A three-dimensional prediction system for water qualitypolluction in coastal waters

Joural of Environmental Sciences Vol. 12 ,No.4,p 430- - 438 ,2000CNI1-2629八XArticle ID: 1001 -0742(2000)04.0430-09 CLC oumber: X824Document code: AA three-dimensional prediction system for water qualitypolluction in coastal watersSHEN Yong -ming' , ZHENG Yong-hong' , Toshimitsu KOMATSU2(1. State Key Laboratory of Coestal and Offshore Engineering, Dalian University of Technology, Dalian 116023, Chin; 2.Department of Civil Engineering. Kyusbu University, Fukuoka 812-8581, Japan)Abstract;" The hydrodynamics and water quelity in Halkata Bay, Japwn are strongly effected by the seasonal veriations in both thegraviational circulation and the strificationon in the bay. The three dimensional hydrodynamics and water quality model has beendeveloped to simulate the long- term transport and fate of pollutants in the system. The model is unique in that it completely integratesthe refined modelling of the hydrodymamics, biochemnical reactions and the eccsystem in the coastal waters. It is a 3 dimensionalsegmented model which is capable of resolving mean daily variations in all the parameters relevant to pllution control. It predicts dailyfluctuations in the oaxygen content at dfferent depths in water throughout the year. It takes into account transport and stting ofpollutant parricles. Iu predicts light penetration from computed turbidity variations. It includes interactions between the ecosysterm andwater quality through nutrient cyeling and phoroasynthesis. The model! has been calbrated well ageinst the date set of hislorical walerquality observations in Hakata Bay.Key words; c∞oastal waters; water quality; ecosystem; turbulence model; numerical modelingIntroductionHakata Bay is a semi-enclosed bay(from 33*34'N to 33*41'N and from 130*13'E to 130*26'E)located at the north side of K yushu Island, Japan. The length and width of Hakata Bay is about 20km and 10 km respectively. The surface area is about 133 km2 and the mean water depth is about10.5m. The bay mouth is about 5.4 km wide. The water in Hakata Bay is thermally stratifiedduring the summer and is influenced by seasonally varying freshwater discharges into the bay. Inorder to simulate the vertical flow structure and pollutant transport in Hakata Bay, manyinterdependent processes need to be simulated. These may be conveniently separated into threemain groups: transport and mixing processes, biochemical interaction of water quality variables andthe utilization and re-cycling of nutrient by living matter.The three-dimensional segmented and layered turbulence model has been developed to simulatethe gravitational circulation and the stratification in Hakata Bay. The results are used to drive thewater quality model which simulates full oxygen and nutrient balance, primary productivity. Themodel incorporates interactions among the following parameters: temperature, salinity, slowdissolved BOD, fast dissolved BOD, slow organic nitrogen, fast organic nitrogen, ammoniacalnitrogen, nitrate nitrogen, dissolved oxygen(DO), suspended solids, slow particulate BOD, fastparticulate BOD, algal carbon, detrital carbon, phosphate, silica.The model is used to simulate the variations in water quality and the ecosystem in Hakata Bay.The model has been calibrated against the data set of historical water quality observations and ingeneral demonstrates excellent agreement with all available data.This paper presents the theory and application of the model to Hakata Bay and ilustrates theuse of the model to study the behavior of pollutants within the system and the potential widerapplication of such models as an environmental mangrament svetemThe mndel is capable of beingused as an environmental management tool to aid中国煤化Iuste water tretmentand discharges into the coastal waters. This enof a wide range ofYHCNMHGaltermative strategies, each resulting in a large su..、...plemented.Foundation item: The National Natural Science Poundation of China(No. 59779023)No.4A three dimensional prediction system for water quality pllution in coastal waters4311 Mathematical modelThe governing differential equations are based on the three dimensional Navier-Stokesequations, including the effects o{ earth' s rotation, bottom friction, wind shear and turbulence,with the hydrostatic pressure approximation and the Boussinesq approximation. Theseapproximations are normally valid for marine and estuaries flows, and simplifty the solution byeliminating the need to solve an lliptic equation for the pressure. The turbulent stress andturbulent mass flux are simulated by the concepts of turbulent viscosity and turbulent dffussion(Rodi, 1984). Then the control equations for three-dimensional tidal flows and water quality canbe obtained:Continuity equation:au. av. aw￥+￥+2=0.(1)Momentum equations:au, a(U2). a(UV). a(UW)。1 aPataXaYaZρ ax+ av,(2)=录("器)+最(.戩)+最(告)xav」a(VU). a(V2)。a(VW) + 1 aPayρ aY(3)=录(。說)+最(.￥)+晶(。誥)- ou,aP.2+pg=0.(4)Turbulent kinetic energy equation:a(Uk)。a(Vk) + a( Wk)at a点(*路)+2(*照)+号(兰路)+G,-e.(5)6x\ axaYlok aYaz\σk aZ )Turbulent kinetic energy dissipation rate equation:ae + a(Ue). a(Ve) + a(We)att- ax+- aYt az=最(。毁)+最(品器)+晶(。能)+号(CuIG2 - C2e).(6)Temperature equation:a(pTCp)、a(pUTCp). a(pVTCp)、 a( pWTCp)Dtaxaz旦(兰a(pTCp))+ a (些a(pTCp)+三(些a(pICp)'H.(7)ax (Oaz\x az )Salinity equation:Sa(US)。a(Vs). a( WS)a (些日长)+.a1%中国煤化工(8)aX (ox aaY (oryConcentration equation:JIYHCNMHGC;、 a(UC)、 a(Vc;)。 a(w;/+- ax+=. a{兰aci=录效)+晶二业)+最(2)+ wC;+1.(i = 1,2,.,N)(9)32SHEN Yong ming et al.Vol. 12State equationρ = 1000 + (0.797 - 0.001875T)S - 1000(0.562(T.- 4)/277)1.85,(10)in whichv。=y+br,(11)(12)/aU;, aU; )au;，Gx=*(ax, +成)ax;,(13)where t is the time; U, V, W the longitudinal, lateral and vertical velocity components in theX，Y and Z directions respectively; P the pressure; ρ the density of water, g the gravitationalacceleration, n the Coriolis parameter( 0 = 2w sinp). k the turbulent kinetic energy, E theturbulent kinetic energy dissipation rate, y，vc, ve the kinematic molecular viscosity , kinematicturbulent viscosity and kinematic effective viscosity, T the temperature of water, Cp the specificheat of water, H the heat exchange term including the solar radiation, atmospheric radiation, longwave radiation from the water surface and evaporation and conduction which are calculated asdescribed in more detail in a reference ( Komatsu, 1999)， S the salinity of water, N the totalnumber of substances incorporated in the model, C; the concentration of substance i(i= 1,2,...，N) standing for concentration of DO, slow dissolved BOD，fast dissolved BOD, slow organicnitrogen, fast organic nitrogen, ammoniacal nitrogen, nitrate nitrogen, suspended solids, slowparticulate BOD，fast particulate BOD，algal carbon, detrital carbon, phosphate and silicarespectively, w the settling velocity for particulate substances, I; the net effect of all the sourceand sink terms simulated in the water quality and ecosystem interactions(Fig. 1) for substance iwhich is calculated as described in more detail in a reference(Shen, 1994), Cg, CeI,Ce2,O,0k,0.the empirical constants recommended in a reference (Rodi, 1984), giving Cp =0.09, C11= 1.44,Cr2= 1.92, σro= 1.0,0k= 1.0 and a。= 1.3. o, is called the turbulent Prandtl or Schmidtnumber. Experiments have shown that, unlike the turbulent diffusivities for momentum and heator mass, a, varies only lttle across any flow and also lttle from flow to flow. Therefore in manycases σ, is often used as a constant. It should be mentioned however that buoyancy affects the valueof a,, and this can be accounted for by the Munk Anderson formula(Rodi, 1984).The temperature in each element is used to determine the rates of reactions, and temperatureand salinity to determine the saturation concentration of dissolved oxygen using Fox' s equation.The suspended solids concentration is used to predict light extinction in the ecosystem part of themodel. The model incorporates a single representative species of phytoplankton to simulate primaryproductivity. Ntrate , organic nitrogen and dissolved oxygen are the "link substances" between thewater quality and algal growth parts of the model.2 Numerical computation2.1 Computational domalnAs shown in Fig. 2, the coastline in the study area includes many islands and forms anintricate area. The model represented this by rectangular grids. The control equations formed bythe finite difference method are solved on a regular grid (250 X 250m) of four sided segments in thehorizontal plane. Each segment is divided into elements by horizontal planes at specified verticallevels. Thus a single segment will contain sever中国煤化工功。In sesatisithe computational domain the segments should:a expected to havesimilar water quality and offer good representatioIYHC N M H Gmputational domainis schematised with a maximum of 5 layers in the vertical and consists oI 4184 segments with 10920elements.2.2 Results and discussionThe model is used to simulate conditions in Hakata Bay for the year 1996. The majority ofeffluent loadings to Hakata Bay are concentrated in the southem and eastern section of the bay.No.4A three dimensional prediction systemn for water quality polution in coastal waters433EMuent loding80DOpunicHyrolyAmmonisalNrfhextionitrogen Iningon、 (irDO>9%) 厂niopmnDeririlcuion、Oiridbuiongr00<5%)Phoboynhese 川LighRuscntionDissovod oxymnRopintionAlgl atonFluwvinlinpulMorulily .DrurialcantondomnmndFig.1 Schematic representation of water quality model interactionskm 120Unitcm8101214161820hmFig. 2 The topography of the Hakate BeyThe model included inputs for 36 effluent discharges discharging into 36 segments along thecoastline. The pollutant loadings are estimated by Kyushu Environmental Evaluation Association,Japan. The solar radiation for an average year and boundary conditions are based mainly on theobservations of the Environmental Protection Department (EPD), Fukuoka City EnvironmentalBureau, Japan taken during 1996 ( Fukuoka City Environmental Bureau, 1996). The values offresh water runoff, rainfall， solar radiation, cloud wT. ni tomoretira wind direction andspeed, relative humidity, evaporation are available中国煤化工EnvironmentalEvaluation Association, Japan. The calibration of thlH.CNMHGrvations at theEPD observation stations for the year 1996(Fukuoka, .996).The simulated spatial distributions of temperature, salinity, dissolved oxygen, organicnitrogen, chlorophyl-a in the surface layer in the summer of 1996(July 31, 1996) are shown inFig. 3 to 7 respectively. Fig. 8 to 14 show the simulated and observed temporal variations oftemperature, salinity, dissolved oxygen,organic nitrogen, ammoniacal nitrogen, nitrate,434SHEN Yong-ming et al .Vol. 1bkmn12厂10unl:002，468101214161820hmFig. 3 Simulated spatial distribution of temperature in the surlace layer inthe summerhm 12Uni:pl ]161820kmFig. 4 Simulated spatial distribution of salinity in the surface layer in thesummerkm 1282untmgi) 121161820 k如Fig. 5 Simuleted spatial distribution of dissolved oxygen in the sufaceLayer in the summerchlorophyl-a(- : model; + : observations) at the EPD observation station C-10(33*36 45"N and .130*22'02"E). The observations shown in these中国煤化工bservations obtainedby the EPD for one full year(1996). These figYHJately reproduces thewater quality processes. The simulated resulCN MH GSbsevatio data oftemperature, salinity， dissolved oxygen， organic nitrogen, ammoniacal nitrogen, nitrate,chlorophyla for one year. The simulated values of temperature, salinity, dissolved oxygen,organic nitrogen, ammoniacal nitrogen, nitrate, chlorophyl-a are within the observation ranges.The agreement with the observation data is satisfactory. The model is calibrated against a field dataNo.4A three-dimensional prediction system for water quality pllution in coastal waters435at the EPD observation station E2, E-6, C1, C-4, C-10, W-3, W-6 and W-7 within the studyarea for one year and in general demonstrates excellent agreement with all available data( Komatsu,1999). Only a part of calibration results at the observation station C-10 are listed in this paperbecause of limited space.bm 121068101214161820kmFig. 6 Simulated spatial dstribution of organic nitrogen in the surface layerin the summerkmn12广可Unl:mohm02468101214161820kmFig. 7 Simulated spatial dstribution of choropyl-a in the surfece layer inthe summer3020Middle leyorBetom layer中国煤化工CNMHGFg.8 Simulated and observed temporal varintions of temperature436SHEN Yong-ming et al.Val. 12°TSufhoe lyer0+」622Midle leyerf4oTBoton lyer01FMAMJ I Aso N D1 , monthFig. 9 Simulated and observed termporal varistions of slinitit30]oLMiddle leyer宫10of_Boma bayeo叶rig. 10 Simulted and observed temporel veristions of disolved oxygenSurfere myeMisdDle Iay中国煤化工TYHCNMHG.丁FMAMJJ ASON DFig. 11 Simulated and observed temporaJ variations of organic nitrogenNo.4A three dimensional prediction system for water quality pollution in coastal waters43711 122Midhe yrBotomiyae. mohFig. 12 Simulated and observed temporal varitions ofammoniacal nitrogen10Surfics Iayt0806040:0.0Midle leyar5 04+020.0.8十0.601, momthFig. 13 Simulated and observed temporl variations of nttate3 ConclusionsAlthough no verification has been made with respect to the eddy viscosity prediction by theturbulence models in this study, the prediction capability of the k-E model has been verifiedextensively by many researchers(Rodi, 1984). After both the turbulence history effect and theturbulence transport have been taken into account, the k-ε model does seem to give a more realisticprediction of eddy viscosity in this study.Since turbulent diffusion in the mixing processes such as the transport of pollutants, suspendedsediment and temperature, etc. is known to be import中国煤化工，and is coelyrelated to eddy viscosity or eddy diffusivity, a moreh as the two-equation k-e model, is desirable to simulate the mixinMHCNMHGThe thermal stratification is induced by seasonally varying meteorological conditions. Thesaline stratification is induced by seasonally varying fresh water discharges to the coastal waters. Inorder to predict seasonal variations in water movement and water quality 8s a result of variations inthermal and saline stratification throughout the year, the three dimensional temperature andsalinityare calculated by solving the transport equations of temperature and salinity.月万数据438SHEN Yong-ming et al .Vol. 12Sufie liyeeo+0+s 162Midle layerBottom lhyerASONDFig.14Simulated and observed temporal variations ofchlorophyll-aThe concentrations of various substances are predicted by solving a series of equations whichdescribe the physical, biological and chemical processes. The model has been calibrated well againstthe data set of historical water quality observations. The model is capable of being used 8S anenvironmental management tool to aid the planning and control of waste water treatment anddischarges into the coastal waters. This enables comparison to be made of a wide range ofalternative strategies each resulting in a large sum of capital expenditure if implermented.Acknowledgements: The model is further refined and documented by the authors with supportfrom the Faculty of Engineering， Kyushu University, Japan under International AcademicCooperation Scheme. The authors also would like to thank Mr. Kenichi Fujita， KyushuEnvironmental Evaluation Association, Japan for his kind assistance in providing the relevant datafor this research.References:a City Environmental Bureau, 1996. The report of water quality observation data in city of Fukuoka[R]. Fukuoka, Japan.Kometsu T, Shen Y M, 1999. A three dimensicnal numerical simulation of hydrodynamics and water quality in coastal areas. TheReport of Environmental Hydraulicg Laboratory[ R]. Fukuoka, Japan: Department of Civil Enginering, Kyushu University.Rodi w, 1984. Turbulence models and their application in hydraulics[M]. Delft, The Netherlands: IAHR Publication.Shen Y M, D G Muphy, 1994. Plluion of the costal environment,ALCS report[R]. Orxlordshire, UK: Hydreulics ResearchWallingford.(Received for reriw October 27, 1999. Acepted November 27, 199)中国煤化工MHCNMHG