It is difficult to effectively identify and eliminate the multiple correlation influence among the independent factors by leastsquares regression. Focusing on this insufficiency, the sediment deposition risk of cascade reservoirs and fitting model of sediment flux into the reservoir are studied. The partial leastsquares regression (PLSR) method is adopted for modeling analysis; the model fitting is organically combined with the nonmodelstyle data content analysis, so as to realize the regression model, data structure simplification, and multiple correlations analysis among factors; meanwhile the accuracy of the model is ensured through cross validity check. The modeling analysis of sediment flux into the cascade reservoirs of LongLiu section upstream of the Yellow River indicates that partial leastsquares regression can effectively overcome the multiple correlation influence among factors, and the isolated factor variables have better ability to explain the physical cause of measured results.
Sediment deposition and the balance problems [
Therefore, research of the risk of sediment deposition, the amount of sediment, and the balance of silt erosion and deposition in river basin cascade development mode can optimize sediment configuration, protect the built reservoir’s usable capacity, extend the life service of the reservoir, and operate cascade reservoirs correctly. This has farreaching significance for the overall efficiency of the cascade development.
In the research on prediction model of sediment erosion’s changes, the domestic and foreign researchers have achieved some achievement, and the prediction models can be roughly divided into three categories: first: conceptual model of sediment deposition, such as regression analysis, mathematical statistics method [
Partial leastsquares regression (PLSR) is a new multivariate data analysis method presented from application areas and mainly adopted for regression modeling analysis of single or multiple dependent variables on the multiple independent variables; it can effectively solve many problems which ordinary regression cannot solve. PLSR can also organically combine the basic functions of regression modeling, principal component analysis, and canonical correlation analysis. Within an algorithm, it can achieve regression modeling data structure simplification and correlation analysis between the two groups of variables. PLSR has been widely applied in many areas. Chun and Keleş used PLSR for high dimensional genomic data analysis and they proposed an efficient implementation of sparse partial leastsquares regression and compared it with wellknown variable selection and dimension reduction approaches via simulation experiments and proved the practical utility of sparse partial leastsquares regression in a joint analysis of gene expression and genomewide binding data [
Based on analysis of the complex causal relationships between the amount of sediment and their influencing factors, this paper proposed to adopt PLSR method to eliminate interference caused by multiple correlations and uncertainties of influencing factors of sediment flux into the reservoir in order to achieve model fitting and prediction of sediment amount of the reservoir in the cascade development mode, providing reliable technical support for joint dispatching, optimization sediment configuration, and extending the life of reservoir.
The main contents of this paper are as follows. The second section is the risk analysis of sediment deposition influence under the mode of drainage basin cascade development. The third section introduces the modeling ideas and procedures of sediment flux into the reservoir PLSR model. The fourth section selects the most representative cascade reservoir upstream of the Yellow River as the modeling instantiated application and modeling analysis. Finally, the results obtained are discussed.
The important means to prevent siltation of the Yellow River is strengthening its scientific use and management to ensure the ecological base flow and sediment transport. The main factors influencing the Yellow River sediment deposition are as follows [
The comprehensive analysis showed the risk of sedimentation basin cascade development mainly in the following aspects [
Suppose that there are
After extracting the first principal components
Denoting dependent variables (sediment storage volume) by
In the first step, the unit vectors
If so, the optimization value of objective function is
In the second step replace
In the
Conduct the regression of
Because
Order
According to principal component analysis, under the premise of the sediment storage data with minimal loss, make dimension reduction for highdimensional data systems; when the original
According to the theory and the specific steps of PLSR modeling, we can use the MATLAB language to compile the PLSR analysis program of sediment storage in cascade development.
The upper reaches of the Yellow River between Longyangxia and Liujiaxia section mainly have six largesized cascade hydropower stations, which are Longyangxia, Laxiwa, Lijiaxia, Gongboxia, Jishixia, and Liujiaxia from upstream to downstream, as shown in Figure
Sketch map of cascade hydropower stations layout between Longyangxia and Liujiaxia section in the Yellow River.
Longyangxia hydropower station is the leading hydropower station in the main stream of the Yellow River, with a total reservoir capacity of 274 × 10^{8} m^{3} and less sediment concentration, at which control basin is one of the few largescale runoff regional stabilities and is located in 1687 km from the source of the Yellow River. Jishixia hydropower station is fifth largescale cascade hydropower station in the LongLiu segment of the Yellow River, with the dam located at the outlet of Jishixia canyon in the Yellow River, up from Gongboxia hydropower station about 55 km, down from Liujiaxia hydropower station about 93 km. It is a daily regulating reservoir with the total capacity of 2.94 × 10^{8} m^{3} [
The basic statistics of other cascade hydropower stations between Longyangxia and Liujiaxia section.
Hydropower stations  Dam height (m)  Dam types  Basin size of controlling (km^{2})  Normal storage level/dead water level (m)  Total capacity/regulation capacity (10^{8} m^{3})  Water storage date (year) 

Longyangxia  178  VA  131420  2600/2530  247/193.5  1986 
Laxiwa  250  VA  132160  2452/2440  10.56/1.5  2009 
Lijiaxia  165  VA  136747  2180/2178  16.5/0.6  1996 
Gongboxia  127  CFRD  143619  2005/2002  6.2/0.75  2004 
Jishixia  100  CFRD  146749  1856/1852  2.94/0.45  2010 
Liujiaxia  147  PG  173000  1735/1694  57/41.5  1968 
Note: the dam type code in Table
Each cascade hydropower station in the LongLiu section is distributed between Tangnaihai and Xunhua Hydrometrical Stations. Tangnaihai Hydrometrical Station is located along the eastern edge of the QinghaiTibet Plateau, the boundary between the natural runoff and manually adjusted section, which is an important control section on the upper reaches of the Yellow River. It is also a storage station of the Longyangxia Reservoir, with 121,972 km^{2} control drainage area, accounting for 92.8% of Longyangxia Gorge Reservoir control area; the annual average sediment concentration is 0.61 kg/m^{3} [
The measured water and sediment statistics of Tangnaihai Hydrometrical Station (1956 to 2004).
Years 
Average annual runoff 
Average annual sediment  

Flood season  Full year  Flood season  Full year  
1956–1985  127.8  213.1  950.3  1301.8 
1986–1996  111.7  187.5  889.7  1289.1 
1997–2004  98.9  167.9  839.5  1106.4 
The average sediment load value monthly measured and year allocation of Tangnaihai Hydrometrical Station (1982).
Month  1  2  3  4  5  6  7  8  9  10  11  12  Full year 

Sediment load (10^{4} t)  2.2  2.2  11.2  29  145  675.7  461.6  303.3  405.9  165  24.5  4.4  2230 


%  0.1  0.1  0.5  1.3  6.5  30.3  20.7  13.6  18.2  7.4  1.1  0.2  100 
The measured water and sediment statistics of Xunhua Hydrometrical Station (1956 to 2004).
Years 
Average annual runoff 
Average annual sediment  

Flood season  Full year  Flood season  Full year  
1956–1985  137.9  232.8  2840.2  3623.6 
1986–1996  75.9  192  1490.2  1909 
1997–2004  55.2  159.2  894.6  1169.8 
Making an exact fitting about the amount of sediment in the reservoir is significant for reasonable prediction of reservoir sedimentation and scientifically determines water demand for sediment. Due to multicorrelations among each factor (such as rainfall amount, natural runoff, sediment transport rate, the amount of water discharged from upper reservoir, water level of the upper reservoir, water level of the downstream reservoir, water temperature and other factors), which influence sediment flux into each cascade reservoir, so adopting the PLSR model established before to fitting.
Main factors affecting the sediment storage are rainfall amount within the drainage area, runoff, upstream water level and the discharging water, the backup water level of downstream reservoir and discharged volume of this level’s reservoir, natural river runoff, water temperature, sediment transport rate, and so on. For this reason, in the mode of cascade development, the PLSR model of sediment quantity is composed of runoff factor component
According to (
Considering the influence on the downstream channel and the reservoir sediment transportation caused by water storage of Longyangxia, this paper takes the Longyangxia and Liujiaxia reservoirs as example of built PLSR fitting model of sediment storage. Selecting the monthly average sediment storage capacity from January 1982 to December 1987 as the fitting time, including important periods from the Longyangxia Reservoir, water level gradually increased to the normal water level during initial impoundment so that it can better analyze the influence that water storage of Longyangxia Reservoir for sediment flux into downstream reservoir. A PLSR fitting model for sediment storage of Longyangxia and Liujiaxia Reservoirs is shown in Figures
Fitting chart of PLSR model for sediment storage of Longyangxia.
Fitting chart of PLSR model for sediment storage of Liujiaxia.
Multicorrelation analysis of factors: take rainfall factor set
The first principal component distribution of rainfall and sediment transport rate factor
According to Figures
Under the cascade development mode, river flow is influenced by the reservoir impoundment of each cascade and discharge flow, reservoir sedimentation encounters greater risks; the relations between the erosion and deposition become more complicated. For this reason, on the basis of systematic analysis for sediment deposition risk of cascade development in the upstream of the Yellow River’s, mainly studied the model and fitting method of sediment flux into the reservoir under cascade development mode.
Considering the difficulty to effectively identify and eliminate the multiple correlation influence among the independent factors by leastsquares regression, the partial leastsquares regression (PLSR) method is adopted for modeling analysis; the model fitting is organically combined with the nonmodelstyle data content analysis, so as to realize the regression model, data structure simplification, and multiple correlations analysis among factors; meanwhile the accuracy of the model is ensured through cross validity check.
The modeling analysis of sediment flux into the cascade reservoirs of LongLiu section upstream of the Yellow River indicates that partial leastsquares regression can effectively overcome the multiple correlation influence among factors, and the isolated factor variables have better ability to explain the physical cause of measured results.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors would like to express their sincere gratitude to anonymous reviewers who gave them some constructive comments, criticisms, and suggestions. This work was supported by the Project of National Natural Science Foundation of China (no. 41301597), the National Key Laboratory of Northwest Arid Area Ecological Hydraulic Engineering Foundation Project of Shaanxi Province in China (106221225), the Open Research Fund of State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin (IWHRSKL201303), CRSRI Open Research Program (CKWV2013202/KY), and Program 2013KCT15 for Shaanxi Provincial Key Innovative Research Team.