Probabilistic Behavior of Water-Quality Loads

A theoretical model is introduced for describing the mechanistic and probabilistic structure of observations of streamflow Q, concentration C, and constituent loads L. The model has application to many water-quality management problems including load estimation, water-quality monitoring network design and total maximum daily load assessment. The statistical behavior of streamflow, concentration, and load is described and expressions are derived for the coefficient of variation of daily concentrations and loads assuming a bivariate lognormal model. The model provides a first-order approximation to continuous empirical observations of C, Q, and L from four watersheds in the Great Lakes Region. The utility of the model is demonstrated by quantifying the amount of "spurious" correlation between load and discharge, by documenting factors which influence bias in water-quality load estimates and those which give rise to increased/decreased variability in water-quality loads and concentrations.