conditions. No field scale data are available for the time delay response with regards to CB acclimation considering multiple varying parameters such as temperature, light intensity or nutrient availability. Without consideration of the time delay, a difference between real ecosystem data and model results occurs. It was also hypothesized that the time delay was constant throughout the water column depth. However, this hypothesis needs to be evaluated through high frequency sampling and field experimentation in order to understand CB behaviour throughout the water column. Furthermore, there is a need to study factors related to cyanobacteria accumulation at the bottom of the water column that are not related to the light and hydrodynamic effects considered in the model. In order to accurately simulate concentrations of cyanobacteria at a DW intake, their movement (or delay in movement) in relation to nutrients released from bottom sediments will need to be elucidated at the full scale of water bodies.

The real physical scale of the 200m length scale (grid size: Δx) of our model can be applied to large water bodies such as Missisquoi Bay. Hence the buoyancy effects from phototaxis behaviour were found to play the dominant role generating upward and downward motions of CB cells. The dispersion of the critical mass of accumulated CB in blooms would be more influenced by the buoyancy force that pushes CB cells away from the bottom of the water column, than by the effect of horizontal advection which transports them away from the shoreline. The cyclic effect of light, hence the cyclic effect of buoyancy or phototactic behavior increases CB cell movement from the bottom to the top of the water column and vice-versa, following which, they are transported as a result of circulation effects induced by wind. Thus, the formation of scum and thin layers at the water's surface are strongly associated with the CB buoyancy mechanism. However, at the bottom of the water column, the thin layer formation is a consequence of the long exposure to light that enables CB to increase their carbohydrate content and induce density changes (becoming greater than water density (Kromkamp & Walsby, 1990)), leading to the downward motion of CB cells to the bottom. These upwards and downwards motions are continuous over a long duration of time and create a cyclic movement of CB. The coupled physical and biological processes governing the thin layer formation of CB at the water surface and bottom were also discussed by Cheriton et al. (2009), who found that biological processes contribute to the formation of a thin layer of phytoplankton and that their aggregation is favoured by the physical environment.
Lake recirculation induced by wind also has a large influence on the horizontal distribution of CB. CB can be advected by the currents of recirculation due to the effects of the wind (Howard, 1997; Howard, 2001; Howard et al., 1996; Kromkamp & Walsby, 1990; Porat et al., 2001; Verhagen, 1994; Visser et al., 1997; Wallace et al., 2000; Webster, 1990; Webster & Hutchinson, 1994). Webster and Hutchinson (1994) showed that phytoplankton mixing occurs when wind speed is greater than 2-3 m/s as a critical threshold value. Wind direction must also be considered because it affects CB accumulation and also prevents blooms. Verhagen's (1994) analysis of CB velocity buoyancy versus water velocity showed that in the region of downwelling water near the downwind shore, if the CB moving velocity induced by their own buoyancy is greater than the descending water velocity, CB will aggregate in the upper water layer near the downwind shore. They concluded that a wind-induced circulation pattern in the vertical plane is essential for the mechanism of CB aggregation in the upper water layer. Through the results shown in **Figure 4.2c** at times 725 minutes and 752 minutes, we can observe CB moving at the upper layer of the water column by the effect of recirculation. However, this recirculation effect can also contribute to CB movement from the top to the bottom of water surface. Thus, water velocity currents and CB buoyancy determine the path of CB in a mixed water column, as has been shown by others (Wallace et al., 2000; Wallace & Hamilton, 1999).

#### **4.5.4 Recurrent risk from cyanobacteria movement and siting of drinking water intakes**

The siting of a DW intake is critical for DW treatment plants. To reduce the risk associated with CB bloom occurrence, it is indispensable to choose an appropriate position for a DW intake in a water body. From **Figures 4.2b and 4.2c**, our results show that the movement of CB blooms can cause a significant risk for a DW intake located at the bottom of the water column. The risk associated with CB blooms would be cyclic (as observed in **Figure 4.3**) as the effects of buoyancy and the currents of recirculation in the water column are of cyclic form (Rabouille et al., 2005). George (1993) and Falconer et al. (1999) demonstrated that within a few hours, wind induced effects could cause a significant growth of phytoplankton cell density by a factor of 1000. The risk to DW intakes can be increased as well by the turbulent effects also caused by wind factors. Turbulent mixing in the bottom of water column could supply new nutrients available for promoting new CB production and entrain cells to the bottom of water column (Velo-Suárez et al., 2010). Therefore, for the long term design of the water intake system for
water sources affected by CB, both light effects and wind stresses must be well integrated to evaluate the risk associated with CB blooms at the first step of design.

One of the outcomes of our current study is to define the possible areas where CB concentration under the coupled effects of light and wind factors might be lower to reduce risks for DW intakes. These zones may depend on dominant species of CB and also the recirculation intensity and dimensions of the water body. The bottom of the water column is a vulnerable location for a DW intake in a shallow water body such as Missisquoi Bay. Our results suggest that an intake raised from the bottom to the middle of the water column would be a better location. However, other factors must be considered, such as the effects of water depth above the intake on pumping, variations in water depth in relation to climate change and climate variability, and physical risks from other activities in the water body. Webster (1990) also found that gradients of plankton concentrations near the lake center were close to zero. However, high frequency sampling throughout the water column are required to confirm zones of low concentrations. Another consideration for DW treatment plants is that even if zones with low concentrations of CB are found, CB from low concentration sources can accumulate within conventional drinking treatment plants and reach high concentrations (Zamyadi et al., 2013a). Thus, although risk of CB breakthrough into DW could be reduced by moving a DW intake, without appropriate treatment processes at the DW treatment plant, the risk of elevated CB and CB toxins would remain.

Light intensity and wind force are two dominant factors associated with the buoyancy effects and advection leading to CB bloom pattern formation. These factors are favourable also for the CB accumulation at the shorelines and the formation of the thin layers at the surface and bottom of the water column. The CB thin layer formation is governed by the buoyancy term via the phototaxis behaviour and their dissipation is favoured when strong winds occur.

Results from this investigation serve as a basis for answering key ecological questions related to CB with regard to the heterogeneity of CB distribution in a well-mixed water system, the sinking and self-shading effects of CB, and buoyancy and sinking rates affecting the formation of thin layers at the surface and bottom of a water body.

Bloom apparition patterns at a given location are largely controlled by the effects of light and wind, but other factors such as the availability of nutrients could also play a role in the distribution of CB in the water column. The effects of light and winds are important for the onset of the CB bloom and create the phenomenon of phyto-convection by two processes: 1) resting
cells present in sediment layers are re-suspended by the circulation effects by wind mixing and phototaxis convection and 2) cell germination is regulated by light conditions, hence the CB population grows (Nguyen-Quang & Guichard, 2010).

Results demonstrated that in a water body where there are CB bloom occurrences and wind speeds are weak, the buoyancy effect is dominant and CB cells could descend to DW intakes. The risk to DW intakes would be cyclic and dependent largely on both light intensity and wind stresses. Due to the recirculation by advection, there will be the zones where the CB concentration is low, although even low concentrations would still be of concern in DW treatment without the availability of appropriate treatment processes and adequate treatment plant operation.

The model based on an eulerian framework demonstrated a good conservation of mass using our new scheme for solving the advection-diffusion equation. All mass losses during each step of simulation were registered and the results showed that mass addition or losses were negligible. This mass conservation scheme will therefore be useful when other processes such as growth and mortality (reaction terms) are considered given that the forcing of the model was accurate, we expect the model will be improved by considering additional processes, however additional high frequency sampling and further testing is required. Nevertheless, the present model demonstrates that wind forcing functions coupled with a set of rather simple physical and biological process equations (CB cell transport equation) explain much of what is observed.

Future development of the model will consider other important processes such as growth, mortality and varying behaviours of different species of CB including their behaviour in relation to surface water hydrodynamics. Future efforts will also involve the quantification of the threshold for the CB bloom onset by light and wind effects using the approach of Nguyen-Quang and Guichard (2010), i.e. to combine our approach with the Boussinesq approximation. The model is a useful tool for water management and water treatment decision making with regards to the DW intake location and identifying periods of high or low risk of CB breakthrough into DW.

## 4.6 Associated content

The supporting information contains the system of equations and boundary conditions for hydrodynamic, transport and buoyancy equation, the methodology of transport equation resolution, the numerical validation results.
# AUTHOR INFORMATION

## Corresponding Author

*Current address: École Polytechnique de Montréal, Department of Civil, Geological and Mining Engineering, P.O. Box 6079, Station Centre-Ville, Montreal, Quebec, Canada, H3C 3A7Phone: 514-340-4711 extension 2983; Fax: 514-340-5918

E-mail: mouhamed.ndong@polymtl.ca

## Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

## Funding Sources

This research was supported financially by the Engineering Research Council of Canada (NSERC), Canada Foundation for Innovation (CFI), Fonds de recherche du Québec – Nature et Technologies (FQRNT), Canada Research Chairs (CRC).

## 4.7 Acknowledgment

This research was supported financially by the Engineering Research Council of Canada (NSERC), Canada Foundation for Innovation (CFI), Fonds de recherche du Québec – Nature et Technologies (FQRNT), Canada Research Chairs (CRC).

## 4.8 References

Belov, A. P., & Giles, J. D. (1997). Dynamical model of buoyant cyanobacteria. Hydrobiologia, 349(1-3), 87-97.

Chen, Y., Qian, X., & Zhang, Y. (2009). Buoyancy Regulating Cyanobacteria in Wind-Driven Currents. Paper presented at the 3rd International Conference on Bioinformatics and Biomedical Engineering Beijing

Cheriton, O. M., McManus, M. A., Stacey, M. T., Steinbuck, J. V., & Ryan, J. P. (2009). Physical and biological controls on the maintenance and dissipation of a thin phytoplankton layer. Marine Ecology Progress, Series 378, 25.

Codd, G., Bell, S., Kaya, K., Ward, C., Beattie, K., & Metcalf, J. (1999). Cyanobacterial toxins, exposure routes and human health. European Journal of Phycology, 34(4), 405-415.

Cuypers, Y., Vincon-Leite, B., Groleau, A., Tassin, B., & Humbert, J. F. (2011). Impact of internal waves on the spatial distribution of Planktothrix rubescens (cyanobacteria) in an alpine lake. (1751-7370 (Electronic)).

Falconer, I., Bartram, J., Chorus, I., Kuiper-Goodman, T., Utkilen, H., & Burch, M. (1999). Toxic cyanobacteria in Water. New York, USA.
Franks, P. J. S. (1992). Sink or swim: accumulation of biomass at fronts. Marine Ecology Progress Series, Series 82, 12.

Franks, P. J. S. (1995). Thin layers of phytoplankton: a model of formation by near-inertial wave shear. *42*(1), 75-91.

Galante, A., Wisen, S., Bhaya, D., & Levy, D. (2012). Modeling local interactions during the motion of cyanobacteria. *J Theor Biol.*, 309, 12.

George, D. G. (1993). Physical and chemical scales of pattern in freshwater lakes and reservoirs. 135(1-3), 1-15.

Ghorai, S., & Hill, N. A. (2005). Penetrative phototactic bioconvection. Physics of Fluids, 17(7), 11.

Hipsey, M. R., Romero, J. R., Antenucci, J. P., & Hamilton, D. (2006). Computational Aquatic Ecosystem Dynamics Model: CAEDYM v2 - v2.3 Science Manual. Contract Research Group, Centre for Water Research, University of Western Australia.

Howard, A. (1997). Computer simulation modelling of buoyancy change in Microcystis. *Hydrobiologia*, 349(1-3), 111-117.

Howard, A. (2001). Modeling Movement Patterns of the Cyanobacterium, Microcystis. *11*(1), 304-310.

Howard, A., Irish, A. E., & Reynolds, C. S. (1996). A new simulation of cyanobacterial underwater movement (SCUM'96). *Journal of Plankton Research*, 18(8), 1375-1385.

Hu, W., F., C. D., Mengersen, K., & Tong, S. (2009). Weather variability, sunspots, and the blooms of cyanobacteria. (1612-9210 (Electronic)).

Kromkamp, J. C., Botterweg, J., & Mur, L. R. (1988). Buoyancy regulation in Microcystis aeruginosa grown at different temperatures. *FEMS Microbiology Letters*, 53(3-4), 231-237. doi: 10.1111/j.1574-6968.1988.tb02669.x

Kromkamp, J. C., & Mur, L. R. (1984). Buoyant density changes in the cyanobacteriumMicrocystis aeruginosa due to changes in the cellular carbohydrate content. *FEMS Microbiology Letters*, 25(1), 105-109.

Kromkamp, J. C., & Walsby, A. E. (1990). A computer model of buoyancy and vertical migration in cyanobacteria. *Journal of Plankton Research*, 12(1), 161-183.

Litchman, E., & Klausmeier, C. A. (2001). Competition of phytoplankton under fluctuating light. *Am Nat*, 157(2), 170-187. doi: 10.1086/318628

Maier, H. R., Dandy, G. C., & Burch, M. D. (1998). Use of artificial neural networks for modelling cyanobacteria Anabaena spp. in the River Murray, South Australia. 105(2-3), 257-272.

McQuaid, N., Zamyadi, A., Prevost, M., Bird, D. F., & Dorner, S. (2011). Use of in vivo phycocyanin fluorescence to monitor potential microcystin-producing cyanobacterial biovolume in a drinking water source. *J Environ Monit*, 13(2), 455-463. doi: 10.1039/c0em00163e

Moreno-Ostos, E., Cruz-Pizarro, L., Basanta, A., Escot, C., & George, D. G. (2006). Algae in the motion: spatial distribution of phytoplankton in thermally stratified reservoirs. *Limnetica*, 25(1-2), 13.

Moreno-Ostos, E., Cruz-Pizarro, L., Basanta, A., & George, D. G. (2009). The influence of wind-induced mixing on the vertical distribution of buoyant and sinking phytoplankton species. *Aquatic Ecology*, 43(2), 271-284.

Ndong, M., Bird, D., Nguyen-Quang, T., de Boutray, M. L., Zamyadi, A., Vincon-Leite, B., Lemaire, B. J., Prevost, M., & Dorner, S. (2014). Estimating the risk of cyanobacterial
occurrence using an index integrating meteorological factors: Application to drinking water production. Water Res, 56C, 98-108. doi: 10.1016/j.watres.2014.02.023

Nguyen-Quang, T., & Guichard, F. (2010). The role of bioconvection in plankton population with thermal stratification. International Journal of Bifurcation and Chaos, 20(06), 1761-1778.

O'Neil, J. M., Davis, T. W., Burford, M. A., & Gobler, C. J. (2012). The rise of harmful cyanobacteria blooms: The potential roles of eutrophication and climate change. Harmful Algae--The requirement for species-specific information, 14(0), 313-334.

Organisme de bassin versant de la baie Missisquoi. (2011). Plan Directeur de l'Eau: Le Portrait du Bassin Versant de la Baie Missisquoi. Québec.

Peretyatko, A., Teissier, S., Backer, S. D., & Triest, L. (2010). Assessment of the risk of cyanobacterial bloom occurrence in urban ponds: probabilistic approach. Annales de Limnologie - International Journal of Limnology, 46(02), 121-133.

Porat, R., Teltsch, B., Perelman, A., & Dubinsky, Z. (2001). Diel Buoyancy Changes by the Cyanobacterium Aphanizomenon ovalisporum from a Shallow Reservoir. Journal of Plankton Research, 23(7), 753-763.

Rabouille, S., Salençon, M.-J., & Thébault, J.-M. (2005). Functional analysis of Microcystis vertical migration: A dynamic model as a prospecting tool: I—Processes analysis. 188(2-4), 386-403.

Rabouille, S., Thébault, J.-M., & Salençon, M.-J. (2003). Simulation of carbon reserve dynamics in Microcystis and its influence on vertical migration with Yoyo model. C R Biol, 326(4), 349-361.

Recknagel, F., French, M., Harkonen, P., & Yabunaka, K.-I. (1997). Artificial neural network approach for modelling and prediction of algal blooms. 96(1-3), 11-28.

Reynolds, C. S., Oliver, R. L., & Walsby, A. E. (1987). Cyanobacterial dominance: The role of buoyancy regulation in dynamic lake environments. New Zealand Journal of Marine and Freshwater Research, 21(3), 379-390.

Ross, O. N., & Sharples, J. (2008). Swimming for survival: A role of phytoplankton motility in a stratified turbulent environment. Impact of Small-scale Physics on Marine Biology Selected papers from the 2nd Warnemünde Turbulence Days 2nd Warnemünde Turbulence Days, 70(3-4), 248-262.

Ryan, J. P., Fischer, A. M., Kudela, R. M., McManus, M. A., Myers, J. S., Paduan, J. D., Ruhsam, C. M., Woodson, C. B., & Zhang, Y. (2010). Recurrent frontal slicks of a coastal ocean upwelling shadow. Journal of Geophysical Research: Oceans, 115(C12), C12070.

Smith, V. H. (1985). PREDICTIVE MODELS FOR THE BIOMASS OF BLUE-GREEN ALGAE IN LAKES1. JAWRA Journal of the American Water Resources Association, 21(3), 433-439.

Smith, V. H., Willén, E., & Karlsson, B. (1987). PREDICTING THE SUMMER PEAK BIOMASS OF FOUR SPECIES OF BLUE-GREEN ALGAE (CYANOPHYTA/CYANOBACTERIA) IN SWEDISH LAKES1. JAWRA Journal of the American Water Resources Association, 23(3), 397-402.

Steffensen, D. A. (2008). Economic cost of cyanobacterial blooms. In H. K. E. In: Hudnell (Ed.), Cyanobacterial Harmful Algal Blooms: State of the Science and Research Needs. (pp. 855-866). New York: Springer Press.

Steinbuck, J. V., Stacey, M. T., McManus, M. A., Cheriton, O. M., & Ryan, J. P. (2009). Observations of turbulent mixing in a phytoplankton thin layer: implications for formation, maintenance, and breakdown. Limnology and Oceanography, 54(4), 16.
Teles, L., Vasconcelos, V., Teles, L., Pereira, E., Saker, M., & Vasconcelos, V. (2006). Time Series Forecasting of Cyanobacteria Blooms in the Crestuma Reservoir (Douro River, Portugal) Using Artificial Neural Networks. Environmental Management, 38(2), 227-237.

Velo-Suárez, L., Fernand, L., Gentien, P., & Reguera, B. (2010). Hydrodynamic conditions associated with the formation, maintenance and dissipation of a phytoplankton thin layer in a coastal upwelling system. 30(2), 193-202.

Verhagen, J. H. G. (1994). Modeling phytoplankton patchiness under the influence of wind-driven currents in lakes. Limnol. Oceanogr., 39(7), 15.

Visser, P., Passarge, J., & Mur, L. (1997). Modelling vertical migration of the cyanobacterium Microcystis. Hydrobiologia, 349(1-3), 99-109.

Wallace, B. B., Bailey, M. C., & Hamilton, D. P. (2000). Simulation of vertical position of buoyancy regulating Microcystis aeruginosa in a shallow eutrophic lake. Aquatic Sciences, 62(4), 320-333.

Wallace, B. B., & Hamilton, D. P. (1999). The effect of variations in irradiance on buoyancy regulation in Microcystis aeruginosa. Limnol. Oceanogr, 44(2), 8.

Wallace, B. B., & Hamilton, D. P. (2000). Simulation of water-bloom formation in the cyanobacterium Microcystis aeruginosa. Journal of Plankton Research, 22(6), 1127-1138.

Walsby, A. E. (2005). Stratification by cyanobacteria in lakes: a dynamic buoyancy model indicates size limitations met by Planktothrix rubescens filaments. New Phytol, 168(2), 365-376. doi: 10.1111/j.1469-8137.2005.01508.x

Wang, Z., & Goodman, L. (2010). The evolution of a thin phytoplankton layer in strong turbulence. The Ecology and Oceanography of Thin Plankton Layers, 30(1), 104-118.

Webster, I. T. (1990). Effect of wind on the distribution of phytoplankton cells in lakes. Limnol. Oceanogr., 35(5), 13.

Webster, I. T., & Hutchinson, P. A. (1994). Effect of wind on the distribution of Phytoplankton cells in lakes revisited. Limnol. Oceanogr., 39 (2), 9.

Wei, B., Sugiura, N., & Maekawa, T. (2001). Use of artificial neural network in the prediction of algal blooms. (0043-1354 (Print)).

Wynne, T. T., Stumpf, R. P., Tomlinson, M. C., Fahnenstiel, G. L., Dyble, J., Schwab, D. J., & Joshi, S. J. (2013). Evolution of a cyanobacterial bloom forecast system in western Lake Erie: Development and initial evaluation. Remote Sensing of the Great Lakes and Other Inland Waters, 39, Supplement 1(0), 90-99.

Zamyadi, A., Dorner, S., Ndong, M., Ellis, D., Bolduc, A., Bastien, C., & Prevost, M. (2013a). Low-risk cyanobacterial bloom sources: Cell accumulation within full-scale treatment plants. Journal american water works association, 105(11), 65-66.

Zamyadi, A., Dorner, S., Sauvé, S., Ellis, D., Bolduc, A., Bastien, C., & Prévost, M. (2013b). Species-dependence of cyanobacteria removal efficiency by different drinking water treatment processes. Water Research, 47(8), 12.

Zamyadi, A., MacLeod, S. L., Fan, Y., McQuaid, N., Dorner, S., Sauvé, S., & Prévost, M. (2012). Toxic cyanobacterial breakthrough and accumulation in a drinking water plant: A monitoring and treatment challenge. Cyanobacteria: Impacts of climate change on occurrence, toxicity and water quality management, 46(5), 1511-1523.
## 4.9 Supporting Information (SI)

### HYDRODYNAMIC MODELING OF LIGHT INTENSITY AND WIND EFFECTS ON THE SPATIAL DISTRIBUTION OF CYANOBACTERIA

<sup>a</sup>Mouhamed Ndong*, <sup>b</sup>David Bird, <sup>c</sup>Tri Nguyen-Quang, <sup>a</sup>René Kahawita, <sup>a</sup>Michèle Prévost, <sup>a</sup>Sarah Dorner

a. Department of Civil, Geologic and Mining Engineering. École Polytechnique de Montréal, C.P. 6079, succ. Centre-ville, Montréal (Québec), Canada, H3C 3A7

b. Department of Biological Sciences, Université du Québec à Montréal, C.P. 8888, succ. Centre-ville, Montréal (Québec), Canada, H3C 3P8

c. Department of Engineering, Faculty of Agriculture, Dalhousie University, PO Box 550, Truro-Bible Hill (Nova Scotia), Canada, B2N 5E3

* Corresponding author. Current address: Department of Civil, Geological and Mining Engineering. École Polytechnique de Montréal, C.P. 6079, succ. Centre-ville, Montréal (Québec), Canada, H3C 3A7.

Tel.: (+1) 514 994 6872

E-mail address: mouhamed.ndong@polymtl.ca

### Supporting Information (SI)

Number of pages: 16

Number of figures: 4

Number of table: 2
### 4.9.1 System of governing equations

Although a 3D model will improve predictions of CB concentrations at precise locations in a water body, the 2D modelling approach presented here is a necessary step to evaluate the relative importance of light and wind effects and to describe cyanobacterial accumulation in relation to environmental forcing.

#### Continuity

$$ \nabla \cdot \mathbf{V} = 0 \qquad 4.1 $$

#### Momentum equation

$$ \rho_w \frac{\partial \mathbf{V}}{\partial t} + \rho_w \nabla \cdot (\mathbf{V} \mathbf{V}) = -\nabla \mathbf{p} + \nu \nabla^2 \mathbf{V} + \rho \vec{g} \qquad 4.2 $$

Where $V$ is the velocity of fluid (m/s); $\mathbf{p}$ is the dynamic pressure (Pa); $\rho$ is the suspension density (kg/m³); $\rho_w$ is the water density (kg/m³); $g$ is the gravitational acceleration (m²/s), $v$ is water viscosity (Pa.s) and $t$ is the time (s).

Equation (4.2) may be expressed in the vorticity and stream function form according to (Nguyen-Quang & Guichard, 2010):

$$ \rho_w \frac{\partial \xi}{\partial t} + \rho_w \nabla \cdot (\mathbf{V} \xi) = \nu \nabla^2 \xi + \nabla \times \rho \vec{g} \qquad 4.3 $$

$$ \xi = - \nabla^2 \varphi \qquad 4.4 $$

The equations (4.3) and (4.4) for Vorticity $\xi$ and stream function $\varphi$ were used in our model principally to eliminate the instability caused by the pressure term in the Navier-Stokes equations during the simulation process.

Vorticity is related to velocity and stream function by the following equation:
$$ \xi = \frac{\partial w}{\partial x} - \frac{\partial u}{\partial z} = \frac{\partial^2 \phi}{\partial x^2} - \frac{\partial^2 \phi}{\partial z^2} \qquad 4.5 $$

If we introduce the horizontal and vertical diffusivity coefficients, respectively, equation (4.3) becomes:

$$ \frac{\partial \xi}{\partial t} + u \frac{\partial \xi}{\partial x} + w \frac{\partial \xi}{\partial z} = \Gamma_x \frac{\partial^2 \xi}{\partial x^2} + \Gamma_z \frac{\partial^2 \xi}{\partial z^2} \qquad 4.6 $$

Where x, z are respectively the horizontal and vertical Cartesian coordinates; u, w correspond respectively to the two components of water velocity (m/s) in the x and z directions while $\Gamma_x$ and $\Gamma_z$ are the horizontal and vertical diffusivity coefficients (m²/s), respectively.

Equation (4.6) does not incorporate buoyancy effects, the specific density of water was assumed to be constant. This implies that CB have a negligible effect on density.

### Transport equation

The form of the transport equation for CB is described as follows. This equation includes the cells' mass conservation equation and a mobility term for CB motion.

$$ \frac{\partial C}{\partial t} + \nabla(VC) + \nabla(FC) = D\nabla^2 C \qquad 4.7 $$

Where C is the CB cell or phytoplankton concentration (cell/m³); V is the fluid medium velocity involving on the CB cells, D is the plankton diffusivity (m²/s) and F is the motion term of CB cells. This motion term can be understood as the taxis term (Nguyen-Quang & Guichard, 2010).

Under the effect of light, this taxis term represents the phototactic behaviour (phototaxis) of CB cells. This phototactic term has been described in other studies (Ghorai et al., 2010; Litchman & Klausmeier, 2001; Mellard et al., 2011; Visser et al., 1997).

We propose here that a simple way to introduce the phototactic behavior of CB is by using F as the sinking velocity (m/s). This sinking velocity may be obtained from equation 19 below as originally proposed by Visser et al. (1997) for the buoyancy effects.
The transport equation combines the effects of cell vertical velocity, F, with the fluid velocity (V). In other words, the combined effects of biological and physical processes via light and wind factors are included in the system of governing equations (4.1), (4.5) and the transport equation (4.7).

## Boundary and initial conditions

The conditions at the free surface determine the hydrodynamic behaviour. Indeed, they are affected by the meteorological factors such as the wind (intensity and direction) and atmospheric pressure.

At the water surface the boundary conditions are expressed as:

$$ \left\{ \begin{array}{l} \boldsymbol{w} = \boldsymbol{\varphi}_s = \mathbf{0} \\ \Gamma_x \frac{\partial \boldsymbol{u}}{\partial z} = \frac{\boldsymbol{\tau}_x^s}{\rho_w} \end{array} \right. \qquad 4.8 $$

Boundary conditions for surface vorticity ($\xi_s$) may be expressed by:

$$ \xi_s = \frac{\tau_x^s}{\Gamma_x \rho_w} \qquad 4.9 $$

Where $\tau_x^s$ is the surface wind stress at the water surface (N m$^{-2}$)

The effect of wind stress may be described by the empirical equation of Cole and Buchak (1995).

$$ \boldsymbol{\tau}_x^s = \mathbf{C}_v \times \boldsymbol{\rho}_a \times \boldsymbol{W}_a^2 = \mathbf{C}_v \times \boldsymbol{\rho}_w \times \boldsymbol{u}_s^2 \qquad 4.10 $$

Where $C_v$ is the drag coefficient; $\rho_a$ is the air density (kg m$^{-3}$); $W_a$ is the wind speed at 10 m above the water surface (m s$^{-1}$) and $u_s$ is the surface water velocity (m s$^{-1}$)

The surface water velocity will be:

$$ \boldsymbol{u}_s = \sqrt{\frac{\rho_a}{\rho_w}} \times \boldsymbol{W}_a \approx 0.03 \times \boldsymbol{W}_a \qquad 4.11 \text{ A} $$
Wind direction change is taken into account by introducing the term cos ($\phi_{dir}$) as suggested by Hsu(1972), so that equation 11a is modified to read:

$$ u_s = \sqrt{\frac{\rho_a}{\rho_w}} \times W_a \approx 0.03 \times W_a \times \cos(\phi_{dir}) \qquad 4.11 \text{ b} $$

Where $\phi_{dir}$ is the wind direction.

At a closed boundary, the vorticity is null ($\xi=0$) and

$$ \left\{ \begin{array}{l} \frac{\partial^2 \varphi}{\partial x^2} = 0 \qquad \textit{at left and right boundaries} \\ \\ \frac{\partial^2 \varphi}{\partial z^2} = 0 \qquad \textit{at bottom} \end{array} \right. \qquad 4.12 $$

### 4.9.2 Method for resolution

#### a) Discretization scheme for diffusion-advection equation

One important feature of the eulerian approach for CB modeling is that we need to know the CB density variation during all simulation steps. Traditional numerical schemes proposed such as QUICK, SIMPLE, etc. (Leonard, 1979; Patankar, 1980) do not allow for convenient monitoring of the CB density variation during each iteration step. That means the conservation property of the numerical algorithm is not sufficient if using these traditional schemes. To avoid this situation when dealing with the CB spatial temporal distribution using a eulerian approach, a constant CB buoyancy has traditionally been assumed for all steps of calculations (Chen et al., 2009; Webster, 1990; Webster & Hutchinson, 1994). This assumption however, does not correspond to physical reality and different models using a Lagrangian approach have shown that CB are able to move due to their own mechanism of buoyancy (dependent on light intensity) even if the aquatic environment is at rest (quiescent medium) (Kromkamp & Mur, 1984). In order to follow the variation of CB cell density in the water column due to the light intensity for each iteration step, while respecting conservation properties, we here propose a new numerical scheme to replace traditional schemes such as QUICK and SIMPLE. We therefore considered a control volume (CV) as is shown in **Figure 4.5**.
<figure><img src="image_18.png" /><figcaption>**Figure 4.5:** Schematic illustration of the distribution of cells and definition of the control volume (CV)</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>**Figure 4.6:** Mass flux distribution in grid meshing</figcaption></figure>

The transport of CB is particular because they can move in the water column using their own mechanism of buoyancy. Unlike suspended particulate matter, the vertical velocity vector of cells may be towards the water's surface independent of the water's velocity. For the mass balance in the CV at time t, some cells may leave whereas other cells may enter according to their density and the horizontal and vertical advection. In this approach, the mechanism for the regulation of buoyancy is dependent on exposure to light and its intensity. The CV receives cells from above when the density of these cells is greater than the density of water and they will tend to
accumulate in the bottom CV. When cell density is less than the density of water, cells will migrate to the control volume above. Following **Figure 4.6**, we can write:

$$ \frac{\partial C}{\partial t} + \frac{\partial (uC)}{\partial x} + \frac{\partial [(w + F)C]}{\partial z} = \frac{\partial^2 (D_x C)}{\partial x^2} + \frac{\partial^2 (D_z C)}{\partial z^2} \qquad 4.13 $$

$$ \frac{\partial C}{\partial t} + \frac{\partial (M_x)}{\partial x} + \frac{\partial (M_z)}{\partial z} + \frac{\partial (M_F)}{\partial z} = \frac{\partial^2 (D_x C)}{\partial x^2} + \frac{\partial^2 (D_z C)}{\partial z^2} \qquad 4.14 \quad \text{A} $$

with

$$ \frac{\partial(M_x)}{\partial x} = \frac{M_{XE} - |M_{XP}| + M_{XW}}{2\Delta x} $$

$$ \frac{\partial(M_z)}{\partial z} = \frac{M_{ZT} - |M_{ZP}| + M_{ZB}}{2\Delta z} $$

$$ \frac{\partial(M_F)}{\partial z} = \frac{M_{FT} - |M_{FP}| + M_{FB}}{2\Delta z} \qquad 4.14 \quad \text{b} $$

$$ \frac{\partial^2 (D_x C)}{\partial x^2} = \frac{D_{XE} C_E - 2 D_{XP} C_P + D_{XW} C_W}{\Delta x^2} $$

$$ \frac{\partial^2 (D_z C)}{\partial z^2} = \frac{D_{ZT} C_T - 2 D_{ZP} C_P + D_{ZB} C_B}{\Delta z^2} $$

$$ \frac{\partial C}{\partial t} = \frac{C_{P}^{t+1} - C_{P}^{t-1}}{\Delta t} \qquad 4.14 \quad \text{c} $$

with

$$ M_{XP} = U_p \cdot C_p $$

$$ M_{ZP} = W_p \cdot C_p $$

$$ M_{FP} = Flot_p \cdot C_p $$
$$M_{XE} = \max(0, -U_E) \cdot C_E$$

$$M_{XW} = \max(0, U_W) \cdot C_W$$

$$M_{ZT} = \max(0, -W_T) \cdot C_T$$

$$M_{ZB} = \max(0, W_B) \cdot C_B$$

$$M_{FT} = \max(0, -\text{Flot}_T) \cdot C_T$$

$$M_{FB} = \max(0, \text{Flot}_B) \cdot C_B$$

$$\frac{C_P^{t+1} - C_P^{t-1}}{\Delta t} + \frac{M_{XE} - |M_{XP}| + M_{XW}}{2\Delta x} + \frac{M_{ZT} - |M_{ZP}| + M_{ZB}}{2\Delta z} + \frac{M_{FT} - |M_{FP}| + M_{FB}}{2\Delta z} \qquad 4.15 \\ = \frac{D_{XE}C_E - 2D_{XP}C_P + D_{XW}C_W}{\Delta x^2} + \frac{D_{ZT}C_T - 2D_{ZP}C_P + D_{ZB}C_B}{\Delta z^2}$$

$$(C_P^{t+1} - C_P^{t-1}) \times \frac{\Delta x \Delta z}{\Delta t} + (M_{XE} - |M_{XP}| + M_{XW}) \frac{\Delta z}{2} + (M_{ZT} - |M_{ZP}| + M_{ZB}) \frac{\Delta x}{2} \\ + (M_{FT} - |M_{FP}| + M_{FB}) \frac{\Delta x}{2} \qquad 4.16 \text{ A} \\ = \frac{\Delta z}{\Delta x} (D_{XE}C_E - 2D_{XP}C_P + D_{XW}C_W) \\ + \frac{\Delta x}{\Delta z} (D_{ZT}C_T - 2D_{ZP}C_P + D_{ZB}C_B)$$

With

$$V_t = \frac{\Delta t}{\Delta x \Delta z} \qquad 4.16 \text{ b}$$

$$M_{XE} \delta_Z = m_{XE}$$

$$M_{ZT} \delta_X = m_{ZT}$$

$$M_{FT} \delta_X = m_{FT}$$

$$|M_{XP}| \delta_Z = m_{XP}$$

$$|M_{ZP}| \delta_X = m_{ZP}$$

$$|M_{FP}| \delta_X = m_{FP}$$

4.16 c

$$M_{XW} \delta_Z = m_{XW}$$

$$M_{ZB} \delta_X = m_{ZB}$$

$$M_{FB} \delta_X = m_{FB}$$

With
$$ \delta_x = \frac{\Delta x}{2} \quad \text{and} \quad \delta_z = \frac{\Delta z}{2} $$

$$ \frac{\Delta z}{\Delta x} \mathbf{D}_{XE} \mathbf{C}_E = \mathbf{Diff}_{XE} \frac{\Delta x}{\Delta z} \mathbf{D}_{ZB} \mathbf{C}_T = \mathbf{Diff}_{ZT} \frac{\Delta z}{\Delta x} \mathbf{D}_{XP} \mathbf{C}_P = \mathbf{Diff}_{XP} \qquad 4.16 \text{ d} $$

$$ \frac{\Delta z}{\Delta x} \mathbf{D}_{XW} \mathbf{C}_W = \mathbf{Diff}_{XW} \frac{\Delta x}{\Delta z} \mathbf{D}_{ZB} \mathbf{C}_B = \mathbf{Diff}_{ZB} \frac{\Delta x}{\Delta z} \mathbf{D}_{ZP} \mathbf{C}_P = \mathbf{Diff}_{ZP} \qquad 4.16 \text{ e} $$

$$ \frac{\mathbf{C}_P^{t+1} - \mathbf{C}_P^{t-1}}{V_t} + (\mathbf{m}_{XE} - \mathbf{m}_{XP} + \mathbf{m}_{XW}) + (\mathbf{m}_{ZT} - \mathbf{m}_{ZP} + \mathbf{m}_{ZB}) + (\mathbf{m}_{FT} - \mathbf{m}_{FP} + \mathbf{m}_{FB}) = (\mathbf{Diff}_{XE} - 2\mathbf{Diff}_{XP} + \mathbf{Diff}_{XW}) + (\mathbf{Diff}_{ZT} - 2\mathbf{Diff}_{ZP} + \mathbf{Diff}_{ZB}) \qquad 4.17 \text{ A} $$

$$ \mathbf{C}_P^{t+1} = \mathbf{C}_P^{t-1} - V_t [(\mathbf{m}_{XE}-\mathbf{Diff}_{XE}) + (\mathbf{m}_{XW}-\mathbf{Diff}_{XW}) + (\mathbf{m}_{ZT}+\mathbf{m}_{FT}-\mathbf{Diff}_{ZT}) + (\mathbf{m}_{ZB}+\mathbf{m}_{FB}-\mathbf{Diff}_{ZB}) + (\mathbf{m}_{XP}+\mathbf{m}_{ZP}+\mathbf{m}_{FP}+2\mathbf{Diff}_{XP}+2\mathbf{Diff}_{ZP})] \qquad 4.17 \text{ b} $$

b) Numerical approach and convergence criterion

For the equations in stream function and vorticity form (equations (4.4) and (4.5)), an iterative method was implemented by using the method of Gauss-Seidel resolution (TDMA: Tridiagonal Matrix Algorithm) as described by Patankar (1980). The convergence criterion $\epsilon$ is:

$$ \epsilon = \left| \frac{\phi - \phi'_{P}}{\max(\phi)} \right| \le 10^{-5} \qquad 4.18 $$

Where $\phi$ is the variable calculated at the current time while $\phi'_{P}$ is the variable calculated at the previous iteration step. The convergence obtained for had to be lower than $10^{-5}$. For the transport equation or mass conservation equation above, we used an explicit iteration scheme in order to deal with CB density and buoyancy change at any time according to the light intensity
(phototaxis effects) in each control volume in the studied area, because the process becomes unstable when using the implicit scheme.

### 4.9.3 Validation benchmarking

The accuracy and precision of the model were evaluated. Unstable and divergent situations caused by the pressure in Navier-Stokes equation for most numerical frameworks using an eulerian approach have been avoided in our model due to the form of the vorticity equation. We validated our model first by using analytical results obtained from Li and Zhang(1993). Thus, the vertical profile of the u-component of fluid velocity in the center of a rectangular basin with a 2000 m X 2000 m of surface area and 10 m of depth may be calculated from the equation below:

$$u=\tau_x^s \sigma (h+\eta)(3\sigma-2)/4\epsilon_v \rho_w \qquad 4.19$$

with

$$\sigma = (h+\Delta z)/(h+\eta) \qquad 4.20$$

where **u**: horizontal velocity in the x direction (m s⁻¹); **h**: water depth(m); **η**: free surface water elevation above the water depth (m); ε_v: vertical diffusivity coefficient (0.01 m²/s); Δz: vertical grid size (m).

Data used in our model are the wind stress of 0.75 N m⁻² and mesh size Δx=100m on a total length of 2000m. The model was simulated for two cases with the water depth of 10m: case 1 with Δz=0.5m; case 2 with Δz=1m and the time step Δt=5seconds.

Water movement patterns were validated and the results are shown in **Figure 4.7a** and **b**.
<figure><img src="image_20.png" /><figcaption>**Figure 4.7:** Model comparison-horizontal velocity u (m/s) at the center of cavity a) dz=0.5 (vertical spatial step) and b) dz=1 (vertical spatial step)</figcaption></figure>

By comparing the analytical solutions of Li and Zhang (1993) with our numerical results, an excellent fit was observed (Table 4.1 and Table 4.2). The accuracy and precision of numerical results depends strongly on the mesh dimensions. Error ranks between our numerical simulations and analytical results by Li and Zhang (1993) are indeed much lower for a finer meshing. Results presented in Table 4.1 and Table 4.2 show that the refinement of the mesh tends to increase the model accuracy and precision.
<table><caption>**Table 4.1:** Model comparaison: Error value for dz=1</caption><thead><tr><td>Depth (m)</td><td>Li and Zhan Formula</td><td>Present Study</td><td>Error</td></tr></thead><tbody><tr><td>0</td><td>0.1875</td><td>0.1943</td><td>4%</td></tr><tr><td>-1</td><td>0.1181</td><td>0.1193</td><td>1%</td></tr><tr><td>-2</td><td>0.0600</td><td>0.0613</td><td>2%</td></tr><tr><td>-3</td><td>0.0131</td><td>0.0146</td><td>11%</td></tr><tr><td>-4</td><td>-0.0225</td><td>-0.0209</td><td>7%</td></tr><tr><td>-5</td><td>-0.0469</td><td>-0.045</td><td>4%</td></tr><tr><td>-6</td><td>-0.0600</td><td>-0.058</td><td>3%</td></tr><tr><td>-7</td><td>-0.0619</td><td>-0.0596</td><td>4%</td></tr><tr><td>-8</td><td>-0.0525</td><td>-0.0501</td><td>5%</td></tr><tr><td>-9</td><td>-0.0319</td><td>-0.0292</td><td>8%</td></tr></tbody></table>

<table><caption>**Table 4.2:** Model comparaison: Error value for dz=0.5</caption><thead><tr><td>Depth(m)</td><td>Li and Zhan Formula</td><td>Present Study</td><td>Error</td></tr></thead><tbody><tr><td>0</td><td>0.1875</td><td></td><td></td></tr><tr><td>-0.5</td><td>0.1514</td><td>0.1519</td><td>0%</td></tr><tr><td>-1</td><td>0.1181</td><td>0.1186</td><td>0%</td></tr><tr><td>-1.5</td><td>0.0877</td><td>0.0881</td><td>1%</td></tr><tr><td>-2</td><td>0.0600</td><td>0.0605</td><td>1%</td></tr><tr><td>-2.5</td><td>0.0352</td><td>0.0356</td><td>1%</td></tr><tr><td>-3</td><td>0.0131</td><td>0.0136</td><td>4%</td></tr><tr><td>-3.5</td><td>-0.0061</td><td>-0.0056</td><td>8%</td></tr><tr><td>-4</td><td>-0.0225</td><td>-0.0220</td><td>2%</td></tr><tr><td>-4.5</td><td>-0.0361</td><td>-0.0356</td><td>1%</td></tr><tr><td>-5</td><td>-0.0469</td><td>-0.0464</td><td>1%</td></tr><tr><td>-5.5</td><td>-0.0548</td><td>-0.0544</td><td>1%</td></tr><tr><td>-6</td><td>-0.0600</td><td>-0.0595</td><td>1%</td></tr><tr><td>-6.5</td><td>-0.0623</td><td>-0.0619</td><td>1%</td></tr><tr><td>-7</td><td>-0.0619</td><td>-0.0614</td><td>1%</td></tr><tr><td>-7.5</td><td>-0.0586</td><td>-0.0581</td><td>1%</td></tr><tr><td>-8</td><td>-0.0525</td><td>-0.0520</td><td>1%</td></tr><tr><td>-8.5</td><td>-0.0436</td><td>-0.0431</td><td>1%</td></tr><tr><td>-9</td><td>-0.0319</td><td>-0.0314</td><td>1%</td></tr><tr><td>-9.5</td><td>-0.0173</td><td>-0.0169</td><td>3%</td></tr></tbody></table>
### 4.9.4 Phototaxis behavior of cyanobacteria buoyancy

The enhanced approach to calculate the velocity of CB as a function of light proposed by Visser et al. (1997) was selected for this study. Although, the Lagrangian approach is interesting for studying the movement of cells, an eulerian approach enables us to explore the temporal spatial distribution of cells in relation to specific points of interest, for example, a drinking water intake. We used the model proposed by Visser et al. (1997). By using a sinusoidal function for light intensity and an extinction coefficient, light intensity at the surface and in the water column was calculated using the following equation:

$$I_{\text{surf}}=I_{\text{m}} \times \sin[(\pi \times t)/(D_{\text{L}} \times 60)] \quad 4.21$$

Where $I_{\text{surf}}$ is the photon irradiance on the surface at different times t (µmol photons m⁻² s⁻¹); $I_{\text{m}}$ is the maximum value of photon irradiance at noon (µmol photons m⁻²s⁻¹); t is the time (min) and $D_{\text{L}}$ is the length of the photoperiod (hour).

$$I_{z}=I_{\text{surf}} \times e^{-(\varepsilon \times z)} \quad 4.22$$

Where $I_z$ is the photon irradiance at the depth of the cyanobacterial colony (µmol photons m⁻²s⁻¹); $\varepsilon$ is the extinction coefficient of the water (m⁻¹) and z is the depth of the colony (m). In this study $\varepsilon$ was assumed to be approximately 1.25 m⁻¹

Under laboratory conditions, Visser et al. (1997) found that the CB behaviour changes when they are exposed to light intensity above or under the compensation value defined as the value where plankton respiration is equal to primary production, and the rate of density change is given by two conditions:

$$\text{If } I_z \le I_c \Delta \rho_{\text{col}} = -f_1 \times (\rho_{\text{col}_1}^{-}) + f_2 \quad 4.23$$

$$\text{If } I_z > I_c \Delta \rho_{\text{col}} = (\frac{N_0}{60}) \times e^{\frac{I_z}{I_0}} + f_3 \quad 4.24$$
Where $I_c$ is the compensation photon irradiance (10.9 µmol photons m⁻²s⁻¹); $I_0$ is the intensity where $I_z$ is maximum (277.5 µmol photons m⁻²s⁻¹); $N_0$ is the normative factor (0.0945 kg m⁻³µmol⁻¹ photons m²); $I_z$ is the photon irradiance (µmol photons m⁻²s⁻¹); $\Delta\rho_{col}$ is the rate of density change (kg m⁻³ min⁻¹) at photon irradiance $I_z$; $\rho_{col1}$ is the initial density (kg m⁻³); $f_1$ is the slope (9.49 10⁻⁴min⁻¹); $f_2$ is the theoretical rate of density change with no carbohydrate storage in the cells(0.984 kg m⁻³ min⁻¹) and $f_3$ is the rate of density change at $I_z=0$ (-0.0165 kg m³ min⁻¹).

In order to update the current density, equation (4.25) is used:

$$ \rho_{col2} = \rho_{col1} + \Delta t \times \Delta \rho_{col} \qquad 4.25 $$

Where $\rho_{col2}$ is the new density of CB (kg m⁻³); $\rho_{col1}$ is the previous density of CB (kg m⁻³) and $\Delta t$ is the time step (min).

Equation (4.25) was obtained through experiments on CB without gas vesicles, thus, a correction is made in order to obtain the real density using the following equation Visser et al. (1997):

$$ \rho_{col} = \rho_{col2} + \text{CorFact} \qquad 4.26 $$

Where $\rho_{col}$ is the real density of CB (kg m⁻³) and CorFact is the factor correction (65 kg m⁻³).

Finally, F (m s⁻¹) the sinking velocity as a function of CB buoyancy is given by Stokes' law:

$$ F = \frac{2gr^2A(\rho_{col} - \rho_w)}{9\Phi\mu} \qquad 4.27 $$

g is the gravitational acceleration (9.8 m s⁻²); r is the effective radius of the colony (m); A is the proportion of cell volume relative to colony volume; $\rho_w$ is the water density (1000 kg m⁻³); $\Phi$ is the form resistance and $\mu$ is the viscosity of the water (10⁻³ kg m⁻¹ s⁻¹).

In order to ensure that the CB model is based on physical reality, the minimum and maximum densities are used as boundaries. These values are:

Minimum buoyancy density=920 kg/m³
Maximum buoyancy density=1065 kg/m³

By taking into account the temporal delay, Wallace and Hamilton (1999) related the rate of
change of density to changing light intensity. This consideration has been introduced by
incorporating the following expression:

$$
G(t) = 1 - e^{-(t/\tau_r)} \qquad 4.28
$$

Where t is the time and τr is the response time.

Finally equations 4.23 and 4.24 have been written in the following forms:

$$
\text{If } I_z \le I_c \Delta \rho_{col} = \left[ -f_1 \times (\rho_{col_1}^{-}) + f_2 \right] \times G(t) \quad 4.29
$$

$$
\text{If } I_z > I_c \Delta \rho_{\text{col}} = \left[ \left( \frac{N_0}{60} \right) \times e^{\frac{I_z}{I_0}} + f_3 \right] \times G(t) \quad 4.30
$$

In their study using the Kromkamp and Walsby(1990) model, Wallace and Hamilton(1999)
suggested that the time response (τr) is around 20 mins for I_z>I_c and suggest a time response of 4
minutes for I_z>I_c for the model of Visser et al.(1997).

For the case when I_z \le I_c, the response time is not clearly defined. We conducted numerical tests for the time response when I_z \le I_c in order to calibrate the model with raw water data collected at the water intake.

Missisquoi Bay is a large bay (77.5 km² in area and latitude and longitude of 45°01′37.63″ North and -73°07′34.84″ West respectively) of Lake Champlain, which straddles the Canada - United States border (Figure 4.8). A detailed description of Missisquoi Bay and available phycocyanin probe monitoring data are provided by Ndong et al. (2014a). Missisquoi Bay is shallow with a mean depth of 2.8 m (Galvez & Levine, 2003), thus the wave base can be deep enough to cause mixing of bottom sediments in areas without rooted aquatic vegetation (Keleti et al., 1979).
<figure><img src="image_21.png" /><figcaption>**Figure 4.8:** Missisquoi Bay with drinking water intake position (PE) in Lac Champlain</figcaption></figure>

**4.9.5 Meteorological data collection**

In 2011, a HOBO weather station (Onset Computer Corporation, Bourne, MA, USA) was installed at a DW treatment plant on the eastern shore of Missisquoi Bay to collect data related to variables that may influence CB blooms such as temperature, humidity, wind speed, wind direction, and photosynthetic active radiation (PAR). Additional monitoring data collected are described in Ndong et al. (2014a).

**4.9.6 References**

Chen, Y., Qian, X., & Zhang, Y. (2009). *Buoyancy Regulating Cyanobacteria in Wind-Driven Currents*. Paper presented at the 3rd International Conference on Bioinformatics and Biomedical Engineering Beijing

Cole, T. M., & Buchak, E. M. (1995). CE-QUAL-W2: A two-dimensional, laterally averaged, hydrodynamic and water quality model, Version 2.0: Users Manual, Instruction Report EL-95-1 (pp. 357): US Army Engineer Waterways Experiment Station, Vicksburg, MS.

Galvez, R., & Levine, S. (2003). Canada-USA Agreement on the Eutrophication Control and Protection of Lake Champlain Quebec: Laval University, Quebec, Canada and Prof. Rubenstein School U. of Vermont, Burlington, VT, USA, p. 4.

Ghorai, S., Panda, M. K., & Hill, N. A. (2010). Bioconvection in a suspension of isotropically scattering phototactic algae. *Physics of Fluids, 22*(7), 16.

Hsu, S. A. (1972). *Wind Stress on a Coastal Water Surface*. Paper presented at the Proc. 13th Coastal Eng. Conf. .
Kromkamp, J. C., & Mur, L. R. (1984). Buoyant density changes in the cyanobacterium *Microcystis aeruginosa* due to changes in the cellular carbohydrate content. *FEMS Microbiology Letters*, 25(1), 105-109.

Kromkamp, J. C., & Walsby, A. E. (1990). A computer model of buoyancy and vertical migration in cyanobacteria. *Journal of Plankton Research*, 12(1), 161-183.

Leonard, B. P. (1979). A stable and accurate convective modelling procedure based on quadratic upstream interpolation. *19*(1), 59-98.

Li, Y. S., & Zhan, J. M. (1993). An efficient three-dimensional semi-implicit finite element scheme for simulation of free surface flows. *International Journal for Numerical Methods in Fluids*, 16(3), 187-198.

Litchman, E., & Klausmeier, C. A. (2001). Competition of phytoplankton under fluctuating light. *Am Nat*, 157(2), 170-187. doi: 10.1086/318628

Mellard, J. P., Yoshiyama, K., Litchman, E., & Klausmeier, C. A. (2011). The vertical distribution of phytoplankton in stratified water columns. *J Theor Biol*, 269(1), 16-30. doi: 10.1016/j.jtbi.2010.09.041

Myer, G., & G.K., G. (1979). Limnology of Lake Champlain: Lake Champlain Basin Study Report No. LCBS-30, New England River Basin Commission, Burlington,VT.

Ndong, M., Bird, D., Nguyen-Quang, T., de Boutray, M. L., Zamyadi, A., Vincon-Leite, B., Lemaire, B. J., Prevost, M., & Dorner, S. (2014). Estimating the risk of cyanobacterial occurrence using an index integrating meteorological factors: Application to drinking water production. *Water Res*, 56C, 98-108. doi: 10.1016/j.watres.2014.02.023

Nguyen-Quang, T., & Guichard, F. (2010). The role of bioconvection in plankton population with thermal stratification. *International Journal of Bifurcation and Chaos*, 20(06), 1761-1778.

Patankar, S. V. (1980). *Numerical heat transfer and fluid flow*. New York: McGraw-Hill.

Visser, P., Passarge, J., & Mur, L. (1997). Modelling vertical migration of the cyanobacterium *Microcystis*. *Hydrobiologia*, 349(1-3), 99-109.

Wallace, B. B., & Hamilton, D. P. (1999). The effect of variations in irradiance on buoyancy regulation in *Microcystis aeruginosa*. *Limnol. Oceanogr*, 44(2), 8.

Webster, I. T. (1990). Effect of wind on the distribution of phytoplankton cells in lakes. *Limnol. Oceanogr.*, 35(5), 13.

Webster, I. T., & Hutchinson, P. A. (1994). Effect of wind on the distribution of Phytoplankton cells in lakes revisited. *Limnol. Oceanogr.*, 39 (2), 9.
# CHAPITRE 5 ARTICLE 3: THERMAL STRATIFICATION AND WATER COLUMN STABILITY EFFECTS ON CYANOBACTERIA DISTRIBUTION IN A DRINKING WATER SOURCE

Ce chapitre présente les résultats de la modélisation de la distribution de la température dans la colonne d'eau en utilisant des données météorologiques réelles. A travers cette étude, l'effet de la stratification thermique et de la stabilité de la colonne d'eau sur la distribution spatio-temporelle des CB est explorée. Ce chapitre est une suite du chapitre précédent visant à mieux comprendre les facteurs qui influencent le comportement des cyanobactéries dans une colonne d'eau. Ce chapitre a été soumis à Water Research en septembre 2014.

## THERMAL STRATIFICATION AND WATER COLUMN STABILITY EFFECTS ON CYANOBACTERIA DISTRIBUTION IN A DRINKING WATER SOURCE

Mouhamed Ndong, David Bird, Tri Nguyen-Quang, Marie-Laure de Boutray, René Kahawita, Michèle Prévost, Sarah Dorner

a. Department of Civil, Geologic and Mining Engineering. École Polytechnique de Montréal, C.P. 6079, succ. Centre-ville, Montréal (Québec), Canada, H3C 3A7

b. Department of Biological Sciences, Université du Québec à Montréal, C.P. 8888, succ. Centre-ville, Montréal (Québec), Canada, H3C 3P8

c. Department of Engineering, Faculty of Agriculture, Dalhousie University, PO Box 550, Truro-Bible Hill (Nova Scotia), Canada, B2N 5E3
**5.1 Abstract**

Cyanobacteria (CB) outbreaks have become more frequent as a result of nutrient enrichment and increasing global temperatures. Within a system, physical factors play a role on a shorter term, including variable solar irradiance, thermal stratification, wind speed and direction, as well as eco-physiological responses such as buoyancy regulation. The effects of thermal stratification on CB distribution and bloom formation have been well described. However, some water bodies can present weak or no thermal stratification. The ecological implications of water column stability related to wind speed intensity need to be explored. To investigate the effects of water column stability on the distribution of CB, a novel deterministic model integrating the dominant processes associated with cyanobacteria movement and transport in surface waters was developed. The model considered CB buoyancy changes in response to light history and intensity. Meteorological and CB data from Missisquoi Bay (Québec, Canada) were used to explore the effects of temperature distribution, irradiance penetration in the water column and wind leading to water column stability. Observed and simulated results demonstrated that the thermal stratification was not strong, as is typical of large, shallow water bodies. In this case, the lack of turbulence, induced by low wind speed, becomes an important process that can lead to CB blooms. A wind speed range above 3 m/s led to stable water column conditions favourable for CB dominance. Weak thermal stratification with optimal water temperatures facilitates their dominance by enabling CB to maintain the same temperature-dependent growth conditions throughout the entire water column.

*Keywords:* hydrodynamic modeling, cyanobacteria, temperature, thermal stratification, drinking water

* Corresponding author Phone: 514-340-4711 extension 2983; Fax: 514-340-5918
E-mail: mouhamed.ndong@polymtl.ca

* Corresponding author. Current address: École Polytechnique de Montréal, Department of Civil, Geological and Mining Engineering, P.O. Box 6079, Station Centre-ville, Montreal, Quebec, Canada, H3C 3A7
## 5.2 Introduction

Surface waters are increasingly threatened by cyanobacteria (CB) occurrences as a result of local-to-global disruptions of elemental cycles such as carbon, nitrogen and phosphorus (Moroney & Somanchi, 1999). CB and their toxic metabolites can pass into drinking water treatment plants (Zamyadi et al., 2012), negatively impact the health of recreational water users (Lévesque et al., 2014), or result in the death of animals directly consuming the water (Gunn et al., 1992), among other concerns. The factors that control CB blooms are nutrient availability, primarily nitrogen and phosphorus, as well as water temperature, availability of solar irradiance, wind mixing, and water body stratification. Among these factors, the surplus of nutrients (phosphorus and nitrogen) has generally been identified as the primary cause of widespread CB blooms (Bergström, 2010; Smeltzer et al., 2012; Smith, 1986; Wang et al., 2002). Through its impacts on the controlling factors, climate change is expected to increase the frequency of CB occurrence (Carey et al., 2012; Paerl & Paul, 2012a; Paerl & Huisman, 2009).

Climate change implies changing precipitation patterns and increased temperatures. In temperate regions, these factors could favour a larger phytoplankton biomass peak (De Senerpont Domis et al., 2013). Increased and intensified precipitation induces an increase of nutrient loads in the water body (King et al., 2007). These nutrient loads combined with (or originating from) climate change could contribute to CB dominance (Jones et al., 2005). Elevated temperature is considered as a primary factor for bloom occurrence. In general, CB biomass increases with temperature (Kosten et al., 2011) and growth is optimal during periods of high temperature (usually when the temperature exceeds 25°C) (Coles & Jones, 2000; Rapala, 1998; Robarts & Zohary, 1987). *Microcystis* spp. lose their buoyancy in the temperature range from 12°C to 18°C (Reynolds, 2006). Higher temperatures favour CB blooms when they are in competition with other phytoplankton species (Jöhnk et al., 2008).

Under the influence of solar radiation and warm air, water temperature can form a gradient within the water column, leading to thermal stratification. It can be persistent (Westwood & Ganf, 2004) and permit vertical variation of phytoplankton composition (Halstvedt et al., 2007; Koreiviene & Karosiene, 2012). In particular, a stable water column permits CB species that can control their buoyancy, including *Microcystis* and *Anabaena*, to outcompete others for light (Paerl, 1988), and
at the same time, to exploit the internal sources of phosphorus and nitrogen, released within the hypolimnion (Bormans et al., 1999; Sondergaard et al., 2003). In eutrophic lakes, CB proliferation is enhanced by phosphorus release from sediments during anoxia (Journey et al., 2013; Nürnberg, 1996). Thermal stratification is under the control of lake morphometry (Bilinska, 2005) and stratification is rarely observed in shallow water bodies (Rucker et al., 1997). Where thermal stratification does not occur, the ecological implications for CB distribution and bloom formation have not been explored in the literature.

Mixing prevents bloom formation and reduces the growth of bloom forming species (1983). CB scum formation at the water surface is favoured by weaker winds (<3 m/s) that do not disrupt water stability (Cao et al., 2006). Thus, in order to address the knowledge gap in the literature concerning weak thermal stratification occurrence in shallow waters, we initiated this study with the following specific objectives: 1) to identify the conditions under which weak or absent stratification can be observed in a shallow lake by modeling, 2) to validate this understanding using recorded water temperature data, 3) to discuss the ecological implications of the presence or absence of thermal stratification for CB bloom occurrence, 4) to investigate CB behaviour and distribution and compare our model to full-scale field data recorded in the water column for different bloom conditions, and 5) to identify critical monitoring parameters needed for future studies.

## 5.3 Methodology

### Theoretical calculations

Water motion and CB buoyancy control the distribution of CB through their effects on advection and vertical velocity induced by changes in specific density (Kromkamp & Walsby, 1990; Reynolds et al., 1987; Thomas & Walsby, 1985; Visser et al., 1997). Two equations govern the hydrodynamic effects:

#### Continuity

$$ \nabla \cdot \mathbf{V} = 0 \qquad 5.1 $$
Momentum

$$ \rho_w \frac{\partial V}{\partial t} + \rho_w \nabla \cdot (VV) = -\nabla \rho + v \nabla^2 V + \rho \vec{g} \qquad 5.2 $$

Where V is the velocity of fluid (m/s); **p** is the dynamic pressure (Pa); **ρ** is the suspension density (kg/m³); **ρ**<sub>w</sub> is the water density (kg/m³); **g** is the gravitational acceleration (m³/s), **v** is water viscosity and **t** is the time (s). Numerical validation for the fundamental hydrodynamic model is available in (Ndong et al., 2014b).

The buoyancy effect is taken into account in the CB transport equation as presented in the following equation:

$$ \frac{\partial C}{\partial t} + \frac{\partial(uC)}{\partial x} + \frac{\partial[(w+F)C]}{\partial z} = \frac{\partial^2(D_x C)}{\partial x^2} + \frac{\partial^2(D_z C)}{\partial z^2} \qquad 5.3 $$

Where C is the concentration of CB cells or phytoplankton (cell/m³), u, w correspond respectively to the two components of water velocity (m/s) in the horizontal (x) and vertical (z) directions, F is CB cells buoyancy (m/s) and D<sub>x</sub> and D<sub>z</sub> are the horizontal and vertical diffusivity coefficients (m²/s), respectively. The CB transport equation treatment with CB buoyancy are described in detail in Ndong et al. (2014b) which is the first model to consider at a full scale the effects of buoyancy in relation to phototaxis. The upward movement is related to the cells' buoyancy as a function of light rather than as a process related to resuspension due to critical shear stress.

Equations 1 through 3 are mainly related by the water velocity. Many other relationships exist among variables but were not considered in this study. Examples of relationships among other variables include density change induced by temperature and cyanobacteria concentration (Nguyen-Quang & Guichard, 2010), temperature and cyanobacteria effects on water viscosity, and the effects of viscosity on cyanobacteria velocity. However, to our knowledge, there have been no studies examining or quantifying the relationships among these factors.
## Water temperature: Conceptual approach and assumptions

CB behaviour in a water body is affected by the hydrodynamics of water movement and their own properties of buoyancy from changes to their density, according to their exposure to or exclusion from light. Water movement and buoyancy changes are both influenced by temperature through water density and viscosity. From the Navier-Stokes equation, it can be deduced that a large vertical gradient of water density changes in a water column can affect surface water hydrodynamics. The influence of viscosity on CB is observed in the CB buoyancy model (Kromkamp & Walsby, 1990; Visser et al., 1997; Wallace et al., 2000) where CB moving velocity is calculated assuming the validity of Stokes' law.

Water temperature is affected by the net heat flux from solar radiation (Shanahan, 1985). It is modelled by using the transport equation and taking account solar radiation as the source of energy as shown in equation 4. The form of the transport equation for temperature including heat balance is described as follows:

$$ \frac{\partial T}{\partial t} + \nabla(VT) = D\nabla^2 T + \frac{1}{\rho c_p} \frac{\partial Qz}{\partial z} \qquad 5.4 $$

Where T is the water temperature (°C); V is the fluid medium velocity, ρ is the water density, Cp is the specific heat of water (J/kg.K), D is the coefficient of diffusion of the temperature (m²/s) and Qz is the solar radiation penetrating into water (W/m²).

The penetration of solar radiation (Qz) into the water column is obtained by using the Beer-Lambert law (Lap & Mori, 2007):

$$ Qz = Qs \times e^{-\varepsilon \times \Delta z} \qquad 5.5 $$

Where ε is the extinction coefficient per m of the water column. In this study ε was assumed to be approximately 1.25 m⁻¹.

Short wave solar radiation from 300 to 3000 nm (Qsw) and net atmospheric long wave radiation from 3 to 10 µm (Qatm) will penetrate the water column, such that Qs=Qsw+Qatm
Long and short wave radiation can be calculated through the following equations:

Short wave radiation(Lap & Mori, 2007):

$$Q_{sw} = (1 - Fa) \times (PAR \times \frac{\alpha}{\beta}) \qquad 5.6$$

Fa (surface albedo) is the fraction of the solar shortwave radiation that is reflected immediately at the surface (0.65)

α is the coefficient to convert PAR in µmol/m²s into W/m² (0.219)
β is the coefficient to convert PAR (W/m²) into short wave radiation which was assumed to be around 50% to 65% (0.50 value in this study).

Net atmospheric long wave radiation:

$$Q_{atm} = Ce \times (1 - RL) \times (1 - 0.17 \times CL^2) \times \sigma \times (Ta + 273.16)^4 \quad 5.7$$

Where Ce is a constant value (9.37.10⁻⁶), RL is the reflectivity of water (0.03); CL is the fraction of sky covered by clouds, σ is the Stefan-Boltzmann constant (5.6697·10⁻⁸ W/m².K⁴), Ta represents air temperature above the water's surface (°C).

For calculated cloud cover fraction, the following formula proposed by Ek and Mahrt (1991) was used:

$$CL = \begin{cases} \left( \frac{RH_{850} - RHC}{1 - RHC} \right)^{xp} & \text{if } \frac{RH_{850} - RHC}{1 - RHC} > 0 \\ 0 & \text{if } \frac{RH_{850} - RHC}{1 - RHC} \le 0 \end{cases} \qquad 5.8$$

Where RHc is a critical relative humidity at which cloud assumed to form and xp is a constant parameter. Their values are: RHcrit= 0.85 and xp = 2 (Grabowska & Mazur-Marzec, 2014).

The equation (5.8) is a formulation of cloud cover which is based on the fractional relative humidity (RH₈₅₀) near the top of the boundary layer. It has been established at layer 850 mb
(altitude 1500 m). In order to use it, we apply a correction by calculated the relative humidity at this layer (RH<sub>850</sub>) by using air temperature and relative humidity recorded by our meteorological station. The following equations are used to calculate RH<sub>850</sub>:

$$Es = 6.1121 \times e^{\frac{Ta \times \frac{18.678-Ta}{234.5}}{254.14+Ta}} \qquad 5.9}$$

$$Ea = \frac{Es \times RH}{100} \qquad 5.10}$$

$$q = \frac{0.622 \times Ea}{P - 0.378 \times Ea} \qquad 5.11}$$

Where q is the specific humidity, Ea is the air vapor pressure (hPa) and Es is the saturation vapor pressure of air at the temperature of the surface water (hPa). The air temperature at 850 mb (altitude h=1500m) is calculated by using the equation:

$$Ta_h = Ta - 6.5 \frac{h}{1000} \qquad 5.12}$$

Where $Ta_h$ is the air temperature at altitude (h) and $Ta$ is the air temperature at ground level (measured with our meteorological station).

The equation (5.9) is used to calculate the air vapor pressure at saturation at an altitude of 1500m (850mb) and equation (5.11) gives the specific humidity at saturation at this layer ($q_{s850}$) by changing $Ea$ by $Es$. Finally, the relative humidity is:

$$RH_{850} = \frac{q}{q_{s850}} \qquad 5.13}$$

**Boundary conditions:**

- Hydrodynamic boundary conditions:

These hydrodynamic conditions are the same mentioned in Ndong et al. (2014b). Vorticity($\xi$) and stream ($\varphi$) functions are used and at the water surface the boundary conditions are expressed as:
$$ \left\{ \begin{array}{l} \varphi_s = 0 \\ \xi_s = \frac{\tau_x^s}{\Gamma_x \rho_w} \end{array} \right. \qquad 5.14 $$

Where $\varphi_s$ is the surface stream, $\xi_s$ is the surface vorticity, $\tau_x^s$ is the surface wind stress (N m$^{-2}$), $\Gamma_x$ is the horizontal diffusivity coefficient (m$^2$/s) and $\rho_w$ is the water density (kg/m$^3$).

- At a closed boundary, the vorticity is null ($\xi=0$) and the stream is expressed by:

$$ \left\{ \begin{array}{l} \frac{\partial^2 \varphi}{\partial x^2} = 0 \qquad \text{at left and right boundaries} \\ \\ \frac{\partial^2 \varphi}{\partial z^2} = 0 \qquad \text{at bottom} \end{array} \right. \qquad 5.15 $$

Where x, z are respectively the horizontal and vertical Cartesian coordinates

- boundary conditions for heat flux

At the water surface, the heat loss flux must be taken into account. Surface water $Q_s$ is a function of short wave radiation (Qsw), net atmospheric long wave radiation (Qatm), long wave back radiation (Qb), sensible heat flux from the water (Lv), latent heat flux from the water (Qlat) as follows (Shanahan, 1985):

$$ Q_s = Q_{sw} + Q_{atm} - Q_{b} - L_{v} - Q_{lat} \qquad 5.16 $$

Long wave back radiation

$$ Q_b = \epsilon \times \sigma \times (T_w + 273.16)^4 \qquad 5.17 $$

Where $\epsilon$ is the emissivity (0.975) and $T_w$ is the water surface temperature (°C).

Sensible heat flux from the water

$$ L_v = C_s \times C_p \times U_z \times \rho_a \times (T_w - T_a) \qquad 5.18 $$
Where Cs is a constant value (1.45 · 10⁻³), Uz is wind speed (m/s), pa is the air density [kg/m³] calculated with the equations:

$$ \rho a = \frac{P \times 100}{Rd \times T\nu} \qquad 5.19 $$

$$ T\nu = (Ta + 273) \times (1 + 0.61 \times q) \qquad 5.20 $$

Rd is the specific gas constant for dry air (287.05 J/kg/K) and Tν is a virtual temperature(°C) that represents the temperature of a quantity of dry air in the same condition of pressure and density as the same quantity of wet air, q is the specific humidity, Ea (air vapor pressure) and Es(saturation vapor pressure of air at the temperature of the surface water) are calculated through equation (5.9), (5.10) and (5.11) by changing Ta by Tw

## Latent heat flux from the water

Latent heat flux follows the relation:

$$ Q_{lat} = \rho a \times L_{el} \times C_{el} \times U_{z} \times (q - q_{s}) \qquad 5.21 $$

Where Lel= latent heat of vaporisation (as constant, Lel=2.5 10⁶ J/kg), Cel= drag coefficient (as constant, Cel=1.2 10⁻³ J/kg), q_s is the specific humidity (kg water/kg air) for saturated air over water at surface temperature at Ta. It is calculated by using formula (5.9), (5.10) and (5.11).

Adiabatic conditions were applied in closed boundaries conditions in order to consider only the heat budget at the upper surface in the water column.

### Boundary conditions for cyanobacteria

The initial CB cell concentration was assumed to be 10 000 cells/mL that is the alert level 1 for CB occurrence at drinking water intake, representative of conditions in Missisquoi Bay (McQuaid et al., 2011). No other sources of cyanobacteria were considered. At closed boundaries conditions, it was expressed as a zero flux.
## Study site: Missisquoi Bay, Québec, Canada

Missisquoi Bay is a shallow water body of Lake Champlain, a transboundary lake situated in Canada (Québec) and the United States of America (Vermont and New York). It is a large Bay (77.5 km² at the latitude and longitude coordinates of 45°01′37.63″ North and -73°07′34.84″ West) with a mean depth of 2.8 m. The bay's morphological characteristics are described in detail in Ndong et al. (2014a). Missisquoi Bay is the source of drinking water for a population of approximately 4500 residents (Organisme de bassin versant de la baie Missisquoi, 2011). As with many surface water bodies, climate change, particularly rising temperatures, is affecting Missisquoi Bay. Jensen and Andersen (1992) suggested that in a shallow water body like Missisquoi Bay, higher temperatures at the sediment-water interface also leads to greater phosphorus release during the summer. Summer air temperatures increased at an annual average rate of 0.037°C from 1976 to 2005 in Lake Champlain (Stager & Thill, 2010). A rising trend of water surface temperature during the month of August was noted from 1964 to 2009 in the same lake (Smeltzer et al., 2012).

Water density and viscosity variation as a result of temperature fluctuations were assumed to be small given that the model was applied to the summer and early fall season exclusively and were therefore not considered in the hydrodynamic and mass transport equations.

## Sampling procedures and meteorological data collection

A multi-probe system from YSI (YSI, Yellow Springs, Ohio) as described by McQuaid et al. (2011) was installed inside the drinking water treatment plant intake in Missisquoi Bay to record temperature, conductivity, turbidity, pH, dissolved oxygen, chlorophyll fluorescence and phycocyanin fluorescence.

For phycocyanin analyses, water samples were collected once per week in the lake at the site of the drinking water intake. On each sampling date, water samples were collected in duplicate every meter in clean 500 mL plastic bottles for chemical analysis and biological extractions. The bottles were rinsed three times with sampled water before they were filled completely and tightly closed. All the samples were preserved on ice in coolers for transport and processed or prepared for storage (pigments) within 24 hours. Phycocyanin and chlorophyll analyses were performed with a Turner Designs 10AU™ Field Fluorometer (Turner Designs, Sunnyvale, CA, USA) using EPA Method 445.0 (Arar & Colling, 1997).
In 2011, a HOBO weather station (Onset Computer Corporation, Bourne, MA, USA) was installed directly at the drinking water treatment plant on the eastern shore of Missisquoi Bay to collect temperature, humidity, wind speed and direction, and photosynthetic active radiation (PAR) data. HOBO TempPro Loggers (0.2°C accuracy) were installed to collect additional temperature data above the drinking water intake.

In order to investigate water temperature, light penetration and CB distribution in the water column, simulations were performed for the summer of 2011; three representative sampling days with different meteorological conditions are described in **Table 5.1**.

<table><caption>**Table 5.1:** Three representative sampling days at Missisquoi Bay, August 2011</caption><thead><tr><th></th><th>03 August 2011</th><th>17 August 2011</th><th>23 August 2011</th></tr></thead><tbody><tr><th scope="row">Meteorological conditions</th><td>Little wind and partially cloudy</td><td>No cloud cover, ambient temperature around 28°C, no wind, no rain</td><td>Windy, sunny, almost no cloud cover</td></tr><tr><th scope="row">Observations on the presence of CB at the drinking water treatment plant intake</th><td>No CB blooms were observed visually (Maximum phycocyanin: 2.9µg/L-PC; alert level was: Caution)*</td><td>A severe CB bloom occurred on this day (visual observation made) (Maximum phycocyanin: 40µg/L-PC; alert level was: Warning)*</td><td>No CB blooms were observed visually (Maximum phycocyanin: 8.3µg/L-PC; alert level was: Caution)*</td></tr></tbody></table>

<footnote>*The alert level to define a bloom was based on cyanobacteria monitoring with phycocyanin concentrations (µg/L) as proposed by Ahn et al. (2007) (No bloom: <0.1µg/L-PC; Caution: between 0.1µg/L and 30µg/L-PC; Warning: between 30 µg/L and 700µg/L-PC; Outbreak: > 700µg/L-PC).</footnote>
These dates were selected based on the availability of data throughout the water column, as full water column data were available on a weekly basis from mid-July to the end of August in 2011.Water column profiles and samples were taken during the day at times ranging from 10:30 am to 12:00pm using the YSI multi-probe, or as described above. Weekly data were available for the entire season from the drinking water intake, which rests on the lake bottom; these were presented in Ndong et al. (2014a).

**5.4 Results**

**5.4.1 Temperature modeling**

A good temperature model is important when considering temperature dependent processes such as CB growth, water density and viscosity changes. In this study, these coupled processes were not considered and the temperature was modelled as a critical first step in the development of a complete coupled hydrodynamic CB transport model. In addition, the model provides detailed results of thermal stratification for periods without measured temperature data and provides a description of fundamental processes governing the movement of CB in surface waters. As such, the model provides a physically realistic prediction of the vertical temperature profile throughout the critical bloom period. The results in **Figure 5.1b** and **c** show that water temperature modeling at the drinking water intake at Missisquoi Bay was in good agreement with measured data. Relative errors were less than 10% (**Figure 5.1c**) recorded just once during the entire simulation (20 days) with a time step of 5seconds). We can observe thermal stratification during some days when water temperature recorded at the surface are high (4^th^-5^th^ August and 8^th^-9^th^ August 2011) (**Figure5.1a**), but there were more days with a weak (or no) thermal stratification.
<figure><img src="image_22.png" /><figcaption>**Figure 5.1:** Time series: a) Simulated profile of temperature in water column; b) measured temperature (data) and simulated temperature (model) at the surface water above the drinking water intake c) Relative error between measured data and model results</figcaption></figure>
Vertical temperature profile presents weak to no stratification for the days of August 3rd 2011, August 17th 2011 and August 23rd 2011 (Figure 5.2). The differences between model results and measured data were less than 1.5°C. A weak (or no) thermal stratification and similar range of temperature were observed during these three days with adequate temperatures for CB growth. It was observed that during these days (Figure 5.2a, b and c), water temperature was around 22°C to 25°C. However, only the 17th of August 2011 had a visible CB bloom at the surface (Table 5.1). Furthermore, the physiological behaviour of CB affected by light intensity should be the same during all the three sampling days because there were no significant differences in light penetration throughout the water column among the three sampling days (Figure 5.2).

<figure><img src="image_23.png" /><figcaption>**Figure 5.2:** Light penetration in water column and temperature (model result vs collected data) during three sampling days: a) August 03rd, 2011, b) August 17th, 2011 and c) August 23rd, 2011</figcaption></figure>

### 5.4.2 Wind effects

Although simulations were performed for the entire season, results are presented for three different days, the 3rd, 17th and 23rd of August 2011, representing three contrasting wind conditions at Missisquoi Bay (Figure5.3).
<figure><img src="image_24.png" /></figure>

**Figure 5.3:** Wind occurrence (speed and direction) 12hours, 6hours and 3hours before sampling: during the day: a) 03 August 2011, b)17 August 2011 and c) 23 August 2011 with wind direction angle (AOC) that exposed drinking water intake to CB occurrence

When mixing induced by wind speed over than 6-8m/s occurred, as was observed on the 3rd and 23rd of August, the accumulated CB at the water's surface were quickly dispersed (Kanoshina et al., 2003). The drinking water intake is located on the North-East side of the Bay (**Figure 5.3**), exposing it to cyanobacteria accumulations from winds coming from 190°to 310°, with an optimal value of 200° (Ndong et al., 2014a). Wind direction was not favourable for bloom accumulation on August 3, 2011 (**Figure5.3**). In contrast, the wind was favourable on Aug. 17, 2011 (**Figure5.3**) with a modest speed (mean 1.5m/s). On August 23rd, 2011 (**Figure5.3**), the wind direction could favour CB blooms at the drinking water intake based upon its position within the water body (i.e., wind was blowing towards the intake) but the associated speed was very high (mean 5m/s) leading to turbulent conditions.
### 5.4.3 Cyanobacteria distribution

CB distribution and water temperature were modelled and compared with data collected for three different sampling days (Table 5.1) in order to investigate water temperature, light penetration and CB distribution in the water column. CB distribution in the water column represented by phycocyanin concentration (Figure5.4) was compared with our results from our numerical model run with meteorological data.

<figure><img src="image_25.png" /></figure>

**Figure 5.4:** Comparison of Cyanobacteria (CB) trend distribution in the water column (model result vs collected data) during three sampling days: a) 03 August 2011, b) 17 August 2011 and c) 23 August 2011

<figure><img src="image_26.png" /></figure>

**Figure 5.5:** Variance of Cyanobacteria (CB) distribution in the water column during three sampling days: 03 August 2011, b) 17 August 2011 and c) 23 August 2011. Model result data at different time (h1:10:30; h2:11:00; h3:11:30 and h4:12:00)
The general trends were well captured by the model during the day of August 17th 2011, though less well on August 03rd 2011 and August 23rd 2011. However, during the three sampling days, it is interesting to note the total number of CB cells recorded in the water column above the drinking water intake. It appears that CB accumulation occurs when wind speed is modest or low and its direction is in the range or zone previously mentioned as being close to optimal (190°-310°) (Figure 5.3b). In contrast, August 23rd 2011 had a favourable wind direction but was intense (Figure 5.3c), causing a high density of CB that were well dispersed throughout the water column (Figure 5.3c) as water column turbulence was also more intense.

## 5.5 Discussion

### 5.5.1 Ecological implications of the absence of stratification

It was suspected that eutrophic shallow water bodies are vulnerable to CB blooms because favourable thermal conditions occur throughout and blooms are generally limited by the stability of the water column, as was also observed in the model. For testing this hypothesis, results from sampling dates were analyzed in order to demonstrate the role of the water column stability in the case of weak stratification as is frequently observed at Missisquoi Bay. Water column stratification has been reported to be a key parameter that intensifies CB accumulation, whereby adequate water temperature conditions enable the initiation of a bloom and stratified conditions favour CB dominance (Kanoshina et al., 2003). Fast migration of buoyant CB is facilitated by increasing stratification (Carey et al., 2012). Stratified conditions can be exploited by many CB species (Walsby, 1975; Walsby, 1997) and stratification has been shown to govern the vertical distribution of algal biomass (Albay & Akçaalan, 2003).

Warming temperatures as a result of global climate change are expected to intensify thermal stratification of surface waters and lengthen the period of seasonal thermal stratification, thereby enhancing conditions for CB (Li & Han, 2012). Stratification favours buoyant CB to the detriment of others algal species (Huisman et al., 2004). There is strong evidence that persistent stratification leads to the formation of CB blooms (Westwood & Ganf, 2004) and that potentially toxic CB occurrences can be promoted by long stratification periods (George & Harris, 1985). All these findings do not explain CB distribution and bloom formation at Missisquoi Bay during our study period. Based on these results, we suspect that the lack of stratification has led to uniform, high velocity movement for cyanobacteria in the water column. When high
temperatures occur, buoyant CB surface bloom formation will be enhanced and their vertical movement as a function of light availability and nutrient status will be more rapid (Paerl & Huisman, 2009). This is due almost entirely to the decrease in water viscosity with rising water temperatures (Hutchinson, 1957), because the effect on the radius and thus the density of cyanobacteria cells is relatively weak. The decreased viscosity leads to a faster movement of CB, both in ascent and descent, because the CB moving velocity is inversely proportional to water viscosity based on Stokes' law (Reynolds, 2006).

In Missisquoi Bay and other shallow water bodies where CB dominate such as Lake Winnipeg (Kling et al., 2011) Lake Erie (Stumpf et al., 2012) and an embayment of Lake Ontario (Hotto et al., 2007), strong thermal stratification does not explain the dominance of CB. For the case where stratification is weak, other physical processes must be considered, knowing that nutrients are sufficient to support CB growth. It is recognized that wind speed is inversely related to CB bloom occurrence by affecting water column stability (Bormans et al., 2004). The mixing of buoyant phytoplankton cells has been observed when wind speed was greater than 2-3 m/s (Webster & Hutchinson, 1994). According to Cao et al. (2006), *Microcystis* scums float to the water's surface when the wind speed is below 3.1 m/s. The spatial distribution of CB has been more linked to wind forced advection than possible transport of nutrients (Kanoshina et al., 2003); however, the presence of nutrients has not been well quantified with regards to cyanobacteria movement and its inclusion in models may improve predictions (Ndong et al., 2014a).

Albay and Akçaalan (2003) observed that surface water with weak thermal stratification can experience severe CB blooms with CB dominance. The shallow layer permits CB to have greater access to light quickly during the day and to maintain their nocturnal dominance (Carey et al., 2012). Based on their buoyant properties, CB will tend to float in stable layers (Marcé et al., 2007). In Missisquoi Bay, conditions throughout the water column are favourable for CB and CB can easily move through the water column. Thus, it is not necessary to have stratification to enable CB dominance, but rather favourable thermal conditions to facilitate CB growth and movement through a reduction of the water's viscosity in the water column. CB are considered to be very strong competitors for light because of their accessory pigments and structural organisation of their light harvesting antennae (e.g (Osborne & Raven, 1986)). Light availability was sufficient for CB on all three days and is therefore not a discriminating factor to explain differences in CB concentrations at the drinking water intake.
In this way, this analysis shows that water column stability induced by modest wind speed is very important in shallow water where CB occurrences are observed and that longer and stronger periods of water column stability lead to favourable conditions for CB such as *Microcystis*, which are often dominant in Missisquoi Bay (McQuaid et al., 2011; Ndong et al., 2014a). Finally, the wind was likely the determining factor to explain differences among the three days.

In order to simulate exact concentrations of CB above the intake, it would be necessary to include all processes that affect absolute numbers of CB in the water body. For example, processes such as flushing events (including flows from rivers and streams draining to Missisquoi Bay), CB growth, CB mortality, the dynamics of nutrients and nutrient loads to the Bay, photo-inhibition, would further improve the numerical model for CB and compare with real concentrations rather than general trends.

It is important to note the importance of the sampling frequency when developing CB models and comparing with field data. Although hydrodynamic models have been used for modeling CB transport and comparing with satellite imagery, these are not sufficient to determine whether or not a drinking water treatment plant is at risk. Satellite images provide CB information at the surface of a water body, whereas drinking water intakes are generally located near the bottom of the water column. Thus, models describing the movement through the water column are needed to understand the risk of CB breakthrough into drinking water treatment plants.

### 5.5.2 Critical findings for cyanobacteria modeling

Hydrodynamic simulations demonstrated that CB blooms occur when a combination and necessary factors such as wind speed, wind direction and water temperatures are favourable. These results support results found in a previous study on the development of an index for evaluating the risk associated with CB blooms occurrence at a drinking water intake using water temperature, wind speed and wind direction. It was shown that water temperature, wind speed and wind direction as factors in eutrophic waters such as Missisquoi Bay could explain up to 68% of the probability that CB blooms occurs at a given location within the water body (Ndong et al., 2014a). This study provides the detailed mechanistic description of the processes involved that explain why these three factors are dominant in a shallow water body such as Missisquoi Bay.

Our finding demonstrated the vulnerability of an intake location according to modest changes in winds patterns. Because of this variability, it may be challenging to predict the most critical
periods of CB accumulation at the water intake. Nevertheless, the model proposed appears highly
useful in the setting the boundary concentrations that may be found at the water intake.

The short term variability of the model shows that CB cells distribution can change
quickly between 10:30 (h1) to 12:00 (h4) (Figure 5.5a,b and c). The rapid changes can be
explained by the rapid buoyancy changes probably caused by the time response delay of 4
minutes (Wallace and Hamilton, 2000) for the Visser and al. (1997) model used in this study. The
time delay needs more investigation for field scale (as opposed to lab-scale) environmental
conditions. We suspect that the time delay response is of longer duration for Missisquoi Bay than
previously reported elsewhere (Ndong et al., 2014b). Meteorological data such as wind, solar
irradiance, humidity, have high hourly variability and this variability is critical for the risk to a
drinking water treatment plant when the density of CB reach a threshold that will allow them to
accumulate in high numbers. Thus, high frequency sampling of CB should be considered (for
example, through the use of phycocyanin probes) and the collection of meteorological data
describing changing conditions would provide the most relevant information for the development
and use of hydrodynamic CB models and operational decisions at drinking water treatment
plants.

**5.6 Conclusions**

Through this study, water temperature at Missisquoi Bay was well modelled. Thermal stratification which is not often observed in shallow lakes such as Missisquoi Bay is not the main process that favours CB blooms occurrence. Water column stability appears to be the key factor that leads to CB bloom occurrence in the case of Missisquoi Bay where nutrients are generally not limiting. The effects of these factors lead to water column hydrodynamic stability resulting from wind speed intensity that represent adequate conditions that permit CB to exploit their physiological characteristics, including specifically their own capacity to move in the water column. Wind speed below 3m/s was found to be favourable for CB occurrence as was also observed by (Webster & Hutchinson, 1994). This study highlights the importance of the primary physical factors used when developing an index for evaluate CB risk occurrence (Ndong et al., 2014a) and illustrates the details of the primary physical processes involved. To estimate actual CB concentrations in the water column, other important processes such as flushing events, growth, mortality, the dynamics of nutrients should be considered. It is important to note the many physical and biological processes that influence CB occurrences. The model results
demonstrate that the greatest data needs are for high frequency sampling throughout the water
column and that these data are needed for fully understanding CB occurrence and behaviours, and
ultimately the risk to users of the water resource.

**5.7 Acknowledgment**

This study was financially supported by the Natural Science and Engineering Research Council of Canada (NSERC), Canada Foundation for Innovation (CFI), Fonds de recherche du Québec – Nature et Technologies (FQRNT), and Canada Research Chairs (CRC).

**5.8 References**

Albay, M., & Akçaalan, R. (2003). Factors influencing the phytoplankton steady state assemblages in a drinking-water reservoir (Ömerli reservoir, Istanbul). Hydrobiologia, 502(1-3), 85-95.

Arar, E. J., & Colling, G. B. (1997). U.S. Environmental Protection Agency Method 445.0, In Vitro Determination of Chlorophyll a and Pheophytin a in Marine and Freshwater Algae by Flurorescence: revision 1.2.
http://www.turnerdesigns.com/t2/doc/appnotes/EPA445.pdf.accesed 08 August 2012.

Bergström, A.-K. (2010). The use of TN:TP and DIN:TP ratios as indicators for phytoplankton nutrient limitation in oligotrophic lakes affected by N deposition. Aquatic Sciences, 72(3), 277-281.

Bilinska, K. (2005). Thermal Stratification in the Waikato hydro lakes. The University of Western Australia, Australia.

Bormans, M., Ford, P., Fabbro, L., & Hancock, G. (2004). Onset and persistence of cyanobacterial bloom in a large impounded tropical river, Australia. Marine and Freshwater Research, 55(1), 15.

Bormans, M., Sherman, B. S., & Webster, I. T. (1999). Is buoyancy regulation in cyanobacteria an adaptation to exploit separation of light and nutrients? Mar. Freshw. Res., 50, 897-906.

Cao, H.-S., Kong, F.-X., Luo, L.-C., Shi, X.-L., Yang, Z., Zhang, X.-F., & Tao, Y. (2006). Effects of Wind and Wind-Induced Waves on Vertical Phytoplankton Distribution and Surface Blooms of Microcystis aeruginosa in Lake Taihu. Journal of Freshwater Ecology, 21(2), 231-238.

Carey, C. C., Ibelings, B. W., Hoffmann, E. P., Hamilton, D. P., & Brookes, J. D. (2012). Eco-physiological adaptations that favour freshwater cyanobacteria in a changing climate. Cyanobacteria: Impacts of climate change on occurrence, toxicity and water quality management, 46(5), 1394-1407.

Coles, J. F., & Jones, R. C. (2000). Effect of temperature on photosynthesis-light response and growth of four phytoplankton species isolated from a tidal freshwater river. J Phycol, 36, 9.

De Senerpont Domis, L. N., Elser, J. J., Gsell, A. S., Huszar, V. L. M., Ibelings, B. W., Jeppesen, E., Kosten, S., Mooij, W. M., Roland, F., Sommer, U., Van Donk, E., Winder, M., &
LÜRling, M. (2013). Plankton dynamics under different climatic conditions in space and time. *Freshwater Biology*, 58(3), 463-482.

Ek, M., & Mahrt, L. (1991). A formulation for boundary-layer cloud cover. *Annales Geophysicae*, 9, 9.

George, D. G., & Harris, G. P. (1985). The effect of climate on long-term changes in the crustacean zooplankton biomass of Lake Windermere, UK. *Nature*, 316, 4.

Grabowska, M., & Mazur-Marzec, A. (2014). Vertical distribution of cyanobacteria biomass and cyanotoxin production in the polymictic Siemianówka Dam Reservoir (eastern Poland). *Arch. Pol. Fish.*, 22, 41-51.

Gunn, G. J., Rafferty, A. G., Rafferty, G. C., Cockburn, N., Edwards, C., Beattie, K. A., & Codd, G. A. (1992). Fatal canine neurotoxicosis attributed to blue-green algae (cyanobacteria). *Vet. Rec.*, 4, 301-302.

Halstvedt, C. B., Rohlack, T., Andersent, T., Skulberg, O., & Edvardsen, B. (2007). Seasonal dynamics and depth distribution of Planktothrix spp. in Lake Steinsfjorden (Norway) related to environmental factors. *J. Plankton Res.*, 29, 471-482.

Hotto, M. A., Satchwell, M. F., & Boyer, L. G. (2007). Molecular Characterization of Potential Microcystin-Producing Cyanobacteria in Lake Ontario Embayments and Nearshore Waters. *Appl Environ Microbiol.*, 73, 4570-4578.

Huisman, J., Sharples, J., Stroom, J., Visser, P. M., Kardinaal, W. E. A., Verspagen, J. M. H., & Sommeijer, B. (2004). Changes in turbulent mixing shift competition for light between phytoplankton species. *Ecology* 85, 10.

Hutchinson, G. E. (1957). A Treatise on Limnology. V. 1, Geology, Physics and Chemistry. New York, NY, USA.

Jensen, H. S., & Andersen, F. O. (1992). Importance of temperature, nitrate, and pH for phosphate release from aerobic sediments of four shallow, eutrophic lakes. *Limnol. Oceanogr.*, 37(3), 13.

Jöhnk, K. D., Huisman, J., Sharples, J., Sommeijer, B., Visser, P. M., & Stroom, J. M. (2008). Summer heat waves promote blooms of harmful cyanobacteria. *Glob Change Biol* 14, 17.

Jones, I., George, G., & Reynolds, C. (2005). Quantifying effects of phytoplankton on the heat budgets of two large limnetic enclosures. *Freshwater Biology*, 50, 8.

Journey, A. C., Beaulieu, M. K., & Bradley, M. P. (2013). Environmental Factors that Influence Cyanobacteria and Geosmin Occurrence in Reservoirs. In I. Jöhnk, edited by Paul M. Bradley, Published: February 27, 2013 under CC BY 3.0 license (Ed.), *Environmental Sciences* » "Current Perspectives in Contaminant Hydrology and Water Resources Sustainability", book

Kanoshina, I., Lips, U., & Leppänen, J. (2003). The influence of weather conditions (temperature and wind) on cyanobacterial bloom development in the Gulf of Finland (Baltic Sea). *2(1)*, 29-41.

King, K. W., Balogh, J. C., & Harmel, R. D. (2007). Nutrient flux in storm water runoff and baseflow from managed turf. *Environmental Pollution*, 150, 321-328.

Kling, H. J., Watson, S. B., McCullough, G. K., & Stainton, M. P. (2011). Bloom development and phytoplankton succession in Lake Winnipeg: a comparison of historical records with recent data. *Aquatic Ecosystem Health & Management*, 14(2), 219-224.

Koreiviene, J., & Karosiene, J. (2012). Temporal and spatial variation of phyto- and zooplankton in the Aukoetadvaris water reservoir during summer stratification. Paper presented at the Proc. 31th International Conference of Polish Phycological Society, Olsztyn.
Kosten, S., Huszar, V., Becares, E., Costa, L., Van Donk, E., Hansson, L.-A., Jeppessn, E., Kruk, C., Lacerot, G., Mazzeo, N., De Meester, L., Moss, B., Lurling, M., Noges, T., Romo, S., & Scheffer, M. (2011). Warmer climate boosts cyanobacterial dominance in shallow lakes. Global Change Biology.

Kromkamp, J. C., & Walsby, A. E. (1990). A computer model of buoyancy and vertical migration in cyanobacteria. Journal of Plankton Research, 12(1), 161-183.

Lap, B., & Mori, K. (2007). A two-dimensional numerical model of wind-induced flow and water quality in closed water bodies. Paddy and Water Environment, 5(1), 29-40.

Lévesque, B., Gervais, M. C., Chevalier, P., Gauvin, D., Anassour-Laouan-Sidi, E., Gingras, S., Fortin, N., Brisson, G., Greer, C., & Bird, D. (2014). Prospective study of acute health effects in relation to exposure to cyanobacteria. Science of the Total Environment, 466-467, 397-403.

Marcé, R., Feijoo, C., Navarro, E., OrdoÑEz, J., GomÀ, J., & Armengol, J. (2007). Interaction between wind-induced seiches and convective cooling governs algal distribution in a canyon-shaped reservoir. Freshwater Biology, 52(7), 1336-1352.

McQuaid, N., Zamyadi, A., Prevost, M., Bird, D. F., & Dorner, S. (2011). Use of in vivo phycocyanin fluorescence to monitor potential microcystin-producing cyanobacterial biovolume in a drinking water source. J Environ Monit, 13(2), 455-463. doi: 10.1039/c0em00163e

Moroney, V. J., & Somanchi, A. (1999). How Do Algae Concentrate CO2 to Increase the Efficiency of Photosynthetic Carbon Fixation. Plant Physiology, 119(1), 9-16.

Ndong, M., Bird, D., Nguyen-Quang, T., de Boutray, M. L., Zamyadi, A., Vincon-Leite, B., Lemaire, B. J., Prevost, M., & Dorner, S. (2014a). Estimating the risk of cyanobacterial occurrence using an index integrating meteorological factors: Application to drinking water production. Water Res, 56C, 98-108. doi: 10.1016/j.watres.2014.02.023

Ndong, M., Bird, D., Nguyen Quang, T., Kahawita, R., Prévost, M., & Dorner, S. (2014b). Hydrodynamic modeling of light intensity and wind effects on the spatial distribution of cyanobacteria Environmental Science and Technology (submitted).

Nguyen-Quang, T., & Guichard, F. (2010). The role of bioconvection in plankton population with thermal stratification. International Journal of Bifurcation and Chaos, 20(06), 1761-1778.

Nürnberg, G. K. (1996). Trophic state of clear and colored, soft- and hardwater lakes with special consideration of nutrients, anoxia, phytoplankton and fish. Lake and Reservoir Management 12, 432-447.

Organisme de bassin versant de la baie Missisquoi. (2011). Plan Directeur de l'Eau: Le Portrait du Bassin Versant de la Baie Missisquoi. Québec.

Osborne, A., & Raven, J. A. (1986). Growth light level and photon absorbtion by cells of Chlamydomonas reinhardtii, Dunaliella tertiolecta, Scenedesmus obliquus and Euglena viridis. Br. Phycol. J., 21, 10.

Paerl, H. W. (1988). Nuisance phytoplankton blooms in coastal, estuarine, and inland waters. Limnology and Oceanography 33, 823-847.

Paerl, H. W., & Paul, V. J. (2012a). Climate change: Links to global expansion of harmful cyanobacteria. Cyanobacteria: Impacts of climate change on occurrence, toxicity and water quality management, 46(5), 1349-1363.

Paerl, W. H., & Huisman, J. (2009). Climate change: a catalyst for global expansion of harmful cyanobacterial blooms. Environmental Microbiology Reports 1(1), 10.
Paerl, W. H., & Paul, J. V. (2012b). Climate change: Links to global expansion of harmful cyanobacteria. Water Research, 46, 14.

Rapala, J. (1998). Toxin production by freshwater cyanobacteria: effects of environmental factors.

Reynolds, C. S. (2006). The Ecology of Phytoplankton (Ecology, Biodiversity and Conservation). Cambridge, UK.

Reynolds, C. S., Oliver, R. L., & Walsby, A. E. (1987). Cyanobacterial dominance: The role of buoyancy regulation in dynamic lake environments. New Zealand Journal of Marine and Freshwater Research, 21(3), 379-390.

Reynolds, C. S., Wiseman, S. W., Godfrey, B. M., & Butterwick, C. (1983). Some effects of artificial mixing on the dynamics of phytoplankton populations in large limnetic enclosures. J. Plankton Res., 5, 29.

Robarts, R. D., & Zohary, T. (1987). Temperature effects on photosynthetic capacity, respiration, and growth rates of bloom-forming cyanobacteria. New Zealand Journal of Marine and Freshwater Research, 21(3), 391-399.

Rucker, J., Wiedner, C., & Zippel, P. (1997). Factors controlling the dominance of Planktothrix agardhii and Limnothrix redekei in eutrophic shallow lakes Hydrobiologia, 342/343, 107-115.

Shanahan, P. (1985). Water Temperature Modeling: A Practice Guide. Paper presented at the In Proceedings Stormwater and Water Quality Model Users Group Meeting, April 12-13, 1984.

Smeltzer, E., Shambaugh, A. d., & Stangel, P. (2012). Environmental change in Lake Champlain revealed by long-term monitoring. Lake Champlain in 2010, 38, Supplement 1(0), 6-18.

Smith, V. H. (1986). Light and Nutrient Effects on the Relative Biomass of Blue-Green Algae in Lake Phytoplankton. Canadian Journal of Fisheries and Aquatic Sciences, 43(1), 148-153.

Sondergaard, M., Jensen, J. P., & Jeppesen, E. (2003). Role of sediment and internal loading of phosphorus in shallow lakes. Hydrobiologia, 506, 135-145.

Stager, J. C., & Thill, M. (2010). Stager, J.C., Thill, M., 2010. Climate change in the Lake Champlain Basin: what natural resource managers can expect and do. Keene Valley, NY and Montpelier, VT.: Prep. for The Nature Conservancy.

Stumpf, R. P., Wynne, T. T., Baker, D. B., & Fahnenstiel, G. L. (2012). Interannual Variability of Cyanobacterial Blooms in Lake Erie. PLoS ONE, 7(8), Special section p1.

Thomas, R. H., & Walsby, A. E. (1985). Buoyancy Regulation in a Strain of Microcystis. Journal of General Microbiology, 131(4), 799-809.

Visser, P., Passarge, J., & Mur, L. (1997). Modelling vertical migration of the cyanobacterium Microcystis. Hydrobiologia, 349(1-3), 99-109.

Wallace, B. B., Bailey, M. C., & Hamilton, D. P. (2000). Simulation of vertical position of buoyancy regulating Microcystis aeruginosa in a shallow eutrophic lake. Aquatic Sciences, 62(4), 320-333.

Walsby, A. E. (1975). Gas vesicles. Annu Rev Plant Physiol, 26, 12.

Walsby, A. E. (1997). Numerical integration of phytoplankton photosynthesis through time and depth in a water column. New Phytol., 136, 20.

Wang, X., Parkpian, P., Fujimoto, N., Ruchirawat, K. M., DeLaune, R. D., & Jugsujinda, A. (2002). Environmental conditions associating microcystins production to Microcystis aeruginosa in a reservoir of Thailand. J Environ Sci Health A Tox Hazard Subst Environ Eng, 37(7), 1181-1207.
Webster, I. T., & Hutchinson, P. A. (1994). Effect of wind on the distribution of Phytoplankton cells in lakes revisited. Limnol. Oceanogr., 39 (2), 9.

Westwood, J. K., & Ganf, G. G. (2004). Effect of cell flotation on growth of Anabaena circinalis under diurnally stratified conditions. J. Plank. Res., 26(10), 14.

Zamyadi, A., MacLeod, S. L., Fan, Y., McQuaid, N., Dorner, S., Sauvé, S., & Prévost, M. (2012). Toxic cyanobacterial breakthrough and accumulation in a drinking water plant: A monitoring and treatment challenge. Cyanobacteria: Impacts of climate change on occurrence, toxicity and water quality management, 46(5), 1511-1523.
# CHAPITRE 6 : DISCUSSION GÉNÉRALE

## 6.1 Évaluation des objectifs et hypothèses de travail par rapport aux résultats obtenus

La forte prolifération de cyanobactéries dans les eaux de surface servant de sources d'approvisionnement en eau potable est un problème complexe du fait de l'ensemble des processus physiques, biochimiques et biologiques impliqués. Elle nécessite une pluridisciplinarité afin de pouvoir bien la comprendre, la prévenir et mettre en place des techniques permettant d'y remédier et qui ne sont pas nuisibles à la population aquatique. C'est dans ce contexte que beaucoup d'études ont été menées afin de déterminer les principales causes d'une forte prolifération de cyanobactéries dans les plans d'eau. Cependant, jusqu'ici il n'y a que les études faites avec des images satellites qui essaient de développer une méthodologie de quantification du risque selon la position d'une prise d'eau (Wheeler et al., 2012). Un système d'alerte est nécessaire afin de réagir aux conditions et d'ajuster l'opération des usines d'eau potable. Dans le cadre de cette thèse, l'évaluation de ce risque d'occurrence des cyanobactéries est faite avec une approche statistique qui ne décrit pas les mécanismes qui contrôlent la distribution spatio-temporelle des cyanobactéries. C'est ce qui a motivé le développement d'un modèle déterministe avec une approche eulérienne qui décrit l'effet d'advection et de flottabilité des cyanobactéries. Ces deux défis majeurs ont été les centres d'intérêt de cette thèse avec les objectifs suivants : 1) Quantifier le risque associé à l'effet du vent et de la température de l'eau ; 2) Développer un modèle avec une approche eulérienne en intégrant les données météorologiques réelles permettant de suivre la distribution spatio-temporelle des cyanobactéries ; 3) Étudier leur comportement face à une éventuelle stratification thermique et valider le comportement avec les données de terrain et les résultats du modèle.

Nos travaux dans le chapitre 3 (article 1) constituent une avancée conséquente dans le domaine de la quantification du risque compte tenu de la position de la prise d'eau. Ils ont permis d'évaluer quantitativement pour la première fois le risque d'occurrence des cyanobactéries à une prise d'eau tenant en compte sa position. Cependant, la température de l'eau et les paramètres météorologiques que sont le vent (vitesse et direction) ont été les seuls facteurs pris en compte vu que cela nécessite des données de haute fréquence.
Il faut noter que la non-linéarité des variables impliquées rend complexe le traitement des données recueillies. Néanmoins, l'hypothèse sur le rôle dominant joué par les facteurs exogènes a été confirmée avec un risque d'occurrence des cyanobactéries de 68 % associé à ces facteurs (température de l'eau, vitesse et direction du vent). Cependant l'indice proposé pourrait être amélioré vu qu'il y a une probabilité de 26 % associé à des faux négatifs. Effet, il serait fort intéressant d'inclure les nutriments en disposant de données de haute fréquence telle qu'il a été le cas pour les facteurs inclus dans le calcul de l'indice météorologique proposé dans le chapitre 3 (article 1). Cette prise en compte des nutriments se justifie par le rôle des nutriments dans le processus de croissance des CB et l'importance du rapport DIN/TP proposé par certains auteurs (Bergström, 2010; Ptacnik et al., 2010) comme indicateur de condition favorable pour une forte prolifération de cyanobactéries et confirmée à travers nos études comme étant une condition nécessaire, mais pas suffisante pour prévenir l'occurrence des CB à un endroit précis d'un plan d'eau.

L'indice proposé est conçu pour évaluer le risque d'occurrence et non la disparition ou la fin d'un épisode de « fleurs d'eau » qui inclurait des processus tels que le « flushing » qui conduit au renouvellement de la masse d'eau, la croissance, la mortalité. Une éventuelle combinaison entre un système de suivi de la phycocyanine et l'évaluation de l'indice proposé pourrait constituer un important outil pour les gestionnaires de plan d'eau et les opérateurs des usines de traitement d'eau potable.

Les résultats obtenus dans notre premier axe de recherche montrent également qu'une analyse séparée des variables impliquées ne permet pas de comprendre les épisodes de « fleurs d'eau ». Seule une approche globale incluant l'ensemble des facteurs impliqués serait mieux adaptée. Néanmoins, l'approche proposée se caractérise par sa nouveauté, sa robustesse et son applicabilité sur d'autres sites. Cependant, il faudra noter que cette approche est purement statistique et ne permet pas d'expliquer l'importance des processus reliés à la distribution des cyanobactéries dans un plan d'eau. C'est ce qui explique l'approche déterministe adoptée par la suite dans le chapitre 4 (article 2). Cette approche déterministe présente aussi une réflexion très avancée afin d'éviter la simplification faite dans presque tous les logiciels commerciaux de modélisation hydrodynamique couplée à la qualité de l'eau (Tableau 1.4). En effet, les
cyanobactéries sont la plupart du temps considérées comme de simples particules avec une vitesse moyenne de sédimentation. Cette simplification fausse complètement le vrai problème et les éventuelles explications qui pourraient en découler pour élucider la distribution des cyanobactéries dans une colonne d'eau.

Il n'y a que CAEDYM (logiciel commercial) qui tente de tenir en compte l'aspect de flottaison selon l'intensité lumineuse (Hipsey et al., 2006). Cependant, dans ce logiciel, l'effet phototaxis est utilisé pour évaluer la vitesse de sédimentation des cellules. Par contre, pour leur remontée et remise en suspension, ce logiciel considère l'effet d'advection comme le principal facteur. Cette simplification permet de contourner l'approche lagrangienne, mais elle ne s'accorde pas avec le fait que le comportement lié à la flottaison (sédimentation et remise en suspension) pourrait dépendre uniquement sur l'effet phototactique (Kromkamp & Walsby, 1990; Reynolds & Irish, 1997; Visser et al., 1997). En effet, le changement de densité des cyanobactéries selon l'intensité lumineuse fait que leur mouvement change dans l'espace et le temps. Jusqu'ici seule une approche Lagrangienne permettait de faire ce suivi spatio-temporel pour une seule cellule rendant presque trop lourd en calcul le suivi de toute une population de cyanobactéries dans un plan d'eau. Il faut retenir que seule l'approche eulérienne permet d'avoir une vue d'ensemble de la distribution des cyanobactéries dans le plan d'eau.

C'est ainsi que nous avons proposé une nouvelle méthodologie avec l'approche eulérienne permettant de faire un suivi de l'ensemble des cyanobactéries. A travers celle-ci, il a été mis en évidence le rôle joué par l'effet phototaxis dans le processus d'accumulation des CB à la surface d'un plan d'eau. Il a été observé un comportement cyclique du risque d'occurrence des CB à la prise d'eau lorsque la flottabilité est dominante et que les intensités de vents enregistrées sont faibles (chapitre 5: article 2), ce qui est observé dans des conditions de faibles intensités de vents (effet advection négligeable) et qui permet de confirmer notre hypothèse selon laquelle dans un milieu naturel, selon certaines conditions hydrodynamiques (présence ou absence de stabilité de la colonne d'eau), la distribution spatio-temporelle des cyanobactéries, leur forte accumulation en surface (présence d'écume) et au fond de la colonne d'eau seraient dépendantes de leur aptitude à la mobilité (présence ou absence de vésicules de gaz).
Dans notre démarche, les processus biologiques n'ont pas été inclus pour le moment (croissance-mortalité). En effet, s'il existe des modèles de croissance jusqu'ici assez acceptables, les différents processus de la phase de décroissance ne sont pas encore bien maitrisés (manque de nutriments, mortalité due à la forte exposition à la lumière ou à la prédation, «flushing»). En fait, la non-maîtrise de cette phase empêche toute validation quantitative de la distribution des cyanobactéries dans un plan d'eau. C'est ainsi que pour une première étape, dans le but de perspective future, nous jugions primordial d'assurer un bilan de masse strictement sans pertes durant la simulation, c'est ce qui nous a motivé à tester beaucoup d'algorithmes proposés pour le modèle de transport. Il s'avère qu'une perte de masse pouvait être minime et acceptable pour un temps de simulation court, ce qui n'était pas le cas pour des temps de simulation assez long de l'ordre de quelques jours à des mois.

L'accumulation des pertes constituait une importante source d'erreur qui rendrait une validation quantitative biaisée. C'est aussi l'une des raisons pour lesquelles nous avons travaillé aussi sur le développement d'algorithmes tenant en compte aussi le mouvement des cyanobactéries selon les disponibilités de la lumière. Notons que la mise en place d'une contrainte qui limite le nombre de cellules que peut contenir un volume donné est nécessaire afin d'éviter une surestimation des concentrations de cellules. En effet, la non prise en compte de cette contrainte, pourrait biaiser une validation en terme quantitative lorsqu'il y a une forte accumulation de CB durant une simulation. L'autre aspect qui mérite une réflexion est la prise en compte de l'hétérogénéité du diamètre des cellules et des colonies de cellules dans l'approche eulérienne. En effet, lors d'un bloom de CB, le diamètre des cellules de CB n'est pas parfaitement homogène. Cet aspect pourrait avoir un grand effet sur la distribution spatio-temporelle des CB au cas où une forte hétérogénéité existe entre les cellules présentes dans l'écosystème. La prise en compte future dans le modèle serait limitée par un temps de calcul qui pourrait s'avérer très important et nécessiterait une grande capacité de stockage de l'outil utilisé pour le traitement numérique.

Il existe aussi un manque d'information concernant le temps de réponse des cyanobactéries en milieu naturel lorsqu'elles changent de densité. En effet, pour modéliser cet aspect, une fonction retard est introduite (Wallace & Hamilton, 2000). Ces auteurs préconisent un temps de réponse de 4 minutes quand l'intensité lumineuse est plus élevée que l'intensité de compensation pour le
modèle de Visser et al. (1997). La question à se poser est la suivante : ce temps de réponse est-il constant ou dépendant de leur position dans la colonne d'eau ?

L'ajustement du modèle par rapport au délai de réponse quand les CB sont exposés ou non à l'intensité lumineuse est un important facteur à prendre en compte afin de se rapprocher d'un modèle plus réaliste. Compte tenu des tests faits sur le temps de réajustement phototactique ou délai de réponse phototactique, le modèle hydrodynamique couplé avec le transport des CB présente une corrélation significative telle que rapportée dans le chapitre 4 (article 2).

Cependant la corrélation trouvée n'est pas très forte même si elle est significative; ce qui nous pousse à suspecter que le délai de réponse pourrait être fonction de la position des CB dans la colonne d'eau comme c'est le cas du coefficient d'extinction (Kirk, 1983). Ce délai de réponse pourrait aussi être fonction de la température dans la mesure où cette dernière a un impact sur le comportement physiologique des CB (Carey et al., 2012). Ce qui rend plus complexe la problématique des cyanobactéries dans les plans d'eau et le besoin jusqu'ici de continuer les investigations afin de disposer enfin d'un modèle pouvant refléter d'une façon encore plus réaliste la distribution spatio-temporelle des cyanobactéries. Pour cela, il sera absolument nécessaire de faire un suivi à haute fréquence de la distribution des cyanobactéries afin d'avoir des résultats permettant de faire une validation tant quantitative que qualitative (distribution dans la colonne d'eau).

## 6.2 Rôle des processus physiques et biologiques dans la distribution spatio-temporelle des cyanobactéries

Les processus qui régissent la distribution spatio-temporelle des cyanobactéries sont d'ordre physique et biologique. Il s'agit respectivement de l'advection et de la flottabilité induite par le changement de densité des CB. Ces derniers sont contrôlés par des facteurs exogènes liés aux conditions météorologiques. Il s'agit du vent (vitesse et direction) et de la radiation photosynthétique active (PAR). Il faut retenir que jusqu'ici, l'effet de la PAR sur la flottabilité a été bien modélisé et validé expérimentalement (Kromkamp & Walsby, 1990; Visser et al., 1997). Ce qui n'empêche pas de suspecter un éventuel effet de la disponibilité des nutriments sur la flottabilité tels que rapportés par certains auteurs (Brookes et al., 1999; Chu et al., 2007; Klemer,
1991). La dominance entre la flottabilité des CB et l'advection est dépendante de l'intensité du vent. En effet, quand l'intensité du vent est très importante, l'advection horizontale entraine les CB dans le mouvement de recirculation de l'eau. Dans le cas d'une contrainte de vent constante, combinée avec le comportement sinusoïdal et journalier de l'intensité lumineuse, un risque cyclique de présence des CB pourrait être observé à la prise d'eau.

Pendant une période d'occurrence de CB avec une faible intensité de vent, la flottabilité des CB serait dominante comparée à l'advection. La formation d'écumes à la surface d'un plan d'eau serait un mécanisme fortement dépendant de la flottabilité des CB. Une comparaison quantitative des données du modèle ne peut être faite qu'en tenant en compte d'un ensemble d'autres processus impliqués tels que la croissance, la mortalité, la dynamique des nutriments et l'effet « flushing ». La fréquence d'échantillonnage devrait être revue pour une assimilation entre les données mesurées et celles obtenues à partir du modèle. L'effet de la turbulence, en plus de favoriser la dispersion des CB, aurait pour conséquence de remettre en suspension les nutriments qui étaient dans les sédiments.

L'absence d'une forte stratification thermique ne nous permet pas de tirer des conclusions sur une éventuelle influence sur la distribution des cyanobactéries dans la colonne d'eau. De ce fait, notre hypothèse, selon laquelle la stratification thermique influence fortement la distribution spatio-temporelle des cyanobactéries dans une colonne d'eau, ne peut pas être confirmée ou infirmée. Sa vérification nécessite de faire l'étude dans un lac assez profond avec un suivi à haute fréquence.

Cependant, nous suspectons que l'absence d'un fort gradient de température dans les lacs peu profonds comme la baie Missisquoi aurait aussi pour conséquence de favoriser une croissance quasi uniforme dans toute la colonne d'eau. Au vu des résultats présentés dans le chapitre 5 (article 3), pour le cas d'un lac peu profond et eutrophe, la stabilité de la colonne d'eau pourrait être le principal facteur qui favoriserait l'occurrence des CB dès que celle-ci est stable et que les températures optimales de croissance des CB sont atteintes.
## 6.3 Emplacement des prises d'eau et risque d'occurrence des cyanobactéries

L'emplacement des prises d'eau des stations de traitement d'eau potable n'inclut pas jusqu'ici les effets d'une éventuelle prolifération d'algues bleu-verts. Il existe un grand vide en termes de conception pour l'emplacement le plus adapté pour une prise d'eau. Il apparaît selon les résultats publiés dans le chapitre 3 (article 1) que la direction des vents joue un grand rôle dans la probabilité d'occurrence des cyanobactéries à la prise d'eau. La conception des prises d'eau devrait tenir compte d'un éventuel risque de prolifération et de transport par advection des CB. En d'autres termes, il faudrait faire une étude d'occurrence du facteur f(p) proposé dans l'article 1. La méthodologie d'évaluation quantitative du risque d'occurrence des cyanobactéries à un endroit donné d'un plan d'eau à partir des paramètres météorologiques et de la température de l'eau devrait permettre de caractériser les emplacements possibles pour une prise d'eau.

Selon le guide de conception du MDDEP (Ministère du Développement durable de l'Environnement et des Parcs, 2002), la localisation d'une prise d'eau tient compte des facteurs suivants :

- la sécurité d'approvisionnement ;

- la qualité de l'eau brute ainsi que l'impact sur l'environnement et le milieu aquatique.

Plus précisément, il est mentionné dans ce guide la disposition suivante :

> « la prise d'eau doit être située à l'endroit où la qualité de l'eau est la meilleure et la moins vulnérable à la pollution tout en posant moins de dommage à la faune aquatique »,

Cette disposition ne peut être prise en compte qu'en intégrant une étude de vulnérabilité basée sur une approche purement déterministe et non sur une évaluation du nombre d'événements (présence de cyanobactéries, déversement de produits chimique) survenu durant les 5 ou 10 dernières années précédant l'étude tel que cela est défini dans le nouveau règlement sur le prélèvement des eaux et leur protection (Gouvernement du Québec, 2014).

A travers notre étude de modélisation, nous remarquons que les processus physiques (advection) peuvent entrainer les cyanobactéries dans différentes zones d'un plan d'eau. De ce fait, l'installation des prises d'eau trop près des berges augmente le risque que les CB entrent dans
l'usine de traitement, et leur localisation au fond de la colonne d'eau ne garantit pas un risque
moindre.

L'approche que nous suggérons à l'issue de cette étude est l'option de prise d'eau à entrées multiples permettant de capter les eaux de meilleure qualité selon des mesures in situ en continue.

## 6.4 Les apports de cette thèse par rapport à la problématique des cyanobactéries dans les plans d'eau

À travers les résultats trouvés, cette thèse a permis :

* de poser les fondements d'une nouvelle approche pour quantifier le risque associé à certaines variables jusqu'ici citées dans la littérature comme ayant une influence sur l'occurrence des cyanobactéries;

* d'aborder la distribution des cyanobactéries selon une approche eulérienne en tenant compte des effets de flottabilité de ces dernières selon la disponibilité de la lumière. Ceci a permis d'étudier les implications écologiques d'une faible stratification thermique sur la distribution spatio-temporelle des cyanobactéries.

En intégrant les données météorologiques, les gestionnaires de plan d'eau pourraient disposer d'un outil intéressant leur permettant d'être avertis du moment propice à l'entrée des cyanobactéries dans l'usine de traitement d'eau potable à partir de la prise d'eau au fond du plan d'eau. Cependant, les processus de « flushing », de croissance et de mortalité devront être inclus en plus de l'intégration des données météorologiques en temps réels permettant de disposer d'un outil de suivi et de surveillance de la prise d'eau.
## CONCLUSIONS ET RECOMMANDATIONS

L'occurrence des blooms de cyanobactéries menace les ressources en eau de surface. La complexité des différents processus impliqués rend difficile la gestion des plans d'eau déjà affectés. En général, ce phénomène affecte un endroit donné d'un plan d'eau. Son apparition dans la zone où est installée une prise d'eau est redoutée dans la mesure où les toxines qu'elles produisent peuvent franchir toute la filière de traitement conventionnel et se retrouver dans l'eau destinée à la consommation. De ce fait, il est opportun d'évaluer le risque d'occurrence des cyanobactéries au niveau des prises d'eau. C'est dans ce contexte qu'une nouvelle méthodologie a été développée afin de répondre à cet objectif. À l'issue de ces travaux, dans le cas de la Baie Missisquoi, il a été démontré que :

* des conditions favorables de température de l'eau, de vitesse et direction du vent auraient une probabilité quantifiable jusqu'à 68 % sur l'occurrence des cyanobactéries,

* les facteurs impliqués dans l'occurrence des cyanobactéries ne devraient pas être analysés séparément si nous voulons évaluer le risque d'occurrence à la prise d'eau,

* la prise en compte des facteurs météorologiques dans les systèmes d'alertes actuels doit se faire dans la mesure où ils jouent un rôle important dans l'occurrence des cyanobactéries à la prise d'eau,

* les variables météorologiques doivent être prises en compte dans les systèmes d'alerte existants (principalement basés sur les comptes taxonomiques ou les concentrations en toxines ou tout autre facteur propre aux cyanobactéries),

* Le rapport DIN/TP concernant la disponibilité des nutriments est un bon indicateur, cependant il ne tient pas compte de la position de la prise d'eau.

Rappelons que la méthodologie proposée utilise une approche statistique et peut s'appliquer à d'autres sites. Elle pourrait être améliorée en tenant compte des nutriments et de la radiation photosynthétique active (PAR). Cependant, cette approche statistique proposée ne nous permet pas de comprendre la distribution spatio-temporelle des cyanobactéries. C'est ainsi qu'une approche déterministe de type eulérienne a été développée. Il s'agit d'un modèle 2D. Elle implique les équations de continuité, de quantité de mouvement, de transport et de flottabilité des cyanobactéries suite aux effets phototactiques. Elle a permis de montrer que :
* la formation de couche de cyanobactéries à la surface de l'eau et leur accumulation à la berge sont liées à la flottabilité des cyanobactéries due à leur changement de densité combiné à l'advection induite par le mouvement de la masse d'eau,

* le processus d'accumulation des cyanobactéries à la surface d'un plan d'eau est le résultat de l'effet phototactique et leur dispersion serait favorisée par des vents forts (>3 m/s),

* le risque qu'une prise d'eau soit affectée pourrait être cyclique dans la mesure où le mouvement des cyanobactéries vers la prise d'eau serait dominé par les mécanismes de flottabilité des cyanobactéries, en particulier à cause de leur changement de densité si elles sont exposées ou non à la lumière durant les conditions de faible intensité de vent (<3 m/s),

* l'effet recirculation crée des zones où les concentrations de cyanobactéries sont faibles durant les périodes durant lesquelles une fleur d'eau est constatée,

* l'effet phototactique serait un élément clé dans le processus d'accumulation des cyanobactéries à la surface d'un plan d'eau tandis que des vents forts (>3 m) contribueraient à la dispersion des cyanobactéries dans la colonne d'eau,

* il est apparu à travers les études de modélisation que le risque d'occurrence des cyanobactéries à la prise d'eau de l'usine pourrait être cyclique durant les périodes de faible intensité de vent (<3 m/s). En effet, dans ces conditions, la flottabilité des cyanobactéries due à leur changement de densité serait dominante,

* la flottabilité des cyanobactéries due à leur changement de densité combiné à l'advection induit par le mouvement de la masse d'eau contribue fortement à la formation de couche de cyanobactéries à la surface de l'eau et à leur accumulation à la berge,

* à cause des effets de recirculation induits par le vent, il existerait des zones où les concentrations de cyanobactéries seraient faibles.

Il faut noter que les processus de croissance, mortalité, « flushing » ainsi que les processus biochimiques n'ont pas été inclus. Néanmoins, la distribution des cyanobactéries suivant les températures enregistrées dans la Baie a été étudiée. À la suite de celle-ci, il apparaît que

* la stratification thermique n'est pas forte dans le cas de la Baie Missisquoi, qui est un lac peu profond et eutrophe,
* dans des conditions de stratification thermique peu significative, pour un plan d'eau eutrophe, la stabilité de la colonne d'eau apparaît comme une des conditions qui pourraient favoriser l'occurrence des CB,

* dans le cas d'un plan d'eau eutrophe et faiblement stratifié, la croissance et la mortalité pourraient être uniforme dans toute la colonne d'eau car elles seraient uniquement dépendantes de la température, ce qui favoriserait une dominance des cyanobactéries dès que des températures optimales de croissance sont atteintes.

A l'issue de ces travaux, les principales recommandations seraient :

* de prendre en compte le facteur $f(p)$ dans le choix de l'emplacement d'une prise d'eau afin de minimiser le risque d'occurrence de cyanobactéries à l'endroit où elle est installée,

* de continuer les études afin d'améliorer l'indice proposé en tenant compte du rapport DIN/TP et de l'intensité lumineuse en plus de la concentration en phycocyanine,

* de modéliser le processus de décroissance après blooms, en investiguant sur les facteurs responsables,

* d'introduire les processus de croissance et mortalité dans le modèle déterministe développé

* de mener une compagne d'échantillonnage à haute fréquence (variabilité horaire ou journalière) afin de bien assimiler les résultats du modèle avec les données issues de la modélisation. En effet, l'échantillonnage hebdomadaire ne permet pas d'affiner les conclusions et rend difficile l'analyse des données.

Les objectifs visés à travers cette thèse ont été atteints. La poursuite de ces études permettraient de disposer de deux outils importants: 1) d'évaluation de risque d'occurrence à la prise d'eau et 2) de compréhension de l'occurrence des cyanobactéries et de la distribution spatio-temporelle des cyanobactéries dans un plan d'eau.
RÉFÉRENCES

Adhikari, B. K., Madramootoo, C. A., & Sarangi, A. (2010). Temporal variability of phosphorus flux from pike river watershed to the Missisquoi Bay of Quebec. *Current Science* 98(1), 7.

Agence de la santé et des services sociaux de la Montérégie-Québec. (2011). Avis de santé Publique: Avis de non-consommation d'eau pour les citoyens utilisant le réseau d'aqueduc connecté à l'usine d'eau potable de Bedford

Ahn, C. Y., Joung, S. H., Yoon, S. K., & Oh, H. M. (2007). Alternative alert system for cyanobacterial bloom, using phycocyanin as a level determinant. *J. Microbiol.*, 45(2), 7.

Albay, M., & Akçaalan, R. (2003). Factors influencing the phytoplankton steady state assemblages in a drinking-water reservoir (Ömerli reservoir, Istanbul). *Hydrobiologia*, 502(1-3), 85-95.

American Public Health Association, American Water Works Association, & Water Environment Federation. (2005). Standard Methods for the Examination of Water and Wastewater (pp. p. 1368). Washington, D.C. (USA): (21st edn.), ed.,A. E. Greenberg, A. D. Eaton, L. S. Clesceri, E. W. Rice, M. A. H. Franson.

Arar, E. J., & Colling, G. B. (1997). U.S. Environmental Protection Agency Method 445.0, In Vitro Determination of Chlorophyll a and Pheophytin a in Marine and Freshwater Algae by Flurorescence: revision 1.2. http://www.turnerdesigns.com/t2/doc/appnotes/EPA445.pdf.accesed 08 August 2012.

Baines, W. D., & Knapp, D. J. (1965). Wind driven water currents. *J. Hydraul. Div.*, 94(4), 17.

Bartram, J., & Chorus, I. (1999). Toxic cyanobacteria in water: a guide to their public health consequences, monitoring and management. In WHO (Ed.). London.

Belov, A. P., & Giles, J. D. (1997). Dynamical model of buoyant cyanobacteria. *Hydrobiologia*, 349(1-3), 87-97.

Belov, A. P., Giles, J. D., & Wiltshire, R. J. (1999). Toxicity in a water column following the stratification of a cyanobacterial population development in a calm lake. *Mathematical Medicine and Biology*, 16(1), 93-110.

Berger, C., Ba, N., Gugger, M., Bouvy, M., Rusconi, F., Couté, A., Troussellier, M., & Bernard, C. (2006). Seasonal dynamics and toxicity of Cylindrospermopsis raciborskii in lake Guiers (Senegal, West Africa). *FEMS microbiology ecology*, 57(3), 355-366.

Bergström, A.-K. (2010). The use of TN:TP and DIN:TP ratios as indicators for phytoplankton nutrient limitation in oligotrophic lakes affected by N deposition. *Aquat. Sci.*, 72(3), 277-281.
Bierman, V. J. J., Dolan, D. M., Stoermer, E. F., Gannon, J. E., & Smith, V. E. (1980). The developpement and calibration of a Multi-Class phytoplankton model for Saginaw bay, Lake Huron. Ann Arbor, Michigan: Great Lakes environmental planning study. Contribution No. 33. Great Lakes basin Commission.

Bilinska, K. (2005). *Thermal Stratification in the Waikato hydro lakes*. (memoire-71 pages), The University of Western Australia, Australia.

Bormans, M., Ford, P., Fabbro, L., & Hancock, G. (2004). Onset and persistence of cyanobacterial bloom in a large impounded tropical river, Australia. *Mar. Freshw. Res.*, 55(1), 1-15.

Bormans, M., Ford, P. W., & Fabbro, L. (2005). Spatial and temporal variability in cyanobacterial populations controlled by physical processes. *J. Plankton Res.*, 27(1), 61-70.

Bormans, M., Sherman, B. S., & Webster, I. T. (1999). Is buoyancy regulation in cyanobacteria an adaptation to exploit separation of light and nutrients? *Mar. Freshw. Res.*, 50, 897-906.

Bouarab, L. M. L., & Dauta, A. (2002). Croissance en autotrophie et en mixotrophie de la microalgue Micractinium pusillum Fres. isolée d'un lagunage naturel : influence de la lumière et de la température. *Rev. Sci. Eau*, 15(1), 73-86.

Bouchard, V. (2004). *Floraison des cyanobactéries au Lac Saint Augustin: dynamique à court terme et stratification*. (mémoire (140 pages)), Université Laval, Québec.

Bowie, G. L., Mills, W. B., Porcella, D. B., Campbell, C. L., Pagenkopf, J. R., Rupp, G. L., Johnson, K. M., Chan, P. W. H., Gherini, S. A., & Chamberlin, C. E. (1985). *Rates, Constants, and Kinetics Formulations in Surface Water Quality Modeling: U.S. Environmental Protection Agency, Environmental Research Laboratory, Office of Research and Development, Athens, Ga. EPA/600/3-85/040 (472 pages).*

Brient, L., Lengronne, M., Bertrand, E., Rolland, D., Sipel, A., Steinmann, D., Baudin, I., Legeas, M., Le Rouzic, B., & Bormans, M. (2008). A phycocyanin probe as a tool for monitoring cyanobacteria in freshwater bodies. *J. Environ. Monit.*, 10(2), 248-255.

Brookes, D. J., Ganf, G. G., Green, D., & Whittington, J. (1999). The influence of light and nutrient on buoyancy, filament aggregation and flotation of Anabaena circinalis. *J. Plankton Res.*, 21(2), 327-341.

Byth, S. (1980). Palm Island mystery disease. *Med. J. Aust.*, 2, 40-42.

Cao, H.-S., Kong, F.-X., Luo, L.-C., Shi, X.-L., Yang, Z., Zhang, X.-F., & Tao, Y. (2006). Effects of Wind and Wind-Induced Waves on Vertical Phytoplankton Distribution and
Surface Blooms of Microcystis aeruginosa in Lake Taihu. *J. Freshw. Ecol.*, **21**(2), 231-238.

Carey, C. C., Ibelings, B. W., Hoffmann, E. P., Hamilton, D. P., & Brookes, J. D. (2012). Eco-physiological adaptations that favour freshwater cyanobacteria in a changing climate. *Water Res.*, **46**(5), 1394-1407.

Chellappa, N. T., Borba, J. M., & Rocha, O. (2008). Phytoplankton community and physical-chemical characteristics of water in the public reservoir of Cruzeta, RN, Brazil. *Braz. J. Biol.*, **68**(3), 477-494.

Chen, Y., Qian, X., & Zhang, Y. (2009). *Buoyancy Regulating Cyanobacteria in Wind-Driven Currents*. Paper presented at the 3rd International Conference on Bioinformatics and Biomedical Engineering Beijing (page: 1-4).

Cheng, Y. S., Yue, Z., Irvin, C. M., Kirkpatrick, B., & Backer, L. C. (2007). Characterization of aerosols containing microcystin. *Marine drugs*, **5**(4), 136-150.

Cheriton, O. M., McManus, M. A., Stacey, M. T., Steinbuck, J. V., & Ryan, J. P. (2009). Physical and biological controls on the maintenance and dissipation of a thin phytoplankton layer. *Marine Ecology Progress, Series* **378**, 25.

Christian, E. W., Steinberg, W., & Hartmann, M. H. (1988). Planktonic bloom-forming cyanobacteria and the eutrophication of lakes and rivers. *Freshw. Biol.*, **20**(2), 279-288.

Chu, Z., Jin, X., Yang, B., & Zeng, Q. (2007). Buoyancy regulation of Microcystis flos-aquae during phosphorus-limited and nitrogen-limited growth. *J. Plankton Res.*, **29**(9), 739-745.

Codd, G., Bell, S., Kaya, K., Ward, C., Beattie, K., & Metcalf, J. (1999). Cyanobacterial toxins, exposure routes and human health. *European Journal of Phycology*, **34**(4), 405-415.

Cohen, Y., Jorgensen, B. B., Revsbech, N. P., & Poplawski, R. (1986). Adaptation to Hydrogen Sulfide of Oxygenic and Anoxygenic Photosynthesis among Cyanobacteria. *Applied and environmental microbiology*, **51**(2), 398-407.

Cole, T. M., & Buchak, E. M. (1995). CE-QUAL-W2: A two-dimensional, laterally averaged, hydrodynamic and water quality model, Version 2.0: Users Manual, Instruction Report EL-95-1 (pp. 357): US Army Engineer Waterways Experiment Station, Vicksburg, MS.

Cole, T. M., & Wells, A. S. (2003). "CE-QUAL-W2: A two-dimensional, laterally averaged, Hydrodynamic and Water Quality Model, Version 3.2," Instruction Report EL-03-1 *US Army Engineering and Research Development Center, Vicksburg, MS*.

Coles, J. F., & Jones, R. C. (2000). Effect of temperature on photosynthesis-light response and growth of four phytoplankton species isolated from a tidal freshwater river. *J Phycol*, **36**, 9.
Comité Interministériel de Concertation sur la Baie Missisquoi. (2003). *Plan d'action 2003-2009 sur la réduction du phosphore*. Baie Missisquoi. région Montérégie.

Commission mixte internationale Canada et États-Unis. (2012). Déclaration et rapport aux gouvernements des États-Unis et du Canada sur l'Étude sur les sources critiques de la baie Missisquoi: Charges en phosphore dans la baie Missisquoi. (Rapport).

Costa, I. A. S., Azevedo, S. M. F. O., Senna, P. A. C., Bernardo, R. R., Costa, S. M., & Chellappa, N. T. (2006). Occurrence of toxin-producing cyanobacteria blooms in a Brazilian semiarid reservoir. *Braz. J. Biol.*, **66**(1), 211-219.

Covelli, P., Marsili-Libelli, S., & Pacini, G. (2001). SWAMP: A Two-dimensional Hydrodynamic and Quality Modeling Platform for Shallow Waters. *Numerical Methods for Partial Differential Equations*, **18**(5), 663-687.

Cronberg, G., Annadotter, H., & Lawton, L. (1999). The occurrence of toxic blue-green algae in Lake Ringsjön, southern Sweden, despite nutrient reduction and fish biMANipulation. *Hydrobiologia*, **404**(0), 123-129.

Cuypers, Y., Vincon-Leite, B., Groleau, A., Tassin, B., & Humbert, J. F. (2011). Impact of internal waves on the spatial distribution of Planktothrix rubescens (cyanobacteria) in an alpine lake. *The ISME Journal*, **5**, 580–589.

De Senerpont Domis, L. N., Elser, J. J., Gsell, A. S., Huszar, V. L. M., Ibelings, B. W., Jeppesen, E., Kosten, S., Mooij, W. M., Roland, F., Sommer, U., Van Donk, E., Winder, M., & LÜRling, M. (2013). Plankton dynamics under different climatic conditions in space and time. *Freshwater Biology*, **58**(3), 463-482.

Deltares Systems. (2014). Technical Reference Manual: D-Water Quality - Water quality and aquatic ecology modelling suite (Version: 5.01.33319).

DePinto, J. V., Bierman, V. J. J., & Verhoff, F. H. (1976). Seasonal Phytoplankton Succession as a Function of Phosphorus and Nitrogen Levels Modeling biochemical Processes in Aquatic Ecosystems (pp. 141-169): R.P. Canale (ed). Ann Arbor Science Publishers, Ann Arbor, Michigan.

Dillenberg, H. O., & Dehnel, M. K. (1960). Toxic water bloom in Saskatchewan 1959. *Can. Med. Assoc. J.*, **83**, 1151-1154.

Dillon, J. (1975). The phosphorus budget of Cameron Lake, Ontario: the importance of flushing rate to the degree of eutrophy of lakes. *Limnol. Oceanogr.*, **20**(1), 28-40.

Downs, T., Schallenberg, M., & Burns, C. (2008). Responses of lake phytoplankton to micronutrient enrichment: a study in two New Zealand lakes and an analysis of published data. *Aquatic Sciences*, **70**(4), 347-360.
Ek, M., & Mahrt, L. (1991). A formulation for boundary-layer cloud cover. *Annales Geophysicae, 9*, 716-725.

El Herry, S., Fathalli, A., Rejeb, A. J.-B., & Bouaïcha, N. (2008). Seasonal occurrence and toxicity of Microcystis spp. and Oscillatoria tenuis in the Lebna Dam, Tunisia. *Water Res.*, 42(4–5), 1263-1273.

Elliott, J. A. (2012). Is the future blue-green? A review of the current model predictions of how climate change could affect pelagic freshwater cyanobacteria. *Cyanobacteria: Impacts of climate change on occurrence, toxicity and water quality management*, 46(5), 1364-1371.

Falconer, I. (2005). *Cyanobacterial Toxins of Drinking Water Supplies: Cylindrospermopsins and Microcystins*. CRC Press: Boca Raton, Florida (279 pages).

Falconer, I., Bartram, J., Chorus, I., Kuiper-Goodman, T., Utkilen, H., & Burch, M. (1999). *Toxic cyanobacteria in Water*. Chorus I. and Bartram J. (eds), New York, USA (pp: 156–178).

Falconer, I. R. (2001). Toxic cyanobacterial bloom problems in Australian waters: risks and impacts on human health. *Phycologia, 40*(3), 228-233.

Fastner, J., Rücker, J., Stüken, A., Preußel, K., Nixdorf, B., Chorus, I., Köhler, A., & Wiedner, C. (2007). Occurrence of the cyanobacterial toxin cylindrospermopsin in northeast Germany. *Environmental Toxicology, 22*(1), 26-32.

Ferber, L. R., Levine, S. N., Lini, A., & Livingston, G. P. (2004). Do cyanobacteria dominate in eutrophic lakes because they fix atmospheric nitrogen? *Freshwater Biology, 49*(6), 690-708.

Fortin, N., Aranda-Rodriguez, R., Jing, H., Pick, F., Bird, D., & Greer, C. W. (2010). Detection of microcystin-producing cyanobacteria in Missisquoi Bay, Quebec, Canada, using quantitative PCR. *Applied and Environmental Microbiology, 76*(15), 5105-5112.

Franks, P. J. S. (1992). Sink or swim: accumulation of biomass at fronts. *Marine Ecology Progress Series, Series 82*, 1-12.

Franks, P. J. S. (1995). Thin layers of phytoplankton: a model of formation by near-inertial wave shear. *Deep Sea Research Part I: Oceanographic Research Papers, 42*(1), 75-91.

Galante, A., Wisen, S., Bhaya, D., & Levy, D. (2012). Modeling local interactions during the motion of cyanobacteria. *J Theor Biol.*, 309, 12.

Galvez, R., & Levine, S. (2003). Canada-USA Agreement on the Eutrophication Control and Protection of Lake Champlain Quebec: Laval University, Quebec, Canada and Prof. Rubenstein School U. of Vermont, Burlington, VT, USA, p. 4.
George, D. G. (1993). Physical and chemical scales of pattern in freshwater lakes and reservoirs. *135*(1-3), 1-15.

George, D. G., & Harris, G. P. (1985). The effect of climate on long-term changes in the crustacean zooplankton biomass of Lake Windermere, UK. *Nature*, **316**, 536-540.

Ghorai, S., & Hill, N. A. (2005). Penetrative phototactic bioconvection. *Physics of Fluids*, **17**(7), 1-11.

Ghorai, S., Panda, M. K., & Hill, N. A. (2010). Bioconvection in a suspension of isotropically scattering phototactic algae. *Physics of Fluids*, **22**(7), 1-16.

Gouvernement du Québec. (2014). Prélèvement des eaux et leur protection (pp. 2729-2759): Gazette Officielle du Québec, 30 juillet 2014, 146e année, no 31.

Government, V. (2009). Lake Champlain Long-term Monitoring. Retrieved water quality division consulté en juin 2009 http://www.anr.state.vt.us/dec/waterq/cfm/champlain/lp_longterm-lakes.cfm

Grabowska, M., & Mazur-Marzec, A. (2014). Vertical distribution of cyanobacteria biomass and cyanotoxin production in the polymictic Siemianówka Dam Reservoir (eastern Poland). *Arch. Pol. Fish.*, **22**, 41-51.

Gregor, J., Geri, R., Marsalek, B., Hetesa, J., & Marvan, P. (2005). In situ quantification of phytoplankton in reservoirs using a submersible spectrofluorometer. *Hydrobiologia*, **548**(1), 141-151.

Gregor, J., Marsálek, B., & Sípková, H. (2007). Detection and estimation of potentially toxic cyanobacteria in raw water at the drinking water treatment plant by in vivo fluorescence method. *Water Research*, **41**(1), 228-234.

Groupe d'étude international sur la baie Missisquoi. (2012). Étude sur les sources critiques de la baie Missisquoi: Rapport final à la Commission mixte internationale. Rapport, (56 pages).

Groupe de travail international de la Baie Missisquoi. (2004). Evaluation d'un modèle hydrodynamique appliqué à la baie Missisquoi. Vermont-Quebec.

Gunn, G. J., Rafferty, A. G., Rafferty, G. C., Cockburn, N., Edwards, C., Beattie, K. A., & Codd, G. A. (1992). Fatal canine neurotoxicosis attributed to blue-green algae (cyanobacteria). *Vet. Rec.*, **4**, 301-302.

Guven, B., & Howard, A. (2006). A review and classification of the existing models of cyanobacteria. *Progress in Physical Geography*, **30**(1), 1-24.
Halstvedt, C. B., Rohlack, T., Andersen, T., Skulberg, O., & Edvardsen, B. (2007). Seasonal dynamics and depth distribution of Planktothrix spp. in Lake Steinsfjorden (Norway) related to environmental factors. *J. Plankton Res.*, **29**, 471-482.

Hamilton, P. B., Ley, L. M., Dean, S., & Pick, F. R. (2005). The occurrence of the cyanobacterium Cylindrospermopsis raciborskii in Constance Lake: an exotic cyanoprokaryote new to Canada. *Phycologia* **44**(1), 9.

Havens, K. E., James, R. T., East, T. L., & Smith, V. H. (2003). N:P ratios, light limitation, and cyanobacterial dominance in a subtropical lake impacted by non-point source nutrient pollution. *122*(3), 379-390.

Hense, I. A. B. (2006). Towards a model of cyanobacteria life cycle - effects of growing and resting stages on bloom formation of N2-fixing species. *Ecological Modelling*, **195**, 205-218.

Hipsey, M. R., Romero, J. R., Antenucci, J. P., & Hamilton, D. (2006). Computational Aquatic Ecosystem Dynamics Model: CAEDYM v2 - v2.3 Science Manual. Contract Research Group, Centre for Water Research, University of Western Australia.

Hoek, V. D. C., Mann, D., Jahns, H. M., & Fogg, G. E. S. (1996). *Book review: algae: an introduction to phycology*. Cambridge University Press (600 pages).

Horne, A. J., & Wrigley, R. C. (1975). The use of remote sensing to detect how wind influences planktonic blue-green algal distribution. *Int. Ver. Theor. Angew. Limnol. Verh.*, **19**, 784-792.

Hotto, M. A., Satchwell, M. F., & Boyer, L. G. (2007). Molecular Characterization of Potential Microcystin-Producing Cyanobacteria in Lake Ontario Embayments and Nearshore Waters. *Appl Environ Microbiol.*, **73**, 4570-4578.

Howard, A. (1994). Problem cyanobacteria blooms: explanation and simulation modeling. *Trans. Inst. Br. Geogr.*, **19**(2), 213-225.

Howard, A. (1997). Computer simulation modelling of buoyancy change in Microcystis. *Hydrobiologia*, **349**(1-3), 111-117.

Howard, A. (2001). Modeling Movement Patterns of the Cyanobacterium, Microcystis. *11*(1), 304-310.

Howard, A., Irish, A. E., & Reynolds, C. S. (1996). A new simulation of cyanobacterial underwater movement (SCUM'96). *Journal of Plankton Research*, **18**(8), 1375-1385.

Hsu, S. A. (1972). *Wind Stress on a Coastal Water Surface*. Paper presented at the Proc. 13th Coastal Eng. Conf. (pp: 2531-2541).
Hu, W., F., C. D., Mengersen, K., & Tong, S. (2009). Weather variability, sunspots, and the
blooms of cyanobacteria. *Ecohealth, 6*(1), 71-78.

Hudnell, H. K., & Paul, V. (2008). Global warming and cyanobacterial harmful algal blooms *Cyanobacterial Harmful Algal Blooms: State of the Science and Research Needs* (Vol. 619, pp. 239-257): Springer New York.

Huisman, J., Jonker, R. R., Zonneveld, C., & Weissing, F. J. (1999). Competition for light between phytoplankton species: experimental tests of mechanistic theory. *Ecology, 80*, 211-222.

Huisman, J., Sharples, J., Stroom, J., Visser, P. M., Kardinaal, W. E. A., Verspagen, J. M. H., & Sommeijer, B. (2004). Changes in turbulent mixing shift competition for light between phytoplankton species. *Ecology* 85, 10.

Hutchinson, G. E. (1957). *A Treatise on Limnology*. *V. 1, Geology, Physics and Chemistry*. New York, NY, USA.

Hyenstrand, P., Rydin, E., & Gunnerhed, M. (2000). Response of Pelagic cyanobacteria to iron additions-enclosure experiments from lake Erken. *Journal of Plankton Research, 22*, 1113-1126.

Imamura, N. (1981). Studies on the water blooms in lake Kasumigaura. *Verh. Internat. Verin. Theor. Limnol.*, **20**, 7.

Institut National Santé publique du Québec (INSPQ). (2005). Propositions de critères d'intervention et de seuils d'alerte pour les cyanobactéries. Rapport (4 pages).

Izydorczyk, K., Carpentier, C. M., wczynski, J., Wagenvoort, A., Jurczak, T., & Tarczynska, M. (2009). Establishment of an Alert Level Framework for cyanobacteria in drinking water resources by using the Algae Online Analyser for monitoring cyanobacterial chlorophyll a. *Water Res.*, **43**(4), 989-996.

Izydorczyk, K., Tarczynska, M., Jurczak, T., Mrowczynski, J., & Zalewski, M. (2005). Measurement of phycocyanin fluorescence as an online early warning system for cyanobacteria in reservoir intake water. *Environ. Toxicol.*, **20**(4), 5.

Jang, M. H., Ha, K., & Takamura, N. (2008). Microcystin production by Microcystis aeruginosa exposed to different stages of herbivorous zooplankton. *Toxicon*, **51**(5), 882-889.

Janse, I., Kardinaal, W. E., Meima, M., Fastner, J., Visser, P. M., & Zwart, G. (2004). Toxic and nontoxic microcystis colonies in natural populations can be differentiated on the basis of rRNA gene internal transcribed spacer diversity. *Appl. Environ. Microbiol.*, **70**(7), 3979-3987.
Jayatissa, L. P., Silva, E. I. L., McElhiney, J., & Lawton, L. A. (2006). Occurrence of toxigenic cyanobacterial blooms in freshwaters of Sri Lanka. *Syst. Appl. Microbiol.*, 29(2), 156-165.

Jensen, H. S., & Andersen, F. O. (1992). Importance of temperature, nitrate, and pH for phosphate release from aerobic sediments of four shallow, eutrophic lakes. *Limnol. Oceanogr.*, 37(3), 13.

Ji, Z. G. (2008). *Hydrodynamics and water quality : modeling rivers, lakes, and estuaries:* Hoboken, N.J. : Wiley-Interscience (704 pages).

Jöhnk, K. D., Huisman, J., Sharples, J., Sommeijer, B., Visser, P. M., & Stroom, J. M. (2008). Summer heat waves promote blooms of harmful cyanobacteria. *Glob Change Biol* 14, 495-512.

Jones, I., George, G., & Reynolds, C. (2005). Quantifying effects of phytoplankton on the heat budgets of two large limnetic enclosures. *Freshwater Biology*, 50, 8.

Journey, A. C., Beaulieu, M. K., & Bradley, M. P. (2013). Environmental Factors that Influence Cyanobacteria and Geosmin Occurrence in Reservoirs *Environmental Sciences "Current Perspectives in Contaminant Hydrology and Water Resources Sustainability"*: Edited by Paul M. Bradley, ISBN 978-953-51-1046-0, Published: February 27, 2013 under CC BY 3.0 license.

Kanoshina, I., Lips, U., & Leppänen, J. (2003). The influence of weather conditions (temperature and wind) on cyanobacterial bloom development in the Gulf of Finland (Baltic Sea). *Harmful Algae*, 2(1), 29-41.

Kardinaal, W. E., Tonk, L., Janse, I., Hol, S., Slot, P., Huisman, J., & Visser, P. M. (2007). Competition for light between toxic and nontoxic strains of the harmful cyanobacterium *Microcystis*. *Appl Environ Microbiol.*, 73(9), 2939-2946.

Keleti, G., Sykora, J., Lippy, E., & Shapiro, M. (1979). Composition and biological properties of lipopolysaccharides isolated from Schizothrix calcicola (Ag.) Gomont (Cyanobacteria). *Applied and environmental microbiology*, 38(3), 471-477.

Kiefer, D. A. (1973). Chlorophyll a fluorescence in marine central diatoms: responses of chloroplasts to light and nutrient stress. *Marine Biology*, 23, 39-46.

King, K. W., Balogh, J. C., & Harmel, R. D. (2007). Nutrient flux in storm water runoff and baseflow from managed turf. *Environmental Pollution*, 150, 321-328.

Kirk, J. T. (1983). *Light and photosynthesis in aquatic ecosystems*: Cambridge Univ. Press, Cambridge and New York (401 pages).
Klemer, R. A. (1991). Effects of nutritional status on cyanobacterial buoyancy, blooms, and dominance, with special reference to inorganic carbon. *Revue canadienne de botanique*, **69**(5), 1133-1138.

Kling, H. J., Watson, S. B., McCullough, G. K., & Stainton, M. P. (2011). Bloom development and phytoplankton succession in Lake Winnipeg: a comparison of historical records with recent data. *Aquatic Ecosystem Health & Management*, **14**(2), 219-224.

Koreiviene, J., & Karosiene, J. (2012). *Temporal and spatial variation of phyto- and zooplankton in the Aukoetadvaris water reservoir during summer stratification* Paper presented at the Proc. 31th International Conference of Polish Phycological Society, Olsztyn.

Kosten, S., Huszar, V., Becares, E., Costa, L., Van Donk, E., Hansson, L.-A., Jeppessn, E., Kruk, C., Lacerot, G., Mazzeo, N., De Meester, L., Moss, B., Lurling, M., Noges, T., Romo, S., & Scheffer, M. (2011). Warmer climate boosts cyanobacterial dominance in shallow lakes. *Global Change Biology*, **18**(1), 118-126.

Kotak, B. G., & Kenefick, S. L. (1993). Occurence and toxicological evolution of cyanobacterial toxins in Alberta lakes and farm dugouts. *Water Research*, **27**, 495-506.

Kromkamp, J. C., Botterweg, J., & Mur, L. R. (1988). Buoyancy regulation in Microcystis aeruginosa grown at different temperatures. *FEMS Microbiology Letters*, **53**(3-4), 231-237. doi: 10.1111/j.1574-6968.1988.tb02669.x

Kromkamp, J. C., & Mur, L. R. (1984). Buoyant density changes in the cyanobacterium Microcystis aeruginosa due to changes in the cellular carbohydrate content. *FEMS Microbiology Letters*, **25**(1), 105-109.

Kromkamp, J. C., & Walsby, A. E. (1990). A computer model of buoyancy and vertical migration in cyanobacteria. *Journal of Plankton Research*, **12**(1), 161-183.

Kuiper-Goodman, T., Falconer, I., & Fitzgerald, J. (1999). Toxic Cyanobacteria in Water: A guide to their public health consequences, monitoring and management. Chapter 4: Human health aspects, Edited by Ingrid Chorus and Jamie Bartram (430 pages).

Lahti, K. R. J., Färdig, M., Niemelä, S., & Sivonen, K. (1997). Persistence of cyanobacterial hepatotoxin, microcystin-LR in participate matter and dissolve in lake water. *Water Research*, **31**, 1005-1012.

Lap, B., & Mori, K. (2007). A two-dimensional numerical model of wind-induced flow and water quality in closed water bodies. *Paddy and Water Environment*, **5**(1), 29-40.

Lavoie, I., Laurion, I., Warren, A., & Warwick, V. (2007). Les fleurs d'eau de cyanobactéries. *INRS rapport no 917*, (33 pages).
Le Vu, B., Vinc¸on-Leite, B., Lemaire, B. J., Bensoussan, N., Calzas, M., Drezen, C., Deroubaix, J. F., Escoffier, N., Degres, Y., Freissinet, C., Groleau, A., Humbert, J. F., Paolini, G., Prevot, F., Quiblier, C., Rioust, E., & Tassin, B. (2010). High-frequency monitoring of phytoplankton dynamics within the European water framework directive: application to metalimnetic cyanobacteria. *Biogeochemistry*, *106*(2), 229-243.

Lehman, J. T., Botkin, D. B., & Likens, G. E. (1975). The assumptions and rationales of a computer model of phytoplankton population dynamic? *Limnology and Oceanography*, 20(3), 343-365.

Lehtimäki, J. S. K., Luukkainen, R., & Niemelä, S. (1994). The effect of incubation time, temperature, light, salinity, and phosphorus on growth and hepatotoxin production by Nodularia strains. *Arch Hydrobiol.*, **130**, 269-282.

Lemmin, U., & Mortimer, C. H. (1986). Test of an extension to internal seiches of defant's procedure for determination of surface seiche characteristics in real lakes. *Limnol. Oceanogr.*, **31**(6), 25.

Leonard, B. P. (1979). A stable and accurate convective modelling procedure based on quadratic upstream interpolation. *Computer Methods in Applied Mechanics and Engineering*, 19(1), 59-98.

Lévesque, B., Gervais, M. C., Chevalier, P., Gauvin, D., Anassour-Laouan-Sidi, E., Gingras, S., Fortin, N., Brisson, G., Greer, C., & Bird, D. (2014). Prospective study of acute health effects in relation to exposure to cyanobacteria. *Science of the Total Environment*, 466-467, 397-403.

Li, Y., & Han, X. (2012). Microcystin-LR causes cytotoxicity effects in rat testicular Sertoli cells. *Environmental Toxicology and Pharmacology*, 33(2), 318-326.

Li, Y. S., & Zhan, J. M. (1993). An efficient three-dimensional semi-implicit finite element scheme for simulation of free surface flows. *International Journal for Numerical Methods in Fluids*, 16(3), 187-198.

Lilover, M. J., & Stips, A. (2008). The variability of parameters controlling the cyanobacteria bloom biomass in the Baltic Sea. *Baltic Sea Science Congress 2007 Baltic Sea Science Congress 2007*, 74, *Supplement*, S108-S115.

Litchman, E., & Klausmeier, C. A. (2001). Competition of phytoplankton under fluctuating light. *Am Nat*, **157**(2), 170-187.

Litchman, E., Klausmeier, C. A., & Bossard, P. (2004). Phytopkankton nutrient competition ender dynamic light regimes. *Limnology Oceanography*, 49, 1457-1462.
Liu, L., Liu, D., Johnson, D. M., Yi, Z., & Huang, Y. (2012). Effects of vertical mixing on phytoplankton blooms in Xiangxi Bay of Three Gorges Reservoir: Implications for management. *Water Res.*, **46**(7), 2121-2130.

Liu, Y., Wang, Z., Guo, H., Yu, S., & Sheng, H. (2013). Modelling the Effect of Weather Conditions on Cyanobacterial Bloom Outbreaks in Lake Dianchi: a Rough Decision-Adjusted Logistic Regression Model. *Environmental Modeling & Assessment*, **18**(2), 199-207.

Livingstone, D. (2003). Impact of Secular Climate Change on the Thermal Structure of a Large Temperate Central European Lake. *Climatic Change*, **57**(1-2), 205-225.

Loogman, J. G. (1982). *Influence of the photoperiodicity on algal growth kinetics*. (memoire (112 pages)), Université d'Amsterdam.

Lund, J. W. G., Kipling, C., & Cren, E. D. (1958). An inverted microscopemethod of estimating algal numbers and the statistical basis of estimations by counting. *Hydrobiologia*, **11**(2), 44.

Lurling, M., & Roessink, I. (2006). On the way to cyanobacterial blooms: impact of the herbicide metribuzin on the competition between a green alga (Scenedesmus) and a cyanobacterium (Microcystis). *Chemosphere*, **65**(4), 618-626.

MacIntyre, S., Flynn, K. M., Jellison, R., & Romero, J. R. (1999). Boundary mixing and nutrient fluxes in Mono Lake, California. *Limnol. Oceanogr.*, **44**(3), 512-530.

MacIntyre, S., Jonsson, A., Jansson, M., Aberg, J., Turney, D. E., & Miller, S. D. (2010). Buoyancy flux, turbulence, and the gas transfer coefficient in a stratified lake. *Geophysical Research Letters*, **37**(24), L24604.

Marce, R., Feijoo, C., Navarro, E., Ordonez, J., Goma, J., & Armengol, J. (2007). Interaction between wind-induced seiches and convective cooling governs algal distribution in a canyon-shaped reservoir. *Freshwater Biology*, **52**, 17.

Marcé, R., Feijoo, C., Navarro, E., Ordonez, J., Goma, J., & Armengol, J. (2007). Interaction between wind-induced seiches and convective cooling governs algal distribution in a canyon-shaped reservoir. *Freshwater Biology*, **52**(7), 1336-1352.

McCarthy, M., Gardner, W., Lehmann, M., & Bird, D. (2013). Implications of water column ammonium uptake and regeneration for the nitrogen budget in temperate, eutrophic Missisquoi Bay, Lake Champlain (Canada/USA). *Hydrobiologia*, **718**(1), 173-188.

McQuaid, N., Zamyadi, A., Prevost, M., Bird, D. F., & Dorner, S. (2011). Use of in vivo phycocyanin fluorescence to monitor potential microcystin-producing cyanobacterial biovolume in a drinking water source. *J Environ Monit*, **13**(2), 455-463.
Medalie, L., Hirsch, R. M., & Archfield, S. A. (2012). Use of flow-normalization to evaluate nutrient concentration and flux changes in Lake Champlain tributaries, 1990–2009. *Lake Champlain in 2010, 38, Supplement 1*, 58-67.

Mehnert, G., Leunert, F., Cirés, S., Jöhnk, K. D., Rücker, J., Nixdorf, B., & Wiedner, C. (2010). Competitiveness of invasive and native cyanobacteria from temperate freshwaters under various light and temperature conditions. *Journal of Plankton Research*, 32(7), 1009-1021.

Mellard, J. P., Yoshiyama, K., Litchman, E., & Klausmeier, C. A. (2011). The vertical distribution of phytoplankton in stratified water columns. *J Theor Biol*, 269(1), 16-30.
doi: 10.1016/j.jtbi.2010.09.041

Merceron, M. (2004). Les cyanobacteries: un danger occulté. *Revue eaux et rivières*, 128, 9-16.

Mimeault. (2002). Mise en valeur de la Baie Missisquoi et du lac Champlain. *Agrosolution*, 13(2), 92-96.

Ministère du Développement durable de l'Environnement et de la Lutte contre les Changements Climatiques. (2013). Bilan de la gestion des épisodes de fleurs d'eau d'algues bleu-vert en 2013.

Ministère du Développement durable de l'Environnement et des Parcs. (2002). Chapitre 9: Approvisionnement en eaux de surface et traitement *Le Guide de conception des installations de production d'eau potable (Guide de conception) (Volume 1: revisée en 2006)*. Québec.

Moll, A., Pätsch, J., & Kühn, W. (2003). ECOHAM2 User Guide The “Ecological North Sea Model, Hamburg, Version 2”. (38 pages).

Mooij, W. M., Janse, J. H., Senerpont Domis, L. N., Hülsmann, S., & Ibelings, B. W. (2007). Predicting the effect of climate change on temperate shallow lakes with the ecosystem model PCLake. *Hydrobiologia*, 584(1), 443-454.

Moreno-Ostos, E., Cruz-Pizarro, L., Basanta, A., Escot, C., & George, D. G. (2006). Algae in the motion: spatial distribution of phytoplankton in thermally stratified reservoirs. *Limnetica*, 25(1-2), 13.

Moreno-Ostos, E., Cruz-Pizarro, L., Basanta, A., & George, D. G. (2009). The influence of wind-induced mixing on the vertical distribution of buoyant and sinking phytoplankton species. *Aquatic Ecology*, 43(2), 271-284.

Moroney, V. J., & Somanchi, A. (1999). How Do Algae Concentrate CO₂ to Increase the Efficiency of Photosynthetic Carbon Fixation. *Plant Physiology*, 119(1), 9-16.
Mur, R. L., Skulberg, M. O., & Utkilen, H. (1999). Cyanobacteria in Environment *Toxic Cyanobacteria in Water: A guide to their public health consequences, monitoring and management*: Edited by Ingrid Chorus and Jamie Bartram.

National climate data and information archive. (2013): http://www.climat.meteo.gc.ca/climateData/. www.climate, visité le 04.02.13.

Ndong, M., Bird, D., Nguyen-Quang, T., de Boutray, M. L., Zamyadi, A., Vincon-Leite, B., Lemaire, B. J., Prevost, M., & Dorner, S. (2014a). Estimating the risk of cyanobacterial occurrence using an index integrating meteorological factors: Application to drinking water production. *Water Res*, 56C, 98-108. doi: 10.1016/j.watres.2014.02.023

Ndong, M., Bird, D., Nguyen Quang, T., Kahawita, R., Prévost, M., & Dorner, S. (2014b). Hydrodynamic modeling of light intensity and wind effects on the spatial distribution of cyanobacteria *Environmental Science and Technology* (soumis).

Nguyen-Quang, T., & Guichard, F. (2010). The role of bioconvection in plankton population with thermal stratification. *International Journal of Bifurcation and Chaos*, 20(06), 1761-1778.

Nicklisch, A., & Kohl, J. G. (1983). Growth kinetics of Microcystis aeruginosa (Kutz) as a basis for modeling its population dynamics. *Internat. Rev. Ges. Hydrobiol.*, 68(3), 10.

Nishizawa, T. U. A., Asayama, M., Fujii, K., Harada, K., Ochi, K., & Shirai, M. (2000). Polyketide synthase gene coupled to the peptide synthetase module involve in the biosynthesis of the cyclic heptapeptide microcystin. *J. Biochem*, 127, 779-789.

Nürnberg, G. K. (1996). Trophic state of clear and colored, soft- and hardwater lakes with special consideration of nutrients, anoxia, phytoplankton and fish. *Lake and Reservoir Management* 12, 432-447.

O'Reilly, C. M., Alin, S. R., Plisnier, P.-D., Cohen, A. S., & McKee, B. A. (2003). Climate change decreases aquatic ecosystem productivity of Lake Tanganyika, Africa. *Nature*, 424, 766-768.

O'Neil, J. M., Davis, T. W., Burford, M. A., & Gobler, C. J. (2012). The rise of harmful cyanobacteria blooms: The potential roles of eutrophication and climate change. *Harmful Algae--The requirement for species-specific information*, 14(0), 313-334.

Okada, M., & Aiba, S. (1983a). Simulation of water-bloom in a eutrophic lake—II. Reassessment of buoyancy, gas vacuole and Turgor pressure of Microcystis aeruginosa. *Water Res.*, 17(8), 877-882.

Okada, M., & Aiba, S. (1983b). Simulation of water-bloom in a eutrophic lake—III. Modeling the vertical migration and growth of Microcystis aeruginosa. *Water Res.*, 17(8), 883-893.
Oquist, G., Chow, W. S., & Anderson, J. M. (1992). Photoinhibition of photosynthesis represents a mechanism for the long term protection of photosystem II. *Planta*, **186**, 450-460.

Organisme de bassin versant de la baie Missisquoi. (2011). Plan Directeur de l'Eau: Le Portrait du Bassin Versant de la Baie Missisquoi. Québec.

Osborne, A., & Raven, J. A. (1986). Growth light level and photon absorbtion by cells of Chlamydomonas reinhardtii, Dunaliella tertiolecta, Scenedesmus obliquus and Euglena viridis. Br. . *Phycol. J.*, **21**, 10.

Ostos, M. E., Pizarro, C. L., Basanta, A., & George, G. D. (2009). The influence of wind-induced mixing on the vertical distribution of buoyant and sinking phytoplankton species. *Aquat. Ecol.*, **43**(2), 14.

Paerl, H. W. (1988). Nuisance phytoplankton blooms in coastal, estuarine, and inland waters. *Limnology and Oceanography* **33**, 823-847.

Paerl, H. W., & Huisman, J. (2008). Blooms like it hot. *Science* **320**, 57-59.

Paerl, H. W., & Paul, V. J. (2012a). Climate change: Links to global expansion of harmful cyanobacteria. *Cyanobacteria: Impacts of climate change on occurrence, toxicity and water quality management*, **46**(5), 1349-1363.

Paerl, W. H., & Huisman, J. (2009). Climate change: a catalyst for global expansion of harmful cyanobacterial blooms. *Environmental Microbiology Reports* **1**(1), 27-37.

Paerl, W. H., & Paul, J. V. (2012b). Climate change: Links to global expansion of harmful cyanobacteria. *Water Research*, **46**, 1349-1363.

Pannard, A., Le Rouzic, B., & Binet, F. (2008). Response of Phytoplankton Community to Low-Dose Atrazine Exposure Combined with Phosphorus Fluctuations. *Arch. Environ. Contam. Toxicol.*, **57**(1), 50-58.

Pant, H. K., & Reddy, K. R. (2001). Phosphorus sorption characteristics of estuarine sediments under different redox conditions. *J Environ Qual*, **30**(4), 1474-1480.

Patankar, S. V. V. (1980). *Numerical heat transfer and fluid flow*. Hemisphere Publishing Corporation, Washington – New York – London. McGraw Hill Book Company, New York (197 pages).

Pearson, L. A., Moffitt, M. C., Ginn, H. P., & BAN. (2008). The molecular genetics and regulation of cyanobacterial peptide hepatotoxin biosynthesis. *Crit Rev Toxicol*, **38**(10), 847-856.
Peretyatko, A., Teissier, S., Backer, S. D., & Triest, L. (2010). Assessment of the risk of cyanobacterial bloom occurrence in urban ponds: probabilistic approach. *Annales de Limnologie - International Journal of Limnology*, **46**(02), 121-133.

Porat, R., Teltsch, B., Perelman, A., & Dubinsky, Z. (2001). Diel Buoyancy Changes by the Cyanobacterium Aphanizomenon ovalisporum from a Shallow Reservoir. *Journal of Plankton Research*, **23**(7), 753-763.

Porcella, D. B., G, T. M., Bowie, G. L., Ginn, T. C., & Lorenzen, M. W. (1983). Assessment methodology for New Cooling Lakes: Vol. 1: Methodology to Assess Multiple Uses for New Cooling lakes. Tetra tech, Inc., Lafayette, California. For Electric Power Research Institute. Report EPRI EA-2059.

Ptacnik, R., Andersen, T., & Tamminen, T. (2010). Performance of the Redfield Ratio and a Family of Nutrient Limitation Indicators as Thresholds for Phytoplankton N vs. P Limitation. *Ecosystems*, **13**(8), 1201-1214.

Rabouille, S., Salençon, M.-J., & Thébault, J.-M. (2005). Functional analysis of Microcystis vertical migration: A dynamic model as a prospecting tool: I—Processes analysis. *Ecological Modelling*, **188**(2-4), 386-403.

Rabouille, S., Thébault, J.-M., & Salençon, M.-J. (2003). Simulation of carbon reserve dynamics in Microcystis and its influence on vertical migration with Yoyo model. *C R Biol*, **326**(4), 349-361.

Rapala, J. (1998). *Toxin production by freshwater cyanobacteria: effects of environmental factors*. Ph. D. thesis. University of Helsinki.

Recknagel, F., French, M., Harkonen, P., & Yabunaka, K.-I. (1997). Artificial neural network approach for modelling and prediction of algal blooms. *Ecological Modelling*, **96**(1-3), 11-28.

Reichwaldt, E. S., & Ghadouani, A. (2012). Effects of rainfall patterns on toxic cyanobacterial blooms in a changing climate: Between simplistic scenarios and complex dynamics. *Water Res.*, **46**(5), 22.

Reynolds, C. S. (1984). *The Ecology of freshwater Phytoplankton*. Cambridge University Press, United Kingdom.

Reynolds, C. S. (2006). *The Ecology of Phytoplankton* (*Ecology, Biodiversity and Conservation*). Cambridge University Press, United Kingdom.

Reynolds, C. S., & Irish, A. E. (1997). Modelling phytoplankton dynamics in lakes and reservoirs: the problem of in-situ growth rates. *Hydrobiologia*, **349**(1-3), 5-17.
Reynolds, C. S., Oliver, R. L., & Walsby, A. E. (1987). Cyanobacterial dominance: The role of buoyancy regulation in dynamic lake environments. *New Zealand Journal of Marine and Freshwater Research, 21*(3), 379-390.

Reynolds, C. S., & Walsby, A. E. (1975). Water-blooms. *Biological Reviews, 50*(4), 437-481.

Reynolds, C. S., Wiseman, S. W., Godfrey, B. M., & Butterwick, C. (1983). Some effects of artificial mixing on the dynamics of phytoplankton populations in large limnetic enclosures. *J. Plankton Res.*, 5, 203-232.

Rinta-Kanto, J., Ouellette, A., Boyer, G., Twiss, M., Bridgeman, T., & Wilhelm, S. (2005a). Quantification of toxic Microcystis spp. during the 2003 and 2004 blooms in western Lake Erie using quantitative real-time PCR. *Environmental science & technology*, 39(11), 4198-4205.

Rinta-Kanto, J. M., Ouellette, A. J. A., Boyer, G. L., Twiss, M. R., Bridgeman, T. B., & Wilhelm, S. W. (2005b). Quantification of toxic myrocystis spp. during the 2003 and 2004 blooms in western Lake Erie using quantitative real-time PCR. *Enviro Sci Tech*, 39, 4198-4205.

Rizvi, S. J. H., & Rizvi, V. H. (1992). *Allelopathy. Basics et Applied Aspects*. London: Chapman & Hall (480 pages).

Robarts, R. D., & Zohary, T. (1987). Temperature effects on photosynthetic capacity, respiration, and growth rates of bloom-forming cyanobacteria. *New Zealand Journal of Marine and Freshwater Research, 21*(3), 391-399.

Ross, O. N., & Sharples, J. (2008). Swimming for survival: A role of phytoplankton motility in a stratified turbulent environment. *Impact of Small-scale Physics on Marine Biology Selected papers from the 2nd Warnemünde Turbulence Days 2nd Warnemünde Turbulence Days*, 70(3-4), 248-262.

Rucker, J., Wiedner, C., & Zippel, P. (1997). Factors controlling the dominance of Planktothrix agardhii and Limnothrix redekei in eutrophic shallow lakes *Hydrobiologia*, 342/343, 107-115.

Ryan, J. P., Fischer, A. M., Kudela, R. M., McManus, M. A., Myers, J. S., Paduan, J. D., Ruhsam, C. M., Woodson, C. B., & Zhang, Y. (2010). Recurrent frontal slicks of a coastal ocean upwelling shadow. *Journal of Geophysical Research: Oceans*, 115(C12), C12070.

Schagerl, M., & Mueller, B. (2006). Acclimation of chlorophyll a and carotenoid levels to different irradiances in four freshwater cyanobateria. *J. Plant Physiol.*, 163, 709-716.

Schelske, C. L., & Stoermer, E. F. (1971). Eutrophication, silica depletion, and predicted changes in algal quality Lake Michigan. *Science*, 173, 423-424.
Schindler, D. W. (1977). Evolution of Phosphorus Limitation in Lakes. *Science*, 195(4275), 260-262.

Schmidt, W., Petzoldt, H., Bornmann, K., Imhof, L., & Moldaenke, C. (2009). Use of cyanopigment determination as an indicator of cyanotoxins in drinking water. *Water Sci Technol*, 59(8), 1531-1540.

Schmittner, A. (2005). Decline of the marine ecosystem caused by a reduction in the Atlantic overturning circulation. *Nature*, 434(7033), 628-633.

Schreurs, H. (1992). *Cyanobacterial dominance, relation to eutrophication and lake morphology*. (thesis), University of Amsterdam (198 pages).

Seaburg, K. G., Parked, B. C., Wharton, R. A., & Simmons, G. M. (1981). Temperature Growth Response of algal isolates from antarctic OASES. *Journal of Phycology*, 17(4), 353-360.

Sevilla, E., Martin-Luna, B., Vela, L., Bes, M. T., Fillat, M. F., & Peleato, M. L. (2008). Iron availability affects mcyD expression and microcystin-LR synthesis in Microcystis aeruginosa PCC7806. *Environ. Microbiol.*, 10(10), 2476-2483.

Shanahan, P. (1985). *Water Temperature Modeling: A Practice Guide*. Paper presented at the In Proceedings of stormwater and water quality model users group meeting. United States Environmental Protection Agency, Environmental Research Laboratory, EPA-600/9-85-003. Athens, Georgia (13 pages).

Shapiro, J. (1997). The role of carbon dioxide in the initiation and maintenance of blue-green dominance in lakes. *Freshwater Biology*, 37, 307-323.

Sherman, B. S., & Webster, I. T. (1994). A model for the light-limited growth of buoyant phytoplankton in a shallow, turbid waterbody. *Aust. J. Mar. Freshwater Res.*, 45, 847-862.

Smeltzer, E., Shambaugh, A. d., & Stangel, P. (2012). Environmental change in Lake Champlain revealed by long-term monitoring. *Lake Champlain in 2010, 38, Supplement 1*(0), 6-18.

Smith, L., Watzin, C. M., & Druschel, G. (2011). Relating sediment phosphorus mobility to seasonal and diel redox fluctuations at the sedimentewater interface in a eutrophic freshwater lake. *Limnol. Oceanogr.*, 56(6), 2251-2265.

Smith, V. H. (1985). Predictive models for the biomass of blue-green algae in lakes. *JAWRA Journal of the American Water Resources Association*, 21(3), 433-439.

Smith, V. H. (1986). Light and Nutrient Effects on the Relative Biomass of Blue-Green Algae in Lake Phytoplankton. *Canadian Journal of Fisheries and Aquatic Sciences*, 43(1), 148-153.
Smith, V. H., Willén, E., & Karlsson, B. (1987). Predicting the summer peak biomass of four species of blues-green algae (cyanophyta/cyanobacteria) in Swedish lakes. *JAWRA Journal of the American Water Resources Association*, 23(3), 397-402.

Sondergaard, M., Jensen, J. P., & Jeppesen, E. (2003). Role of sediment and internal loading of phosphorus in shallow lakes. *Hydrobiologia*, 506, 135-145.

SooHoo, J. B., Kiefer, D. A., Collins, D. J., & McDermid, I. S. (1986). In vivo fluorescence excitation and absorption spectra of marine phytoplankton. *Journal of Plankton Research*, 8, 197-214.

Stager, J. C., & Thill, M. (2010). Stager, J.C., Thill, M., 2010. Climate change in the Lake Champlain Basin: what natural resource managers can expect and do (pp. 44 pages). Keene Valley, NY and Montpelier, VT.: Prep. for The Nature Conservancy.

Statistics Canada. (2006). Community Profiles-Missisquoi Bay Area, Statistics Canada, Government of Canada.

Steffensen, D. A. (2008). Economic cost of cyanobacterial blooms. In H. K. E. In: Hudnell (Ed.), *Cyanobacterial Harmful Algal Blooms: State of the Science and Research Needs*. (pp. 855-866). New York: Springer Press.

Steinbuck, J. V., Stacey, M. T., McManus, M. A., Cheriton, O. M., & Ryan, J. P. (2009). Observations of turbulent mixing in a phytoplankton thin layer: implications for formation, maintenance, and breakdown. *Limnology and Oceanography*, 54(4), 16.

Stull, R. (2000). *Meteorology for Scientists and Engineers: a technical companion book with Ahrens' Meteorology Today*. (502 pages). Publisher by Pacific Grove, CA : Brooks/Cole.

Stumpf, R. P., Wynne, T. T., Baker, D. B., & Fahnenstiel, G. L. (2012). nterannual Variability of Cyanobacterial Blooms in Lake Erie. *PLoS ONE*, 7(8), Special section p1.

Tang, E. P. Y., Tremblay, R., & Vincent, W. F. (1997). CYANOBACTERIAL DOMINANCE OF POLAR FRESHWATER ECOSYSTEMS: ARE HIGH-LATITUDE MAT-FORMERS ADAPTED TO LOW TEMPERATURE?1. *Journal of Phycology*, 33(2), 171-181.

Taranu, Z. E., Zurawell, R. W., Pick, F. R., & Gregory-Eaves, I. (2012). Predicting cyanobacteria dynamics in the face of global change: the importance of scale and environmental context. *Global Change Biol.*, 18(12), 14.

Teixeira, M. G. L. C., Costa, M. C. N., Carvalho, V. L. P., Pereira, M. S., & Hage, E. (1993). Gastroenteritis epidemic in the area of the Itaparica Dam, Bahia, Brazil. *Bulletin of the Pan American Health Organization* 27, 244-253.
Teles, L., Vasconcelos, V., Teles, L., Pereira, E., Saker, M., & Vasconcelos, V. (2006). Time Series Forecasting of Cyanobacteria Blooms in the Crestuma Reservoir (Douro River, Portugal) Using Artificial Neural Networks. *Environmental Management, 38*(2), 227-237.

Tetra Tech, I. (1980). Methodology for Evaluation of Multiple Power Plant Cooling System Effects, Volume V: Technical Basis for computations. Tetra Tech, Inc., Lafayette, California. For Electric Power Research Institute. Report EPRI EA-1111.

Tetra Tech Inc. (2007). EFDC Water Quality Model Theory and Computation Volume 3: Water Quality Module (pp. 90 pages).

Thomas, R. H., & Walsby, A. E. (1985). Buoyancy Regulation in a Strain of Microcystis. *Journal of General Microbiology, 131*(4), 799-809.

Thomas, R. H., & Walsby, A. E. (1986). The Effect of Temperature on Recovery of Buoyancy by Microcystis. *Journal of General Microbiology, 132*(6), 1665-1672.

Tillett, D. D. E., Erhard, M., Von Döhren, H., Börner, T., & Neilan, B. A. (2000). Structural organization of microcystin biosynthesis in Microcystis aeruginosa PCC7806: an integrated peptide-polyketide synthetase system. *Chem Biol.*, 7, 753-764.

Trojanowska, A., & Izydorczyk, K. (2010). Phosphorus Fractions Transformation in Sediments Before and After Cyanobacterial Bloom: Implications for Reduction of Eutrophication Symptoms in Dam Reservoir. *Water, Air, & Soil Pollution, 211*(1-4), 287-298.

Turner, P. C., Gammie, A. J., Hollinrake, K., & Codd, G. A. (1990). Pneumonia associated with cyanobacteria. *Br. Med. J.*, **300**, 1440-1441.

Van Liere, L., & Walsby, A. (1982). Interactions of cyanobacteria with light. In I. C. N. a. W. B. (Ed.) (Ed.), *The biology of cyanobacteria* (pp. (pp. 9-47)): Blackwell, Oxford and University of California Press, Berkeley.

Velo-Suárez, L., Fernand, L., Gentien, P., & Reguera, B. (2010). Hydrodynamic conditions associated with the formation, maintenance and dissipation of a phytoplankton thin layer in a coastal upwelling system. *30*(2), 193-202.

Verhagen, J. H. G. (1994). Modeling phytoplankton patchiness under the influence of wind-driven currents in lakes. *Limnol. Oceanogr.*, **39**(7), 15.

Vermont Department of Environmental Conservation Watershed Management Division (VTDEC). (2009). https://anrweb.vermont.gov/dec/dec/LongTermMonitoringLakes.aspx
Retrieved consulté le 15 Août 2014

Vezie, C., Rapala, J., Vaitomaa, J., Seitsonen, J., & Sivonen, K. (2002). Effect of nitrogen and phosphorus on growth of toxic and nontoxic Microcystis strains and on intracellular microcystin concentrations. *Microb. Ecol.*, **43**(4), 443-454.
Vincent, W. F. (1981). Rapid physiological assays for nutrient demand by the plankton. I. Nitrogen. *Journal of Plankton Research*, 3(4), 685-697.

Vincent, W. F., Neale, P. J., & Richerson, P. J. (1984). Photoinhibition: algal response to bright light during diel stratification and mixing in a tropical alpine Lake. *Journal of phycology*, 20, 201-211.

Visser, P., Passarge, J., & Mur, L. (1997). Modelling vertical migration of the cyanobacterium *Microcystis*. *Hydrobiologia*, 349(1-3), 99-109.

Vox Media Inc. (2014, on August 3, 2014). A toxic algae scare has left 500,000 people in Ohio without drinking water Retrieved 11 September 2014, 2014

Wagner, C., & Adrian, R. (2009). Cyanobacteria dominance: quantifying the effects of climate change. *Limnol. Oceanogr.*, 54(2), 2460–2468.

Wallace, B. B., Bailey, M. C., & Hamilton, D. P. (2000). Simulation of vertical position of buoyancy regulating Microcystis aeruginosa in a shallow eutrophic lake. *Aquatic Sciences*, 62(4), 320-333.

Wallace, B. B., & Hamilton, D. P. (1999). The effect of variations in irradiance on buoyancy regulation in Microcystis aeruginosa. *Limnol. Oceanogr*, 44(2), 273-284.

Wallace, B. B., & Hamilton, D. P. (2000). Simulation of water-bloom formation in the cyanobacterium *Microcystis aeruginosa*. *Journal of Plankton Research*, 22(6), 1127-1138.

Walsby, A. E. (1975). Gas vesicles. *Annu Rev Plant Physiol*, 26, 427-438.

Walsby, A. E. (1978). The properties of buoyancy-providing role of gas vesicles in Trichodesmium *Ehrenberg. Br. Phycol. J.*, 13, 103-113.

Walsby, A. E. (1997). Numerical integration of phytoplankton photosynthesis through time and depth in a water column. *New Phytol.*, 136, 189-208.

Walsby, A. E. (2005). Stratification by cyanobacteria in lakes: a dynamic buoyancy model indicates size limitations met by Planktothrix rubescens filaments. *New Phytol*, 168(2), 365-376.

Walsby, A. E., Reynolds, C. S., Oliver, R. L., & Kromkamp, J. (1989). The role of gas vacuoles and carbohydrate content in the buoyancy and vertical distribution of Anabaena minutissima in Lake Rotongaio, New Zealand. *Arch. Hydrobiol. e Beiheft Ergeb. Limnol.*, 32, 25.

Wang, L., Cai, Q., Zhang, M., Xu, Y., Kong, L., & Tan, L. (2011). Vertical distribution patterns of phytoplankton in summer *Microcystis* bloom period of Xiangxi Bay, three geoges reservoir, China. *Fresenius Environmental Bulletin*, 20(3), 553-560.
Wang, X., Parkpian, P., Fujimoto, N., Ruchirawat, K. M., DeLaune, R. D., & Jugsujinda, A. (2002). Environmental conditions associating microcystins production to Microcystis aeruginosa in a reservoir of Thailand. *J Environ Sci Health A Tox Hazard Subst Environ Eng*, 37(7), 1181-1207.

Wang, Z., & Goodman, L. (2010). The evolution of a thin phytoplankton layer in strong turbulence. *The Ecology and Oceanography of Thin Plankton Layers*, 30(1), 104-118.

Watzin, M. C., Miller, E. B., Shambaugh, A. D., & Kreider, M. A. (2006). Application of the WHO alert level framework to cyanobacterial monitoring of Lake Champlain, Vermont. *Environ Toxicol.*, 21(3), 278-288.

Webster, I. T. (1990). Effect of wind on the distribution of phytoplankton cells in lakes. *Limnol. Oceanogr.*, 35(5), 989-1001.

Webster, I. T., & Hutchinson, P. A. (1994). Effect of wind on the distribution of Phytoplankton cells in lakes revisited. *Limnol. Oceanogr.*, 39 (2), 365-373.

Wei, B., Sugiura, N., & Maekawa, T. (2001). Use of artificial neural network in the prediction of algal blooms. (0043-1354 (Print)).

Westwood, J. K., & Ganf, G. G. (2004). Effect of cell flotation on growth of Anabaena circinalis under diurnally stratified conditions. *J. Plankton Res.*, 26(10), 1183-1197.

Wheeler, S. M., Morrissey, L. A., Levine, S. N., Livingston, G. P., & Vincent, W. F. (2012). Mapping cyanobacterial blooms in Lake Champlain's Missisquoi Bay using QuickBird and MERIS satellite data. *Lake Champlain in 2010, 38, Supplement 1 (0)*, 68-75.

WHO. (1998). Guidelines for drinking-water quality, 2nd ed. Addendum to Volume 2. Health criteria and other supporting information. Geneva. World Health Organization (pp. 127 pages).

Wilson, A. E., Sarnelle, O., Neilan, B. A., Salmon, T. P., Gehringer, M. M., & Hay, M. E. (2005). Genetic variation of the bloom-forming Cyanobacterium Microcystis aeruginosa within and among lakes: implications for harmful algal blooms. *Appl Environ Microbiol*, 71(10), 6126-6133.

Wolk, C. P. (1996). Heterocyst formation. *Annu Rev Genet*, 30, 59-78.

Wongsai, S., & Luo, K. (2007). *Understanding environmental factors associated with cyanobacterial bloom*. Paper presented at the In: Paper Presented at the 3rd IASTED International Conference on Environmental Modelling and Simulation, EMS 2007, Honolulu, HI, United States.

Wool, T. A., Ambrose, R. B., Nartin, J. L., & Comer, E. A. (2002). Water Quality Analysis Simulation Program (WASP) Version 6.0 Draft: User's Manual. USEPA-Region 4.
Wu, S., Wang, S., Yang, H., Xie, P., Ni, L., & Xu, J. (2008). Field studies on the environmental factors in controlling microcystin production in the subtropical shallow lakes of the Yangtze River. *Bull. Environ. Contam. Toxicol.*, **80**(4), 329-334.

Wu, T., Qin, B., Zhu, G., Luo, L., Ding, Y., & Bian, G. (2013). Dynamics of cyanobacterial bloom formation during short-term hydrodynamic fluctuation in a large shallow, eutrophic, and wind-exposed Lake Taihu, China. *Environmental Science and Pollution Research*, **1-11**.

Wynne, T. T., Stumpf, R. P., Tomlinson, M. C., Fahnenstiel, G. L., Dyble, J., Schwab, D. J., & Joshi, S. J. (2013). Evolution of a cyanobacterial bloom forecast system in western Lake Erie: Development and initial evaluation. *Remote Sensing of the Great Lakes and Other Inland Waters, 39, Supplement 1*(0), 90-99.

Yu, Q., Liu, J., Zhang, Y., & Li, J. (2002). Simulation of rice biomass accumulation by an extended logistic model including influence of meteorological factors. *International Journal of Biometeorology*, **46**(4), 185-191.

Zamyadi, A., Dorner, S., Ndong, M., Ellis, D., Bolduc, A., Bastien, C., & Prevost, M. (2013a). Low-risk cyanobacterial bloom sources: Cell accumulation within full-scale treatment plants. *Journal American Water Works Association*, **105**(11), 65-66.

Zamyadi, A., Dorner, S., Sauvé, S., Ellis, D., Bolduc, A., Bastien, C., & Prévost, M. (2013b). Species-dependence of cyanobacteria removal efficiency by different drinking water treatment processes. *Water Res.*, **47**(8), 2689-2700.

Zamyadi, A., Dorner, S., Sauvé, S., Ellis, D., Bolduc, A., Bastien, C., & Prévost, M. (2013c). Species-dependence of cyanobacteria removal efficiency by different drinking water treatment processes. *Water Research*, **47**(8), 12.

Zamyadi, A., MacLeod, S. L., Fan, Y., McQuaid, N., Dorner, S., Sauvé, S., & Prévost, M. (2012). Toxic cyanobacterial breakthrough and accumulation in a drinking water plant: A monitoring and treatment challenge. *Cyanobacteria: Impacts of climate change on occurrence, toxicity and water quality management*, **46**(5), 1511-1523.

Zhang, M., Duan, H., Shi, X., Yu, Y., & Kong, F. (2012). Contributions of meteorology to the phenology of cyanobacterial blooms: Implications for future climate change. *Water Res.*, **46**(2), 442-452.

Zhang, M., Kong, F., Wu, X., & Xing, P. (2008). Different photochemical responses of phytoplankters from the large shallow Taihu Lake of subtropical China in relation to light and mixing. *Hydrobiologia*, **603**(1), 267-278.

Zheng, L., Xie, P., Li, Y. L., Yang, H., Wang, S. B., & Guo, N. C. (2004). Variation of intracellular and extracellular microcystins in a shallow, hypereutrophic subtropical
chinese lake with dense cyanobacterial blooms. *Bull. Environ. Contam. Toxicol.*, **73**(4), 698-706.

Zilberg, B. (1966). Gastroenteritis in Salisbury European children - a five-year study. *Cent. Afr. J. Med.*, **12**(9), 164-168.