Ratio Estimators

Beale's ratio estimator has been used to estimate nutrient loads entering the Great Lakes [ Dolan et al., 1981; Richards and Holloway, 1987; Preston et al., 1989]. The ratio estimator assumes a constant ratio between concentration and discharge. It is defined by:

where

is Beale's Ratio Estimator;

is the average water discharge during the period for which an estimate is desired;

is the average of the sampled loads;

is the average of the discharges when samples were collected;

;

.

Ratio estimators, like the rating curve, are essentially empirical. They have no statistical or physical justification. Researchers recommend stratifying the data, and applying the ratio estimator separately to each stratum [ Preston, et al., 1989]. No methods have been published for estimating the bias and precision of ratio estimators.