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

Abstract

1. We conducted a statistical reassessment of data previously reported in the lake total phosphorus (TP) input/output literature (n ¼ 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: TP out ¼ TP in / (1 + rs w ), where TP in is the flow-weighted input TP concentration, s w is the lake hydraulic retention time and r is a first-order rate constant for phosphorus loss. 3. The inflow-weighted TP input concentration is a moderately strong predictor (r 2 ¼ 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 ¼ 0.35). 4. Of the approaches tested, the best fit to observed data was obtained by estimating r 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 r as the ratio of a putative particle settling velocity to the mean lake depth yielded poorer predictions of lake TP (r 2 ¼ 0.77) than the approach described above, and in fact did not improve model performance compared with simply assuming that r 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.

Global phosphorus retention by river damming

“…As shown in Fig. S1, the modelpredicted R TP and R RP values exhibit positive trends with the hydraulic residence time, τ r , as expected from the literature (28)(29)(30). The trends are fitted to the classic Vollenweider model for P sequestration in lakes (Eq.…”

“…2). For TP retention in lakes, σ has been related to the relative thickness of the photic zone and the average particle settling velocity (30,32,33). Nonlinear least squares regressions yield the following statistically significant average values of σ: 0.801 y −1 for R TP (P < 0.05) and 0.754 y −1 for R RP (P < 0.05).…”

“…P retention in lakes and reservoirs correlates with the hydraulic residence time (τ r ) (28)(29)(30). Accordingly, τ r explains more than 45% of the variability of the R TP and R RP values generated by 6,000 Monte Carlo iterations of the P mass balance model.…”

A model‐based assessment of non‐compliance of phosphorus standards for lakes in England and Wales

“…A high number of similar empirical steady state mass balance models have been developed (e.g., Brett and Benjamin, 2008) but the OECD model has been calibrated against the widest range of data and has achieved the highest r 2 , with a value of 0.86 for log transformed predicted and measured concentrations. The model ignores differences between lakes in the proportions of soluble and particulate phosphorus load, stratification, seasonal variation of phosphorus fluxes and the morphology of the water bodies and is not applicable for lakes with high internal loading which are not in a steady state (Hakanson, 1999).…”

Historical changes (1905–2005) in external phosphorus loads to Loch Leven, Scotland, UK

“…After the reduction in external input, the TP retention rate fell to about 15%. Given that TP retention in lakes tends to be negatively correlated with hydraulic retention time (Brett & Benjamin, 2008), and that the latter two years were much drier than the earlier years, this suggests that that the lake is now retaining significantly less TP from external sources than it was in the 1970s and 1980s. However, total (rather than relative) export of TP from the lake has changed very little from year to year.…”