Bias and variance of planning level estimates of pollutant loads

Abstract

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 extensive literature on sampling properties, bias, and precision of loads estimated from monitoring data, the unconstrained and often inconsistent alternatives for choosing 'representative' runoff volumes and concentrations for use in planning level estimates limit the opportunities of generalizing analytical 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 variance of planning level load estimators are derived both under mild parametric assumptions and using a distribution free approximation. Common use of the mean, median, or geometric mean of event concentrations is shown to result, 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 characteristic concentration in planning level load estimates. While analogous to load estimation from monitoring data, the results presented here are distinct 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 with a simple example drawn from Chesapeake Bay.