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.

The role of phosphorus and nitrogen on chlorophyll a: Evidence from hundreds of lakes.

The effect of nutrients on phytoplankton biomass in lakes continues to be a subject of debate by aquatic scientists. However, determining whether or not chlorophyll a (CHL) is limited by phosphorus (P) and/or nitrogen (N) is rarely considered using a probabilistic method in studies of hundreds of lakes across broad spatial extents. Several studies have applied a unified CHL-nutrient relationship to determine nutrient limitation, but pose a risk of ecological fallacy because they neglect spatial heterogeneity in ecological contexts. To examine whether or not CHL is limited by P, N, or both nutrients in hundreds of lakes and across diverse ecological settings, a probabilistic machine learning method, Bayesian Network, was applied. Spatial heterogeneity in ecological context was accommodated by the probabilistic nature of the results. We analyzed data from 1382 lakes in 17 US states to evaluate the cause-effect relationships between CHL and nutrients. Observations of CHL, total phosphorus (TP), and total nitrogen (TN) were discretized into three trophic states (oligo-mesotrophic, eutrophic, and hypereutrophic) to train the model. We found that although both nutrients were related to CHL trophic state, TP was more related to CHL than TN, especially under oligo-mesotrophic and eutrophic CHL conditions. However, when the CHL trophic state was hypereutrophic, both TP and TN were important. These results provide additional evidence that P-limitation is more likely under oligo-mesotrophic or eutrophic CHL conditions and that co-limitation of P and N occurs under hypereutrophic CHL conditions. We also found a decreasing pattern of the TN/TP ratio with increasing CHL concentrations, which might be a key driver for the role change of nutrients. Previous work performed at smaller scales support our findings, indicating potential for extension of our findings to other regions. Our findings enhance the understanding of nutrient limitation at macroscales and revealed that the current debate on the limiting nutrient might be caused by failure to consider CHL trophic state. Our findings also provide prior information for the site-specific eutrophication management of unsampled or data-limited lakes.

Internal cycling, not external loading, decides the nutrient limitation in eutrophic lake: A dynamic model with temporal Bayesian hierarchical inference.

Lake eutrophication is associated with excessive anthropogenic nutrients (mainly nitrogen (N) and phosphorus (P)) and unobserved internal nutrient cycling. Despite the advances in understanding the role of external loadings, the contribution of internal nutrient cycling is still an open question. A dynamic mass-balance model was developed to simulate and measure the contributions of internal cycling and external loading. It was based on the temporal Bayesian Hierarchical Framework (BHM), where we explored the seasonal patterns in the dynamics of nutrient cycling processes and the limitation of N and P on phytoplankton growth in hyper-eutrophic Lake Dianchi, China. The dynamic patterns of the five state variables (Chla, TP, ammonia, nitrate and organic N) were simulated based on the model. Five parameters (algae growth rate, sediment exchange rate of N and P, nitrification rate and denitrification rate) were estimated based on BHM. The model provided a good fit to observations. Our model results highlighted the role of internal cycling of N and P in Lake Dianchi. The internal cycling processes contributed more than external loading to the N and P changes in the water column. Further insights into the nutrient limitation analysis indicated that the sediment exchange of P determined the P limitation. Allowing for the contribution of denitrification to N removal, N was the more limiting nutrient in most of the time, however, P was the more important nutrient for eutrophication management. For Lake Dianchi, it would not be possible to recover solely by reducing the external watershed nutrient load; the mechanisms of internal cycling should also be considered as an approach to inhibit the release of sediments and to enhance denitrification.