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Meri-Rastilantie 3 B, FI-00980 Journal of Food, Agriculture & Environment Vol.7 (3&4) : 734-738. 2009 www.world-food.net Helsinki, Finland e-mail: [email protected]

A study on water resources consumption by principal component analysis in Qingtongxia irrigation areas of Plain,

De Zhou 1*, Rongqun Zhang 2*, Liming Liu 1, Lingling Gao 2 and Simin Cai 2 1 College of Resources and Environment, China Agricultural University, Yuanmingyuan West Rd, Haidian District, , 100193, China. 2 College of Information and Electrical Engineering, China Agricultural University, 17 Tsinghua East Rd, Haidian District, Beijing 100083, China. *e-mail:[email protected], [email protected]

Received 22 July 2009, accepted 6 October 2009.

Abstract Principal component analysis (PCA) is a valid method used for data compression and information extraction in water resources. PCA finds linear combinations of the original measurement variables that describe the significant variations in the data. In this paper, PCA is used to extract three principle components from 12 factors such as population size (PS), value of industrial output (VIO), gross output value of agriculture (GVA), sown area of rice (SAR), sown area of wheat (SAW), sown area of corn (SAC), agricultural water consumption (AWC), industrial water consumption (IWC), urban water consumption (UWC), rural people and livestock water consumption (RPLWC), annual water amount (AWA), annual water discharge amount (AWDA) which reflect the status of water resources consumption in Yinchuan Plain, China, and our calculations show that the comprehensive scores of water resources consumption is dropping year by year during 1996-2002. The result shows that the use of water resources in Yinchuan Plain is faced with a lot of pressure. This paper has testified the scientific nature of PCA, and provided evidence for decision-making of rational use of regional water resource.

Key words: Principle component analysis, Yinchuan Plain, water resources consumption.

Introduction With the completed of Qingtongxia Water Conservancy Hubs, and (3) the maximum of regional water resources carrying capacity. the history that the farmers bring in water directly to irrigate from In the meantime, a lot of research methods were created, such as the has come to an end in Qingtongxia irrigation areas comprehensive index method, fuzzy comprehensive evaluation in Yinchuan Plain. At the same time, the capacity of water supply method and principle component analysis. Therefore, carrying and the modulus of water supply for the industrial and agricultural capacity of water resources can be calculated according to the production were enhanced. So, if there is no irrigation there would above method. Fu and Ji 9 adopted the principle component be no agricultural production 1. However, with the development analysis method to undertake comprehensive evaluation of the of socio-economic and the area increasing of agricultural irrigation, regional water resource carrying capacity. They obtained the contradictions among agricultural water consumption, correspondent classifying standard of the principle component industrial water consumption and other aspects were increased to judge water resources carrying by the use of the principle continuously. Therefore, the unreasonable utilization of water component analysis 9. Zheng and Wang focused on the resources is becoming serious. That is to say, how to reasonable construction of evaluation of water resources, systematic analyze use of water resources were depended primarily on the modes of the quantity of water resources, main utility condition and quality production and the ways of life. So, how to enhance the level of of water environment, evaluation of regional development to the water resources sustainable use has received substantial attention need of water resources and bearing property 10. Some foreign of scholars both at home and abroad 2-4.The concept of water researchers have conducted many studies of water resources by resource carrying capacity was first posted by the China Xinjiang principle component analysis 11-13. Bengraine and Marhaba applied Water Resource Soft-Science Research Panel 5. It is clear that the the PCA to monitor spatial and temporal changes in water quality, study of water resources carrying capacity becomes a new focus and this study shows the importance of environmental monitoring these days. However, an explicit definition of this concept has associated with simple but powerful statistics to better understand generally not been acknowledged at home and abroad up until a complex water system 14. In this paper we analysed the main now 6. Lot of scholars have conducted in-depth study for water trends in the development of water resources consumption by resources carrying capacity 6-8, and the theory and method of means of PCA, using data of nature, society, economics and water water resources carrying capacity is only at the exploratory stage. resources of the Yinchuan Plain in 1996-2002. The aim of the study Generally speaking, the following major objectives: was to solve the contradiction between water resources (1) the evaluation of regional water resources carrying capacity, exploitation and utilization in Yinchuan Plain and provide decision (2) the certain status of regional water resources carrying capacity support for making policies.

734 Journal of Food, Agriculture & Environment, Vol.7 (3&4), July-October 2009 Materials and Methods The amount of annual rainfall totals about 185 mm, most of which Study area: Yinchuan Plain is located in the north part of falls during the summer months between June and September. Autonomous Region (Fig. 1), northwest China. From west to east, The annual evaporation is 1825 mm, nearly ten times more than the plain consists of the tilted plain of Helan mountain, the alluvial- annual precipitation, and drought index is 6.5. The annual average proluvial plain of the Yellow River, and an alluvial-lacustrine runoff in the Yellow River is 1030 m3/s and the total volume of plain15. Its northern boundary is adjacent to Helan Mountain’s annual water flow through the Yinchuan Plain is 3.25×1010 m 310. southwest border; in the east it is adjacent to . The Soil is fertile and it has good irrigation conditions. Therefore, the Yellow River passes through the plain along the east boundary plain is one of bases of grain production. with a total length of about 193 km. It is 7,790 km2 in area, and wide east-west about 42-60 km. Its altitude is 1100-1150 m. Native Data and method: In this study, the data were mainly collected vegetation is typical desert steppe, and vegetation is mainly from Ningxia Statistical Yearbook 1996-2007, Water Resources artificial oasis now. The main soil types are irrigation-silted soil, Communique of Ningxia Autonomous Region 1996-2007, the sierozem and bog soil, etc. Main crops are wheat, rice, maize etc. Optimal Allocation of Water Resources and Sustainable Use of Yinchuan Plain is located in the temperate arid zone, which has Strategic Research in Ningxia, Medinm and long-term planning of continental climate with the average annual temperature of 9°C. water resources in Ningxia Autonomous Region, which include basic history and status of the water resources use in the Yinchuan Plain, such as population size (PS),value of industrial output (VIO), gross output value of agriculture (GVA), sown area of rice (SAR), N sown area of wheat (SAW), sown area of corn (SAC), agricultural Helan Ordos water consumption (AWC), industrial water consumption (IWC), Mountain urban water consumption (UWC), rural people and livestock water consumption (RPLWC), annual water amount (AWA) and annual Plateau water discharge amount (AWDA). In addition, the standardized values of factors were calculated from the original data by SPSS 16-17 (Table 1). The above 12 factors can reflect water resources consumption fundamentally. Therefore, in order to choose rational index system and evaluate the water consumption of the Yinchuan Channel Plain scientifically, it is necessary to choose some indexes which can reflect the water resources consumption and utilization Darain situation, the relationship between supply and demand. NingXia Plain boundary Principal component analysis: Principal component analysis City (PCA) is a statistical technique for determining the key variables YinChuan Plain in a multidimensional data set that explains the differences in the Figure 1. Location of the study area on the Yinchuan Plain in China. observations and can be used to simplify the analysis and visualization of multidimensional data sets 18. In recent years, the Table 1. Standardization values of original data during 1996-2002. Population Value of industrial Gross output value of Sown area of Sown area of Sown area of Year size (x1) output (x2) agriculture (x3) rice (x4) wheat (x5) corn (x6) 1996 -1.2550 -1.1033 -1.2665 -1.2024 -1.3875 -1.3495 1997 -0.9001 -0.7670 0.6839 0.1469 -0.4904 -0.6472 1998 -0.5340 -0.6320 1.7477 0.0184 0.7578 0.7573 1999 -0.2123 -0.3850 0.3293 1.3034 1.2259 1.5275 2000 0.4976 0.3036 -0.5572 0.9179 0.4458 -0.8285 2001 -1.2550 -1.1033 -1.2665 -1.2024 -1.3875 -1.3495 2002 -0.9001 -0.7670 0.6839 0.1469 -0.4904 -0.6472

Table 1. (Continue). Agricultural Rural people and Annual Annual water Industrial water Urban water Year water livestock water water discharge consumption (x8) consumption (x9) consumption (x7) consumption (x10) amount (x11) amount (x12) 1996 -1.5949 0.2706 -0.2862 -1.1603 0.1649 0.3857 1997 1.3818 1.3668 1.1522 -0.7101 0.7905 -0.0644 1998 0.4309 1.0847 0.8439 -0.6741 0.8983 1.3379 1999 -0.5623 -1.1883 -1.8787 -0.4580 1.1140 1.1578 2000 0.3568 0.0046 -0.3376 0.4425 -0.5102 -0.9819 2001 0.6713 -0.3903 0.0220 1.1989 -1.1293 -1.1031 2002 -0.6835 -1.1480 0.4843 1.3610 -1.3282 -0.7319

Journal of Food, Agriculture & Environment, Vol.7 (3&4), July-October 2009 735 Table 2. PCA general approach: correlations matrix variables.

Z(x1) Z(x2) Z(x3) Z(x4) Z(x5) Z(x6) Z(x7) Z(x8) Z(x9) Z(x10) Z(x11) Z(x12)

Z(x1) 1.0000

Z(x2) 0.9883 1.0000

Z(x3) -0.2469 -0.2995 1.0000

Z(x4) 0.0934 -0.0035 0.3309 1.0000

Z(x5) 0.1034 -0.0290 0.5515 0.4328 1.0000

Z(x6) 0.2882 0.2164 0.5532 0.3814 0.7148 1.0000

Z(x7) 0.0736 0.0484 0.5766 0.1071 0.4119 0.0941 1.0000

Z(x8) -0.6582 -0.6351 0.4803 -0.2245 -0.1031 -0.4310 0.5195 1.0000

Z(x9) -0.0272 0.0543 0.3194 -0.3597 -0.4182 -0.3701 0.5053 0.6798 1.0000

Z(x10) 0.9823 0.9870 -0.3009 -0.0496 0.0402 0.1873 0.1448 -0.5833 0.0569 1.0000

Z(x11) -0.8161 -0.8633 0.6204 0.3689 0.3412 0.2378 0.0929 0.4565 -0.1612 -0.8760 1.0000

Z(x12) -0.6633 -0.7023 0.5935 0.2573 0.2811 0.4304 -0.2282 0.2263 -0.2130 -0.7645 0.8706 1.0000 method of principal component analysis has been widely used in three variables. Table 3 contains all 7 principal components and many fields such as evaluation of irrigation water quality, evaluation their corresponding eigenvalues. The results showed that of the of river water quality monitoring stations and comprehensive first three components, the first component accounted for about evaluation of the regional water resource carrying capacity 5, 6, 17, 19. 42.35%, the second component about 25.68% and the third The method of principal component analysis (PCA), using component about 19.45% of the total variance in the data set. coefficients of linear correlation offers this possibility 20, 21. Principal These three components together accounted for about 87.48% of component analysis is also known as eigenvector analysis, the total variance and the rest of the components only accounted eigenvector decomposition. Generally, the principle component for about 12.52%. Therefore, our discussion should focus only of random vector X is obtained from the weight of X special linear on the first three components (Table 4). combination. Therefore, it is difficult to give explanation for the Table 3. Eigenvalue contribution rates and accumulated physical meaning of this linear combination when the contribution rates of the principal components. dimensionless variables are different. In order to perform a PCA of the original data, random variables X have to be standardized. Total % of Variance Cumulative % PCA seeks to establish combinations of variables capable of F1 5.08 42.35 42.35 describing the principal tendencies observed while studying a F2 3.08 25.68 68.03 14 given matrix . In mathematical terms, PCA relies upon an F3 2.33 19.44 87.47 eigenvector decomposition of the covariance or correlation matrix.

The basic ideas of principal component analysis are to define Fn as a linear combination of weight X, find a linear combination of Now, we will discuss the components separately, the three

Fn for the weight X, and Fn reflects the changes of the weight X as histogram representation of the first three component loadings is far as possible. Here, F1 is called the first principle component of given in Fig. 2a-c. This diagram was constructed using the X, and if it not yet fully reflects the changes of the weight X, we eigenvectors from the first three components. It is clear that the then find F2, F3,…, Fr (r

component F2 has high positive loadings of SAC, SAW, SAR, and

Fn=A1 X1+A2 X2+...+An Xn (1) negative loadings for IWC and UWC. The third component F3 has high positive loadings of AWC, UWC, IWC, and negative loadings Given X observations on n variables, the goal of PCA is to reduce only for AWDA. the dimensionality of the data matrix by finding r new variables, It should be pointed out that a loading reflects only the relative where r is less than n. Each principal component is a linear importance of a variable within a component, and does not reflect combination of the original variables, and so it is often possible to the importance of the component itself 22. These phenomena could ascribe meaning to what the components represent. be an extreme stress as PS, VIO, GVA, sown area, AWC, IWC, UWC and RPLWC for water consummation. From the eigenvectors

Results and Discussion obtained in the PCA, the first component, F1, can be given as: Data analysis: The correlation matrix of the standardized value for the data from Table 1 is given in Table 2. In a PCA, the number F1= -0.402x1- 0.415x2+ 0.269x3+ 0.076x4+ 0.95x5+ 0.024x6+ 0.05x7+ of components is equal to the number of variables. However, a 0.287x8 + 0.011x9 - 0.416x10 + 0.427x11 + 0.371x12 (2) component is not only comprised of a single variable but rather all 19 of the variables used in a study . Table 4 shows the results of the Similarly, the second component F2 and the third component F3 PCA, the corresponding eigenvalues, which are extracted by each can be expressed as: factor, and the variance percentages (accounted for and F2 = 0.198x1 + 0.134x2 + 0.2482x3 + 0.372x4 + 0.467x5 + 0.519x6 + accumulative) corresponding to the principal components. 0.0.058x7- 0.294x8- 0.318x9+ 0.126x10 + 0.127x11 + 0.0.179x12 (3) Our analysis indicates that we can summarize the data with just

736 Journal of Food, Agriculture & Environment, Vol.7 (3&4), July-October 2009 Table 4. Loading values of the principal components. F1 F2 F3 A1 A2 A3 Population size (x1) -0.9065 0.3472 0.2007 -0.4021 0.1978 0.1314 Value of industrial output (x2) -0.9359 0.2357 0.1993 -0.4151 0.1343 0.1305 Gross output value of agriculture (x3) 0.6053 0.4357 0.6093 0.2685 0.2482 0.3989 Sown area of rice (x4) 0.1730 0.6526 -0.0285 0.0767 0.3718 -0.0187 Sown area of wheat (x5) 0.2145 0.8195 0.2429 0.0951 0.4669 0.159 Sown area of corn (x6) 0.0551 0.9111 0.0798 0.0244 0.519 0.0522 Agricultural water consumption (x7) 0.1131 0.1016 0.9168 0.0502 0.0579 0.6003 Industrial water consumption (x8) 0.6489 -0.5167 0.5386 0.2878 -0.2944 0.3526 Urban water consumption (x9) 0.0261 -0.5586 0.7413 0.0116 -0.3182 0.4854 Rural people and livestock water consumption (x10) -0.9379 0.2216 0.2632 -0.416 0.1262 0.1723 Annual water amount (x11) 0.9617 0.2233 -0.0747 0.4266 0.1272 -0.0489 Annual water discharge amount (x12) 0.8368 0.3157 -0.2458 0.3712 0.1798 -0.1609

0.8 1.5 . 1.0 0 7 0.5 0.6 0.0 0.5 -0.5 0.4 -1.0 0.3 Loading (eigen vectors) PS PS . VIO VIO SAC SAC SAR SAR 0 2 GVA GVA ICW SAW SAW UWC AWC AWA AWA

AWDA .

RPLWC RPLWC 0 1 0 Figure 2a. Component loadings for the first component F . 1 1997 1998 1999 2000 2001 2002 Figure 3. General score in 1996-2002. 2.0 1.0 Discussion From Fig. 3, we know that the water resource of Yinchuan Plain is 0.0 dissipative increasing, (the pressure to supply water for Yin Chuan -1.0 Plain is increasing) during 1996 to 2002. It is mainly due to the

PS PS irrigation area of Qingtongxia is increasing, which added from VIO VIO Loading (eigen vectors) SAC SAC SAR SAR GVA GVA ICW

SAW SAW 4 2 4 2 UWC AWC AWA AWA 27.65×10 hm to 30.07×10 hm during 1995 to 2000. At the same AWDA RPLWC RPLWC time, some other factors such as the increasing population, the

Figure 2b. Component loadings for the first component F2. enhancing levels of industrialization and urbanization, would bring amount of pressure to the area of agricultural water. 1.5 Furthermore, the intensified idea of protecting environment made 1.0 ecological water consumption also an increasing trend. It is 0.5 estimated that the demand of water will reach 2.45×108 m3 by 20101. 0.0 Base on the irrigated area of Qingtongxia had been assigned 4,000×108 m3 of Yellow River water volume from the central -0.5 government, and they reduced the Yellow River irrigation water

Loading (eigen vectors) -1.0 about 33% on the winter irrigation water in 2002. According to the PS PS

VIO VIO document which the Ministry of Water Resources promulgated, SAC SAC SAR SAR GVA GVA ICW SAW SAW UWC AWC AWA AWA the irrigated area of Qingtongxia further reduced the available AWDA RPLWC RPLWC Yellow River irrigation water about 30% on the second quarter of Figure 2c. Component loadings for the first component F . 3 2003. As a result, about 13.3×104 hm2 farmland were affected 23, and henceforth they would continue to reduce the available water F = 0.131x + 0.13x + 0.398x - 0.019x + 0.159x + 0.052x + 0.6x + 3 1 2 3 4 5 6 7 for the irrigated area. The land is mainly used for growing food. 0.352x + 0.485x + 0.173x - 0.048x - 0.161x (4) 8 9 10 11 12 Some high need water crops, such as rice and wheat, take huge proportion of crop planting area, and unreasonable agricultural We substitute the standardized values of the indexes into Eq. (2)- structure would further reduce the available water of the area. The (4), and then we will get the scores of the three principal Ningxia municipality government resolutely makes a decision to components, respectively, and multiply the normalized scores by decrease the planting area of early season crops and rice, the weight, respectively, to get the values of the corresponding encourage and lead farmer grow vegetables and fruits with high years (Fig. 3). economic value so as to adjust agriculture industry structure. The advantage of this is multifaceted. On the one hand, it would

Journal of Food, Agriculture & Environment, Vol.7 (3&4), July-October 2009 737 alleviate the negative effect of low field caused in short water A generalised conceptual framework. Environmental Modelling & supply. On the other hand, when the agriculture structure is Software 22(5):733-742. changed, it would increase the income of the farmers effectively 5Feng, L.H., Zhang, X.C. and Luo, G.Y. 2008. Application of system and promote sustainable development of agriculture economic. dynamics in analyzing the carrying capacity of water resources in Yiwu City, China. Mathematics and Computers in Simulation Therefore, the government should take some measures such as 79:269-278. adjusting the proportion of the various factors that consume huge 6Feng, L. H. and Huang, C. F. 2008. 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A comprehensive evaluation of the regional water components has been applied. The efficiency of the new algorithm resource carrying capacity-application of main component analysis was illustrated on a data set concerning the Yinchuan Plain. PCA method. Resources and Environment in the Yangtze Basin 8(2):168- showed a relatively different separation of the variables and no 173 (In Chinese). separation of scores described by the first three principal 10Zheng, J. and Wang, Y. 2006. Research on the bearing capacity of water components. Principal component analysis constitutes a valuable resources in Yinchuan Plain. Journal of Ningxia University (Natural tool that allows the identification of tendencies using univariate Science Edition) 27(1):80-83 (In Chinese). 11 statistical methods. The most important contribution of PCA in Céréghino, R. and Park, Y.-S. 2009. Review of the self-organizing map (SOM) approach in water resources: Commentary. Environmental this study was the identification of the changes of water Modelling & Software 24(8):945-947. consumption. In spite of the impact on consumption of water in 12Ekasingh, B., Ngamsomsuke, K., Letcher, R.A. and Spate, J. 2005. A Yinchuan plain has a lot of factors, we have obtained the main data mining approach to simulating farmers’ crop choices for integrated factors by PCA, which can reasonable reflect the status of water water resources management. Journal of Environmental Management resources consumption in Yinchuan Plain. Three principle 77(4):315-325. components including people size, development of socio- 13Madulu, N.F. 2003. Integrated water supply and water demand for economic and water consumption can comprehensively express sustainable use of water resources. Physics and Chemistry of the the changes of water resources consumption.Yinchuan Plain is Earth, Parts A/B/C 28(20-27):879-892. 14 an area relatively rich in water resources, however, the current Bengraine, K. and Marhaba, T.F. 2003. Using principal component analysis to monitor spatial and temporal changes in water quality. water exploitation and utilization have only reached a relative low Journal of Hazardous Materials 3:179-195. degree, especially agricultural irrigation mechanisms are not very 15Jin, X.M., Wan, L., Zang, Y.K., Xue Z.Q. and Yin,Y. 2007. A study of reasonable, and this is the stress of water resources. With the the relationship between vegetation growth and groundwater in the development of science and technology, water resources Yinchuan Plain. Earth Science Frontiers 14(3):197-203. development and the level of utilization, improvement and use of 16Santos, J.S.D., Oliveira, E.D., Bruns, R.E. and Gennari, R.F. 2004. water resources are tending towards a healthy circle. Evaluation of the salt accumulation process during inundation in water resource of Contas river basin (Bahia-Brazil) applying principal Acknowledgments component analysis. Water Research. 38(6):1579-1585. 17 This project was supported by the National Natural Science Fund, Mandal, U.K., Warrington, D.N., Bhardwaj, A.K., Bar-Tal, A., Kautsky, L., Minz, D. and Levy, G.J. 2008. Evaluating impact of irrigation China (No. 40871103). We want to extent our heartfelt gratitude to water quality on a calcareous clay soil using principal component Associate Researchers Yuanpei Zhang (Institute of Resource and analysis. Geoderma. 144(1-2):189-197. Environment, Ningxia Academy of Agricultural and Forestry) for 18Raychaudhuri, S., Stuart, J.M. and Altman, R.B. 2000. 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