A review and reassessment of lake phosphorus retention and the nutrient loading concept

1. We conducted a statistical reassessment of data previously reported in the lake total phosphorus (TP) input/output literature (n = 305) to determine which lake characteristics are most strongly associated with lake phosphorus concentration and retention. We tested five different hypotheses for predicting lake TP concentrations and phosphorus retention. 2. The Vollenweider phosphorus mass loading model can be expressed as: TPout = TPin/(1 + sigma tau(w)), where TPin is the flow-weighted input TP concentration, tau(w) is the lake hydraulic retention time and sigma is a first-order rate constant for phosphorus loss. 3. The inflow-weighted TP input concentration is a moderately strong predictor (r(2) = 0.71) of lake phosphorus concentrations when using log-log transformed data. Lake TP retention is negatively correlated with lake hydraulic retention time (r(2) = 0.35). 4. Of the approaches tested, the best fit to observed data was obtained by estimating sigma as an inverse function of the lake's hydraulic retention time. Although this mass balance approach explained 84% of the variability in log-log transformed data, the prediction error for individual lakes was quite high. 5. Estimating sigma as the ratio of a putative particle settling velocity to the mean lake depth yielded poorer predictions of lake TP (r(2) = 0.77) than the approach described above, and in fact did not improve model performance compared with simply assuming that sigma is a constant for all lakes. 6. Our results also demonstrate that changing the flow-weighted input concentration should always have a directly proportionate impact on lake phosphorus concentrations, provided the type of phosphorus loaded (e.g. dissolved or particulate) does not vary.