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.

Combined inverse modeling approach and load duration curve method for variable nitrogen total maximum daily load development in an agricultural watershed

“…Then the duration curves on catchment export load, TMDL, requiring load reduction (the difference between the catchment export load and the TMDL) and required percent reduction (the ratio between the required load reduction and the catchment export load) were synchronously developed through classification with respect to the stream flow for a particular day to describe their variability. Finally, the percent exceedance for a set requiring load or percent reduction was used to evaluate the uncertainty of exceeding the TMDL or target in-stream concentration for nutrients (Bonta and Cleland 2003).…”

“…The total maximum daily load (TMDL) program, which incorporates the control of NPS into water quality management, has been widely applied in the USA (USACE 2006) and other countries (Kang et al 2006;Chen et al 2009;Hsu et al 2009). Due to the significant variability in TMDL magnitude with changing stream flows, TMDL development must be based on the designed water flows to assure that water quality is compliant with the target across a range of flow conditions (Bonta and Cleland 2003;Chen et al 2007a, b).…”

Changes in concentration–discharge regression parameters due to coal mining and reclamation activities / Changements dans les paramètres de régression entre concentration et débit, causés par l’exploitation minière de charbon et des activités de reconversion

“…More representative average concentrations and load rates can be computed, compared with using simple averages of raw data. Estimates of the percent of time that concentrations and load rates are exceeded can also be determined (Bonta & Cleland, 2003). Average concentrations and load rates are dependent on measured discharge.…”

“…A FDC graph shows the percent of time that flow rates are exceeded at a point in the stream channel. When there is a relation between concentration (C) and instantaneous discharge (Q), loadduration curves and concentration-duration curves can be constructed by combining the statistical regression relations between constituent C and Q with the discharges comprising the FDC (Bonta & Cleland, 2003). However, even if no relation exists between C and Q for an individual constituent, the distribution of C data can be interpreted using the frequency distribution of raw data in a similar manner, except that concentrations are random at any flow rate.…”

Uncertainties in Flow Duration Curves in anthropized catchments

“…Its temporal and spatial heterogeneity make it necessary to consider average values that causes uncertainties in modelling and forecasting catchment water balances and river flow rates [5][6][7]. More, uncertainty may be also associated to possible non-stationarity of hydrological systems, due to the climate change [8,9] and to anthropic modification of soil use and of hydrographic network.…”