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V UNITED STATES ENVIRONMENTAL PROTECTION AGENCY
# ?, WASHINGTON, D.C. 20460
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OFFICE OF WATER
June 22, 2007
Dear Colleague:
Today we are making available the technical document "Options for the Expression of Daily Loads in
TMDLs." This document was drafted to provide technically sound options for developing daily load
expressions as a routine process in TMDLs calculated using allocation time frames greater than daily
(e.g., annual, monthly, seasonal). The document is written for TMDL practitioners who are familiar with
the relevant technical approach and regulatory requirements pertaining to TMDLs.
In November 2006 EPA issued the Memorandum "Establishing TMDL "Daily" Loads in Light of the
Decision by the U.S. Court of Appeals for the D.C. Circuit in Friends of the Earth, Inc. v. EPA et. al., No.
05-5015 (April 25, 2006) and Implications for NPDES permits," which recommends that all TMDLs and
associated load allocations and wasteload allocations include a daily time increment in conjunction with
other appropriate temporal expressions that may be necessary to implement the relevant water quality
standard. That Memorandum also indicated that additional technical information would be forthcoming,
such as today's document.
Although this document is a draft, EPA intends that TMDL practitioners will make use of the technical
information in developing TMDLs and provide feedback on the approaches as a result of their experience.
Comments on the document should be sent to Rosaura Vega (vega.rosaura@epa.gov) and Mike Haire
(haire.michael@epa.gov) by February 1, 2008.
Thanks again for your interest,
John Goodin /s/
Chief, Watershed Branch
Attachment
Copy of the document: "Options for Expressing Daily Loads in TMDLs/'
For more information on this technical document, please refer to the above contacts or the appropriate
Regional TMDL coordinator:
Region 1 - Steve Winnett (winnett. steven@epa. gov)
Region 2 - Antony Tseng (tseng. antonv@epa. gov)
Region 3 - Tom Henry (henry ,thomas@epa. gov)
Region 4 - William Melville (melville.william@epa.gov)
Region 5 - Dean Maraldo (maraldo.dean@epa.gov)
Region 6 - Curry Jones (iones.currv@epa.gov)
Region 7 - Bruce Perkins (perkins ,bruce@epa. gov)
Region 8 - James Ruppel (ruppel.iames@epa.gov)
Region 9 - Peter Kozelka (kozela.peter@epa.gov) / Terry Fleming (fleming.terrance@epa.gov)
Region 10 - Bruce Cleland (cleland.bruce@epa.gov) / Laurie Mann (mann.laurie@epa.gov)
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Options for Expressing Daily
Loads in TMDLs
U.S. Environmental Protection Agency
Office of Wetlands, Oceans & Watersheds
June 22, 2007
DRAFT
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Disclaimer
This document provides technical information to TMDL practitioners who are familiar with the relevant
technical approaches and legal requirements pertaining to developing TMDLs and refers to statutory and
regulatory provisions that contain legally binding requirements. This document does not substitute for
those provisions or regulations, nor is it a regulation itself. Thus, it does not impose legally binding
requirements on EPA or States, who retain the discretion to adopt approaches on a case-by-case basis that
differ from this information. Interested parties are free to raise questions about the appropriateness of the
application of this information to a particular situation, and EPA will consider whether or not the
technical approaches are appropriate in that situation.
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Options for Expressing Daily Loads in TMDLs
Contents
Executive Summary vii
Effect of Daily Loads on TMDL Development Methodologies vii
Effect of Daily Loads on National Pollutant Discharge Elimination System Permits viii
Additional Benefits of Daily Load Identification viii
Types of Daily Load Expressions viii
Why Was this Document Developed? 1
Technical Background 1
Document Purpose 2
Document Organization 3
1. Process for Deriving Daily Load Expressions from Typical Non-daily TMDL Analyses..4
Step 1. Evaluate Non-daily TMDL Approach 7
Step 2. Develop Daily Dataset 8
Step 3. Select Daily Load Expression 9
2. Developing a Daily Dataset from a Non-daily Analysis 12
Developing Daily Datasets from Commonly Used TMDL Approaches 13
Dynamic Models 13
Load Duration Model 13
General Watershed Models 14
Export Coefficients 15
Steady-State and Mass-Balance Models 15
Options for Estimating Flows to Support Development of the Daily Load Dataset 16
Estimating Flows from Nearby USGS Gages 16
Estimating Flows from Existing Models 17
Estimating Flows Using Rainfall Distribution 17
Estimating Flows Using Regression Equations 17
3. Selecting the Daily Load Expression 18
Types of Daily Load Expressions 18
Static Daily Load Expressions 18
Using the Daily Load Dataset to Identify a Maximum Daily Load 19
Using Statistical Analysis to Identify a Maximum Daily Load 19
Variable Daily Load Expressions 21
Flow Variable 21
Temporally Variable 22
Considerations for Selecting the Appropriate Daily Load Expression 23
Pollutant Source Types and Critical Conditions 23
Source Behavior. 25
Waterbody Type 26
References 27
Appendix A: Example Applications for Identifying Daily Load Expressions 29
Appendix B: Identifying Daily Expressions for Non-daily Concentration-based TMDLs...47
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Options for Expressing Daily Loads in TMDLs
Tables
Table 1. Summary statistics of daily loads dataset 9
Table 2. Target option and pollutant source type considerations 24
Table 3. Target option and critical condition considerations 25
Table 4. Target option and source behavior considerations 26
Table 5. Target options and waterbody considerations 26
Table 6. Summary of examples of identifying daily load expressions for Non-daily TMDLs 29
Table 7. Daily maximum and average allowable total phosphorus loads by month 32
Table 8. TMDL Summary for fecal coliform in Carter Creek 38
Table 9. Daily maximum and average allowable loads by month 40
Table 10. Water quality standards 43
Table 11. Sources in the Anacostia TMDL analysis 43
Table 12. Daily Load expression option used for each source 44
Table 13. Nontidal Anacostia (MS4, NPS, Other PS) 45
Table 14. Nontidal Anacostia (MS4, NPS, Other PS) 45
Table 15. Tidal—MD (all flow ranges) 45
Table 16. Tidal—DC Upper Anacostia (all flow ranges) 45
Table 17. Tidal—DC Lower Anacostia (all flow ranges) 46
Table 18. Multipliers used to convert an LTA to MDL 49
Figures
Figure E-1. Process for identifying daily load expressions for non-daily TMDLs viii
Figure 1. Process for identifying daily load expressions from non-daily analysis 5
Figure 2. Example—observed water quality and flow data for Smith River 7
Figure 3. Daily time series under existing conditions for Smith River 8
Figure 4. Modeled allowable daily loads under TMDL conditions for Smith River 8
Figure 5. Example—comparison of daily loads to a daily maximum load target based on the median daily
load 10
Figure 6. Example—comparison of daily loads to a daily maximum load target based on the 95th
percentile daily load 10
Figure 7. Example—comparison of post-TMDL monitoring to established daily targets 11
Figure 8. Example—Mass-balance model representation 16
Figure 9. Load duration curve representing dynamic allowable daily fecal coliform loads based on
observed flow 21
Figure 10. Daily load expressions by flow category 22
Figure 11. Example of a seasonally variable daily load expression 22
Figure 12. Average monthly flow and concentration in Bird Creek 30
Figure 13. Estimated daily phosphorus loads 31
Figure 14. Daily maximum and average allowable total phosphorus loads by month 32
Figure 15. Modeled aluminum daily loads under TMDL conditions along with observed loads and modeled
and observed daily flow 33
Figure 16. Daily maximum and average allowable load along with the range of allowable loads simulated
under TMDL conditions 34
Figure 17. Example BATHTUB calibration for representative growing season 35
Figure 18. Daily maximum and average allowable loads by season 36
Figure 19. Load duration analysis for fecal coliform in Carter Creek 37
Figure 20. Flow versus daily maximum load 38
Figure 21. Observed versus simulated daily flow 39
Figure 22. Observed versus simulated TSS 39
Figure 23. Daily maximum and average allowable loads by month 40
Figure 24. Vollenweider loading plot 41
Figure 25. Example of a concentration-based TMDL 47
Figure 26. Example of a frequency-concentration plot 48
Figure 27. Log probability display 50
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Options for Expressing Daily Loads in TMDLs
Acronyms
AnnAGNPS
Annualized Agricultural Nonpoint Source Pollution Model
BMP
best management practice
CAFO
concentrated animal feeding operation
CFR
Code of Federal Regulations
CSO
combined sewer overflow
CV
coefficient of variation
DC.
District of Columbia
EMC
event mean concentration
EPA
U.S. Environmental Protection Agency
GWLF
Generalized Watershed Loading Functions
HSPF
Hydrologic Simulation Program—Fortran
ICPRB
Interstate Commission on the Potomac River Basin
LA
load allocation
LSPC
Loading Simulation Program in C++
LTA
long-term average
MDL
maximum daily limit
MOS
margin of safety
MS4
municipal separate storm sewer system
NPDES
National Pollutant Discharge Elimination System
PCB
polychlorinated biphenyls
SWAT
Soil and Water Assessment Tool
SWMM
Storm Water Management Model
TAM
Tidal Anacostia Model
TMDL
total maximum daily load
TSD
Technical Support Document
TSS
total suspended solids
USGS
U.S. Geological Survey
WASP
Water Quality Analysis Simulation Program
WLA
wasteload allocation
WQBEL
water quality-based effluent limit
WQS
water quality standard
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Options for Expressing Daily Loads in TMDLs
Vi DRAFT (6/22/07)
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Options for Expressing Daily Loads in TMDLs
Executive Summary
This document was produced to provide technical information to developers of total maximum daily loads
(TMDLs) in light of the District of Columbia (D.C.) Circuit Court of Appeals decision in Friends of the
Earth, Inc. v. EPA, et at, No. 05-5015 (D.C. Cir. 2006), in which the D.C. Circuit held that two TMDLs
for the Anacostia River (one established by U.S. Environmental Protection Agency [EPA] and one
approved by EPA) did not comply with the Clean Water Act because they were not expressed as daily
loads. As a result of the decision, EPA issued a memorandum entitled Establishing TMDL "Daily" Loads
in Light of the Decision by the U.S. Court of Appeals for the D.C. Circuit in Friends of the Earth, Inc. v.
EPA et. al.. No. 05-5015 (April 25, 2006) and Implications for NPDES Permits in November 2006 that
recommends that all TMDLs and associated load allocations (LAs) and wasteload allocations (WLAs)
include a daily time increment in conjunction with other temporal expressions (e.g., annual, seasonal) that
may be necessary to implement the relevant water quality standards.
This document was written to provide technically sound options for developing daily load expressions as
a routine process in TMDLs calculated using allocation time frames greater than daily (e.g., annual,
monthly, seasonal). It is written for TMDL practitioners—those individuals developing TMDLs who are
familiar with relevant technical approaches and regulatory requirements. It is not intended to address
issues associated with how to develop a TMDL; however, many of the issues presented are relevant to the
task of TMDL development and, in light of the recommendation that TMDLs include a daily load
expression, should be considered at the beginning of the development process.
Effect of Daily Loads on TMDL Development Methodologies
Including daily load expressions as a routine component in all TMDLs will require no fundamental
changes in the way TMDLs are presently developed. In practice, TMDLs are developed for a variety of
pollutants, environmental settings, pollutant source types, and waterbody types. They may be calculated
using an assortment of analytical approaches and commonly use time steps ranging from daily to annual
to express the loading capacity and associated allocations. In an effort to fully understand the physical and
chemical dynamics of a waterbody, many TMDLs are developed using methodologies that result in
identified allocations of monthly or greater time periods. EPA encourages TMDL developers to continue
to apply accepted and reasonable methodologies when calculating TMDLs for impaired waterbodies and
to use the most appropriate averaging period for developing allocations based on factors such as available
data, watershed and waterbody characteristics, pollutant loading considerations, applicable standards, and
the TMDL development methodology, among other things.
For a variety of reasons, EPA recognizes that it might continue to be appropriate and necessary to identify
non-daily allocations in TMDL development despite the need to also identify daily loads. For parameters
such as sediment, for which narrative water quality criteria often apply, attainment of WQS cannot always
be judged on a daily basis. Assessment of cumulative loading impacts is necessary to understand how to
achieve WQS and to estimate the allowable loading capacity; therefore identifying long-term allocations
for such situations is appropriate and informative from a management perspective. For TMDLs in which
it is determined that a non-daily allocation is more meaningful in understanding the pollutant/waterbody
dynamics, EPA recommends that practitioners identify and include such an allocation, as well as a daily
load expression with the final TMDL submission.
This document provides a description of the general process TMDL practitioners can use to develop daily
load expressions, describes ways to obtain and develop additional data if necessary, describes the types of
daily load expressions that can be used, discusses selection of daily load target value(s), and describes
important factors to consider when determining what type of expression to use.
DRAFT (6/22/07)
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Options for Expressing Daily Loads in TMDLs
The recommended options are based on the following assumptions:
1. Methods and information used to develop the daily load should be consistent with the approach
used to develop the loading analysis.
2. The analysis should avoid added analytical burden without providing added benefit.
3. The daily load expression should incorporate terms that address acceptable variability in loading
under the long-term loading allocation. Because many TMDLs are developed for precipitation-
driven parameters, one number will often not represent an adequate daily load value. Rather, a
range of values might need to be presented to account for allowable differences in loading due to
seasonal or flow-related conditions (e.g., daily maximum and daily median).
4. The methodologies provided in this document are applicable to a wide variety of TMDL
situations; however, the specific application (e.g., data used, values selected) should be based on
knowledge and consideration of site-specific characteristics and priorities.
5. The TMDL analysis on which the daily load expression is based fully meets the EPA
requirements for approval, is appropriate for the specific pollutant and waterbody type, and
results in attainment of water quality criteria.
Effect of Daily Loads on National Pollutant Discharge Elimination
System Permits
EPA does not believe that the D.C. Circuit Court decision requires any changes in the way WLAs are
currently implemented in National Pollutant Discharge Elimination System (NPDES) permits. Water
quality-based effluent limits (WQBELs) in NPDES permits that implement WLAs in approved TMDLs
must be "consistent with the assumptions and requirements of any available WLA for the discharge"
(Title 40 of the Code of Federal Regidations [CFR] 122.44(d)(l)(vii)(B)). Note that these provisions do
not require that effluent limits in NPDES permits be expressed in a form that is identical to the form in
which the wasteload allocation for the discharge is expressed in a TMDL. Permit limits need only be
"consistent with the assumptions and requirements" of a TMDL's wasteload allocation. States should
continue to use existing guidance and policy memoranda to guide the development of WQBELs that are
consistent with both 40 CFR 122.44(d)(l)(vii) and 40 CFR 122.45(d).
Additional Benefits of Daily Load Identification
For TMDLs in which long-term allocations are determined to be informative given the
pollutant/waterbody dynamics, the daily load expression can additionally provide a tool for gauging
whether load reductions are on track with meeting long-term TMDL allocations and, therefore, WQS.
This is particularly useful when dealing with parameters for which no numeric criteria exist. Using post-
TMDL monitoring data, observed loads can be calculated and compared to established daily load targets
to determine progress in reducing watershed loads to levels required by the TMDL. It is important to note
that for pollutants where the WQS has a longer than daily duration (e.g., monthly or seasonal average),
individual values that are greater than the daily expression do not necessarily constitute an exceedance of
the applicable standard.
Types of Daily Load Expressions
Conceptually, as shown in Figure E-l, the process for deriving daily loads for TMDLs typically based on
non-daily allocations, builds on the data and information used in the non-daily TMDL analysis,
supplementing that data as necessary and identifying a daily load dataset—a population of continuous or
viii
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Options for Expressing Daily Loads in TMDLs
frequent allowable daily loads that meet the loading capacity and therefore represent maintenance of
WQS. The daily dataset is then used to identify the daily load expression for the TMDL.
Depending on the approach used to develop the non-daily TMDL, the daily load dataset might be readily
available or additional analysis might be needed. For example, when using a dynamic model with daily
output or load duration curves, the daily load dataset is available as an output of the technique itself.
Practitioners may select the daily load expression directly from the results of the analysis technique.
However, when a technical approach results in longer term output (e.g., general watershed models and
export coefficients), additional analysis (usually obtaining flow data) is required before the daily load
dataset can be developed. This document provides options for supplementing typical non-daily TMDL
analyses to develop the daily load dataset from TMDL approaches that result in longer term allocations.
Two basic options are available for presentation of daily loads. The first option is a static expression—a
single daily load number or set of numbers applicable to all conditions in the waterbody. The second
option is a variable expression that may be used when the applicable daily load value is determined as a
function of a particular characteristic that affects loading or waterbody response, such as flow or season.
Of these, the most common options will be targets that vary by flow (flow variable) and those that vary by
month or by season (temporally variable). Because TMDLs are unique in nature, there is no specific
format for presenting static or variable daily loads and the options presented in this document do not
preclude variable targets based on other characteristics.
Selecting the appropriate type of daily load expression (static or variable) and the associated target value
is driven by the characteristics of the waterbody for which the non-daily loadings are calculated as well as
characteristics of the TMDL analysis used for the non-daily allocation. Factors such as data availability,
assumptions made during the non-daily analysis, and time period addressed by the non-daily allocation
may all affect the selection of the daily expression. When deciding, practitioners should take into account
management implications, critical loading conditions, and pollutant sources and behavior while
maintaining consistency with assumptions from the non-daily analysis. While TMDLs differ from one to
the next, there are some general tendencies that can be used to guide selection of the appropriate daily
load expression. Factors associated with specific parameters of concern provide limited direction as to the
appropriate daily load option to use. Other considerations such as critical conditions and pollutant source
types will be more indicative of the approach to use. Because of to the complexities of TMDL analysis,
multiple critical considerations will affect how practitioners select the daily load option (static or variable)
and the target value.
This document provides options for developing a daily load expression from a long-term allocation. It
addresses selecting the appropriate averaging period or critical conditions for which the daily load value
(or values) is protective. It shows illustrations of graphical and tabular options for identifying and
presenting daily load options. A series of tables highlights the types of situations for which each daily
load option might be appropriate depending on pollutant source type, critical condition, waterbody type,
and so on. Finally, it presents a number of examples highlighting various approaches to identifying daily
load expressions for long-term allocations for a variety of situations, parameters, and analytical methods.
DRAFT (6/22/07)
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Options for Expressing Daily Loads in TMDLs
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Options for Expressing Daily Loads in TMDLs
Why Was this Document Developed?
Section 303(d) of the Clean Water Act requires that total maximum daily loads (TMDLs) be developed
for all waterbodies for which controls are not stringent enough to meet applicable water quality criteria
(Title 40 of the Code of Federal Regidations [CFR] Part 130). TMDLs are developed for a variety of
pollutants, environmental settings, pollutant source types, and waterbody types. Depending on all these
factors, TMDLs are calculated using a variety of analytical approaches and express allocations on
timesteps ranging from daily to annual. For many TMDL pollutants, such as nutrients and sediment,
primary threats to achieving water quality standards (WQS) can depend on cumulative load, and accuracy
of pollutant loading estimates increases as the length of the calculation period increases. Therefore,
establishing longer-term allocations is appropriate given the chronic nature of the pollutant loading and
resulting impairments. Control of such pollutants is also best tracked when management measures are
implemented and then monitored over a long-term period. For these reasons, many approved TMDLs
have been expressed as maximum monthly, seasonal, or annual loads as opposed to daily loads.
For more information...
To read EPA's memo regarding development
of daily loads in TMDLs, go to
http://www.epa.aov/owow/tmdl/pdf/anacostia
memol 11506.pdf
As a result of the recent D.C. Circuit Court of Appeals
decision in Friends of the Earth, Inc. v. EPA, et al, No.
05-5015 (D.C. Cir. 2006), EPA recommends that all future
TMDLs and associated load allocations (LAs) and
wasteload allocations (WLAs) also be expressed in terms
of a daily time increment. While TMDL analytical
approaches that result in longer (non-daily) averaging periods may continue to be used to demonstrate
consistency with applicable water quality criteria, all final TMDL submissions should include an adequate
expression of daily loads in addition to any longer-term loading expression that may be developed as a
result of the TMDL analysis (USEPA 2006a). The information presented in this document aims to
help practitioners develop a daily load expression that is meaningful, useful and consistent with the
analysis used to calculate the non-daily TMDL and corresponding loading capacity.
Technical Background
Section 303(d)(C) of the Federal Water Pollution Control Act (the Clean Water Act) directs that TMDLs
"shall be established at a level necessary to implement the applicable water quality standards with
seasonal variations and a margin of safety." The accompanying regulations at 40 CFR 130.2 define the
TMDL as "the sum of the individual WLAs for point sources and LAs for nonpoint sources and natural
background." WLAs and LAs are defined as "portions of a receiving water's loading capacity," while
loading capacity is defined as "the greatest amount of load that a water can receive without violating
water quality standards." In essence, a TMDL is a strategy that meets the loading capacity and, thus,
achieves WQS.
Loading capacity of most waterbodies is not constant in time. Depending on the constituent of concern, it
can vary with stream flow, temperature, and many other variables. In some situations it makes sense to
specify a constant maximum daily load that will result in achieving WQS under critical conditions (e.g.,
low flow) and all other conditions less stringent than the critical conditions. This type of approach is
commonly used to develop permit limits for controlled effluent discharges such as wastewater treatment
plants, but might be impractical for many nonpoint sources that vary naturally in response to precipitation
and season.
There is no requirement that a daily load expression result in a single, constant daily load limit that is
applicable to all situations, although this is one potential formulation. Rather, the maximum daily load(s)
that are permissible are those that meet the loading capacity. As the loading capacity varies based on
ambient conditions, so too may the maximum daily load that satisfies the loading capacity.
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Options for Expressing Daily Loads in TMDLs
TMDLs that include time-variable loading limits are often generated by using a dynamic modeling
technique, which can include both continuous simulation models and statistical approaches. EPA's
Technical Support Document for Water-quality Based Toxics Control (USEPA 1991) (referred to as the
TSD in this document) says, "Dynamic modeling techniques explicitly predict the effects of receiving
water and effluent flow and of concentration variability... These methods calculate a probability
distribution for RWCs [receiving water concentrations] rather than a single, worst-case concentration
based on critical conditions... they determine the entire effluent concentration frequency distribution
required to produce the desired frequency of criteria compliance/' In other words, such models can be
used to predict a stream's loading capacity and compliance with numeric criteria by calculating daily or
even hourly flow and predicted concentrations, then relating them to numeric water quality criteria.
For other situations, the loading capacity is evaluated in terms of cumulative loads to achieve WQS. For
instance, to achieve control of nuisance algal concentrations in a lake it might be most relevant to evaluate
the cumulative phosphorus loading over the growing season rather than the load on individual days. In
this situation, a model that demonstrates achieving WQS presents (explicitly or implicitly) a series of
time-varying daily loads that achieves compliance.
In sum, while TMDLs should contain an expression of daily load, this daily load may be either a constant
daily maximum load or a time-varying daily maximum load.
Expressing long-term LAs as daily loads can also be used to inform post-TMDL monitoring and tracking.
While TMDL analyses might determine that an annual sediment load of 500 kg/year is consistent with
meeting WQS and beneficial uses, without an understanding of when and how that 500 kg is delivered
over the course of a year, it can be difficult to understand from routine water quality monitoring whether
the TMDL is being met. Ideally, the process of translating a long-term load into a daily load can result in
identifying expected variability in loads under a TMDL scenario. Monitoring data collected during a
given sampling event can then be compared to the identified daily load values to evaluate whether the
TMDL is being attained.
Document Purpose
The information in this document was developed recognizing that a significant portion of TMDLs will
continue to be developed using analytical approaches that calculate long-term loading estimates (USEPA
2006a). To help states and Regions ensure that TMDLs also include a daily expression, methods are
needed to derive daily expressions from non-daily loads calculated using common TMDL approaches.
This document was developed to help satisfy that need.
It is important to note that factors involved in TMDL development
vary greatly from one analysis to the next. Such differences are related
to waterbody type, watershed size, pollutants of concern, critical
conditions, and available data, as well as to resources available for
TMDL development including scheduling, available funds, and
technical expertise. It is not possible to provide prescriptive
instructions for translating loading expressions on the basis of specific
waterbody types or pollutant types because there are simply too many
possible combinations of pollutant/waterbody type/analytical techniques. In general, however, available
translation options can be categorized on the basis of the characteristics of the original technical analysis
and supporting data availability, as well as system characteristics such as pollutant type, active source
types, and factors that define critical conditions. This document describes the general process for deriving
a daily load from a non-daily load on the basis of TMDL analysis characteristics. It also identifies various
Options for the derivation
of daily loads are driven by:
¦ Characteristics of the
original analysis
¦ Supporting data availability
¦ Source characteristics
¦ Critical loading period(s)
2
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Options for Expressing Daily Loads in TMDLs
graphical and tabular options for presenting the daily expression. Finally, the document discusses critical
issues to consider in crafting an appropriate daily expression that acknowledges expected loading
variability and is appropriate to the TMDL characteristics (e.g., pollutant, source).
This document is written for TMDL practitioners—those
individuals developing TMDLs who are familiar with the
relevant technical approaches and legal requirements. It is
written to provide them with technically sound options for
developing daily load expressions for ongoing or future
TMDLs calculated using allocation time frames greater than
daily (e.g., annual, monthly, seasonal). It is not intended to
address issues associated with how to develop a TMDL;
however, many of the issues presented are relevant to the task of developing TMDLs and, in light of the
recommendation that TMDLs include a daily load expression, should be considered at the beginning of
the development process. The recommended analytical approaches are based on the following basic
assumptions:
Benefits of Including a Daily Load
Expression in a TMDL
Inform post-TMDL monitoring
Act as an instantaneous measure to
track water quality improvement
Provide higher temporal resolution
information to support implementation
1. Methods and information used to develop the daily load should be consistent with the approach
used to develop the non-daily loading analysis.
2. The analysis should avoid added analytical burden without providing added benefit.
3. The daily load expression should incorporate terms that address acceptable variability in loading
under the long-term loading allocation. Because many TMDLs are developed for precipitation-
driven parameters, one number will often not represent an adequate daily load value. Rather, a
range of values might need to be presented to account for allowable differences in loading due to
seasonal or flow-related conditions (e.g., daily maximum and daily average).
4. The methodologies provided in this document are applicable to a wide variety of TMDL
situations; however, the specific application (e.g., data used, values selected) should be based on
knowledge and consideration of site-specific characteristics and priorities.
5. The TMDL analysis on which the daily load expression is based fully meets the EPA
requirements for approval, is appropriate for the specific pollutant and waterbody type, and
results in attainment of water quality criteria.
Document Organization
Section 1 provides an introduction to the three-step conceptual process for deriving daily load expressions
from non-daily allocations. Typical technical approaches used for developing TMDLs are discussed along
with typical outputs in relation to the three-step process. Section 2 provides options for using the non-
daily analysis output to develop a daily load dataset necessary for identifying the daily load expression. In
addition, the section outlines common problems and issues likely to be encountered by TMDL developers
in the translation process and provides suggestions for how to handle them. Section 3 provides
illustrations of graphical and tabular options for identifying and presenting daily load options and
addresses the types of situations for which each might be appropriate. This section also provides guidance
related to crafting the daily load expression, including selecting the appropriate averaging period or
critical conditions for which the daily load value (or values) is protective. Appendix A contains a number
of examples highlighting various approaches to converting long-term LAs to daily load expressions.
Examples are presented for a variety of situations highlighting TMDLs developed for different
parameters, using various analytical methods and applying different daily load expressions. Finally,
Appendix B discusses an approach for identifying a daily expression for concentration-based TMDLs.
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Options for Expressing Daily Loads in TMDLs
1. Process for Deriving Daily Load Expressions from Typical
Non-daily TMDL Analyses
Whether TMDLs are expressed as daily allocations or non-
daily allocations depends on such considerations as
expressions of applicable WQS, pollutant type and behavior,
source characteristics, critical conditions, and TMDL
development methodology. If it is deemed appropriate to
express a TMDL on a non-daily time frame, that non-daily
TMDL should also include a daily expression. Conceptually,
the process for identifying the appropriate daily load
expression from a non-daily analysis is the same regardless of
pollutant type, waterbody type, or source type. The process,
illustrated in Figure 1, relies on capitalizing on the data and
information used in the analysis, supplementing that data as necessary and identifying a daily dataset—a
population of continuous or frequent allowable daily loads that meets the loading capacity and, therefore,
represents maintenance of WQS. The daily dataset is then used to identify the daily load expression for
the TMDL.
The first step in the process to identify the daily load expression, an evaluation of the technical approach
to developing the non-daily load, provides the analyst with an understanding of what information is
available for the process. If a model was used to develop the non-daily load, was the output on an hourly,
daily, or monthly time step? Was another type of analysis used that perhaps was based on an assumption
of a steady delivery of pollutant to the waterbody?
The second step results in the creation of the daily load dataset from which the daily expression will be
created. In some cases, these data are produced from the non-daily load analysis (e.g., daily model
output), while in others, these data must be developed through additional calculations.
While a wide variety of approaches are applicable to TMDL development, they can all be considered to
result in analytical output of either subdaily/daily or greater than daily, regardless of how the TMDL
allocations are expressed (daily, monthly, or annually). For example, dynamic watershed models (e.g.,
Hydrologic Simulation Program—Fortran [HSPF]) might produce simulated data on an hourly, daily, or
monthly time step, while other methods such as loading coefficients might produce annual loading
estimates. Understanding the technical approach used to develop the TMDL provides the ability to answer
the first critical questions in the process to identify the daily load expression.
The third step involves working with the dataset to identify the most appropriate daily load expression on
the basis of the practitioner's knowledge of the system. Once the daily load dataset is available, the
exercise is one of selecting the right daily load expression. This will
be determined by such factors as expression of the WQS, pollutant
type and characteristics, pollutant source type and behavior, critical
loading and impairment conditions, and implementation and
monitoring plans. Daily load expressions can take a variety of
forms, including dynamic daily loads that are dependent on
environmental conditions (e.g., flow), temporally variable daily
loads that establish static daily maximum loads for specific time
periods, or a single, static maximum daily load for critical
conditions or for all conditions.
What Are the Goals of this Section?
¦ Introduce the conceptual process for
deriving daily load expressions from
typical non-daily analyses
¦ Illustrate the process with an example
application
¦ Introduce concepts and critical issues
that will be discussed in more detail in
Sections 2 and 3
A Note about Concentration-
based TMDLs
The main sections of this
document focus on TMDLs that
support load-based allocations.
For TMDLs that establish
concentration-based allocations,
information for identifying daily
expressions is included in
Appendix B.
4
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Options for Expressing Daily Loads in TMDLs
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5
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Options for Expressing Daily Loads in TMDLs
The daily load expression will provide an alternative or supplementary expression to the longer-term
loading capacity and allocations established in the TMDL. Allocations based on monthly, seasonal, or
annual timeframes are valuable components to guide management measures and implementation plans
because they are related to the overall loading capacity of the waterbody, while the daily expressions
represent day to day snapshots of the total loading capacity based on ambient conditions.
The daily expression can provide a useful tool for tracking the progress toward meeting the longer-term
allocations and goals. Follow-up monitoring data can be compared with daily maximum loads to gather
insight into how the waterbody is responding to implementation efforts and whether short-term loads and
conditions are within the range of conditions represented by the longer term TMDL allocations. The daily
expression of the TMDL supports and informs monitoring efforts and other implementation activities
such as implementing best management practices (BMPs) and establishing permit limits.
Is One Number Enough?
In establishing a daily load expression for a non-daily TMDL, it will often be useful to identify a daily maximum
and a daily average. Daily maximums are typically established to allow for infrequent, high-concentration inputs,
while daily or monthly averages are provided to represent more consistent or persistent loading conditions.
Identifying both a daily maximum load and some value representative of average conditions in non-daily TMDLs
can represent the range of conditions that are acceptable on a daily basis and that will meet the overall TMDL
allocations and, therefore, the applicable WQS.
Consider, as an example, a phosphorus TMDL established with seasonal LAs to meet an allowable in-stream
concentration based on historical water quality data. The allocations were determined using a dynamic model
providing daily output. The following provides a variety of loading values for the TMDL condition, including the
original seasonal allocations and the corresponding maximum daily load, average daily load, and the 50th, 75th,
and 95th percentile loads by season:
Example loads
Winter
Spring
Summer
Fall
Allocation: Seasonal load (kg/season)
370,080
247,860
191,700
229,230
Seasonal daily average (kg/day)
4,112
2,754
2,130
2,547
Seasonal daily maximum (kg/day)
153,504
86,680
121,561
171,456
Seasonal 50th percentile (kg/day)
324
433
101
121
Seasonal 75th percentile (kg/day)
3,010
1,651
589
1,012
Seasonal 95th percentile (kg/day)
19,074
15,489
10,954
11,141
Suppose the daily load expression specified a single, maximum daily load set at the 95th percentile load for each
season. If the daily maximum were reached (but not exceeded) every day, the maximum would be satisfied, but it
would be impossible to meet the total seasonal LA or the corresponding seasonal average. As a result, long-term
loading would not be controlled to the extent required to meet WQS. Alternatively, if only a daily average load
were established, it might be difficult to gauge the importance of infrequently high loads to the overall LA—
especially in situations with infrequent monitoring data. If monitoring is conducted only monthly and a load is
measured that is well in exceedance of the daily average for that season, it would be difficult to gauge if that load
were out of the range of acceptable values without having a daily maximum target for comparison. As a result,
practitioners established the TMDL to include a maximum daily load using the 95th percentile load for each
season along with an allowable daily average load for each season (shown in bold).
6
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Options for Expressing Daily Loads in TMDLs
The process outlined in the flowchart presented in Figure 1 is further illustrated below with an example
aluminum TMDL for the Smith River. The example takes an existing TMDL developed with a long-term
approach and examines what would be needed to incorporate a daily load. Issues associated with each
step are highlighted with discussion and graphs. In addition to highlighting key concepts related to
identification of the daily load expression, the Smith River example also provides context for the post-
TMDL uses of the resulting daily load targets. (Sections 2 and 3 of this document provide further details
related to application of each step—creating the daily load dataset and selecting target values).
Step 1. Evaluate Non-daily TMDL Approach
As shown in Figure 1, the first step in the process to identify a daily load expression for long-term
allocations is to evaluate the TMDL approach and the available data and output. Important aspects of the
TMDL for this example include the following:
• The TMDL for the Smith River was calculated using a continuous watershed model. As a result,
model output provides simulated daily flow, concentration, and load.
• The initial TMDL calculation satisfies in-stream water quality criteria—in this case, an acute
concentration of 0.75 mg/L aluminum.
• Allocations are presented as monthly loads based on the average allowable monthly loads over a 5-
year simulation period. Allowable monthly loads are simply the total of the individual allowable daily
loads within the respective month.
• The resulting time series of allowable daily loads is the result of various scenarios of load reductions
from watershed sources (e.g., land uses, point sources). Reductions to modeled loads were applied
iteratively until the time series of daily concentrations resulted in continuous attainment of all
applicable criteria.
Figure 2 presents the available water quality and flow data for the Smith River in comparison to the acute
criterion.
Figure 2. Example—observed water quality and flow data for Smith River.
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7
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Options for Expressing Daily Loads in TMDLs
Step 2. Develop Daily Dataset
As illustrated in the process flowchart (Figure 1), the second step in identifying a daily load expression
involves developing a daily load dataset from which the target(s) is selected. Because the model used to
calculate the TMDL for the Smith River was a dynamic watershed model, the daily load dataset was
obtained directly from the model output.
Figure 3 presents the time series of existing daily aluminum concentrations simulated by the watershed
model, the corresponding daily flow, and observed aluminum concentrations. In Figure 4, modeled daily
loads (modeled daily aluminum concentration multiplied by the modeled daily flow) under the TMDL
condition are presented; the TMDL conditions represent a loading scenario under which all applicable
water quality criteria are attained. This time series of allowable daily loads serves as the daily load
dataset that is used to identify the daily load expression of the TMDL. Table 1 provides summary
statistics of the daily load dataset, illustrating the magnitude and distribution of allowable daily loads.
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Figure 4. Modeled allowable daily loads under TMDL conditions for Smith River.
8
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Options for Expressing Daily Loads in TMDLs
Table 1. Summary statistics of daily loads dataset
Statistic
Aluminum load
(lb/day)
Minimum
367
25th percentile load
557
Median (50th percentile)
690
Average
968
75th percentile
1,090
Maximum
40,161
Step 3. Select Daily Load Expression
The final step of the process is to select the daily load expression that represents the longer-term TMDL
allocations. To provide some perspective, it helps to think about how the identified load value will be
used after the TMDL is implemented and what the resulting implications of each load would be. The
maximum daily load can provide a tool for gauging whether load reductions are on track with meeting
long-term TMDL allocations and, therefore, WQS. This is particularly useful when dealing with
parameters for which no numeric criteria exist. Using post-TMDL monitoring data, observed loads can be
calculated and compared to established daily load targets to determine progress in reducing watershed
loads to levels required by the TMDL.
The level at which the target is established can affect its usefulness in evaluating follow-up monitoring
and tracking progress. From Figure 4 and Table 1, it is evident that a very wide range of daily load values
make up the total load under the TMDL scenario. Selecting, for example, the 50th percentile load as the
maximum daily load does not address the expected variation and ignores a significant portion of the
loading capacity, and for management purposes, the target could be said to be too conservative. Using the
median (i.e., 50th percentile) load as the allowable daily maximum load, 691 lbs/day in the above
example, essentially assumes that under the TMDL loading scenario (attaining applicable criteria), 50
percent of expected loads will exceed the allowable maximum.
There are a few points to consider in relation to setting the daily maximum. With a daily maximum load
representing long-term allocations, there will be some exceedances that will occur while still maintaining
the longer-term goals. Setting an appropriate target can diminish the effect of those exceedances on a
manager's ability to confidently evaluate progress. If the target is set at the average or median daily
allowable load, so many of the observed loads will exceed the average load that it will be difficult to gage
at what point there is a problem and when conditions are not improving, or even worsening. The daily
load expression could be set at a high percentile of the distribution, representing a value that should be
rarely exceeded if the time series that represents the TMDL calculation is met. However, setting a target
too high will also not be very informative. If the daily target is based on the maximum allowable load, by
the time monitoring data exceed the target, there is likely already a problem.
For the daily load target to be both protective of WQS and informative for post-implementation
monitoring, practitioners should identify a range of daily loads. At the very least, they should identify a
daily maximum load or a daily average load in conjunction with the long-term average load established
by the non-daily TMDL analysis. Ideally, both a daily maximum and daily average load will be identified
in conjunction with the long-term allocation.
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9
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Options for Expressing Daily Loads in TMDLs
Figure 5 and Figure 6 help to illustrate the concept further. Figure 5 compares the time series of allowable
daily loads to a maximum daily load target based on the 50th percentile load (691 lbs/day), while Figure 6
compares the daily loads to a maximum target based on the 95th percentile (2,182 lbs/day). Under TMDL
conditions, one would see fewer exceedances when comparing loads to the 95th percentile target versus
the 50th percentile target. However, setting the daily load expression at the 95th percentile will not in itself
be protective of WQS unless the relationship of load to dilution capacity contained in the TMDL scenario
is maintained.
Distribution of Daily Loads Exceeding the Target (50th percentile)
10,000 n
9,000
8.000
7.000
Figure 5. Example—comparison of daily loads to a daily maximum load target
based on the median daily load.
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based on the 95th percentile daily load.
10
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Options for Expressing Daily Loads in TMDLs
For monitoring purposes, using the 95th percentile load as a daily maximum value acts as a more effective
trigger, indicating when conditions might be off track for meeting the longer-term goals of the TMDL. If
monitoring data routinely exceed the 95th percentile load, it would be evident that loading reductions have
not been sufficient to meet the TMDL. However, it is also important to recognize that using only a daily
maximum target can mislead post-TMDL evaluation if used without longer-term targets. For example, if
loads were as high as the 95th percentile value on a daily basis, loading conditions would far exceed the
TMDL. The daily load target(s) should be expressed in such a way as to recognize average and extreme
loads since both can occur while still maintaining the overall distribution of the allowable conditions
represented by the TMDL analysis.
Therefore, for the Smith River, a dual target was established using the 95th percentile load as the daily
maximum value to address variability in instantaneous concentrations and the 50th percentile load as the
allowable daily median to represent long-term loading goals. Section 3 includes further discussion related
to selecting specific daily load expressions.
Selecting the daily load target(s) can also be helpful in tracking post-TMDL implementation and water
quality improvements. Monitoring conducted in the Smith River following implementation of the TMDL
is shown in Figure 7. The graph compares observed pollutant loads to the daily maximum target (set as
the 95th percentile allowable load). The observed data are also used to calculate a median daily load on the
basis of on all previous samples; this median is compared to the supplementary daily target expressed as a
median load. As shown in the figure, while monitoring data include some exceedances of the daily
maximum load, the median target is still met, maintaining the overall distribution of the allowable
conditions represented by the TMDL analysis. Without including both a maximum and average daily
targets, it is difficult to evaluate post-TMDL monitoring to determine how observed conditions relate to
TMDL conditions.
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Aluminum Observed Load
¦Allowable Daily Max
Running Median Observed Load
Allowable Daily Median
Figure 7. Example—comparison of post-TMDL monitoring to established daily targets.
The previous pages introduced several important issues in identifying daily load expressions for
corresponding long-term TMDL allocations. The example illustrated key points related to crafting
expressions that address expected variability in loading as well as identifying daily loads in a way that
informs the post-implementation monitoring process. The next section provides greater detail regarding
Step 2 of the process—creating the daily loads dataset.
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11
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Options for Expressing Daily Loads in TMDLs
2. Developing a Daily Dataset from a Non-daily Analysis
This section discusses Step 2—Develop Daily Dataset—of the
process to identify daily load expressions for non-daily
analysis. This step is important to create a dataset that
represents the variation and magnitude of allowable daily
loads that result in attainment of long-term loading goals—a
dataset from which the daily expression for the TMDL will be
established. Whether the dataset is obtained directly from
model output or is derived through additional analysis, it
represents the distribution of daily loads under TMDL
conditions. At its simplest, the dataset should be able to
account for the basic variation of daily loads in relation to watershed conditions, such as relating loads
that occur during wet periods with high flows and those occurring during dry periods with low flows.
What Are the Goals of this Section?
¦ Discuss how to create a daily load
dataset based on typical TMDL
analyses
¦ Review commonly used TMDL
methodologies and their output
¦ Provide guidance for developing daily
load datasets when supplemental
analysis is required
This section provides guidance on generating the daily dataset from the following commonly used
approaches for developing TMDLs:
• Dynamic Model. Many TMDLs use dynamic, time-variable watershed and receiving water models
using daily or smaller time steps to establish the link between source loading and water quality
response and to evaluate load reduction and management scenarios. These models provide continuous
simulation of watershed and in-stream processes on the basis of a variety of inputs, including weather
conditions, land use and other watershed characteristics, and waterbody characteristics (e.g., physical,
chemical). Dynamic models can include watershed models (e.g., HSPF) or receiving water models
(e.g., Water Quality Analysis Simulation Program [WASP]). Many dynamic watershed models also
include an in-stream component that simulates in-stream fate and transport. While process, resolution,
and detail vary greatly depending on the model used and the type of application, dynamic models
typically provide daily or subdaily output for flow and loads.
• Load Duration. The load duration methodology relies on using observed flows and water quality
criteria to establish loading capacities for various flow conditions. This builds on using flow duration
curves, which use hydrologic data from stream gages to evaluate the cumulative frequency of historic
flow data over a specified period. A duration curve relates flow values to the percent of time those
values have been met or exceeded. A criterion concentration can then be converted into a distribution
of allowable loads as a function of daily flow. Duration curve analysis identifies intervals, which can
be used as a general indicator of hydrologic condition (e.g., wet versus dry and to what degree). For
more information on using load duration curves, see Cleland (2002; 2003) and USEPA (2006b).
• General Watershed Model. For this document, general watershed models are assumed to be those
that provide simulation capabilities and output on a non-daily basis, typically monthly or event-based
The models simulate basic watershed processes related to weather, erosion, and runoff and pollutant
washoff, and they typically do not involve waterbody response or in-stream fate and transport.
Examples of general watershed models include Generalized Watershed Loading Functions (GWLF)
or Annualized Agricultural Nonpoint Source Pollution Model (AnnAGNPS).
• Export Coefficients/Pollutant Budgets. This category encompasses a number of approaches built on
empirical relationships among watershed processes and pollutant loading as well as the use of
literature values of typical watershed loading rates. Examples include using monthly load rates from
various land uses to calculate allowable loading from an impaired watershed. Another example is
12 DRAFT (6/22/07)
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Options for Expressing Daily Loads in TMDLs
using an empirical relationship that allows a user to calculate an allowable load depending on
desirable conditions (e.g., target runoff/waterbody concentration or indicator levels).
• Steady-State or Mass-Balance Analysis. These approaches rely on the assumption of conservation
of mass into a waterbody. The analysis might calculate loads entering a waterbody on the basis of
literature values or observed data and calculate the resulting waterbody concentrations on the basis of
estimated losses (e.g., settling, decay) and inputs. The approach relies on identifying the necessary
loads entering a waterbody that will meet the desired waterbody target after the consideration of all
inputs and losses. These approaches can be applied for a steady-state critical condition, in which case
they might result in a daily load; in other instances they are based on longer time periods, such as
average monthly loading rates.
For TMDL approaches using a dynamic model with daily output, load duration curves, continuous
monitoring data, and in some cases, steady-state analysis, the daily load dataset is available as an output
of the technique itself. As mentioned in the previous section, when a technical approach results in longer-
term output, additional analysis is required. General watershed models and export coefficients are two
techniques for which additional analysis is usually needed to create the necessary daily load dataset. In
some instances, additional analysis might be required for steady-state or mass-balance calculations as
well. The following section describes in more detail the options for developing a daily load dataset from
various technical approaches with daily and non-daily output.
Developing Daily Datasets from Commonly Used TMDL Approaches
This section discusses the approaches and considerations for
developing the dataset of allowable daily loads given the use of
some commonly used TMDL approaches.
Dynamic Models
Daily Output Methodologies
Detailed dynamic watershed
models
Load duration curves
Continuous monitoring data
Steady state/mass balance
Non-daily Output Methodologies
¦ General watershed models
¦ Export coefficients
¦ Mass balance calculations
¦ Steady state models
Dynamic models can be readily used to generate time series of
daily loads for a TMDL allocation scenario. As discussed above,
these models typically provide daily or subdaily output for flow and
pollutant concentrations. Examples of dynamic watershed models
frequently applied to TMDL development include the Soil and
Water Assessment Tool (SWAT), HSPF and other similar dynamic
models derived from the same algorithms such as WinHSPF and
Loading Simulation Program in C++ (LSPC), and the Storm Water Management Model (SWMM).
Despite the ability to output daily calculations, many TMDLs developed with such models present long-
term LAs (e.g., monthly, annual). TMDL development with dynamic models generally involves designing
the model to simulate a given time period that includes a variety of conditions. Depending on the
characteristics of the system, a long simulation can be used that includes periods of drought and high
flows or a shorter simulation can be run that includes a particularly critical condition (e.g., the 2-year low
flow). The model is calibrated to observed data for the given model period and existing loading for the
period is determined. Next, source loads are reduced until simulated loads meet WQS or representative
targets. The daily loads for the model period can then be extracted from model output to be used in
establishing the daily load expression.
Load Duration Model
Load duration curves (Cleland 2002, 2003; USEPA 2006b) are widely used to develop TMDLs,
especially for pollutants where numeric water quality criteria are applicable. This approach involves
calculating the allowable loadings over the range of flow conditions expected to occur in the impaired
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13
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Options for Expressing Daily Loads in TMDLs
waterbody. This method generally presents loading data as a function of flow and can be used to
extrapolate the daily load expression. The approach involves the following steps:
1. A flow duration curve for the stream is developed by generating a flow frequency table and
plotting the data points. The data reflect a range of natural occurrences from extremely high flows
to extremely low flows.
2. The flow duration curve is translated into a load duration (or TMDL) curve by multiplying each
flow value by the WQS/target for a particular contaminant, then multiplying by a conversion
factor. The resulting points are plotted to create a load duration curve.
3. Each water quality sample is converted to a load by multiplying the water quality sample
concentration by the average daily flow on the day the sample was collected. Then, the individual
loads are plotted as points on the TMDL graph and can be compared to the WQS/target, or load
duration curve.
4. Points plotting above the curve represent deviations or exceedances from the WQS/target and the
daily allowable load. Those plotting below the curve represent compliance with standards and the
daily allowable load.
The load duration approach can be used to calculate a series of allowable daily loads, which is then used
as the daily load dataset for identifying the daily load expression.
General Watershed Models
A variety of watershed and receiving water models capable of simulating different aspects of hydrologic
and water quality processes exist; however, a relatively small number are commonly applied to TMDL
development. This section focuses on those that are designed to predict average pollutant loads over time
(annual, seasonal, monthly) as opposed to daily or shorter periods. The models simulate basic watershed
processes related to weather, erosion, and runoff and pollutant washoff, and they typically do not involve
waterbody response or in-stream fate and transport. In general, these models are continuous simulation,
distributed models that produce monthly or annual loading estimates on the basis of daily weather inputs
and runoff calculations. An example is the GWLF model and its improved Windows version, BasinSim
1.0 (available at http://www.vims.edu/bio/vimsida/bsabout.html).
Loads produced by such models can be translated to daily datasets in several ways. The simplest approach
is simply to divide the load output by the number of days; however, this is likely to produce inappropriate
results if the parameter of interest derives from washoff of nonpoint sources and is thus highly correlated
to flow. As above, a better approach is to recognize the relationship between load and flow. To translate
long-term TMDL loads developed by such models, an estimate or a simulation of daily flow data is
needed. The flow can then be used to distribute the monthly load or seasonal load into variable daily
loads. Data manipulation required to do this differs from model to model; however, the general process is
the same:
• Start the analysis at the model basic time step (e.g., monthly).
• For each month, separate the approximately constant loads (point source, groundwater) from the
surface washoff loads.
• Calculate an event mean concentration (EMC) for the surface washoff load by dividing the surface
washoff load by the estimated surface runoff.
• Obtain daily, surface-runoff, flow data (1) from the model, if available, (2) baseflow separation on
flow at nearby gages that represent similar watershed characteristics, (3) using established regression
14
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Options for Expressing Daily Loads in TMDLs
equations from U.S. Geological Survey (USGS), or (4) using site-specific data. (For ways to develop
flow data, see the discussion in the next section.)
• Multiply the daily surface flow volumes by the pollutant EMCs to derive the surface daily loads.
• Add the constant daily loads to the surface daily loads to derive the daily load dataset.
Export Coefficients
Export coefficients and export coefficient-based models such as PLOAD are applied in TMDL analyses
to develop long-term estimates of pollutant yield on the basis of established loading rates by land use
type. The methodology is often applied in watersheds where site-specific monitoring data are scarce but
where good information exists regarding land use and practices.
Results of an export coefficient assessment differ from watershed model results in that the technique does
not base results on calculations of flow. To obtain flow data necessary for establishing daily load
expressions, more analysis is necessary. Even though flows are not inherently available as a product of
the analysis technique, the translation process assumes that loading is related to runoff and distributes the
available load according to daily flows. Using the loads calculated in the analysis and available flow data,
a representative pollutant concentration can be calculated. The same techniques discussed under general
watershed models can then be used to develop daily loads for the representative period. Sources of flow
data are varied and can include modeled flows, nearby USGS gages, or estimations based on rainfall
distribution patterns. In some areas, regression equations might have been developed for predicting flows
in un-gaged streams.
Steady-State and Mass-Balance Models
Steady-state approaches rely on the assumption of conservation of mass into a waterbody. A typical
TMDL analysis might calculate loads entering a waterbody using literature values or observed data, then
calculate the resulting waterbody concentrations considering estimated losses (e.g., settling, decay) and
inputs. The approach relies on identifying the necessary loads entering a waterbody that will meet the
desired waterbody target after the consideration of all inputs and losses. These methodologies are
generally applied for a single critical condition, such as during the 7Q10 low flow, to ensure criteria are
met at all times. In other situations, mass balance calculations provide long-term TMDL loads by
estimating watershed loading from back calculations of known waterbody concentrations and inflow
volumes. Applying steady-state analyses to TMDL development is most appropriate in situations where
streamflow and water quality are dominated by a relatively constant input, for example by a point source
or sources. Mass-balance calculations are also frequently applied to lakes and impoundments.
Other scenarios in which steady-state/mass-balance models have been applied are in cases where
monitoring data are lacking such that a more detailed watershed model is not justified and cannot be
reasonably calibrated. When applied to TMDL development in this case, steady-state models represent a
screening level of analysis pending development of more detailed monitoring data to support a more
detailed TMDL analysis. Output of the steady-state analysis represents a reasonable maximum daily load
expression for the critical conditions being evaluated and no further analysis or translation is necessary, if
it is expressed in a per day basis.
In summary, a steady-state model is used to calculate the allowable loads from all represented sources,
under a specific waterbody conditions (e.g., 7Q10 flow, impoundment design volume) given a desired
water quality endpoint. Figure 8 provides an illustration of a mass-balance-type model showing a stream
broken into model segments and point source inputs along the length. Results represent the allowable
loads from point sources for the modeled condition (7Q10 flow). In some cases, the predicted input loads
at critical conditions could be considered the maximum daily load for all conditions. In other cases, it
DRAFT (6/22/07)
15
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Options for Expressing Daily Loads in TMDLs
might be preferable, if data are available, to extrapolate the allowable load at critical conditions to
comparable loads at other flow regimes.
CO
T—
CD
f\J
o
CO
OJ
o
(N
O)
O)
00
o
o
o
o
o
o
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q:
q:
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OR0019223
2.1 MGD
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.5 MGD
OR0018236
1.2 MGD
FLOW
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Figure 8. Example—Mass-balance model representation
Other mass-balance-type calculations include load estimates established for longer-term periods (e.g.,
monthly, annual). For example, a lake impaired by eutrophication might have a monthly average
phosphorus concentration established as a target to support designated uses. To calculate the TMDL, the
target concentration can simply be multiplied by the lake volume and an appropriate conversion factor,
resulting in an allowable in-lake monthly load. A mass balance calculation could then be used to identify
the allowable incoming watershed load, after subtracting out the losses (e.g., settling, uptake, outflow).
When using a mass balance approach, the resulting allowable load will be calculated in the same units as
the target; for example, monthly in the lake example. These in turn can be converted to constant daily
loads or daily load series as a function of flow.
Options for Estimating Flows to Support Development of the Daily
Load Dataset
In cases where daily loads are not an output of the TMDL analysis, daily flows are typically used to
distribute the non-daily output into a series of daily loads, as discussed in previous sections. However,
continuous or frequently measured daily flows are not always available. This section provides some
options for developing flow data when data are not available for a waterbody. There could be a high
degree of error associated with making these flow estimates (depending on the approach that is selected
and the available data), and practitioners should consider this when developing the margin of safety
(MOS) for the TMDL and recognize it in the final TMDL report.
Estimating Flows from Nearby USGS Gages
Obtaining flows from a nearby USGS gage is likely the
most straightforward option for developing flows to be used
in creating the daily load dataset. If no gage is in the TMDL
watershed, one outside the watershed may serve as a
surrogate. Be careful to locate a gage with a data record
covering the same time period for which the TMDL analysis
was performed and in near enough proximity that regional
characteristics such as soil types and vegetative cover is
similar. In addition, practitioners should make an effort to
select a gaged watershed with land use characteristics
similar to the TMDL watershed, having no significant flow
restrictions or augmentations (e.g., impoundments,
When a Daily Dataset Cannot Be
Developed with the Available Data
In certain circumstances, data limitations
could be such that it is inappropriate or
infeasible to derive flows and, therefore,
daily loads through the options identified in
this section. For example, there might be no
nearby gages in watersheds similar to the
target, rainfall data may be unreliable, not
available, or the region could be arid.
In these cases, it might be most appropriate
to establish a daily maximum load target on
the basis of the long-term average using a
statistic approach or assuming a particular
critical condition. For more information, see
Section 3.
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Options for Expressing Daily Loads in TMDLs
diversions, withdrawals) that would skew results of the comparison. Daily flows for the gaged watershed
can then be adjusted for the TMDL watershed on the basis of the ratio of the watershed areas. In many
cases, it will be appropriate to use a baseflow separation program to evaluate the components of flow that
are due to surface washoff
Estimating Flows from Existing Models
If hydrologic modeling has been conducted in the watershed, modeled flows might be available. To be
appropriate, the modeled flows should be representative of the period covered by the TMDL loading
analysis, and they should be available on a daily time-step. While an option, this might not be a very
likely one, and if data to support such a model existed for the watershed, chances are good that the TMDL
would have been based on it rather than the coarser technique. Nevertheless, a hydrologic model of the
watershed might be available to provide sufficient flow data for distributing the non-daily output into a
series of allowable daily loads.
Estimating Flows Using Rainfall Distribution
Simplified modeling approaches (such as the Soil Conservation Service Curve Number approach) can be
used to estimate runoff as a function of rainfall, soil type, and cover. Rather than running a continuous
simulation, an option is to convert a statistical distribution of rainfall directly into a frequency distribution
of flows.
Estimating Flows Using Regression Equations
For various areas around the country, regression equations might have been developed by water resource
agencies to estimate flows for un-gaged streams. The USGS National Streamflow Statistics Program can
provide flow percentiles for some areas of the country. These percentile flows can be used to construct a
flow duration percentile curve. Currently the capability is available only for 11 states in the United States,
allowing flow statistics to be computed for un-gaged watersheds. The stream statistics program uses
regression analysis to relate streamflow statistics computed for a group of selected stream gaging stations
(usually within a state) and basin characteristics measured for the stations. Basin characteristics measured
for un-gaged sites are entered into the resulting equations to obtain estimates of the streamflow statistics.
Alternatively, you could contact state or local agencies to see if any local regression equations are
available for estimating flows from un-gaged watersheds.
Select Sources for Information on Regression Equations
ENSR. 2003. Determining Streamflow Statistics for Ungaged Watersheds in Maine. 04933-003-100. Prepared for
New England Interstate Water Pollution Control Commission. May 2003.
Flynn, R.H. Development of Regression Equations to Estimate Flow Durations and Low-Flow-Frequency
Statistics in New Hampshire Streams. U.S. Geological Survey Water-Resources Investigations Report
02-4298. U.S. Geological Survey, Reston, VA. .
Ries, K.G., III, and P.J. Friesz. 2000. Methods for estimating low-flow statistics for Massachusetts streams. U.S.
Geological Survey Water Resources Investigations Report 00-4135. U.S. Geological Survey, Reston,
VA. .
Stuckey, M.H. 2006. Low-flow, base-flow, and mean-flow regression equations for Pennsylvania streams, U.S.
Geological Survey Scientific Investigation Report 2006-5130. U.S. Geological Survey, Reston, VA.
USGS National Streamflow Statistics Program: http://water.usqs.gov/osw/streamstats/ssonline.html
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17
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Options for Expressing Daily Loads in TMDLs
3. Selecting the Daily Load Expression
This section provides guidance related to Step 3—Select Daily
Load Expression. Once the daily dataset is created in Step 2,
use it to identify an appropriate daily load expression to
supplement the longer term TMDL allocations. This section
provides information to support crafting the daily load
expression, including discussing types of daily loads
expressions as well as how to identify appropriate target values
on the basis of system characteristics. In addition, various
options for presenting the daily load expression in graphical
and tabular form are included.
Types of Daily Load Expressions
Two basic options are available for presenting daily loads. First, a static expression—a single daily load
number or set of numbers applicable to all conditions in the waterbody—may be presented. Second, a
variable expression may be used in which the applicable daily load value is determined as a function of a
particular characteristic that affects loading or waterbody response, such as flow or season. Of these, the
most common options will be targets that vary by flow (flow variable) and those that vary by month or by
season (temporally variable). Because TMDLs are unique in nature, there is no specific format for
presenting static or variable daily loads and the options presented here do not preclude variable targets
based on other characteristics.
What Are the Goals of this Section?
¦ Present different options for
expressing the daily load (static and
variable)
¦ Provide guidance for selecting the
appropriate option
¦ Provide guidance for selecting
appropriate target values ( e.g., load
percentiles)
¦ Present example graphic and tabular
representations of daily expressions
Static Daily Load Expressions
A static daily load expression consists of a single number (e.g., daily maximum) or set of numbers (e.g.,
daily average and daily maximum) that represent the daily load value for all conditions. Such an
expression is generally suitable for situations in which source inputs are relatively constant such as an
effluent dominated stream in a small watershed. In addition, a static daily load expression may be
developed for waterbodies where more complex loading and parameter interactions are involved as long
as the expression addresses the variability of the daily loading expected to occur under the allowable
loading scenario (the TMDL condition).
For example, in a watershed impaired by organic enrichment and oxygen depletion for which dynamic
modeling results have determined a long-term load that satisfies water quality criteria, an approach would
be to use statistical considerations to specify a limit on the daily load that is consistent with achieving the
long-term TMDL load as determined by the model output.
Achieving the cumulative load over a given period of time is equivalent to achieving the average daily
load over the same period of time. However, there will be natural variations in the individual loads while
still maintaining the average, with some days exceeding the average and some well below it. Therefore,
the question for the daily maximum load expression would be, given a certain average daily load, what is
the maximum daily load consistent with attaining that average? The answer depends on the distribution of
daily loads about the average. For example, suppose WQS will be attained if the pollutant load during the
month of June does not exceed 30 kg. This is equivalent to an average load of 1 kg/d; however, the load
on individual days will vary. The daily loads under the TMDL allocation scenario meet the average of 1
kg/d, but have a possible range from 0.1 to 10 kg/d (on the basis of predicted modeled values). Clearly, a
daily load up to 10 kg/d is consistent with meeting standards, as long as the average daily load (and
therefore, the cumulative monthly load) is met. Therefore, the maximum daily load expression could be
18
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Options for Expressing Daily Loads in TMDLs
set at 10 kg/d, as long as the TMDL allocations also specify that the cumulative load limit of 30 kg (or the
equivalent daily average of 1 kg) is also met.
Using the Daily Load Dataset to Identify a Maximum Daily Load
The daily load dataset that is consistent with the TMDL serves as the starting point for identifying the
static daily load expression. In the case where a long term daily load dataset is available, in which
multiple years of data and a variety of environmental conditions are represented, it is preferable to select a
maximum daily load as a percentile of the load distribution. A sufficiently long-term dataset allows for
minimizing error associated with the fact that the daily load dataset might not exactly match a normal or
lognormal distribution. For dynamic model output, the maximum daily load expression would be taken
directly from the output scenario representing the TMDL.
Instead of selecting the maximum load value as the daily load, it is advisable to select a value that
represents a high percentile (e.g., 95th or 99th), but not the maximum, of the distribution to protect against
the presence of anomalous outliers. For example, selecting the 95th percentile implies a 5 percent
probability that a daily load will exceed the specified value under the TMDL condition. Selecting higher
percentile values as the maximum daily target is justified when there is high confidence in the accuracy of
the dataset for extreme values. In cases where the analysis is based on a number of assumptions and there
is a higher uncertainty in the analysis, it might be more appropriate to select a lower and, therefore, more
conservative, maximum, providing an MOS. Whether the maximum daily load selected is based on the
75th or the 99th percentile load or some value in between, the TMDL developer should determine this on
the basis of the site-specific issues and characteristics.
Using Statistical Analysis to Identify a Maximum Daily Load
In other cases, long periods of continuous simulation data will not be available—either because the
analysis was developed without using a daily or subdaily dynamic model or because the period of
prediction is too short to reliably estimate upper percentiles. EPA's Technical Support Document for
Water Quality-based Toxics Control (USEPA 1991) describes a statistical approach to identifying a
maximum daily load in such circumstances. The approach included in the Technical Support Document
(TSD) is considered here for two cases—normally distributed daily loads and lognormally distributed
daily loads. (Further details on the derivation of the approach as well as definition of parameters are in
USEPA 1991.)
Which Number is the Right Number?
For a static expression, the maximum daily load value is set to represent the allowable upper limit of load values
that are consistent with the long-term average required by the TMDL. This means selecting some appropriate
maximum load from the daily load dataset (i.e., some percentile load value) that will account for high-flow events
while not relying too heavily on potential outlier values. Some factors to consider when deciding which number
(e.g., 90th, 95th, or 99th percentile) to set as the daily maximum load include the following:
¦ Confidence in the Original Analysis Representing Actual Conditions—A lower percentile is appropriate if
there is concern that the model could over-predict loads on individual days. If the model calibration is well
within the range of observed data, a higher number could be used.
¦ Representativeness of Underlying Dataset—TMDL analyses are highly dependent on the data on which
they are built. For example, the data available for model calibration could skew the simulated conditions if the
data do not cover a wide range of conditions. Fewer data translate into a calibration with more uncertainty;
therefore, a lower value should be selected.
¦ Type of Error Associated with Analysis—Policy decisions regarding the balance of Type I errors (judging a
daily load acceptable when it is actually not consistent with the longer-term average implied by the TMDL) and
Type II errors (judging a daily load unacceptable when it is actually consistent with the TMDL).
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19
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Options for Expressing Daily Loads in TMDLs
In the case where the daily data are normally distributed about the mean, the maximum daily load
expressed as the /;th percentile of the distribution is calculated as
MDL = /u + Z a = /u + Z CV/
r* p r p / fi
?
where MDL is the maximum daily limit, is the mean of the distribution (in this case, the average load
to achieve WQS), G is the standard deviation of the daily loads, CV is the coefficient of variation of the
daily loads (standard deviation divided by the mean), and Zp is the /;th percentage point of the standard
normal distribution. (Z-scores are published in basic statistical reference tables and are often included as a
spreadsheet function [e.g., NORMSINV(y) in MS Excel]. For the 95th percentile, Zp = 1.645, and for the
99th percentile, Zp = 2.326.)
In the case where the daily data are lognormally distributed about the mean—as is often the case with
loads that are dependent on flow magnitude—the MDL corresponding to a long-term average (LTA)
calculated in the TSD relates the permit MDL to the desired LTA as
MDL = LTA ¦ exp (zp cry - 0.5 crv2)
?
where
Zp = pth percentage point of the standard normal distribution, as above
CV = coefficient of variation of the untransformed data
i (CT= +l)
As a result, the LTA multipliers for the MDL given in Table 5-2 of the TSD as a function of CV can be
used to derive the MDL from the long-term average load that meets loading capacity where the lognormal
assumption is appropriate. (Of course, this reasoning applies only when direct limitations on individual
daily loads are not needed to achieve WQS.)
For example, suppose the loading capacity for the month of June is 60 kg, so the average daily load is 2
kg/d. Suppose further that these data are lognormally distributed, with a coefficient of variation of the
untransformed data of 0.5 and that the 95th percentile value is to be selected as the daily load expression
(Zp = 1.645). Then
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Options for Expressing Daily Loads in TMDLs
Variable Daily Load Expressions
An alternative to the static daily expression is the variable daily load. A variable daily load might be the
preferable approach for waterbodies where loading rates change significantly because of the
characteristics of different source inputs or waterbody conditions. A variable expression can also be used
to inform the post-implementation monitoring process more readily than a static expression because
monitoring data can be more easily compared to corresponding flow range or temporal targets.
Flow Variable
Developing a flow-variable target begins with load frequency analysis of the daily load dataset.
Establishing a load duration curve of the allowable daily loads can represent the daily load expression.
The curve represents a dynamic expression of the allowable daily load as a function of the measured flow
for the respective day (Figure 9). Alternatively, separate daily loads can be identified for select flow
conditions. For example, EPA's An Approach for Using Load Duration Curves in the Development of
TMDLs (USEPA 2006b) illustrates grouping flow intervals into five zones representing high flows (0-10
percent), moist conditions (10-40 percent), mid-range flows (40-60 percent), dry conditions (60-90
percent), and low flows (90-100 percent). For each of these flow categories, a daily maximum load and a
daily average load can be identified as the daily load expression for the respective TMDL. For example,
Figure 10 illustrates an example TMDL setting the 95th percentile load for each flow category as the daily
maximum load along with the 50th percentile load as the allowable daily median load.
observed flow.
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21
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Options for Expressing Daily Loads in TMDLs
1 .E+09
re
c 1.E+08
O 1.E+07
_l
E
|
o
2 1.E+06
re
o
v
1 .E+05
2.1 E+07
9.7
E+06
=8=
5.8E+06
4.3E+I
1.0E+06
High Flow (0-10) Moist (10-40) Mid Range (40-60) Dry(60-90) Low Flow (90-100)
Flow Zones (flow exceedance percentile)
¦06
• 3.0E+06
2.0E-
06 1.3E+06
: 25th-75th O Average ~Median n95th
Figure 10. Daily load expressions by flow category.
Temporally Variable
Temporally variable targets might be desirable when source inputs vary significantly by month or by
season. For this method, the daily load time series is segregated into suitable time periods, load values for
each period are ranked according to frequency, and appropriate targets are identified (e.g., mean and 95th
percentile). Figure 11 presents a graphical example of a seasonally variable daily load expression with a
daily maximum load set at the 95th percentile load and a corresponding daily average load.
1.E+03
^ 1.E+02
re
T3
£
"§ 1.E+01
m
D
o
¦C
a
m
o
Q.
ro
o
1.E+00
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i109.22 I
¦ 26.35
O
T
¦ 25th-75th o Average
~ Median D 95th
.13
o
00
o
c
0.83
Winter
Spring
Summer
Fall
Figure 11. Example of a seasonally variable daily load expression.
22
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Options for Expressing Daily Loads in TMDLs
Considerations for Selecting the Appropriate Daily Load Expression
Selecting the appropriate type of daily load expression
(static or variable) and the associated target value is
driven by the characteristics of the waterbody for which
the TMDL was calculated as well as characteristics of the
analysis used for developing the non-daily TMDL
allocations. Factors such as data availability, assumptions
made during the TMDL analysis, and time period
addressed by the non-daily allocations can all affect the
selection of the daily expression. When making the
decision, the practitioner should take into account
management implications, critical loading conditions, and
pollutant sources and behavior while maintaining
consistency with assumptions from the non-daily TMDL
analysis. While TMDLs differ from one to the next, there
are some general tendencies that can be used to guide
selection of the appropriate daily load expression. This
section outlines basic issues to consider in crafting the
expression on the basis of the analysis categories of
pollutant source type, waterbody type, and critical
conditions.
Factors associated with specific parameters of concern can provide some direction as to the appropriate
daily load option to use; however, other considerations such as critical conditions and pollutant source
types will be more indicative of the approach to use. The tables below provide a general rating (high,
medium, low) of the appropriateness of the various daily load options compared to several critical TMDL
considerations such as pollutant source type, critical conditions, pollutant behavior, and waterbody type.
Because of the complexities of TMDL analysis, multiple critical considerations will affect selection of the
daily load option and target selection. The matrixes are not absolute; they are presented as a broad guide
to the types of expressions that will generally be appropriate for the specific TMDL analysis. Where
possible, examples of typical situations in which the option might be considered are listed.
Pollutant Source Types and Critical Conditions
The type of pollutant sources involved in the TMDL can affect the expression of the daily load in a
number of ways. For example, pollutant source type can be a good indicator of critical conditions. Point
source-dominated waterbodies tend to experience water
quality problems due to discharges overwhelming
receiving streams. In a point source-dominated, impaired
segment, critical conditions generally occur during low
flows when less stream flow is available to dilute the
discharge. Target selection will generally focus on
ensuring that WQS are attained during critical low flows.
Static, daily load expressions could be reasonable in some
situations either by using the TSD approach to identify
maximum daily loads associated with a long-term average
load or by applying steady-state model results directly as
the maximum daily load. Nutrient and bacteria
contributions from failing onsite sewage treatment systems,
in general considered a nonpoint source of pollution,
behave like point sources in this regard.
Maintain Consistency with
the Original Approach
In developing the daily load dataset, you
should take care to not apply different
assumptions from those used in the original
TMDL analysis. For example, if a PLOAD
analysis predicts annual loads using
precipitation data from 1990 to 1996, flow
data obtained to develop a daily load dataset
should be from the same period.
Another example is presented by a TMDL
with an annual LA based on a series of
modeled daily loads representing a loading
scenario that meets WQS. You should
develop the daily load expression from the
range of modeled daily loads, rather than
using a separate analysis. For example,
developing a daily target by multiplying
observed or modeled flow by the numeric
criteria to develop a load duration curve is
inconsistent with the loads used to calculate
the original allocations.
Legend
High—usually the most appropriate option
for the factor under consideration given
relatively straightforward applications.
Medium—often an appropriate option for the
factor under consideration and may be
prioritized over options rated High when
particularly unique situations are present or
other considerations override the current
factor in importance.
Low—sometimes an appropriate option for
the factor under consideration, especially if
analysis factors present unique situations
such that the High or Medium options are
less appropriate.
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23
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Options for Expressing Daily Loads in TMDLs
Nonpoint source-dominated streams tend to experience impaired conditions as a result of rainfall events
and associated runoff. As a result, flow-variable daily load expressions might be a good option to use in
crafting the daily target. Critical conditions are often associated with high flows; however, this is not
always the case because some nonpoint sources (e.g., septic systems) can contribute to impaired
conditions during low flows.
Finally, in waterbodies with a mix of both point and nonpoint sources, there could be multiple critical
conditions or none apparent at all. For example, in a watershed where metals loading is attributed to
mining activity as well as legacy land use issues, continually flowing mine discharges can contribute to
the impairment during low flows, while runoff from abandoned mine lands contributes during rainfall
events. A variable daily load expression might be most appropriate for mixed source watersheds; although
practitioners might consider crafting a static expression as well. A variable expression could also be a
good option for states that need to develop batches of TMDLs for multiple watersheds where some
watersheds could be dominated by point sources and others by nonpoint sources, yet the TMDL
submittals, including the LAs, need to be consistent in format. Table 2 and Table 3 provide a general
ranking of the appropriateness of using the various daily load options in relation to pollutant source type
and critical condition considerations.
Table 2. Target option and pollutant source type considerations
Pollutant source types
Daily load expression option
Static
Flow range variable
Temporally variable
Point source-dominated
¦ Water quality problems
often related to discharge
that overwhelms
receiving stream's
dilution capacity
¦ Critical conditions
generally occur during
low flows
High—Could be appropriate for
steady state analysis TMDLs or
when dynamic modeling output
is used in conjunction with the
TSD approach for identifying the
maximum daily load (e.g.,
nutrient loads from a
wastewater treatment plant)
Medium—Consider when
discharges are related to
precipitation and critical
conditions occur at a
particular flow range (e.g.,
municipal separate storm
sewer systems [MS4s],
stormwater, combined
sewer overflows [CSOs],
surface mines)
Low—Might be
appropriate if
discharges are
seasonal in nature
(e.g., power plants,
wastewater treatment
plants [WWTPs] in a
summer vacation area
where population
increases)
Nonpoint source-
dominated
¦ Water quality problems
often related to
precipitation/runoff events
¦ Critical conditions
generally occur during
high flows
Medium—Could be appropriate
to apply TSD approach to long-
term average load to develop
corresponding maximum daily
value. Consider if parameters
are relatively constant but from
nonpoint sources (e.g., septics,
abandoned mine land seeps,
sediment oxygen demand,
sediment as in-stream source of
metals)
High—Might be
appropriate when problem
conditions occur with
varying intensity across
different flow ranges (e.g.,
streambank erosion)
Medium—Could be
appropriate when
sources are seasonal in
nature (e.g.,
agricultural, summer
season campground
package plants)
Mixed point source and
nonpoint source
¦ Water quality problems
associated with
precipitation/runoff events
(nonpoint source) and
dry-weather point source
discharges
¦ Different sources impact
stream at different flow
ranges
Medium—Could be appropriate
to apply TSD approach to long-
term average load to develop
corresponding maximum daily
value
High—Could be
appropriate for problem
conditions that occur with
varying intensity across
different flow ranges
Medium—Could be
appropriate when
sources are seasonal in
nature (e.g.,
agricultural, summer
season campground
package plants)
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Options for Expressing Daily Loads in TMDLs
Table 3. Target option and critical condition considerations
Critical condition
Daily load expression option
Static
Flow range variable
Temporally variable
Low flow
High—Consider when steady-
state analysis was used for
non-daily TMDL; point source
dominated with little nonpoint
source influence; critical
conditions occur at multiple
flow ranges
Low
Medium—Consider when
problem conditions occur
seasonally (e.g., nuisance
algal growth in-stream due to
summer low flows, slow flow
rate, lack of shading)
High flow
Low
High—Consider when critical
conditions are associated with
precipitation/runoff events and
sources include multiple
source types
Medium—Consider when
critical conditions are
associated with
precipitation/runoff events and
occur seasonally
Seasonal
Low
Low
High—Consider when critical
conditions are driven by
seasonal factors (e.g.,
seasonal water quality criteria)
Source Behavior
Source behavior is another factor in selecting and applying the TMDL analysis approach, and therefore
should be a consideration when selecting how to express the daily load. Major sources having seasonal
impacts to a receiving water include certain land uses and activities including agricultural lands (e.g.,
fertilizer application to crops, grazing, tilling); forest areas (e.g., managed areas that may be burned or
cleared); and urban areas (e.g., salting for deicing). For clearly seasonal pollutant sources, a temporally
variable daily load is suitable. Constant sources might fit well with a static expression, while those that
are precipitation driven (e.g., MS4s, CSOs, concentrated animal feeding operations [CAFOs]) might be
more appropriate for a flow-variable target. In addition, when selecting the target option, practitioners
should consider assumptions made during the TMDL analysis with respect to source behavior. If the
analysis assumed a constant delivery rate of pollutant, a static daily load could be selected. For example,
atmospheric deposition rates of parameters such as nutrients, mercury, and polychlorinated biphenyls
(PCBs) differ for wet and dry conditions; however, assumptions could be made during the TMDL
development process that certain pollutants are delivered on a more or less constant basis. Table 4
reviews source behavior considerations in relation to selecting the daily load expression.
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25
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Options for Expressing Daily Loads in TMDLs
Table 4. Target option and source behavior considerations
Source behavior
Daily load expression option
Static
Flow range variable
Temporally variable
Seasonal
(e.g., agricultural
nonpoint loading)
Low
Medium—Might be appropriate
if seasonal source is also
associated with specific flow
regimes
High—Could be
appropriate when seasonal
sources dominate the
waterbody response
Constant
(e.g., atmospheric
mercury)
High—May be appropriate to
consider when source is fairly
constant in nature or when the
TMDL approach assumes a
constant loading rate
Medium—Might be appropriate
if impact of constant source is
more critical during certain flow
regimes (e.g., low flows) than
others
Low
Precipitation driven
Medium—Might be appropriate
to apply the TSD approach to
develop single maximum
associated with long-term
average derived by dynamic or
general watershed model
High—Might be appropriate
when major sources are
precipitation driven
Medium—Consider using
if seasonal considerations
are significant
Waterbody Type
Waterbody type affects selection of the daily load target less critically than the considerations discussed
previously. However, some waterbody specific factors can affect daily load target selection. For example,
in tidal areas, the flow-variable approach might not be readily applicable because flow in the waterbody
cannot be readily measured nor is it necessarily an accurate indicator of available dilution. However, a
flow-variable approach would still be applicable if the allowable loading is driven primarily by the load
contained in free-flowing streams entering the waterbody. For lakes and impoundments, as well as free-
flowing streams, selection of the daily load will be determined more by other factors such as pollutant
source and critical condition than by the waterbody type itself. Table 5 discusses factors to consider
related to waterbody type.
Table 5. Target options and waterbody considerations
Waterbody type
Daily load expression option
Static
Flow range variable
Temporally variable
Lake/Impoundment
Medium—Consider when
major sources are point
sources or with dynamic
model output and the TSD
approach
High—Consider when loads
are driven by surface washoff
in the watershed
Medium—Consider for
situations where long-term
and seasonal control of
nutrients/sediment is
important for meeting lake
targets
Free-flowing
river/stream
Medium—Consider for point
sources; dynamic model
output/TSD
High—Consider when loads
are driven by surface washoff
in the watershed.
Medium—Consider when
major sources are seasonal in
nature or if critical conditions
occur seasonally
Tidal/estuarine
Medium
Medium—Consider when
loads are driven by surface
washoff in the watershed
High—Consider when major
sources are seasonal in
nature or if critical conditions
occur seasonally
26
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Options for Expressing Daily Loads in TMDLs
References
Cleland, B. 2002. TMDL Development from the "Bottom Up. "—Part II: Using Duration Curves to
Connect the Pieces. America's Clean Water Foundation, Washington, DC.
Cleland, B. 2003. TMDL Development from the "Bottom Up"—Part III: Duration Curves and Wet-
Weather Assessments. America's Clean Water Foundation, Washington, DC.
D.C. Cir. (United States Court of Appeals for the District of Columbia). 2006. Friends of the Earth, Inc.
v. EPA, etal. No. 05-5015.
ENSR. 2003. Determining Streamflow Statistics for Ungaged Watersheds in Maine. 04933-003-100.
Prepared for New England Interstate Water Pollution Control Commission. May 2003.
Flynn, R.H. Development of Regression Equations to Estimate Flow Durations and Low-Flow-Frequency
Statistics in New Hampshire Streams. U.S. Geological Survey Water-Resources Investigations
Report 02-4298. U.S. Geological Survey, Reston, VA. .
Ries, K.G., III, and P.J. Friesz. 2000. Methods for estimating low-flow statistics for Massachusetts
streams. U.S. Geological Survey Water Resources Investigations Report 00-4135. U.S.
Geological Survey, Reston, VA. .
Stuckey, M.H. 2006. Low-flow, base-flow, and mean-flow regression equations for Pennsylvania streams,
U.S. Geological Survey Scientific Investigation Report 2006-5130. U.S. Geological Survey,
Reston, VA.
USEPA (U.S. Environmental Protection Agency). 1991. Technical Support Document for Water Quality-
based Toxics Control. EPA/505/2-90-001. U.S. Environmental Protection Agency, Office of
Water, Washington, DC.
USEPA (U.S. Environmental Protection Agency). 2006a. Establishing TMDL "Daily" Loads in Light of
the Decision by the U.S. Court of Appeals for the D.C. Circuit in Friends of the Earth, Inc. v.
EPA, et al., No.05-5015, (April 25, 2006) and Implications for NPDES permits. Memorandum
from Benjamin Grumbles, assistant administrator, Office of Water. U.S. Environmental
Protection Agency, Washington, DC.
USEPA (U.S. Environmental Protection Agency). 2006b. An Approach for Using Load Duration Curves
in Developing TMDLs. U.S. Environmental Protection Agency, Office of Wetlands, Oceans and
Watersheds, Washington, DC.
DRAFT (6/22/07)
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Options for Expressing Daily Loads in TMDLs
28 DRAFT (6/22/07)
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Options for Expressing Daily Loads in TMDLs
Appendix A: Example Applications for Identifying Daily Load
Expressions
This appendix presents example applications to identify daily load expressions for TMDLs for which
long-term allocations were developed. Multiple scenarios are illustrated, covering a variety of TMDL
technical approaches, pollutant source types, and parameters of concern as well as several different daily
load expression options. Table 6 summarizes the characteristics of each example. Note that with the
exception of the Anacostia River total suspended solids (TSS) TMDL example, all examples are
hypothetical cases developed to highlight critical aspects of the conversion process. An effort was made
to present examples representative of relatively typical TMDLs with respect to technical approaches,
parameters of concern, critical analysis considerations, and pollutant source types. As with all TMDLs,
unique aspects of a particular analysis should be considered when converting long-term loads to daily
loads. In addition, for each example, conversion of the long-term load to a daily load is illustrated for the
overall loading capacity (sum of WLAs and LAs) and is not broken down into source categories. For
cases in which it is desirable to identify daily load expressions by source category, it is assumed that the
same steps can be applied to the source-specific loads (see the Anacostia example for an alternative
approach).
Table 6. Summary of examples of identifying daily load expressions for Non-daily TMDLs
Example
Parameter
Critical condition/source
behavior
TMDL method
Daily load option
1. Bird Creek
Nutrient
¦ Source inputs vary both by
time of year and by
precipitation and flow
General Watershed
Model (GWLF)—
Monthly Output
Monthly Variable
2. Red River
Metals
¦ Little apparent loading
relationship to flow
¦ Sources include legacy land
use (abandoned mine
drainage) and active,
precipitation-driven sources
(e.g., urban runoff) and point
sources
Dynamic Model
(LSPC)—Daily Output
Static
3. Royal Lake
Nutrients
¦ Lake conditions and source
impacts are seasonal
¦ Sources are both nonpoint
and point
General Watershed
Model (GWLF)—
Monthly Output
Seasonally Variable
4. Carter Creek
Bacteria
¦ Critical conditions are
dependent on flow with
varying sources dominated
different flow conditions
Load Duration
Flow Variable
5. Muddy River
TSS
¦ Dominated by nonpoint
sources
¦ Chronic loading is concern
Dynamic Model
(SWAT)—Daily Output
Flow Variable
6. Pine Lake
Nutrients
¦ Limited water quality data
¦ Sources include both
nonpoint and point sources
Empirical—Annual
Output
Static
7. Anacostia River
TSS
¦ Major sources are
precipitation driven
¦ Critical conditions are high
flow
Dynamic Model
(HSPF)—Daily Output
Static and Flow
Variable*
*depending on source
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29
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Options for Expressing Daily Loads in TMDLs
Example 1: Bird Creek Nutrient TMDL
Problem Definition Bird Creek was identified as impaired due to nutrients because of concerns over impacts on
biological communities and excessive nutrient loading to a downstream lake. The watershed is
primarily agricultural, including extensive cropland and a number of livestock operations.
TMDL Technical The TMDL was developed for phosphorus using GWLF to estimate watershed loads. Because
no numeric water quality criteria are available for nutrients, a target loading rate was developed
using a reference watershed—a watershed similar in characteristics (e.g., soils, elevation,
topography) to the impaired watershed and that supports its designated uses was identified as a
reference watershed. GWLF was applied to the reference watershed to identify an acceptable
loading rate (mass/area/time), and the loading rate was applied to the impaired watershed area
to establish a target annual phosphorus load.
The model was then run for a variety of management scenarios to identify allocation and load
reduction scenarios that met the target load. Load reductions were focused on controllable
sources (e.g., agricultural uses) during times of highest loading and greatest impact (e.g., spring
and summer).
TMDL Allocation TMDL allocations were expressed on a monthly basis to account for the temporal variations in
loading and resulting in-stream concentrations due to weather variations as well as source
activity. Highest flows occur during late winter and spring resulting from the combination of rain-
on-snow events, the melting of any remaining snow accumulated during preceding winter
months, and spring rain showers. Low flows occur during summer months because of infrequent
precipitation. Therefore, weather and flow conditions affect the seasonal variability in loading
due to precipitation-driven loading from cropland and smaller urban areas. In addition, source
loading varies temporally due to source activity, particularly summer and early fall grazing of
livestock, as well as the increased activities for cropland use during spring and summer. As
shown in Figure 12, average monthly flow and average monthly phosphorus concentration do
not follow the same pattern throughout the year. During winter and spring, flow and
concentration follow a similar pattern because in-stream phosphorus is primarily dominated by
runoff carrying phosphorus from cropland and developed areas. During the late summer and
early fall, in-stream conditions are also affected by sources that are not controlled by
precipitation and runoff events, such as grazing livestock with access to the streams and nearby
areas.
-Q-
-Qn
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Average monthlyflow —O—Average monthly TMDL concentration
Figure 12. Average monthly flow and concentration in Bird Creek.
Supplementary The GWLF model provides monthly output including flow volume and nutrient load. In addition to
the model output, continuous daily flow data are available for the watershed from a USGS gage.
The flow from this gage was used in the model calibration, and therefore the model appropriately
represents the observed flow magnitudes and patterns.
30
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Options for Expressing Daily Loads in TMDLs
Daily Load Dataset
GWLF model output was used with available continuous observed flows to develop the daily
load dataset for identifying the daily load expression. Because phosphorus is predominantly
loaded by surface pathways and major point sources are not present, it is not necessary to
separately account for non-flow-related components. For each month, modeled phosphorus load
and flow were used to calculate an average monthly phosphorus concentration. (Monthly
concentrations are shown in Figure 12.) For example, for February the average flow was 18.27
ft3/s, and the average monthly phosphorus load under TMDL conditions was 567.67 kg/month.
Therefore, the average phosphorus concentration for February is as follows:
567.67-
kg
month
18.27
ft3
month
28 days
day
86,400 5
0.0353
ft3
1,000,000
mg
kg
m
= 0.45 —
L
Daily flows (from gage data) were multiplied by the average phosphorus concentration for the
respective month (and a conversion factor) to calculate a series of daily phosphorus loads, as
shown in Figure 13.
Crafting the
Appropriate Daily
Load Expression
1.E+03
1.E+02
1.E+01
1.E+00
1.E-02 ,
1.E-03
-
-
j
h
*
lu
r
1
i
i
A
f
ill
I
\
n
r
If
M
life
rV
\
i
n
1
5
i
o
i
O
a
a
i
c\
a
i
£
a
i i
i
N C
T> C
i
c
c
i
M
f)
USGS daily flow (cfs) •
-TMDL load (lb/day)
Figure 13. Estimated daily phosphorus loads.
The factors and key issues considered in identifying the appropriate daily load expression
include the following:
¦ Non-daily Allocation Expression—allocations were expressed on a monthly basis.
¦ Source Behavior—Sources are primarily nonpoint sources with a mix of precipitation-driven
sources (e.g., cropland runoff) and sources with direct input to the stream (e.g., livestock
grazing near receiving streams).
¦ Flow Variation—In-stream conditions do vary with flow because of weather and resulting flow
patterns. However, source activities that are not dependent on flow conditions also affect the
in-stream conditions.
¦ Temporal Variation—In-stream conditions vary widely among months and seasons. Not only
are in-stream conditions influenced by temporal patterns in weather and the resulting runoff
patterns, but also by source activity that varies by month and season (e.g., grazing
schedules/locations, crop harvesting)
¦ Follow-up Monitoring—A year-long, intensive monitoring study is scheduled for the watershed
within the next 5 years. The monitoring will include weekly sampling, reflecting a wide variety
of conditions. During routine monitoring, the stream is sampled quarterly.
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31
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Options for Expressing Daily Loads in TMDLs
Daily Load The daily load expression for Bird Creek was established on a monthly basis to be consistent
Expression w'th the overall monthly allocations and includes a daily maximum (based on the 95th percentile
load occurring during that month) and a daily average for each month, as shown in Figure 14
and Table 7. Expressions were established as monthly-variable to account for the variation in in-
stream conditions resulting from both environmental conditions (e.g., weather, flow) as well as
source behavior.
Monthly values will also provide greater insight into tracking progress during post-TMDL
monitoring. Because an intensive monitoring study will provide multiple data points within each
month as well as across months, the monthly expressions will provide a more accurate target to
which data can be compared, rather than using a single value that is averaged over the entire
year and does not represent the widely fluctuating conditions across months. Including both an
average and a maximum daily load also provides more confidence and flexibility in tracking the
post-TMDL water quality. Comparing data only to the maximum might provide biased results if
sampling captures an unusually high event that results in localized peaks in phosphorus but
does not affect longer-term conditions. Tracking against the average will provide a better
understanding the long-term conditions.
Figure 14. Daily maximum and average allowable total phosphorus loads by month.
Table 7. Daily maximum and average allowable total phosphorus loads by month
Month
Daily load targets
Daily average
(lb/day)
Daily maximum
(lb/day)
Jan
5.7
19.5
Feb
76.0
235.9
Mar
26.2
75.6
Apr
3.1
8.9
May
3.8
10.3
Jun
1.2
2.9
Jul
1.1
2.8
Aug
0.2
0.4
Sep
0.4
0.7
Oct
0.6
1.9
Nov
1.4
3.8
Dec
1.3
3.9
32
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Options for Expressing Daily Loads in TMDLs
Example 2: Red River Aluminum TMDL
Problem Definition
TMDL Technical
Approach
Red River was listed as impaired by a number of metals, including aluminum. The observed
impairments are primarily due to recent and historical mining activities but are also influenced by
urban runoff and industrial point sources.
The TMDL was developed for aluminum using a dynamic watershed model, HSPF, to link
watershed sources to in-stream response and identify the loading capacity to meet applicable
water quality criterion (acute and chronic). The model was calibrated to existing conditions and
then run for a variety of load reduction scenarios to identify allocations that met the criteria in all
impaired segments.
Crafting the
Appropriate Daily
Load Expression
3,500
3,000
~ 2,500
>
5
£ 2,000 J»
¥
.£ 1,500 --
E ^
D
< 1,000
500 --
iff
io 1 -1-0 --p i--oh 1-®— + - -
0
500
1,000
1,500 42
2,000 |
2,500
3,000
3,500
Jan-99 Jul-99 Jan-00 Jul-00 Jan-01 Jul-01 Jan-02 Jul-02 Jan-03 Jul-03
O Obs. Load -
-Modeled Allowable Load -
Modeled Flow
TMDL Allocation
Expression
Supplementary
Data
Daily Load Dataset
Figure 15. Modeled aluminum daily loads under TMDL conditions along with observed
loads and modeled and observed daily flow.
TMDL allocations were expressed as annual loads based on an average annual load over the 5-
year simulation period, representing a variety of climatic and source loading conditions.
Because the TMDL analysis used a dynamic model, it produces a time series of allowable daily
loads. Supplementary data are not necessary to develop the daily load dataset for identifying the
daily load expression.
The modeling analysis provides daily output of simulated loads, providing the daily load dataset.
Alternatively, the daily load dataset could be developed using the observed flow record and
multiplying it by the allowable criterion (much like a load duration analysis). However, because
the TMDL allocations are based on the model output, it is most appropriate to again use the
modeled output for identifying the daily load expression.
The factors and key issues considered in identifying the appropriate daily load expression
include the following:
¦ Non-daily Allocation Expression—allocations were expressed on an annual basis.
¦ Source Behavior—Sources include precipitation-driven nonpoint sources (e.g., urban runoff),
discharges from active mines, and seeps/discharges from abandoned mine lands. Industrial
discharges also impact the river.
¦ Flow Variation—In-stream conditions do vary with flow because of weather and resulting flow
patterns. However, flow is not the only factor affecting loading to the river. There are a
number of significant sources in the watershed that are not dependent on rainfall and
resulting runoff and can impact the stream during all flow conditions (e.g., abandoned mine
lands).
¦ Temporal Variation—While in-stream flow conditions vary among months and seasons and
follow typical patterns from year to year, the pollutant loading and in-stream response does
not exhibit an identifiable temporal pattern. This is likely due to the mix of sources contributing
aluminum loading to the river and impacting the in-stream conditions.
Daily Load
Expression
The river experiences critical conditions during low- and mid-range flow periods when inputs
from abandoned mine lands impact in-stream concentrations and also during high flows when
DRAFT (6/22/07)
33
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Options for Expressing Daily Loads in TMDLs
precipitation-driven runoff and discharges carry pollutant loads from urban areas and mine sites.
There is also no defined pattern of variation among months or seasons. Therefore, daily load
expressions were not based on flow conditions or for varying time periods. Instead, a static
target was established on the basis of the long-term simulation data from the watershed model.
Using the range of allowable daily loads, a daily maximum and a daily average were identified.
The daily maximum target based on the 95th percentile and the daily average are presented in
Figure 16 along with the range of allowable loads simulated by the model.
100,000
10,000
1,000
100 =
10
Daily maximum = 95th percenfle load = 253 lb/day
Daily average = 97 lb/day
Range of Allowable Daily Loads
Figure 16. Daily maximum and average allowable load along with the range of allowable
loads simulated under TMDL conditions.
34
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Options for Expressing Daily Loads in TMDLs
Example 3: Royal Lake Nutrient TMDL
Problem Definition Royal Lake was listed as impaired by nutrients and nuisance algal growth. The lake drains a mix
of land uses, primarily high- and low-density residential with some isolated areas of concentrated
animal operations. The lake experiences increased algal growth and resulting decreased
dissolved oxygen in summer months—during times of warmer temperatures, more sunlight, and
increased nutrient loads.
TMDL Technical The TMDL was developed for phosphorus using GWLF (through BasinSim) to estimate
Approach watershed loads and BATHTUB to simulate in-lake response. (Figure 17 presents the BATHTUB
calibration for total phosphorus and chlorophyll a for a representative growing season.) The
TMDL was established to meet a chlorophyll a target concentration, representing an acceptable
level of algal growth based on literature values and historical data. The chlorophyll a target is
expressed as a growing season average of 20 |jg/L.
. ESTIMATE x OBSERUED
. ESTIMATE x OBSERUED
TMDL Allocation
Expression
Supplementary
Data
Daily Load Dataset
Crafting the
Appropriate Daily
Load Expression
Figure 17. Example BATHTUB calibration for representative growing season.
The watershed and lake models were applied for a variety of load reduction scenarios to identify
allocations to meet the target in-lake conditions.
TMDL allocations were expressed on a seasonal basis to meet the established water quality
target representing a growing-season (i.e., summer) chlorophyll a concentration. Watershed
loading also experiences seasonal variation due to seasonal patterns in precipitation and runoff,
further supporting the use of seasonal allocations. Allocations were established by land use and
subwatershed as well as for several point sources in the watershed (e.g., campgrounds,
WWTPs).
As opposed to using the original version of GWLF, which calculates the water balance on a daily
basis but provides only monthly output, the BasinSim interface allows the user to obtain the
calculated daily flows, concentrations and loads. Those daily values can provide the necessary
information to develop a time series of daily loads for identifying the daily load expression to
accompany the seasonal allocations.
Estimated daily total phosphorus loads were provided by the model for the 5-year simulation
period.
The factors and key issues considered in identifying the appropriate daily load expression
include the following:
¦ Non-daily Allocation Expression—allocations were expressed on a seasonal basis to be
consistent with the established chlorophyll a target of a growing season average.
¦ Impairment Conditions—Nutrient-related impairments occur in the lake primarily during
summer months when algal productivity is the highest. However, source loading throughout
the year contributes to the nutrients available in the lake to support algal growth.
¦ Source Behavior—Because nonpoint sources are primarily precipitation driven, nonpoint
loading is dependant on prevailing weather and resulting flow patterns. Precipitation and
resulting runoff and tributary inflow to the lake exhibit strong seasonal variation, with the
highest flows during winter and spring and the lowest flows during summer. Because point
DRAFT (6/22/07)
35
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Options for Expressing Daily Loads in TMDLs
sources discharge year-round, their relative impact is also seasonal, depending on how much
water is available in watershed streams for dilution. Because summer experiences the lowest
flows, point source impacts are the strongest during those months.
¦ Temporal Variation—Both in-lake conditions and source loading vary temporally. In-lake
conditions vary most notably by season, with minimal variation among months within a
season.
Daily Load The daily load expression for Royal Lake was established on a seasonal basis to be consistent
Expression w'th the TMDL allocations and includes a daily maximum and a daily average for each season,
as shown in Figure 18. Seasonally variable daily load targets also capture the variations in both
in-lake conditions and source loading and impacts. The daily maximum for each season is
equivalent to the 99th percentile load in the series of allowable daily loads occurring during that
season. The 99th percentile was chosen because of the relatively long simulation period, the
confidence that the higher predicted loads were not outliers, and the extreme range of the
simulated loads.
Figure 18. Daily maximum and average allowable loads by season.
36
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Options for Expressing Daily Loads in TMDLs
Example 4: Carter Creek Bacteria TMDL
Problem Definition Carter Creek was listed as impaired by bacteria with expected sources including commercial,
residential, and agricultural runoff as well as failing septic systems.
TMDL Technical The TMDL was developed using a load duration approach. Using a continuous flow record, a flow
Approach duration curve was developed on the basis of the flow percentile, or the percent of time the
respective flow value has been met or exceeded. The flow duration curve was then converted to
a load duration curve by multiplying the individual daily flows by the bacteria target, equivalent to
the not-to-exceed water quality criterion for fecal coliform of 400 counts/100 mL. Figure 19
presents the load duration analysis, including observed loads calculated on the basis of observed
bacteria data and corresponding daily flows.
Figure 19. Load duration analysis for fecal coliform in Carter Creek.
TMDL Allocation TMDL allocations were expressed for various flow regimes to represent times of varying source
Expression loading and in-stream conditions. For example, precipitation driven runoff from residential areas
and agricultural areas are expected to be dominant sources of bacteria during wet-weather
conditions. In addition, the stream experiences elevated bacteria levels during low flows, likely
due to failing septic systems that deliver bacteria loads through subsurface flows, influencing in-
stream conditions during baseflow. The following flow categories were used for establishing
allocations:
¦ High-flow zone: flows in the 0 to 10 percentile range, related to flood flows
¦ Moist zone: flows in the 10 to 40 percentile range, related to wet-weather conditions
¦ Mid-range zone: flows in the 40 to 50 percentile range, median stream flow conditions
¦ Dry zone: flows in the 60 to 90 percentile range, related to dry-weather flows
¦ Low-flow zone: flows in the 90 to 100 percentile range, related to drought conditions
For each flow category, an allowable daily load was identified using the median load for that flow
range. The allowable load was compared to the existing load to identify necessary load
reductions.
Table 8 presents the TMDL allocations establishing using the load duration approach.
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37
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Options for Expressing Daily Loads in TMDLs
Table 8. TMDL Summary for fecal coliform in Carter Creek
03
¦o
E
|
o
o
15
o
High
flows
Moist
conditions
Mid-range
flows
Dry
conditions
Low flows
TMDL component
0-10
10-40
40-60
60-90
90-100
Current Load1
298,727
14,298
120
324
95
TMDL1 = LA + WLA + MOS
13,897
3,729
1,664
802
411
LA
12,507
3,356
1,497
722
370
WLA
0
0
0
0
0
MOS (10%)
1,390
373
166
80
41
Load Reduction (%)
96%
77%
0%
0%
0%
Supplementary
Data
Current load represents median existing load for the respective flow zone. TMDL represents median
allowable daily load for the respective flow zone.
Because the TMDL analysis used the load duration approach, it is based on the available
observed flow and water quality data. Supplementary data are not necessary to develop the daily
load dataset for identifying the daily load expression.
Daily Load Dataset The load duration analysis calculates a series of allowable daily loads using observed flow
records and the water quality criterion, providing the daily load dataset.
Crafting the
Appropriate Daily
Load Expression
Daily Load
Expression
The load duration analysis identifies allowable daily loads for five flow categories. However, these
loads represent average conditions and are used to identify general load reductions necessary to
meet WQS. To supplement the non-daily TMDL allocations, corresponding daily maximum loads
should be identified to better gauge instantaneously measured in-stream conditions. For
example, while overall load reductions are not identified for the low-flow ranges, the stream does
experience occasional elevated bacteria during these times. A daily maximum would provide
more confidence in targeting and tracking control of low-flow sources.
The daily load expression for Carter Creek was established as a dynamic, flow-variable daily
maximum, as represented by the load duration curve in Figure 19. By setting the daily maximum
as a flow-variable value, the expression is consistent with the non-daily TMDL analysis in its
intent and underlying data, and the expression inherently accounts for varying source behavior
and resulting water quality conditions across the flow conditions. As an alternative presentation to
the load duration curve, the corresponding flow and allowable daily load values can be plotted as
a rating curve, shown in Figure 20. This graph presents the allowable daily load based on flow
magnitude rather than flow frequency. This presentation also provides an equation representing
the relationship between flow and daily maximum load to allow for easy calculation of the
allowable daily load on the basis of an observed flow value.
70,000
V
= 9.7863X - 1E-12
1,000 2,000 3,000 4,000 5,000 6,000 7,000
Row (cfs)
Figure 20. Flow versus daily maximum load.
38
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Options for Expressing Daily Loads in TMDLs
Example 5: Muddy River Sediment TMDL
Problem Definition
TMDL Technical
Approach
Muddy River was listed as impaired by sediment because of elevated TSS concentrations and
expected impairments to benthic communities and aquatic life habitat.
The TMDL was developed for using a dynamic watershed model, SWAT, to link watershed
sources to in-stream response. The model was used to identify the loading capacity to meet a
TSS target established to represent support of designated uses. The target was expressed as a
monthly average concentration of 40 mg/L on the basis of historical monitoring data for
reference stream reaches and was consistent with available literature on acceptable levels of
TSS to support fishery uses. Figure 21 presents the model calibration for hydrology, and Figure
22 presents the model calibration for TSS.
Sources loads were reduced in a variety of management scenarios to select the model scenario
that met the established water quality target and represented feasibly source controls.
I Avg Monthly Rainfall (in)
Avg Modeled Flow (Same Period)
Avg Observed Flow (1/1 /1996 to 12/31 /1996 )
Figure 21. Observed versus simulated daily flow
TMDL Allocation
Expression
Obs erred Modeled
Figure 22. Observed versus simulated TSS.
TMDL allocations were expressed as annual loads that are based on an average annual load
over the 15-year simulation period, representing a variety of climatic and source loading
conditions. Because in-stream impairment from sediment is a chronic issue with conditions
dependent more on cumulative loading than on instantaneous inputs and because nonpoint
sources dominate the sediment loading to the river, an annual allocation was appropriate for the
TMDL.
Supplementary
Data
Because the TMDL analysis used a dynamic model, it produces a time series of allowable daily
loads. Supplementary data are not needed to develop the daily load dataset for identifying the
daily load expression.
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39
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Options for Expressing Daily Loads in TMDLs
Daily Load Dataset The modeling analysis provides daily output of simulated loads, providing the daily load dataset.
Crafting the
Appropriate Daily
Load Expression
Developing the daily load expression for Muddy River is driven primarily by source behavior and
times of critical loading. The majority of sediment loading to the river is dependent on
precipitation events and resulting erosion and runoff as well as streambank erosion from
increased in-stream flows.
Daily Load To capture the dependency of sediment loading on surface runoff (reflected in-stream by
Expression resulting flow conditions), the daily load expression for Muddy River was established as flow-
variable targets. Modeled allowable daily loads were arranged according to their corresponding
daily flows and the associated flow exceedance percentile. The flows and daily loads were
grouped into 10 flow categories using increments of 10-percentile (e.g., 0-10, 10-20). A daily
maximum load and daily average load were calculated for each of 10 flow ranges, as shown in
Figure 23 and Table 9. Because there was high confidence in the model predictions and the
underlying observed dataset, the daily maximum was set at the 99th percentile load for each flow
grouping, rather than using a lower, more conservative load.
Row Exceedance Range
Figure 23. Daily maximum and average allowable loads by month.
Table 9. Daily maximum and average allowable loads by month
Flow
exceedance
range
Minimum flow in
range
(ft3/s)
Maximum flow
in range
(ft3/s)
Allowable
median load
(lb/day)
Allowable daily
maximum load
(lb/day)
0-10
0.0
3.9
165,078
2,284,880
10-20
3.9
4.8
24,017
74,641
20-30
4.8
6.7
10,414
40,257
30-40
6.7
10.8
5,135
13,877
40-50
10.8
20.7
1,381
3,991
50-60
20.7
39.0
321
1,227
60-70
39.0
75.1
263
722
70-80
75.1
157.9
112
255
80-90
157.9
394.8
63
116
90-100
394.8
4,958.0
24
84
40
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Options for Expressing Daily Loads in TMDLs
Example 6: Pine Lake Nutrient TMDL
Problem Definition
TMDL Technical
Approach
Pine Lake is impaired due to excessive nutrients. Eutrophic conditions result in frequent algal
blooms, which affect water supply intake and recreational uses (e.g., boating, fishing). In
addition, increased algal production and subsequent decay of plant matter depletes dissolved
oxygen in the lake, impacting the aquatic life uses. No numeric criteria are available for nutrients.
The TMDL for Pine Lake was developed for phosphorus using an empirical method to identify
allowable input loads. Vollenweider (1975) developed an empirical relationship between areal
phosphorus loading and lake residence time and depth to characterize lake trophic status.
Figure 24 presents Vollenweider's loading plot, where Lp is the areal loading of total phosphorus
in grams per square meter per year (g/m2/yr), H is mean depth in meters and rw is hydraulic
residence time in years.
Q.
O)
10
1 ::
0.1 1:
0.01
Dangerous
"eutrophic"
Permissible
"oligotrophic"
0.1
+H—
100
-t—I II I Mil
1 10
HItk (m yr-1)
Figure 24. Vollenweider loading plot.
1000
TMDL Allocation
Expression
Supplementary
Data
Daily Load Dataset
The allowable loading rate for Pine Lake was identified to represent the middle of the
mesotrophic boundary (between eutrophic and oligotrophic). Using the lake's mean depth and
hydraulic residence time identified an allowable average annual areal loading rate of 2.7 g/m2/yr.
Multiplying that rate by the lake's surface area of 300 acres (1,214,100 m2) results in an
allowable annual phosphorus load of 1,821,150 g/yr or 4,015 Ib/yr.
TMDL allocations were expressed as allowable annual phosphorus loads. The loading capacity
was calculated on the basis of the allowable loading rate identified using the Vollenweider
relationship. Existing loads to the lake were calculated using export coefficients found in
available literature for watershed land uses for nonpoint sources and using available discharge
flow and concentration data for point sources. The existing load was compared to the allowable
load to identify necessary load reductions, which were then distributed among targeted sources
to identify source allocations, also expressed as annual loads.
Very limited recent water quality, loading, or inflow data are available for Pine Lake. Very few in-
lake water quality data points exist within the past two decades, and no flow data are available
for the surrounding watershed.
Sufficient flow data are not available to support distributing the annual loading capacity for Pine
Lake. In addition, because the area that drains directly to the lake (rather than through tributary
inflows) is approximately 40 percent of the drainage area, using tributary flows to distribute the
allowable load could produce misleading results. Precipitation data could be used to distribute
the annual load over a determined time frame; however, distributing the annual load developed
with an empirical method into daily loads using precipitation data would force an inappropriate
level of resolution on the approach. Therefore, a statistical approach will be used to identify a
maximum daily load corresponding to the allowable average annual load.
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Options for Expressing Daily Loads in TMDLs
Crafting the
Appropriate Daily
Load Expression
EPA's Technical Support Document for Water Quality Based Toxics Control (USEPA 1991),
referred to as the TSD, provides a method for identifying a maximum daily limit that is based on
a long-term average and considering variation in a dataset. The method is represented by the
following equation
MDL = LTA
[:a-0.5o~]
Daily Load
Expression
References
where
MDL = maximum daily limit
LTA = long-term average
z = z statistic of the probability of occurrence
ct2 = ln(CV2+1)
CV = coefficient of variation
The daily load expression is identified as a static daily maximum load, calculated using the
method in the TSD for identifying maximum daily limits that are based on long-term averages.
Assuming a probability of occurrence of 95 percent and a CV of 0.3 (based on available data),
the maximum daily load corresponding to the average annual load of 4,015 Ib/yr (and average
daily load of 11 lb/day) is 17 lb/day.
USEPA (U.S. Environmental Protection Agency). 1991. Technical Support Document for Water
Quality-based Toxics Control. EPA 440/4-91-001. U.S. Environmental Protection
Agency, Office of Water, Washington, DC.
Vollenweider, R.A. 1975. Input-Output Models with Special Reference to the Phosphorus
Loading Concept in Limnology. Schweiz. Z. Hydrol. 37:53-84.
42
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Options for Expressing Daily Loads in TMDLs
Example 7: Anacostia River TSS TMDL
Problem Definition In 1998 the District of Columbia (DC) listed the Anacostia River as impaired by TSS, biochemical
oxygen demand, bacteria, organics, metals, and oil and grease. And Maryland has placed the
Anacostia River on its 303(d) list as impaired by nutrients (1996), sediments (1996), fecal
bacteria-nontidal waters (2002), impacts to biological communities (2002), toxics-PCBs (2002),
toxics-heptachlor epoxide (2002) and fecal bacteria-tidal waters (2004).
A TSS TMDL was calculated for the Tidal Anacostia in DC in 2002; it was replaced by a
watershed-wide TMDL in 2007 in which maximum daily loads for each source category were
calculated.
Table 10. Water quality standards
Jurisdiction
Tidal
Nontidal
Maryland
TSS— From April 1 to Oct. 31, seasonal secchi
application depth > 0.4 m.
Narrative based on protection of
aguatic life uses
District of
Columbia
TSS— From April 1 to Oct. 31, seasonal average
secchi depth > 0.8 m
Chlorophyll a—July 1 to September 30, seasonal
average = 25 |jg/L
Narrative based on protection of
aguatic life uses
TMDL Technical The modeling framework used for the TMDL analysis was a linked watershed/hydrodynamic/
Approach water quality model, an application of the USGS ESTIMATOR model and a reference approach
for sediment endpoints. The watershed model, HSPF, was linked to a customized hydrodynamic
and water quality model, Tidal Anacostia Model (TAM)/WASP. Results from the ESTIMATOR
model were used to calibrate the watershed model.
TMDL Allocation
Expression
Supplementary
Data
Daily Load Dataset
The modeling application developed for the TMDL analysis simulates daily values of both total
suspended sediment concentrations and water clarity on the basis of various inputs including:
information on tides, precipitation, and tributary flows; daily estimates of sediment loads from the
various sources; DC's MS4s; and CSOs from DC's combined storm sewer and sanitary sewer
system (CSS).
In the TMDL, the 3-year time period 1995-1997 was chosen as the simulation period for load
reduction scenarios to meet tidal water clarity criteria. This period was selected because it
represents a relatively dry year, wet year, and average year, according to precipitation data. The
TMDL was calculated as a seasonal average load and was based on the most critical loading
period from that 3-year period (i.e., the highest single daily loading predicted during the 3-year
period).
The sediment TMDLs for both Maryland and DC tidal and nontidal waters of the Anacostia
River are 7097.6 tons/year annually and 3396.1 tons/growing season for the growing season
from April 1 to October 31.
No additional data were required to develop the daily load dataset; however, model output was
processed and provided in spreadsheet format for the conversion to daily loads. Observed flow
data for the Anacostia River were included in the spreadsheet for each day as well.
Modeled daily TSS loading rates for the period 1995-1997 consistent with the annual/seasonal
TMDL loads were provided in a spreadsheet format for the following sources:
Table 11. Sources in the Anacostia TMDL analysis
Nontidal Anacostia
Tidal-Anacostia
Maryland MS4
DC MS4
Maryland Other Point Sources
DC Other Point Sources
Maryland Nonpoint Sources
DC Nonpoint Sources
Maryland MS4
Maryland Nonpoint Sources
DC Upper Anacostia MS4
DC Lower Anacostia MS4
DC Lower Anacostia CSO
DC Upper Anacostia CSO
DC Lower Anacostia Other Point Sources
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The factors and key issues considered in identifying the appropriate daily load expression
include the following:
¦ Non-daily TMDL Allocation Expression—allocations were expressed on a seasonal basis.
¦ Source Types—sources of sediment in the Anacostia River watershed are mainly nonpoint
sources and include sediment from historical land activities (clearing of forests), surface
mining and construction as well as general nonpoint source runoff from urban areas.
Streambank and stream channel erosion is believed to be the largest significant source of
sediment in the watershed. Tidal resuspension of bed sediment is also included in the list of
nonpoint sources of sediment in the watershed. Point sources include the MS4s of
Montgomery and Prince George's Counties and DC, multiple NPDES permitted municipal and
industrial facilities, as well as multiple CSO discharges.
¦ Source Behavior— Because of the urban nature of the watershed, natural hydrologic
functions of the Anacostia River and its tributaries have been significantly altered.
Precipitation flowing over land surfaces causes soil to be eroded and carried into nearby
streams either directly or through storm sewers. The altered urban hydrology causes
atypically high flows in streams during storms, and atypically low flows during dry periods.
The high flows occurring during storm events cause excessive erosion of streambanks and
streambeds, leading to the degraded stream channel conditions that can be observed in
many areas of the Anacostia watershed today. The high storm flows transport this eroded
sediment downstream to the main tributaries and, eventually, to the tidal Anacostia River.
¦ Flow Variation—with the exception of the Other Point Sources in the watershed, all major
source categories are associated with precipitation and runoff events and, thus, higher flow
conditions. The critical condition for water clarity in the tidal Anacostia is the occurrence of
high-flow events, which cause tributaries and storm sewers to discharge large amounts of
sediment into the tidal river.
Daily Load Load duration analysis was performed on the time series for each pollutant source and daily
Expression maximums were identified to accompany the long-term LA. The daily load expressions
developed for the Anacostia River TSS TMDL apply separate methods for unique source
categories. Separate approaches were used to identify the maximum daily load expression for
MS4s and nonpoint sources, CSOs, and for other point sources.
Table 12. Daily Load expression option used for each source
MS4 and NPS
CSO
Other point source
Tidal
Sinqle Load
Sinqle Load
Sinqle Load (TSD)
Nontidal
Flow variable
NA
Sinqle Load (TSD)
Nontidal MS4 and NPS:
¦ Conducted flow duration analysis with daily loading times series over the simulation period
(1995-1997) for each contributing source. Divided flows into five strata corresponding to
quintiles (< 20%, 20-40%, 40-60%, 60-80%, > 80%).
¦ Determined maximum daily TSS load over the simulation period for each source and for each
quintile.
¦ Applied the maximum daily load identified in the step above as the basis of the maximum
daily load expression for each source.
Tidal MS4 and NPS
¦ Used the TMDL condition daily loading time series for the simulation period for each source
¦ Determined the maximum daily TSS load for the period for each source
¦ Applied the maximum daily load identified in the step above as the basis of the maximum
daily load expression for each source
CSOs
¦ Used the TMDL condition daily loading time series for the simulation period for each CSO
source
Crafting the
Appropriate Daily
Load Expression
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¦ Separated the contributing CSO discharges into two categories: DC Tidal Upper Anacostia
and DC Tidal Lower Anacostia.
¦ Summed the contributing CSO daily loading time series within these two categories - DC
Tidal Upper Anacostia and DC Tidal Lower Anacostia.
¦ Determined the average and maximum daily TSS loads over this period of simulation for the
DC Tidal Upper Anacostia and DC Tidal Lower Anacostia.
¦ Applied the maximum and average daily load obtained in the step above as the basis for the
maximum daily load expression for each source.
Other point sources
¦ Used the TMDL condition daily loading time series for the simulation period for each other
point source.
¦ Converted these values, where necessary, from long-term averages to maximum daily loads
by multiplying them by a factor of 3.11 (from TSD Table 5-2). To meet the WLA, compliance
with the long-term average loads is also necessary.
Note: The following daily loads are DRAFT and have not been approved by EPA. Annually
Based and Seasonally Based Maximum Daily Loads were developed. Below, the Seasonally
Based Maximum Daily Loads are presented.
Seasonally Based Maximum Daily Loads
Table 13. Nontidal Anacostia (MS4, NPS, Other PS)
Flow range
MD Nontidal
DC Nontidal
MD Nontidal
DC Nontidal
(m3/s)
MS4-WLA
MS4-WLA
Other PS-WLA
Other PS-WLA
<0.98
0.24
0.03
0.618
0.0066
0.98-1.79
1.20
0.12
0.618
0.0066
1.79-2.71
0.48
0.05
0.618
0.0066
2.71-4.54
9.88
0.77
0.618
0.0066
>4.54
274.46
20.20
0.618
0.0066
Table 14. Nontidal Anacostia (MS4, NPS, Other PS)
Flow range
(m3/s)
MD Nontidal LA
DC Nontidal LA
Nontidal TMDL
<0.98
0.27
0.01
0.75
0.98-1.79
1.38
0.04
2.94
1.79-2.71
0.66
0.02
1.41
2.71-4.54
11.00
0.24
22.10
>4.54
1,124.84
0.84
1,420.54
Table 15. Tidal—MP (all flow ranges)
Background
MD Tidal
MS4-WLA
MD Tidal LA
TMDL to MD/DC Border
1420.54
18.85
0.0005
1,439.39
Table 16. Tidal—DC Upper Anacostia (all flow ranges)
Background
DC Upper
Anacostia
MS4-WLA
DC Upper
Anacostia
CSO-WLA
DC Upper
Anacostia LA
TMDL to Upper / Lower
Boundary
1,439.39
24.68
84.61 (max)
21.94 (avg)
--
1,548.67
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Options for Expressing Daily Loads in TMDLs
Table 17. Tidal—DC Lower Anacostia (all flow ranges)
Background
DC Lower
Anacostia
MS4-WLA
DC Lower
Anacostia
Other PS-WLA
DC Lower
Anacostia
CSO-WLA
DC Lower
Anacostia
LA
Total TMDL
1,548.67
14.76
0.0043
67.10 (max)
25.85 (avq)
-
1,630.54
References USEPA (U.S. Environmental Protection Agency). 1991. Technical Support Document for Water
Quality-based Toxics Control. EPA 440/4-91-001. U.S. Environmental Protection
Agency, Office of Water, Washington, DC.
ICPRB (Interstate Commission on the Potomac River Basin). 2007. DRAFT Report: Total
Maximum Daily Loads of Sediment/Total Suspended Solids for the Anacostia River
Basin, Montgomery and Prince George's Counties, Maryland and The District of
Columbia. Prepared for U.S. Environmental Protection Agency Region 3, Watershed
Protection Division, by Interstate Commission on the Potomac River Basin, Rockville,
MD.
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Options for Expressing Daily Loads in TMDLs
Appendix B: Identifying Daily Expressions for Non-daily
Concentration-based TMDLs
Some TMDLs rely on establishing a concentration-based loading capacity, often equivalent to an
applicable numeric water quality criterion. As with load-based TMDLs, if the established concentration-
based TMDL is not on a daily time step, the TMDL should also include a daily expression representing
the non-daily allocation. This appendix presents an approach for identifying a daily expression
corresponding to the non-daily allocations developed in concentration-based TMDLs.
Numeric water quality standards or other water quality targets (representing narrative water quality
criteria) have a duration component. For some criteria or targets, the duration is expressed as a daily
average or never to exceed value. As an example, waters designated for support of semi-permanent,
warm-water fish life in South Dakota must not exceed a daily maximum of 158 mg/L TSS. For
concentration-based TMDLs established to meet these targets, the TMDL is already expressed on a daily
basis. However, many water quality criteria or representative TMDL targets are based on longer time
steps, including monthly or even annual averages. Figure 25 illustrates an example TMDL developed to
attain the water quality criterion of an annual average concentration of 25 mg/L TSS. For concentration-
based TMDLs set equivalent to longer-term targets, the TMDLs should also include a daily expression.
Middle Fork LeBuche River
TMDL versus Existing Conditions
Month
Figure 25. Example of a concentration-based TMDL.
The daily expression representing the non-daily concentration-based TMDL should account for variability
occurring in the system. Water quality and quantity vary overtime in terms of volumes discharged and
constituent concentrations. Variations occur because of a number of factors, including changes in weather
conditions, precipitation, seasonality, and source inputs. Figure 25 shows how concentrations vary for a
parameter when water quality data are plotted against time.
Understanding the variability associated with water quality conditions is a key part of evaluating an
impaired waterbody. Water quality at a location over time can be described using common descriptive
statistics, such as the monthly or annual average concentration, the standard deviation, and the coefficient
DRAFT (6/22/07)
47
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Options for Expressing Daily Loads in TMDLs
of variation. The coefficient of variation is a statistical measure of the relative variability of a dataset and
is defined as the ratio of the standard deviation to the mean. Another way to describe water quality
patterns is by constructing a frequency-concentration plot of the data. Figure 26, for example, depicts the
Middle Fork LeBuche TMDL with a frequency-concentration plot of data that reflects attainment of water
quality standards.
Middle Fork LeBuche River
Relative Frequency Distribution
Total Suspended Solids (mg/L)
Figure 26. Example of a frequency-concentration plot.
On the basis of the frequency-concentration curve's shape, data can be described in terms of a particular
type of statistical distribution. Choices often include a normal distribution (bell-shaped), lognormal
distribution (positively skewed), or other variations on the lognormal distribution. EPA's Technical
Support Document for Water Quality-Based Toxics Control (USEPA 1991) uses lognormal distributions
to determine maximum daily and monthly average effluent limits, based on achieving a long-term average
(LTA) target and an understanding of variability.
The TSD provides a statistical framework to identify a target maximum daily concentration
corresponding to an LTA and based on a coefficient of variation and the assumption of a lognormal
distribution. The equation for determining the maximum daily limit (MDL) is as follows (USEPA 1991):
MDL = LTA x
where
MDL = Maximum daily limit
LTA = Long-term average (in the same units as the MDL)
Z = z-score associated with target recurrence interval
o2 = ln(CV2 + 1)
CV= Coefficient of variation
48
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Options for Expressing Daily Loads in TMDLs
Details regarding the mathematics used to derive this equation are described in USEPA (1991).
The z-score is sometimes called the standard score for normal distributions because it provides a useful
way to compare sets of data with different means and standard deviations. The z-score for an item (or a
particular recurrence interval) indicates how far and in what direction that item deviates from its
distribution's mean (expressed in units of its distribution's standard deviation). For instance, a z-score of
+1.0 indicates that item (or recurrence interval) is one standard deviation in the positive direction from the
mean. Z-scores are published in basic statistical reference tables and are often included as a spreadsheet
function (e.g., NORMSINV(y) in Microsoft Excel).
Using this relationship, the TSD includes a table of ITA toMDL multipliers for several recurrence
interval/coefficient of variation combinations (USEPA 1991). Table 18 provides a summary of these
multiplier values for several averaging periods used in TMDL development (e.g., 30-day, 60-day ... 365-
day). These averaging periods are also expressed as a recurrence interval to identify the appropriate z-
score for use in the equation. For example, the daily maximum of a 30-day averaging period equates to a
96.8 percent recurrence interval (e.g., [30/31]% or [k/k+l]% where k is the number of averaging period
days) with a corresponding z-score of 1.849. If the coefficient of variation for a parameter is 1.0, the
multiplier to convert the LTA to an MDL is 3.30 (Note: key boxes for this combination are shaded in
Table 18).
Table 18. Multipliers used to convert an LTA to MDL
Averaging
period
(days)
Recurrence
interval
Z-score
Coefficient of variation
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
30
96.8%
1.849
1.41
1.89
2.39
2.87
3.30
3.67
3.99
4.26
4.48
60
98.4%
2.135
1.50
2.11
2.80
3.50
4.18
4.81
5.37
5.87
6.32
90
98.9%
2.291
1.54
2.24
3.05
3.91
4.76
5.57
6.32
7.00
7.62
120
99.2%
2.397
1.58
2.34
3.24
4.21
5.20
6.16
7.06
7.89
8.66
180
99.4%
2.541
1.62
2.47
3.51
4.66
5.87
7.06
8.20
9.29
10.3
210
99.5%
2.594
1.64
2.52
3.61
4.84
6.13
7.42
8.67
9.86
11.0
365
99.7%
2.778
1.70
2.71
4.00
5.51
7.15
8.83
10.5
12.13
13.7
Figure 27 graphically illustrates a log probability plot of the EPA equation using data that reflect
conditions associated with attainment of the water quality standards. The x-axis is expressed as the z-
score of a normal probability distribution; the y-axis displays concentrations on a logarithmic scale. A
probability plot is one method that can be used to check the assumption of lognormality. If the data follow
the pattern of a lognormal distribution, they will fall approximately along a straight line, as shown in
Figure 27.
Figure 27 also shows translation of the recurrence interval for an annual averaging period (e.g., 365 days)
to the corresponding maximum daily concentration limit. The following calculations demonstrate
identification of the MDL on the basis of the corresponding LTA:
MDL = LTA x
where
LTA = 25 mg/L
z = 2.778 (based on recurrence interval of 99.7%)
CV= 1.164
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49
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Options for Expressing Daily Loads in TMDLs
o2 = In (CV2 + 1) = ln(1.1642 + 1) = 0.857
Therefore,
MDL = 25-^x e[2-778x0-926-°-5xa857] =25-^x8.533 = 213.3-^.
L L L
t
£
in
o
CO
T3
a>
T3
c
a>
o.
V)
3
CO
re
o
Middle Fork LeBuche River
Log Probability Plot
+
-3.0 -2.0 -1.0 0.0 1.0
Z-Score
2.0
3.0
Figure 27. Log probability display.
50
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