Cross-lake comparisons of physical and biological settling of phosphorus: A phosphorus budget model with Bayesian hierarchical approach

Phosphorus (P) is viewed as one limiting factor for phytoplankton growth in freshwater lakes. Simple budget models are very efficient for cross-lakes comparisons, while neglecting key distinction between algal P and other forms. Here, a phosphorus budget model was developed to balance between process resolution and cross-system applicability, in which lake total phosphorus (TP) was divided into algal-bound P and other fractions. The model was tested for six lakes on the Yunnan Plateau, China and the Markov Chain Monte Carlo (MCMC) algorithm of Bayesian hierarchical inference was employed for parameters estimation. The model results showed that (a) both algal species composition and P loading are key factors that influence the efficiency of converting phosphorus into algal P; (b) variability of the settling velocity of non-algal P and algal P decreases with increasing TP concentrations, representing a lower capacity for restoration; and (c) settling velocity declined exponentially with the increase of trophic state index, indicating a potential rapid rise of P removal rates during eutrophication restoration. Two conceptual models were then proposed to identify the prior countermeasures for eutrophication restoration in the lakes: (a) for Conceptual Model II, e.g. Lake Lugu, increasing the physical settling of phosphorus should be given priority to; (b) for Conceptual Model I, including the other five lakes, increasing the biological settling of phosphorus should be paid extra attention.