Modeling the water quality difference between the near-shore and offshore zones of Lake Ontario

We present a simple mathematical model that simulates the persistent difference in nutrient (phosphorus and chloride) concentration between the near-shore and offshore zones of Lake Ontario. The model is developed based on the mass transfer assumed in the highly-cited “nearshore phosphorus shunt” hypothesis (Hecky et al., 2004; Canadian Journal of Fisheries and Aquatic Sciences). The hypothesis stated that filtration of plankton by the invasive Dreissenids (zebra and quagga mussels) changed the phosphorus pathways which leads to increased nutrient levels in nearshore despite decades of reductions in loadings to the Great Lakes. The steady-state solutions of our model imply that the concentration differences in both phosphorus and chloride between nearshore and offshore depend critically on the mixing rates and upon loading, with simple functional form.  Applying a uniform initial condition with input concentration from Niagara River, the model approaches steady state solution for nearshore-offshore chloride difference after several months. This timescale depends on the size of the nearshore and offshore zones, and the mixing rates, but not upon the loading terms. We find good agreement between observed gradients between the near-shore and offshore and the predictions of the steady-state concentration differences, using published values of nutrient loading, horizontal and vertical exchange rates. We will discuss the implications of these results in terms of understanding the recent nearshore water quality issues in the Great Lakes.