Spatial Variability and Periodicity of Precipitation in the Middle Reaches of the Yellow River , China

1College of Water Resources and Architectural Engineering, Northwest A&F University, Yangling, Shaanxi 712100, China 2Institute of Soil and Water Conservation, Northwest A&F University, Yangling, Shaanxi 712100, China 3Institute of Soil and Water Conservation, Chinese Academy of Sciences and Ministry of Water Resources, Yangling, Shaanxi 712100, China 4School of Atmospheric Science, Nanjing University of Information Science & Technology, Nanjing 210044, China


Introduction
Time series analysis of hydroclimatic observations provides direct information about hydrological changes and, therefore, plays a key role in understanding and managing water resources.Increasing knowledge is needed on large-scale variations of hydrological variables and water cycle parameters in order to assess their potential impact on water resources availability and hydrologic hazards.Precipitation is a major factor in agriculture and in recent years interest has increased in learning about precipitation variability for periods of months to years.Therefore, the spatial and temporal variability of the precipitation time series is important from both the scientific and practical point of view [1,2].
For the last several years, a number of researches have been used to measure rainfall variability with various approaches in many different regions in the world; for example, Barros et al. [3] showed that most of the annual precipitation trends since 1960 in the Southern South America to the east of the Andes region could be described by the first two rainfall eigenvectors of the principal component analysis (PCA).Coulibaly [4] used the wavelet and cross-wavelet to identify and describe spatial and temporal variability in Canadian seasonal precipitation and gained further insights into the dynamical relationship between the seasonal precipitation and the dominant modes of climate variability in the northern hemisphere.Feidas et al. [5] analyzed the precipitation in Greece and found that there was a link between precipitation variability in Greece and the Mediterranean pressure oscillation.Modarres and da Silva [6] analyzed the time series of annual rainfalls, number of rainy-days per year, and monthly rainfall of 20 stations by the Mann-Kendall test to assess climate variability in the arid and semiarid regions of Iran.Liu et al. [7] investigated the spatial and temporal patterns of the precipitation trends in the Yellow River Basin, China, and showed a decreasing trend in most of stations.Li et al. [8] evaluated the variation of annual and seasonal precipitation by using the Mann-Kendall test and Hurst exponent methods in Xinjiang, China.Xue et al. [9] decomposed the autumn precipitation series by using ensemble empirical mode decomposition (EEMD) method in the Weihe River Basin and got the period characteristics of multiscales in precipitation.Yu et al. [10] investigated precipitation signals and its impact assessment on soil hydrological process by using Hilbert-Huang transform and continuous wavelet transform approaches.
The Yellow River is noted for its small water and huge sediment discharge in the world.The middle reaches of the Yellow River flow through the Loess Plateau, rainfall is one of the most important reasons causing the soil erosion in this region.The water from the middle reaches accounted for 44.3% of the Yellow River streamflow, but the sediment has accounted for 88.2% of the Yellow River sediment [11].The annual average sediment discharge of the Yellow River was 16 × 10 8 t (according to the observed data from Shan County hydrological station during .In recent years, many studies have reported significant decrease beyond expectations in streamflow and sediment discharge in the Middle Yellow River [11][12][13][14][15][16][17].The observed average annual streamflow form Toudaoguai station to Tongguan station (located in the Middle Yellow River) was 124.9 × 10 8 m 3 during 1952-2013, while it was 68.9 × 10 8 m 3 during 2000-2013.The 56.0 × 10 8 m 3 decrease in streamflow accounted for 44.8% of the average annual streamflow (1952-2013) (the Ministry of Water Resources of China, 2014).
So far, most of the studies for precipitation variation were focused on analysis in yearly, while fewer studies were conducted on the periodicity of precipitation time series for identifying climate change signals in the middle reaches of the Yellow River.The periodicity of precipitation is a key factor for soil erosion, especially in the Loess Plateau.Therefore, the objectives of this study were to investigate temporal and spatial variation characteristics of precipitation of flood season precipitation (  ) and precipitation of main flood season ( mf ) using monthly precipitation datasets from 1958 to 2013 and to explore the trends of   and  mf in the future by Hurst exponent.The results may have important implications on water management and environmental phenomena, such as soil instability, erosion, and desertification.

Study Region.
The study area is situated in the arid and subhumid Loess Plateau region in the middle reaches of the Yellow River (MRYR), between Hekouzhen (Toudaoguai) and Tongguan section, with an area of 290 000 km 2 between 104 ∘ -113 ∘ E and 32 ∘ -40 ∘ N, accounting for 38% of Yellow River Basin area.It encompasses parts of 159 counties, across the Ningxia Hui Autonomous Region (Ningxia), Shanxi, Inner Mongolia Autonomous Region (Inner Mongolia), and the Gansu and Shaanxi provinces.The natural environment is featured by a gradual increase in precipitation from northwest to southeast, concentrated mainly in summer, and dominated usually in the form of rainstorms.A digital elevation model (DEM) of the region is shown in Figure 1.The annual sediment transportation into the Yellow River accounts for 90% of the total sediment discharge, making the MRYR one of the most soil-eroded areas of the Loess Plateau.The area has thick (50-80 m) loess layers.The particle composition is mainly fine sand, silt (up to 50% of the total), and clay.The loess has high porosity and is prone to landslides.The soil is typical black loam soil with a loose structure that is readily degraded [18].

Data.
The daily and monthly rainfall data of 26 national meteorological stations (apart from the mountain station) used in this work were extracted from the National Meteorological Information Centre (NMIC) (Table 1 and Figure 1), including daily precipitation (  , mm), monthly precipitation (  , mm), and yearly precipitation (  , mm) from 1958 to 2013.The dataset has been quality ensured by NMIC.We performed further routine quality assessment and error correction procedures on the data following methods described by Peterson et al. [19].Missing values are infrequent (during certain months in 1968 precipitation data was missing from Wuqi station, during certain months in 1969 precipitation data was missing from Lishi station, and during one month in 2013 precipitation data was missing from Baoji station).The missing data in these three stations were processed in the following ways: (1) if data were missing only for 1 day, the missing data were replaced by the average value of its neighboring days and (2) if consecutive days were missed, those were estimated by simple linear interpolation method using the data of neighboring stations ( 2 > 0.95) [20,21].Due to urbanization, data from Yaoxian station were used instead of Tongchuan station after 1999; data from Maiji station were used instead of Tianshui station after 2004; data from Fengxiang station were used instead of Baoji station after 2005; data from Jinghe station were used instead of Xi'an station after 2006.Considering the hydrogeology condition in study area, the distribution of precipitation in rainy season is the driving force for soil erosion and flood for this region, because it is well known that individual rainfall events can contribute approximately 60% to 90% of the yearly rainfall total [22].In general, the flood season refers to June-October, and main flood season refers to July-August [17,23], in the Loess Plateau.Consequently, this study focused only on precipitation in flood season and main flood season, which are critical agricultural months in the study area.

Empirical Orthogonal Function.
The empirical orthogonal function (EOF) had been used in atmospheric science since the early 1950s and EOF techniques are deeply rooted in statistics, especially in principal component analysis [24,25].It provides a compact description of the temporal and spatial variability of a dataset of a single variable in terms of orthogonal components or, also called, statistical "modes." The main features of spatial variability can be outlined using EOF analysis.Essentially, the EOF reduces the data dimensionality, and the smaller set of uncorrelated variables is much easier to understand and further analyze than a larger set of correlated variables.Therefore, the EOF has become a popular tool in meteorology, geology, and geography [26][27][28].More details on EOF can be found in Kim et al. [29].

Ensemble Empirical Mode
Decomposition.EEMD, a fundamental part of the Hilbert-Huang transform, is an adaptive method that decomposes a time series into intrinsic mode functions (IMFs) ranging from high-to low-frequency modes, each of which represents a specific frequency range, and a long-term trend [30].The first IMF has the highest frequency and so on.The sum of these IMFs and the long-term trend reproduces the original time series.The length of the time series determines the number of IMFs.It improves upon the empirical mode decomposition (EMD) method [31,32], which is an adaptive data analysis method to decompose any complicated data series into a finite and often small number of amplitude-frequency modulated oscillatory components.
Based on EMD algorithm [31], EEMD method can be briefly described as follows [33]: Step 1: set the ensemble number and the amplitude of the added white noise; Step 2: add a white noise series to the targeted data with the set amplitude; Step 3: decompose the data with added white noise into IMFs; Step 4: repeat Steps 2 and 3 again and again, but with different white noise series each time; then, the final ensemble means of corresponding IMFs of the decompositions are obtained.The basics and effectiveness of this method applied to geophysical data analyses have been documented in many recent works [32][33][34].For more details about EMD and EEMD, refer to Wu and Huang [33].In this study, the ensemble number is set to 100 and the amplitude of added white noise is set to 0.2 times of standard deviation of that of the data based on suggestion by Wu and Huang [33].

Hurst Exponent Analysis.
The fractal theory for time series research has been widely applied in climate change, geography, and other fields [35], used to analyze future precipitation trend in this study.The Hurst exponent, estimated by R/S analysis, is used as a measure of the long-term memory of the time series.Hurst's index () has a strong ability to predict future trends for a time series in relation to past trends, and it has been used to predict hydrological and climatological processes [8,36]. ranges between 0 and 1, where (1)  = 0.5 means the various essential elements are completely independent and the change is random; (2) 0.5 <  < 1 shows that the time series has a long-term trend which is likely to continue in the future; the closer the  value to 1, the stronger the continuity; and (3) 0 <  < 0.5 also indicates the time series has a long-term trend.However, its future tendency will be the opposite; the closer the  value to 0, the stronger the reverse tendency.

Annual Variability of Flood Season Precipitation and Main
Flood Season Precipitation.The mean annual precipitation (  ), precipitation of flood season (  ), and precipitation of main flood season ( mf ) were 499.9 mm, 383.3 mm, and 211.0 mm in the research region, respectively (Table 2).The   and  mf account for 76.67% and 42.21% of the annual mean precipitation, respectively.The difference between the maximum and minimum values for each variable was small.The coefficients of variation (CVs) of   ,   , and  mf were 0.166, 0.190, and 0.254, respectively, showing that all of their changes are stable.Both the annual average precipitation of flood season and the annual average precipitation of main flood season had no significant trends with a linear increase from 1958 to 2013 (Figure 2).Moreover, there was significant ( < 0.01) synchronized variation between the   and  mf .

Spatial Patterns of the Precipitation by EOF.
The EOFs of the precipitation series in flood season were calculated during 1958-2013.The significance of eigenvectors derived from EOF was tested with North's method [37].The results showed  that the first three eigenvectors were valuable signals both in flood season and main flood season.The first three EOFs during the study period explained approximately 45.2%, 20.8%, and 6.0% of total variance, respectively.It is generally assumed that those EOFs, whose accumulated variance is more than 70% of the total variance, have significance in explaining the original data [28,29].In this study, the first three EOFs explained 72% of the total variance in flood season precipitation.Therefore, the first three EOFs were used in this study to explain the original data.The EOFs of the precipitation series in main flood season were also calculated during the study period.The first three EOFs explained 71.8% of the total variance in main flood season.Therefore, the first three EOFs of precipitation in flood season were also used in this study to explain the original data.
The first EOF values for   and  mf were both positive (Figure 3), which indicated the precipitation was affected by the East Asian monsoon.The second EOFs for both   and  mf indicated that precipitation had obvious northsouth differences, and the zero contours for   and  mf were High: 0.37 both located in the area around Linfen, Luochuan, Xifeng, and Pingliang.It means that the trend in the precipitation variation is opposite for the northern and the southern areas of the study area, which reveals that precipitation increased in the northern area and decreased in the southern area.
In the third EOFs, the zero contours for   and  mf were both located in the area around Yulin, Suide, Luochuan, and Wugong, which indicated an approximately east-west direction.

Decomposing Annual Flood Season and Main Flood
Season Rainfall Time Series Using EEMD.By employing the EEMD technique, the original annual   and  mf time series from 26 stations are decomposed into four independent IMFs and one residue, respectively.For example, the results for the Suide station are illustrated in Figures 4 and 5.It can be observed that precipitation data are decomposed into IMFs, and we can also see that the IMFs present changing frequencies, amplitudes, and wavelengths.For all IMFs, IMF1 has the maximum amplitude, highest frequency, and shortest wavelength.The following IMF components decrease in the amplitude and frequency and increase in the wavelength.The last residue (RES) is a mode slowly varying around the longterm average.There are few periodic variabilities of   in the MRYR.Both the periodicity properties of regional precipitation series and the periodicity properties of   at each station show few periodic variabilities (Table 3).The periodicity of IMF1 at each station ranges from a minimum of 2.3 to a maximum of 3.1, the periodicity of IMF2 at each station ranges from a minimum of 4.3 to a maximum of 6.2, the periodicity of IMF3 at each station ranges from a minimum of 8 to a maximum of 14, and the periodicity of IMF4 at each station ranges from a minimum of 18.6 to a maximum of 48.1.However, only the periodicity of IMF2 at Linfen station and the periodicity of IMF4 at Suide, Lishi, and Yan'an station pass the statistical significance.
The periodic variability of  mf at each mode (Table 4) is similar to that in   .Only the periodicity of IMF1 at Hengshan station, the periodicity of IMF2 at Xifeng station, the periodicity of IMF3 at Suide and Xixian station, and the periodicity of IMF4 at Lishi, Yan'an, Yuncheng, and Baoji station pass the statistical significance.It also means that there is less periodic variability of  mf in the MRYR.
Though there were few stations passing the significant test for precipitation period, the IMF2 component of Linfen station for   , the IMF1 component of Hengshan station, and the IMF2 component of Xifeng station for  mf in Tables 3 and  4 showed that there were obvious periodic variability within 3-4 years and 6-8 years, respectively.According to multiple timescale analysis of sea surface temperature (SST) data in Niño-3 region (5 ∘ N-5 ∘ S, 150 ∘ -90 ∘ W) during 1881-2002 [38], there was also obvious periodic variability within 3-4 years and 6-8 years.Hence, the high-frequency components of annual flood season and main flood season precipitation series were consistent with SST which demonstrated that the short-term variation of annual flood season and main flood season precipitation in some area of the study area may be affected by SST.Further study will be required to explain the observed precipitation periodicities associating with the influencing climatic factors.  in the variability of precipitation.Most of the stations in the study area have long-term persistence.The stations where there is no long-term persistence in the variability ( < 0.5) are Wuzhai and Pingliang station.The main flood season precipitation in the region shows the  value range from a minimum of 0.51 to a maximum of 0.72, indicating the trend will be maintained in the future.The  value of 0.44 for Pingliang station indicates an opposite precipitation trend in the future.The present trends of   and  mf for most of the stations are decreasing (see Supplementary Material available online at http://dx.doi.org/10.1155/2016/9451614).According to above results of Hurst index, the trends of future precipitation in these stations will be persistent.

Conclusions
In this paper, analysis of the trends, periodic variability, and temporal-spatial patterns of the flood season precipitation and main flood season precipitation in the middle reaches of the Yellow River support the following conclusions.

Figure 1 :
Figure 1: Location of the selected 26 meteorological stations on a DEM of middle reaches of the Yellow River, China.

Figure 2 :
Figure 2: Mean annual flood season and main flood season precipitation in the middle reaches of the Yellow River during 1958-2013.

Figure 3 :Figure 4 :
Figure 3: First three EOFs of the   and  mf in MRYR.

Figure 5 :
Figure 5: EEMD of the  mf time series from 1958 to 2013 at the Suide station.

Table 1 :
Geographical coordinates, annual mean precipitation (  ) for 26 meteorological stations across the middle reaches of the Yellow River.

Table 2 :
Statistics for annual precipitation (  ), precipitation of flood season (  ), and precipitation of main flood season ( mf ) of the Middle Yellow River from 1958 to 2013.

Table 3 :
The mean periods of various time-scale components for   during 1958-2013 in the MRYR obtained by the EEMD.
Note: * and * * represent significant trend tested at 0.1 and 0.05 significant levels, respectively.
4.4.Future Trend of Flood Season and Main Flood Season Precipitation.The Hurst index provides statistical predictions concerning future trend.The Hurst index based on the   and  mf time series at 26 stations from 1958 to 2013 is shown in Table 5.The  value of ranges from a minimum of 0.49 to a maximum of 0.73.An  value which is greater than 0.5 refers to the persistence of the series, which indicates the same trend in the time series in the future, with a greater value for more persistence.This means that there is a long-term persistence

Table 4 :
The mean periods of various time-scale components for  mf during 1958-2013 in the MRYR obtained by the EEMD.
Note: * and * * represent significant trend tested at 0.1 and 0.05 significant levels, respectively.