Rethinking the lake trophic state index

Lake trophic state classifications provide information about the condition of lentic ecosystems and are indicative of both ecosystem services (e.g., clean water, recreational opportunities, and aesthetics) and disservices (e.g., cyanobacteria blooms). The current classification schemes have been criticized for developing indices that are single-variable based (vs. a complex aggregate of multi-variables), discrete (vs. a continuous), and/or deterministic (vs. an inherently random). We present an updated lake trophic classification model using a Bayesian multilevel ordered categorical regression. The model consists of a proportional odds logistic regression (POLR) that models ordered, categorical, lake trophic state using Secchi disk depth, elevation, nitrogen concentration (N), and phosphorus concentration (P). The overall accuracy, when compared to existing classifications of trophic state index (TSI), for the POLR model was 0.68 and the balanced accuracy ranged between 0.72 and 0.93. This work delivers an index that is multi-variable based, continuous, and classifies lakes in probabilistic terms. While our model addresses aforementioned limitations of the current approach to lake trophic classification, the addition of uncertainty quantification is important, because the trophic state response to predictors varies among lakes. Our model successfully addresses concerns with the current approach and performs well across trophic states in a large spatial extent.

Example application of a continuous lake trophic state index on lakes with limited data

Lake trophic state indices have long been used to provide a measure of the trophic state of lakes. Over time it has been determined that these indices perform better when they utilize multiple metrics and provide a continuous measurement of trophic state. We utilize such a method for trophic state that is based upon a Proportional Odds Logistic Regression (POLR) model and extend this model with a Bayesian multilevel model that predicts nutrient concentrations from universally available GIS data. This Bayesian multilevel model provides relatively accurate measures of trophic state and has an overall accuracy of 60%. The approach illustrates a method for estimating a continuous, mutli-metric trophic state index for any lake in the United States. Future improvements to the model will focus on improving overall accuracy and use variables that are more sensitive to change over time.

Example application of a continuous lake trophic state index on lakes with limited data

Lake trophic state indices have long been used to provide a measure of the trophic state of lakes. Over time it has been determined that these indices perform better when they utilize multiple metrics and provide a continuous measurement of trophic state. We utilize such a method for trophic state that is based upon a Proportional Odds Logistic Regression (POLR) model and extend this model with a Bayesian multilevel model that predicts nutrient concentrations from universally available GIS data. This Bayesian multilevel model provides relatively accurate measures of trophic state and has an overall accuracy of 60%. The approach illustrates a method for estimating a continuous, mutli-metric trophic state index for any lake in the United States. Future improvements to the model will focus on improving overall accuracy and use variables that are more sensitive to change over time.