Quantificational analysis on progress of river water quality in China

Available online at www.sciencedirect.comJOURNAL OFENVIRONMENTALScienceDirectSCIENCES'JESISSN 101-0742JLLEwww.josc.nc.cnQuantificational analysis on progress of river water quality in ChinaYUN Yi, ZOU Zhihong*, FENG Wei, RU MaiSchool of Eeconomics and Management, Beihang Universit, Bejing 100191, China. E-mail: winielowd81@163.comReceived 01 Jaouary 2008; revised 15 February 2008; acped 28 April 2008Abstractthe theory of Markov process was established. The transition possibility with a weight to calculate the degree of absolute advancementwas given based on the result of water quality evaluation. The concept of relative advancement was presented. It was used to evaluatethe extent of water quality changed in a period of time. The method was used to calculate the degrees of relative advancemeat for 4rivers in China, and the results were analyzed.Key words: water quality evaluation; pssibilit transition matrix; Markov process;, degree of advancementDOL: 10.1016/S1001-0742(08)62339-6Introductionvaried from -1 to 1. DRP is the output of the model and theinput of the model is the level of water quality at diferentRiver plluion is a serious problem in China. In recent time in difrent places.years, the govemment worked hardly to improve the water1.1 Establishing possibility transition matrixquality of rivers, and some delightful change has happened.It is necessary to know the dynamic change of waterAccording to the Environmental quality standards forquality in a period of time. Some traditional methods can surface water (GB3838-2002, State Environmental Protec-be used to evaluate the static state of river water quality tion Administration of China, 2002), the water quality ofon time in one place such as factor analysis models (Chen rivers was cassied into 6 levels: levelI, II, iI, IV, V,et al, 2002), fuzzy synthetic evaluation (Zou et al., 2006)，under level V. In this study, we set E as 6 levels,E={1,2,matter element model (Wang et al, 2004), Logistic curve 3,4,5, 6].model (Jin et al, 2003), artificial neural network (Ni andTake a river as an example. There are k monitor places inBai, 2000) and Gary analysis method (Zhang et al, 2004). the river and n monitor samples in every place at diferentOn the basis of the results of water quality evaluation, times, in which each one can be defined as YI1,Y2, .. andyn.a quantitative value is needed to figure out how the river Therefore, there are tally nxk monitoring samples in thewater quality changed in a period of time, to check whether river. The sum of samples that have level i water quality isit is improved, and to compare the change level in diferent Mi. In the last monitoring, the number of samples that haverivers. A mathematical model based on Markov process is level i water quality is counted m: Thus, there are:0≤mdeveloped to quantify the change of water quality in rivers.≤k,0≤ Mi≤k andSm=kZM=nk,i∈E. .If the level of water quality is i in a monitor place at1 Mathematical modelone time and the level change toj level in the same place atanother time, then the sum of the changes can be calculatedMarkov process is a special stochastic process (Guan,as nyj. Thus, there is Eq. (1).1993), and has been used in forecasting (Wang et al, 2005;Yu et al, 2003;Li and Wang, 2002; Zhang etal, 2005;Ma 0≤mj≤(n-1)kZw=(n-1)k, ij∈E(1)and Yang, 2000; He and Xie, 1998; Zhong and Zeng, 1997;Jiang, 1996; Liu and Tan, 2002; He et al., 2003). Basedh the water qualityon Markov process theory, two concepts were imported:chang中国煤化工his river is njy/M;degree of absolute progress (DAP) and degree of relativeprogress (DRP). DAP is used to express how much theaccordMHsituation should beconsidCNMH G no psibsi twater quality changed in a period of time, and DRP is thechange in the last monitoring, in other words, the waterstandardized value of DAP, which means the value of DRPquality changed, but it was not be monitored at the last* Corresponding author. E-mail: zouzhihong@buaa.cdu.cnmonitoring. Thereby, m; should be subtracted from Mi. AtNo. 6Quantificational analysis on progress of river water quality in China77last, the transition possibility of which the water qualityTable 1 Water quality levels of the river studiedchanged from i level to j level can be calculated accordingMonth Monitor 1 Monitor 2Monitor3 Monitor4 Monitor 5to Eq. (2):anhiji=M:- m;'0≤pj≤1;Pv=12)MarAprMayThe matrix P = (p:)NxN can be founded, and it is theJunpossbility transition matrix of the river.2 Results and discussion1.2 Degree of absolute progress calculationIntending water quality can be forecasted from theThe study was applied to develop a model to analyzepossibility transition matrix of the river, but it is stillthe water quality changes of four rivers in China in 2005.unknown about how much the water quality changed in theThese four rivers are the Songhua River, the Haihe River,time of monitoring. A farther work should be done, and thethe Yellow River, and the Yangtze River. As mentionedfollowing situation should be considered:above, the input of the model is the water quality level of(1) Endow the ransition possibility with the weight,each river at diferent time and different monitoring places.which can figure out if the water quality deteriorated orThe source data for study were provided by Environmentalimproved. If the water quality changed from low levelMonitoring Center of China (CNEMC). There are 27to high level, it is deteriorated, so the weight should bemonitoring points along the four rivers. The level of waternegative. If the water quality changed from high level toquality was evaluated every week. Taking the Songhualow level, it is improved, so the weight should be positive.River as an example, the level of water quality is given(2) Endow the transition possibility with the weight,in Table 2.which can figure out the extent the water quality deteriorat-Table2 Water quality level of the Songhua River in 2005ed or improved. It follows more deterioration, punishment,and improvement and encouragement.Month Monitor 1 Monitor2 Monitor3 Monitor4 Monitor 5(3) If the degrees of deterioration and improvement arethe same, the absolute value of the weight is the same too.FebBased on the considerations above, the equation of theweight is:wij=(i-j)li-j\unsosij=(i-j)li-jlPijo ij∈EulThe matrix S = (Sij)NxN is called advancement matrixAugof possibility transition matrix P = (Puy)NxN.sepDetTherefore, the equation of DAP is:lovDAP=Esj=Z(i-Di-jipi, i,j∈EDecif DAP > 0, the water quality improved, if DAP < 0, the .water quality deteriorated. The absolute value cDAP canThe results of m, Mi, and nj are calculated as follows:figure out the degree of the water quality changed, butthe value extension of DAP is unknown, therefore, it ism6=0necessary to calculate DRP.M=0 M2=15 M3=18 M4=20 Ms=5 M6=2 .m1=0 m12=0 13=0 14=0 用s=0 16=013 Degree of relative progress calculation021 =0 n2=10 123=3 024= 0126= 0(3)After the calculation of DAP, degree of relative progress(DRP) should be calculated. When the water quality im-n65=1 n66=0 .proved most, the value of DRP is 1, and when the waterquality deteriorated most, the value of DRP is -1. TheThe possibility transition matrix is then establishedrange ofDRPis (-1, 1).based on the results.Suppose that the water quality levels of the river studiedare that as shown in Table 1 when the water qualityimproved most. Under this situation, DAP is 25. When thePi =water quality deteriorated most, DAP is -25. Therefore, it6/19is defined that DRP = DAP/25, DRP∈(-1, 1). DRP can0001/21/2indicate that the degree of the water quality changes more中国煤化工(4)clearly.DRP for diferent rivers can be calculated and compared.0HCNMHGIfDRP1 < DRP2 < .. < DRPn, the water quality in the lastU.412 u.2x4 U.UDy0.316 0.579 0.053 0.053river has the largest positive changes and that in the firstriver has the smallest.0.5772YUN YietalVol. 21Tnable 3 Water quality level of the Haihe River in 2005MonthMonitor 1Monitor 2Monitor 3Monitor 4Monitor 5Monitor 6Monitor 7Monitor 8AprMayunulAugOctNovDecTherefore, the advancement matrix S\ can be calculated the river water quality changes. The conclusion of the caseas Eq. (5), based on the equation of DAP, DAP1 = 2.525，studies indicated that the water quality improvements ofDRP1 = DAP1/25 = 0.101.four rivers are limited, and the Haihe River became worse. .More attention should be paid to protecting the rivers frombeing polluted.0.231Acknowledgments1=00.2350.316-0.053 -0.212(5)This work was supported by the National Natural Sci-0.5ence Foundation of China (No.50778009).The calculation ofDRP for other three rivers is the same.The DRP of the Haihe River, the Yellow River and theReferencesYangtze River are: DRP2 = -0.136, DRP3 = 0.056, DRP4= 0.147, rspectively. The DPR value for the four rivers Chen DI, Ma A Q, Xu ZM, Chen G D, 2002 The apicacionwere in the sequence of DRP2 < DRP3 < DRP1 < DRP4.of factor analysis in water quality evaluation. Hydrology,2(3): 29 31.The calculation result showed that DRP of the HaiheGuan J, 1993. Stochastic service process and application inRiver is negative, it can be concluded that the water qualitymanagement. Bejing: Beihang University Press.deteriorated. The same conclusion can be directly obtainedHe B, Chen C, Gao D H, 2003. Evaluation of water quality basedfrom Table 3, because the water quality of the Haiheon Markov process. Enironmental Engineering. 21(2): 60-River in monitor 2, monitor 3 and monitor 4 deterioratedgradually. The level of water quality in monitor 3 and He B, Xie K G, 1998. A Markov random model predictingmonitor 4 became worse than class V at one time, and thecomprehensive atmospheric quality. The Administrationother positions remained the same. Generally speaking, theand Technique of Envirormental Monitoring, 10(2): 18 -21.water quality of the Haihe River was getting worse. This is Jiang C Y, 1996. Grey Markov foreasing model. Joumal ofconsistent with the calculation results.Chongqing Jianzhu University, 18(3): 116-122.The water quality of the other three rivers turned toJin J L, Liu L, Ding J, Fu Q, 2003. Logistic curve model ofbe better in 2005, such as the Songhua River. As showngroundwater quality evaluation. Environmental Pollutionand Control, 25(1): 46 48.in Table 2, the water quality in monitor 2, monitor 3Liz Q, Wang S J, 2002. Appling of grey Markov model inand monitor 4 improved at a certain extent. The waterpredictingthe DO' density of ground water. Chongqingquality in monitor 1 deteriorated slightly, and in monitorEmironmental Science, 24(3): 35 -37.5 it fuctuated randomly. They all afected the results Liu W L, Tan Q, 20020. Aplication of transfer matrix analysisof the calculation. Although the DRP is positive, theto the teaching eect. Systems Engineering- Theory andabsolute value is small. This indicates that although thePractice, 22(6): 135-138.water quality of the Songhua River improved in 2005, the MaZQ, Yang HJ, 200.0 Grey markorian model for prediction ofimprovement is not significant. The situation of the Yellowurban sewage drainage. Journal of Hohai University, 28(5):River and the Yangtze River is similar; the water qualitydid not improve much. The water quality in the YangtzeNi s H, Bai Y H, 2000. Application of BP neural network modelin groundwater quality evaluation. Systems Engineering-River has the most improvement among the four rivers,Theory and Practice, 20(8): 124-127.while the Yellow River has the least.State Environmental Protection Administration of China, 2002.General Administration of Quality Supervision, Inspection3 Conclusionsand Quarantine of China (GB38382-2002), Environmentalquality standards for surface water. Beijing: China Environ-The study established a mathematical model based onMarkov process to analyze the changes of water quality in中国煤化工Mate emem moela period of time. The key point is the introduction of thetion. System SciencesYHconcept DRP. The developed model has been applied toWangZE, Pan D H, Song J Q, 2005. Forecasting of exchangefour Chinese rivers in 2005. The calculation results showedrate using the continuous time Markov process. Systemthat the value of DRP can reflect the actual situation ofQuanifcational analysis on progress of river water quality in ChinaEngineering- Theory Methodology Application, 14(3): 22 Zhong Z L, Zeng G M, 1997. Markov process applied to perdi-225.tion for river comprehensive water quality. EnvironmentalZhang K Z, Mao S H, Yuan W H, 2005. Appling modificationEngineering, 15(2): 41-44.grey model based on Markov-chain to highway networkZou Z H, Yun Y, Sun J H, 2006. Entropy method for de-planning. Journal of Wuhan University of Technology,termination of weight of evaluating indicators in fuzzy29(4): 503- -505.synthetic evaluation for water quality assessment. JournalZhang L, Wang G X, Luo M R, 2004. Aplication of an improvedof Envirormental Sciences, 18(5): 1020 -1023.grey association analysis method in water environmentalYuM, Ccn Y T, WangS K, Yu M, 2003. The fuzzy model ofquality assessment. 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