Approximate Dynamic Lake Phosphorus Budget Models

Impoundments or natural lakes having short hydraulic detention times may become eutrophic through anthropogenic nutrient loading episodes. Subsequent lake recovery may be influenced by nutrient transport from the lake bottom to the water column. Order‐of‐magnitude analysis is used to derive simple mathematical models of eutrophic lake recovery. Total phosphorus concentration (P) is used as an indicator of lake water quality. Sedimentation of particulate P from the water column and cycling from lake sediments control the rate of change of lake water P in response to a step change in external P loading. The rate of P desorption from the solid phase is more important than film transport rates across the lake bottom/water column boundary. Comparisons between exact and approximate longterm predictions of lake water total phosphorus concentration generally differ by less than 0.2%. The approximate models are convenient because they are more compact in form and appear to behave similarly to an exact analytical solution to the lake model.