Modeling lake recovery lag times following influent phosphorus loading reduction.

Internal feedback of nutrients may impede timely improvement in lake water quality. We describe a parsimonious, mechanistic framework for modeling lag times to recovery of phosphorus-enriched lakes, given decreases in external loading. The approach assumes first-order kinetics in a two-compartment system taking account of phosphorus storage in and loading from benthic sediments. Bayesian parameter modeling, published sediment phosphorus release rates, and a prior dynamic calibration for one lake are used to derive estimates of key parameters. Applications are developed for an example lake, as are maps displaying estimated times to attainment of a phosphorus criterion in lakes across a midwestern state, and lag time estimates for fractional water column concentration decrease averaged over HUC-8s. Mean lag times to 50 and 75% declines in water column phosphorus concentration were estimated as 13.1 and 39.0 years respectively, across more than 70,000 lentic water bodies in the continental United States.