2015 IEEE European Modelling Symposium

Two-Dimensional Water Environment Numerical Simulation Research Based on EFDC in ,Northeast Gula Tang1, 2, 3*, Jing Li4, Yunqiang Zhu1, Zhaoliang Li2, Françoise Nerry2

1 State Key Laboratory of Resources and Environmental Information Systems, Institute of Geographical Sciences and Natural Resources Research, Chinese Academy of Sciences, , China 2 ICube (UMR 7357), UdS,CNRS, Strasbourg, France 3 University of Chinese Academy of Sciences, Beijing, China 4 Institute of Environmental Sciences of Province, Heilongjiang, China e-mail:[email protected]

Abstract—This paper establishes a two-dimensional (2D) from which massive industrial effluents and sanitary numerical simulation model for water environment of sewage are discharged into the Mudan River in various Mudan River using hydrodynamic and water quality model means, bringing low water quality in Mudan River. based on EFDC. It simulates the migration of CODCr and According to findings by Yu HAO et al. [1], water bodies in NH3-N in urban sections of the trunk stream in glacial and urban sections of Mudan River trunk stream are in organic non-glacial periods. It also calibrates and verifies bed pollution, with major over standard factors of roughness and integrated attenuation coefficient of pollutants. As the findings reveal, bed roughness and permanganate and ammonia nitrogen. integrated attenuation coefficient of pollutants vary Water quality modeling plays an increasingly significantly in icebound and non-icebound seasons: important role in water environment protection, roughness coefficient in icebound season is higher than that management and decision-making support. It helps to in non-icebound season while attenuation rate in icebound predict and assess water quality responses to natural season is lower than that in non-icebound season. In phenomena and man-made pollution. With water quality addition, main factors for attenuation rate drop in icebound modeling, it is possible to improve the understanding of season are, according to simulation results, temperature relationships between the cause and effect that influence drop, upstream inflow decrease, and ice layer cover. Ice aquatic ecosystems, and then improve the decision-making sheet is the major contributor of roughness increase. It is [2] feasible to apply the 2D water environment numerical model for environmental management . established in this paper to urban sections of Mudan River This paper has a numerical simulation of the transport trunk stream. and diffusion process of CODCr and NH3-N in urban sections of Mudan River trunk stream according to the Keywords-water environment;numerical simulation model; environmental fluid dynamics code (EFDC) hydrodynamic glacial period;non-glacial period and water quality model highly recommended by United States Environmental Protection Agency (EPA). I. INTRODUCTION Mudan River is the second largest tributary of the II. PRINCIPLE OF THE MODEL , which originated from Mudan Ling of Changbai Mountain in China. The river, which flows A. Introduction to the Model in NS direction, is of a length of 726 km, a total drop of The EFDC model is the integrated hydrodynamic and 1007 m and an average slope of 1.39‰.The Mudan River water quality model developed by John Hamrick et al.[3] basin, with a total area of 37,023 km2, is distributed in from Virginia Institute of Marine Science School of Heilongjiang Province and Jilin Province. The basin area Marine Science, the College of William and Mary. As a in Heilongjiang is 28,543 km2, making up to 77% of the multi-parameter finite difference model, it can simulate total area. The river flows through Dunhua City of Jilin one-dimensional, two dimensional, and three dimensional Province as well as counties in Heilongjiang Province, hydrodynamics and water quality of water bodies in rivers, such as Ning’an, Hailin, , Linkou, and Yilan, lakes, reservoirs, wetlands, river mouths, bays, and oceans. and finally feeds into the Songhua River in the western The model consists of six modules: hydrodynamics, water suburb of Yilan County. The river mouth of the Mudan quality, toxic substances, substrate, stormy waves, and River has a mean annual discharge of 258.5 m3/s, mean sediment. It is used to simulate processes such as surface annual runoff of 5.26 billion m3, and a maximum runoff of water flow field, material transport (including water 14.9 billion m3, which is about 10% of the total runoff of temperature, salinity, tracer agent, cohesive sediment, and Songhua River System. non-cohesive sediment), and water body eutrophication. Numerous residential complexes and industrial parks The model has been widely applied across the world are distributed along the trunk stream of the Mudan River, thanks to its powerful simulation capabilities.

978-1-5090-0206-1/15 $31.00 © 2015 IEEE 238 DOI 10.1109/EMS.2015.86 B. Governing Equations physical vertical coordinate origin. The continuity The hydrodynamic equations in the EFDC model are equation (4) has been integrated with respect to z over the based on a three-dimensional incompressible, graded- interval (0,1) to produce the depth integrated continuity density turbulence boundary layer equation set, including equation (5) using the vertical boundary conditions, w = 0 the momentum equation, continuity equation, and material at z = (0,1) , which follows from the kinematic conditions [4] transport equation. The Boussinesq assumption is often and equation (9). adopted to facilitate the processing of buoyancy lift terms caused by density contrast. Transformation of curvilinear C. Turbulence Closure Model orthogonal coordinates and σ coordinate transformation To provide the vertical turbulent viscosity and are adopted horizontally and vertically respectively. The diffusivity, the second moment turbulence closure model governing equations after the two types of transformation will be used, the model relates the vertical turbulent are as follows. viscosity and diffusivity to the turbulent intensity, q a Momentum equations: turbulent length scale, l and a Richardson number R by: ∂+∂+∂+∂−+∂−∂ q txyyxz()(mHu m Huu )( m Hvu )()( mwu mf v xyyx m u m ) Hv （1） −−11 −1 ==φ + + + =− ∂ζ + − ∂ − ∂ ∂ +∂ ∂ + Aqlvv0.4(1 36 R q ) (1 6 R q ) (1 8 Rql q ) （10） mHyx()( g p m yx h z x H ) z p z ( mHA Vz u ) Q u ∂+∂+∂+∂++∂−∂()(mHv m Huv )( m Hvv )()( mwv mf v m u m ) Hu A ==φ ql0.5(1 + 36 R )−1 ql （11） txyyxz xyyx （ ） bb q − 2 =− ∂ζ + − ∂ − ∂ ∂ +∂1 ∂ + 2 mHxy()( g p m xy h z y H ) z p z ( mH A Vz v ) Q v gHbl∂ R = z （12） q qH22 ∂=−p gH()ρρρ −−1 =− gHb （3） z 00 Where the so-called stability functions φ and φ Continuity equations： v b account for reduced and enhanced vertical mixing or ∂+∂+∂+∂=()mmHumHvmwζ ( ) ( ) ()0 （4） txyyxz transport in stable and unstable vertically density stratified ∂+∂+∂=ζ 11 （ ） txyyx()m ( m H udz ) ( m H vdz )0 5 ∫∫00 environments, respectively. The turbulence intensity and the turbulence length scale are determined by a pair of ρρ= (,,)pST （6） transport equations: Transport equations： ∂+∂+∂+∂=∂∂+222212− txyyxzzqzq()(mHq m Huq )( m Hvq )()( mwq mH A q ) Q −1 (13) ∂+∂+∂+∂=∂∂+ （ ） −−11322 txyyxzzbzC()(mHC m HuC )( m HvC )()( mwC mH A C ) Q 7 +∂+∂+∂−222()mH A()()() u v mgA b mH B l q vz z bz 1 ∂+∂+∂+∂ txyyxz()(mHT m HuT )( m HvT )() mwT ∂+∂+∂+∂=∂∂+222212− （8） txyyxzzqzl()(mHql mHuql )()()( mHvql mwql mH A ql ) Q −1 =∂()mH A ∂ T + Q − (14) zbzT +∂+∂+∂−+mH−−1132 E A()()() u22 v mgE E lA b mHB q()1 E()κ L 2 l In these equations, u and v are the horizontal 11312vz z bz velocity components in the curvilinear, orthogonal LHz−−−111=+−()(1 z ) − 1 （15） coordinates x and y , mx and my are the square roots of Where B1 , E1 , E2 , and E3 are empirical constants, Qq and the diagonal components of the metric tensor, mmm= x y Ql are additional source-sink term such as subgrid scale is the Jacobian or square root of the metric tensor horizontal diffusion. The vertical diffusivity, Aq is in determinant, A is the vertical turbulent, A is the vertical v b general taken equal to the vertical turbulent viscosity A . turbulent diffusivity, f is the Coriolis parameter, p is the v physical pressure, The density, r , is in general a function D. Numerical Solution Techniques of temperature, T , and salinity or water vapor, C , in In the above-mentioned equation set, second-order hydrospheric and atmospheric flows respectively and can accuracy finite difference is adopted in the solution of be a weak function of pressure, consistent with the equations (1), (2), and (4). Staggered grid scatter is incompressible continuity equation under the anelastic adopted horizontally [5]. Second-order accuracy finite ρ approximation, 0 is the reference density, Qu and Qv are difference in three time level scheme is adopted in time the momentum source-sink terms, the source and sink integration. The solution is divided into the internal mode terms, Q and Q include subgrid scale horizontal diffusion and the external mode, i.e. free surface gravity waves and c t shear stresses are solved in splitting methods [6]. Semi- and thermal sources and sinks. The vertical velocity, with implicit difference schemes are adopted in the solution in physical units, in the stretched, dimensionless vertical the external mode. Two dimensional water level elevation coordinate z is w , and is related to the physical vertical * is calculated simultaneously. In this mode, pre-processing velocity w by: is conducted in the conjugate gradient method before =−∂+*1111ζζζ−− ∂+ ∂ +− −− ∂+ ∂ [7] ww z()(1)()txxyy um vm zumhvmh xxyy （9） solution . The solution method allows large-scale time The system of eight equations (equations 1-8) provides step calculation. Time step is only constrained by the a closed system for the variables u , v , w , p , z , r , C , explicit central difference stability criterion or the high- order windward advection algorithm of the non-linear and T , provided that the vertical turbulent viscosity and [8] diffusivity and the source and sink terms are specified. The accelerating algorithm . Implicit difference scheme with =+ consideration of vertical diffusion is adopted in the total depth, H hz, is the sum of the depth below and [9] the free surface displacement relative to the undisturbed solution in the internal model .

239 The three time level and step by step algorithm trunk stream and effluent discharge from riverside resolves the solution [10] of temperature, q2 and ql2 in the discharge outlets. The concentration boundary conditions material transport equation. To minimize numerical include pollutant concentration in upstream inflow to the diffusion, the multidimensional positive definite advection Xige water quality monitoring section, pollutant transport algorithm is adopted in the model [11, 12]. The concentration in inflow from Hailang River, concentration algorithm adopts first-order accuracy spatially and second- of pollutants from riverside discharge outlets. Sections order accuracy temporally. verified in the model are four water quality monitoring sections: Wenchun Bridge, Hailang River, Jiangbing III. MODELING Bridge, and Chai River Bridge. Parameters to be calibrated in the model consist of This paper studies a total river length of 77.7km, with integrated attenuation rates and bed roughness coefficients the Xige water quality monitoring section as the start of CODCr and NH3-N in the glacial period and non-glacial section and the Chai River Bridge water quality period. Parameters are identified in a combined method of monitoring section as the end section. There is one major empirical value method and trial method: Firstly, adopt tributary feeding into this section, i.e. the Hailang River empirical parameters already calibrated in existing (Fig.1). Due to nearly half year of icebound season in the research results. Secondly, persistently bring simulated Mudan River, pollutant integrated attenuation rate and results closer to observed values by adjusting empirical roughness are significantly different under the impact of parameters. Finally, identify model parameters that can ice sheets. Therefore, simulation is divided into two meet the model simulation requirements. periods in the model, the glacial period and the non-glacial period. The non-glacial period starts from May 2009 to October 2009 and the glacial period starts from November IV. VERIFYING SIMULATION RESULTS 2009 to February 2010. In the model, January 1st, 2009 is defined as the first day. Counting of days hereinafter is A. Analysis of Model Parameter Calibration based on this day. Considering effluent discharge features Table I is the results of model parameter calibration in the Mudan River basin, this paper focuses on two water after calculation. Bed roughness values are respectively quality indexes: CODCr and NH3-N. 0.043 and 0.035 in icebound season and non-icebound season, which are identical to the research findings by Mei WANG et al. [12]. In non-icebound season, attenuation -1 rates of CODCr and NH3-N are respectively 0.03d and 0.05d-1. In icebound season, the rates, however, turn to 0.01d-1 and 0.02d-1. The attenuation rate in icebound season is lower than that in non-icebound season. There are mainly three reasons. Firstly, low water temperature in icebound season influences the degradation of pollutants by microorganism. Secondly, the river has weaker dilution of pollutants discharged into it due to reduced inflow in icebound season. Also, water body flow ability drops due to ice sheet resistance. This influences the physical, chemical, and biological reaction processes of pollutants. Finally, ice layer isolates water body and the atmosphere in icebound season. This almost completely stops the reoxygenation formed in nature aeration, making a low dissolved oxygen concentration. Sources of dissolved oxygen required by microorganism degradation are limited. Thus, the degradation rate drops.

Fig. 1: Schematic Diagram of Urban Sections in Mudan River. TABLE I: RESULTS OF MODEL PARAMETER CALIBRATION. Water Water Attenuation Rate Quality Bed Roughness According to the actual terrain of urban sections in Stage (d-1) Mudan River trunk stream, orthogonal curvilinear grids Factor are adopted in the mesh generation of water bodies. Water Non- CODCr 0.03 0.035 Icebound bodies are divided into 4,320 cells, with a grid matrix of Season NH3-N 0.05 0.035 864 rows×5columns and a cell size between 24×43.6m ~ Icebound CODCr 0.01 0.043 176.9×241.3m. The flow boundary conditions of the Season NH3-N 0.02 0.043 model include upstream inflow discharge of the Xige water quality monitoring section, water discharge to downstream from the Chai River Bridge water quality monitoring section, discharge of Hailang River into the

240 B. Verifying CODCr Simulation Results in Non-Glacial C. Verifying CODCr Simulation Results in Glacial Period Period

Fig. 2 and Table II are the CODCr simulation results in Fig. 3 and Table III are the CODCr simulation results urban sections of Mudan River trunk stream in non-glacial in the glacial period. As analysis in Table III reveals, the period. As analysis in Table II, the average relative errors average relative errors in the four verified sections in the four verified sections Wenchun Bridge, Hailang Wenchun Bridge, Hailang River, Jiangbing Bridge, and River, Jiangbing Bridge, and Chai River Bridge are Chai River Bridge are respectively 3.92%, 12.09%, 1.97%, respectively 15.98%, 9.64%, 4.94%, and 11.36%. The and 19.53%. The simulation accuracy meets the simulation simulation accuracy is above 80%, which meets the requirements. According to Fig. 3, the simulated value simulation requirements. According to Fig. 2, the trend complies with the actual trend. It is noteworthy that the trends of Wenchun Bridge and Jiangbing Bridge simulation results can fully reflect the trend of COD in Cr sections are highly identical to the actual trends. The non-icebound season. It is noteworthy that the trends of simulation accuracy is comparatively lower but is still Hailang River and Jiangbing Bridge are highly identical to above 80%. the actual trends.

a. Wenchun Bridge b. Hailang River

a. Wenchun Bridge b. Hailang River

c. Jiangbing Bridge d. Chai River Bridge Fig. 3: Comparison between Computed Values and Observed Values of c. Jiangbing Bridge d. Chai River Bridge CODCr in Verified Sections in Glacial Period. Fig.2: Comparison between Computed Values and Observed Values of CODCr in Verified Sections in Non-Glacial Period. TABLE III: COMPARISON BETWEEN COMPUTED VALUES AND OBSERVED VALUES OF CODCR IN VERIFIED SECTIONS TABLE II: COMPARISON BETWEEN COMPUTED VALUES AND IN GLACIAL PERIOD. OBSERVED VALUES OF CODCR IN VERIFIED SECTIONS IN Days 366 397 NON-GLACIAL PERIOD. * 4.81 4.14 Days 121 152 182 213 244 274 O Wenchun Bridge C* 4.48 4.18 Wenc O* 6.16 6.65 8.63 6.91 7.03 5.15 R* 6.86 0.97 hun C* 5.6 5.14 6.92 5.68 5.92 5.7 O 3.98 3.88 Bridge R* 9.09 22.71 19.81 17.8 15.79 10.68 Hailang River C 4.47 4.34 Hailan O 5.39 5.58 6.51 6.58 5.76 4.46 R 12.31 11.86 g C 5.39 5.46 6.2 5.61 5.83 6.02 O 4.32 4.37 River R 0 2.15 4.76 14.74 1.22 34.98 Jiangbing Bridge C 4.47 4.35 Jiangb O 5.81 4.7 5.82 5.75 5.79 5.07 R 3.47 0.46 ing C 5.81 5.53 6.13 5.59 5.81 5.25 O 6 4.2 Bridge R 0 17.66 5.33 2.78 0.35 3.55 Chai River Bridge C 4.8 5 Chai O 6.16 6.65 8.63 6.91 7.03 5.15 R 20 19.05 River C 6.16 6.38 6.54 6.01 6.15 5.89 *O: Observed Results (mg/L); *C: Computed Results (mg/L); *R: Relative Bridge R 0 4.06 24.22 13.02 12.52 14.37 Errors (%) *O: Observed Results (mg/L); *C: Computed Results (mg/L); *R: Relative Errors (%)

241 D. Verifying NH3-N Simulation Results in Non-Glacial E. Verifying NH3-N Simulation Results in Glacial Period Period

According to Fig. 4, the NH3-N simulation results in Fig. 5 and Table V are the NH3-N simulation results in urban sections of Mudan River trunk stream in non-glacial urban sections of Mudan River trunk stream in the glacial period can well illustrate the trend of NH3-N concentration period. in non-glacial period. Trends of Hailang River and Similar to those above mentioned, the simulation Jiangbing Bridge are highly identical to the actual trends. results can well illustrate the trend of NH3-N concentration However, there is certain deviation, compared to the actual in the glacial period. The average relative errors in the four trends, in the later stage trends of Hailang River and verified sections Wenchun Bridge, Hailang River, Jiangbing Bridge. Jiangbing Bridge, and Chai River Bridge are respectively 8.01%, 13.02%, 11.93%, and 11.28%. The simulation As statistical analysis in Table IV reveals, the average accuracy is above 85%, which meets the simulation relative errors in the four verified sections Wenchun requirements. Bridge, Hailang River, Jiangbing Bridge, and Chai River Bridge are respectively 12.24%, 19.68%, 16.86%, and 8.26%. The simulation accuracy meets the simulation requirements.

a. Wenchun Bridge b. Hailang River

a. Wenchun Bridge b. Hailang River

c. Jiangbing Bridge d. Chai River Bridge Fig. 5: Comparison between Computed Values and Observed Values of NH3-N in Verified Sections in Glacial Period.

TABLE V: COMPARISON BETWEEN COMPUTED VALUES AND c. Jiangbing Bridge d. Chai River Bridge OBSERVED VALUES OF NH -N IN VERIFIED SECTIONS IN Fig. 4: Comparison between Computed Values and Observed Values of 3 GLACIAL PERIOD. NH3-N in Verified Sections in Non-Glacial Period. Days 366 397 TABLE IV: COMPARISON BETWEEN COMPUTED VALUES AND O* 0.28 0.25 OBSERVED VALUES OF NH3-N IN VERIFIED SECTIONS IN Wenchun Bridge C* 0.3 0.28 NON-GLACIAL PERIOD. R* 3.87 12.15 Days 121 152 182 213 244 274 O 0.49 0.53 O* 0.41 0.41 0.29 0.25 0.27 0.27 Wenchu Hailang River C 0.43 0.45 C* 0.4 0.44 0.31 0.27 0.3 0.37 n Bridge R 12.02 14.02 R* 2.68 7.06 7.27 7.14 13.06 36.26 O 0.5 0.53 O 0.49 0.49 0.41 0.28 0.32 0.42 Hailang Jiangbing Bridge C 0.45 0.45 C 0.49 0.44 0.37 0.34 0.43 0.6 River R 9.27 14.58 R 0 8.85 10.46 20.42 35.44 42.89 O 1.39 1.57 O 0.44 0.44 0.33 0.32 0.31 0.43 Jiangbin Chai River Bridge C 1.5 1.34 C 0.44 0.44 0.37 0.35 0.44 0.57 g Bridge R 7.91 14.65 R 0 1.14 14.11 9.03 45.25 31.64 *O: Observed Results (mg/L); *C: Computed Results (mg/L); *R: Relative Chai O 0.71 0.71 0.46 0.48 0.52 0.61 Errors (%) River C 0.71 0.57 0.45 0.42 0.51 0.53 Bridge R 0 19.18 2.83 12 2.32 13.21 To conclude, the simulation accuracy after parameter *O: Observed Results (mg/L); *C: Computed Results (mg/L); *R: Relative calibration is high in the 2D water environment numerical Errors (%) simulation model in urban sections of Mudan River trunk stream. The simulation results can well demonstrate the migration of pollutants in the river section. Therefore, the

242 numerical simulation model can be applied in water ACKNOWLEDGMENT quality prediction and forecast in Mudan River trunk This research was supported by the project of Mudan stream. River Water Quality Integrated Security Technology and

Engineering Demonstration (No. 2012ZX07201002-5). It’s one of the Major Projects of Water Pollution Control and Management Technology of China. The authors deeply appreciate the editors and the anonymous reviewers for their insightful comments and suggestions.

REFERENCES

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