3/16/04

**Publication List Related to**

**Total Maximum Daily Loads (TMDLs)**

Publications and abstracts are listed in reverse chronological order. A
limited number of reprints are available, and can be requested by
referring to the NAEW number. Use your browser's "find" feature to
search for words of interest. For more information, please contact:

> James V. Bonta
>
> Research Hydraulic Engineer
>
> N. Appalachian Experimental Watershed
>
> PO Box 488
>
> Coshocton, Ohio 43812
>
> USA
>
> email: <bonta@coshocton.ars.usda.gov>
>
> phone: 740-545-6349
>
> fax: 740-545-5125

Bonta, J.V. and B. Cleland. 2003. Incorporating natural variability,
uncertainty, and risk into water quality evaluations using duration
curves. J. of the American Water Resources Association 39(6):1481-1496.
**(NAEW #390)**

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 DCs. Duration curves (DCs) are 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 by
using simple derived distributions. DCs 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).
FDCs computed from annual runoff data vary compared with a FDC developed
by 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.

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Bonta, J.V. 2002. Framework for estimating TMDLs with minimal data.
Proceedings of the ASAE Conference on Watershed Management to Meet
Emerging TMDL Environmental Regulations, Fort Worth, Texas. March 11-13,
2002. pp. 6-12. **(NAEW #372)**

Abstract

Current regulations specify the derivation of total maximum daily loads
(TMDLs) for surface waters. Yet these standards are often derived from
incomplete information. In some cases these quantities are assigned to
watersheds for which there are little data, and are established in terms
of loads when only concentration data are available. Furthermore, they
are often assigned under conservative conditions with no estimation of
risk and uncertainty of the estimate. Flow-duration curves and
regressions between flow rate and constituent concentration have
historically been used to compute average total loads to determine
water-quality trends. However, intermediate calculations in this
methodology, not often used, have utility for TMDL estimation. From
these intermediate calculations, one can determine the percent of time
that a concentration and load (TMDL) will be exceeded, the duration of
concentrations/loads, etc. The method can be used by itself or as a
supplement to more complex watershed modeling. It is useful for
determining the range of concentrations expected from a watershed, for
characterizing actual in-stream conditions, and for tracking actual
in-stream conditions after implementation of best-management practices.
The method is simple to use, and is promising for areas where there are
no flow data, and for which there are only a few samples. The concepts
of the method are presented, along with those for using this method when
data are scanty and for determining uncertainty in the TMDL estimates.

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