Modeling spring-summer phytoplankton bloom in Lake Michigan with and without riverine nutrient loading

Abstract

There were two phytoplankton blooms captured by remote sensing in Lake Michigan in 1998, one from March to May, and one during June. In this paper, those phytoplankton blooms were simulated by a coupled physical–biological model, driven by observed meteorological forcing in 1998. The model reasonably reproduced the lake currents. The biological model results, with and without riverine nutrient loading, were compared with the remote sensing data. A 3-month-long donut-like phytoplankton bloom that appeared in southern Lake Michigan was reasonably well simulated only when riverine input was included, indicating the importance of riverine nutrient input for supporting the growth of phytoplankton in Lake Michigan. The model with riverine input also captured a second event-driven phytoplankton bloom during June with weaker magnitude that occurred in mid-south Lake Michigan, which lasted for about 20 days. The major reason for the weaker bloom in June was that vertical mixing in the hydrodynamic model was too weak (leading to a mixed-layer depth of 20 m) to bring the bottom nutrient-rich water up to the epilimnion. High chlorophyll concentration that persisted in Green Bay for almost a year was simulated with less intensity.

Appendix A: The mathematical expressions for each term of Eqs. (1)–(4) are given as

$$ P\left(\mathrm{uptake}\right)={\mu}_{\mathrm{max}}^P\cdotp \mu (T)\cdotp \mu (I)\cdotp \mu (N)P $$

(a1)

$$ P\left(\mathrm{respiration}\right)={\gamma}_P\cdotp P\exp \left({\gamma}^T\cdotp T\right) $$

(a2)

$$ Z\left(\mathrm{respiration}\right)={\gamma}_Z\cdotp Z\exp \left({\gamma}^T\cdotp T\right) $$

(a3)

$$ D\left(\mathrm{remineralization}\right)={d}^R\cdotp D\exp \left({\gamma}^T\cdotp T\right) $$

(a4)

$$ ZP\left(\mathrm{grazing}\right)={G}_{\mathrm{max}}\frac{\sigma_PP}{1+{\sigma}_PP+{\sigma}_DD}Z $$

(a5)

$$ ZD\left(\mathrm{grazing}\right)={G}_{\mathrm{max}}\frac{\sigma_DD}{1+{\sigma}_PP+{\sigma}_DD}Z $$

(a6)

$$ P\left(\mathrm{mortality}\right)={\varepsilon}_PP $$

(a7)

$$ Z\left(\mathrm{mortality}\right)={\varepsilon}_ZZ $$

(a8)

$$ P\left(\sin \mathrm{king}\right)=-{w}_P\frac{\partial P}{\partial z} $$

(a9)

$$ D\left(\sin \mathrm{king}\right)=-{w}_D\frac{\partial D}{\partial z} $$

(a10)

where the definition of each parameter in the equations (a1–a10) is given in Appendix B.

1.1 Appendix B

Table 3

Table 3 Biological model parameters