, the M–K trends have been calculated for
all the stations, and field significance tests indicated that the trend
in the East River basin is field significant. However, as stated previously that the change points in the variance and mean are also
field significant in the East River basin, then the trend in the East
0.5
(a)
ACF
0
-0.5
Table 3
Results of analysis of trends in APF series without change points.
Stations
MK
S
Direction
Qianjiang
Panjiangqiao
Zhexiang
Chongwei
0.54
0.45
1.68
0.48
0.46
1.61
2.11
1.48
0.77
1.47
0.06
0.98
0.78
0.72
0.01
0.06
0.55
1.94
1.66
0.91
1.57
0.10
1.06
0.89
0.67
0.01
0.05
0.48
+
+
+
Liuzhou
Pingle
Nanning
Guigang
Pingshi
Lishi
Hengshi
Gaodao
Shijiao
Shuangjie
Note: MK denotes Mann–Kendall trend, S denotes Spearman test. ‘+’ denotes
increasing trends and ‘’ decreasing trends. Underlined bold number denotes significant trends at 95% confidence level.
River basin may be caused by the change points, and these will
be further analyzed. In addition, to remove the influence of change
points, the trends have been done for the stations without change
points. Results show that amongst the 14 stations without change
points of APF series, significant trend was detected for the APF series at only one station, i.e. the Chongwei station (Table 3) and not
field significant in the West River, North River and East River basin.
So there is no field significant trend in the West River, North River
and East River basin.
Besides, trend has also been done for the stations with change
points. Trend analysis was done separately for the subseries
divided by the change points. If abrupt changes occurred to both
the mean and the variance of APF, the change point of mean values
was taken as the time point for the division of the entire APF series.
Amongst the 14 stations with change points in variance and/or
mean, significant trend was identified in the subseries prior to
the change point at the Jiangbianjie station and in the subseries
posterior to the changes point at the Heyuan station (Table 4).
Besides, the direction of trends of the subseries prior to and posterior to the change points was the same at 6 stations and adverse
direction of trends was found in the subseries prior to and posterior to the change points at the other 8 stations (Table 4), implying
different causes behind the abrupt behavior of APF series at different hydrological stations.
0.5
(b)
0
0
5
10
15
20
-0.5
0
5
10
15
20
0.5
0.5
(c)
-0.5
(d)
0
0
0
5
10
15
20
+
+
+
+
+
+
-0.5
0
5
10
15
20
Lag time (year)
Fig. 4. Autocorrelation analysis of APF series at: (a) Qianjiang station; (b) Changba station; (c) Heyuan station; and (d) Changle station.
3269
Q. Zhang et al. / Journal of Hydrology 519 (2014) 3263–3274
Table 4
Trends prior to and posterior to change points.
Stations
Change points
Dahuangjiangkou
Wuzhou
Gaoyao
Jiangbianjie
Sancha
Baise
Xinhe
Changba
Longchuan
Heyuan
Lingxia
Boluo
Changle
1991
1991
1991
1971
1990
1979
1990
1979
1978
1968
1987
1966
1981
Prior to change points
Posterior to change points
MK
S
Direction
MK
S
Direction
0.38
1.35
1.35
2.84
0.47
1.16
0.54
0.56
1.07
0.42
0.19
0.72
0.56
0.22
1.32
1.31
3.10
0.49
1.37
0.41
0.41
1.22
0.46
0.46
0.78
0.56
+
+
+
+
+
+
0.19
0.06
0.32
0.82
0.48
1.43
1.33
0.26
0.26
2.08
0.92
1.08
0.98
0.24
0.02
0.27
0.84
0.45
1.41
1.36
0.29
0.14
2.01
0.54
0.85
0.94
+
+
+
+
Note: The bold values denote 95% confidence level.
Table 5
Results of analysis of trends by ignoring the presence of change points.
Stations
MK
S
Direction
Dahuajiangkou
2.54
2.77
+
Wuzhou
2.13
1.62
0.06
2.09
1.80
0.06
+
Gaoyao
Jiangbianjie
Sancha
Baise
Xinhe
Jinji
Changba
2.59
2.65
2.25
1.99
0.98
2.25
1.97
0.98
+
+
2.44
2.48
+
+
Longchuan
3.21
3.16
Heyuan
4.23
4.56
Lingxia
2.53
1.22
0.47
2.30
0.93
0.31
Boluo
Changle
Note: The bold values denote 95% confidence level.
When change points were considered, almost no significant
trends were found in the APF series of the Pearl River basin. Then
the impact of change points on the detection of trends was analyzed by analyzing trends of the APF series without considering
change points (Table 5, some case studies are shown in Fig. 5).
There were 9 out of 14 stations that were dominated by significant
x 10
4
temporal trends when ignoring the presence of change points. No
statistically significant trends were detected with the consideration of change points (Table 4) but significant trends were
obtained under the absence of change points (Table 5). The exception is the Jiangbianjie station. Trends of APF series which were
influenced by change points at 4 stations as shown in Table 5 are
illustrated in Fig. 5. It can be observed from Fig. 5a that no evident
trends of APF series at the Dahuangjiangkou station were identified
prior to and posterior to the change points. However, significant
trends were obtained without taking change point into consideration. This kind of significant trend is evidently the result of an
abrupt increase in the mean of APF series. A similar phenomenon
can also be seen from Fig. 5b and d, i.e. due to an abrupt increase
or decrease in the mean values, significant trends were attained
if the absence of change points was premised; however, no significant trends were obtained in the subseries divided by the change
points. At the Jiangbianjie station (Fig. 5c), the subseries prior to
the change point had an increasing trend with increasing magnitude, and a decreasing trend was seen after the change point. A
slight decreasing tendency was detected for the entire APF series,
showing critical impact of change point on the trends of the APF
series. Thus, abrupt behavior of the time series must be taken into
account in trend analysis, or else, results of trends could be misleading. This suggest that a prerequisite to trend analysis is to
explore abrupt behavior or change points in the time series.
4
6
(a) Dahuangjiangkou
3
x 10 4
(b) Wuzhou
4
2
2
0
1950
3000
1991
1960
1970
1980
(c) Jiangbianjie
1991
1990
2000
2010
1971
Q/m 3 /s
Q/m 3 /s
1
0
1950
8000
1960
1970
1990
2000
2010
1990
2000
2010
(d) Heyuan
1968
6000
2000
1980
4000
1000
0
1950
2000
1960
1970
1980
1990
Time (year)
2000
2010
0
1950
1960
1970
1980
Time (Year)
Fig. 5. Influences of change points on trends of APF series. Analysis of change is significant at 95% confidence level for (a), (b) and (d) and change point at (c) is not statistically
significant.
3270
Q. Zhang et al. / Journal of Hydrology 519 (2014) 3263–3274
Besides, it should be noted here that as the APF series used in the
paper are not long enough, the sub-series after the initial step of
change point analysis may be short for the trend detection, and
then the results of trend for the sub-series at some stations may
not be robust, and this leaves good space for the ongoing
investigations.
4.3. GAMLSS modeling
The above-mentioned analyses show that both long-term
trends and abrupt changes can result in nonstationarity in annual
peak flood series. In this section, GAMLSS models were taken as a
framework for parametric modeling of nonstationary annual peak
flood records. In the case for the stations with no change point was
observed, four different models have been analyzed that: (1) stationary model (no trends); (2) nonstationary model in h1; (3) nonstationary model in h2; and (4) nonstationary in h1 and h2 (Villarini
et al., 2009, 2010). As introduced in Section 3.3, the Gamma, Weibull, Gumbel, and Lognormal distributions have been used as the
distribution for the four different models, then the models with
the minimum AIC scores were selected, and results are shown in
Table 6.
It can be found from Table 6 that the gamma distribution performed the best for most of the stations (8 stations) for the APF series free of change points, followed by the Weibull distribution and
lognormal distribution. The Gumbel distribution was found to be
not appropriate (Table 6). With respect to the test of stationarity,
five stations were stationary, five stations were nonstationary in
h1 (for mean), and four stations were nonstationary in h2 (for variance). No models of nonstationarity in h1 and h2 were selected
(nonstationary in mean and variance). Results from GAMLSS models suggested that a majority of stations (9 stations in this study)
were nonstationary for APF series free of change points, and this
result seems to go against the results of trends and abrupt changes.
In fact, the AIC values were not distinctly different for these 9 models tested by the Chi-square test at the 95% confidence (El Adlouni
et al., 2007) (Table 7). Thus, for stations with APF series free of
change points, the difference of AIC values is not evident for stationary and nonstationary models and shows no obvious impact
on the selection of models. In this sense, GAMLSS-based modeling
results are not against results of analysis of trends and abrupt
changes, implying no evident trends are found in the APF series
free of change points (Table 3).
For the APF series with change points (abrupt changes in mean
and/or variance), the change points or trends were included in the
analysis by GAMLSS models and AIC scores were used to select the
appropriate models. As shown in Table 8, it can be seen from
results of analysis that GAMLSS models indicate abrupt changes
in mean and/or variance of the APF series consistent with change
points detected by the Pettitt technique. However, abrupt changes
in variance at the Jiangbianjie, Jinji and Changle stations were not
corroborated by the GAMLSS models. With respect to the distribution functions, the gamma and lognormal distributions were
mostly selected (selected for 13 stations). Based on the AIC scores
Table 6
Summary of results for the GAMLSS models in the absence of a change point.
Stations
CDF
Stationary
Nonstationary in h1
Nonstationary in h2
Nonstationary in h1and h2
Qianjiang
Panjiangqiao
Zhexiang
Chongwei
Liuzhou
Pingle
Nanning
Guigang
Pingshi
Lishi
Hengshi
Gaodao
Shijiao
Shuangjie
WEI
GA
WEI
GA
GA
GA
GA
GA
LOGNO
LOGNO
GA
WEI
WEI
GA
Y
Y
–
–
–
Y
–
–
–
–
Y
–
–
Y
–
–
Y
Y
Y
–
–
–
Y
Y
–
–
–
–
–
–
–
–
–
–
Y
Y
–
–
–
Y
Y
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
Table 7
AIC values for the probability distribution of the highest goodness-of-fit for the stations listed in Table 6.
Stations
Qianjiang
Panjiangqiao
Zhexiang
Chongwei
Liuzhou
Pingle
Nanning
Guigang
Pingshi
Lishi
Hengshi
Gaodao
Shijiao
Shuangjie
AIC
Stationary
Nonstationary in h1
Nonstationary in h2
Nonstationary in h1and h2
1143.55
983.85
1076.38
1074.58
1210.46
1076.62
1099.90
1114.98
696.79
913.48
818.81
1039.91
1140.33
974.01
1145.53
985.76
1074.34
1072.75
1209.12
1076.92
1099.45
1116.95
695.99
913.27
820.13
1040.39
1141.08
976.00
1145.11
983.81
1078.32
1076.46
1212.45
1078.56
1098.34
1114.20
698.08
914.35
820.81
1036.80
1139.88
975.06
1147.10
985.79
1076.34
1073.60
1211.12
1078.71
1098.51
1116.04
697.39
914.53
822.13
1037.57
1141.48
977.04
Note: The bold values denote 95% confidence level.
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Q. Zhang et al. / Journal of Hydrology 519 (2014) 3263–3274
Table 8
Summary of results for the GAMLSS models in the presence of a change point.
Stations
CDF
Change point in mean
Trends before CP
Trends after CP
Change point in variance
Dahuajiangkou
Wuzhou
Gaoyao
Jiangbianjie
Sancha
Baise
GA
GA
GA
WEI
GA
GA
LOGNO
Y
Y
Y
–
Y
Y
N
–
–
–
Y
–
–
–
–
–
–
–
–
–
–
–
–
–
N
–
–
Y
Longchuan
GA
GA
LOGNO
–
Y
Y
–
–
–
–
–
–
N
–
Y
Heyuan
GA
Y
–
Y
Y
Lingxia
Boluo
Changle
GA
Y
–
–
Y
GA
LOGNO
–
–
–
–
–
–
Y
N
Xinhe
Jinji
Changba
Note: Bold numbers denote stations with change point in variance; Underlined and bold numbers denote stations with change point in both mean and variance. The presence
or absence of a change point or trend (in the location parameter h1 before and after the change point) based on GAMLSS is identified with Y (yes) and N (no), respectively. CP
means change point.
Table 9
AIC values for probability distributions of the highest goodness-of-fit for the stations listed in Table 8, and bold numbers denote stations with the difference between the two
models’ AIC value is significant at 95% confidence based on the Chi-square test (El Adlouni et al., 2007).
Stations
AIC
Dahuangjiangkou
Wuzhou
Gaoyao
Sancha
Baise
Xinhe
Changba
Longchuan
Heyuan
Lingxia
Stations
Stationary
CP in mean
1240.30
1254.92
1264.57
1089.52
1017.44
917.66
949.34
919.78
1035.63
963.69
1230.32
1244.45
1255.48
1084.84
1018.00
917.43
946.26
910.79
1015.21
959.56
AIC
Jiangbianjie
Xinhe
Jinji
Longchuan
Heyuan
Lingxia
Boluo
Changle
Stationary
CP in variance
906.46
917.66
1019.01
919.78
1035.62
963.69
1087.31
984.57
908.43
914.90
1021.35
910.58
1024.72
951.63
1074.79
980.93
(b) Xinhe
500
2000
Discharge (m3 s)
30000
15000
Discharge (m3 s)
(a) Dahuangjiangkou
3500
Note: CP denotes change point.
1950
1970
1990
1950
2010
10000
(c) Lingxia
1960
1980
Time (year)
1990
2010
2000
2000
6000
(d) Heyuan
Discharge (m3 s)
6000
2000
Discharge (m3 s)
1970
Time (year)
Time (year)
1950
1970
1990
2010
Time (year)
Fig. 6. Fitting of the APF series for four stations using the GAMLSS model. Five percentiles are represented (5th, 25th, 50th, 75th, and 95th).
0.5
Deviation
0.5
-1.5
-0.5
(b) Xinhe
-0.5
(a) Dahuangjiangkou
-1.5
Deviation
1.5
Q. Zhang et al. / Journal of Hydrology 519 (2014) 3263–3274
1.5
3272
-4
-2
0
2
4
-4
Unit normal quantile
0
2
4
1.5
0.5
Deviation
0.0
(d) Heyuan
-1.5
-0.5
1.0
(c) Lingxia
-1.5
Deviation
-2
Unit normal quantile
-4
-2
0
2
4
-4
Unit normal quantile
-2
0
2
4
Unit normal quantile
Fig. 7. Worm plots for the four hydrological stations to assess the fitting of the GAMLSS model to the data as illustrated in Fig. 6. For a good fit, the data points should be
aligned preferably along the red solid line but within the two dashed black lines. (For interpretation of the references to color in this figure legend, the reader is referred to the
web version of this article.)
(Table 9), the change point model and stationary model were significantly different in the AIC scores for most of the stations, and
these further verify the results of GAMLSS models. The results of
four stations, i.e. Dahuangjiangkou, Xinhe, Lingxia and Heyuan stations are shown here as case studies. Fitting of the APF series for
the four stations using the GAMLSS model with respect to abrupt
changes in mean, variance and both mean and variance is shown
in Fig. 6. Fig. 7 shows worm plots for the four stations to evaluate
the goodness-of-fit of the GAMLSS models to the data. It can be
seen from the figure that GAMLSS models had good fitting performance for the APF series at these four stations. Change points of
mean can be observed in the APF series at the Dahuangjiangkou
station which evidently influences the stationarity of the APF series. Besides, abrupt changes in variance also have a crucial impact
on the stationarity properties of the APF series. It can be seen from
Fig. 6b that at the Xinhe station, the 50% percentile curve is not evidently influenced and little influence can also be found for the 25%
and 75% percentile curves. However, the 5% and 95% percentile
curves are significantly impacted by the abrupt changes of variance. A similar phenomenon can also be observed for the Lingxia
station (Fig. 6c), and GAMLSS models present different change
properties of APF series of the Lingxia station during different time
intervals. Due to the interference of abrupt changes in mean or variance, the 5%, 25% and 50% percentile curves exhibit a downward
tendency and the 75%, 95% curves an upward tendency (Fig. 6d).
4.4. Long-term persistence
Long-term persistence was analyzed using the aggregated variance method (AVM) and differenced variance technique (DVT)
(Table 10). It can be seen from Table 10 that the Hurst coefficients
of APF series at most of the stations (22 stations) were smaller than
0.65, indicating no evident influence of long-term persistence on
the APF changes. However, the Hurst coefficients of APF from other
Table 10
Values of the Hurst exponent H estimated using the aggregated variance method and differential difference method and the corresponding p value from testing the hypothesis of
H = 0.5.
Stations
Qianjiang
Panjiangqiao
Zhexiang
Liuzhou
Pingle
Nanning
Guigang
Pingshi
Lishi
Hengshi
Gaodao
Shijiao
Shuangjie
No change point and trend
Stations
AVM
P value
0.38
0.62
0.79
0.53
0.28
0.5
0.01
0.45
0.51
0.07
0.5
0.12
0.23
0.621
0.323
0.172
0.449
0.647
0.521
0.789
0.5
0.467
0.7
0.531
0.735
0.66
Note: The bold values denote 95% confidence level.
Dahuangjiangkou
Wuzhou
Gaoyao
Jiangbian
Sancha
Baise
Xinhe
Jinji
Changba
Longchuan
Heyuan
Lingxia
Boluo
Changle
Chongwei
Having change point or trend
DTV
P value
0.75
0.61
0.61
0.29
0.64
0.51
0.26
0.61
0.75
0.67
0.65
0.66
0.47
0.49
0.51
0.056
0.105
0.155
0.522
0.141
0.32
0.448
0.257
0.035
0.032
0.018
0.215
0.428
0.401
0.265
Q. Zhang et al. / Journal of Hydrology 519 (2014) 3263–3274
6 hydrological stations (larger than 0.65) were evidently larger
than 0.5, indicating that changing properties of APF series of these
stations can be interpreted by long-term persistence. However, due
to the limited sample size, the estimated Hurst coefficient had significant uncertainty. The significance of the Hurst coefficient (H)
not being 0.5 was tested using the bootstrap resampling procedure.
Here two assumptions was made: the null hypothesis, Ho: H 6 0.5;
the alternative hypothesis, Ha: H > 0.5.The distribution function of
H, related to the null hypothesis, was built by resorting to the bootstrap resampling technique. Then the H value of APF series of each
hydrological station was obtained and then the p value related to
the null hypothesis (Table 10). For most of the stations, the p value
could not justify the rejection of the null hypothesis; even the H
value was evidently larger than 0.5. However, the p values for Dahuangjiangkou, Changba, Longchuan, and Heyuan stations were
small enough (significant at 90% confidence) and could justify
the rejection of the null hypothesis. Thus, for the majority of
hydrological stations with the exception of Dahuangjiangkou,
Changba, Longchuan and Heyuan stations, the H value only could
justify the conclusion that the APF series at a certain hydrological
station was not subject to long-term persistence.
Furthermore, it can be seen from Table 10 that a larger Hurst
coefficient is usually identified in the APF series with change points
or significant trends and these may be owning to that long-term
persistence was also the component of multi-scale temporal fluctuations, and was also the cause behind the local abrupt changes
and significant trends. However, abrupt behaviors of APF are the
results of combined influences from human activities, climate
changes and also the long-term persistence. Thus, it is technically
and practically hard to assert that the abrupt behavior and/or
trends of the APF series are the result of human activities or
long-term persistence. The East River basin can be taken as an
exceptional case. The hydrological processes of the East River basin
are heavily influenced by water reservoirs (Zhou et al., 2012; Zhang
et al., 2014) while two out of four stations are characterized by evident long-term persistence.
(2)
(3)
(4)
(5)
3273
Clarification of causes behind the abrupt behavior of APF will
go a long way toward the interpretation of mechanisms
behind stationarity and/or nonstationarity of APF series.
The occurrence of change points has a critical impact on
trends of APF series. No evident trends can be attained if
change points are taken into consideration in the detection
of trends. Without consideration of change points, significant trends can be obtained in the APF series at 9 out of 14
stations. These results indicate that change point has a considerable influence on trends as a result of abrupt increase or
decrease in mean values.
The APF series which are free of change points and trend are
stationary, and these results have been further verified by
Pettitt method and the GAMLSS models. Besides, the gamma
distribution is the most frequently selected distribution for
the GAMLSS models used in the Pearl River basin.
Some APF series which are characterized by abrupt changes
or trend are also dominated by larger Hurst coefficient values. Long-term persistence can describe statistical features
in terms of abrupt changes and/or trends. However, it is hard
to assert that the abrupt behavior and/or trends of the APF
series are the result of human activities or long-term persistence, especially in the East River basin.
Stationarity/nonstationarity of the APF series in the Pearl
River basin is tested using the Pettitt technique, GAMLSS
models and long-term persistence. And it can be concluded
that the nonstationarity in the Pearl River basin is mainly
caused by the existence of the change points. The results
of this study are of theoretical and practical importance in
terms of estimation of flood frequency and also evaluation
of flood risk in a changing environment. It should be noted
that as the length of the time series is limited, the detected
change points or trends may not be robust enough statistically, then a regional procedure may be further used to
increase the power of statistical test. Besides, the nonstationarity linked with climatic oscillations should also be
analyzed in the ongoing investigation.
5. Conclusions
The assumption of stationarity of APF series is of significant
interest for management of flood hazards, water resources management, and design of hydraulic facilities, such as water reservoirs. Floods frequently occur in the Pearl River basin and
mitigation of floods is of practical significance in the sustainable
development of regional socio-economy. However, due to considerable influence of altered precipitation regime (Zhang et al.,
2009b, 2012b) and human activities, such as water reservoirs
(Chen et al., 2010), on APF, the stationarity assumption of the
APF series may be invalidated. However, little information to that
effect is available in the Pearl River basin. From analysis done on
whether the assumption of stationarity of APF series from 28
hydrological stations distributed across the Pearl River basin is
valid or not, the following conclusions are drawn:
(1) Abrupt changes in variance and mean are analyzed using the
Pettitt technique. Change points are identified in the APF
series at 14 stations, however, abrupt changes in the variance and mean of APF series are only field significant in
the East River basin. Causes behind abrupt changes in mean
and variance are complex, The APF series of the East River
basin are heavily influenced by hydrological regulations of
water reservoirs, and the APF series of the West River basin
are influenced mainly by confluences of streamflows from
tributaries and altered precipitation characteristics, particularly spatiotemporal variations of precipitation maxima.
Acknowledgments
This work was financially supported by Xinjiang Science and
Technology Planning Project (Grant No.: 201331104), National
Natural Science Foundation of China (Grant No.: 41071020), and
fully supported by a grant from the Research Grants Council of
the Hong Kong Special Administrative Region, China (Project No.
CUHK441313). Our cordial gratitude is also extended to the editor,
Prof. Dr. András Bárdossy, and also two anonymous reviewers for
their professional and pertinent comments and suggestions which
are greatly helpful for further improvement of the quality of this
manuscript. Besides, we again owe our special thanks to the editor,
Prof. Dr. András Bárdossy, for his hard work and his great efforts in
processing this manuscript.
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