The free surface elevation of the flow is calculated by the continuity equation:

The momentum equations for the depth-integrated two-dimensional model in the Cartesian coordinate system are:

where u and v are the depth-integrated velocity components in x and y directions, respectively; t is the time; g is the gravitational acceleration; h is the water surface elevation; r is the density of water; h is the local water depth; f_Cor is the Coriolis parameter; t_xx, t_xy, t_yx and t_yy are depth integrated Reynolds stresses; t_sx, t_sy and t_bx, t_by are surface and bed shear stresses in x and y directions, respectively.

The turbulence Reynolds stresses in Equations (2) and (3) are approximated according to the Bousinesq’s assumption that are related to the main rate of the strains of the depth-averaged flow field and an eddy viscosity coefficient n_t which is computed using the Smagorinsky scheme (Smagorinsky, 1993) [3] :

The parameter a ranges from 0.01 to 0.5. In this study, it was taken as 0.1.

In CCHE2D model, three approaches are adopted to simulate non-uniform sediment transport. One is the bed load transport, which is to simulate the bed load only without considering the diffusion of suspended load. The second approach is the suspended load transport, which simulates suspended load and treats bed-material load as suspended load. The third approach is to simulate bed load and suspended load separately (Jia and Wang, 1999 [4] , Jia et al., 2002 [5] , Wu, 2008 [6] ).

In this study, CCHE2D was used to simulate sediment transport in Lake Pontchartrain during the BCS opening for flood release. In this period, sediment transport in the lake is primarily dominated by suspended sediment. So the second sediment transport approach, suspended load, was used for this study, and the non-uniform suspended sediment (SS) transport equation can be written as:

where c_k is the depth-averaged concentration of the kth size class of SS; D_cx and D_cy are the mixing coefficients of SS in x and y directions, respectively; S_ck is the source term and can be calculated by:

where c_t*k is the equilibrium sediment concentration of the kth size class of suspended load; w_sk is the settling velocity of the kth size class; a_t is the adaptation coefficient of suspended load, and it can be estimated using the formula proposed by Wu (2008) [6] .

In natural lakes, the wind shear stresses (t_sx and t_sy) at the free surface are expressed by

where ρ_a is the air density; U_wind and V_wind are the wind velocity components at 10 m elevation in x and y directions, respectively. Although the drag coefficient C_d may vary with wind speed (Koutitas and O’Connor, 1980 [7] ; Jin et al., 2000 [8] ), for simplicity, many researchers assumed the drag coefficient was a constant on the order of 10⁻³ (Huang and Spaulding, 1995 [9] , Rueda and Schladow, 2003 [10] , Chao et al., 2004 [11] ). In this study, C_d was taken as.

Phytoplankton (free-floating algae) and aquatic plants are the two major primary producers in surface water. Algae play a central role in the eutrophication process. Algal concentration is typically expressed in biomass as carbon per unit volume, and in practice, total algal biomass is often represented by chlorophyll a. The relationship between chlorophyll a and algal biomass can be expressed as

in which M is the algal biomass; C_Chl is the concentration of chlorophyll a; a is the carbon to chlorophyll ratio.

The transport equation of algal biomass can be written as

in which D_mx, D_my and D_mz are the mixing coefficients of algae in x and y directions, respectively; S_m is the effective source.

The effective source term for algal biomass S_m in Equation (10) can be calculated by

in which G_p is the growth rate of algae (day⁻¹); D_p is the death rate of algae (day⁻¹); and P_set is the effective algal settling rate (day⁻¹).

Algal bloom is a rapid increase or accumulation in the population of algae in an aquatic system. When conditions of nutrients, sunlight, and water temperature are favorable, algal bloom may occur. The algal growth rate is determined by the availability of nutrients, the intensity of light, and by the ambient temperature. The effects of each factor are considered to be multiplicative:

in which P_mx is the maximum algal growth rate (day⁻¹); and f_N, f_I and f_T are the limitations due to nutrient availability, light intensity, and temperature, respectively.

The nutrient limitation factor f_N is determined by the concentration of nitrogen and phosphorus. It is calculated based on Michaelis-Menten Equation and Liebig’s law of the minimum (Cerco and Cole, 1995 [12] ; Wool et al., 2001 [13] ):

where DIN and DIP are the concentrations of dissolved inorganic nitrogen and dissolved inorganic phosphorus; K_mN and K_mP are the half-saturation constants for nitrogen and phosphorus uptake, respectively.

The light limitation factor f_I is obtained by integrating the Steele equation over depth and time (Chapra, 1997 [14] ):

in which f_d is the fractional daylight; I₀ is the daily averaged light intensity at the water surface; I_m is the saturation light intensity of algae. K_e is the total light attenuation coefficient, and it is determined by the effects of water, chlorophyll and suspended sediment (SS), and can be expressed by (Chao et al., 2007, [15] ):

where K₀ is the light attenuation by pure water; C_chl is the concentration of chlorophyll a and c is the concentration of suspended sediment. The light attenuation coefficient K_e is greatly affected by the high concentration of SS.

The temperature limitation factor f_T is calculated using the following formula (Cerco and Cole, 1995 [12] ):

in which T is the temperature (˚C); T_m is the optimal temperature for phytoplankton growth (˚C); KTg₁ and KTg₂ are coefficients representing the effects of temperature on growth below and above T_m, respectively.

Algae losses mainly include endogenous respiration, mortality and grazing by zooplankton. In this study, the zooplankton predation was not considered, and the algal death rate is given as follows:

where k_pr and k_pd are the rates of endogenous respiration and mortality, respectively (day⁻¹); q_pr is the temperature coefficient.

The effective algal settling rate P_set in Equation (11) is given as:

where w_s4 is the settling velocity of algae (m/day).

In this study, the decoupled approach was used to simulate the concentration of algal biomass. At each time step, the flow fields and sediment distribution were first obtained using the CCHE2D hydrodynamic model, and then the concentration of algal biomass was solved numerically using Equation (10).

CCHE2D model is a finite element model utilizing a special method based on the collocation approach called the efficient element method (Jia et al., 2013) [2] . This model is based on the 2D Reynolds-averaged Navier-Stokes equations. By applying the Boussinesq approximation, the turbulent stress can be simulated by the turbulent viscosity and time-averaged velocity. There are several turbulence closure schemes available within CCHE2D, including the parabolic eddy viscosity, mixing length, Smagorinsky scheme, k-e and nonlinear k-e models.

In the numerical model, the unsteady equations are solved using the time-marching scheme. The velocity correction method is applied to solve the dynamic pressure and enforce mass conservation. The system of the algebraic equations is solved using the Strongly Implicit Procedure (SIP). The flow fields and sediment transport are solved simultaneously. While the algae biomass module is decoupled with hydrodynamic model, and the concentration of algae biomass (or chlorophyll a) is simulated separately.

Figure 2 shows the bathymetry of Lake Pontchartrain. It covers an area of 1630 square

km with a mean depth of 4 meters. It is an oval-shaped quasi-enclosed water body with the main east-west axis spanning 66 km, while the shorter north?south axis is about 40 km. Wind and tide are the major driving mechanisms of the lake circulations. The lake has a diurnal tide with a mean range of 11 cm. Higher salinity waters from the Gulf of Mexico can enter the lake through two narrow tidal passes: the Rigolets and Chef Menteur. When Bonnet Carré Spillway (BCS) is opened for flood release, large amount of fresh water, sediment and contaminants will discharge into Lake Pontchartrain.

Lake Pontchartrain is a large and shallow lake, and the vertical stratification of the lake is not significant. A 2D depth-averaged model, CCHE2D was applied to simulate the flow field, sediment transport, and algal biomass distribution in the lake due to the flood release from BCS. Based on the bathymetric data, the computational domain was divided into a number of grids using the CCHE Mesh Generator (Zhang and Jia, 2009 [16] ). The computational domain was represented by a 224 ´ 141 irregular structured mesh in the horizontal plane.

The period from March 1-31, 1998, was selected for model calibration. At the three narrow passes: Rigolets, Chef Menteur, and IHNC, the measured water surface elevation obtained from USGS were set as tidal boundaries. The wind speeds and directions at the New Orleans International Airport obtained from the National Climatic Data Center, NOAA, were used for model simulation. For calibration runs, a few parameters, such as drag coefficient C_d, Manning’s roughness coefficient, etc., were adjusted to obtain a reasonable reproduction of the field data provided by USGS. In this study, drag coefficient C_d = 0.001 and Manning’s roughness coefficient = 0.025. Simulated water surface elevations and depth-averaged velocities were compared with the field measurements. Figure 3 shows the simulated and measured water surface elevations at the Mandeville Station. Figure 4 and Figure 5 show the simulated and measured depth- averaged velocities in x and y directions at the South Lake Site. In general, the

flow fields produced by the numerical model were in good agreement with field measurements.

In response to the high flood stage of the Mississippi River and to protect the city of New Orleans, the Bonnet Carré Spillway (BCS) was built between 1929 and 1936. The spillway diverts Mississippi River flood waters to the Gulf of Mexico via Lake Pontchartrain. The design capacity of the spillway is 7080 m³/s. It was first operated in 1937 and ten times thereafter (1945, 1950, 1973, 1975, 1979, 1983, 1997, 2008, 2011, and 2016).

During the BCS opening, a large amount of fresh water and sediment discharged from the Mississippi River into Lake Pontchartrain and then into the Gulf of Mexico. The fresh water dominated the whole lake and the lake salinity reduced significantly. A lot of sediment deposited into the lake or was transported into the Gulf of Mexico. The contaminated sediment from Mississippi River could bring a lot of pollutants, such as nutrients, Al, Cu, Cr, Hg, Pb, Zn, etc., to the lake, and caused a lot of environmental problems (Penland et al., 2002) [1] .

The calibrated model was applied to simulate the lake flow fields and sediment transport during the BCS opening between 3/17-4/18, 1997. In this period, the averaged discharge was about 4358 m³/s, and the maximum flow discharge was about 6800 m³/s. The spillway partial opening was completed on March 27. The US Army Corps of Engineers (USACE) began to close the spillway on April 2, and it was completely closed by April 18. During this period, the averaged suspended sediment concentration at the spillway gate was about 240 mg/l. The flow hydrograph and sediment concentration were set as inlet boundary conditions at BCS. The water surface elevations at Rigolets and Chef Menteur Pass obtained from USGS were set as tidal boundaries. The wind speeds and directions at the New Orleans International Airport were used for model simulation.

Figure 6 shows the flow circulations in Lake Pontchartrain when the spillway opened

completely. The flow discharge over the spillway dominated the lake hydrodynamics and caused the entire lake water to be moved eastward through Rigolets and Chef Menteur Pass into the Gulf of Mexico. The flow pattern was completely different from the one induced by tide and wind.

Figure 7 shows the comparisons of suspended sediment (SS) concentration obtained from numerical model and remote sensing imageries provided by NOAA. The simulated suspended sediment concentrations are generally in good agreement with satellite imageries. The numerical results and satellite imageries show that a large amount of sediment discharged into the lake, moved eastward along the south shore and gradually expanded northward, eventually affecting the entire lake after one month of diversion.

The nutrient levels in the Mississippi River are much higher than those in Lake Pontchartrain. When the BCS is opened for flood release, the river water with high nutrient concentrations flows into the lake. As shown in Equation (12), the algal growth rate is depended on the nutrient levels, light intensity and water temperature. So the BCS opening event will affect the growth of algae. It was reported, in Lake Pontchartrain, the low ratio between dissolved inorganic nitrogen (DIN) and dissolved inorganic phosphorus (DIP) indicate that the nitrogen is the limiting nutrient for algae growth (Dortch et al., 1998 [17] , McCorquodale et al., 2004 [18] ).

In 1997, the BCS was opened from March 18 to April 17. It was observed that the

DIN concentrations in the lake increased about 10 times, from normal 0.05 mg/l to 0.5 mg/l (Dortch et al., 1998 [17] , McCorquodale et al., 2004 [18] ). The higher nitrogen level would greatly increase the algae growth rate. The field observations showed that a visually obvious algal bloom became apparent over large parts of the lake by the end of May, and the peak bloom occurred in mid-June.

The developed model was applied to simulate the algae biomass distribution after the BCS opening event. The simulation period was selected from May 28 to July 2, 1997. In this period, wind and tide were the most important forces for flow circulations. After obtaining the wind data and water surface elevation in this period, the model was first applied to simulate the flow fields in Lake Pontchartrain. The initial chlorophyll concentration was estimated using satellite imagery (Figure 8). The nutrient levels were much higher than the saturated levels for algae growth. During this period, the concentration of suspended sediment was lower than 10 mg/l (McCorquodale et al., 2004) [18] . Based on the observed light intensity and water temperature data provided by USACE (Figure 9 and Figure 10), the model was used to simulate the algal biomass distribution. Since the algal biomass is often represented by chlorophyll concentration, the

model simulates the chlorophyll concentration, and their relationship can be obtained using Equation (9). Due to the lack of observed algae biomass data (or chlorophyll concentration), the satellite imagery was used for model validation. Figure 11(a) shows the observed algal bloom distribution obtained from remote sensing imagery acquired on June 13, 1997. Figure 11(b) shows the simulated chlorophyll a concentration. The area with higher chlorophyll a concentration might be the potential area for algal blooming. It can be found that the simulated results and satellite imagery show a similar pattern.