Page Banner

United States Department of Agriculture

Agricultural Research Service

Title: Incorporating Natural Variability, Uncertainty, and Risk into Water-Quality Evaluations Using Duration Curves

Authors
item Bonta, James
item Cleland, Bruce - AM. CLEAN WATER FOUND

Submitted to: Journal of the American Water Resources Association
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: September 16, 2003
Publication Date: December 1, 2003
Citation: BONTA, J.V., CLELAND, B. INCORPORATING NATURAL VARIABILITY, UNCERTAINTY, AND RISK INTO WATER-QUALITY EVALUATIONS USING DURATION CURVES. JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION. 2003. v.39(6). p.1481-1496.

Interpretive Summary: Quantifying natural variability, uncertainty, and risk is one of the greatest challenges facing those engaged in developing total maximum daily loads (TMDLs). TMDLs are regulated levels of the maximum allowable chemical or sediment load that a stream can assimilate for a specific use. There is one daily-load value for each chemical constituent of interest, and often this value does not have information about how often the value is expected to occur and what errors there may be. Duration curves (DCs) are tools that can solve some of these problems, and are plots of percent of time that flow rates, concentrations, or chemical load rates are exceeded. Flow (FDC), concentration (CDC), and load-rate (LDC) duration curves can be developed. Often there are mathematical relationships between flow rate and chemical constituent or sediment concentration in a stream. Some concentrations will increase with increasing flow rate and some will decrease, and for some constituents, there is no defined relationship. DCs require different interpretations, depending on whether there is correlation between concentration and flow rate, and whether the concentration increases or decreases with flow rate. FDCs computed from annual runoff data from experimental watersheds can vary from year to year, compared with a FDC that is developed from data including all years, causing uncertainty in the analysis of DCs. Uncertainty in the relationships between concentration and flow can be expressed mathematically and included in CDCs and LDCs. This study visually shows how an alternative interpretation of DCs can be obtained that quantifies natural uncertainty and variability in flow rates and concentrations. DCs can be used to show how much response there is in a watershed after implementation of best-management practices to improve water quality. DCs are a good tool for visualizing complex water quality and hydrology relationships to lay persons. Research needs are outlined that will lead to improved utility of DCs. The research will benefit state and Federal agencies involved in defining TMDLs, and watershed focus groups.

Technical Abstract: Quantifying natural variability, uncertainty, and risk is one of the greatest challenges facing those engaged in TMDL development because of regulatory, natural, and analytical constraints. Duration curves (DCs) are tools that can solve some of these problems, as are plots of percent exceedance versus flow rate, concentration, or load rate. DCs are graphically presented by means of simple derived distributions - the distribution of a new variable is derived from the distribution of another variable and a function between the two variables. Flow (FDC), concentration (CDC), and load-rate (LDC) duration curves can be developed. DCs require different construction methods and interpretations, depending on whether there is statistically significant correlation between C and Q, and the sign of the C-Q regression slope (positive or negative). Percent exceedance for DCs corresponds to risk for true probability distributions, however, DCs are not composed of independent quantities. FDCs computed from annual runoff data vary compared with a composite FDC. Confidence intervals of data about regressions can be used to develop confidence limits for the CDC and LDC. DCs provide an alternate expression to a fixed TMDL and quantifies natural uncertainty and variability as a load rate that is exceeded a percentage of the time, lying between confidence limits at a specified confidence level. DCs potentially can be used to quantify watershed response in terms of changes in exceedances, concentrations, and load rates after implementation of best-management practices. Research needs are outlined that may lead to improved utility of DCs.

Last Modified: 7/31/2014
Footer Content Back to Top of Page