An analysis of sampling programs to evaluate compliance with numerical standards: total phosphorus in Platte Lake, MI

Abstract

Platte Lake has a numerical standard for total phosphorus mandated in 2000 following judicial proceedings that requires volume weighted total phosphorus to be below 8 mg/m3 95% of the time. Compliance has been evaluated using an extensive monitoring program that collects samples at roughly biweekly intervals. Analysis indicates that the lake has been and remains in violation of the numerical standard. This large dataset provides a unique opportunity to utilize statistical methods to evaluate compliance while controlling the Type I and Type II errors and to determine the minimum number of samples needed to detect changes in total phosphorus concentrations. Regression and analysis of variance were used to improve the sampling design. Similar techniques were used to design optimal monitoring programs for hypothetical lakes having a large range of total phosphorus concentrations and trophic conditions. Lakes with low total phosphorus concentrations require relatively few measurements during the year, but laboratory uncertainty necessitates multiple replicates. Lakes with higher total phosphorus concentrations require frequent sampling to obtain an acceptable estimate of the annual average concentration because large temporal and depth gradients are expected. Fewer replicates are indicated because laboratory measurements of higher concentrations are more reliable. A review of several national-scale studies indicates that few lakes have sufficient data to perform credible compliance evaluation or reliably detect changes in lake concentrations in response to shifts in watershed loads. Further, many laboratories have limited capability to measure the low concentrations of total phosphorus typically associated with oligotrophic lakes.