Abstract. 1 Introduction. 1.1 Importance of water quality at EOF

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1 Development of water quality models within the TELEMAC system and recent applications C. Moulin,* A. Petitjean," J. Gailhard^ "Laboratoire National d'hydraulique, 6 Quai Watier, Chatou, France ^Departement Environnement, 6 Quai Watier, Chatou, France Abstract The impact of industrial activity on water quality is currentely a major concern at EOF. That is why mathematical and computational tools have been developed and validated to support decision makers in managing the environment. This paper presents recent developments in that field within the TELEMAC system. Specific attention has been devoted to deal with tidal flats and mass conservation problems. The application of the system to water quality modeling is illustrated with 2 examples : a maritime application concerning the impact of sewage on the Morbihan Gulf, and a fluvial application dealing with heavy metals in the River Seine. 1 Introduction 1.1 Importance of water quality at EOF Water is of the utmost importance to EDF as it is the source of energy for hydroelectricity and because it is a convenient means for cooling thermal power plants. EDF, who manages 75% of surface water in France, has learnt to share water with other users and to feel concerned about the impact of its activities on water quality. For example, important research efforts are devoted to the study

2 662 Computer Techniques in Environmental Studies of the impact of power plant outfalls and to the impact of reservoir emptying on downstream water quality. 1.2 General considerations on water quality Obviously the definition of the scales of a water quality problem is of major importance because the temporal and spatial variations of processes and parameters cover a wide range of scales. For example the temperature of a river has daily, seasonal and yearly variations and it can also be measured at a local scale or more globally across the area of a catchment. The choice of the physical, chemical or biological variables to be considered in the model, and the description of their interaction, is often difficult and must be adapted for the relevant scales of the problem. Generally, the variation in the concentration of a given substance with time is the result of advective and dispersive transport, of internal reactions, and of the action of external sources and sinks. A good knowledge of hydrodynamic variables is required when travel time directly influences physical or chemical processes. In particulate transport the behaviour of suspended sediments has to be represented carefully since suspended sediments act as the first link to the ecosystem during the propagation of a pollutant. 2 Water quality models within the TELEMAC system 2.1 TELEMAC-2D and SUBIEF Most of the processes of sub-aqueous systems can be expressed mathematically by a set of differential equations. These equations can be treated within the TELEMAC system, which is a set of programs developed by the Laboratoire National d'hydraulique (LNH) to deal with free surface flows. These programs share the same finite element library and the same pre-and post-processors. TELEMAC-2D computes the hydrodynamics of the flow by solving the shallow water equations [1]. Different turbulence models are available including the Elder model and a k-epsilon model. SUBIEF computes the transport of one or several tracers within a 2D free surface flow with the " homogeneous concentration over the depth "

3 Computer Techniques in Environmental Studies 663 approximation. The model also assumes that the tracers are carried passively in the flow and do not affect the hydrodynamics as SUBIEF uses the hydrodynamic data produced by TELEMAC-2D. This data then allows the creation of the convective field used to solve the transport equations. This approach significantly reduces the computational time. SUBIEF has an open architecture in which the number of variables, and all their physical constants and interactions are not part of the model but are only part of the data. As a result of recent developments, SUBIEF can now be used as the basis for water quality models and several pre-programmed modules of water quality are available: - heavy metals model, - biomass model, - dissolved oxygen model, - thermal model. 2.2 Conservative or non-conservative formulation? In this section we discuss the choice of the form of the tracer transport equation as it can be written in a conservative or non-conservative form. The conservative variable is the tracer mass : M = hc where : h is the water depth c is the tracer concentration In the conservative formulation, the equation to be solved is : Jp + div(mu) = div(k.h grade) + SM (1) with u : depth-integrated velocity (m/s) K: dispersion tensor SM : source terms of tracer mass

4 664 Computer Techniques in Environmental Studies Obviously, eqn. (1) provides the best basis for building a mass-conservative discretization of the transport equation. However, one is more often interested in concentrations than in masses, e.g. the final results of a thermal application are usually in temperature rather than heat. When M is obtained, we then have to compute : c = yl h where c > o when h~0. An immediate consequence of such an operation (c» o) would be the loss of the monotonicity of the concentration computation. If M has a linear spatial discretization, then c does not belong to the finite element approximation subspace. Also giving a minimum value for h in order to achieve monotonicity would not give a general method. Hence this formulation has not been retained in SUBIEF. Starting from eqn (1): ^ 4- div(hc u) = div(k.h grade) + SM the non-conservative formulation is obtained by splitting the equation into : c -= 4- h hu.grade + c div(hu) dt at = div(k.h grade) 4- SM As (h,u) obeys the continuity equation : ^ 4- div(hu) = SH (2) dt (assumed to be correctly computed) where S% are source terms for h, we get: 4-u.grade - div(k.h grade) 4- SMdt J SM is given by an imposed concentration q of tracer within the water discharge to be diluted. Hence, we have SM = Cj SH and :

5 Computer Techniques in Environmental Studies 665 ^ _, ^ gp +u. grade = i-div(k.h grade) + ^^Sh (3) A finite element formulation of eq.(3) can be summarised as : [gp + u.gradc ] cpj dq [ JLdiv(K.h grade) + ^ "^]9i dq (4) i o Specific developments have been made to ensure a correct treatment of tidal flats and mass conservation. 2.3 Mass conservation and choice of a numerical scheme At a continuous level, eqn.(3) is theorically mass conservative. However, we have to obtain a discrete formulation of eqn.(3), starting from a discretisation of eqn.( 1), in order to get a numerical proof of the tracer mass conservation. The first advection scheme implemented in SUBIEF was the method of characteristics with a linear interpolation. Its main advantage was monotonicity but it tended to be highly diffusive and no theoretical proof of the tracer mass conservation could be obtained. A theoretically mass conservative method may also be obtained with a pure finite element method, without fractional steps. Good mass conservation has been obtained with a SUPG weighing function (Hervouet & Moulin, [2]), but with the down-side of this technique being a decrease on the monotonicity of the solution. PSI advection schemes seem to be a good answer to this monotonicity problem (Janin& al., [3]). 2.4 Tidal flats Equation (3) includes some terms where there is division by h. However, their effect is minimal when applied on the dispersion and on the source terms. There would be no problems with division by h if we considered that eqn.(3) had only to be solved where there is water (h#0). However, in order to acieve this in the numerical solution choices have to be made as to how dry zones are defined.

6 666 Computer Techniques in Environmental Studies A first approach to dealing with dry elements is to solve eq.(4) over the whole finite element domain, making sure that the 1/h terms are correctly computed, using some criteria such as : assuming -L = 0 if h < e h computing -L if h > e This method raises two questions : - Defining e, - Solving eqn.(4) over the whole domain will not prevent the tracer concentration from reaching dry areas, especially in the case of a highly diffusive advection scheme. A second way of dealing with dry elements is to solve eqn.(4) over a subdomain defined by the wet elements only. This solution has physical backing as eqn.(4) does not have to be solved where there is no water. As a result this method will obviously not allow tracers to appear in dry areas. However the problem is still how to determine whether an element is dry or wet. One solution is simply to define a "mask" term which is calculated for each element: mask(iel) = 0 if the element is dry mask(iel) = 1 if the element is wet and solving : mask(iel) + u. grade 2^ iel I/ci at mask(iel) M-div(K.h grade) 4- Lh This solution works well with element by element techniques in which the system matrices are built for each element (Hervouet, [3]). A criterion has been found at LNH to define the dry elements without any "h < e" test.

7 Computer Techniques in Environmental Studies User interface and quality assurance 3.1 User interface for water quality models An interface has been developed which allows the easy formulation of water quality models. The water quality model can be simply described in a single file which defines variables, parameters and equations (fig.l). A filter then interprets this file and automatically translates the water quality model into SUBIEF format, creating a number of data files which include some internal source code. For post-processing, RUBENS is a graphics visualization software package that offers many types of graphics representations and allows the manipulation and processing of visual data as well as the superimposition of measurements onto the visual data. 3.2 Quality Assurance procedures The TELEMAC software is developed under EDF Quality Assurance procedures. The model validation stage is of prime (if costly) importance. Validation of SUBIEF was performed by Laboratoire d'hydraulique de France (LHF Grenoble) so that the validation team was independent from the development one. The validation document follows the recommendation of the Group of European Hydraulics Laboratories and provides the user with a data base of test cases representative of phenomena encountered in practical studies [4,5]. As a complement to the validation stage, feedback from users is taken into account through a Users Club. 4 Examples of application 4.1 Study of heavy metals in Seine river Although the impact on the downstream ecosystem is very low, the Environment Department of EDF-DER and LNH are involved in the study of the influence of copper and zinc downstream of nuclear power plants. Numerical modelling is a part of the study which also includes accurate chemical and toxicity analyses.

8 668 Computer Techniques in Environmental Studies The Transactions on Ecology and the Environment vol 10, 1996 WIT Press, ISSN first two steps in the modeling proceedure consists of setting up the hydrodynamics and the sediment transport model. A 10 km long reach of the Seine river downstream of Nogent sur Seine was modelled with TELEMAC-2D. The erosion and deposition of suspended sediments were taken into account in SUBIEF using relevant source and sink terms, S = Qe-Qd where Qd and Qe are the deposition and erosion rate per unit area per second (kg/m2/s). The deposition rate is given by Krone's formulation [7]. for where u* is the shear velocity, u*d the critical shear velocity under which deposition occurs, C the concentration and Ws the settling velocity. The erosion rate is given by Partheniades [6]. r 1 for u* > where u*e is the critical shear velocity above which erosion occurs. It is dependant on soil concentration C M is determined experimentally. The computations predicted the regions of the river where deposition was most likely to occur. These corresponded to areas of low shear stresses. Deposition was found to be concentrated in a section of the river which is 300 m long. This region should be a sediment trap and field studies are to be intensified in this area. The third step in the modelling proceedure is the development of the heavy metal transport model itself. Heavy metals are represented by dissolved and participate phases. Adsorption and desorption of metal on the sediment are represented by first order reversible reactions which lead to an equilibrium characterized by the distribution coefficient Kd. The parti cu late metal can also be deposited on the bottom depending on the flow conditions. Before the final model can be used to simulate resuspension of heavy metals during floods, calibration measurements have to be made. Experience has shown that the quality of the final results directly depends on the calibration of

9 Computer Techniques in Environmental Studies 669 the model, although the calibration proceedure may be time consuming. The hydrodynamic model requires data from field surveys which calibrate the roughness coefficients of the river bed. The sediment submodel needs measurements and constraints on the settling velocity, the erosion rate, and the critical deposition and erosion shear stress for each granulometric class. The ionexchange model is calibrated with both in situ and laboratory experiments which determine Kd for each metal. 4.2 Pollution of the Morbihan Gulf A second application, supported by the administration of the Morbihan district, deals with the Morbihan Gulf, in south Brittany. It is a complex tidal system, with a large surface area (125 km2) compared to the width of its entrance (less than 1 km). The Gulf also has many islands and tidal flats illustrated in fig.2. Due to the location of the Gulf and its pleasant climate, tourist development and water quality has become a major concern for the Morbihan district. Hence a numerical model was set up to simulate the impact of pollution discharge at points around the Gulf. The aim of the model was to assist decision makers in choosing solutions which improved the protection of the environment [8]. The first step was to reproduce the complex flow patterns within the Gulf as a validation test for the model. The flow was calculated with TELEMAC-2D on a mesh including more than 9000 nodes. The flow is dominated by the tide whose amplitude at the entrance reaches 4.3 meters. In the narrow straits strong currents can reach 9 knots, while, in contrast, many eddies appearing in the lee of islands have low velocities. The results from TELEMAC-2D are in close agreement with the available measurements and show many of the details of the complex flow pattern, e.g. correctly reproducing the secondary flow that exists in transversal channels. Pollution due to faecal bacteria, mainly produced by sewage discharged by 18 outfalls, was modelled with SUBIEF. The faecal bacteria are non-conservative pollutants which survive for 1 or 2 days in this salty environment. T90 was calibrated by comparison with IFREMER measurements on oysters. Concentrations that were lower than 10 bacteria per 100 ml were obtained almost everywhere in the Gulf and in the downstream part of the rivers (fig.2).

10 670 Computer Techniques in Environmental Studies Nevertheless water quality might be improved in the upper reaches of some rivers. Refurbishment of water filtering systems in these area should improve the present situation. In the near future the model will be extended to larger time scales to deal with other pollutants such as inorganic particles containing nitrogen or phosphorus. 5 Conclusion In this paper, we have shown how a finite element system, initially devoted to hydrodynamics and sediment transport, can be used to deal with water quality problems. Work is still in progress which is attempting to extend the modelling to long term simulations. The choice of the ecological model and its calibration nevertheless remain a difficult problem. The examples have shown that a mixed approach combining experimental and numerical models is required to produce results within a reasonable time frame. The broadening of the project team, which should include hydraulic engineers, environmentalists and economists, is another way to progress on applied studies. Acknowledgements We are gratefully indebted to: - J. Gailhard for providing computational and experimental results of heavy metals on Seine river, - J.M. Janin for providing computational and experimental results on Morbihan Gulf.

11 References Computer Techniques in Environmental Studies 671 [1] Hervouet J.M., Van haren L. TELEMAC-2D release 3.0. Principle note. EDF-DER HE-43/94/052/B. [2] Hervouet J.M., Moulin C. New advection schemes in TELEMAC-2D release 2.3. Assesment of the SUPG method. EDF-DER HE-43/94/052/B. [3] HERVOUET J.M. Element by element methods for solving shallow water equations with F.EM. IXth International Conference on Computational Methods in Water Resources, Denver, USA, [4] MOULIN C. SUBIEF release 3.1 : validation document. EDF-DER, to be published. [5] IAHR Guidelines for documenting the validity of computational modelling software. [6] PARTHENIADES E. Erosion of Cohesive Soils. Journal of the Hydraulics Division, ASCE, Vol. 91, 1965 [7] KRONE R.B. Flume Studies of the Transport of Sediment in Estuarine Shoaling Process. Technical Report Hydraulics Engineering Laboratory, Univ. of California, Berkeley, [8] JANIN J.M., MARCOS F. Qualite des eaux du Golfe du Morbihan. Utilisation d'un modele hydrodynamique. IVth Journees nationales Genie Cotier, Genie Civil, Dinard, France, 1996.

12 672 Computer Techniques in Environmental Studies Water Quality file [T] = Temperature ( C) [NO] = organic nitrogen (mgn/1) [NH4] = mineral nitrogen NH4 (mgn/1) [N03] = mineral nitrogen NO3 (mgn/1) [PHY] = phytoplancton (^gchla/1) d/dt[t] = l/{p>{c){h> ({RS}+{RA}-{RE}-{CV}-{CE}) {M> - {Mineralisation}*[T]/20*[NO] {N} - {Nitrification}*[T]/20*[NH4] d/dt[no] {f}*((l-{d})*{dp})*[phy] -{M} d/dt[nh4] = {f}*({d}*{dp}-{e}{cp})*[phy] - {N} + {M} d/dt[n03] «-{f}*((l-{e})*{cp})*[phy] + {N} d/dt[phy] = ({CP}-{DP})*[PHY] input files & source code water quality model interpreter TELEMAC-2D hydrodynamics results SUBIEF () advection dispersion source terms module Finite Element Water Quality module TELEMAC/SUBtEF Temperature + Eutrophisation model Figure 1 : generation of water quality models within SUBIEF

13 Computer Techniques in Environmental Studies 673 Number of bacteria per 100 ml _ Figure 2 : Finite Element mesh of the Morbihan Gulf and computed bacteria concentrations