Phosphorus Retention in Lakes: A Critical Reassessment of Hypotheses and Static Models

Various hypotheses and models for phosphorus (P) retention in lakes are reviewed and 39 predictive models are assessed in three categories, namely mechanistic, semi-mechanistic, and strictly-empirical models. A large database consisting of 738 data points is gathered for the analyses. Assessing four pairs of competing hypotheses used in mechanistic models, we found that (i) simulating lakes as mixed-flow reactor is superior to plug-flow reactor hypothesis; (ii) modeling P loss as a second-order reaction outperforms the first-order reaction; (iii) P loss is better explained as a removal process throughout the lake volume than as a settling process across the sediments; and (iv) considering a fraction of P loading is associated with fast settling particles enhances lake total phosphorus (TP) predictions. Due to the systematic approach used for combining the hypotheses, some models are for the first time developed and assessed. For instance, the preeminent mechanistic model combines, for the first time, the second-order reaction hypothesis with the hypothesis that a specific proportion of P loading settles rapidly at the lake entrance. Results also showed that semi-mechanistic models outperform both mechanistic and strictly-empirical models since they take the form of a mechanistic model based on the physical representation of the lakes and utilize statistically acquired equations for unknown parameters. The best-fit model is a semi-mechanistic model that adopts the mixed-flow reactor hypothesis with a second-order volumetric reaction rate that is calculated as a non-linear function of inflow TP concentration, lake average depth, and water retention time. This model predicts 77.8% of the variability of log10-transformed lake TP concentration, which is 4.2% higher than the best mechanistic model and 0.8% higher than the best strictly-empirical model. The findings of this study not only shed light on the understanding of P retention in lakes but also can be useful for assessment of data-limited lakes and large-scale hydrological models to simulate the P cycle.