Stoch Environ Res Risk Assess (2009) 23:1103–1111
DOI 10.1007/s00477-008-0285-8
ORIGINAL PAPER
Scaling properties of the runoff variations in the arid
and semi-arid regions of China: a case study
of the Yellow River basin
Qiang Zhang Æ Chong-Yu Xu Æ Tao Yang
Published online: 8 October 2008
Springer-Verlag 2008
Abstract We analyzed long daily runoff series at six
hydrological stations located along the mainstem Yellow
River basin by using power spectra analysis and multifractal detrended fluctuation analysis (MF-DFA) technique
with aim to deeply understand the scaling properties of the
hydrological series in the Yellow River basin. Research
results indicate that: (1) the runoff fluctuations of the
Yellow River basin exhibit self-affine fractal behavior and
different memory properties at different time scales. Different crossover frequency (1/f) indicates that lower
crossover frequency usually corresponds to larger basin
area, and vice versa, showing the influences of river size on
higher frequency of runoff variations. This may be due to
considerable regulations of river channel on the runoff
variations in river basin of larger basin size; (2) the runoff
fluctuations in the Yellow River basin exhibit short-term
memory properties at smaller time scales. Crossover
analysis by MF-DFA indicates unchanged annual cycle
within the runoff variations, implying dominant influences
of climatic changes on changes of runoff amount at longer
time scales, e.g. 1 year. Human activities, such as human
withdrawal of freshwater and construction of water reservoirs, in different reaches of the Yellow River basin may
be responsible for different scaling properties of runoff
variations in the Yellow River basin. The results of this
study will be helpful for hydrological modeling in different
time scales and also for water resource management in the
arid and semi-arid regions of China.
Keywords River flow Scaling features Multifractal detrended fluctuation analysis (MF-DFA) Spectra analysis The Yellow River
1 Introduction
Q. Zhang (&)
State Key Laboratory of Lake Science and Environment,
Nanjing Institute of Geography and Limnology, Chinese
Academy of Science, 210008 Nanjing, China
e-mail: zhangqnj@gmail.com
Q. Zhang
Institute of Space and Earth Information Science, The Chinese
University of Hong Kong, Shatin, Hong Kong, China
C.-Y. Xu
Department of Geosciences, University of Oslo,
PO Box 1047, Blindern, 0316 Oslo, Norway
T. Yang
State Key Laboratory of Hydrology-Water Resources and
Hydraulics Engineering, Hohai University, 210098 Nanjing,
China
The well-evidenced global warming has the potential to
alter the hydrological cycle over the earth and will give
rise to altered spatial–temporal distribution of water
resources (USEPA 1995; Xu and Singh 2004; Zhou et al.
2006; Zhang et al. 2008a). Hydrologists have been
endeavoring to develop and/or employed appropriate
hydrological models and robust statistical techniques in
the study of hydrological characteristics and possible
mechanisms behind them in the watersheds (e.g. Gupta
et al. 1994; Xu et al. 2005; Zhang et al. 2005). However,
more and more scholars have found that the hydrological
characteristics and hydrological responses to the climate
variability depend heavily on the season and the geographic regions (e.g. Xu et al. 2006). It should be noted
that the characteristics of the runoff fluctuations depend
on the size of the watersheds, the topography, land-use
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patterns, hydrogeology and drainage network morphology,
the transferability of hydrological models hinges on how
well they can be extrapolated across spatial and temporal
scales (Zhou et al. 2006). The pioneering work by Hurst
(1951) leads to massive study on scaling properties of
hydrological series and scaling behaviors have also been
identified in hydrological series (e.g. Puente et al. 2001;
Koutsoyiannis 2002; Bunde et al. 2006; Zhang et al.
2008c). Scaling properties can well reflect physical and
dynamical mechanisms of hydrological phenomena and
are also helpful for hydrological modeling on different
time scales and for better understanding of other geophysical phenomena (Kestener and Arneodo 2008).
Therefore, better understanding of the scaling features of
the runoff fluctuations will be greatly important for prediction and extrapolation of the runoff series from a
shorter time scale to a longer time scale. Thus, the study
of the scaling properties of the hydrological series is one
of the major issues in hydrological sciences (e.g. Sposito
1998).
Research of scaling characteristics in runoff series can
be dated back to 1950s when Hurst (1951) performed the
R/S analysis on annual runoff series from various rivers
(e.g. Nile River) and found that the annual runoff series
exhibited long-term dependencies. Hurst’s finding is now
accepted as the first example for self-affine fractal
behavior in hydrological series (e.g. Feder 1988). Bunde
et al. (2006) systematically studied the temporal correlations and multifractal properties of long river discharge
records from 41 hydrological stations around the globe
Stoch Environ Res Risk Assess (2009) 23:1103–1111
using detrended fluctuation analysis (DFA), wavelet
analysis and multifractal DFA, suggesting that the daily
runoff are long-term correlated and are characterized by a
correlation function C(s) that decays as C(s)*s-c. The
exponent c varies from river to river in a wide range
between 0.1 and 0.9. Livina et al. (2003) studied the
spectra properties of the magnitudes of daily river flux
increments, the volatility, indicating that the volatility
series exhibits strong seasonal periodicity and power–law
correlations for time scales less than 1 year. The above
researches demonstrated that the hydrological system is a
complex dynamic system characterized by nonstationary
input (precipitation) and output (evaporation, human
withdrawal of freshwater and infiltration), which display
self-similar and exhibit self-affine fractal behaviors over a
certain range of time scales (Feder 1988; Mandelbrot and
Wallis 1969). Better understanding of the scaling and
multifractality features of the runoff fluctuations will be
greatly useful in hydrological modeling (Rodriguez-Iturbe
and Rinaldo 1997) and will be beneficial for extrapolation
between scales of observations of hydrology of the
watersheds (Zhu et al. 2006). This is the main motivation
of this study.
Located in the semi-humid, semi-arid and arid climatic
zones, the Yellow River (Huanghe in Chinese) is the second largest river in China, being the important source for
water supply in the North-western and Northern China
(Fig. 1). However, it is also the region of shortage of water
resource and this water resource shortage tends to be
increasingly serious reflected by more frequent zero-flow
Fig. 1 Location of the study region and the hydrological stations (the river reach between the headwater and Hekou is the upper Yellow River;
Hekou and Taohuayu is the middle Yellow River and the river downstream to the Taohuayu is the lower Yellow River)
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Stoch Environ Res Risk Assess (2009) 23:1103–1111
Fig. 2 Six streamflow series
from six hydrologic gauging
stations along the mainstem
Yellow River. The x axis
denotes time in days. Locations
of these six hydrologic stations
are shown in Fig. 1
1105
6000
Tangnaihai station
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2000
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0
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6000
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10000
12000
14000
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18000
20000
6000
Lanzhou station
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2000
Streamflow (m3/s)
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0
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12000
5500
4000
14000 15000
Toudaoguai station
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0
0
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6000
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10000
12000
14000
16000
18000
20000
Longmen station
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0
0
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12000
14000 15000
20000
Huayuankou
station
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18000
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Lijin station
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events in the Yellow River basin during the last decades
(Zhang et al. 2008b). Thus, integrated water resource
management based on good knowledge of hydrological
principles becomes urgent. Due to massive impacts of
deteriorating water shortage on regional economic development such as agricultural production, more and more
relevant studies have been conducted on runoff changes
and possible underlying causes (e.g. Liu and Zheng 2004).
However, so far, no report is available in terms of the study
of scale invariance features of the runoff series in the
Yellow River basin although researches about the scaling,
non-linearity, multifractal behaviors of the runoff series of
the rivers of the world can be found widely in the literatures (Schertzer and Lovejoy 1987; Gupta and Waymire
1990; Rodriguez-Iturbe and Rinaldo 1997; Pandey et al.
1998; Zhang et al. 2008c). Therefore some questions still
remain unanswered: (1) Do the statistics of the river flow
exhibit scaling, if so, what type of scaling? (2) Are the
scaling behaviors, if any, similar to those of the river flow
of other rivers of the world? If not, what are the differences? We approach these issues by analyzing runoff data
collected from six hydrological stations, corresponding to
different basin areas, along the mainstem Yellow River.
Therefore, the objectives of the current paper are: (1) to
analyze characteristics of the hydrological stochastic processes; and (2) to characterize the scaling properties of
4000
6000
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10000
12000
14000
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different time scales in the hydrological series of the Yellow River basin.
2 Data and methods
2.1 Data
The long daily runoff records from six hydrological stations along the mainstem Yellow River basin were
analyzed (Figs. 1, 2). The detailed information of the data
can be referred to Table 1 and the locations of the hydrological stations can be referred to Fig. 1. The data series are
of good quality with no missing data within the study time
interval.
Table 1 Detailed information of the hydrological gauging stations
Station name
Drainage area (km2)
Series length
Tangnaihai st.
Lanzhou st.
121,972
222,551
1956.1.1–2005.12.31
1967.1.1–2005.12.31
Toudaoguai st.
367,898
1958.1.1–2005.12.31
Longmen st.
497,552
1965.1.1–2005.12.31
Huayuankou st.
730,036
1957.1.1–2005.12.31
Lijin st.
751,869
1964.1.1–2005.12.31
The location of the stations can be referred to Fig. 1
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2.2 Methods
Stoch Environ Res Risk Assess (2009) 23:1103–1111
Step 4
2.2.1 Power spectra analysis
We apply the spectra analysis techniques and calculate the
power spectrum S(f) of the time series Ri as the function of
frequency f (Bunde et al. 2006). If short- or long-term
memory exists in the series, we have S(f) * f-b, where b
is related to the correlation exponent c by b = 1-c. Generally, the power spectra of runoff will have different
frequency regimes of power law like nature (Tessier et al.
1996). The regimes are usually separated by the crossover
frequency fc. Most river runoff series present multiscaling/
multifractal features with respect to time (Pandey et al.
1998). The power spectrum density is the Fourier transform
of the autocorrelation function C(r), b = 1 - c. The shortor long-term memory
can be distinguished by the integral
R1
timescale T ¼ 0 CðrÞdr being finite or infinitely large
(Trenberth 1985). The 1/f, likes the power spectrum scaling, is an interesting feature for complex system. In such
scaling, the power spectrum of a given time series is
characterized by inverse power law (Pritchard 1992).
2.2.2 Multifractal detrended fluctuation analysis
(MF-DFA)
MF-DFA is a generalized standard DFA by identifying the
scaling of the qth-order moments of the time series (Kantelhardt et al. 2002). The MF-DFA procedure involves of
five steps (Movahed et al. 2006). The first three steps are
the same as those in the conventional DFA algorithm.
Assume that xk is a time series, k = 1,…, N.
P
Step 1
Determine the ‘profile’ Yi ¼ ik¼1 ½xk hxi;
i ¼ 1; . . .; N; where hxi is the mean of xk
Step 2
Divide the profile Y(i) into Ns = int(N/s) nonoverlapping segments of equal lengths s; int(N/s)
denotes the integer part of N/s. Since the length N
of the series is often not a multiple of the timescale
s considered, a short part at the end of the profile
may remain. To retain this part of the series, the
same procedure is repeated starting from the
opposite end. Thereby, 2Ns segments are obtained
Step 3
Calculate the local trend for each of the 2Ns
segments by a least squares fit of the series. Then
P
determine the variance F 2 ðs; mÞ ¼ 1s si¼1 fY½ðm
2
1Þs þ i ym ðiÞg ; for each segment m, m = 1,…, Ns,
P
and F 2 ðs; mÞ ¼ 1s si¼1 fY½N ðm Ns Þs þ i ym
ðiÞg2 ; for m = Ns ? 1,…, 2Ns. Here, ym(i) is the
fitting polynomial in segment m. Linear,
quadratic, cubic or higher order polynomials
can be used in the fitting procedure (DFA1,
DFA2, DFA3,…, DFAm)
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Step 5
Average over all segments to obtain the qthorder fluctuation function, defined as Fq ðsÞ ¼
P s 2
q=2 1=q
g ; where q 6¼ 0, s C
f2N1 s 2N
m¼1 ½F ðs; mÞ
m?2
Determine the scaling behavior Fq(s) sh(q) of
the fluctuation functions by the log–log plot of
Fq(s) versus s for each value of q
For stationary time series, the exponent h(2) for small
time scales is identical to the well-known Hurst exponent
H. For non-stationary signal, the relation between the
exponent h(2) for small scales and the Hurst exponent H is
H = h(2) - 1 (Hu et al. 2001). It is well known that for
uncorrelated series, the scaling exponent H equals to 0.5;
0.5 \ H \ 1 indicates long memory or persistence;
0 \ H \ 0.5 indicates short memory or anti-persistence.
This method was successfully used in characterization of
scaling properties of the runoff series of the Yangtze River
basin (Zhang et al. 2008c). Hence we can use the value of
h(2) to determine its correlations and scaling properties.
3 Results
3.1 Scaling properties revealed by power spectra
Figure 3 demonstrates the power spectra of the daily runoff
records of Yellow River basin in a log S(f)–log (f) plot. The
spectra of the runoff series of these six stations are almost
in the same shape with different frequency regimes of
power–law-like nature. The difference is the crossover
frequency 1/f: 15 days for Tangnaihai station and Lanzhou
station; 18 days for Toudaoguai station; 25 days for
Longmen station and Huayuankou station and 39 days for
Lijin station. Therefore, inference can be obtained about
the changes of the crossover frequency with different basin
areas: shorter crossover frequency usually corresponds to
larger basin area, and vice versa. The finding is in good
agreement with that of the Danube River, being the second
longest river in Europe (2,850 km long with drainage area
of 817,000 km2): the crossover f shifts with basin area with
frequencies corresponding to approximately 1/f = 60 days
for Ceatal Izmail (807,000 km2) and Orsova
(576,232 km2), 20 days for Nagymaros (183,534 km2) and
10 days for Ingolstadt (20,001 km2) and Dillingen
(11,315 km2) (Dahlstedt and Jensen 2005). In the low
frequency domain, the power–law has a b exponent closing
to 0.8 for the Tangnaihai station, Lanzhou stations, Huayuankou station and Lijin station: b = 0.77 for Tangnaihai
station; b = 0.82 for Lanzhou station; b = 0.69 for Huayuankou station and b = 0.7 for Lijin station (Fig. 3a),
which corresponds to the logarithmic decaying correlation
Stoch Environ Res Risk Assess (2009) 23:1103–1111
1107
Fig. 3 Power spectra of the
daily streamflow records of
Yellow River basin in log S(f)–
log (f) plot. a Tangnaihai
station; b Lanzhou station; c
Toudaoguai station; d Longmen
station; e Huayuankou station
and f Lijin station. The dashed
lines indicate spectra exponents
b = 1 (1/f noise) and 2 (white
noise). Solid lines show the
local slope of the power spectra
curves
in the long time limit. This value range means that in the
longer time scale, the runoff fluctuations in the upper and
lower Yellow River basin are denoted as flicker (or 1/f)
noise (acceptable for b from 0.7 to 1.3, e.g. Zhu et al.
2006). The crossover frequency is lower in the lower
Yellow River than that in the upper Yellow River. In the
low frequency domain, the power law has the b close to 1
indicating logarithmic decaying correlations in the longer
time scale. In the time scales of about 30 days, the spectra
are dominated by the inverse power law, showing the
features of 1/f noise (Pritchard 1992). The power law has b
exponent of 0.61 and 0.54 for Toudaoguai and Longmen
station in the middle Yellow River basin.
In the higher frequency domain, the b values fall inside
the range of 1.7–2.55: b = 2.54 for Tangnaihai station;
b = 1.7 for Lanzhou station; b = 2.42 for Toudaoguai
station; b = 1.89 for Huayuankou station and b = 2.3 for
Lijin station, which indicate long-term correlations but
cease to follow a power–law. In the Mississippi River
(Dahlstedt and Jensen 2005), similar phenomenon was
identified: in the lower frequency, the power–law has an
exponent close to 1 corresponding to logarithmic decaying
correlation in the long time limit, and the power–law
exponent close to 3 can be identified in the higher frequency (Jensen 1998). The power law for the Longmen
station in the higher frequency domain has the b value of
1.2, close to 1 and in an intermediate range. This intermediate range spectrum can be interpreted as a Lorentzian
(red-noise, with f-2), or as a reminiscent of 1/f noise (Zhu
et al. 2006). Different scaling behaviors of the river flow
are identified in the different parts of the Yellow River
and in the different magnitude of frequency domains.
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Stoch Environ Res Risk Assess (2009) 23:1103–1111
exploring scaling properties of compartments of climatic
changes and hydrological series (Pandey et al. 1998; Zhang
et al. 2008c). In this paper, MF-DFA analysis was also
performed on the daily runoff series of the six hydrological
stations along the mainstem Yellow River. Figure 4 illustrates log–log plots of Fq(s) versus s of runoff series of the
six hydrological gauging stations in the Yellow River
basin. Based on log–log plots of Fq(s) versus s of runoff
series, one crossover point can be detected for six curves of
Fq(s) versus s. The timing for these crossover points is
between 338 and 407 days. It is attributed to the 1-yearperiod. To determine statistical properties of the fluctuations of runoff series, we compute the three scaling
exponents for smaller time scales. The h(2) values of the
runoff series of these six stations are 1.45 ± 0.0151
(Tangnaihai station), 1.3628 ± 0.0118 (Lanzhou station),
Generally, the runoff fluctuations in the upper and lower
Yellow River basin demonstrate similar scaling properties
and the runoff fluctuations in the middle Yellow River
basin exhibit different scaling properties: in the longer time
scale, the runoff demonstrates long-term persistence and in
the shorter time scale, however the runoff exhibits a Lorentzian or a reminiscent of 1/f noise (Zhu et al. 2006).
Different drainage areas, topography, land-use pattern,
drainage network morphology and different intensity of
human exploitation of water resources in the different river
reaches can be responsible for these differences.
3.2 Scaling properties revealed by MF-DFA
The temporal correlations are further studied by using MFDFA technique, and this method was widely used in
6
6
Lanzhou station
Tangnaihai station
0.5 ± 0.0231
5
Crossover point
4
3
1
0
1
2
Crossover point
4
3
1.3628 ± 0.0118
1.45 ± 0.0151
2
0.6276 ± 0.0291
5
log10 F(s)
log10 F(s)
Fig. 4 Log–log plots of Fq(s)
versus s of streamflow series of
Tangnaihai station, Lanzhou
station, Toudaoguai station,
Longmen station, Huayuankou
station and Lijin station of the
Yellow River basin
2
3
1
4
0
1
2
log10 s
6
0.6665 ± 0.0185
5
4.5
Crossover point
4
log10 F(s)
log10 F(s)
Longmen station
0.6674 ± 0.0207
5
3
4
Crossover point
3.5
1.2933 ± 0.0172
3
2
1.1980 ± 0.0098
2.5
1
0
1
2
3
2
4
0
1
2
6
4
6
Huayuankou station
Lijin station
0.6758 ± 0.0293
0.7268 ± 0.0206
5
log10 F(s)
5
Crossover point
4
3
2
3
log10 s
log10 s
log10 F(s)
4
5.5
Toudaoguai station
0
1
2
Crossover point
4
3
1.2261 ± 0.0062
log10 s
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3
log10 s
3
4
2
1.3131 ± 0.0114
0
1
2
log10 s
3
4
Stoch Environ Res Risk Assess (2009) 23:1103–1111
1.2933 ± 0.0172 (Toudaoguai station), 1.1980 ± 0.0098
(Longmen station), 1.2261 ± 0.0062 (Huayuankou station)
and 1.3131 ± 0.0114 (Lijin station), respectively. Based
on the relation between the exponent h(2) for small scales
and the Hurst exponent H, i.e. H = h(2) – 1, the h(2)
values of these six hydrological stations are all larger than
0 but are smaller than 0.5, indicating short-term memory.
Moreover, h(2) values of Tangnaihai, Lanzhou, and Lijin
are all larger than 0.3, and the h(2) values of the rest stations are all smaller than 0.3. It implies that scaling
properties of the runoff series in the middle Yellow River
basin are different from those of the upper and lower
Yellow River basin. This result is in good agreement with
those by spectra analysis technique (Fig. 3). The crossovers
indicate that the periods of the runoff series roughly equal
to 1 year. Therefore, we can say that the runoff series are
mainly controlled by precipitation variations. As for the
shifts of frequency revealed by spectra analysis, for the
shorter period, less than 1–2 months, periods of crossover
tend to be longer from the upper to the lower Yellow River
basin, it may be because of other influencing such as
human withdrawal of fresh water, regulations of water
reservoirs (Fig. 1 also illustrates the location of the reservoirs) other than climatic changes. The mechanisms for
runoff fluctuations are different from one rive to another in
the world. The Mary River in Australia is rather dry in
summer and the Gaula River in Norway is frozen in winter
(Bunde et al. 2006). Therefore no universal scaling
behaviors exist in the runoff series of the rivers over the
globe, which is different from the climate data with universal long-term persistence of observed temperature
variations (e.g. Eichner et al. 2003).
4 Discussions and conclusions
With the help of power spectra analysis and MF-DFA, we
studied systematically the scaling properties of the runoff
fluctuations within the Yellow River basin based on the
long daily runoff data of six hydrological stations.
Research results indicate that the runoff fluctuations exhibit
self-affine fractal behavior and memory properties at different time scales. In the Fq(s) versus s plot, the crossover
scales separate regimes with different scaling exponents,
showing the multiple scaling exponents or multifractal
properties in the hydrological series in the Yellow River
basin.
The crossover frequency (1/f) analysis results indicate
that lower crossover frequency usually corresponds to
larger basin area, and vice versa. Similar phenomenon was
found within the Danube River, the second longest river in
Europe. Besides, the b exponents in the lower frequency
domain and higher frequency domain are different
1109
significantly. The b exponent in the lower frequency
domain lies between 0.7 and 0.82 for the hydrological
stations in the upper and lower Yellow River basin and is
about 0.6 for the hydrological stations in the middle Yellow River basin. In the low frequency domain, the runoff
fluctuation is in the logarithmic decaying correlation in the
long time limit. The scaling properties of hydrological
series of Longmen station are different from those of the
rest stations of the Yellow River basin. This point can be
further confirmed by MF-DFA analysis. Increasing crossover frequency (i.e. 1/f) may be due to accumulative
regulation effect of water reservoirs and river channels
from the upper to the lower Yellow River basin. Increasing
intensity of human activities from the upper to the lower
Yellow River basin may also be responsible for the
increasing crossover frequency (i.e. 1/f).
MF-DFA analysis results indicate that the runoff variations of the Yellow River basin are characterized by shortterm memory. h(2) values indicate different scaling properties of the hydrological processes in the different reaches
of the Yellow River basin. Generally, similar scaling
properties can be identified in the runoff fluctuations in the
upper and lower Yellow River basin. And the runoff
variations in the middle Yellow River basin demonstrate
different scaling properties, particularly the hydrological
processes of the Longmen station. The h(2) value of the
runoff variations of the Longmen station is far less than 3,
being distinctly different from those of the runoff series of
the other hydrological stations, particularly of the stations
in the upper and the lower Yellow River basin. This point
is in agreement with the result obtained by spectra analysis
technique.
Different scaling properties are identified at the different
time scales and in the different reaches of the Yellow River
basin, indicating the different and uneven features of
topography, drainage sizes, land-use patterns, hydrogeology
and drainage network morphology, different intensity of
human exploitation of water resources in the different river
reaches of the Yellow River. The mechanisms for runoff
fluctuations are different from one rive to another in the
world. The Mary River in Australia is dry in summer and
the Gaula River in Norway is frozen in winter (Bunde et al.
2006). Therefore no universal scaling behaviors exist in the
runoff series of the rivers over the globe, which is different
from the climate data with universal long-term persistence
of observed temperature variations (e.g. Eichner et al.
2003). Similarly, the Yellow River is of large drainage area
and is featured by complicated and extremely uneven spatial and temporal distribution of precipitation variability,
evaporation change, and also different intensity of human
influences on runoff fluctuations. In the Yellow River basin,
intensifying human activities heavily influence the hydrological processes via increasing human withdrawal of
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freshwater, construction of water reservoir (see Fig. 1 for
the locations of the water reservoirs in the Yellow River
basin). The influence intensity and even the ways in which
the above-mentioned factors impact the hydrological series
of the Yellow River basin may decide the scaling properties
of the hydrological series of the study region. In the headwater region of the Yellow River basin, more influences of
the climatic changes are exerted on hydrological processes.
In the middle and lower Yellow River basin, influences of
human activities tend to be increasing. This is why the
scaling properties of runoff variations of the two stations in
the upper Yellow River basin are different from those in the
middle and the Yellow River basin. Furthermore, booming
agriculture in the middle Yellow River basin leads to more
human withdrawal of freshwater than in the upper and the
lower Yellow River basin, giving rise to different scaling
properties of runoff series in the middle Yellow River when
compared to those in the upper and the lower Yellow River
basin.
Our study also imply impacts of regulations of water
reservoir on scaling properties of the runoff series, i.e.
regulation of water reservoir seems to cause smaller h(2)
value. This point can be well proved by the locations of the
stations and water reservoirs and also the changes of h(2)
values (Figs. 1, 4). Even so, crossover analysis indicates
that annual cycles of the runoff series are kept unchanged
but periods of tens of days are different in different reaches
of the Yellow River basin. Thus, we can tentatively conclude that human activities, particularly human withdrawal
of freshwater, water reservoir, can modify the shorter
periods of runoff variations. However, long periods, e.g.
1 year, are mainly controlled by climatic variations. The
result of this study will be of scientific and practical merits
in regional hydrological modeling and basin-scale water
resource management in the arid and semi-arid regions of
China.
Acknowledgments The research was financially supported by the
innovative project from Nanjing Institute of Geography and Limnology, CAS (Grant No.: CXNIGLAS200814; 08SL141001),
National Natural Science Foundation of China (Grant No.:
40701015), National Scientific and Technological Support Program
(Grant No.: 2007BAC03A0604), and by the Outstanding Overseas
Chinese Scholars Fund from CAS (The Chinese Academy of Sciences). Thanks should be given to Yellow River Conservancy
Commission for providing hydrological data. Cordial thanks should
be extended to two anonymous reviewers and the editor-in-chief,
Prof. Dr. George Christakos, for their invaluable comments and
suggestions, which greatly improved the quality of this paper.
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