Exploring the type and strength of nonlinearity in water quality responses to nutrient loading reduction in shallow eutrophic water bodies: Insights from a large number of numerical simulations.

Reducing the load of nutrients is essential to improve water quality while water quality may not respond to the load reduction in a linear way. Despite nonlinear water quality responses being widely mentioned by studies, there is a lack of comprehensive assessment on the extent and type of nonlinear responses considering the seasonal changes. This study aimed to measure the strength of nonlinearity of theoretically possible water quality responses and explore their potential types in shallow eutrophic water bodies. Hereto, we generated 14,710 numerical water body cases that describe the water quality processes using the Environmental Fluid Dynamics Code (EFDC) and applied eight load reduction scenarios on each water body case. Inflows are simplified from Lake Dianchi. The climate conditions consider three cases: Lake Dianchi, Wissahickon Creek, and Famosa Slough. We then developed a nonlinearity strength indicator to quantify the strength and frequency of nonlinear water quality responses. Based on the quantification of nonlinearity, we clustered all the samples of water quality responses using K-Means, an unsupervised Machine Learning algorithm, to find the potential types of nonlinear water quality responses for TN (total nitrogen), TP (total phosphorus), and Chla (chlorophyll a). Results show linear or near-linear response types account for 90%, 69%, and 20% of TN, TP, and Chla samples respectively. TP and Chla could perform more types of nonlinearity. Representative nonlinear water quality responses include disproportional improvement, peak change (disappear, move forwards or afterward), and seasonal deterioration of TN after load reduction. This study would contribute to the current understanding of nonlinear water quality responses to load reduction and provide a basis to study under which conditions the nonlinear responses may emerge.