Modeling lake recovery lag times following influent phosphorus loading reduction
Lag times in lake response to nutrient reduction efforts make it challenging for stakeholders to develop effective strategies for management and resource allocation. Given the influence of biogeochemical internal cycling and legacy nutrients accumulated within the sediments of many lakes, improvements in water column nutrient concentrations as a result of input reductions may not be detectable for a long time. This paper describes the development of a methodology for estimating lag times to recovery of phosphorus-enriched lakes, given a hypothetical decrease in influent phosphorus loading. The approach, which is based on first-order kinetics in a two-compartment system, takes dynamic account of phosphorus storage in, and loading from, the benthic sediments in providing a means of estimating the time required for water column phosphorus to decline to a lower concentration. Bayesian parameter estimation employing steady state input/output data and published sediment phosphorus release rates are used to derive distributions of key parameters. Applications of the approach are developed for an example lake, as are maps graphically displaying estimated times to attainment of a phosphorus water concentration criterion in thousands of lakes across a midwestern state in the U.S., and time estimates for fractional water column concentration decreases spatially averaged across HUC-8 hydrologic units for more than 70,000 lakes across the continental United States. An advantage of this approach is the ability to apply multiple scenarios of influent reductions and target concentrations to one lake or numerous lakes to improve understanding of lag times and to inform development of expectations for lake recovery.