Investigation of the Complexity of Streamflow Fluctuations in a Large Heterogeneous Lake Catchment in China

Theor Appl Climatol DOI 10.1007/s00704-017-2126-5

ORIGINAL PAPER

Investigation of the complexity of streamflow fluctuations in a large heterogeneous lake catchment in China

Xuchun Ye1,2,3 & Chong-Yu Xu1,2 & Xianghu Li3 & Qi Zhang3

Received: 13 December 2016 /Accepted: 7 April 2017 # Springer-Verlag Wien 2017

Abstract The occurrence of flood and drought frequency is as the Hurst exponent and fitted parameters a and b from the highly correlated with the temporal fluctuations of streamflow q-order Hurst exponent h(q). However, the relationship be- series; understanding of these fluctuations is essential for the tween the width of the singularity spectrum (Δα)andwater- improved modeling and statistical prediction of extreme shed area is not clear. Further investigation revealed that in- changes in river basins. In this study, the complexity of daily creasing forest coverage and reservoir storage can effectively streamflow fluctuations was investigated by using multifractal enhance the persistence of daily streamflow, decrease the hy- detrended fluctuation analysis (MF-DFA) in a large heteroge- drological complexity of large fluctuations, and increase the neous lake basin, the Poyang Lake basin in China, and the small fluctuations. potential impacts of human activities were also explored. Major results indicate that the multifractality of streamflow fluctuations shows significant regional characteristics. In the 1 Introduction study catchment, all the daily streamflow series present a strong long-range correlation with Hurst exponents bigger River flow series represents a valuable historical record that than 0.8. The q-order Hurst exponent h(q)ofallthe carries lots of mechanism information about the hydrological hydrostations can be characterized well by only two parame- cycle. Investigation of inherent disciplinarian of streamflow se- ters: a (0.354 ≤ a ≤ 0.384) and b (0.627 ≤ b ≤ 0.677), with no ries is one of the basic ways to understand the dynamic charac- pronounced differences. Singularity spectrum analysis point- teristics of the hydrological cycle. According to well-evidenced ed out that small fluctuations play a dominant role in all daily global warming processes, atmospheric circulation and global streamflow series. Our research also revealed that both the hydrological cycle have shown a tendency towards being accel- correlation properties and the broad probability density func- erated gradually (Menzel and Bürger 2002;XuandSingh2005; tion (PDF) of hydrological series can be responsible for the IPCC 2013). According to this change, floods and/or droughts multifractality of streamflow series that depends on watershed may occur at modified severity and frequency, causing consider- areas. In addition, we emphasized the relationship between able socioeconomic loss and extensive degradation of the aquatic watershed area and the estimated multifractal parameters, such ecosystem (Bond et al. 2008; Zhang et al. 2008b; Vicuña et al. 2013;Wangetal.2014;Lietal.2016). In addition, the contin- uous intensified anthropogenic stresses in some areas increased * Xuchun Ye the complexity of the hydrological system and the risk of water [email protected] utilization (e.g., Zhang et al. 2012; Bonacci et al. 2016). Therefore, increasing attention has been paid to the investigation 1 State Key Laboratory of Hydrology–Water Resources and Hydraulic of hydrological variability and modeling for sustainable hydro- Engineering, Hohai University, Nanjing 210098, China environmental protection and disaster prevention. 2 Department of Geosciences, University of Oslo, 0316 Oslo, Norway Temporal fluctuations of streamflow are directly correlated 3 Key Laboratory of Watershed Geographic Science, Nanjing Institute with the occurrence of flood and drought frequency; under- of Geography and Limnology, Chinese Academy of Sciences, standing of these fluctuations can improve the statistical pre- Nanjing 210008, China diction and modeling of floods and droughts in river systems X. Ye et al.

(Bunde et al. 2003;Regoetal.2013). Since the mid-twentieth width of the singularity spectrum is not well related to the century, scientists have realized the existence of scaling be- watershed area, although significant differences can be found havior in nature for hydrological and climatological time se- in the spectrum width of different rivers all over the world. ries (Lovejoy and Schertzer 1991; Zhang et al. 2008a; Labat These multifractal differences may come from the heteroge- et al. 2011). The complex behavior of these series can be neity of river basins with different climates and landscapes. characterized by the so-called Hurst exponent (or scaling ex- Furthermore, studies reported two possible sources of the ponent), which was first proposed by Hurst in studying the multifractality of streamflow records: one is due to a broad long-range correlation of storage capacity of reservoirs in the probability density function (PDF) of the time series, and the Nile River (Hurst 1951). The Hurst exponent is a dimension- other one is due to different correlations in small- and large- less estimator of the self-similarity of a time series, which can scale fluctuations (e.g., Movahed et al. 2006). Although both be used as a measure indicator of time series data to follow a of the sources can be affected by basin factors, no studies have random walk or biased random walk process (Ihlen 2012). examined the effect of the watershed area on the source of Therefore, the exponent provides a feasible way to quantify streamflow multifractality. the correlation properties of time series and makes it possible As an important influencing factor, human activities have a to identify similarities between different phenomena (Chianca potential to exert tremendous influences on the hydrological et al. 2005). It has been reported that the property of persis- processes of a river and so the multifractality of streamflow tence widely exists in hydrological and climatological series series. The study of White et al. (2005) indicated that the water over different time scales (Hurst 1951; Zhang et al. 2008a; reservoirs had evident modification to the periodicity proper- Rego et al. 2013). However, this long-range dependence was ties of streamflows during the operation of dams in the described by a single spectral scaling exponent at earlier ap- Colorado River in the Grand Canyon. Zhang et al. (2009) plications. Due to the highly nonlinear characteristics of pointed out that the water reservoirs could obviously alter streamflow processes, a multifractal description is required the scaling properties at a larger time scale in the East River, to fully characterize this complexity (e.g., Pandey et al. a tributary of the Pearl River. Zhou et al. (2014)investigated 1998). In recent years, multifractal analysis has drawn consid- the effect of dam construction on hydrological processes in the erable attention, and a number of studies have reported the Yangtze River and revealed that the fractal dimension spec- long memory and multifractal properties of streamflow for trum showed a significant difference during the construction various rivers (e.g., Kantelhardt et al. 2006;Regoetal. of the Gezhouba Dam. In addition, after the construction of 2013). To describe the complex behavior of the time series, the Gezhouba Dam, the minimal multifractal dimension at the the multifractal detrended fluctuation analysis (MF-DFA) pro- Yichang station started to be less than that at the Cuntan sta- posed by Kantelhardt et al. (2002) from a modified version of tion, suggesting that the streamflow becomes less fluctuated. DFA has been applied to detect the multifractal properties of These studies mainly focused on the effect of huge water nonstationary time series that are related to geophysical reservoirs. Furthermore, these studies ignored the effect of phenomena. other human activities, such as land cover changes, and some- Temporal fluctuation of streamflow series is mainly con- times, different human activities may accumulate or counter- trolled by local climate condition (mainly precipitation) and act each other and their specific effect cannot be well highly impacted by other basin factors, such as watershed recognized. area, river network, plant coverage, and water conservancy Up to date, although numerous studies have reported the project. Previous studies have examined the effect of the multifractal properties of streamflows for various rivers, the watershed area on the multifractality of streamflow link between these properties and the physical processes/ fluctuation. For example, Zhou et al. (2007) analyzed the daily factors that influence the streamflow is not generally under- streamflows of four small agricultural watersheds ranging stood (Hirpa et al. 2010). For example, how will the changes from 0.01 to 334 km2 and reported that the multifractal pa- in the watershed area affect the strength of the multifractal rameters do not change with watershed areas. Mudelsee effect of streamflow series and the source of streamflow (2007) investigated the relationship between long memory multifractality? In addition, the effect of human activities, and basin size of 28 stations located in six major river basins such as changes in land use and reservoir storage, on around the world and got the result that larger basins have streamflow fluctuations and on the multifractal properties is stronger memory than small basins. Similarly, Hirpa et al. not clear. It is also necessary to understand the integrity and (2010) revealed that large watersheds have more persistent discrepancy of streamflow multifractality in some large het- streamflow fluctuations and stronger long memory than small erogeneous basins from a geographical perspective on hydrol- watersheds do. Also, they concluded that a tendency towards ogy. Undoubtedly, a better understanding of the statistical smaller multifractality strength with a larger watershed area characteristics of hydrological series in terms of multifractal can be expected in a relatively homogeneous catchment. parameters is of scientific and practical interest. With these However, Koscielny-Bunde et al. (2006) pointed out that the motivations, attempts were made in this study through Investigation of the complexity of streamflow fluctuations investigating the complexity of streamflow fluctuations by Ministry of Water Resources of China. To ensure quality con- using the multifractal framework in the large heterogeneous trol before analysis, the extreme values and consistency of the Poyang Lake catchment in China. The lake catchment, which data series were well tested, and corrections were made to the is located in the middle reach of the Yangtze River, has expe- detected error records. All the hydrostations belong to the five rienced great hydro-ecological environment changes under subriver basins, among which Waizhou, Xiajiang, and intensified anthropogenic stresses that resulted from rapid lo- Xiashan are located in the lower, middle, and upper reaches cal socioeconomic development (Guo et al. 2008; Zhang et al. of the Ganjiang River, respectively; Lijiadu and Meigang are 2011;Yeetal.2013). Especially, in the recent couple of years, located in the lower reaches of the Fuhe and Xinjiang Rivers; the lake catchment has attracted wide public concerns due to Dukengfeng, Tankou, and Hushan are located at the branches frequent droughts that occurred in the lake area, which caused of the Raohe River; and Wanjiabu belongs to one branch of a huge challenge to the health of hydro-ecological processes in the Xiushui River (Fig. 1). The gauged areas of the nine this region as well as the lower Yangtze River (Min and Zhan hydrostations varied from 1760 to 80,948 km2. Table 1 pre- 2012; Zhang et al. 2012; Yao et al. 2016). Therefore, this study sents the details of the rivers, hydrostations, gauged area, av- not only presents a procedure for investigation of the com- erage runoff, average annual runoff depth, and period of plexity of streamflow fluctuations in large heterogeneous measurements. catchments but also produces a result that is of great impor- In addition, daily precipitation records of six meteorologi- tance for the general understanding of the physical mechanism cal stations (Ganzhou, Ji’an, Zhangshu, Nancheng, Guixi, of streamflow fluctuations and for water resource manage- Jingdezhen) inside the catchment were also used in this study ment in the Yangtze River basin. (see Fig. 1a). The dataset of all the meteorological stations covers the period 1960–2010 with no missing data on the variables. 2 Study region and data

The Poyang Lake catchment, located in the middle reach 3 Methodology of the Yangtze River in southeast China (Fig. 1), belongs to a subtropical monsoon climate zone. The average an- 3.1 Multifractal detrended fluctuation analysis nual air temperature is 17.5 °C, and the average annual precipitation is 1665 mm. The largest freshwater lake in Multifractal detrended fluctuation analysis (MF-DFA) was China, the Poyang Lake, located in the northern part of used in this study to analyze the hydro-meteorological data. the catchment, is fed mainly by five rivers: Xiushui, This method is a generalization of detrended fluctuation anal- Ganjiang, Fuhe, Xinjiang, and Raohe, and discharges into ysis (DFA) in identification of the scaling properties of the q- the Yangtze River from a narrow outlet (Fig. 1a). The lake order moments of the time series, which may be nonstationary catchment covers an area of 162,225 km2 with elevation (Kantelhardt et al. 2002). Essentially, the MF-DFA method is varying from 2200 m (above sea level) in mountainous to determine the generalized Hurst exponent from a nonsta- regions to about 30 m in alluvial plains around the lake. tionary time series. For a time series xk (k =1,…, N), the Land use in the catchment consists of forest (46%), shrub- procedure of this method consists of five steps (Kantelhardt land (25%), cropland (25%), and small areas of pasture, et al. 2002): urban centers, and open water (Ye et al. 2011). The lake catchment is a typical agricultural region, in Step 1. Determine the Bprofile^ which 13% of the land area is being irrigated. Due to the rapid economic development and population explosion in the catchment, a total of 9530 reservoirs were built for water utilization across the catchment until 2007 (Ye et al. 2013). The three i ∑ x −x ; ⋅ i ; …; N biggest reservoirs inside the catchment, Zhelin Reservoir YiðÞ¼ ðÞk ðÞ¼ 1 ð1Þ k¼1 (50.17 × 108 m3) in the Xiushui River, Wan’an Reservoir 8 3 (11.16 × 10 m ) in the Ganjiang River, and Hongmen where x is the mean of series xk. Reservoir (5.24 × 108 m3) in the Fuhe River, are marked in Fig. 1, while numerous small reservoirs that spread in the Step 2. Divide the profile Y(i)intoNs =int(N/s)nonoverlap- catchment are not shown. ping segments of equal lengths s;int(N/s) denotes the The daily streamflow records used in this study correspond integer part of N/s. Since the length N of the series is to nine hydrostations across the lake catchment. These hydro- often not a multiple of the time scale s considered, a logical data were collected from the Hydrological Bureau of short part at the end of the profile may remain. To the Yangtze River Water Resources Commission of the retain this part of the series, the same procedure is X. Ye et al.

Fig. 1 a Topography and river network of the Poyang Lake catchment, with the nine hydrostations and six meteorological stations marked. b Location of the catchment in China

repeated starting from the opposite end. Thereby, for each segment v, v =1,…, Ns,and 2Ns segments are obtained. s noh i 2 Step 3. Calculate the local trend for each of the 2Ns seg- 2 1 F ðÞ¼s; v ∑ Y N−ðÞv−N s s þ i −yvðÞi ð3Þ ments by a least squares fit of the series. Then deter- s i¼1 mine the variance for each segment v, v = Ns +1,…,2Ns. Here, yv(i) is the fitting polynomial in segment m. Linear, quadratic, cubic, or higher order polynomials s 2 2 ; 1 ∑ Yv− s i −y i can be used in the fitting procedure (MF-DFA1, MF- F ðÞ¼s v fg½ðÞ1 þ vðÞ ð2Þ … m s i¼1 DFA2, MF-DFA3, ,MF-DFA ).

Table 1 List of hydrostations used in this study River Gauging Gauged area Average runoff Average annual runoff Period station (km2) (m3/s) depth (mm)

Ganjiang Waizhou 80,948 2164.87 841 1960–2010 Xiajiang 62,710 1646.72 828 1960–2010 Xiashan 15,975 439.78 868 1960–2003 Fuhe Lijiadu 15,811 390.24 777 1960–2010 Xinjiang Meigang 15,535 566.98 1159 1960–2010 Raohe Dukengfeng 5013 143.24 901 1960–2010 Tankou 1760 53.61 960 1960–2010 Hushan 6374 221.19 1094 1960–2007 Xiushui Wanjiabu 3548 109.39 981 1960–2010 Investigation of the complexity of streamflow fluctuations

Step 4. Average over all segments to obtain the qth-order in the data series. For monofractal data, the spectrum f(α)will fluctuation function, defined as be a single point, and both functions τ(q)andh(q) are linear.

. 3.2 Data preprocessing . ()1 q 2N s ÂÃq 1 2 2 Streamflow variation is strongly influenced by seasonal fac- FqðÞ¼s ∑ F ðÞs; v ð4Þ 2N s v¼1 tors and shows remarkable characteristics of the annual cycle, which may affect the accurate estimation of the scaling expo- where q ≠ 0ands ≥ m +2. nent (Hu et al. 2001; Kantelhardt et al. 2006;Bashanetal. 2008). Therefore, it is necessary to remove the seasonal com- h(q) Step 5. Determine the scaling behavior Fq(s) ~s of the ponent from the original series in order to address the corre- fluctuation function by the log-log plot of Fq(s)ver- lations. In practice, before the first step of MF-DFA, all the sus s for each value of q, where h(q) is the general- data are adjusted with the seasonal mean and standard devia- ized Hurst exponent, which can be determined by tion denoted xd and σd as proposed by Dahlstedt and Jensen the slope of logFq(s) and logs in a logarithmic plot. (2005). The seasonal adjustment is done by

In general, the time series is multifractal when the exponent xdðÞ; y −xd sx ¼ ð9Þ h(q)dependsonq whereas the time series is monofractal when σd h(q) is independent of q. For stationary time series, h(2) is x d,y identical to the well-known Hurst exponent H,andh(2) varies where ( ) denotes the measured value of daily streamflow d y … N x σ between 0 and 1. The exponent h(2) can be used to analyze at day number in year number =1, , y; d and d are correlations in time series. The scaling exponent H =0.5 further defined as means that the time series are uncorrelated; 0.5 < H < 1 im- N y H x 1 ∑ xd; y plies long-range correlation or persistence, and 0 < <0.5 d ¼ y ðÞ ð10Þ N y y¼1 implies short memory or anti-persistence. sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi The q-order Hurst exponent h(q) is only one of sev- N y hi 1 2 eral types of scaling exponents used to parameterize the σd ∑ xd; y −xd ¼ N y ðÞ ð11Þ multifractal structure of time series. The typical proce- y y¼1 dure in the literature of MF-DFA is to first convert h(q) After this processing, the adjusted data have σs = 1 and s to the q-order mass exponent τ(q) and thereafter convert = 0, which can be easily checked. τ(q)totheq-order singularity exponent α and singular- Figure 2 shows the fluctuation function of the daily ity dimension f(α)(Ihlen2012). streamflow series of four representative hydrostations. In this τðÞ¼q hqðÞq−1 ð5Þ practice, the MF-DFA1 (linear fitting of MF-DFA) method was applied with q = 2 and 10 ≤ s ≤ 4000 days. It can be seen 0 α ¼ τ ðÞq ð6Þ from the figure that there is obviously a crossover point appearing at about 360 days for the raw series without the f ðÞ¼α qα−τðÞq ð7Þ elimination of seasonal effect. However, this crossover According to the extended equation from the multiplicative vanished after the elimination processing for all the original cascade model that is widely applied in hydrological series data series. analysis (Kantelhardt et al. 2002), the q-order Hurst exponent h(q) can be fitted well by a two-parameter formula:

aq bq 4Results hq 1 − lnðÞþ ðÞ¼q q ð8Þ ln2 4.1 Multifractal features where a and b are the two parameters with the value between 0 In order to correctly estimate the multifractal properties of and1anda < b. The result can be further used to estimate the daily streamflow series, we first analyze the relationship be- singularity exponent α and singularity dimension f(α). In ad- tween the order m and q when the local trend function yv(i)is dition, the plot of α versus f(α) is referred to as the multifractal fitted with a different order of polynomial. The result shows Δα singularity spectrum. The width of the spectrum that the slopes of the three log10Fq(s) ~ log10s curves with (αmax − αmin) characterizes the strength of multifractal effects different order m (m = 1, 2, 3) are almost the same under X. Ye et al.

Fig. 2 The fluctuation function F2(s)vss of daily streamflow of four representative stations: a Waizhou, b Lijiadu, c Meigang, and d Wanjiabu. The diamonds and circles indicate the series with and without a seasonal trend, respectively. The vertical line indicates the value of s at the crossover point with a seasonal trend

different time scales. Therefore, hereafter, MF-DFA1 was all the hydrostations are bigger than 0.8. According to the used to analyze the multifractality in this study. meaning of h(2), we can conclude that the streamflow records With MF-DFA1 analysis, Fig. 3 presents the log-log plots of all the hydrostations across the Poyang Lake catchment are of the fluctuation function Fq(s) for the five different values of characterized by strong long-range correlation or long-term q at four representative hydrostations. It is noted that a scaling persistence. behavior exists in the fluctuation function. The regression After further analysis of daily precipitation by using the lines show obvious dependence on q values. This dependence same MF-DFA1 procedure, we obtained h(2) values of implies the presence of multifractality in the analyzed data. 0.589, 0.577, 0.574, 0.561, 0.573, and 0.554 for the six mete- Table 2 summarizes the scaling parameters that were used orological stations across the Poyang Lake catchment. As to parameterize the multifractal structure of streamflow series. these h(2) values are smaller than 0.6, precipitation series in For all the hydrostations, the time scale is in the interval 10 ≤ s- the study area are close to white noise and have very weak ≤ 4000 days. From Table 2, one can see that the h(2) values of long-range correlation. Therefore, it is clear that the long-range

Fig. 3 The fluctuation function F2(s)vss of daily streamflow of four representative stations for q = −10, −4, 0, 4, and 10: a Waizhou, b Lijiadu, c Meigang, and d Wanjiabu Investigation of the complexity of streamflow fluctuations

Table 2 The estimated multifractal parameters for the nine have a multifractal structure that is insensitive to local fluctu- hydrostations ations with large magnitudes. In contrast, the singularity spec- River Gauging station h(2) abΔα trum will have a long left tail when the time series have a multifractal structure that is insensitive to local fluctuations Ganjiang Waizhou 0.929 0.360 0.627 0.757 with small magnitudes. Therefore, singularity spectrum anal- Xiajiang 0.914 0.354 0.634 0.802 ysis revealed that the effect of small fluctuations plays a dom- Xiashan 0.872 0.371 0.646 0.739 inant role in daily streamflow series. This is also one of the Fuhe Lijiadu 0.879 0.368 0.632 0.715 important reasons for the long-range correlation of the daily Xinjiang Meigang 0.834 0.384 0.653 0.700 streamflow series in the study region. In addition, it seems Raohe Dukengfeng 0.824 0.381 0.666 0.754 from Fig. 5 that the hydrostations with a larger watershed area Tankou 0.810 0.382 0.677 0.776 and small magnitudes of fluctuations are more prominent in Hushan 0.860 0.375 0.651 0.752 the streamflow series as the right parts of the hooked curves Xiushui Wanjiabu 0.820 0.381 0.675 0.790 are relatively bigger than the left parts. For example, it is obvious that the right parts of the hooked curves of Waizhou and Xiajiang are relatively bigger than those of Wanjiabu and correlation of streamflow series in the Poyang Lake catchment Dukengfeng. The width of the spectrums (Δα) of the nine does not come from the long-term memory of precipitation. hydrostations ranges from 0.700 to 0.802 (Table 2), which h q By fitting ( ) from the multiplicative cascade model in the may reveal spatial differences in the complexity of the daily − ≤ q ≤ range 10 10 for all the nine streamflow series, we obtained streamflow. the respective parameters a and b of each hydrological station, and the results are listed in Table 2. The fitted parameters a (0.354 ≤ a ≤ 0.384) and b (0.627 ≤ b ≤ 0.677) of each 4.2 Source of multifractality hydrostation show a little difference. Figure 4 shows that in each case, the variations of h(q) for positive and negative values of q Normally, there are two different types of multifractality in can be well characterized by these two parameters. This result, to time series that can be distinguished. The first one is due to a large extent, indicates that only two parameters a and b are a broad probability density function (PDF) of the time series, sufficient to describe h(q), which strongly supports the idea of and the second one is due to different correlations in small- Buniversal^ multifractal behavior of river streamflow as sug- and large-scale fluctuations (Movahed et al. 2006). An easy gested by Lovejoy and Schertzer (1991). way to distinguish them is to analyze the correspondent shuf- Figure 5 presents the multifractal singularity spectrums for fled time series. Because the random shuffling series will de- the daily streamflow records of the nine hydrostations. The stroy the long-range correlation, one can expect hshuf (q) = 0.5 singularity spectrums are not symmetric, and all show a right if only correlation multifractality is present. However, if only hooked convex curve. As Ihlen (2012) pointed out, the singu- the broad PDF is responsible for the multifractality, h(q)=h- larity spectrum will have a long right tail when the time series shuf(q) = 0 can be expected. If both kinds of multifractality are

Fig. 4 The h(q) and their fitted lines (dotted line) for the nine hydrostations: a Waizhou, b Xiajiang, c Xiashan, d Lijiadu, e Meigang, f Dukengfeng, g Tankou, h Hushan, and i Wanjiabu. a and b are the least squares fitting parameters in Eq. 8 X. Ye et al.

Fig. 5 Singularity spectrums for daily streamflow records of the nine Fig. 7 Linear relationship between watershed area and the change range h q hydrostations of shuf( ) present, the shuffled series will show weaker multifractality It is worth noting that the possible source of multifractality when compared with the original series (Movahed et al. may vary according to the watershed area. As Fig. 6 presents, 2006). Waizhou and Xiajiang, showing an almost independent vari- h q q Figure 6 presents the comparison of h(q)vsq curves for the ation of shuf( )on , are the two hydrostations having the 3 2 original and shuffled daily streamflow series for all the nine largest watershed area (>60 × 10 km ) in the study region hydrostations. It can be seen that h(q) of the original series while the most dependent relationships are found for Tankou behaves as a monotonically decreasing function of q for all the and Wanjiabu stations, which have the smallest watershed 3 2 stations. This behavior is associated with the presence of area (<4 × 10 km ). On this basis, we statistically analyzed h q − ≤ q ≤ multifractality in the studied series. For the shuffled series, the change range of shuf( )within 10 10 of the nine hydrostations in the study region. Figure 7 shows a good lin- hshuf(q)vsq curves show to be almost independent of the q p R2 value and approximate to 0.5 only at Waizhou and Xiajiang, ear relationship ( <0.01, = 0.828) between the watershed h q which indicates that the multifractality of the two area and the change range of shuf( ). According to the fact h q hydrostations is mainly due to different fluctuations of that one can expect shuf( ) = 0.5 when only correlation small- and large-scale correlations while for the other multifractality is present, we herein define the change range h q hydrostations, h (q)vsq curves show to be somewhat q of 0.2 as the critical value that whether shuf( ) has changed shuf q value dependent. Especially, the dependent relationship is significantly or not according to values (this is also equal to h q − ≤ q ≤ rather obvious for Tankou and Wanjiabu stations (Fig. 6g, i). shuf( ) that varied between 0.4 and 0.6 within 10 10). This result shows that the multifractality of the seven The result from Fig. 7 indicates that the multifractality of the hydrostations is not removed by the shuffling series, and streamflow series of the hydrostation that has a watershed area 3 2 therefore, their multifractalities originate from the correlation larger than 44 × 10 km is probably due to different fluctua- properties as well as PDF of the hydrological series. tions of small- and large-scale correlations whereas both

Fig. 6 The generalized Hurst exponents h(q) for the original and shuffled series of the nine stations: a Waizhou, b Xiajiang, c Xiashan, d Lijiadu, e Meigang, f Dukengfeng, g Tankou, h Hushan, and i Wanjiabu. The time scale s is in the interval 10 ≤ s ≤ 4000 days Investigation of the complexity of streamflow fluctuations

indicates that the long-range correlation or persistence of daily streamflow series has been enhanced. Different from the change in the exponent h(2), the width of the singularity spectrums (Δα) of all the hydrostations did not show the same change direction. Δα values of Waizhou, Xiashan, Meigang, and Dukengfeng showed a little increase, indicating a strengthened multifractal effect in streamflow series, while the other five hydrostations showed a slight decrease, which indicates a weakened multifractal effect. Figure 9 further presents the shape changes of singularity spectrums before and after 1990 for the nine hydrostations. From the figure, we can see that all the hydrostations show a slight right move of the Fig. 8 Changes in forest coverage and reservoir storage in the Poyang Lake catchment. The vertical dashed line divides the study period into spectrum or relatively increased right part of the spectrum two parts where forest coverage and reservoir storage in the catchment are after 1990. Overall, this result implies that the effect of human obviously different activities in the catchment decreased the hydrological complexity of large fluctuations while increased that of small sources can be expected for the hydrostation that has a water- fluctuations. shed area smaller than 44 × 103 km2.

5Discussion 4.3 Effect of human activities Observed streamflow fluctuations are the results of the com- Over the past few decades, the Poyang Lake catchment has plex interactions between precipitation input and the basin been subjected to intensive human activities. Figure 8 shows factors that modify it (Pandey et al. 1998). Watershed area is that forest coverage and reservoir storage in the catchment one of the basin factors that have important impact on the have been changed greatly. Especially, this change is quite multifractality of streamflow series (Mudelsee 2007; Hirpa obvious before and after 1990. Because the effects of specific et al. 2010). Here we statistically analyzed the relationship human activities may accumulate or counteract each other, between estimated multifractal parameters and the corre- they are not easily distinguished by visual inspection. In this sponding watershed areas. As presented in Fig. 10a, the expo- study, we first divided the streamflow series into two parts: nent h(2) shows a strong increasing relationship with water- before 1990 and after 1990, according to the changes in forest shed area (p <0.01,R2 = 0.795). This result confirms that coverage and reservoir storage in the catchment during the large watersheds have more persistent streamflow fluctuations past decades, and then compared the multifractal properties and stronger long memory than small watersheds do, which is that may be affected by human activities. also reported by Hirpa et al. (2010). Our study further revealed h As listed in Table 3, the calculated exponent (2) of all the that both parameters a (p <0.05,R2 =0.742)andb (p <0.01, hydrostations shows varying degrees of increase after 1990, R2 = 0.567) show a decreasing linear relationship with water- with comparison to the former time period. This result shed area (Fig. 10b, c). For these two parameters, many stud- h Δα ies have reported that they can be regarded as the multifractal Table 3 The estimated values of (2) and before and after 1990 for B ^ the nine hydrostations fingerprint of a considered river and particularly important when checking models for river flows (e.g., Koscielny-Bunde River Gauging station Before 1990 After 1990 et al. 2006; Hirpa et al. 2010). Additionally, there is no pronounced difference between the fitted parameters a and b of h(2) Δα h(2) Δα all the hydrostations (0.354 ≤ a ≤ 0.384, 0.627 ≤ b ≤ 0.677), Ganjiang Waizhou 0.925 0.801 0.930 0.809 which may well suggest regional characteristics of Xiajiang 0.905 0.869 0.921 0.809 multifractality in the Poyang Lake catchment, while spatial Xiashan 0.875 0.793 0.870 0.852 discrepancy may correspond to the heterogeneous landscape Fuhe Lijiadu 0.842 0.834 0.908 0.735 and watershed areas among different river subbasins. Xinjiang Meigang 0.811 0.786 0.847 0.808 However, more studies are needed to further confirm this re- Raohe Dukengfeng 0.801 0.819 0.830 0.853 lationship in varied regions with different climates and Tankou 0.802 0.813 0.809 0.801 landscapes. h a b Hushan 0.824 0.833 0.899 0.831 In addition to the three parameters ( (2), ,and ), Fig. 10 Xiushui Wanjiabu 0.791 0.825 0.849 0.821 presents the relationship between the width of the singularity spectrum (Δα)andwatershedarea.Itcanbeseenfrom X. Ye et al.

Fig. 9 Changes in singularity spectrums before and after 1990 for the nine hydrostations: a Waizhou, b Xiajiang, c Xiashan, d Lijiadu, e Meigang, f Dukengfeng, g Tankou, h Hushan, and i Wanjiabu

Fig. 10dthatΔα shows a slight increase with watershed area; bigger than that of the Waizhou station in the lower reach however, this relationship has no statistical meaning, with (Table 2). p > 0.5 and R2 = 0.051. Normally, due to the effectiveness A previous study by Zhang et al. (2008a) pointed out that of the filter function of larger watersheds, a narrower singu- the multifractality of the streamflow series of four larity spectrum of streamflow series is expected (Hirpa et al. hydrostations with very large watershed areas in the Yangtze 2010). However, our observation did not well support this River basin is mainly due to the correlation properties within conclusion, and the same result is also reported by the hydrological series. However, a study by Rego et al. Koscielny-Bunde et al. (2006). One possible explanation for (2013) reported that the multifractality of some Brazilian riv- this may lie in the significant heterogeneous landscapes as ers may originate from both the correlation properties and the well as the complicated river network that exists in different PDF of the hydrological series. Up to date, there is no study subbasins across the catchment. For example, Δα of the that examined the correlation between the watershed area and Xiajiang station in the middle reach of the Ganjiang River is possible source of multifractality. In this study, we quantified

Fig. 10 Relationship between watershed area and the multifractal exponents: a h(2), b a, c b,andd Δα Investigation of the complexity of streamflow fluctuations this relationship by a linear regression function. The streamflow series, from which it can be concluded that multifractality of streamflow series from hydrostations with multifractalities of streamflow series from hydrostations watersheds bigger than 44 × 103 km2 is more likely to origi- with watersheds bigger than 44 × 103 km2 are more like- nate from correlation properties, while both the correlation ly to originate from correlation properties, while both the properties and the PDF of the hydrological series can be ex- correlation properties and the broad PDF of the hydro- pected for those small watersheds. logical series can be expected for those smaller water- Human activities have a potential to exert tremendous in- sheds in the study area. In addition, we also emphasized fluences on the hydrological processes of a river and the the relationship between watershed area and the estimat- multifractality of streamflow series (Zhou et al. 2014). ed multifractal parameters. The Hurst exponent increases However, the result of our study pointed out that the regularity obviously with increasing watershed area; both parame- of increased forest coverage and reservoir storage in the ters a and b show a decreasing linear relationship with change in spectrum widths after 1990 is not clear. The reason watershed area. However, due to spatial heterogeneity of for this is that in the Poyang Lake catchment, numerous res- landscapes in the catchment, the relationship between the ervoirs are scattered in the upper and middle reaches of small width of the singularity spectrum (Δα)andwatershed tributaries. Their effects on the multifractality strength of the area is not clear. streamflow series observed in the mainstream are not sensi- (3) We confirm that human activities (mainly changes in tive. Anyway, their filter effect on streamflow fluctuations can forest coverage and reservoir storage) have exerted a still be reflected by the change in the shapes of the singularity certain influence on the multifractality of streamflow se- spectrums of the hydrostations. A modeling study in the ries. The calculated Hurst exponent of all the Xinjiang River subbasin in the study area indicated a decrease hydrostations in the study catchment shows varying de- in annual streamflow when forest coverage increased (Guo grees of increase according to increasing forest coverage et al. 2008). In addition, the decrease in streamflow caused and reservoir storage after 1990, with comparison to the by increased forest coverage is particularly strong in the wet former time period. Their effect on streamflow fluctua- season through the increase of evapotranspiration, but tions can also be reflected by the change in the shapes of streamflow will increase in the dry season due to increased the singularity spectrums of all the hydrostations. groundwater contribution (Guo et al. 2008). However, their effects on the multifractality strength of the streamflow series are not sensitive. Overall, the effect of human activities after 1990 decreased the hydrological 6 Conclusion complexity of large fluctuations while increased that of small fluctuations. In this study, we investigated the complexity of streamflow fluctuations by using the multifractal framework in a typical heterogeneous lake catchment in China. Seasonal components 2)Acknowledgments This work was financially supported by of all observed daily streamflow series were eliminated, and a the Key Laboratory of Watershed Geographic Sciences, Nanjing linear fitting procedure (MF-DFA1) was applied in detrended Institute of Geography and Limnology, Chinese Academy of fluctuation analysis. Major conclusions are as follows: Sciences (WSGS2015003), Fundamental Research Funds for the Central Universities (XDJK2016C093), National Natural (1) The multifractality of streamflow fluctuations shows sig- Science Foundation of China (41571023), and Natural Science nificant regional characteristics. In the study catchment, Foundation of Jiangxi Province (20161BAB203103). observed daily streamflow series present strong long- range correlations with calculated Hurst exponents of References all the hydrostations bigger than 0.8. 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