Bias and variance of planning level estimates of pollutant loads

Planning level techniques typically use the product of runoff volume and a characteristic concentration to estimate mean annual contaminant loads when monitoring data are inadequate or unavailable. In contrast to the extensiv e literature on sampling properties, bias, and precision of loads estimated from monitoring data, the unconstrained and often inconsistent alternative s for choosing "representative" runoff volumes and concentrations for use i n planning level estimates limit the opportunities of generalizing analytic al results on the properties of these estimators; The ease with which these simple load estimates can be calculated belies their inherent uncertainty, motivating this examination of their bias and variability. The mean and va riance of planning level load estimators are derived both under mild parame tric assumptions and using a distribution free approximation. Common use of the mean, median, or geometric mean of event concentrations is shown to re sult, in general, in biased estimates of the mean annual load. Sensitivity analysis of the mean and variance demonstrates the need to incorporate the relative variance as well as the correlation of cumulative discharge and ch aracteristic concentration in planning level load estimates. While analogou s to load estimation from monitoring data, the results presented here are d istinct and unrelated to retransformation or sampling biases that have been well documented in the river load literature. Substantive implications for regional assessments, planning, and watershed management are illustrated w ith a simple example drawn from Chesapeake Bay.