Modeling the role of wind and warming on Microcystis aeruginosa blooms in shallow lakes with different trophic status

Abstract

This study focuses on the role of wind exposure and storm events, in interaction with trophic status and temperature, on the competition between two species: Microcystis aeruginosa and a typical green alga. It is based on a water column model containing ecological and fluid mechanic features including mixing and shear stress at the bottom. This model addresses for the first time the impact of storm events (inducing sediment and nutrient resuspension) on algal dynamics. Simulations with realistic environmental forcings were performed with different sets of wind, temperature, and trophic conditions. With normal temperatures, conditions for dominance and bloom formation of M. aeruginosa in summer are restricted to hypertrophic waters with low wind exposure. Higher wind exposure (above 2 m s⁻¹) impairs the formation blooms even in favorable trophic conditions and enhances the dominance of green algae. Hotter temperatures allow the dominance of M. aeruginosa for lower phosphorus conditions and higher wind exposure and lead to the exclusion of green algae for high phosphorus content and low wind exposure. Nevertheless, high wind exposure (above 3 m s⁻¹) still prevents dense bloom formation and allows the coexistence of both species. Storm events bring two counterbalancing features: sediment and nutrient resuspension. The first leads to a decrease of phytoplankton density in response to high turbidity, and the second leads to an increase and better maintenance of M. aeruginosa blooms due to high phosphorus concentration released in the water. This result depends on the timing of the event and on general wind exposure as phosphorus release only benefits M. aeruginosa if exposure to wind is low.

Appendices

Appendix 1: computation of the bottom shear stress

Wave contribution

The wave contribution τ _bw is effective mainly for shallow lakes. It expresses the action of the oscillating boundary layer associated with waves as:

$$ {\tau}_{\mathrm{b}\mathrm{w}}=\frac{1}{2}\rho {f}_{\mathrm{w}}{U}_{\mathrm{b}}^2 $$

(18)

with the friction factor f _w :

$$ {f}_{\mathrm{w}}=2{\left(\frac{U_{\mathrm{b}}{A}_{\mathrm{b}}}{\upsilon}\right)}^{-0.5} $$

(19)

where A _b stands for the maximum wave orbital amplitude and U _b stands for the maximum wave orbital velocity. Using the standard wave theory, these quantities A _b and U _b are given by:

$$ {A}_{\mathrm{b}}=\frac{H}{2 \sinh \left(2\pi d/L\right)} $$

(20)

$$ {U}_{\mathrm{b}}=\rho \frac{H}{T \sinh \left(2\pi d/L\right)} $$

(21)

where the wave height H, wave period T, and wave length L are estimated using the following formula (CERC 1984):

$$ H=\frac{u_{\mathrm{w}}^2}{g}0.283 \tanh \left[0.53{\left(\frac{ gd}{u_{\mathrm{w}}^2}\right)}^{3/4}\right] \tanh \left[\frac{0.00565{\left(\frac{g\mathrm{Fetch}}{u_{\mathrm{w}}^2}\right)}^{1/2}}{ \tanh \left[0.53{\left(\frac{ gd}{u_{\mathrm{w}}^2}\right)}^{3/8}\right]}\right] $$

(22)

$$ T=\frac{u_{\mathrm{w}}}{g}7.54 \tanh \left[0.833{\left(\frac{ gd}{u_{\mathrm{w}}^2}\right)}^{3/8}\right] \tanh \left[\frac{0.0379{\left(\frac{g\mathrm{Fetch}}{u_{\mathrm{w}}^2}\right)}^{1/2}}{ \tanh \left[0.833{\left(\frac{ gd}{u_{\mathrm{w}}^2}\right)}^{3/8}\right]}\right] $$

(23)

$$ L=\frac{ gT \mathit{^2}}{2\pi } \tanh \frac{2\pi d}{L} $$

(24)

where Fetch denotes the fetch length (in meters) of wind.

Current contribution

The contribution for the shear stress due to currents follows from the choice of eddy diffusivity. In a parallel flow approximation with constant pressure gradient, the velocity profile satisfies:

$$ \frac{\partial u}{\partial t}={d}_t\left(z,t\right)\frac{\partial^2u}{\partial {z}^2}-\frac{1}{\rho}\frac{\mathrm{d}p}{\mathrm{d}x} $$

(25)

For a steady velocity, this imposes a linear variation of shear with z. The parabolic form of d _t , coupled with the constancy of shear and mass conservation for a steady velocity, imposes the following profile:

$$ u(z)=A{u}_{*\mathrm{s}} \ln \left(1+z/\left(d{z}_{\mathrm{b}}\right)\right)+B{u}_{*\mathrm{s}} \ln \left(1-z/\left(d{z}_{\mathrm{s}}+d\right)\right)+C $$

(26)

where the coefficients A, B, and C are functions of z _b and z _s. This profile leads to the bottom shear stress exerted for the turbulent countercurrent:

$$ {\tau}_{\mathrm{bTurb}}={A}_1\rho {u}_{*\mathrm{s}}^2 $$

(27)

in which A ₁ is an involved function of the two dimensionless quantities z _s and z _b.

Appendix 2: phosphorus parameters

Table 3 Phosphorus parameters

Appendix 3

Fig. 7

Effect of initial M. aeruginosa density on simulation results

Appendix 4

Fig. 8

Percentage of light lost for all depths and dates of Fig. 3