INCORPORATING NATURAL VARIABILITY,UNCERTAINTY, AND RISK INTO WATER QUALITY EVALUATIONS USING DURATION CURVES1

ABSTRACT: Quantifying natural variability, uncertainty, and risk with minimal data is one of the greatest challenges facing those engaged in water quality evaluations, such as development of total maximum daily loads (TMDL), because of regulatory, natural, and analytical constraints. Quantification of uncertainty and variability in natural systems is illustrated using duration curves (DCs), plots that illustrate the percent of time that a particular flow rate (FDC), concentration (CDC), or load rate (LDC; “TMDL”) is exceeded, and are constructed using simple derived distributions. Duration curves require different construction methods and interpretations, depending on whether there is a statistically significant correlation between concentration (C) and flow (Q), and on the sign of the C‐Q regression slope (positive or negative). Flow DCs computed from annual runoff data vary compared with an FDC developed using all data. Percent exceedance for DCs can correspond to risk; however, DCs are not composed of independent quantities. Confidence intervals of data about a regression line can be used to develop confidence limits for the CDC and LDC. An alternate expression to a fixed TMDL is suggested as the risk of a load rate being exceeded and lying between confidence limits. Averages over partial ranges of DCs are also suggested as an alternative expression of TMDLs. DCs can be used to quantify watershed response in terms of changes in exceedances, concentrations, and load rates after implementation of best management practices.