Consideration of variability and uncertainty in phosphorus total maximum daily loads for lakes

A simplified framework for considering variability and uncertainty in developing lake phosphorus total maximum daily, loads (TMDLs) is demonstrated. Explicit consideration of these factors can increase the probability that TMDL implementation will meet a defined water quality goal at an acceptable frequency. Although a lake goal is typically expressed as a seasonal or yearly average phosphorus concentration, effects of temporal variations can be captured by correlating average phosphorus concentrations with the frequency of algal blooms (defined by extreme values of chlorophyll a) or the frequency, of exceeding numeric water quality standards that are directly linked to algal blooms, such as hydrogen ion concentration or transparency. The margin of safety (MOS) required to achieve the lake goal at a defined frequency and with a defined confidence level can be estimated by including stochastic terms in the phosphorus balance equation to reflect variability and uncertainty. Given limitations in the data and models typically used in developing TMDLs, the cost of the MOS, expressed in terms of percent of the total allocated load or safety factors in the design of control measures, can be large. The MOS would be expected to increase with the percent load reduction required under the TMDL, as the forecast loads become increasingly dependent on assumptions regarding the performance of best management practices or other measures for reducing loads. The magnitude and cost of the MOS can be reduced by implementing TMDLs in an iterative fashion with ongoing data collection, and, model refinement to reduce uncertainties associated with forecasting the performance of phosphorus load controls and lake responses.