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Water Research 85 (2015) 393e403

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Mathematical model for interactions and transport of phosphorus andsediment in the Three Gorges Reservoir

Lei Huang a, Hongwei Fang a, Danny Reible b, *

a State Key Laboratory of Hydro-science and Engineering, Department of Hydraulic Engineering, Tsinghua University, Beijing, 100084, Chinab Department of Civil & Environmental Engineering, Texas Tech University, Lubbock, TX, 79409-1023, USA

a r t i c l e i n f o

Article history:Received 10 February 2015Received in revised form11 July 2015Accepted 25 August 2015Available online 1 September 2015

Keywords:Phosphorus transportSediment transportMathematical modelThree Gorges Reservoir

* Corresponding author.E-mail address: danny.reible@ttu.edu (D. Reible).

http://dx.doi.org/10.1016/j.watres.2015.08.0490043-1354/© 2015 Elsevier Ltd. All rights reserved.

a b s t r a c t

Phosphorus fate and transport in natural waters plays a crucial role in the ecology of rivers and reser-voirs. In this paper, a coupled model of hydrodynamics, sediment transport, and phosphorus transport isestablished, in which the effects of sediment on phosphorus transport are considered in detail. Phos-phorus adsorption is estimated using a mechanistic surface complexation model which is capable ofsimulating the adsorption characteristics under various aquatic chemistry conditions. The sedimentdynamics are analyzed to evaluate the deposition and release of phosphorus at the bed surface. Inaddition, the aerobic layer and anaerobic layer of the sediments are distinguished to study the distri-bution of phosphorus between dissolved and particulate phases in the active sediment layer. The pro-posed model is applied to evaluate the effects of various operating rules on sediment and phosphorusretention in the Three Gorges Reservoir (TGR). Results show that the proposed model can reasonablyreflect the phosphorus transport with sediment, and management scenarios that influence sedimentretention will also influence the phosphorus balance in the TGR. However, modest operational changeswhich have only minor effects on sediment retention also have limited influence on the phosphorousbalance.

© 2015 Elsevier Ltd. All rights reserved.

1. Introduction

Phosphorus, one of the key nutrients affecting water quality, isthe major limiting factor for eutrophication (Schindler, 2006; Elseret al., 2007). Thus the phosphorus transport process plays a crucialrole in the aquatic ecological environment. In recent decades, hu-man activities have greatly changed the inherent characteristics ofmany inland waters (Zhang et al., 1999; Syvitski et al., 2005; Daiet al., 2008) resulting in substantial effects on nutrients, includingphosphorous. Impoundment of rivers for reservoirs can result in asignificant increase in sediment and phosphorus retention, posingserious environmental concerns (Camargo et al., 2005; Yao et al.,2009). Operational controls on the reservoir can be used to mini-mize the retention of phosphorous. This has encouraged thedevelopment of models of phosphorous transport to evaluatedifferent operating scenarios and develop optimal control ap-proaches. To maximize their utility, these models should accuratelydescribe key phosphorous transport processes, particularly

phosphorousesediment interactions.Sediment particles have a strong affinity to phosphorus due to

the high specific surface areas and surface active sites (Davis andKent, 1990; Wang et al., 2009; Fang et al., 2013). Most phos-phorus in waters are adsorbed by sediment particles and trans-ported in the particulate phase (Withers and Jarvie, 2008). Theadsorbed phosphorus may accumulate at the bed surface due tosediment deposition and can later be released by resuspension.Phosphorus partitioning from the solids to the interstitial watersalso exchanges with the overlying water (House and Denison,2002; Wang et al., 2003) as a result of hyporheic exchange andother processes. Understanding phosphorusesediment in-teractions is critical to understanding phosphorous transport in thesystem.

Mathematical modeling is an effective tool for predicting thephosphorus transport, and a great number of water quality modelshave been developed over recent decades (Wool et al., 2001; Parket al., 2008). Early models often ignored sediment dynamics,which does not allow evaluation of the effect of sediment man-agement operations on phosphorus transport (Broshears et al.,2001). Subsequently, a great number of models that incorporatesediment dynamics were proposed (Larsen et al., 1979; Wool et al.,

L. Huang et al. / Water Research 85 (2015) 393e403394

2001; Chu and Rediske, 2011). Most of these models considerlargely empirical relationships, such as a linear distribution coef-ficient Kd or first order adsorption (rate constant k1) and desorption(rate constant k2) to represent the adsorption of phosphorus bysediment (Wool et al., 2001). Other simplifications included asedimentation coefficient Ks and an erosion coefficient Ku to char-acterize the deposition and resuspension of phosphorus at the bedsurface (Chu and Rediske, 2011), or a constant phosphorus releaserate at the sedimentewater interface (Larsen et al., 1979). It isdifficult to choose reasonable values for these parameters due tothe lack of a fundamental mechanistic basis, and these parametersare site-specific and not easily extended. In addition, most of thesemodels do not represent a comprehensive evaluation of the effectsof sediment on phosphorus transport but are instead focused onspecific processes.

This paper aims to develop a model of the coupled hydrody-namics, sediment and phosphorus transport, inwhich the effects ofsediment on phosphorus transport are comprehensively consid-ered. A mechanistic surface complexation model, which can betterdescribe surface adsorption phenomena by treating surfaceadsorption reactions as complexation reactions, is applied toanalyze the adsorption of phosphorus on sediment particles. Thenthe riverbed deformation is included to characterize the depositionand resuspension of phosphorus at the bed surface. In addition, theaerobic and anaerobic layers are distinguished to study the distri-bution of phosphorus in the active sediment layer, which accountsfor the exchange of phosphorus between the bottom sediment andthe overlying water. The proposed model is applied to predictingphosphorus transport in the Three Gorges Reservoir (TGR) in cen-tral China and evaluating the effectiveness of various operatingrules on sediment and phosphorus retention in the reservoir.

2. Materials and methods

2.1. Description of study area

The Three Gorges Project (TGP), the largest hydraulic project intheworld, is located in the Yangtze River as shown in Fig. 1. The TGPis made up of the concrete gravity dam, reservoir, and power sta-tion and navigation structures. The Three Gorges Dam (TGD) has a

Fig. 1. Sketch map of the T

crest elevation of 185 m with the normal pool level (NPL) of 175 mrelative to the Chinese water datum. The return periods of thedesign flood and themaximum flood for the dam are 1000 year and10000 year þ10%, respectively. The total capacity of the ThreeGorges Reservoir (TGR) formed by the TGP is 393 � 108 m3, with aflood control capacity of 221.5 � 108 m3. The surface area is1084 km2 under the NPL of 175 m, with the watershed area of over1.0 � 106 km2. The flow velocity of the main channel decreased to0.13e0.24 m/s after impoundment (Wu et al., 2012). It is estimatedthat the monthly retention time of the TGR ranges from 5 to 77 dwith the mean value of 27 d (Xu et al., 2011), indicating that themain stem is vertically well-mixed and remains unstratified for themajority of the year. The total installed hydroelectric capacity is22500MW. The impoundment of the TGR started on June 1st, 2003,and subsequently the first generating unit was put into operation.On October 26th, 2010, the water level at the dam first reached theNPL of 175 m.

The TGP is operated to support a variety of objectives includingflood control, hydropower generation, navigation, and water stor-age. There are also many complex problems associated withreservoir operation including sedimentation and ecological im-pacts. Table 1 shows the variations of annual runoff and sedimentdischarge before and after the impoundment of the TGR (CWRC,2000e2010). Cuntan station is located in the tail of the TGR andcan be regarded as the upstream control section. Yichang station is38 km downstream from the TGD and can be regarded as thedownstream control section. Then the sediment delivery ratio(SDR) is estimated to be 27.6% (¼0.54/1.96) in the post-TGP period(2003e2010), which is much smaller than that of the pre-TGPperiod (1950e2002). Simultaneously, the upstream nutrients arealso intercepted by the TGR due to the strong affinity of phosphorusto sediment particles. An accurate simulation of the sediment andphosphorus transport and its response to operating conditions isnecessary for the optimal operation of the TGR.

2.2. Hydrodynamic-sediment-phosphorus transport model

2.2.1. Hydrodynamic moduleThe hydrodynamic module consists of continuity equation and

momentum equation, assuming vertically and laterally uniform

hree Gorges Reservoir.

Table 1Comparison of annual runoff and sediment discharge before and after the impoundment of the TGR (CWRC, 2000e2010).

Station Pre-TGP(1950e2002) Post-TGP(2003e2010)

Annual runoff(109 m3)

Sediment discharge(108 t/a)

Sediment concentration(kg/m3)

Annual runoff(109 m3)

Sediment discharge(108 t/a)

Sediment concentration(kg/m3)

Cuntan 345 4.30 1.24 326 1.96 0.598Yichang 434 4.95 1.13 396 0.54 0.136

L. Huang et al. / Water Research 85 (2015) 393e403 395

conditions (i.e. 1 dimension in length along the TGR):

Continuity equation : BvZvt

þ vQvx

¼ 0 (1)

Momentum equation :vQvt

þ v

vx

�Q2

A

�þ gA

vZvx

þ gQ jQ jC2AR

¼ 0

(2)

where B is the river width; Z is the water level; Q is the discharge; Ais the cross sectional area; g is the acceleration of gravity; C is theChezy resistance coefficient; and R is the hydraulic radius.

2.2.2. Sediment transport moduleThe sediment transport is described using a non-equilibrium

approach, considering the exchange between suspended sedi-ment and bottom sediment. The governing equation can be writtenas

vðASÞvt

þ vðQSÞvx

þ auBðS� S*Þ ¼ v

vx

�ExA

vSvx

�(3)

where S and S* are the average suspended sediment concentrationand the sediment carrying capacity of the cross section, respec-tively; and S* is expressed as (Fang and Wang, 2000)

S* ¼ k�

U3

gRu

�m

(4)

where k and m are empirical coefficient and exponent; U is theaverage velocity of the cross section; u is the settling velocityexpressed as

u ¼��

13:95n

D

�2 þ 1:09gs � g

ggD

�1=2� 13:95

n

D(5)

where n is the kinematic viscosity of water associated with tem-perature; D is the diameter of sediment particles; and g and gs arethe specific weight of water and sediment respectively. In Eq. (3), Exis the diffusion coefficient; a is the restoring saturation coefficient,reflecting the rate of S approaching S* under non-equilibriumtransport, and different values are applied for deposition anderosion, i.e., aD and aE, thus the third term on the left of Eq. (3)represents the sediment deposition or erosion at the bed surface.Then the equation of the riverbed deformation can be expressed as

rsð1� εÞ vzvt

¼ auðS� S*Þ (6)

where rs is the density of sediment particles with the value of2650 kg/m3; ε is the porosity of the bottom sediment; z is theelevation of the bed surface, and Dz can represent the thickness ofdeposition or erosion.

2.2.3. Phosphorus transport moduleFig. 2 shows a conceptual model including the physical and

chemical dynamics involved in phosphorus transport. Phosphorusin waters is transported in the dissolved form through convection-diffusion and the adsorbed phosphorus is transported by the mo-tion of the suspended sediment particles (Withers and Jarvie,2008). In addition, the bottom sediment has significance in-fluences on phosphorus transport (House and Denison, 2002;Wang et al., 2003). Phosphorus in waters exchanges with that inthe pore water of the active sediment layer and the adsorbedphosphorus also exchanges with that in the active sediment layerdue to the deposition and resuspension of sediment particles. Thus,this model includes both the water and active sediment layer,involving the convection-diffusion, adsorption-desorption,deposition-resuspension, as well as other physical and chemicalprocesses. The TGR is an unstratified reservoir with essentiallyuniform oxygen concentration from the surface to the bed sedi-ments, thus maintaining oxic conditions at the sediment surface.Deeper in the sediments, however, microbial reduction and slowoxygen transport from the sediment surface result in the devel-opment of an anaerobic layer. Thus as with DiToro (2001), the activesediment layer is divided into a thin aerobic layer and an anaerobiclayer to consider the chemical reactions related to redox conditions.

The phosphorus transport module consists of four governingequations describing the concentration variations of phosphorusdissolved in water (Cw), bound to suspended sediment particles(Cs), and total phosphorous in the aerobic layer (CTb,1) and anaerobiclayer (CTb,2). The temporal evolutions of the phosphorus concen-trations are obtained by solving the basic convection-diffusionequations, and the expressions are as follows:8>>>>>>>>><>>>>>>>>>:

vðACwÞvt

þ vðQCwÞvx

¼ v

vx

�ExA

vCw

vx

�� lACw þ Sw

vðASCsÞvt

þ vðQSCsÞvx

¼ v

vx

�ExA

vðSCsÞvx

�þ Ss

BHivCb;i

Tvt

¼ Sbi

(7)

where l is the net algal uptake rate for the dissolved phosphorus;i ¼ 1, 2 correspond to aerobic and anaerobic layers, and H1 and H2are the thickness of aerobic and anaerobic layers respectively; thesource terms Sw, Ss and Sbi are functions of R1 ~ R13which representvarious processes related to phosphorus transport (Fig. 2) and willbe introduced in the following sections. The algal uptake rate wasestimated from Hamilton and Schladow (1997) and has only aminor influence on phosphorus dynamics but is included here forcompleteness.

2.2.3.1. Sources of phosphorus. Prior to the development ofanthropogenic sources, the weathering of phosphorus-bearingminerals was the main source of phosphorus in waters. Theseminerals weather as a result of the reaction with dissolved carbondioxide in the form of carbonic acid:

Ca5ðPO4Þ3OHþ 4H2CO3/5Ca2þ þ 3HPO2�4 þ 4HCO�

3þH2O

(8)

Fig. 2. Conceptual model of phosphorus transport. The study area is divided into water, aerobic and anaerobic layers in the vertical direction, with the thickness of H, H1 and H2

respectively; and R1 ~ R13 represent various processes related to phosphorus transport.

L. Huang et al. / Water Research 85 (2015) 393e403396

Now the sources of phosphorus are dominated by human ac-tivities, including industrial and domestic wastewater point sour-ces and agricultural diffuse sources. Research shows that the networldwide input of dissolved phosphorus from land to the oceans is4e6 Tg P/y, which represents a doubling of pre anthropogenic inputfluxes (Filippelli, 2008). The source term R1 denotes the totalphosphorus emissions in the model.

2.2.3.2. Adsorption of phosphorus by suspended sediment.Adsorption, the accumulation of ions at the solid/liquid interface ofsuspended sediment is of great significance to phosphorus trans-port. Various types of hydroxyl groups and other charged speciesexist on the surface of sediment particles (Davis and Kent, 1990).Mechanistic surface complexation models describe surfaceadsorption as chemical reactions between these charged groupsand contaminant ions, with the capability of reflecting theadsorption characteristics of sediment particles under differentaquatic chemistry conditions. The surface protonation and depro-tonation of the sediment are expressed as follows

> SOHþ Hþ4> SOHþ2 K int

a1 (9)

> SOH4> SOþ Hþ K inta2 (10)

where > S represents the surface of sediment particles, and Ka1int and

Ka2int are the intrinsic acidity constants. The phosphorus adsorption

is expressed as follows

> SOHþ Hþ þ PO3�4 4> SPO2�

4 þ H2O K int1 (12)

> SOHþ 2Hþ þ PO3�4 4> SHPO�

4 þ H2O K int2 (13)

> SOHþ 3Hþ þ PO3�4 4> SH2PO4 þH2O K int

3 (14)

where K1int, K2

int and K3int are the intrinsic surface complexation

constants. These constants are further corrected with an electro-static factor to reflect the effect of the charge at the solid/liquidinterface. Then the surface adsorption problem is reduced to thesolution of the mass-action and mass-balance expressions. Athorough review of the computational formulation of surfaceadsorption equilibrium problems is present by Tadanier and Eick(2002).

Based on the various considerations of the interfacial structure,a number of different surface complexation models have beenproposed. The constant capacitance model (CCM) has been exten-sively applied to describe surface adsorption. Fig. 3 shows thesimulation results of CCM for phosphorus adsorption underdifferent sediment concentrations as measured by Yu et al. (2010)from a mixture of samples collected from Cuntan, Qingxichang,and Wanxian. Parameters are listed in Table 2, and a surface sitedensity of 2.31 sites/nm2 is applied, which is recommended byDavis and Kent (1990) for general modeling of bulk compositematerials. Surface area of 17.48 m2/g is the site specific value, andother parameters in Table 2 refer to Huang et al. (2014). Therefore, a

Fig. 3. Simulation of phosphorus adsorption under different sediment concentrationsby CCM. Data refer to Yu et al. (2010).

L. Huang et al. / Water Research 85 (2015) 393e403 397

function of Kd(F) can be obtained using CCM to estimate thepartition of phosphorus at the solid/liquid interface, where thevariable F represents a variety of internal and external factors, suchas specific surface area (Chen and Fang, 2013), mineral compositionand surface charge distribution of sediment particles (Huang et al.,2012; Chen et al., 2013), as well as sediment concentration, pH andionic strength etc.

Mechanistic surface complexation models have been widelyapplied to adsorption since first proposed in the early 1970s. Thesemodels have also been introduced for the simulation of pollutanttransport in groundwater (Kent et al., 2000; Curtis et al., 2006), butthe coupling of surface complexation models into surface waterquality models is rarely reported. In this model, the constantcapacitance model is applied to analyze the adsorption of phos-phorus on sediment particles, and expressed by the source term R2,i.e.,

R2 ¼ ASk2ðKdðFÞCw � CsÞ (15)

where k2 is the desorption rates.

2.2.3.3. Phosphorus exchanges between adjacent layers. Similar tothe phosphorus in the water layer, phosphorus in the active sedi-ment layer also includes phosphorus bound to the sediment par-ticles and that dissolved in the pore water. However, thepartitioning is significantly affected by redox conditions (Patrickand Khalid, 1974). Research shows that Fe/Al (hydr)oxides have ahigh affinity for phosphorus and dominate the adsorption ofphosphorus on sediment particles (Wang et al., 2009). The dis-solved Fe2þ is oxidized to the particulate FeOOH under aerobicconditions (Eq. (16)), and have a strong adsorption capacity tophosphorus. But the particulate FeOOH is reduced to the dissolvedFe2þ under anaerobic conditions (Eq. (17)), resulting in the releaseof adsorbed phosphorus into the pore water. The oxygenated sur-face waters maintain a thin aerobic layer where iron oxidationoccurs and a thicker anaerobic layer dominated iron hydroxide

Table 2Parameters for the simulation of phosphorus adsorption on sediment particles in theTGR (Davis and Kent, 1990; Huang et al., 2014).

Parameter Value Parameter Value

logKa1 �1 logK3 30.72logKa2 �8 Site density (sites/nm2) 2.31logK1 19.65 Surface area (m2/g) 17.48logK2 24.91 C (F/m2) 1

reduction. In the current calculations, the thickness of aerobic layeris set as 1 cm, and 10 cm for the anaerobic layer (estimated fromChomat and Westphal, 2013). Sensitivity analyses showed nodependence of the conclusions on the aerobic thickness over therange of 0.1 cme1 cm.

Aerobic layer : 4FeðIIÞ2þ þ O2 þ 6H2O/4FeOOHðsÞ þ 8Hþ

(16)

Anaerobic layer : 4FeOOHðsÞ þ CH2Oþ 8Hþ/4FeðIIÞ2þ

þ CO2 þ 7H2O

(17)

In the model, the total phosphorus concentration in the activesediment layer is denoted as CT

b,i, and fdi and fpi represent the per-centages of the dissolved and particulate phases, respectively,where i ¼ 1, 2 correspond to aerobic and anaerobic layers. fdi and fpiare functions of dissolved oxygen concentrations.

Phosphorus exchanges between water and sediment areassumed proportional to the concentration differences. The sourceterms R3 and R4 denote the phosphorus exchange between thewater layer and the pore water of aerobic layer, and that betweenaerobic and anaerobic layers, respectively.

R3 ¼ BKL01

�Cw � fd1C

b;1T

�(18)

R4 ¼ BKL12

�fd1C

b;1T � fd2C

b;2T

�(19)

where KL01 and KL12 denote the mass transfer coefficients.In addition, phosphorus exchanges also occur between aerobic

and anaerobic layers due to the activities of benthic organisms.Similarly, the exchange capacity is assumed to be proportional tothe concentration differences, denoted as the source term R5.

R5 ¼ Bu12

�fp1C

b;1T � fp2C

b;2T

�(20)

where u12 is the bioturbation mixing rate, affected by the benthicbiomass, activity, water temperature, and dissolved oxygenconcentration.

2.2.3.4. Riverbed deformation. The suspended sediment particleswould accumulate at the riverbed due to deposition, and the bot-tom sediment would also be eroded to resuspension under certainflow conditions, which simultaneously causes the deposition andrelease of phosphorus at the bed surface. The source terms R6、R7、R10 and R12 are used to represent the phosphorus variationsin different layers related to sediment deposition, as shown inFig. 2. Among them, R6 and R7 represent the increments of phos-phorus dissolved in pore water and that bound to the sedimentparticles in the aerobic layer, respectively; R10 and R12 representthe buried phosphorus in the aerobic and anaerobic layers tomaintain the constant thickness. Depending on the differentthickness of deposition Dz, these source terms are expressed in Eq.(21) ~ Eq. (24).

Expressions of the source terms related to sediment deposition:

R6 ¼ BDzεCw=Dt (21)

R7 ¼ BDzð1� εÞrsCs=Dt (22)

L. Huang et al. / Water Research 85 (2015) 393e403398

R10¼(BDzCb;1

T

.Dt Dz�H1

BhH1C

b;1T

.DtþðDz�H1ÞðεCwþð1�εÞrsCsÞ=Dt

iDz>H1

(23)

R12 ¼

8><>:

BDzCb;2T

.Dt Dz � H2

BhH2C

b;2T

.Dt þ ðDz� H2ÞCb;1

T

.Dt

iH2 <Dz � H1 þ H2

BhH2C

b;2T

.Dt þ H1C

b;1T

.Dt þ ðDz� H1 � H2ÞðεCw þ ð1� εÞrsCsÞ=Dt

iDz>H1 þ H2

(24)

Expressions of the source terms related to sediment erosion:

R8 ¼(BjDzjfd1Cb;1

T

.Dt �H1 � Dz<0

BhH1fd1C

b;1T

.Dt þ ðjDzj �H1Þfd2Cb;2

T

.Dt

iDz< �H1

(25)

R9 ¼(BjDzjfp1Cb;1

T

.Dt �H1 � Dz<0

BhH1fp1C

b;1T

.Dt þ ðjDzj �H1Þfp2Cb;2

T

.Dt

iDz< �H1

(26)

R11 ¼ BjDzjCb;2T

.Dt (27)

R13 ¼ BjDzjCb;2T

.Dt (28)

Similarly, the source terms R8, R9, R11 and R13 are used torepresent the phosphorus variations in different layers related tosediment erosion, as shown in Fig. 2. Among them, R8 and R9represent the reduction of phosphorus dissolved in pore water andthat bound to the sediment particles in the aerobic layer, respec-tively; R11 and R13 represent the backfilling of phosphorus in theaerobic layer and anaerobic layers to maintain the constant thick-ness. The expressions of these source terms are shown in Eq.(25) ~ Eq. (28).

Finally, the sources terms Sw, Ss and Sbi in Eq. (7) are expressed asfollows:8>><>>:

Sw ¼ R1� R2� R3� R6þ R8Ss ¼ R2� R7þ R9Sb1 ¼ R3� R4� R5þ ðR6þ R7Þ � ðR8þ R9Þ � R10þ R11Sb2 ¼ R4þ R5þ R10� R11� R12þ R13

(29)

And substituting Eq. (29) into Eq. (7), the phosphorus transportmodule is then established.

2.3. Data collection

The calculation range from Cuntan to the TGD is divided into295 segments, with a total length of 604 km, i.e., an average dis-tance of about 2 km between adjacent cross sections. Cuntan,Qingxichang and Wanxian are the key hydrological stations that

measure water discharge and sediment load (Fig. 1). A nine yearseries of measured data from 2003 to 2011, including discharge,sediment and phosphorus concentration in Cuntan, and water levelat the Dam, are used as the boundary conditions, as shown in Fig. S1in the supplementary material. All the data are daily-averagedvalues except for the monthly phosphorus concentration.

In addition, the measured phosphorus concentration from May

to September 2004 is used for model validation, including the dataof Qingxichang, Wanxian and Fengjie, which are 479.30 km,291.61 km and 160.91 km upstream from the TGD respectively.

The calculation is carried out from 2003 to 2011, and themeasured sediment gradations of suspended and bed sediment areapplied, as shown in Table S1. Relevant parameters are shown inTable 3. The dry bulk density rb and porosity ε of the bottomsediment are obtained from the Bulletin of the Yangtze RiverSediment published annually by the CWRC (2000e2010). Diffusioncoefficient Ex is calculated with the empirical formula proposed byElder (1959), i.e., Ex ¼ 5.86hu*, where h is the water depth and u* isthe friction velocity. The algal uptake rate of phosphorus l refers toHamilton and Schladow (1997). Desorption rate k2 originates fromthe kinetic adsorption experiment (Yu et al., 2010). Mass transfercoefficient KL01 and KL12 are derived from the molecular diffusioncoefficient, which ranges from 10�5 to 10�6 cm2/s for generalcontaminants. The arithmetic mean for the biodiffusion coefficientis 1.23 � 10�7 cm2/s for freshwater (Reible, 2014), with which thebioturbation mixing rate u12 is obtained. And the percentages ofthe dissolved and particulate phases fdi and fpi refer to DiToro(2001).

The vast majority of the flow discharge, sediment load andphosphate load in the system is in the main stem of the river, andsmall lateral inflows are ignored to simplify the model calculation.The initial total phosphorus concentration in the active sedimentlayer is assumed to be zero. In order to minimize the influence ofinitial conditions, the model runs 1 year to convergence before theactual model calculation. A time step of 36 s is used throughout thesimulation.

3. Model calibration

3.1. Hydrodynamic and sediment transport

The variations of water level, discharge and sediment concen-tration at Qingxichang and Wanxian are shown in Fig. S2 in thesupplementary material. Data from May to September 2004 areused for model validation. Overall, the simulation results are ingood agreement with the measured values, and the flooding con-ditions around September 6th, 2004 is well reproduced. In addition,the average sediment concentrations in Qingxichang are greaterthan Wanxian due to the sediment deposition in the reservoir, i.e.,the sediment concentration decreases gradually along the river.

To further verify the applicability of the hydrodynamic andsediment transport models, the measured and calculated deposi-tion is compared in Fig. 4, including both the annual and cumula-tive depositions. The measured data show that the total sediment

Table 3Major parameters in the phosphorus transport model.

Parameter Symbol Value Unit Reference

Water kinematic viscosity v 1.06 � 10�6 m2/sSediment density rs 2650 kg/m3

Dry bulk density of bottom sediment rb 1110 kg/m3

Porosity of bottom sediment ε 0.58 /Thickness of the aerobic layer H1 1.0 cm a

Thickness of the anaerobic layer H2 10.0 cm a

Diffusion coefficient Ex 0.04 m2/s b

Recovery saturation coefficient aD 0.3 / c

aE 1.0 / c

Sediment carrying capacity coefficient k 0.1 / c

Sediment carrying capacity exponent m 0.92 / c

Phosphorus uptake rate by algae l 2.28 � 10�3 1/d d

Desorption rate k2 1.46 � 10�5 1/s e

Mass transfer coefficient KL01 8.0 � 10�8 m/s f

Mass transfer coefficient KL12 1.2 � 10�8 m/s f

Bioturbation mixing rate u12 2.24 � 10�10 m/s f

Percentages of the dissolved phase fd1 0.000026 / g

fd2 0.000520 / g

Percentages of the particulate phase fp1 0.999974 / g

fp2 0.999480 / g

a Chomat and Westphal, 2013.b Elder, 1959.c Fang et al., 2008.d Hamilton and Schladow, 1997.e Yu et al., 2010.f Reible, 2014.g DiToro, 2001.

Fig. 4. Comparison between the measured and calculated deposition (A denotesannual deposition; and C denotes cumulative deposition).

L. Huang et al. / Water Research 85 (2015) 393e403 399

input from 2003 to 2011 is 16.9 � 108 t, and about 12.6 � 108 t ofsediment deposits in the reservoir, with a comprehensive SDR ofabout 25.5%. And the calculated cumulative deposition is12.3 � 108 t, i.e., a SDR of 27.4%, which well represents the actualdeposition. In addition, the annual depositions are also wellreproduced, with most errors less than 12% except for some indi-vidual years, i.e., 2004, 2010 and 2011. The calculated values ofannual SDR range from 5.54% to 39.2%, which are in good agree-ment with the measured values that range from 6.79% to 44.3%.Details are shown in Table S2.

3.2. Phosphorus transport

Variations of dissolved and total phosphorus concentration atQingxichang, Wanxian and Fengjie are shown in Fig. 5. Althoughthe variation of the calculated phosphorus concentration showscertain fluctuations, the normalized root mean square error(NRMSE) of dissolved and total phosphorus concentration are 0.254

and 0.341 respectively, indicating that the calculated phosphorusconcentrations are in good agreement with the measured values.

Similar to sediment concentration, the phosphorus concentra-tion also decreases gradually along the river due to the accumula-tion of phosphorus at the bed surface with sediment deposition.Fig. 5 shows that the average dissolved phosphorus concentrationsat Qingxichang, Wanxian and Fengjie are 0.042 mg/L, 0.040 mg/Land 0.036 mg/L respectively, i.e., Qingxichang has the highestaverage dissolved phosphorus concentration, followed byWanxian,and then Fengjie. Apparently, total phosphorus concentration fol-lows a similar trend, with the average total phosphorus concen-trations of 0.386 mg/L, 0.297 mg/L and 0.196 mg/L at Qingxichang,Wanxian and Fengjie respectively. Statistics show that the averagevalue of dissolved phosphorus concentrations at these three sta-tions corresponds to about 13% of the total phosphorus concen-tration, with the rest (87%) in the particulate form, verifying thatmost phosphorus would transport in the particulate phase. Inaddition, small peak values of total phosphorus concentration arealso observed around September 6th, 2004, similar to water level,discharge and sediment concentration, indicating that morephosphorus transports during the flood period.

To establish an intuitive feeling of the applicability of thephosphorus transport model, the measured and calculated valuesof dissolved and total phosphorus concentration are shown inFig. 6. In Fig. 6, x-axis and y-axis represent the measured andcalculated values respectively, and logarithmic coordinates areapplied. Solid line indicates that the calculated values equal to themeasure values, i.e., y ¼ x. The dashed lines correspond to theboundaries of 200% and 50% deviations (± a factor of two). Overall,the model predicted results are generally close to the line of perfectagreement, within a bound of 50% and 200% agreement.

The relatively good agreement between the model and obser-vations supports its use to evaluate TGP operations. Cuntan stationand the TGD can be regarded as the upstream and downstreamcontrol sections respectively. The interception effects of the TGP areanalyzed by comparing the fluxes of these two cross sections.Statistics show that about 72.6% of sediment deposit in the

Fig. 5. Variations of dissolved and total phosphorus concentration at Qingxichang, Wanxian and Fengjie).

Fig. 6. Comparison between the measured and calculated values of dissolved and totalphosphorus concentration, with the unit of mg/L.

Fig. 7. Schematic diagrams of the optimal operating rules of the TGR. (a) Impoundingin advance; (b) Dynamic water level control.

L. Huang et al. / Water Research 85 (2015) 393e403400

reservoir from 2003 to 2011 (i.e., a SDR of 27.4%), and about 51.4% ofthe total phosphorus is trapped in the reservoir, mainly caused bythe deposition of particulate phosphorus, as shown in Table S3. Ifthe phosphorus sorption to sediment is set to 0, the calculatedphosphorus interception rate (PIR) is only 6.65%, which is mainlydue to the algal uptake effects. In other words, if the factor for algaluptake is set to 0, the difference of PIR should be about 6.65%, i.e., aminor effect of algal uptake on phosphorus transport, indicating thesubstantial effects of sediment on phosphorus transport.

Fig. 8. Variations of the sediment delivery ratio and phosphorus interception rate withnumber of days that impoundment is initiated prior to October 1st.

Fig. 9. Schematic diagrams of the scouring and deposition during the flood process.Qc-1 and Qc-2 represent two different critical discharge (Qc-1<Qc-2);△t represents thetime spent for the reservoir water level lowered from PFWL to FCWL or raised fromFCWL to PFWL.

L. Huang et al. / Water Research 85 (2015) 393e403 401

As phosphorus accumulates at the bed surface with sedimentdeposition, the phosphorus concentration in the bottom sedimentincreases gradually with time. During summer flood conditions, thebottom sediment is easily eroded and the phosphorus will bereleased into the overlying water, potentially causing seriousaquatic environmental problems. The accumulation of phosphorusat the bed surface would be a long-term risk to the overlying waterquality.

4. Model application

Optimal reservoir management and operation are vitallyimportant to meet the objectives of the TGR with respect to floodcontrol, hydropower generation and navigation improvementwhile minimizing nutrient concerns. Under TGR design conditions(Fig. 7), the reservoir water level is kept at the flood control waterlevel (FCWL) of 145 m during the entire flood season. In October,the water level is raised gradually to the NPL of 175 m. FromNovember to next April, the water level should be kept as high aspossible for hydropower generation. Then the water level will befurther lowered, but should not fall below the dry control waterlevel (DCWL) of 155 m before the end of May to maintainnavigation.

The design operating rules are proposed mainly based on theconsideration of flood and sedimentation controls. In recent years,both runoff and sediment discharge has decreased. As a result thedesigned operating rules of the TGR give too much priority to lowprobability floods. Huge amounts of flood water have to be spilledduring the flood season, and the reservoir cannot be fully refilledduring the refill period for most years, affecting the comprehensivebenefits of the reservoir. Recently, a few optimal operational stra-tegies have been proposed (Li et al., 2010; Liu et al., 2011), such asimpounding in advance, and dynamic water level control. Thesestrategies attempt to maximize hydropower generation, decreasespilled water and improve the refill probability without decreasingthe flood control standard. But how these optimal operating ruleswould influence the phosphorus balance has not been studied. Inthis section, the effect of several management scenarios are eval-uated for the effects on phosphorus retention in the TGR.

4.1. Impounding in advance

Based on the analysis of historical data, flooding in the YangtzeRiver mainly occurs in July and August, and is less likely to appear inSeptember. To decrease spilled water and improve the refill prob-ability, it is appropriate to advance the post-flood periodimpounding period as shown in Fig. 7(a). In this section, 6 man-agement scenarios are presented, i.e., starting impoundment onSeptember 1st, 5th, 10th, 15th, 20th and 25th, and compared to thedesigned operating rules which starts impoundment on October1st. The proposed model is applied to calculate the interceptioneffects of the reservoir (i.e., SDR and PIR) with the measured hy-drology and water quality data in 2010, and results are shown inFig. 8.

Advancing impounding can improve the refill probability, butwill also increase sediment interception due to the high operatingwater level in September. Results show that the SDR decreasesalong with the number of days that impoundment is initiated priorto October 1st. For example, the SDR is 42.8% when startingimpoundment on September 1st, while it is 44.8% for the designedoperating rules (Table S4). As a result, 4.72 � 106 t of additionalsediment deposits in the reservoir (the annual sediment dischargein 2010 is 2.29 � 108 t).

In addition, most phosphorus accumulates at the bed surfacewith sediment deposition. Results show that about 48.4% of the

phosphorus deposits in the TGR (2010), and only 51.6% is trans-ported to the downstream under the design operating rules. Whenimpoundment is initiated in September, the PIR increases graduallyfrom 48.4% to 50.1% (Table S4), potentially affecting the aquaticenvironment of the reservoir. Therefore, when the impoundment isadvanced to improve the refill probability, the interception effectsof sediment and phosphorus by the TGP should also be consideredto balance the tradeoff between the ecological and economicbenefits and maximize the comprehensive benefits.

4.2. Dynamic water level control

Generally, the reservoir water level is not allowed to exceed theFCWL during the flood season to ensure adequate flood storagecapacity. The release of large amounts of flood water affects therefill probability during the post-flood period. A constant FCWLlimits the storage capacity during floods. An alternative scenario isto maintain a constant pre-flood water level (PFWL), but lower it tothe FCWL before an expected flood exceeding a discharge of Qc, asshown in Fig. 7(b). Various values of PFWL and Qc will be consid-ered in this section.

Physical processes involved in the dynamic water level controlare more complex than impounding in advance. (1) A higher PFWLindicates that more sediment deposits in the reservoir during smallfloods (i.e., Q < Qc). (2) It is well known that scouring occurs during

Fig. 10. Variations of the sediment delivery ratio and phosphorus interception rateunder different operating rules. (a) Sediment delivery ratio; (b) Phosphorus inter-ception rate.).

L. Huang et al. / Water Research 85 (2015) 393e403402

rising flood while deposition occurs in falling flood flows (Fig. 9).The reservoir water level is lowered from PFWL to 145 m before theheavy floods (i.e., Q > Qc), increasing the flood discharge andsediment flushing. (3) Thewater level is raised from 145m to PFWLafter the heavy floods, increasing sediment deposition during thefalling flood, and a higher PFWL represents more sedimentdeposition.

Fig. 10 shows the calculated SDR and PIR under different man-agement scenarios. It is assumed that the value of Qc is 35000 m3/s,40000 m3/s and 45000 m3/s, while that of PFWL is 147 m, 149 m,150 m, 151 m, 153 m and 155 m, i.e., totally 18 management sce-narios are presented. It can be found that the SDR decreases withthe increasing PFWL, but the decreasing rate diminishes gradually.However, the PIR first increases and then decreases with theincreasing PFWL. Maximum values are observed at PFWL ¼ 151 m.Moreover, there is no apparent trend for the variations of SDR andPIR with Qc. For example, the PIR is largest when the Qc is40000 m3/s, while similar values exist when the Qc are 35000 m3/sand 45000 m3/s. Details are shown in Table S5.

It is worth noting that the derived results only correspond to thehydrology and water quality conditions in 2010. For other hydrol-ogy and water quality conditions, specific analysis is needed.Nonetheless, the model calculations suggest that modifications ofthe TGR operations would maintain flood management whileallowing manipulation of phosphorous loadings.

5. Conclusions

In this paper, a model of the coupled hydrodynamics, sedimentand phosphorus transport is developed, in which the effects of

sediment on phosphorus transport are considered. The modelstructure should be generally applicable to a variety of river andreservoir conditions. It is tested here by application to the predic-tion of phosphorus transport in the Three Gorges Reservoir (TGR)and evaluating the effects of various operating rules on the sedi-ment and phosphorus balance. The main conclusions of the appli-cation to the TGR are as follows:

(1) The model was able to effectively describe the phosphorousdynamics in the TGR and provide a basis for evaluating theeffect of reservoir operations on phosphorous.

(2) A large amount of phosphorus may accumulate in thereservoir. The model suggests that under current conditions,over 70% of the sediment load and more than half of thephosphorous load are intercepted by deposition in thereservoir. As a result, the sediments have accumulated sig-nificant quantities of phosphorous, which may be of concernif conditions were to change and the sediments wereresuspended.

(3) Management scenarios that influence sediment retentionwill also influence the phosphorus balance in the TGR.However, the model suggests that the evaluated scenarioshave relatively modest effects on the sediment and phos-phorous retention by the reservoir.

Acknowledgments

This research was financially supported by the National NaturalScience Foundation of China (No. 51139003).

Appendix A. Supplementary data

Supplementary data related to this article can be found at http://dx.doi.org/10.1016/j.watres.2015.08.049.

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