Maximum Likelihood Estimation of Water Quality Concentrations from Censored Data

Abstract

Concentration data for water quality parameters reported as less than the detection limit (DL) may be considered to have come from a censored probability distribution. Traditionally, if it was necessary to assign a value to a sample reported as less than DL, various ad hoc methods were used such as selecting arbitrary values (0, 1/2 DL, DL, etc.). As analytical methods improved, DL's became smaller and the choice of ad hoc methods had less of an effect. However, there are two cases where the choice of estimation method is still a problem: (1) it is desired to calculate a differential loading (i.e. downstream minus upstream); (2) a loading estimate is desired in a tributary whose flow rate is extremely large. Both cases apply in connecting channels such as the Niagara and Detroit Rivers. The background for development of a nonarbitrary method for handling these situations is presented and the resultant estimator is used on water quality data from the connecting channels and Lake Ontario. The equations for confidence intervals for estimated mean concentrations or loadings are also presented. The effect of changing the DL is discussed.