A mass-balance approach for predicting lake phosphorus concentrations as a function of external phosphorus loading: Application to the Lake St. Clair – Lake Erie System (Canada – USA)

A mass balance model is presented that links the total phosphorus concentration in lakes to the water residence time, Rw (lake volume divided by the annual water inflow) and the total phosphorus residence time, Rp (average standing stock of lake total phosphorous divided by the external annual total phosphorus input). Following a change in the external load, the lake total phosphorus concentration asymptotically approaches a new value that depends on the Rp:Rw ratio, with the rate of approach controlled by Rp. We applied this approach to a recent reanalysis of the water and total phosphorus budgets of the Lake Erie system of the Laurentian Great Lakes for the 2003-2016 period. We generated load–response relationships and response matrices that relate the steady state total phosphorus concentrations to external total phosphorus loads, for the whole Lake Erie system and for the individual basins (Lake St. Clair, western basin, central basin, eastern basin) and connecting channels (St. Clair River, Detroit River). These relationships and matrices provide a simple but robust framework to gauge the potential response of total phosphorus concentrations to total phosphorus load reductions, such as the 40% reduction proposed for Lake Erie under the Canada-United States Great Lakes Water Quality Agreement. The mass balance analysis further highlights the importance of inter-basin total phosphorus transfers. For example, around 70% of the total phosphorus concentration in the eastern basin is contributed by inflow from the central basin. Consequently, total phosphorus load abatements in watersheds upstream of the eastern basin, rather than in the direct watershed itself, will have the greatest impact on the eastern basin's concentration. Overall, our results illustrate how simple mass balance calculations can provide useful guidance to efforts to manage phosphorus enrichment of lakes.