Numerical survey of contaminant transport and self-cleansing of water in nador lagoon, morocco

Numerical simulations are presented of the flow hydrodynamics and hypothetical contaminant dispersion patterns in Nador Lagoon, a shallow lagoon with a barrier island situated on the coast of Morocco. It is found that the natural circulation forced by the tidal flow in the lagoon is greatly affected by the development of an artificial inlet in the barrier island. The case study demonstrates the potential use of modern computational hydraulics as a tool integrated in the decision support system designed to manage a lagoon ecosystem.


I. Introduction
The Nador Lagoon (Fig 1) is located on the eastern coast of Morocco. It is a barrier lagoon of plan area about 115 km 2 , and horizontal dimensions about 25 km by 7.5 km. The lagoon is shallow with a water depth not exceeding 8 m. Its barrier island is 25 km long with an average width of 300-400 m (reaching 2 km in certain places) and is cut by an artificial inlet. The lagoon is nourished by sev eral tributaries which nowadays serve as receiving waters for sewage discharged from upstream outfalls. There are three main urban centres in the surrounding area (which contribute to the sewage discharge), and two saline workings on the banks of the lagoon. The lagoon also hosts a fish farm that is of considerable importance to the local economy.
The lagoon ecosystem is particularly sensitive to water contamination; and its evaluation and analysis is vitally important from both environmental and socio-economic points of view. Reliable and computationally efficient estimates of the likely deterioration in water quality due to contamination could inform government regulations concerning environmental protection of the lagoon. Moreover, the implementation of countermeasures is impossible without an accurate picture of various key processes, including the stagedischarge inflow conditions from the feeder river system, the transport of contaminants within the lagoon itself, and its capacity for self-cleansing. To this end, computational shallow flow simulations supplemented by species advection-diffusion models (representing the transport, dispersion, and fate of contaminants) are useful both for the design of long-term prevention and mitigation measures, and for the day to day management of the lagoon. Although no field data are presently available for the Nador Lagoon, several non -validated theoretical studies have been undertaken into contaminant and bed-load transport in the lagoon. [1,2] In this study, a two-dimensional finite volume model is constructed of the Nador Lagoon, which couples the shallow water equations and the species transport equation to simulate the transport of passive contaminants by tidal and river circulation within the lagoon. The resulting coupled equations are expressed as a hyperbolic system of conservation laws with source terms [3,4], and discretized spatially using a finite volume scheme [5] such that mass and momentum are conserved in each computational cell, even in the presence of flow discontinuities. A Godunov-type shock-capturing scheme is used to provide high-resolution solution of the nonhomogenous hyperbolic system of equations on a triangular unstructured computational mesh that is boundary fitted to the Nador Lagoon. Roe's approximate Riemann solver is used to determine the advective fluxes at cell interfaces [6]. Time integration is by means of a second order Runge-Kutta algorithm. The method is high resolution, well-balanced, and aimed at representing 2D domains with complicated boundary and bed geometry. The main advantages of the finite volume method used herein are: (i) its implementation on unstructured meshes that fit a complicated 2D domain; (ii) the simultaneous advection in time of the water flow and the pollutant concentration, solving both problems to with the same order of accuracy; (iii) the ability to handle calculations of slowly varying flows or concentrations as well as rapidly varying flows containing shocks and/or fronts, and (iv) satisfaction of the exact C-property; and (v) guaranteed positivity of water levels and pollutant concentrations in the transient simulations. All computations are undertaken on a personal computer with Core 2 Duo processor of 2.10GHz CPU.
This short paper is structured as follows. Section II states the governing shallow water and species transport equations. Section III briefly describes the numerical solver. The Nador Lagoon simulations are presented in Section III, and the results interpreted in terms of the impact of an artificial inlet on the lagoon circulation system and its flushing characteristics. The results provide insight into the likely behavior of pollutan ts in the Nador Lagoon, and indicate hydrodynamic flow structures due to its complicated bed topography and friction. Finally, the water quality renewal capacity of the Nador Lagoon is investigated by considering the self-cleansing processes for two artificial inlet options. Section IV concludes the paper.

II. Mathematical Model
For shallow flow domains, such as the Nador Lagoon, where the flow is mainly horizontal the vertical acceleration can be ignored and hydrostatic pressure is assumed. This implies that all waves simulated are long waves, whose amplitude is much smaller than both the depth and the wavelength. Moreover, the domain is sufficiently small that the effect of Coriolis acceleration owing to the Earth's rotation can also be ignored. In such cases, an adequate mathematical description of the flow hydrodynamics is provided by the two -dimensional (2D) shallow water equations. These are coupled with advection-diffusion equation to represent the transport of waterborne contaminants. The resulting equation system is written in tensor notation as [7] () 0 where i and j are indices and the Einstein summation convention is used, i.e. repeated indices mean a summation over the space coordinates; i x is the Cartesian coordinate; h is water depth; t is time; i u is the depth-averaged velocity component in the i-th direction; b Z is the bed elevation above a fixed horizontal datum; where a  is the air density and i w is the velocity of wind in the i-th direction.
Equations (1), (2) and (3) are written in the following conservative form: (4) where W and S are the vectors of conserved variables and source terms, F is the advective flux vector, and G is the diffusion flux vector.

III. Numerical formulation
The integral of Equation (4) over a triangular element is written as the sum of each edge contribution,   The source terms are balanced by means of a two-dimensional implementation of the upwind scheme proposed by Vazquez et al. [9,10] for treating the homogeneous part of shallow water equations, which satisfies the exact conservation C-property. Integration of the source term over the control volume i V gives,  (12) where I is the identity matrix, . To obtain higher-order spatial accuracy, the fluxes at each edge are calculated using a piecewise linear function of the state variable W inside the control volume. For the cell-centred mesh, the MUSCL (Monotone Upstream Centred Scheme for Conserved Laws) approach is adopted [12], whereby the left and right values of the state variables are evaluated from: is the wave celerity. The Courant number CFL is set to 0.8 for all cases considered herein. Fig. 1 shows the computational mesh fitted to the Nador Lagoon, based on interpolated measurements of the lagoon bed terrain. The mesh comprises a total of 9240 traingles, and is refined according t o boundary and bed gradient criteria, in order that the mesh density be more concentrated in the more complicated bed and nearshore regions of the lagoon. Initially, the flow conditions are quiescent and the contaminant is distributed uniformly throughout the domain; i.e. 0 0 ( 0) 0

IV. Simulations of the Nador Lagoon
is the wave amplitude, k  is the angular frequency and k  is the tide phase of the k-th tidal constituent, noting that k = M 2 , S 2 , N 2 or K 1 in the present simulations. For water exiting the lagoon, the contaminant concentration is treated as having a transmissive boundary condition. For water entering the lagoon, the concentration at the open boundary nodes is set to zero, assuming that the incoming tide contains clean water. The water flow is forced with the main semidiurnal M 2 tide, of which produces a maximum current speed of approximately 1.45 m/s through the lagoon inlet. Table I lists the physical and numerical parameters for this test case.   T ABLE I  PARAMET ERS AND REFERENCE QUANT IT IES CONSIDERED IN T HE PRESENT ST  The numerical model is used to assess the relative performance of two tidal inlet options in terms of certain key hydrodynamic characteristics of the Nador Lagoon, including water renewal and contamination dispersion. The existing inlet is denoted Inlet O. The proposed new inlet is denoted N. Wind effects are neglected. Uniform contamination at a concentration c = 1 is imposed throughout the domain. Fig. 2 shows the time-dependent decay in average concentration over the entire lagoon, where the average concentration is defined by: For both inlet options, about 70% of the contaminant (by mass or volume ???) has been remov ed by the end of the sixth day. At all times, the average concentration obtained for Option N remains consistently below that of Option O. The results show that the tidal flushing is initially effective at decontaminating the lagoon, but that a residual level of contamination persists after a week.
Next, we define the normalized concentration as / max CC , where max C denotes the maximum value of the initial released concentration distribution C 0 (X,Y). Table II presents the predicted results for water decontamination at three stations, owing to the tidal flushing through either Inlet O or Inlet N at three different times t = 1h, 3 days, and 6 days after the initial contamination has occurred. Station 1 is located towards the north-west of the lagoon in a relatively stagnant sub-basin, and it is not surprising that tidal flushing through either inlet has a much reduced effect. Stations 2 and 3 are located in the main basin, with Station 2 located nearer both Inlet O and Inlet N than Station 3. The normalized contaminant concentrations are quite similar between Stations 2 and 3 indicating that the tidal flushing at both inlets has a fairly uniform effect throughout the main body of the lagoon.   Fig. 3 and Fig.4 present predicted contamination concentration contours and depth -averaged velocity vectors for Inlet O and Inlet N respectively. In both cases, the intial effect of decontamination in the lagoon due to the tidal forcing is evident in a zone near the inlet(s). Later, the decontamination occurs quite uniformly in the main basin, but zones of high concentration are evident in the northwest sub -lagoon region. Option N seems better at reducing this contamination than Option O. By the sixth day, the contamination has been considerably reduced throughout the basin, regardless of which Inlet is considered. The tidal circulation patterns generated by Inlet O comprise three primary counter-rotating gyres in the main basin, with secondary gyres in the northwest and southeast basins. For Inlet N, the situation is similar, except that there are four counter rotating gyres in the main basin, and this tends to contribute rather more to mixing in the basin. In both cases, Station 1 is located near the middle of the northwest sub-basin, and close to a nearly stagnant zone within a gyre. Station 2 is near the shear layers delineating the boundary of one of the primary gy res in the main basin. Station 3 is in the shear layer between two counter rotating gyres, perhaps demarking a southwestern sub -basin. The flow patterns are quite similar at each of the Stations, as are the concentrations.

Inlet Option
The numerical simulations indicate that Inlet N is more effective at water renewal in the lagoon than Inlet O. Obviously, the distribution of contaminants depends strongly on the tidal characteristics and the domain geometry. The present test cases demonstrate the effectiveness o f the present finite volume model at representing steep horizontal gradients in the shallow flow and the plume like behavior of the initial decontamination zone within a complicated domain both in terms of bed terrain and boundary configuration.
The present finite volume solver required CPU time of 3 days and 11 hours to simulate tidal flows lasting 6 days on a personal computer (whose configuration is described above).

V. Conclusions
A numerical model based on the conservative form of a coupled system of two-dimensional shallow water flow and advection-diffusion equations has been used to simulate contaminant transport in the Nador lagoon, which has complicated bathymetry and an irregular coastal geomet ry. The simulations, though highly idealized, indicate the potential of the model in predicting contaminant transport at field-scale, and in evaluating the relative impacts on tidal flushing of two inlet options, O and N. It is found that situating inlet N to the northwest of inlet O leads to an additional gyre being created in the lagoon to the benefit of its decontamination by tidal flushing.