Experimental study on desorption of soluble matter as influenced by cations in static water Experimental study on desorption of soluble matter as influenced by cations in static water

Experimental study on desorption of soluble matter as influenced by cations in static water

  • 期刊名字:水科学与水工程
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  • 论文作者:Wen-sheng XU,Li CHEN,Xiao-xia
  • 作者单位:Division of Soil and Water Conservation,State Key Laboratory of Water Resources and Hydropower Engineering Science
  • 更新时间:2020-07-08
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WSEWater Science and Engineering, 2014, 7(4): 384-394doi:10.3882/jissn. 1674-2370.2014.04.004http://www.waterjournal.cne-mail: wse2008@vip. 163.comExperimental study on desorption of soluble matter asinfluenced by cations in static waterWen-sheng XU*', Li CHEN, Xiao-xia TONG', Xiao-ping CHEN', Ping-cang ZHANG'1. Division of Soil and Water Conservation, Changiang River Scientific Research Institute,Wuhan 430010, P R. China2. State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University,Wuhan 430072, P. R. ChinaAbstract: With variation of drainage basin environments, desorption of soluble matter hasbecome one of the significant erosion processes in rivers. It has a considerable impact on flow andsediment transport, as well as processes of river bed deformation and landform evolutionthroughout a watershed. In this study, considering influences on sediment movement, especiallyon cohesive sediment transport, Cat+ and H+ were chosen as characteristic ions of soluble matter,and the total desorption quantity of Ca2+ and pH value when the desorption equilibrium is reachedwere employed as two indexes representing the desorption of soluble matter. By means of anindoor experiment, desorption of soluble matter as influenced by cations in static water wasinvestigated. The results show that the total desorption quantity of soluble matter increases withthe initial cation concentration until a maximum desorption quantity value is obtained andmaintained. The total desorption quantity of soluble matter depends on properties of the specificcations in static water, and the stronger the affinity is between the cation and sediment surface, thehigher the total desorption quantity will be. Finally, a strong approximate linear relationshipbetween desorption quantities for different kinds of soluble matters was obtained, which meansthat variation of pH values can accurately reflect the desorption results of soluble matter.Key words: soluble matter; desorption; cation; sediment; static water; indoor experiment1 IntroductionErosion of soluble matter occurs along with sediment erosion. These are the two mainerosion processes of land surfaces induced by runoff. Due to variation of the drainage basinenvironment, a large amount of soluble matter is eroded by water flow and transported intorivers, where it interacts with river flow, sediment transport, and river bed topography,resulting in considerable impacts on flow and sediment transport, as well as the processes ofriver bed deformation and landform evolution throughout the basin (Wang et al. 2009a; Xuet al. 2010; Semenov and Zimnik 2010; Reczynski et al. 2010). In China, the average erosionThis work was supported by the National Natural Science Foundati中国煤化工014) and theFundamental Research Funds for the Changjiang River, (Grant No.CKSF2013012/TB).YHCNMHG'*Corresponding author (e-mail: wenshengxu521@aliyun.com)Received Sep.16, 2013; accepted Sep.1, 2014modulus of soluble matter actually reaches 52 X 102 kg/(km^ *a) for rivers flowing into oceans,putting it at the highest level in the world (Yang et al. 2000). Therefore, substantially erodedsoluble matter has become one of the important factors in river systems, and it is necessary toinvestigate the erosion of soluble matter.On account of its considerable impact on water quality of rivers, soluble matter hascaught the attention of many hydrochemists and geochemists around the world (Meybeck andHelmer 1989; Wang et al. 2009b; Viers et al. 2009; Hurwitz et al. 2010; Li et al. 2011;Soumya et al. 2011). However, in these studies the soluble matter was more associated withriver environment evolution, rock weathering, geo-chemical cycles, and global climate change,and took less consideration of the process of erosion. In general, soluble matter mainlyincludes Na*, K, Ca2+, Mg2, CI, SO4-, HCO3, CO3-, as well as a small quantity ofdissolved heavy metal ions (Chen et al. 2005). According to the characteristics of solublematter release, the erosion of soluble matter contains two kinds of processes: one is solublematter being desorbed from sediment surfaces into water, and the other is the desorbed solublematter subsequently being transported by water flow (Shaw 1992; Xu et al. 2009). Therefore,investigation of desorption will provide a reliable basis for further understanding the erosionmechanism of soluble matter.In terms of hydro-chemical principles (Chen 2006), water quality is one of the mostimportant factors in desorption of soluble matter, which has been studied by many researchers.For instance, Tran et al. (2002) compared the effects of the pH value on desorption ofCd+ insandy soils with and without infiltration. Singh et al. (2006) investigated the desorption ofZn^+ under the influences of Cat+ in the soils of Canterbury Plain, New Zealand. Arias et al.(2005) experimentally studied the effects of the pH value and concentration of electrolytes insolutions on desorption of Cu2+ and Zn'. Nevertheless, the previous achievements mainlyfocused on the desorption of heavy metal ions, and the desorption conditions for heavy metalions differed greatly from the environment of a single actual desorption process.Water quality parameters mainly involve electrolyte type, concentration, composition insolution, and so forth. The authors have already investigated the desorption of soluble matteras influenced by Nat in static water (Xu et al. 2009). However, because of the complexity ofeffects of water quality on desorption, the influences of cations on desorption of soluble matterwere further explored in this study through static indoor experiments. For experiments, Ca2*,which has a significant impact on movement of sediment, especially sediment with fine sizesand a high concentration in natural water bodies, and H , which has a remarkable influence onsurface charge properties of fine-size sediment, were chosen as the representative ions ofsoluble matter, and the total desorption quantity of Ca2+ and pH values when desorptionequilibrium is acquired were correspondingly employed as the two indexes representing thedesorption of soluble matter. This study reasonably simula中国煤化工ofsolubleYHCNMHGWen-sheng XU et al. Water Science and Engineering, Oct. 2014, Vol. 7, No. 4, 384-39485matter, supplying a theoretical basis for understanding the erosion mechanism of solublematter in overland flow. Moreover, it is helpful to establish an erosion model of soluble matterin overland flow and to forecast variation of the water environment in a basin.2 Experiment design2.1 Materials and methodsExperiments were conducted in the State Key Laboratory of Water Resources andHydropower Engineering Science at Wuhan University. Considering that the main objective ofthis study was to explore the erosion mechanism of soluble matter in overland flow in theYangtze River Basin, and soluble matter mostly comes from accumulated loose surfacematerials on slopes, sediment (top soil) on hillslopes was chosen for testing samples. Twokinds of sediment, A and B, were sampled from the different locations in the Y angtze RiverBasin. Both of them were brown red loam soil. Sampling locations (A: 30932'36"N,114921'56"E; B: 30°32'12"N, 114920'34"E) were west of Luojia Hill at Wuhan University. Inthe region, temperature ranges from -17.3°C (January 31, 1969) to 41.3°C (August 10, 1934),with an annual average temperature of around 16.8C. The annual average precipitation is1 284.0 mm. The southwestern monsoon brings very distinct wet and dry seasons, with themajority of precipitation falling in the summer, and an annual average moisture content of77% (Zhou et al. 1999). The sampling locations were relatively pristine, densely vegetated,and hardly disturbed by human activites. For sampling, the surface sediments from twclocations with a depth of less than 20 cm were collected after the leaves, sticks, and stones hadbeen removed with a plastic scoop. Collcted samples were stored in large plastic bags andtransported to the laboratory. Before the test, the samples were naturally air dried, thoroughlymixed, and passed through a 4-mm sieve to remove the coarser particles. The pH value ofsediment was considered that of a mixture with a sediment-to-deionized water mass ratio of1:5. The pH value of the mixture was measured after shaking for one hour on an end-over-endshaker followed by one hour of equilibration. The pH values of samples A and B were 4.60 and5.70, respectively, and the grain size distribution curves for samples A and B are shown in Fig. 1.100+ SampleA-e Sample B8(复60402(100.10.01Grain size (mm)Fig. 1 Grain size distribution curves for sedim中国煤化工YHCNMHG386Wen-sheng XU et al. Water Science and Engineering, Oct. 2014, Vol. 7, No. 4, 384-394For experiments, a series of sediment samples with a mass of 100 g and 500 ml ofsolution were added into crystallizing dishes with volume capacities of 1 000 ml. The solutionwas composed of deionized water and electrolytes with a predetermined concentration. Irorder to reduce the impact of deionized water on the desorption of soluble matter, thedeionized water was filtrated with an ultrapure-water machine before use. It was shown thatthe ultrapure deionized water had a pH value of 7.4 and could be considered not to containCa2+ orH+.Then, the dishes were placed on a magnetic stirrer and stirred for 20 minutes at the samespeed, after which the dishes were sealed with plastic film and stored in a glass tank fordesorption equilibration so that the soluble matter could be fully desorbed from sedimentsurfaces. The tank was half-filled with water whose temperature was maintained at 25°C. Theequilibration time is very important in determining whether soluble matter was fully desorbedor not. In this study, the equilibration time was determined to be 23 hours through severaliterations of experiments, which agreed with the results of previous studies (Tran et al. 2002;Arias et al. 2005; Singh et al. 2006).After equilibration, the dishes were carefully taken out of the tank. Next, the supernatantsolution in the dish was poured into a glass beaker with a volume capacity of 500 ml andcollected. After filtration with a medium-speed quantitative filter paper seated on the filterholder, a clear sample solution was obtained. Then, according to the Ethylene DiamineTetraacetic Acid (EDTA ) titration method introduced in the Monitoring and Analysis MethodGuide. for Water and Waste Water (Wei et al.1997), we could easily detect the concentration ofCat in a predetermined volume of sample solution using an automatic potential titrator.Therefore, the total desorption amount of Ca2+ could be obtained through a simple calculation,which reflected the desorption results of soluble matter. In addition, the pH value of thefiltrated sample solution was detected with a portable pH measuring instrument.2.2 Experiment parametersThe parameters used in this experiment mainly included initial concentrations and typesof cations in solution. Three types of cations were used: Na,NH4 , and Ht. For each cation,we chose seven initial concentrations corresponding to the seven experimental conditions ofcase 1 to case 7. All parameters are presented in Table 1.Table 1 Initial concentration of each cation in solutionunit: mmol/LInitial concentrationCationCase I .Case 2Case 3Case 4Case 5Case 6Case 7Na*).0.010.025.050.0100.0150.0NH;*0.0H+.2.429.959.8中国煤化工YHCNM HGWen-sheng XU et al. Water Science and Engineering, Oct. 2014, Vol. 7, No. 4, 384-394383 Effects of initial cation concentrations on total desorptionquantity of soluble matterThe total desorption quantity of soluble matter is an obvious indicator of the amount ofsoluble matter released from sediment surfaces to a solution when equilibrium betweendesorption and adsorption is attained on the interface of the sediment surface and solution. ThepH value of a solution directly reflects the concentration of Ht, with a lower pH valuecorresponding to a higher concentration of Ht in a given volume of solution (Xu et al.2009).Taking Nat as an example, Fig. 2 presents the variation of the total desorption quantity ofCa2+ with the initial concentration of Nat in the solution. It is observed that Ca2+ is leastdesorbed when there is no Nat in the solution. As the initial Nat concentration increases, thtotal desorption quantity of Ca-t increases, and the increase rate of the desorption quantityfalls. This implies that there exists a maximum desorption quantity of Ca- as the initial Natconcentration increases. In addition, the total desorption quantity of Ca-+ is higher for sampleB than for sample A.Fig.3 shows the relationship between the initial concentration of Nat and the pH valuewhen desorption equilibrium is achieved. It can be seen that the pH value has the greatestvalue when there is no Nat in the solution, and that it decreases at a falling speed with theincrease of the initial concentration of Na, with the result that the pH value tends toward acertain minimum value as the initial Na“concentration continuously increases. In addition, thepH value of sample A is generally lower than that of sample B.90十Sample A5.8+ Sample A、7s-。- Sample B。Sample B, 6(鲁5.04:告4.64.2 |0 406080100120140160020406080100 120140 16(Initial concentration of Na+ (mmol/L)Fig. 2 Variation of total desorption quantity of Ca+Fig. 3 Variation of pH value withwith initial Na " concentrationinitial Na+ concentrationThis discussion on the variation of both the total desorption quantity of Ca2+ and the pHvalue with the initial concentration of cations in the solution is easily summarized by sayingthat soluble matter is least desorbed when there is no initial cation in the solution and its totaldesorption quantity increases at a falling speed as the initial concentration of cations increases.This is due to the desorption of soluble matter consisting of two processes: diffusion and ionexchange (Li 2001; Xu et al. 2010). In a solution that is initially without cations, solublematter is desorbed through a process of diffusion, in which soluble matter directly diffusesfrom sediment surfaces into a solution due to a conce中国煤化Ile matterYHCNMHG388Wen-sheng XU et al. Water Science and Engineering, Oct. 2014, Vol. 7, No. 4, 384-394between sediment surfaces and the solution. However, as it is attracted by molecular andelectrostatic attraction forces induced by the inner sediment particle core, soluble matter isconsequently less desorbed.In a solution with a low concentration of cations, the cations are found to have a greaterchance of both diffusing to sediment surfaces from a solution and subsequently exchangingions with soluble matter originally attracted on sediment surfaces when cations' initialconcentration increases. As a result, more soluble matter is desorbed from sediment surfacesand then diffused into a solution, which manifests as the total desorption quantity of solublematter in the solution increasing. However, the total amount of exchangeable soluble matter onthe sediment surfaces is finite, and the ion exchange process between the soluble matteroriginally adsorbed on the sediment surfaces and the cations in a solution is reversible, so, asthe soluble matter is continually exchanged, the exchange intensity gradually weakens. As aresult, it can be seen that the total desorption quantity of soluble matter gradually increases toa maximum constant amount at a falling speed, with the increase of the initial concentration ofcations in the solution. .4 Effects of different cations on total desorption quantity ofsoluble matterWhen soluble matter is naturally desorbed into overland flow, more than one type ofcation is usually contained in the water body at the same time, with each type havingindividual special chemical properties, inducing different influences on the desorption process,and consequently causing different effects on the total desorption quantity of soluble matter.This is discussed below.Because the results of sediment samples A and B are similar, only one of them israndomly selected for illustration here. As an example, Fig. 4 shows the relationship betweenthe total desorption quantity of Cat+ released from sediment sample A and the initialconcentration of different types of cations. It can be seen that there is a similar variation of thetotal desorption quantity of Cat ' with the initial concentration of different types of cations. Atthe same initial concentration, the total desorption quantity of Ca2+ differs for different typesof cations, with the highest total desorption quantity of Cat+ in the solution with Ht, and thelowest one in the solution with Na* .Fig.5 shows the variation of the pH value with the initial concentrations of differenttypes of cations when desorption equilibrium is attained. It can be observed that the pH valuestill has a similar variation profile with the initial concentrations of different types of cations.At the same initial concentration, the pH value is highest in the solution with Na, and lowestin the solution with H . As the initial concentration of cations increases, the difference in thepH value between the solutions with different types of qrtia~ i中国煤化工finally, aconstant value is maintained between the solutions with NFYHCNMH GWen-sheng XU et al. Water Science and Engineering, Oct. 2014, Vol. 7, No. 4, 384-394899060:二 :45- Na++ Na*0 NHfθ NH:→H+- H+0 4060 80100 1201401602014016(Initial concentration of cation (mol/L)Initial concentration of cation (mmo/L)Fig. 4 Variation of total desorption quantity of Ca2+ withFig. 5 Variation of pH value with initialinitial concentration of different kinds of cationsconcentration of different kinds of cationsIn order to further explore the effects of cation type on the desorption of soluble matter,the variation of the total desorption amount of soluble matter with the initial concentration ofdifferent cations was fitted with the Langmuir equation, which is mostly used with highprecision (Tran et al. 2002; Arias et al. 2005; Xu et al. 2010). The Langmuir equations for thetotal desorption amount of Ca + and pH value are as follows:τ=Tmx K,C(1)1+ K,CPin K,C(2)1+K2Cwhere C is the initial concentration of cations in solution (mmol/L), T is the total desorptionquantity ofCat (mg/L), P is the pH value, Tmax is the maximum desorption amount of Ca-(mg/L), Pmin is the minimum pH value, K is the desorption coefficient, and K, is theequilibrium coefficient.Table 2 shows the ftted parameters of Eq. (1) and Eq. (2). From the ftted results it can beseen that the maximum desorption amount of Cat+ is different for different types of cations,with an ascending order of Na, NH4, to Ht, which is similar to the variation of desorptioncoefficients, but is entirely opposite to the variation of the minimum pH value. The resultsgiven in Table 2 are in considerably good agreement with those presented in both Fig. 4 and Fig. 5.Table 2 Fitted parameters of Eq. (1) and Eq. (2)Eq.(1)Eq.(2)CationTmax (mg/L)KiR'PminKzR?Na+57.800.083 10.9843.92-1.083 60.999NH4*69.930.1143 .0.9913.68-1.287 2H86.960.361 60.9951.81-0.479 10.989Note: R' is a orrelation coefficient between the calculated and observed values.Desorption coefficient K and equilibrium coefficient K2 are two extremely significantfactors influencing the total desorption quantity of Ca2+ and the pH value when desorptionequilibrium is reached. They are dominated by the properties of soluble matter, cation type,sediment characteristics, and the interface action between中国煤化工2001). In"YHCNMHG390Wen-sheng XU et al. Water Science and Engineering, Oct. 2014, Vol. 7, No. 4, 384-394our experiment K,and K2 were mainly determined by the type of cations contained in thesolution. The hydrochemistry properties of Na,NH4, and Ht are remarkably different. As aresult, the desorption coefficient K,and equilibrium cofficient Kz present considerablevariation along with the cation type.From the analysis above it can be concluded that the total desorption quantity of solublematter has similar variation with the initial concentration of cations for both different sedimentsamples and various types of cations. However, the total desorption quantity of soluble matteris entirely different for various types of cations, with the result that the desorption amount is .highest in the solution with H , lowest in the solution with Na , and in between the two formervalues in the solution with NH4, due to the diversity of affinity between the cation andsediment surface. The affinity differs for different cations because of the difference of theirspecial hydrated ionic radii, which results in the number of cations joining in the exchangewith soluble matter being different, and then a different amount of soluble matter beingdesorbed for different cations (Shaw 1992). According to Li's experimental results (Li 2001),the affinity for Ht, NH4, and Nat with sediment surfaces follows an order of Ht > NH4 >Nat , which leads to the same order of the influences on the total desorption quantity of solublematter. Therefore, the stronger the affinity is, the greater the ability of cations to exchange ionswith the soluble matter originally adsorbed on sediment surfaces, which can subsequentlycause more soluble matter to be released into the solution: a stronger affinity will give rise to ahigher total desorption quantity of soluble matter.5 Analysis of relationship between total desorption quantity ofsoluble matter and pH valueNatural sediment surfaces are covered by many types of soluble matter. When desorptionis complete, a dynamic equilibrium between desorption and adsorption of soluble matter onthe interfaces between the sediment surface and solution will be obtained, which subsequentlyinduces the existence of a certain quantitative relationship among the total desorption amountsfor different types of soluble matter.Fig.6 presents the variation of the pH value against the total desorption quantity ofsoluble matter for (a) different sediment samples with a cation type of Nat and (b) differenttypes of cations with sediment sample A. As shown in Fig. 6, the pH value decreases with theincrease of the total desorption quantity, irrespective of the sediment sample type and cationtype. The pH value was observed to have similar variation with the total desorption amount ofsoluble matter for different sediment samples (Fig. 6(a)), resulting in sediment sample A beingrandomly selected to be further analyzed as an example (Fig. 6(b)). Fig. 6(b) shows that therate of decrease of the pH value changes depending on the specific cation type. The figure alsoshows that, as the total desorption quantity of Catt increases, the pH value decreases at afalling rate in the solutions with Na+ and NH4 , and it decr中国煤化invariablerate in the solution with Ht. With the same total desorpticference inYHCNMHGWen-sheng XU et al. Water Science and Engineering, Oct. 2014, Vol. 7, No. 4, 384-394391pH values for different types of cations is negligible with a low desorption amount of Cat ,whereas it gradually increases when the total desorption quantity of Ca2+ increases. Duringthis process, the difference in pH value between the solutions with Nat and NHA* cationsgradually increases and finally stabilizes. With a high total desorption amount of Ca2 , the pHvalue is greatest in the solution with Na , lowest in the solution with H , and in between thesetwo values in the solution with NH4*.6.-.-SampleA4.8一Na*- o Sample Be NH.0 t-+H+国48.43.61304607590.6L45607590Total desorption quantity of Ca2+ (mg/L)(a) Diferent sediment samples with Na*(b) Dfferent cation types with sediment sample AFig. 6 Variation of pH value with total desorption quantity of Ca2To further examine the relationship between the total desorption quantity of solublematter and the pH value, a regression analysis was conducted. The regression equation weused is as follows:P=aT'+b(3)where T' is the logarithm of the total desorption quantity of Cat,and a and b are coefficients.The results are shown in Table 3. It can be seen that the logarithm of total desorptionquantity of Cat has a strong linear relationship with the pH value, and the correlationcoefficients (r2) between T' and P are mostly greater than 0.99, except for H, where r2 =0.86. This proves that desorption of Catf and Ht are two companion processes. It can beconcluded that the variation of the pH value can accurately represent the desorption quantityof soluble matter.Table 3 Parameters of ftted equations used for simulating relationship between pH valueand desorption quantity of Ca2CationSediment sampleA. -1.075.800.99B-1.457.35NH:°-1.276.00H+-3.288.660.86Based on these analyses, it can be concluded that, under influences of cations, thedesorption processes for different types of soluble matter originally adsorbed on sedimentsurfaces occur simultaneously, and that they correlate with one another. This is not surprising,because for any specific cation there is a similar chance of diffusing to different adsorptionsites on sediment surfaces. Thus, for different cations, th中国煤化工a specific"TYHCNMHG392Wen-sheng XU et al. Water Science and Engineering, Oct. 2014, Vol. 7, No. 4, 384-394cation exchanging with different types of soluble matter originally adsorbed on sedimentsurfaces, which results in a strong correlation between desorption processes of different typesof soluble matter. Nevertheless it should be noted that competition for desorption exists, andthe exchange energy for different types of soluble matter changes with cations, meaning thatthe chances for different types of desorbed soluble matter to be adsorbed to sediment surfacesagain are different. Therefore, in the same desorption environment, different types of solublematter will show different desorption amounts.6 ConclusionsAs one of the significant erosion processes in rivers, desorption of soluble matter hasconsiderable influence on flow and sediment transport. In order to understand the erosionmechanism of soluble matter from sediment in overland flow, based on indoor experiments ondesorption of soluble matter as influenced by cations in static water, the following conclusionscan be drawn:. (1) The higher the initial concentration of cations is in the solution, the larger the totaldesorption quantity of soluble matter will be. A maximum value of the total desorptionquantity of soluble matter will be reached asymptotically.(2) The type of cations has a considerable effect on the total desorption quantity ofsoluble matter. The stronger the affinity is between cations and sediment surfaces, the higherthe total desorption quantity of soluble matter will be. The experimental results show that thetotal desorption quantity ofCa2+ for Ht, NH4, and Nat follows an order ofHt> NH4+> Nat.(3) Strong correlation was observed for the desorption processes of different types ofsoluble matter, as exemplified by the relation between the pH value and the total desorptionquantity of Cat, although the total desorption quantity varies from one to another. As the totaldesorption quantity of soluble matter increases, the pH value decreases. This suggests that thevariation of the pH value can be used to represent the extent and quantity of desorption ofsoluble matter.While soluble matter is naturally desorbed in overland flow with dynamic waterenvironments, the present experiments were only conducted in static water conditions, withoutconsideration of the action of water flow. Therefore, further investigation of desorption ofsoluble matter as influenced by dynamic water flow is warranted.AcknowledgementsWe wish to thank Dr. Hu Peng of Zhejiang University, China for his valuable suggestions.ReferencesArias, M., Perez-Novo, C, Osorio, F, Lopez, E., and Soto, B. 2005. Adsorption and desorption of copper andzinc in the surface layer of acid soils. Journal of Colloid and Interface Science, 288(1), 21-29. [doi:10.1016/jcis.2005.02.053]Chen, J. S, Wang, F. Y, Meybeck, M., He, D. W., Xia, X. H, an中国煤化工1d temporalanalysis of water chemistry records (1958-2000) in the"YHCNMHGin. GlobalWen-sheng XU et al. Water Science and Engineering, Oct. 2014, Vol. 7, No. 4, 384-39439Biogeochemical Cycles, 19(3), 1-24 (GB301 6). [doi:10. 1029/2004GB002325]Chen, J. S. 2006. Principle of Water Quality in Rivers and Water Quality of Rivers in China. Bejjing: SciencePress. (in Chinese)Hurwitz, S, Evans, W. C, and Lowenstern, J. B. 2010. 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