An Approach for Using Load Duration
1 Curves in the Development of TMDLs
-------
An Approach for Using Load Duration Curves in
the Development of TMDLs
EPA 841-B-07-006
August 2007
Watershed Branch (4503T)
Office of Wetlands, Oceans and Watersheds
U.S. Environmental Protection Agency
1200 Pennsylvania Ave. NW
Washington, DC 20460
Document posted at:
http://www.epa.gov/owow/tmdl/techsupp.html
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
U.S. Environmental Protection Agency
August 2007
Office of Wetlands, Oceans, & Watersheds
U.S. Environmental Protection Agency
This guide provides an overview on the use of duration curves for developing Total
Maximum Daily Loads (TMDLs). It is written for TMDL practitioners who are familiar
with relevant technical approaches and legal requirements. The guide describes basic
steps needed to develop duration curves, which identify loading capacities, load and
wasteload allocations, margins of safety, and seasonal variations. The guide also
discusses some considerations and limitations in using the approach, and includes several
case examples.
The duration curve approach allows for characterizing water quality concentrations (or
water quality data) at different flow regimes. The method provides a visual display of the
relationship between stream flow and loading capacity. Using the duration curve
framework, the frequency and magnitude of water quality standard exceedances,
allowable loadings, and size of load reductions are easily presented and can be better
understood.
The duration curve approach is particularly applicable because stream flow is an
important factor in the determination of loading capacities. This method accounts for
how stream flow patterns affect changes in water quality over the course of a year (i.e.,
seasonal variation that must be considered in TMDL development). Duration curves also
provide a means to link water quality concerns with key watershed processes that may be
important considerations in TMDL development. Basic principles of hydrology can help
identify the relative importance of factors such as water storage or storm events, which
subsequently affect water quality.
Water quality analysts should assess the appropriateness of using this framework to
develop a particular TMDL. An underlying premise of the duration curve approach is
correlation of water quality impairments to flow conditions. The duration curve alone
does not consider specific fate and transport mechanisms, which may vary depending on
watershed or pollutant characteristics. Such processes may include sediment attenuation,
plant uptake of nutrients, chemical transformations, or bioaccumulation. Practitioners
should consider using a separate analytical tool to develop a TMDL when factors other
than flow significantly affect a water body's loading capacity.
EPA 841-B-07-006 i August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
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.
EPA 841-B-07-006 ii August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
Table of Contents
1. DEVELOPMENT OF FLOW DURATION CURVES 1
a. What is a Flow Duration Curve? 1
b. Where to Get Flow Information 2
c. Duration Curve Intervals and Zones 2
2. DEVELOPMENT OF LOAD DURATION CURVES AND TMDLs 3
a. Numeric Water Quality Targets 3
b. Interpreting Load Duration Curves to Assess Water Quality 5
c. Margin of Safety 6
d. Development of Allocations 7
e. Seasonal Variation 9
f. Summary 11
3. APPROPRIATE USE OF LOAD DURATION CURVES 12
a. Appropriate When Flow is Primary Driver 12
b. Water Quality Standards Designed for All Flow Regimes 12
4. CONSIDERATIONS 13
a. Source Characterization 13
b. Large Scale Watershed Situations 13
c. Range of Flows Versus Single Condition 14
d. Storm Events and Hydrograph Separation 15
e. Utility in Identifying Potential Source Areas 16
5. CONNECTING TO IMPLEMENTATION AND RESULTS 17
APPENDICES
A. LOAD DURATION CURVE TMDLs - CASE EXAMPLE 19
B. ADDITIONAL EXAMPLES OF USING LOAD DURATION CURVE APPROACH 37
C. TARGETING POTENTIAL SOLUTIONS AND CONNECTING TO IMPLEMENTATION 55
D. ACRONYMS AND REFERENCES 65
List of Figures
Figure 1-1 General Form of the Flow Duration Curve 1
Figure 1-2 General Form of the Flow Duration Curve 3
Figure 2-1 Nitrate Loading Capacity Using Duration Curve Framework 4
Figure 2-2 Ambient Water Quality Data Using a Duration Curve Framework 5
Figure 2-3 Example TMDL Using Duration Curve Framework 9
Figure 2-4 Mississippi River Seasonal Flow Patterns 10
Figure 2-5 Mississippi River Monthly Variation 10
EPA 841-B-07-006 iii August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
List of Figures (cont.)
Figure 4-1 Fraction Analysis of Storm Flow Relative to Total Streamflow 15
Figure 5-1 Duration Curve with Contributing Area Focus 17
Figure 5-2 Documenting Erosion Control Program Results 18
Figure B-1 Chloride Loading Capacity Using Duration Curve Framework 38
Figure B-2 Nitrate Loading Capacity Using Duration Curve Framework 39
Figure B-3 Phosphorus Loading Capacity Using Duration Curve Framework 40
Figure B-4 Example Sediment Rating Curve 41
Figure B-5 Sediment Loading Capacity Using Duration Curve Framework 42
Figure B-6 Bacteria Loading Capacity Using Duration Curve Framework 43
Figure B-7 Concentration-Based TMDL 44
Figure B-8 TSS Loading Capacity Using Duration Curve Framework 45
Figure B-9 Middle Fork LeBuche River TMDL Using Duration Curve Framework . 47
Figure B-10 Bacteria Loading Capacity Using Duration Curve Framework 48
Figure B-ll Development of E. Coli Upper Target 49
Figure B-12 Development of Daily Value Based on Monthly Target 50
Figure B-13 Relationship Between 30-day Geometric Mean and Daily Target 51
Figure B-14 Monthly Bacteria Loading Capacity Using Duration Curve Framework . 53
Figure C-1 Duration Curve as General Indicator of Hydrologic Condition 57
Figure C-2 Duration Curve with Contributing Area Focus 58
Figure C-3 Duration Curve with Targeted Activity Focus 59
Figure C-4 Duration Curve with Delivery Mechanism Focus 60
Figure C-5 Documenting Program Results Using Duration Curve Framework 63
Figure C-6 Documenting Program Results Using Duration Curve Framework 63
List of Tables
Table 2-1 Approaches for Developing TMDL "Margin of Safety" 6
Table 2-2 Example TMDL Using Duration Curve Framework 8
Table 4-1 Example Source Area / Hydrologic Condition Considerations 16
Table 5-1 Example TMDL Summary Using Duration Curve Framework 18
Table B-l Calculation of Chloride Loads 38
Table B-2 Calculation of Phosphorus Loads 39
Table B-3 Calculation of Bacteria Loads 43
Table B-4 Middle Fork LeBuche River TMDL Summary 46
Table B-5 Werbaldo Creek TMDL Summary 51
Table B-6 Swamp Creek Monthly Mean Flows 52
Table C-l Example Management Practice / Hydrologic Condition Considerations... 62
EPA 841-B-07-006
IV
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
1. DEVELOPMENT OF FLOW DURATION CURVES
la. What is a Flow Duration Curve?
Flow duration curve analysis looks at the cumulative frequency of historic flow data over
a specified period. A flow duration curve relates flow values to the per cent of time those
values have been met or exceeded. The use of "percent of time " provides a uniform
scale ranging between 0 and 100. Thus, the full range of stream flows is considered.
Low flows are exceeded a majority of the time, while floods are exceeded infrequently.
A basic flow duration curve runs from high to low along the x-axis, as illustrated in
Figure 1-1. The x-axis represents the duration amount, or "percent of time ", as in a
cumulative frequency distribution. The y-axis represents the flow value (e.g., cubic feet
per second) associated with that "percent of time " (or duration).
Flow duration curve development typically uses daily average discharge rates, which are
sorted from the highest value to the lowest (Figure 1-1). Using this convention, flow
duration intervals are expressed as a percentage, with zero corresponding to the highest
stream discharge in the record (i.e., flood conditions) and 100 to the lowest (i.e., drought
conditions). Thus, a flow duration interval of sixty associated with a stream discharge of
440 cubic feet per second (cfs) implies that sixty percent of all observed daily average
stream discharge values equal or exceed 440 cfs.
Figure 1-1. General Form of the Flow Duration Curve
Salt Creek near Greenview, TT,
Flow Duration Curve
USGSGage: 055S2000
Dry
Conditions
1 ' ' I ' ' ' ' I
0 10
20
Flow Duration Interval (%)
USGS Flow Data
1,804 square miles
EPA 841-B-07-006
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
lb. Where to Get Flow Information
Information on river flows across the United States is
readily available from the U.S. Geological Survey
(USGS). Stream flow conditions on any given day can be
highly variable, depending on watershed characteristics
and weather patterns. Due to the wide range of
variability that can occur in stream flows, hydrologists
have long been interested in knowing the percentage of
days in a year when given flows occur. The mechanics of
constructing the flow duration curve in Figure 1-1
involved three steps. Daily average flow data was first
downloaded from the USGS National Web site
(http://waterdata.usgs.gov/nwis/sw). Data was then read
into a spreadsheet to determine duration curve intervals
covering the full range of flows. Lastly, flow duration
curve information was copied from the spreadsheet into a
graphics package to create the labeled display.
Not all waters or watersheds have gaging stations or flow data available. In such cases
estimation techniques are needed (USEPA, 2007). For instance, it may be appropriate to
use flow data of a similar, representative water body to develop the duration curve, based
on regression methods or drainage area ratios. The use of rainfall / runoff models can
also be used to develop stream flow estimates for use in a duration curve analysis.
Ic. Duration Curve Intervals and Zones
Duration curve analysis identifies intervals, which can be used as a general indicator of
hydrologic condition (i.e., wet versus dry and to what degree). Flow duration curve
intervals can be grouped into several broad categories or zones. These zones provide
additional insight about conditions and patterns associated with the impairment. A
common way to look at the duration curve is by dividing it into five zones, as illustrated
in Figure 1-1: one representing high flows (0-10%), another for moist conditions (10-
40%), one covering mid-range flows (40-60%), another for dry conditions (60-90%), and
one representing low flows (90-100%).
This particular approach places the midpoints of the moist, mid-range, and dry zones at
the 25th, 50th, and 75th percentiles respectively (i.e., the quartiles). The high zone is
centered at the 5th percentile, while the low zone is centered at the 95th percentile. Other
schemes can be used, depending on local hydrology and the water quality issues being
addressed by assessment efforts. For example, Figure 1-2 shows a flow duration curve
for a stream in the arid Southwest, where there is no flow more that half the time. In this
case, an alternative approach might consider use of two, three, or four zones, depending
on the water quality concerns being addressed by the TMDL. Again, the benefit of using
zones is to provide insight regarding patterns associated with concerns.
EPA 841-B-07-006
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
Figure 1-2. General Form of the Flow Duration Curve
Rio Puerco near Guadalupe, NM
Flow Duration Curve
USGSGage: 08334000
X
s
o
69 eft
3.8 eft
Dry Conditions with
No Flow
I ' ' ' ' I ' ' ' ' I ' ' '
10 W 30 40 50 60 70 80
Flow Duration Interval (%)
90
USGS Flow Data
100
420 square miles
2. DEVELOPMENT OF LOAD DURATION CURVES AND TMDLs
Flow duration curves serve as the foundation for development of load duration curves, on
which TMDLs can be based. A load duration curve is developed by multiplying stream
flow with the numeric water quality target (usually a water quality criterion) and a
conversion factor for the pollutant of concern. The following section provides a general
discussion of the elements to be addressed in developing a TMDL using the load duration
curve framework. A specific case study is presented in Appendix A, which illustrates
how this framework was applied to develop a fecal coliform TMDL.
2a. Numeric Water Quality Targets
The numeric water quality target represents the quantitative value used to measure
whether or not the applicable water quality standard (WQS) is attained. Generally, the
target is the water quality criterion contained in the WQS for the pollutant of concern.
The target may be constant across all flow conditions (e.g., chloride, nitrate, phosphorus,
or bacteria). The target could also vary with flow (e.g., sediment). Because the water
quality criterion is crucial in the development of the loading capacity, the absence of
numeric criteria poses challenges (e.g., sediment, nutrients). As efforts continue to
develop and adopt numeric sediment and/or nutrient criteria, practitioners should evaluate
whether an appropriate interim or site-specific, numeric endpoint can be identified prior
using the duration framework for TMDLs. Otherwise, alternative analytical methods
should be explored.
EPA 841-B-07-006
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
Numeric water quality targets are translated into TMDLs through the loading capacity.
EPA's current regulation defines loading capacity as "the greatest amount of loading that
a water can receive without violating water quality standards". The loading capacity
provides a reference, which helps guide pollutant reduction efforts needed to bring a
water into compliance with standards.
Basic hydrology represents a logical starting point to identify a loading capacity. First,
loads are directly proportional to flows (i.e., load equals flow times concentration times a
conversion factor). Second, water quality parameters are often related to stream flow
rates. For instance, sediment concentrations typically increase with rising flows as a
result of factors such as channel scour from higher velocities. Other parameters, such as
chloride, may be more concentrated at low flows and more diluted by increased water
volumes at higher flows.
Flow patterns play a major role when considering loading capacities in TMDL
development, regardless of the technical approach used. Duration curves, however,
provide the added benefit of looking at the full range of flow conditions. Figure 2-1
illustrates an example loading capacity curve developed using a duration curve
framework based on the flow duration curve shown in Figure 1-1. A sample calculation
is shown at one point along the curve corresponding to a flow duration interval of 60
using a nitrate target of 10 mg/L. Appendix B provides specific details on how loading
capacity duration curves are developed for use in TMDLs.
Figure 2-1. Nitrate Loading Capacity Using Duration Curve Framework
Salt Creek near Greenview, IL
Load Duration Curve
10000
1000
^
"a
High
Flows
Moist
Conditions
Mid-range
Flows
Dry
Conditions
Low
Flows
440 eft * 10 mg/L * 0.002695
= 11.86 tons /day
10
Flow Duration Interval
1,804 square miles
EPA 841-B-07-006
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
2b. Interpreting Load Duration Curves to Assess Water Quality
When using the duration curve framework in the context of developing a TMDL, it is
important to keep in mind that the entire duration curve should be applied to account for
the various flow regimes. Ambient water quality data, taken with some measure or
estimate of flow at the time of sampling, can be used to compute an instantaneous load.
Using the relative percent exceedance from the flow duration curve that corresponds to
the stream discharge at the time the water quality sample was taken, the computed load
can be plotted in a duration curve format (Figure 2-2).
By displaying instantaneous loads calculated from ambient water quality data and the
daily average flow on the date of the sample (expressed as a flow duration curve
interval), a pattern develops, which describes the characteristics of the water quality
impairment. Loads that plot above the curve indicate an exceedance of the water quality
criterion, while those below the load duration curve show compliance.
The pattern of impairment can be examined to see if it occurs across all flow conditions,
corresponds strictly to high flow events, or conversely, only to low flows. Impairments
observed in the low flow zone typically indicate the influence of point sources, while
those further left generally reflect potential nonpoint source contributions. This concept
is illustrated in Figure 2-2. Data may also be separated by season (e.g., spring runoff
versus summer base flow). For example, Figure 2-2 uses a "+" to identify those ambient
samples collected during primary contact recreation season (April - October).
Figure 2-2. Ambient Water Quality Data Using a Duration Curve Framework
I Group by Hydrologic Condition |
Identify
- Storm flows
- Season
10 20 30 40 SO 60 70
Flow Duration Interval
90 100
EPA 841-B-07-006
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
The utility of duration curve zones for pattern analysis can be further enhanced to
characterize wet-weather concerns. Some measure or estimate of flow is available to
develop the duration curves. As a result, stream discharge measurements on days
preceding collection of the ambient water quality sample may also be examined. This
concept is illustrated in Figure 2-2 by comparing the flow on the day the sample was
collected with the flow on the preceding day. Any one-day increase in flow (above some
designated minimum threshold) is assumed to be the result of a surface runoff event
(unless the stream is regulated by an upstream reservoir). In Figure 2-2, these samples
are identified with a shaded diamond.
2c. Margin of Safety
A "margin of safety" (MOS) is typically expressed either as unallocated assimilative
capacity or as conservative analytical assumptions used in establishing the TMDL (e.g.,
derivation of numeric targets, modeling assumptions or effectiveness of proposed
controls). The "margin of safety" may be explicitly stated as an added, separate quantity
in the TMDL calculation. The "margin of safely" may also be implicit, as in
conservative assumptions. Table 2-1 presents six common approaches for incorporating
a "margin of safety" into TMDLs. Some States may have established approaches for
determining the MOS either explicitly or implicitly as a step in their TMDL development
process (as indicated in Table 2-1). These approaches should be taken into consideration
when identifying the MOS using a duration curve framework.
Table 2-1. Approaches for Developing TMDL "Margin of Safety"
Type of . ,
T»/T -eve* Approaches
Margin of Safety vv
Explicit
Set numeric targets at more conservative levels than analytical
results indicate
Add a safety factor to pollutant loading estimates
Do not allocate part of available loading capacity; reserve for
MOS
Implicit
Conservative assumptions in derivation of numeric targets
Conservative assumptions when developing numeric model
applications
Conservative assumptions when analyzing prospective
feasibility of practices and restoration activities.
Using a duration curve framework, one option could be to identify an explicit "margin of
safety" for each listed reach and corresponding set of flow zones. For example, one way
to define the MOS could be based on the difference between the loading capacity as
calculated at the mid-point of each of the five flow zones, and the loading capacity
calculated at the minimum flow in each zone. Given that the loading capacity is typically
much less at the minimum flow of a zone as compared to the mid-point, a substantial
"margin of safety" is provided. The "margin of safety" ensures that allocations will not
EPA 841-B-07-006 6 August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
exceed the load associated with the minimum flow in each zone. This approach also
allows for recognition that the uncertainty associated with effluent limits and water
quality may vary across different flow conditions. For instance, because of changes in
variability at different flow regimes, the uncertainty may be greater under high flow
conditions than at low flow (or vice versa).
Because the allocations are a direct function of flow, accounting for potential flow
variability is an appropriate way to address the "margin of safety". Although minimum
flows over long periods of record at the USGS gage sites are typically used when
defining the MOS for the low flow zone, the effect of point source discharges on effluent
dominated streams should also be considered. Adjustments to the MOS may be needed
to account for situations where the only flow under low flow conditions is treatment plant
discharges.
An explicit "margin of safety" identified using a duration curve framework is basically
unallocated assimilative capacity intended to account for uncertainty (e.g., loads from
tributary streams, effectiveness of controls, etc.). As new information becomes available,
this unallocated capacity may be attributed to nonpoint sources including tributary
streams (which could then be added to the load allocation); or it may be attributed to
point sources (and become part of the waste load allocations).
2d. Development of Allocations
Allocations represent those portions of a receiving water's loading capacity attributed to
point sources (waste load allocations) or to nonpoint sources and natural background
(load allocations). Allocations are a key part of the TMDL; they represent the basic road
map to water quality standards attainment. The duration curve framework provides a
reasonable way to define allocations because it allows adjustments, which reflect
differences in the types of sources that may be dominant under various flow conditions.
For instance, in effluent dominated streams wastewater treatment facilities (WWTFs)
exert a significant influence on water quality at low flows. Under a duration curve
framework, the allocation or portion of the loading capacity attributed to WWTFs can be
greater in the low flow zone. Similarly, runoff from nonpoint sources tends to dominate
water quality under high flow conditions. Thus, the allocation or portion of the loading
capacity for nonpoint sources can be greater under moist and high flow conditions using a
duration curve framework.
Waste load allocation development for continuous point source discharges is relatively
straightforward using a duration curve framework. Consideration of pollution control
measures is typically done in conjunction with NPDES permit development. Waste load
allocations (WLAs) can be expressed at one level across the entire duration curve, or
WLAs may be tiered to specific flow levels and the corresponding flow duration interval.
Common methods used for allocating waste loads described in TMDL guidance (EPA,
1991) include equal percent removal, equal effluent concentrations, and hybrid methods.
These allocation schemes can easily be applied to a duration curve framework.
EPA 841-B-07-006 7 August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
Storm water and nonpoint sources of pollutants, on the other hand, present a greater
challenge because pollutants are transported to surface waters by a variety of mechanisms
(e.g., runoff, snowmelt, groundwater infiltration). Best management practices (BMPs)
generally focus on source control and / or delivery reduction. Common methods in use to
develop either WLAs for storm water or load allocations for nonpoint sources are also
applicable under a duration curve framework. Examples include consideration of
jurisdictional area, land use, or impervious cover.
An advantage of the duration curve framework is that allocations can be adjusted by
zone. This may be needed to account for different source areas and delivery mechanisms
that may dominate under different flow conditions. Table 2-2 summarizes the TMDL
framework using the duration curve approach, showing the TMDL (equivalent to the
loading capacity), the "margin of safety", and the amount available for allocations (both
load and waste load).
Table 2-2. Example TMDL Using Duration Curve Framework
Segment
ID
Q21-01
Name
TMDL
Component
Quepote Brook
KorstonDPW (WWTP)
Loburn (WWTP)
KorstonDPW (MS4/P1)
Loburn (MS4/P2)
TMDL
MOS
LA
WLA
WLA
WLA
WLA
Duration Curve Zone
(Expressed as T-org/day)
High
Moist
Mid
Dry
Low
19.87
4.31
9.18
0.12
0.05
3.81
2.40
9.37
3.92
3.10
0.12
0.05
1.33
0.85
4.09
0.76
1.88
0.12
0.05
0.80
0.48
2.20
0.66
0.79
0.12
0.05
0.36
0.22
1.29
0.77
0.35
0.12
0.05
0.00
0.00
Figure 2-3 illustrates a TMDL using a duration curve framework. Waste load allocations
are specified for municipal treatment plants that reflect NPDES permit limits. In the case
of both Table 2-2 and Figure 2-3, these waste load allocations are based on technology-
based effluent limits at facility design flows. The waste load allocations are constant
across all flow conditions and ensure that water quality standards will be attained.
Waste load allocations are also identified for municipal separate storm sewer systems
(MS4), which reflect increased loads under higher flow conditions. In the Figure 2-3
example, storm water waste load allocations for MS4 communities are based on the
percent jurisdictional area approach. In this case, three percent of the watershed falls
within the jurisdiction of MS4 communities. Thus, the MS4 wasteload allocation is three
percent of the available allocation for each zone. The remaining ninety-seven percent is
designated for nonpoint sources and natural background as load allocation for each zone.
Load allocations and MS4 waste load allocations have been determined at the mid-point
of each zone based on appropriate portions. The allocation curves are determined by
interpolating between these points.
EPA 841-B-07-006
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
Figure 2-3. Example TMDL Using Duration Curve Framework
Jones River
TMDL Summary
10000
Waste Load Allocation Wastewater Treatment Facilities
I 1 1 1 1 1 1 1 1
10
20
30
40
SO
60
70
80
90 100
Flow Duration Interval (%,
2e. Seasonal Variation
The Clean Water Act (CWA) §303(d) states that in identifying TMDLs: "such load shall
be established at a level necessary to implement the applicable water quality standards
with seasonal variations". Seasonal variation in flow is a key part of TMDL
development. Figure 2-4 shows an example of seasonal flow patterns using monthly
statistics for the Mississippi River at Winona. Flow is expressed as a unit area rate (i.e.,
cubic feet per second (cfs) per square mile). Unit area rates, determined by dividing the
drainage area at the gage into the flow, enable a consistent way to compare flows from
watersheds of different sizes.
Another way to view seasonal variation is through the use of flow duration curves.
Figure 2-5 illustrates monthly flow data expressed as duration curve intervals for the
Mississippi River at Winona. The "box and whisker" format allows analysis of general
patterns by conveying information on the distribution of the data. For example, April
flows for the Mississippi River at Winona and its tributaries are typically in the high and
moist zones (median flow around 9%). Accordingly, consideration of seasonal variation
in TMDL development and implementation planning to address water quality concerns in
April would focus on source areas typical of these conditions. For this region, moist
conditions in April generally reflect more saturated soil conditions, when upland sources
such as cultivated fields exert a greater influence on stream flow and water quality.
EPA 841-B-07-006
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
Figure 2-4. Mississippi River Seasonal Flow Patterns
Mississippi River at Winona
(1970-2004)
2.0
1.5--
g.
0.5 --
0.0
r
90th
75th
Median
25th
10th
Watershed Size: 59,200 square miles
Figure 2-5. Mississippi River Monthly Variation
Mississippi River at Winona
(1970 - 2004)
Flow Duration Interval (%)
3 00 Ot -t*. W
3 O O O O O
Month
|-J-| | | | Median = 9%
T0II-
1 *
;
J Median = 46%
1
^
/
1
y
T
^
1
^
April-Oct Zone
|^ |»OUi |
pc
^-LTSthJ
^ 1 Median |
*^^]
-^
/f/gA
Moist
Mid
Dry
Low
* Aierage
Watershed Size: 59,200 square mites
EPA 841-B-07-006
10
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
Conversely, August and September flows generally fall in the mid-range zone (median
flow around 46%). Flows from tributary rivers to the upper Mississippi are even lower,
typically falling into the dry zone during these months. This shifts TMDL development
and implementation planning to source areas representative of these conditions. For
these tributaries to the Mississippi River, source assessment and implementation planning
might focus on wastewater treatment plant discharges or activities that have a direct
influence on streamside riparian areas (e.g., straight pipes and livestock access).
2f. Summary
The use of duration curves provides a technical framework for identifying "daily loads"
in TMDL development, which accounts for the variable nature of water quality
associated with different stream flow rates. Specifically, a maximum daily concentration
limit can be used with basic hydrology and a duration curve to identify a TMDL that
covers the full range of flow conditions. With this approach, the maximum "daily load"
can be identified for any given day based on the stream flow. Identification of a loading
capacity using the duration curve framework is driven by the flow duration curve and a
water quality criterion or target value. The target may be constant across all flow
conditions (e.g., chloride) or the target may vary with flow (e.g., sediment rating curves).
Under the duration curve framework, the loading capacity is essentially the curve itself.
The loading capacity, which sets the "total maximum daily load" on any given day, is
determined by the flow on the particular day of interest. The use of duration curve zones
can help provide a simplified summary through the identification of discrete loading
capacity points by zone. Using a duration curve framework, an explicit "margin of
safety" can be identified for each listed reach and corresponding set of flow zones.
Allocations within the TMDL are set in a way that reflects dominant concerns associated
with appropriate hydrologic conditions.
Appendix B includes example calculations for chloride, nitrate, phosphorus, total
suspended solids, and bacteria. Appendix B also provides a discussion on ways the
duration curve framework can be used to address different averaging periods (other than
daily) in identifying loading capacities, particularly where a concentration-based target
exists (expressed as monthly, seasonal, or annual average values).
EPA 841-B-07-006 11 August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
3. APPROPRIATE USE OF LOAD DURATION CURVES
A few words about the appropriate use of the duration curve approach follow. First and
perhaps most importantly, water quality analysts should assess the appropriateness of
using this framework to develop a particular TMDL. Practitioners should also consider
the suitability of using it as the sole basis for assessment versus supplementing its use
with other analytical tools, such as water quality models.
3a. Appropriate When Flow is Primary Driver
An underlying premise of the duration curve approach is correlation of water quality
impairments to flow conditions. The duration curve alone does not consider specific fate
and transport mechanisms, which may vary depending on watershed or pollutant
characteristics. Such processes may include sediment attenuation, plant uptake of
nutrients, or chemical transformations.
The duration curve is more appropriate in cases where flow is a primary driver in
pollutant delivery mechanisms, and other processes are a relatively insignificant part of
the total loading. Flow, in many cases, is the principal force behind habitat modification,
stream bank erosion, and other concerns preventing attainment of designated uses. Use
of a duration curve in flow-induced nonpoint source situations more generally reflects
actual loadings than in cases where flow is only one of many components influencing the
overall loading. Practitioners should consider using a separate analytical tool to develop
a TMDL when factors other than flow significantly affect a water body's loading
capacity. For example, use of the duration curve approach may not work in situations
involving lakes or large coastal embayments, where factors other than stream flow exert a
major effect on observed water quality conditions.
3b. Water Quality Standards Designed for All Flow Regimes
Another assumption behind the duration curve framework is that applicable water quality
standards are protective of the designated use(s) over the entire flow regime. For a
majority of pollutants, water quality criteria do not identify specific restrictions. When
these special conditions exist, practitioners should evaluate the appropriateness of the
duration curve method, or determine if there is a means to work within those provisions.
A possible scenario of a flow provision is where criteria explicitly state applicability at
the 7Q10 flow. This reduces the importance of the criteria during the remaining flows
(e.g., moderate to wet weather). In this example, the utility of the duration curve method
is better suited as a diagnostic tool identifying magnitude and frequency of concerns
across all flows. Similarly, the State adopted water quality standards may include a flow
exemption (e.g., high flows), which should be considered when using the duration curve
framework for TMDL development. Another situation may be where the bacteria
criterion applies only during the swimming season. In order to work within this type of
provision, the duration curve could be analyzed for just the relevant months or time
period.
EPA 841-B-07-006 12 August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
4. CONSIDERATIONS
This section discusses some potential concerns and considerations with utilizing the
duration curve approach to develop TMDLs.
4a. Source Characterization
The duration curve method, by itself, is limited in the ability to track individual source
loadings or relative source contributions within a watershed. Additional analysis is
needed to identify pollutant contributions from different types of potential sources and
activities (e.g., construction zone versus agricultural area) or individual sources of a
similar source category (e.g., WWTF #1 versus WWTF #2). Without such analysis, it
could be difficult to distinguish WLAs and LAs for individual sources.
Practitioners interested in more precise source characterization should consider
supplementing the duration curve framework with a separate analysis. An added
analytical tool might aid in evaluating allocation scenarios and tracking individual
sources or source categories. This could allow for improved targeting of monitoring and
restoration activities.
Information about individual sources could also be made available, where existing load
contributions and reductions are central to evaluating potential water quality trading
options. For example, a duration curve analysis might highlight the importance of low
flow, point source issues. Depending on the manner in which the analysis is applied, the
resulting TMDL could be based on the assumption that all point sources should be treated
the same (i.e., the same loading from each source despite their relative location in the
watershed and existing effluent loads).
Use of a separate or supplemental analysis is also beneficial in cases where bacteria pose
a water quality problem. In this context, applying a duration curve in concert with
microbial or bacterial source tracking data might allow for distinction of various bacteria
sources (i.e., domestic pet, human, geese, deer, etc.). This information can provide
direction on how the TMDL loadings could be allocated. For instance, practitioners may
choose to impose load reductions to sources that are anthropogenic or controllable, and
carry over wildlife sources at existing loading rates.
4b. Large Scale Watershed SituationsError! Bookmark not defined.
Depending on the pollutant of concern as well as the number and types of sources, it can
be beneficial to divide a watershed into subwatersheds as a first step in the TMDL
development process. Basically, a duration curve analysis is performed for each
subwatershed, resulting in multiple, more refined loading capacity curves and subsequent
allocations. Working on a subwatershed level is important in addressing issues with
relative source contributions or spatial variations in the loading capacity, and can be
EPA 841-B-07-006 13 August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
useful in calculating more site-specific allocations. The following examples illustrate
when it might be necessary to discern relative source contributions, isolate impaired
waters, or address spatial variation.
Discerning relative source contributions. In cases involving multiple point
sources within a watershed, where each point source has a different effect on the
receiving water, it might be useful to evaluate each point source individually (i.e.,
divide the watershed so that some or all of the point sources are isolated). The
resulting duration curves could show that the loading of one point source
comprises a larger portion its relative loading capacity than another, potentially
highlighting the relative impact of each point source. When there are multiple
nonpoint source loadings, applying the duration curve framework on a
subwatershed scale may also help to reveal more localized impacts.
Isolating impaired waters. Sometimes only a few tributaries within a watershed
are impaired, warranting a TMDL analysis on a smaller scale. Rather than
evaluating the entire watershed, isolating the impaired tributaries into individual
subwatersheds can allow for a more meaningful, site-specific duration curve
analysis.
Addressing spatial variation in loading capacity. Larger watersheds comprised of
multiple second and third order streams often exhibit a range of assimilative
capacities in different parts of the watershed. An illustration of an extreme case is
the differing loading capacities of a headwater stream versus a first-order stream
near the mouth of a watershed. As such, it might be advantageous to divide a
larger watershed into smaller units.
It is important to note that subwatersheds are interconnected, which may need to be
accounted for on a case-by-case basis. Also, dealing with ungaged, headwater streams
could present some obstacles in constructing a duration curve, as there is usually less data
available on such waters.
4c. Range of Flows Versus Single Condition
Summarizing a duration or loading capacity curve into a single point may be practicable
from an implementation standpoint, but could negate the strength of the duration curve
framework. One aspect of concern regarding this practice is the selection of a single
condition (i.e., one point as opposed to using the entire curve). Some TMDLs focus on
capturing the magnitude of the highest observed exceedance. However, such TMDLs
may be overly protective of the water quality standard, potentially inviting issues
regarding reasonable assurance. Alternatively, some TMDLs focus on the average or
median flow exceedance value, potentially resulting in allocations that are not protective
enough during higher flow events. For this reason it is appropriate to apply the entire
duration curve in the context of a TMDL. Another option is to categorize the duration
curve into several zones, allowing the resultant TMDL to adequately capture different
types of flow events.
EPA 841-B-07-006 14 August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
4d. Storm Events and Hydrograph Separation
Surface runoff following rain events can be one of the most significant transport
mechanisms of sediment and other nonpoint source pollutants. Precipitation is obviously
the driving mechanism responsible for storm flows and associated surface runoff.
Rainfall / runoff models, such as HSPF, SWAT, or SWMM, are generally used to provide
detailed estimates of the timing and magnitude of storm flows. However, these can also
be very rigorous and time-consuming approaches.
Use of duration curves can help provide another method to examine general watershed
response patterns. Streamflow hydrographs can be separated into base-flow and surface-
runoff components (Sloto and Grouse, 1996). The base-flow component is traditionally
associated with groundwater discharge and the surface-runoff component with
precipitation that enters the stream as overland flow. Information from hydrograph
separation can be displayed using duration curve intervals to examine the percentage (or
fraction) of total flow that consists of base flow and storm flow.
Figure 4-1 illustrates the potential effect that storm flows may exert across the range of
flow conditions, grouped by duration curve zone using data for the LaPlatte River. In
Figure 4-1, surface runoff has its greatest effect during high flow conditions (median
value of 61 percent). In such cases, sediment and other pollutants delivered to stream
systems associated with surface erosion will also be greatest during high flows.
Figure 4-1. Fraction Analysis of Storm Flow Relative to Total Streamflow
LaPlatte River at Shelburne Falls
Storm Flow Duration Curve (1990-2005)
High
Flows
Mid-range
Flows
Note: Increased fraction of surface runoff
under high flow conditions
0 10 20 30 40 50 60 70 80 90 100
Flow Duration Interval (%)
USGS Gage Duration Interval & Hydrograph Separation 44.6 square miles
EPA 841-B-07-006
15
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
4e. Utility in Identifying Potential Source AreasError! Bookmark not defined.
Duration curves are based on the entire range of flow conditions observed for any given
drainage. A major advantage of their use is the ability to consider the general hydrologic
condition of the watershed, and subsequently, to enhance development of source
assessments. Pollutant delivery mechanisms likely to exert the greatest influence on
receiving waters (e.g., point source discharges, surface runoff) can be matched with
potential source areas appropriate for those conditions (e.g., riparian zones, impervious
areas, uplands). Table 4-1 illustrates an approach, as a simple example, which could be
used to assess source areas based on the potential relative importance of delivery
mechanisms under the range of hydrologic conditions.
Table 4-1. Example Source Area / Hydrologic Condition Considerations
Contributing Source Area
Point Source
On- site waste water systems
Riparian Areas
Storm water: Impervious Areas
Combined sewer overflows
Storm water: Upland
Bank erosion
Duration Curve Zone
High
Flow
H
H
H
Moist
H
H
H
H
M
Mid-
Range
H
H
H
H
M
Dry
M
M
H
H
Low
Flow
H
Note: Potential relative importance of source area to contribute loads under given
hydrologic condition (H: High; M: Medium)
Table 4-1 describes an array of potential contributing source areas common to many
watersheds where TMDLs are being developed. This table provides an organizational
framework, which can be used to guide source assessment efforts. For instance, point
sources tend to have the most dominant effect on water quality under low flow
conditions. Thus, Table 4-1 identifies the low flow zone as a relative high priority for
assessment of point sources.
Similarly, surface runoff from upland sources tends to exert a greater effect on water
quality during higher flow conditions (e.g., high, moist, mid-range zones). Accordingly,
Table 4-1 identifies these zones as a relative high priority for assessment of storm water
sources from upland areas.
Ambient water quality monitoring data displayed in a duration curve framework (as
shown earlier in Figure 2-2) coupled with the Table 4-1 format can also help identify
potential source areas more likely to dominate under the different zones. Patterns
associated with certain source categories are often apparent when visually assessing data
by flow conditions.
EPA 841-B-07-006
16
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
5. CONNECTING TO IMPLEMENTATION AND RESULTS
A major advantage of the duration curve framework in TMDL development is the ability
to provide meaningful connections between allocations and implementation efforts.
Because the flow duration interval serves as a general indicator of hydrologic condition
(i.e., wet versus dry and to what degree), allocations and reduction targets can be linked
to source areas, delivery mechanisms, and the appropriate set of management practices.
The use of duration curve zones (e.g., high flow, moist, mid-range, dry, and low flow)
allows the development of allocation tables, which can be used to summarize potential
implementation actions that most effectively address water quality concerns.
In general, wasteload allocations from WWTPs exert a significant influence under low
flows. For total sediments, high flow conditions may result in stream bank erosion and
channel processes playing a greater role. For urban watersheds, water quality concerns
during mid-range flows and moist conditions might be best addressed through low impact
development techniques or site construction BMPs, as illustrated in Figure 5-1. For
agricultural areas, appropriate implementation efforts might include activities under such
provisions as the Conservation Reserve Program (CRP) and Conservation Reserve
Enhancement Program (CREP).
Appendix C provides an expanded discussion on the utility of the duration curve
framework in targeting potential solutions and connecting to implementation and results.
Included is a form similar to Table 4-1, which could be used to assess and target the
management options appropriate for the different flow conditions.
Figure 5-1. Duration Curve with Contributing Area Focus
Willow Creek near Turkey Gap
100
Flow Duration Interval (%)
TARGETED Activities: Construction Site Runoff Control
EPA 841-B-07-006
17
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
A common challenge faced by TMDL practitioners is explaining how allocations
translate into potential actions. Table 5-1 uses a duration curve framework to summarize
TMDL targets in a way that highlights implementation opportunities. Figure 5-2
illustrates how a duration curve framework can be used to document results following
implementation of erosion controls, showing those zones where "on the ground" efforts
were most effective. These summaries can be combined with other basic elements of
watershed planning to help guide problem solving discussions in a meaningful way.
Table 5-1. Example TMDL Summary Using Duration Curve Framework
TMDL
SUMMARY
TMDL1
Allocations
Margin of Safety
Implementation
Opportunities
Loads expressed as (tons per day)
High
173.35
118.32
55.03
Post
Development
BMPs
Streambank
Stabilization
Moist
67.20
48.24
18.96
Mid-Range
40.21
34.47
5.74
Erosion Control Program
Dry
27.57
21.83
5.74
Riparian Buffer Protection
Low
18.96
6.90
12.06
Municipal WWTP
Note: 1- Expressed as a "daily load"; represents the upper range of conditions needed to attain
and maintain applicable water quality standards
Figure 5-2. Documenting Erosion Control Program Results
Quail Fork
10
20
30
40
50
70
80
90
100
Flow Duration Interval (%)
EPA 841-B-07-006
18
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
APPENDIX A
Load Duration Curve TMDLs
Case Example
Pee Dee River Basin, South Carolina
Fecal Coliform TMDL
This appendix describes a case example where load duration curves were used to support
TMDL development. The example is taken from a fecal coliform TMDL prepared by the
South Carolina Department of Health and Environmental Control (DHEC), which was
developed to address impairments in sixteen segments of thirteen waters in the Pee Dee
River Basin (Hills Creek, Lynches River, North and South Branch of Wildcat Creek, Flat
Creek, Turkey Creek, Nasty Branch, Gulley Branch, Smith Swamp, Little Pee Dee River,
Maple Swamp, White Oak Creek, and Chinners Swamp).
The full TMDL document, available at:
http://www.scdhec.gov/environment/water/tmdl/docs/tmdl peedee fc.pdf
provides background information on the waterbodies, including water quality and
pollutant source assessments. Sections 4 and 5 (titled "Technical Approach and
Methodology" and "TMDL Calculations") of the Pee Dee River Basin TMDL are
excerpted into this technical appendix. These sections describe how the duration curve
framework was used.
Section 4 provides an explanation of steps used to perform TMDL calculations. Section
5 describes the results of these calculations and how this information was used to address
each component of the TMDL.
Pee Dee River Basin
EPA 841-B-07-006 19 August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
SECTION 4
TECHNICAL APPROACH AND METHODOLOGY
A TMDL is defined as the total quantity of a pollutant that can be assimilated by a
receiving water body while achieving the WQS. A TMDL is expressed as the sum of all
WLAs (point source loads), LAs (nonpoint source loads), and an appropriate MOS,
which attempts to account for uncertainty concerning the relationship between effluent
limitations and water quality.
This definition can be expressed by the following equation:
TMDL = E WLA + E LA + MOS
The objective of the TMDL is to estimate allowable pollutant loads and to allocate these
loads to the known pollutant sources in the watershed so the appropriate control measures
can be implemented and the WQS achieved. 40 CFR § 130.2 (1) states that TMDLs can
be expressed in terms of mass per time, toxicity, or other appropriate measures. For fecal
coliform, TMDLs are expressed as cfu per day where possible or as percent reductions,
and represent the maximum one-day load the stream can assimilate while still attaining
the WQS.
4.1 Using Load Duration Curves to Develop TMDLs
LDCs are graphical analytical tools that illustrate the relationships between stream
flow and water quality and assist in decision making regarding this relationship. Flow is
an important factor affecting the loading and concentration of fecal coliform. Both point
and nonpoint source loads of pollutants to streams may be affected by changes in flow
regime. Given an understanding of the potential loading mechanisms of fecal coliform,
and how those mechanisms relate to flow conditions, it is possible to infer and quantify
the major contributing sources of pollutants to a stream by examining the relationship
between flow and pollutant concentration or load. Of critical importance is that the
incremental watershed LDC approach makes effective use of existing data. The lack of
instream flow data at most water quality monitoring locations would typically be
identified as a significant data gap for application of watershed and water quality models.
However, since the incremental watershed LDC approach makes use of drainage area
ratio-based flow estimates, the lack of flow information at these locations is not limiting.
The incremental watershed approach also allows for assessment of land use, soil, and
source contribution differences between observation points. The fecal coliform TMDLs
presented in this report are designed to be protective of typical flow conditions. The
following discussion provides an overview of the approach used to develop LDCs and
TMDL calculations. Results and calculations are presented in Section 5.
EPA 841-B-07-006 20 August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
4.2 Explanation of Steps Used to Perform TMDL Calculations
The following discussion provides a summary of the steps involved in the
calculation of the key components of the fecal coliform TMDLs presented in Section 5 of
this report.
Step 1: Develop Flow Percentiles for each WQM Station. Direct flow
measurements are not available for all of the WQM stations addressed in this report. This
information, however, is vitally important to understanding the relationship between
water quality and stream flow. Therefore, to characterize flow, in some cases flow data
were derived from a flow estimation model for each relevant watershed. Flow data to
support development of flow duration curves will be derived for each SCDHEC WQM
station from USGS daily flow records (USGS 2005b) in the following priority:
i) In cases where a USGS flow gage coincides with, or occurs within one-half
mile upstream or downstream of a SCDHEC WQM station and simultaneous
daily flow data matching the water quality sample date are available, these
flow measurements will be used.
ii) If flow measurements at the coincident gage are missing for some dates on
which water quality samples were collected, gaps in the flow record will be
filled, or the record extended, by estimating flow based on measured
streamflows at a nearby gage. First, the most appropriate nearby stream gage
is identified. All flow data are first log-transformed to linearize the data
because flow data are highly skewed. Linear regressions are then developed
between 1) daily streamflow at the gage to be filled/extended; and 2)
streamflow at all gages within 93 miles (150 kilometers) that have at least
300 daily flow measurements on matching dates. The station with the
strongest flow relationship, as indicated by the highest correlation coefficient
(r-squared value), is selected as the index gage. R-squared indicates the
fraction of the variance in flow explained by the regression. The regression is
then used to estimate flow at the gage to be filled/extended from flow at the
index station. Flows will not be estimated based on regressions with
r-squared values less than 0.25, even if that is the best regression. This value
was selected based on familiarity with using regression analysis in estimating
flows. In some cases, it will be necessary to fill/extend flow records from two
or more index gages. The flow record will be filled/extended to the extent
possible based on the strongest index gage (highest r-squared value), and
remaining gaps will be filled from successively weaker index gages (next
highest r-squared value), and so forth.
iii) In the event no coincident flow data are available for a WQM station, but flow
gage(s) are present upstream and/or downstream, flows will be estimated for
the WQM station from an upstream or downstream gage using a watershed
area ratio method derived by delineating subwatersheds, and relying on the
Natural Resources Conservation Service runoff curve numbers and antecedent
rainfall condition. Drainage subbasins will first be delineated for all impaired
303(d)-listed WQM stations, along with all USGS flow stations located in the
EPA 841-B-07-006 21 August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
Step 2: Develop Flow Duration Curves. Flow duration curves serve as the
foundation of LDC TMDLs. Flow duration curves are graphical representations of the
flow regime of a stream at a given site. The flow duration curve is an important tool of
hydrologists, utilizing the historical hydrologic record from stream gages to forecast
future recurrence frequencies.
Flow duration curves are a type of cumulative distribution function. The flow
duration curve represents the fraction of flow observations that exceed a given flow at the
site of interest. The observed flow values are first ranked from highest to lowest, then,
for each observation, the percentage of observations exceeding that flow is calculated.
The flow rates for each 5th percentile for each WQM station are provided in Appendix D.
The flow value is read from the ordinate (y-axis), which is typically on a logarithmic
scale since the high flows would otherwise overwhelm the low flows. The flow
exceedance frequency is read from the abscissa, which is numbered from 0 to
100 percent, and may or may not be logarithmic. The lowest measured flow occurs at an
exceedance frequency of 100 percent, indicating that flow has equaled or exceeded this
value 100 percent of the time, while the highest measured flow is found at an exceedance
frequency of 0 percent. The median flow occurs at a flow exceedance frequency of
50 percent.
While the number of observations required to develop a flow duration curve is not
rigorously specified, a flow duration curve is usually based on more than 1 year of
observations, and encompasses inter-annual and seasonal variations. Ideally, the drought
and flood of record are included in the observations. For this purpose, the long term flow
gaging stations operated by the USGS are ideal.
A typical semi-log flow duration curve exhibits a sigmoidal shape, bending
upward near a flow duration of 0 percent and downward at a frequency near 100 percent,
often with a relatively constant slope in between. However, at extreme low and high
flow values, flow duration curves may exhibit a "stair step" effect due to the USGS flow
data rounding conventions near the limits of quantitation. The extreme high flow
conditions (<10th percentile) and low flow conditions (>95 percentile) are not considered
in development of these TMDLs. The overall slope of the flow duration curve is an
indication of the flow variability of the stream.
Flow duration curves can be subjectively divided into several hydrologic
condition classes. These hydrologic classes facilitate the diagnostic and analytical uses
of flow and LDCs. The hydrologic classification scheme utilized in the development of
these TMDLs is presented in Table 4-1.
EPA 841-B-07-006 22 August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
Table 4-1 Hydrologic Condition Classes
Flow Duration
Interval
0-10%
10-40%
40-60%
60-90%
90-100%
Hydrologic Condition
Class*
High flows
Moist Conditions
Mid-Range Conditions
Dry Conditions
Low Flows
Source: Cleland2003.
Step 3: Estimate Current Point Source Loading. In SC, NPDES permittees that
discharge treated sanitary wastewater must meet the state WQS for fecal coliform
bacteria at the point of discharge (see discussion in Section 2). However, for TMDL
analysis it is necessary to understand the relative contribution of WWTPs to the overall
pollutant loading and their general compliance with required effluent limits. The fecal
coliform load for continuous point source dischargers was estimated by multiplying the
monthly average flow rates by the monthly geometric mean using a conversion factor.
The data were extracted from each point source's DMR from 1998 through 2004. The
90th percentile value of the monthly loads was used to express the estimated existing load
in counts/day. The current pollutant loading from each permitted point source discharge
as summarized in Section 3 was calculated using the equation below.
Point Source Loading = monthly average flow rates (mgd) * geometric mean of
corresponding fecal coliform concentration * unit conversion factor
Where:
unit conversion factor = 37,854,120 100-ml/million gallons (mg)
Step 4: Estimate Current Loading and Identify Critical Conditions. It is
difficult to estimate current nonpoint loading due to lack of specific water quality and
flow information that would assist in estimating the relative proportion of non-specific
sources within the watershed. Therefore, existing instream loads were used as a
conservative surrogate for nonpoint loading. It was calculated by multiplying the
concentration by the flow matched to the specific sampling date. Then using the
hydrologic flow intervals shown in Table 4-1, the 90th percentile nonpoint loading within
each of the intervals would then represent the nonpoint loading estimate for that interval.
Existing loads have been estimated using a regression-based relationship developed
between observed fecal coliform loads and flow or flow exceedance percentile.
In many cases, inspection of the LDC will reveal a critical condition related to
exceedances of WQSs. For example, criteria exceedances may occur more frequently in
wet weather, low flow conditions, or after large rainfall events. The critical conditions
are such that if WQSs were met under those conditions, WQSs would likely be met
overall. Given that the instantaneous fecal coliform criterion indicates that no more than
10 percent of samples should exceed 400 cfu/100 ml, it is appropriate to evaluate existing
EPA 841-B-07-006
23
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
loading as the 90th percentile of observed fecal coliform concentrations. Together with
the MOS, the reduction calculated in this way should ensure that no more than 10 percent
of samples will exceed the criterion.
Existing loading is calculated as the 90th percentile of measured fecal coliform
concentrations under each hydrologic condition class multiplied by the flow at the middle
of the flow exceedance percentile. For example, in calculating the existing loading under
dry conditions (flow exceedance percentile = 60-90%), the 75th percentile exceedance
flow is multiplied by the 90th percentile of fecal coliform concentrations measured under
the 60-90* percentile flows. The "high flow" or "low flow" hydrologic conditions will
not be selected as critical conditions because these extreme flows are not representative
of typical conditions, and few observations are typically available to reliably estimate
loads under these conditions. This methodology results in multiple estimates of existing
loading. However, TMDLs are typically expressed as a load or concentration under a
single scenario. Therefore, these TMDLs will assume that if the highest percent
reduction associated with the difference between the existing loading and the LDC
(TMDL) is achieved, the WQS will be attained under all other flow conditions.
Step 5: Develop Fecal Coliform Load Duration Curves (TMDL). Load
duration curves are based on flow duration curves, with the additional display of
historical pollutant load observations at the same location, and the associated water
quality criterion or criteria. In lieu of flow, the ordinate is expressed in terms of a fecal
coliform load (cfus/day). The curve represents the single sample water quality criterion
for fecal coliform (400 cfu/100 ml) expressed in terms of a load through multiplication by
the continuum of flows historically observed at the site. The points represent individual
paired historical observations of fecal coliform concentration and flow. Fecal coliform
concentration data used for each WQM station are provided in Appendix A. The fecal
coliform load (or the y-value of each point) is calculated by multiplying the fecal
coliform WQS by the instantaneous flow (cfs) from the same site and time, with
appropriate volumetric and time unit conversions.
TMDL (cfu/day) = WQS * flow (cfs) * unit conversion factor
Where: WQS = 400 cfu/WOml
unit conversion factor = 24,465,525 ml*s/ft3 *day
The flow exceedance frequency (x-value of each point) is obtained by looking up
the historical exceedance frequency of the measured flow, in other words, the percent of
historical observations that equal or exceed the measured flow. It should be noted that
the site daily average stream flow is often used if an instantaneous flow measurement is
not available. Fecal coliform loads representing exceedance of water quality criteria fall
above the water quality criterion line.
EPA 841-B-07-006 24 August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
Step 6: Develop LDCs with MOS. An LDC depicting slightly lower estimates
than the TMDL is developed to represent the TMDL with MOS. An explicit MOS is
defined for each TMDL by establishing an LDC using 95 percent of the TMDL value
(5 percent of the 400 cfu/100 ml instantaneous water quality criterion) to slightly reduce
assimilative capacity in the watershed, thus providing a 5 percent MOS. The MOS at any
given percent flow exceedance, therefore, is defined as the difference in loading between
the TMDL and the TMDL with MOS.
Step 7: Calculate WLA. As previously stated, the pollutant load allocation for
point sources is defined by the WLA. A point source can be either a wastewater
(continuous) or stormwater (MS4) discharge. Stormwater point sources are typically
associated with urban and industrialized areas, and recent USEPA guidance includes
permitted stormwater discharges as point source discharges and, therefore, part of the
WLA.
The LDC approach recognizes that the assimilative capacity of a water body
depends on the flow, and that maximum allowable loading will vary with flow condition.
TMDLs can be expressed in terms of maximum allowable concentrations, or as different
maximum loads allowable under different flow conditions, rather than single maximum
load values. This concentration-based approach meets the requirements of 40 CFR,
130.2(i) for expressing TMDLs "in terms of mass per time, toxicity, or other appropriate
measures" and is consistent with USEPA's Protocol for Developing Pathogen TMDLs
(USEPA 2001).
WLA for WWTP. Wasteload allocations may be set to zero in cases of
watersheds with no existing or planned continuous permitted point sources. For
watersheds with permitted point sources, wasteloads may be derived from NPDES permit
limits. A WLA may be calculated for each active NPDES wastewater discharger using a
mass balance approach as shown in the equation below. The permitted average flow rate
used for each point source discharge and the water quality criterion concentration are
used to estimate the WLA for each wastewater facility. All WLA values for each
subwatershed are then summed to represent the total WLA for the watershed.
WLA (cfu/day) = WQS *flow * unit conversion factor
Where: WQS = 400 cfu/lOOml
flow (mgd) = permitted flow or design flow (if unavailable)
unit conversion factor = 37,854,120 100-ml/mg
WLA for MS4s. Because a WLA for each MS4 cannot be calculated as an
individual value, WLAs for MS4s are expressed as a percent reduction goal (PRG)
derived from the LDC for nonpoint sources. The method for estimating the percent
reduction of fecal coliform loading is described in Step 8.
EPA 841-B-07-006 25 August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
Step 8: Calculate LA. Load allocations can be calculated under different flow
conditions as the water quality target load minus the WLA. The LA is represented by the
area under the LDC but above the WLA. The LA at any particular flow exceedance is
calculated as shown in the equation below.
LA = TMDL - MOS - £WLA
However, to express the LA as an individual value, the LA is derived using the
equation above but at the median point of the hydrologic condition class requiring the
largest percent reduction as displayed in the LDCs provided in Appendix E. Thus, an
alternate method for expressing the LA is to calculate a PRG for fecal coliform. Load
allocations are calculated as percent reductions from current estimated loading levels
required to meet water quality criteria.
Step 9: Estimate WLA Load Reduction. The WLA load reduction was not
calculated because it was assumed that the continuous dischargers (NPDES permitted
WWTPs) are adequately regulated under existing permits and, therefore, no WLA
reduction would be required. For the MS4 permittees, the percent reduction was assumed
to be the same as the nonpoint load reduction.
Step 10: Estimate LA Load Reduction. After existing loading estimates are
computed for the three different hydrologic condition classes described in Step 2,
nonpoint load reduction estimates for each WQM station are calculated by using the
difference between estimated existing loading (Step 5) and the LDC (TMDL). This
difference is expressed as a percent reduction, and the hydrologic condition class with the
largest percent reduction is selected as the critical condition and the overall PRG for the
LA.
Results of all these calculations are discussed in Section 5.
EPA 841-B-07-006 26 August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
SECTION 5
TMDL CALCULATIONS
5.1 Results of TMDL Calculations
The calculations and results of the TMDLs for the 303(d)-listed WQM stations in
the Pee Dee River Basin are provided in this section. The methods for deriving these
results are specified in Section 4. The Lynches River and various tributaries contributing
to WQM station PD-113 are interstate water bodies. The TMDLs established in Section
5.7 of this report for WQM station PD-113 are achievable if WQS for fecal coliform are
met at the state line.
5.2 Critical Conditions and Estimated Loading
USEPA regulations at 40 CFR 130.7(c) (1) require TMDLs to take into account
critical conditions for stream flow, loading, and water quality parameters. Available
instream WQM data were evaluated with respect to flows and magnitude of water quality
criteria exceedance using LDCs. Load duration curve analysis involves using measured
or estimated flow data, instream criteria, and fecal coliform concentration data to assess
flow conditions in which water quality exceedances are occurring (SCDHEC 2003). The
goal of flow weighted concentration analysis is to compare instream observations with
flow values to evaluate whether exceedances generally occur during low or high flow
periods (SCDHEC 2003).
To calculate the fecal coliform load at the WQS, the instantaneous fecal coliform
criterion of 400cfu/100ml is multiplied by the flow rate at each flow exceedance
percentile, and a unit conversion factor (24,465,525 ml*s /ft *day). This calculation
produces the maximum fecal coliform load in the stream without exceeding the
instantaneous standard over the range of flow conditions. The allowable fecal coliform
loads at the WQS establish the TMDL and are plotted versus flow exceedance percentile
as an LDC. The x-axis indicates the flow exceedance percentile, while the y-axis is
expressed in terms of a fecal coliform load.
To estimate existing loading, the loads associated with individual fecal coliform
observations are paired with the flows estimated at the same site on the same date. Fecal
coliform loads are then calculated by multiplying the measured fecal coliform
concentration by the estimated flow rate and a unit conversion factor of 24,465,525 ml*s /
ft3*day. The associated flow exceedance percentile is then matched with the measured
flow from the tables provided in Appendix D. The observed fecal coliform loads are then
added to the LDC plot as points. These points represent individual ambient water quality
samples of fecal coliform. Points above the LDC indicate the fecal coliform
instantaneous standard was exceeded at the time of sampling. Conversely, points under
the LDC indicate the sample met the WQS.
EPA 841-B-07-006 27 August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
The LDC approach recognizes that the assimilative capacity of a water body
depends on the flow, and that maximum allowable loading varies with flow condition.
Existing loading, and load reductions required to meet the TMDL water quality target,
can also be calculated under different flow conditions. The difference between existing
loading and the water quality target is used to calculate the loading reductions required.
Given that the instantaneous fecal coliform criterion indicates that no more than
10 percent of samples should exceed 400 cfu/100 ml, it is appropriate to evaluate existing
loading as the 90l percentile of observed fecal coliform concentrations. Together with
the MOS, the reduction calculated in this way should ensure that no more than 10 percent
of samples will exceed the criterion.
Existing loading is calculated as the 90th percentile of measured fecal coliform
concentrations under each hydrologic condition class multiplied by the flow at the middle
of the flow exceedance percentile. For example, in calculating the existing loading under
dry conditions (flow exceedance percentile = 60-90 percent), the 75th percentile
exceedance flow is multiplied by the 90th percentile of fecal coliform concentrations
measured under 60-90th percentile flows.
After existing loading and percent reductions are calculated under each
hydrologic condition class, the critical condition for each TMDL is identified as the flow
condition requiring the largest percent reduction. However, the "high flow" (<10th
percentile flow exceedance) or "low flow" (> 90th percentile flow exceedance) hydrologic
conditions will not be selected as critical conditions because these extreme flows are not
representative of typical conditions, and few observations are available to reliably
estimate loads under these conditions. In the example shown in Table 5-1 for WQM
station PD-333, the critical condition occurs under "Moist Conditions," when a
93 percent loading reduction is required to meet the WQS.
Table 5-1 Estimated Existing Fecal Coliform Loading for Station PD-333 (Hills
Creek with Critical Condition Highlighted
Hydrologic
Condition
Class*
High Flows
Moist
Conditions
Mid-Range
Conditions
Dry
Conditions
Low Flows
Estimated
Existing
Loading
(cfu/100
ml)
6.54E+11
2.53E+12
7.10E+10
1.82E+11
1.08E+11
Percent
Reduction
Required
NA
93%
NA
70%
NA
* Hydrologic Condition Classes are derived from
Cleland2003.
EPA 841-B-07-006
28
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
The LDC for WQM station PD-333 shown in Figure 5-1 indicates actual fecal
coliform loads are exceeding the instantaneous load of the WQS during "moist" and
"dry" flow conditions. LDCs similar to Figure 5-1 for all of the 303(d)-listed WQM
stations in this report used to estimate existing loading and identify critical conditions are
provided in Appendix E. The LDCs were developed for the time period from January
1990 through October 2002 if data were available.
Figure 5-1 Estimated Fecal Coliform Load and Critical Conditions, Station PD-
333 (Hills Creek)
Fecal Coliform Load Duration Curve 1990-2000, Station PD-333
1.E+09
20
30
40 50 60
Flow Exceedance Percentile
70
80
90
100
Load at WQ Criterion
Load at WQ Target A FC Observations
90 Percentile FC Load
The existing instream fecal coliform load (actual or estimated flow multiplied by
observed fecal coliform concentration) is compared to the allowable load for that flow.
Any existing loads above the allowable LDCs represent an exceedance of the WQS. For
a low flow loading situation, there are typically observations in excess of criteria at the
low flow side of the chart. For a high flow loading situation, observations in excess of
criteria at the high flow side of the chart are typical. For water bodies impacted by both
point and nonpoint sources, the "nonpoint source critical condition" would typically
occur during high flows, when rainfall runoff would contribute the bulk of the pollutant
load, while the "point source critical condition" would typically occur during low flows,
when treatment plant effluents would dominate the base flow of the impaired water.
Based on these characteristics, critical conditions for each WQM station are summarized
in Table 5-2.
EPA 841-B-07-006
29
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
Table 5-2
Summary of Critical Conditions for each WQM Station as derived
from Load Duration Curves
SCDHEC
WQM
Station
PD-333
PD-113
PD-179
PD-180
PD-342
PD-066
PD-040
PD-098
PD-239
PD-065
PD-187
PD-320
PD-030A
PD-030
PD-037
PD-352
Moist
Conditions
Mid-
Range
Conditions
Dry
Conditions
The existing load for each WQM station was derived from the critical condition
line depicted on the LDCs described above and provided in Appendix E. Estimated
existing loading is derived from the 90th percentile of observed fecal coliform loads
corresponding to the critical condition identified at each WQM station identified in
Table 5-2. This estimated loading is indicative of loading from all sources including
continuous point source dischargers, leaking sewer lines, MS4s, SSOs, failing OSWD
systems, land application fields, wildlife, pets, and livestock. The total estimated existing
load for each station is provided in Table 5-3.
Table 5-3 Estimated Existing Loading at each WQM Station
SCDHEC
WQM
Station
PD-333
PD-113
PD-179
PD-180
PD-342
90th
Percentile
Load
Estimation
(cfu/day)
2.53E+12
3.15E+12
7.76E+11
2.31E+11
3.72E+11
Flow
Exceedance
Percentile
25
25
25
25
75
EPA 841-B-07-006
30
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
SCDHEC
WQM
Station
PD-066
PD-040
PD-098
PD-239
PD-065
PD-187
PD-320
PD-030A
PD-030
PD-037
PD-352
90th
Percentile
Load
Estimation
(cfu/day)
1.36E+13
1.37E+11
4.31E+ 11
1.63E+11
1.51E+12
2.54E+11
1.33E+12
1.05E+13
6.61E+11
7.54E+11
3.08E+11
Flow
Exceedance
Percentile
25
50
75
25
50
75
75
75
50
50
75
5.3 Waste Load Allocation
Table 5-4 summarizes the WLA of the NPDES-permitted facilities within the
watershed of each WQM station. The WLA for each facility is derived from the
following equation:
WLA = WQS * flow * unit conversion factor (#/day)
Where: WQS = 400 cfu/lOOml
flow (cfs) = permitted flow
unit conversion factor = 37,854,120 100-ml/mg
EPA 841-B-07-006
31
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
Table 5-4 Wasteload Allocations (WLA) for NPDES Permitted Facilities
Water Quality Monitoring Station / Permittee
HUC 3050106020
PD-333 Hills Creek at S-13-105
Pageland Northwest WWTP
HUC 3040202030
PD-179 North Branch Wildcat Creek at S-29-39 1 Mile
South of Tradesville
Buford High School WWTP
HUC 3040202050
PD-066 Upper Lynches River
Jefferson WWTP
HUC 3040204030
PD-030A Little Pee Dee River Below JCT with Maple SWP
Dillon Little Pee Dee WWTP (Outfall 001)
NPDES Permit
Number
SC0021504
SC0030210
SC0024767
SC0021776
Flow
(mgd)
0.3
0.035
0.15
4.0
Load
(cfu/day)
4.54E+09
5.30E+08
2.27E+09
6.06E+10
* Ceased Discharging in 1999.
When there are no NPDES WWTPs discharging into the contributing watershed
of a WQM station, then the WLA for continuous point sources is zero. See Subsection
4/2 (Step 7) and Section 5.7 for an explanation of how the WLA for NPDES dischargers
is depicted in a LDC.
The cities of Sumter and Florence are the only MS4s within the watersheds of this
report. Because of insufficient data, it is not possible to express a WLA for MS4s as a
load or concentration; therefore, the WLA is expressed as a PRG. Each MS4 was
assigned a PRG equal to the PRG identified in the LA for each WQM station. The PRGs
that will serve as a component of the WLA are provided in Table 5-5. When multiple
WQM stations fall under one MS4 jurisdiction, multiple PRGs can occur. In these cases
the highest PRG is selected as the overall reduction requirement incorporated into the
TMDL of each station. For example, by reviewing the LDCs in Appendix E, Stations
PD-098 and PD-040 have PRGs of 94 and 75 percent, respectively. Therefore, using a
conservative approach, the highest reduction goal of 94 percent is selected and
incorporated into the TMDLs (see Table 5-5) for WQM stations PD-098 and PD-040.
The PRGs in this TMDL report apply also to the fecal coliform WLAs attributable to
those areas of the watershed which are covered or will be covered under NPDES MS4
permits. Compliance by those municipalities within the terms of their individual MS4
permits will fulfill any obligations they have toward implementing TMDLs for fecal
coliform.
EPA 841-B-07-006
32
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
Table 5-5 WLA for MS4 Entities in Turkey Creek and Gulley Branch
Watersheds
MS4 Entity
Sumter
Florence
WQM Stations
PD-098, PD-040
PD-065
Percent Reduction Goal
94
99
5.4 Load Allocation
As discussed in Section 3, nonpoint source fecal coliform loading to the receiving
streams of each WQM station originate from a number of different sources. For a select
group of WQM stations (Table 3-3, Table 3-10, and Table 3-19) nonpoint sources of
fecal coliform loading is the sole reason the primary contact recreation use is not
supported. As discussed in Section 4, nonpoint source loading was estimated and
depicted for all flow conditions using LDCs (See Figure 5-1 example and Appendix E).
Figure 5-1, the LDC for PD-333, displays the relationships between the TMDL water
quality target, the MOS, and the PRO that can serve as an alternative for expressing the
LA. The data analysis and the LDCs demonstrate that exceedances at many of the WQM
stations are the result of nonpoint source loading such as failing OSWD systems, leaking
sewer lines, cattle in streams, and fecal loading from land application fields, wildlife and
pets transported by runoff events. The LAs, calculated as the difference between the
TMDL, MOS, and WLA, for each WQM station are presented in Table 5-6. Where
MS4s are present then the LA is not calculated and is expressed as a PRG.
5.5 Seasonal Variability
Federal regulations (40 CFR §130.7(c)(l)) require that TMDLs take into
consideration seasonal variation in watershed conditions and pollutant loading. Seasonal
variation was accounted for in these TMDLs by using more than 5 years of water quality
data (1990-2002) whenever possible and by using the longest period of USGS flow
records when estimating flows to develop flow exceedance percentiles.
5.6 Margin of Safety
Federal regulations (40 CFR §130.7(c)(l)) require that TMDLs include an MOS. The
MOS is a conservative measure incorporated into the TMDL equation that accounts for
the uncertainty associated with calculating the allowable fecal coliform pollutant loading
to ensure WQSs are attained. USEPA guidance allows for use of implicit or explicit
expressions of the MOS, or both. When conservative assumptions are used in
development of the TMDL, or conservative factors are used in the calculations, the MOS
is implicit. When a specific percentage of the TMDL is set aside to account for
uncertainty, then the MOS is considered explicit.
EPA 841-B-07-006
33
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
For the explicit MOS the water quality target was set at 380 cfu/100 ml for the
instantaneous criterion, which is 5 percent lower than the water quality criterion of
400 cfu/100 ml. The net effect of the TMDL with MOS is that the assimilative capacity
of the watershed is slightly reduced. These TMDLs incorporates an explicit MOS by
using a curve representing 95 percent of the TMDL as the average MOS. The MOS at
any given percent flow exceedance, therefore, can be defined as the difference in loading
between the TMDL and the TMDL with MOS. For consistency, the explicit MOS at
each WQM station will be expressed as a numerical value derived from the same critical
condition as the largest load reduction goal at the respective 25th, 50th, or 75th flow
exceedance percentile (see Table 5-6).
There are other conservative elements utilized in these TMDLs that can be recognized as
an implicit MOS such as:
The use of instream fecal coliform concentrations to estimate existing
loading; and
The highest PRG for nonpoint sources, based on the LDC used.
This conservative approach to establishing the MOS will ensure that both the 30-day
geometric mean and instantaneous fecal coliform bacteria standards can be achieved and
maintained.
5.7 TMDL Calculations
The fecal coliform TMDLs for the 303(d)-listed WQM stations covered in this report
were derived using LDCs. A TMDL is expressed as the sum of all WLAs (point source
loads), LAs (nonpoint source loads), and an appropriate MOS, which attempts to account
for uncertainty concerning the relationship between effluent limitations and water quality.
This definition can be expressed by the following equation:
TMDL = Z WLA + ZLA + MOS
For each WQM station the TMDLs presented in this report are expressed in cfus per day
or as a percent reduction. The TMDLs are presented in fecal coliform counts to be
protective of both the instantaneous, per day, and geometric mean, per 30-day, criteria.
To express a TMDL as an individual value, the LDC is used to derive the LA, the MOS,
and the TMDL based on the median percentile of the critical condition (i.e., the median
percentile of the hydrologic condition class requiring the greatest percent reduction to
meet the instantaneous criterion which is the water quality target). The WLA component
of each TMDL is the sum of all WLAs within the contributing watershed of each WQM
station which is derived from each NPDES facilities' maximum design flow and the
permitted 1-day maximum concentration of 400 cfu/100 ml. When MS4s do not exist in
the contributing watershed, the LDC and the simple equation of:
Average LA = average TMDL - MOS - £ WLA
EPA 841-B-07-006 34 August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
can provide an individual value for the LA in cfu per day which represents the area under
the TMDL target line and above the WLA line. Percent reductions necessary to achieve
the water quality target are also provided for all WQM stations as another acceptable
representation of the TMDL. Like the LA, the percent reduction is derived from the
median percentile of the critical condition (i.e.., the median percentile of the hydrologic
condition class requiring the greatest percent reduction to meet the instantaneous criterion
which is the water quality target). Table 5-6 summarizes the TMDLs for each WQM
station, and Figures 5-2 through 5-17 present the LDCs for each station depicting the
TMDL, MOS, and WLA (if applicable).
Table 5-6 TMDL Summary for Select WQM Stations in Pee Dee River Basin
(HUCs 03040202, 03040205, 03040201, 03040204)
SCDHEC
WQM
Station
WLAs
(cfu/
day)
MS4 WLA
(Percent
reduction)
LA (cfu/day
or%
reduction)
MOS
TMDL
(cfu/day or
%
reduction)
Percent
reduction
Lynches River HUC 03040202020
PD-333
4.54E+09
NA
1.80E+11
9.74E+09
1.95E+11
93
Upper Lynches River HUC 03040202030
PD-113
PD-179
PD-180
0
5.30E+08
0
NA
NA
NA
5.99E+11
1.13E+11
1.12E+11
3.15E+10
5.97E+09
5.92E+09
6.30E+11
1.19E+11
1.18E+11
81
85
51
Upper Lynches River HUC 03040202040
PD-342
0
NA
1.62E+11
8.51E+09
1.70E+11
57
Upper Lynches River HUC 03040202050
PD-066
2.27E+09
NA
2.56E+12
1.35E+11
2.69E+12
81
Tributary to Pocotaligo River HUC 03040205080
PD-040
PD-098
PD-239
0
0
0
94
94
NA
3.44E+10
2.70E+10
1.54E+11
1.81E+09
1.42E+09
8.12E+09
3.62E+10
2.84E+10
1.62E+11
75
94
5
Tributary to Pee Dee River HUC 03040201 130
PD-065
PD-187
PD-320
0
0
0
99
NA
NA
1.39E+10
8.74E+10
4.22E+11
7.34E+08
4.60E+09
2.22E+10
1.47E+10
9.20E+10
4.44E+11
99
66
68
Little Pee Dee River HUC 03040204030
PD-030A
PD-030
6.06E+10
0
NA
NA
4.90E+12
2.51E+11
2.61E+11
1.32E+10
5.22E+12
2.64E+11
53
62
Little Pee Dee River HUC 03040204070
PD-037
0
NA
7.16E+10
3.77E+09
7.54E+10
91
Little Pee Dee River HUC 03040204090
PD-352
0
NA
1.90E+11
9.98E+09
2.00E+11
39
EPA 841-B-07-006
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
Figure 5-2 TMDL for PD-333 Hills Creek
Fecal Coliform Load Duration Curve 1990-2000, Station PD-333
1.E+13
1.E+12
1.E+11
o
O
1.E+10
1.E+09
10 20
30 40 50 60 70
Flow Exceedance Percentile
90 100
Load at WQ Criterion ~ ~ Load at WQ Target A FC Observations ^^"Wasteload Allocation
1.E+14
1.E+13
Figure 5-3 TMDL for PD-113 Lynches River
Fecal Coliform Load Duration Curve 1990-2002, Station PD-113
8
1.E+09
10 20 30 40 50 60 70 80
Flow Exceedance Percentile
90 100
Load at WQ Criterion ~ ~ Load at WQ Target A FC Observations ^^^Wasteload Allocation
EPA 841-B-07-006
36
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
APPENDIX B
Additional Examples of Using
Load Duration Curve Approach
This technical appendix discusses basic application of duration curves in TMDL
development and provides several examples, including the derivation of loading
capacities, wasteload allocations, and load allocations. The duration curve framework is
well suited as a tool to support TMDL development because flow data is an important
factor in the determination of loading capacities. This technical appendix also provides a
discussion on ways the duration curve framework can be used to address different
averaging periods (other than daily) in identifying loading capacities, particularly where a
concentration-based target exists (expressed as monthly, seasonal, or annual average
values).
Bl. LOADING CAPACITY
Calculation of the loading capacity for impaired segments identified on the §303(d) list is
an important first step in the TMDL development process. EPA's current regulation
defines loading capacity as "the greatest amount of loading that a water can receive
without violating water quality standards ". The loading capacity provides a reference,
which helps guide pollutant reduction efforts needed to bring a water into compliance
with standards.
Chloride represents a good starting point to describe the use of duration curves in TMDL
development because of its conservative nature as a pollutant. For example, Kansas has
established 860 mg/L as the water quality criterion for chloride to protect aquatic life. To
illustrate key steps, the flow duration curve for the Arkansas River (based on daily
average stream discharge data) starts the process of identifying a loading capacity for
chloride using the duration curve framework.
In-stream loads for chloride, expressed as tons per day, are calculated using the equation
summarized in Table B-l. The loading capacity for the Arkansas River is shown in
Figure B-l. It is derived directly from the water quality criteria (860 mg/L) and the
duration curve using the "flow to load" calculation described in Table B-l across the
range of all daily average flows. Load capacity calculations for other parameters (e.g.
nutrients, bacteria, sediment) are developed in a similar fashion.
EPA 841-B-07-006 37 August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
Table B-l. Calculation of Chloride Loads
Load (tons per day) = Flow (cfs) * Concentration (ntg/L) * Factor
multiply by 86,400 to convert
multiply by 7.48 to convert
divide by 453,592 to convert
multiply by 3.7854 to convert
divide by 2,000 to convert
multiply by 0.002695 to convert
seconds per day
ft3
mg
liters
pounds
(ft3 / sec) * (mg/L)
»
»
»
»
»
»
ft3 / day
gallons / day
pounds
gallons
tons
tons / day
Figure B-l. Chloride Loading Capacity Using Duration Curve Framework
Arkansas River near Hutchinson
Load Duration Curve (Aquatic Life CriteriaAcute)
100000
l-
o
10
High
Flows
Moist
Conditions
Mid-range
Flows
Dry
Conditions
1,100 cfs * 860 mg/L * 0.002695
= 2,549 tons /day
Low
Flows
97 eft * 860 mg/L * 0.00269S
= 225 tons/day
-H
10 20 30 40 SO 60 70 SO
Flow Duration Interval (%)
90
100
31,724 square miles
Nutrients have been the focus of TMDL efforts to address a variety of water quality
problems including eutrophication, aquatic life impairments, and drinking water supply
concerns. Duration curves can be used to support TMDL development where numeric
targets exist for either nitrogen or phosphorus (similar to the chloride example). A
loading capacity for nitrate in the Sangamon River is depicted in Figure B-2 using the
drinking water maximum contaminant level (MCL) of 10 mg/L. It is derived directly
from the MCL (10 mg/L) and the duration curve using the "flow to load" calculation
described in Table B-l across the range of all daily average flows.
EPA 841-B-07-006
38
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
Figure B-2. Nitrate Loading Capacity Using Duration Curve Framework
Sangamon River near Fisher
Load Duration Curve
1000
100
a
"w
83
0.1
0.01
0.001
High
Flows
Moist
Conditions
Mid-range
Flows
Dry
Conditions
Low
Flows
217 eft * lOmg/L * 0.002695
= 5.84 tons /day
17eft * lOmg/L * 0,002695
= 0.46 tons/day
10
20
30
40
70
80
90
100
Flow Duration Interval (%
240 square miles
Figure B-3 shows the total phosphorus loading capacity curve for the Portneuf River
using the TMDL target of 75 ng/L. In this example, loads are expressed as pounds per
day (as described in Table B-2). Again, loading capacities developed using the duration
curve framework provides information that adds a focus to discussions regarding
allocations and implementation planning, particularly when used in conjunction with
ambient water quality monitoring data.
Table B-2. Calculation of Phosphorus Loads
Load (tons per day) = Flow (cfs) * Concentration (fig/L) * Factor
multiply by 86,400 to convert
multiply by 7.48 to convert
divide by 1,000 to convert
divide by 453,592 to convert
multiply by 3.7854 to convert
multiply by 0.005393 to convert
seconds per day
ft3
Mg
mg
liters
(ft3 / sec) * (ug/L)
»
»
»
»
»
»
ft3 / day
gallons / day
mg
pounds
gallons
pounds / day
EPA 841-B-07-006
39
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
Figure B-3. Phosphorus Loading Capacity Using Duration Curve Framework
Portneuf River at Pocatello
Load Duration Curve
100000
10000
B,
3
9
k.
c
JS
D-
M
**
O
1000
100
1.
01
High
Flows
Moist
Conditions
Mid-range
Flows
Dry
Conditions
Low
Flows
356 cfs * 75 ug/L * 0.005393
= 144 pounds / day
116 eft * 75ug/L * 0.005393
= 46.9 pounds /day
+
+
+
+
+
0 10 20 30 40 SO 60 70 §0 90 100
Flow Duration Interval (%)
1,250 square miles
Sediment concerns have long challenged TMDL practitioners for several reasons. First,
States typically do not have established numeric criteria for sediment, instead relying on
narrative components of their water quality standards. Second, sediment problems can
result from changes in processes that influence either surface or channel erosion.
Sediment concerns are also associated with changes that affect the capacity of watersheds
to store and transport sediment throughout the drainage network. TMDL assessments
typically consider the influence of land management activities on changes in erosion
processes, water discharge amounts and timing, as well as channel form (EPA, 1999).
There is a wide range in methods that have been employed towards sediment TMDL
development. Some use fixed numeric targets, often based on values recommended by
the European Inland Fisheries Advisory Commission (EIFAC), which could be used to
establish categories of risk to fisheries. With this approach, the process outlined to
generate loading capacities described for chloride, nitrate, and phosphorus (Figures B-l
to B-3) would be applied.
The "Protocolfor Developing Sediment TMDLs" (EPA, 1999) indicates the suitability of
using sediment targets, which relate concentrations to stream flow for reference streams
that reflect unimpaired conditions. A target can be identified by developing a sediment
rating curve for an appropriate reference stream based on the regression slope, by plotting
flow against suspended sediment concentration. Figure B-4 illustrates an example rating
curve for a reference stream.
EPA 841-B-07-006
40
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
Figure B-4. Example Sediment Rating Curve
Flat Brook
Regression Analysis (1968 - 2001 Monitoring Data)
C 100
u
E
3
-o
c
y=0.0934x
0*94
= ft 0934 * (335
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
Figure B-5. Sediment Loading Capacity Using Duration Curve Framework
Flat Brook
Load Duration Curve (derivedfrom sediment rating curve)
10000
a
w
tn
K
,S 100
B
O)
a
B
§ 0.1
High
flows
Moist
Conditions
Mid-range
flows
Dry
Conditions
335 eft * 16.9 m^L * 0.002695
= 15.3 tons/day
32cfs * 2.07 mg^L * 0.002695
= 0.18 tons/day
+
+
-I-
+
+
+
Low
flows
10 20 30 40 50 £0 70 SO
Flow Duration Interval (%)
90 100
64 square miles
Bacteria is a major pollutant leading to §303(d) listings and subsequent TMDL
development. Typically, loads are expressed as chemical mass per time, such as pounds
per day. Given the nature of bacteria measurements (e.g., counts per 100 milliliters), an
appropriate expression of loads for bacteria TMDLs is organisms per day. Table B-3
describes an approach used in TMDL development to calculate bacteria loads, which
includes needed conversion factors.
Loading capacities calculated in this manner result in extremely large numbers (i.e.,
numbers of organisms in the billions, trillions, or quadrillions per day). In order to avoid
difficulties of communicating information associated with large counts (e.g., macro
numbers of microorganisms), bacteria loading capacities are expressed as million
organisms per day (mega- or M-org/day), billion organisms per day (giga- or G-org/day),
or trillion organisms per day (tera- or T-org/day), similar to computer abbreviations of
MB for megabytes, GB for gigabytes, or TB for terabytes.
As an example, waters designated for support of immersion recreation in South Dakota
must achieve a daily maximum fecal coliform concentration of 400 cfu / lOOmL between
May and September. Figure B-6 shows an example "daily maximum" loading capacity
curve for Split Rock Creek using the 400 cfu / 100 mL target and a duration curve
derived with daily average flows. This load duration curve is based on daily average
flows measured between May and September, in order to ensure consistency with the
water quality criterion for fecal coliform.
EPA 841-B-07-006
42
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
Table B-3. Calculation of Bacteria Loads
Load (org/day) = Concentration (org/lOOmL) * Flow (cfs) * Factor
multiply by 3785.2 to convert
divide by 100 to convert
multiply by 7.48 to convert
multiply by 86,400 to convert
divide by 1,000,000,000
multiply by 0.02446 to convert
mL per gallon
gallon per ft3
seconds per day
billion
(org/lOOmL) * ft3 / sec
»
»
»
»
»
»
org / 100 gallon
org / gallon
org / ft3
ft3 / day
G-org
G-org / day
Figure B-6. Bacteria Loading Capacity Using Duration Curve Framework
Split Rock Creek at Corson
Load Duration Curve (May-September)
« 100000
1000
E
O 100
S3
u
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
B2. MULTIPLE AVERAGING PERIODS
Connecting to "Non-Daily" Targets Sediment
The following sediment example represents one type of problem where an array of
different approaches can bring multiple averaging periods into the technical analysis.
The duration curve framework can accommodate different averaging periods (other than
daily) in identifying loading capacities, particularly where a concentration-based target
exists (expressed as monthly, seasonal, or annual average values).
Figure B-7 illustrates an example TMDL developed to attain the water quality criteria
expressed as an annual average concentration of 25 mg/L total suspended solids (TSS).
Figure B-7 portrays this TMDL in the context of existing conditions, both individual
measurements and the current annual average (40.4 mg/L). Use of these "non daily"
averaging period TMDLs is one way to account for variability.
Figure B-7. Concentration-Based TMDL
Middle Fork LeBuche River
TMDL versus Existing Conditions
1000
JE
sfi
-a
100
o
QC
a
c
a.
E«
as
o
H< i
TMDL (AnnualAverage) - 25 mg/L
%. I i
* * X *
>!.«.«.,..« *X- - -
,»'*j».,* * ./V <
. V
.
'.*'***.
*
**» t *., t.»v *.. ".It *. *T
, .*.;,» v * ..v /v*. »
. » * * x» .
mCurrent Average
TMDL
Current Average = 40.4 mg/L
Needed Reduction = 38%
Jan-79
Jan-89
Month
Jan- 99
Statistical methods, which consider patterns and variability in a consistent manner, offer a
way to connect targets that use multiple averaging periods. Using an approach described
in EPA's "Technical Support Document for Water Quality-Based Toxics Control" (1991
TSD), the maximum daily concentration for the Middle Fork LeBuche River is 213 mg/L
total suspended solids (based on achieving an annual average of 25 mg/L with a
coefficient of variation of 1.164). In-stream loads for TSS, expressed as tons per day, are
calculated using the equation summarized in Table B-l. The loading capacity for the
EPA 841-B-07-006
44
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
Middle Fork LeBuche River is shown in Figure B-8. It is derived directly from the daily
concentration target (213 mg/L) and the duration curve using the "flow to load"
calculation described in Table B-l across the range of all daily average flows.
Figure B-8. TSS Loading Capacity Using Duration Curve Framework
Middle Fork LeBuche River
Load Duration Curve
10000
c
o
IS
o
100
c
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
appropriate source areas, delivery mechanisms, and water quality management control
strategies to address short term problems. Similarly, average values within each zone can
be calculated and compared to the long term average (or "non daily") benchmark curve.
In the case of the M.F. LeBuche TMDL, benchmarks are exceeded under high flows,
moist conditions, and mid-range flows.
In addition to providing the needed linkage between the "daily load" and the applicable
water quality standards, the duration curve framework provides the groundwork for the
transition from the TMDL to implementation efforts. Reduction estimates can be
developed for each duration curve zone benchmark, which serve to guide problem
solving discussions on appropriate management strategies (based on knowledge
associated with likely source areas, delivery mechanisms, and appropriate control
measures that correspond to particular hydrologic conditions). As shown in Table B-4,
implementation opportunities are highlighted that correspond to the flow conditions best
suited for the array of control options.
Table B-4. Middle Fork LeBuche River TMDL Summary
TMDL
SUMMARY
TMDL1
Allocations
Margin of Safety
Benchmark
Reduction Estimate
Implementation
Opportunities
Loads expressed as (tons per day)
High
173.35
118.32
55.03
20.35
63%
Post
Development
BMPs
Streambank
Stabilization
Moist
67.20
48.24
18.96
7.89
27%
Mid-Range
40.21
34.47
5.74
4.72
19%
Erosion Control Program
Dry
27.57
21.83
5.74
3.24
0%
Riparian Buffer Protection
Low
18.96
6.90
12.06
2.22
0%
Municipal WWTP
Notes: 1. Expressed as a "daily load"; represents the upper range of conditions needed to
attain and maintain applicable water quality standards
2. Based on annual average target identified in the applicable water quality
standards
3 . Developed using long-term fixed station ambient water quality monitoring data
EPA 841-B-07-006
46
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
Figure B-9. Middle Fork LeBuche River TMDL Using Duration Curve Framework
Middle Fork LeBuche River
Load Duration Curve
10000
"a
>-
D. 1000
0.1
High
Flows
Moist
Conditions
Mid-range
Flows
Dry
Conditions
Low
Flows
TMDL (daily maximum based on 213 mg/L)
Benchmark (boxed on 25 mg/L animal average)
-TMDL
« All Data
-,- Apr-Oct
» >50%SF
-SOU
10
20
30
40 SO 60 70
90 100
Flow Duration Interval
Connecting to "Non-Daily" Targets Bacteria
Many State water quality standards for pathogens include a 30-day or monthly geometric
mean averaging period and an upper limit (either a single sample maximum or no more
than a set percent exceedance value). A challenge facing TMDL practitioners is
identifying the appropriate target that will protect both criteria values. Michigan's
applicable water quality standards (WQS) for bacteria, for instance, focus on E. Coli and
indicate that all waters be protected for total body contact recreation from May 1 to
October 31. Target levels for TMDL development are derived from Rule 62 of the WQS,
which state that:
"R 323.1062 Microorganisms.
Rule 62. (1) All waters of the state protected for total body contact
recreation shall not contain more than 130 E. coli per 100 milliliters (ml),
as a 30-day geometric mean. ... At no time shall the waters of the state
protected for total body contact recreation contain more than a maximum
of 300 E. coli per 100 ml. "
When the duration is expressed as a daily average or "never to exceed" value, the daily
target is explicitly stated in the applicable water quality criteria (USEPA, 2007). For
example, using Michigan's bacteria criteria, the "daily" value is the maximum of 300 E.
EPA 841-B-07-006
47
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
Coli per 100 mL to protect for total body contact recreation. Procedures described in
Table B-3 and Figure B-6 are then used to develop the loading capacity using a duration
curve framework. Another example is shown in Figure B-10.
Figure B-10. Bacteria Loading Capacity Using Duration Curve Framework
Werbaldo Creek
Load Duration Curve
1000
High
Flows
\
Moist
Conditions
Mid-range
Flows
Dry
Conditions
Low
Flows
3.94 eft * 300org/100L * 0.02446
= 28.9 G-org/ day
1.31 eft * 300 org/lOOmL * 0.02446
= 9.64 G-org/day
4-
4-
10
20
30
40
SO
60
TO
80
90
100
Flow Duration Interval (%)
TMDLs must be established at a level necessary to attain and maintain the applicable
water quality standards. In the case of the Werbaldo Creek E. Coli example (Figure B-
10), this includes both a not to exceed value and a 30-day geometric mean of 130 per 100
mL. Material in EPA's November 2004 promulgation of water quality criteria for coastal
recreational waters elaborates on the intended purpose behind each of the two criteria
values. In particular, the preamble of the coastal recreational water rule states:
"the geometric mean is the more relevant value for ensuring that appropriate
actions are taken to protect and improve water quality because it is a more
reliable measure, being less subject to random variation " (EPA, 2004).
The rule provides a context for multi-value bacteria criteria with respect to Clean Water
Act implementation programs, such as TMDLs and NPDES permit requirements. This
context is to meet the geometric mean criteria for bacterial indicators, such as E. coli,
enterococci, or fecal coliform.
For this reason, a linkage analysis may be needed to demonstrate consistency between the
not to exceed value used as the "daily" TMDL target and the 30-day geometric mean.
EPA's development of ambient water quality criteria for bacteria, specifically E. Coli,
EPA 841-B-07-006
48
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
defines the statistical relationship between these two criteria values. This relationship
can be used to demonstrate that attaining the maximum daily target in the TMDL will
also achieve the 30-day geometric mean criteria.
The concepts used to develop the "not to exceed value ", often referred to as the single
sample maximum (SSM), are described in the "Ambient Water Quality Criteria for
Bacteria 1986". The method used to develop the SSM values for E. Coli in the 1986
document is based on a recognition of the inherent variability that occurs in water quality.
In particular, the relationship between the 30-day geometric mean and the SSM is based
on the assumption that bacteria data can be described using a log-normal frequency
distribution. The method used to identify the upper target values in the 1986 document
provides a way to develop a linkage analysis, which describes the connection between the
"daily" value and the 30-day geometric mean.
Specifically, the log-normal distribution has been used to identify upper targets in
conjunction with geometric mean and a measure of variability (in this case, a log standard
deviation). Figure B-l 1 illustrates this concept for E. Coli bacteria. As shown in Figure
B-ll, upper targets are based on the assumption of a log-normal distribution using a log
standard deviation of 0.4 centered on 130 cfu /100 mL, i.e. the target geometric mean.
Figure B-ll. Development of E. Coli Upper Targets
Example Log-Normal Frequency Distribution
o
U
Log-Normal Criteria Curve (LNCC)
Geometric Mean = 130 cfu / lOOmL
Log Standard Deviation = 0.4
82% : (full body contact recreation)
o%
109/o 20%
30%
40%
50%
60%
70%
80%
90% 100%
Frequency Interval (%)
Figure B-l2 illustrates the same concept for E. Coli bacteria where the applicable criteria
is simply a geometric mean (no single sample maximum). As shown in Figure B-12, the
1-day monthly maximum is based on the same assumptions behind development of the E.
Coli criteria, specifically a log-normal distribution using a log standard deviation of 0.4
EPA 841-B-07-006
49
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
centered on 130 cfu / 100 mL (i.e. the target geometric mean). The daily target is set at
the recurrence interval associated with a 30-day averaging period using percentiles along
the curve, specifically 96.8% [e.g., (30/31)%, or (k/k+l)% where k is the number of
averaging period days]. Note that the "daily" target set in the Werbaldo Creek TMDL is
much lower than one based solely on the 30-day geometric mean criteria using the same
assumptions behind establishing the single sample maximum (e.g., 300 versus 713).
Figure B-12. Development of Daily Value Based on Monthly Target
Example Log-Normal Frequency Distribution
E
Log-Normal Criteria Curve (LNCQ
Geometric Mean = 130 cfu / lOOmL
Log Standard Deviation = 0.4
F.L= 96.8% (1-day maximum recurrence
over 30-day period)
o%
10% 20%
30%
40%
50%
fiO%
70%
80%
90% 100%
Frequency Interval
Using a "daily" target of 300 organisms per 100 mL is more restrictive than one based on
a geometric mean of 130 using the same assumptions behind development of the E. Coli
criteria. The linkage analysis can also use these same assumptions to determine the 30-
day geometric mean that corresponds to a "daily" target of 300 E. Coli per 100 mL.
Figure B-13 shows the graphic results of this analysis, indicating that the resultant 30-day
geometric mean will be 54.6. Thus, a daily target of 300 will be protective of the 30-day
geometric mean in the water quality standards.
Table B-5 provides a summary of the Werbaldo Creek TMDL using a duration curve
framework based on multiple averaging periods (similar to the sediment example in
Table B-4). The 30-day geometric mean must be met before full compliance with the
bacteria water quality standards is achieved in Werbaldo Creek. Based on the linkage
analysis, the 30-day geometric mean component of the water quality criteria will be met
provided the maximum daily target is met. If subsequent data or information
demonstrates that, for some reason, the maximum daily target is met and the 30-day
geometric mean is not met, the TMDL should be revised with allocations lowered to
ensure attainment of both criteria values.
EPA 841-B-07-006
50
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
Figure B-13. Relationship Between 30-day Geometric Mean and Daily Target
Example Log-Normal Frequency Distribution
o
U
Log-Normal Criteria Curve (LNCC)
Geometric Mean = 54.6 cfu / lOOmL
Log Standard Deviation = 0.4
F.L= 96.8% (1-day maximum recurrence
over 30-day period)
0%
10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Frequency Interval (%)
Table B-5. Werbaldo Creek TMDL Summary
TMDL SUMMARY
TMDL1
Allocations
Margin of Safety
Benchmark2
Reduction Estimate3
Implementation
Opportunities
Loads expressed as (G-orgper day)
High
77.15
53.84
23.30
130
92%
Moist
28.93
20.09
8.84
130
90%
Long-term CSO
Control Program
Mid-Range
16.07
12.86
3.21
130
75%
Dry
9.64
6.91
2.73
130
40%
Low
5.87
4.26
1.61
130
20%
Riparian Protection
Illicit Discharge Detection &
Elimination
Address on-site wastewater
disposal problems
Notes: 1. Expressed as a "daily load"; represents the upper range of conditions
needed to attain and maintain applicable water quality standards
2. Based on the 30-day geometric mean identified in the applicable water
quality standards
3. Developed using ambient water quality monitoring data
EPA 841-B-07-006
51
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
Use of Monthly Duration Curves. In order to ensure consistency with the geometric
mean criterion, 30-day or monthly mean flows can also be used to identify loading
capacities that supplement daily load targets. This approach offers another way to
develop a quantitative analysis of seasonal variation indicative of the 30-day or monthly
target in the water quality standards (i.e., larger loads in months with higher flows and
smaller loads in months with lower flows). Table B-6 summarizes a portion of individual
monthly mean flow values using USGS data for Swamp Creek near Kenmore, WA.
Summary statistics for each month using the full record are included at the bottom of
Table B-6.
As seen in Table B-6, seasonal patterns reflect higher flows in late fall and early winter
(e.g., December, January) with a transition to lower flows in summer months. However,
interannual variation is another factor to consider when identifying loading capacities.
Average values for the same month can vary by as much as an order of magnitude due to
varying weather conditions (e.g., an unusually dry December or an abnormally wet June),
as shown in Table B-6 for the Swamp Creek. Flow duration curves developed using
individual monthly average values (as opposed to daily average flows) provide a way to
consider interannual variation. The duration curve framework uses a frequency
distribution based on all individual months over the same period (such as all values in
Table B-6). Figure B-14 shows the loading capacity curve for Swamp Creek using the
frequency distribution of mean monthly flows.
Table B-6. Swamp Creek Monthly Mean Flows
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
Maximum
Average
Median
25th %
10'"%
Minimum
Individual Monthly Mean Flows (cfs)
Jan
27.1
63.5
42.5
94.1
87.7
46.6
24.8
110.4
80.0
41.3
58.5
27.1
140.5
77.0
83.5
55.5
35.6
22.7
Feb
79.2
80.0
57.3
105.7
89.8
66.7
40.9
56.4
59.9
18.7
53.1
79.2
105.7
62.5
57.5
51.5
35.4
18.7
Mar
33.2
59.2
30.3
68.6
57.5
71.8
29.0
25.3
79.0
46.1
74.8
33.2
115.1
56.6
54.3
38.2
29.8
25.3
Apr
39.0
41.3
34.6
48.3
28.8
38.9
31.1
19.8
25.9
48.4
23.1
39.0
50.7
34.6
34.6
29.7
22.2
15.9
May
11.0
15.8
22.5
13.7
17.8
30.2
19.9
24.0
15.6
22.4
17.4
11.0
30.2
18.5
17.4
15.5
14.0
11.0
June
5.7
21.9
20.8
8.4
12.2
19.3
26.7
7.7
7.8
22.6
10.8
5.7
26.7
12.8
11.3
8.0
6.5
5.7
July
6.0
10.1
14.0
10.2
13.5
8.4
6.7
10.3
6.8
6.4
7.0
6.0
14.0
7.7
6.7
6.0
5.0
4.3
Aug
5.5
9.2
6.9
7.6
12.5
7.5
7.4
5.1
6.4
5.4
6.6
5.5
13.0
7.1
6.7
5.3
4.3
3.6
Sept
7.5
8.8
15.4
12.3
13.0
12.9
10.0
9.1
6.0
8.7
5.1
7.5
22.8
10.3
9.6
7.0
5.4
5.1
Oct
14.4
7.6
53.9
18.5
10.3
13.4
35.1
18.0
5.8
10.1
22.1
14.4
53.9
15.5
12.7
9.1
7.2
5.8
Nov
14.9
37.1
74.2
24.9
91.1
80.6
26.1
66.1
13.1
42.2
26.3
14.9
91.1
38.7
26.3
24.4
14.7
11.1
Dec
86.5
69.5
131.2
110.0
59.2
86.1
23.8
61.4
54.1
35.6
42.2
86.5
131.2
72.9
69.5
55.6
39.1
16.4
EPA 841-B-07-006
52
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
Figure B-14. Monthly Bacteria Loading Capacity Using Duration Curve Framework
Swamp Creek
Load Duration Curve
B 100
^
I '
o
0.1
u
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
EPA 841-B-07-006 54 August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
APPENDIX C
Targeting Potential Solutions and
Connecting to Implementation
Traditional approaches towards TMDL development tend to focus on targeting a single
value, which depends on a water quality criterion and design flow. The single number
concept does not work well when dealing with impairments caused by NFS pollutant
inputs (Stiles, 2001). One of the more important concerns regarding nonpoint sources is
variability in stream flows, which often causes different source areas and loading
mechanisms to dominate under different flow regimes. Because NFS pollution is often
driven by runoff events, TMDL development should consider factors that ensure
adequate water quality across a range of flow conditions.
Cl. "BOTTOM UP" APPROACHES
An important key to the success of the TMDL program,
in terms of engaging the public, is building linkages to
other programs, such as nonpoint source (NFS)
management. Many successful efforts to develop
TMDLs have involved the §319 program as a way to
utilize local groups in data collection, analysis, and
implementation. Watershed analysis has been used to
build a "bottom up " approach, which defines one way to
establish a meaningful, value-added framework linking
water quality concerns to proposed solutions. TMDL
development using a "bottom up " approach considers the
interaction between watershed processes, disturbance
activities, and available methods to reduce pollutant
loadings, specifically BMPs.
A "bottom up " approach capitalizes on the networks of programs and authorities across
jurisdictional lines. Information on management measures related to both source control
and delivery reduction methods is linked to conditions for which specific restoration
strategies may be most appropriate. This information can then be incorporated into the
allocation part of TMDL development using a duration curve framework.
EPA 841-B-07-006
55
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
C2. PROBLEM SOLVING FRAMEWORK
The "two Ps" - practical approaches and partnerships - are critical to successful
watershed planning and implementation. On the practical side, a "bottom up " approach
must overcome the challenge of translating detailed technical concepts and information
into "plain English ". On the partnership side, key stakeholders must be engaged in the
process, so that meaningful results with measurable improvements are achieved.
A problem solving framework, constructed around a set of fundamental questions, can
help focus development of practical approaches and encourage participation among key
partners. A basic set of questions using a "bottom up" approach to address water quality
problems often includes:
WHY the concern?
WHAT reductions are needed?
WHERE are the sources?
WHO needs to be involved?
WHEN will actions occur?
These simple, practical questions can be easily used to keep assessment efforts connected
with implementation activities. Methods to communicate technical information, such as
duration curves, can be an important part of the problem solving process.
C3. ENGAGING STAKEHOLDERS
Public involvement is fundamental to
successful TMDL development and
implementation. Duration curves provide
another way of presenting water quality data,
which characterizes concerns and describes
patterns associated with impairments. As a
communication tool, this framework can help
elevate the importance of monitoring
information to stakeholders.
The extended use of monitoring information and the alternative way to present TMDLs
using duration curves offers an opportunity for enhanced targeting, both in field
investigation efforts and implementation planning. As an assessment and communication
tool, duration curves can help narrow potential debates, as well as inform the public and
stakeholders so they become engaged in the process. Duration curves offer an
opportunity for enhanced targeting, both in TMDL development and in water quality
restoration efforts. In particular, duration curves can add value to the TMDL process by
identifying:
EPA 841-B-07-006
56
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
targeted participants (e.g., NPDES permitees) at critical flow conditions;
targeted programs (e.g., Conservation Reserve Program);
targeted activities (e.g., conservation tillage or contour farming); and
targeted areas (e.g., bank stabilization projects).
Targeted Participants
Figure C-l represents the first of several hypothetical
examples to illustrate the potential use of duration
curves, both as a diagnostic indicator and as a
communication tool for targeting in the TMDL
process. The target curve in Figure C-l is derived
using flow duration intervals that correspond to
stream discharge values and numeric criteria for E.
Coli.
The area circled on the right side of the duration curve represents hydrologic conditions
where the target is exceeded. In this example, wastewater treatment plants exert a
significant influence at low flows. Duration curves support a "bottom up" approach
towards TMDL development and restoration efforts by identifying targeted participants,
in the case of Figure C-l, point sources. For urban watersheds, water quality concerns
experienced during low flow conditions might involve detecting illicit connections under
an MS4 stormwater program. In an agricultural setting showing similar patterns,
potential solutions could include livestock management through riparian fencing or off-
site watering BMPs.
Figure C-l. Duration Curve as General Indicator of Hydrologic Condition
Pipe Creek below Elfton
Sample Load Duration Curve
a ID 20 30 40 50 GO 70
Flow Duration Interval
TARGETED Participants: Point Sources
EPA 841-B-07-006
57
August 2007
-------
Targeted Programs
An Approach for Using Load Duration Curves in the Development of TMDLs
Figure C-2 illustrates the added value duration
curves can provide by highlighting potential
contributing areas. As seen in this hypothetical
example, the target is met when the hydrologic
condition of the watershed is above a flow
duration interval of 70 (generally low flow and
dry conditions). Problems start to develop
under mid-range flows and sometimes dry
conditions, as indicated by the circled area.
Wet-weather events can range from high flows and moist conditions after severe
thunderstorms to lower surface runoff volumes following light rains. Watershed
conditions, land use, and proximity of source areas to streams should also be considered.
For this particular watershed (Figure C-2), the increased load may be the result of
pollutant delivery associated with rainfall and runoff from riparian areas. In more urban
watersheds, runoff from impervious areas could also contribute flow and pollutants in
response to light rain, exhibiting a pattern similar to Figure C-2.
Duration curves can be used as a diagnostic tool, which supports a "bottom up " approach
towards TMDL development and water quality restoration by identifying targeted
programs, namely those focused on riparian protection. In agricultural areas, such as the
Willow Creek example watershed (Figure C-2), this might include activities such as the
Conservation Reserve Program (CRP) and Conservation Reserve Enhancement Program
(CREP).
Figure C-2. Duration Curve with Contributing Area Focus
Willow Creek near Turkey Gap
Sample Load Duration Curve
Flow Duration Interval (%)
TARGETED Programs: Riparian Buffers (&g. CRP, CREP)
EPA 841-B-07-006
58
August 2007
-------
Targeted Activities
An Approach for Using Load Duration Curves in the Development of TMDLs
The focus on contributing areas is further illustrated
with another hypothetical example, shown in Figure
C-3, where total suspended solids associated with
surface erosion is the pollutant of concern. Here,
the duration curve is expressed in terms of yield to
show how distributions derived from a flow
duration curve can be extended to other measures,
again as a simple targeting tool.
In the Chicken Run example (Figure C-3), observed values only exceed the target when
the hydrologic condition of the watershed is below 55 (generally higher flows). For the
Chicken Run example watershed, duration curves can be used to support a "bottom up "
approach towards TMDL development.
Chicken Run is also an agricultural watershed. Wet-weather events expected to deliver
pollutants under moist conditions are generally associated with more saturated soils. In
addition to riparian areas, a larger portion of the watershed drainage area is potentially
contributing runoff.
In this case, consideration might be given to targeted activities such as conservation
tillage, contour strips, and grassed waterways. For urban watersheds, water quality
concerns experienced during mid-range flows and moist conditions might be best
addressed through site construction BMPs under an MS4 storm water management
program (SWMP). Critical area ordinances are another set of management measures that
would address water quality concerns under these flow conditions. Thus, water quality
data and a duration curve framework can help guide local implementation efforts to
achieve meaningful results.
Figure C-3. Duration Curve with Targeted Activity Focus
Chicken Run above \ It. Pleasant
Sample Yield Duration Curve
Flow Duration Interval (%)
TARGETED Activities: Contour Strips, Conser\'ation Tillage
EPA 841-B-07-006
59
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
Figure C-4 illustrates another hypothetical
example, where transport and delivery
mechanisms that occur under high flow
conditions typically include stream bank
erosion and channel processes. Targeted areas
for water quality improvement might consider
bank stabilization efforts. For urban
watersheds, targeted areas might involve post
development BMPs intended to address
channel protection.
Figure C-4. Duration Curve with Delivery Mechanism Focus
Rock Creek near Moose Junction
Sample Yield Duration Curve
1000
0.001
90
100
Flow Duration Interval
TARGETED Areas: Streambank Erosion, Bank Stability
EPA 841-B-07-006
60
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
CONNECTING TO IMPLEMENTATION AND RESULTS
A major advantage of the duration curve framework in TMDL development is the ability
to provide meaningful connections between allocations and implementation efforts.
Because the flow duration interval (FDI) serves as a general indicator of hydrologic
condition (i.e., wet versus dry and to what degree), allocations and reduction targets can
be linked to source areas, delivery mechanisms, and the appropriate set of management
practices. The use of duration curve zones (e.g., high flow, moist, mid-range, dry, and
low flow) allows the development of allocation tables, which can be used to summarize
potential implementation actions that most effectively address water quality concerns.
Connections to Management Practices
Development of wasteload allocations for continuous point source discharges is relatively
straightforward using a duration curve framework, when compared to either storm water
or nonpoint sources. Consideration of pollution control measures is typically done in
conjunction with NPDES permit development. Wasteload allocations (WLAs) can be
expressed at one level across the entire duration curve, or WLAs may be tiered to specific
flow levels and the corresponding flow duration interval. Storm water or nonpoint
sources, on the other hand, present a much greater challenge because pollutants are
transported to surface waters by a variety of mechanisms (e.g., runoff, snowmelt,
groundwater infiltration). Best management practices (BMPs) generally focus on source
control and / or delivery reduction. Table C-l illustrates an approach, which could be
used to assess the management options in a way that considers the potential relative
importance of hydrologic conditions.
Documenting Results
Figure C-5 illustrates the advantage of the duration curve framework in documenting
results using Charles River data. This location has been monitored since 1989. Based on
this water quality information, significant reductions in bacteria loads to the river have
occurred over the past ten years through CSO controls plus illicit discharge detection and
elimination. These improvements are reflected in the data using a duration curve
framework, particularly in the moist, mid-range, and dry zones. Individual allocations
can help focus implementation efforts to address remaining problems that occur under
high flow conditions.
Figure C-6 illustrates another example of the advantage of this framework using Big
Sioux River data. This location has been monitored by the State of South Dakota since
1974. As noted in Figure C-6, significant reductions in bacteria loads to the river have
occurred over the past fifteen years. These improvements are reflected in the data using a
duration curve framework, particularly in the high, moist, mid-range, and dry zones. The
duration curve framework can help focus efforts to address remaining problems with
management strategies most appropriate for those flow conditions.
EPA 841-B-07-006 61 August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
Table C-l. Example Management Practice / Hydrologic Condition Considerations
Management Practice
Bacteria Source Reduction
Remove Illicit Discharges
Address Pet & Wildlife Waste
Combined Sewer Overflow Management
Combined Sewer Separation
CSO Prevention Practices
Septic System Management
Managing Private Systems
Replacing Failed Systems
Installing Public Sewers
Storm Water Infiltration / Retention
Infiltration Basin
Infiltration Trench
Infiltration / Biofilter Swale
Storm Water Detention
Created Wetland
Low Impact Development Practices
Disconnecting Impervious Areas
Bioretention
Pervious Pavement
Green Roof
Rain Gardens
Agricultural Management Practices
Managing Manure Application
Pasture / Grazing Management
Managing Barnyards
Managing Recreational Sources
Designate No Discharge Areas
Address Discharges from Boats
Other
Point source controls
Riparian buffers
Pet waste education & ordinances
Note: Potential relative importance of mai
given hydrologic condition (H: Hig
Duration Curve Zone
High
Moist
H
M
Mid-
Range
M
H
H
Dry
H
H
H
Low
H
lagement practice effectiveness under
h; M: Medium; L: Low)
EPA 841-B-07-006
62
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
Figure C-5. Documenting Program Results Using Duration Curve Framework
Charles River Watertown Dam
Load Duration Curve (1989 - 2004 Monitoring Data)
High
Moist
Mid-range
Low
20 30 40 50 60 70 SO
Flow Duration Interval (%)
90
100
Figure C-6. Documenting Program Results Using Duration Curve Framework
Big Sioux River at Brandon
Load Duration Curve (1974 - 2005 Monitoring Data)
High
Moist
Mid-range
Low
10 20 30 40 SO £0 70
Flow Duration Interval
80 90 100
3,72 9 square miles
EPA 841-B-07-006
63
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
EPA 841-B-07-006 64 August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
APPENDIX D
Acronyms and References
ACRONYMS
7Q10
90th
ALC
ARA
BMP
BST
CFR
cfs
cfu
C.L.
cms
CREP
CRP
CSO
CWA
DC
EIFAC
EPA
FDI
F.I.
FR
geo. mean
GIS
GM
G-org
GWLF
HSPF
LA
LC
LDC
LNCC
MCL
MOS
the 7-day average low flow occurring once in 10 years
90th percentile
aquatic life criteria
antibiotic resistance analysis
best management practice
bacteria source tracking
Code of Federal Regulations
cubic feet per second
colony forming units
confidence level
cubic meters per second
Conservation Reserve Enhancement Program (U.S. Department of
Agriculture)
Conservation Reserve Program (U.S. Department of Agriculture)
combined sewer overflow
Clean Water Act
duration curve
European Inland Fisheries Advisory Committee
U.S. Environmental Protection Agency
flow duration interval
frequency interval
Federal Register
geometric mean
geographic information system
geometric mean
billion organisms
generalized watershed loading function
hydrological simulation program - FORTRAN
load allocation
load (duration) curve
load duration curve
log-normal criteria curve
maximum contaminant level
margin of safety
EPA 841-B-07-006
65
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
MS4
NPDES
NFS
org
PS
Q-based
R. curve
SF
SS
SWAT
SWMP
TMDL
T-org
TSD
TSS
USGS
WLA
WQ
WQS
WWTF
WWTP
Z-90th
ZMC
7Q10
municipal separate storm sewer system
National Pollutant Discharge Elimination System
nonpoint source
organisms
point source
flow data-based
regression (or rating) curve
storm flow
suspended sediment
soil and water assessment tool
storm water management program
total maximum daily load
trillion organisms
technical support document
total suspended solids
U.S. Geological Survey
waste load allocation
water quality
water quality standard
wastewater treatment facility (also referred to as a WWTP)
wastewater treatment plant (also referred to as a WWTF)
90th percentile of a particular zone
zone median concentration
Lowest streamflow for 7 consecutive days that occurs on average once
every 10 years
REFERENCES
Bonta, J.V. March 2002. Framework for Estimating TMDLs with Minimal Data. ASAE
Proceedings of the Watershed Management to Meet Emerging TMDL
Regulations Conference. Fort Worth, TX. pp. 6-12.
Cleland, B.R. June 2007. TMDL Development From the "Bottom Up" - Part IV:
Connecting to Storm Water Management Programs. National TMDL Science
and Policy 2007 WEF Specialty Conference. Bellevue, WA.
Cleland, B.R. November 2003. TMDL Development From the "Bottom Up" - Part III:
Duration Curves and Wet-Weather Assessments. National TMDL Science and
Policy 2003 -- WEF Specialty Conference. Chicago, IL.
Cleland, B.R. November 2002. TMDL Development From the "Bottom Up" - Part II:
Using Duration Curves to Connect the Pieces. National TMDL Science and
Policy 2002 -- WEF Specialty Conference. Phoenix, AZ.
EPA 841-B-07-006
66
August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
Hornberger, G.M., J.P. Raffensperger, P.L. Wiberg, and K.N. Eshleman. 1998. Elements
of Physical Hydrology. Johns Hopkins University Press. Baltimore, MD. 302 p.
Leopold, L.B. 1994. A View of the River. Harvard University Press. Cambridge, MA.
Linsley, R.K., M.A. Kohler, and J.L. Paulus. 1982. Hydrology for Engineers (3rd ed.).
McGraw-Hill. New York, NY.
Mehan, G.T. November 2001. Testimony on TMDL Program before Subcommittee on
Water Resources and Environment - U.S. House of Representatives.
Washington, DC.
Rosgen, D.L. 1996. Applied River Morphology. Wildland Hydrology. Pagosa Springs,
CO.
Searcy, James, K. 1959. Flow-Duration Curves; Manual of Hydrology: Part 2. Low-
Flow Techniques. U.S. Geological Survey Water-Supply Paper 1542-A. 33 p.
Sheely, L.H. July 2002. Load Duration Curves: Development and Application to Data
Analysis for Streams in the Yazoo River Basin, MS. Special Project - Summer
2002. Jackson Engineering Graduate Program.
Simon, A and C.R. Hupp. March 1986. Channel Evolution in Modified Tennessee
Channels. Proceedings of Fourth Interagency Sedimentation Conference. V.2,
Section 5, pp. 5-71 to 5-82. Las Vegas, NV.
Simon, A., E. Langendoen, R. Bingner, R. Wells, Y. Yuan, and C. Alonso. 2004.
Suspended-Sediment Transport and Bed-Material Characteristics of Shades
Creek, Alabama and Ecoregion 67: Developing Water Quality Criteria for
Sediment. USDA Agricultural Research Service, National Sedimentation
Laboratory. Oxford, MS.
Sloto, R.A. and M.Y. Grouse. 1996. HYSEP: A Computer Program for Stream/low
Hydrograph Separation and Analysis. U.S. Geological Survey Water Resources
Investigations Report 96-4040. Lemoyne, PA. 46 p.
South Carolina Department of Health & Environmental Control. 2005. Total Maximum
Daily Load (TMDL) for Fecal Coliformfor Hills Creek, Lynches River, North and
South Branch of Wildcat Creek, Flat Creek, Turkey Creek, Nasty Branch, Gulley
Branch, Smith Swamp, Little Pee Dee River, Maple Swamp, White Oak Creek,
and Chinners Swamp of the Pee Dee River Basin, South Carolina. SCDHEC
Technical Report Number: 029-05.
EPA 841-B-07-006 67 August 2007
-------
An Approach for Using Load Duration Curves in the Development of TMDLs
Stiles, T.C. November 2002. Incorporating Hydrology in Determining TMDL Endpoints
and Allocations. National TMDL Science and Policy 2002 - WEF Specialty
Conference. Phoenix, AZ.
Stiles, T.C. March 2001. A Simple Method to Define Bacteria TMDLs in Kansas.
ASIWPCA / ACWF / WEF TMDL Science Issues Conference: On-site Program.
St. Louis, MO. pp 375-378.
Sullivan, J. A. March 2002. Use of Load Duration Curves for the Development of
Nonpoint Source Bacteria TMDLs in Texas. AS AE Proceedings of the Watershed
Management to Meet Emerging TMDL Regulations Conference. Fort Worth,
TX. pp. 355-360.
U.S. Environmental Protection Agency. 2007. Options for Expressing Daily Loads in
TMDLs. Office of Wetlands, Oceans, & Watersheds. Washington, DC.
U.S. Environmental Protection Agency. 2004. Total Maximum Daily Load (TMDL) for
Siltation, Turbidity, and Habitat Alteration in Shades Creek Jefferson County,
Alabama. USEPA Region 4. Atlanta, GA.
U.S. Environmental Protection Agency. 1999. Protocol for Developing Sediment
TMDLs. Office of Water. EPA 841-B-99-007. Washington, D.C.
U.S. Environmental Protection Agency. April 1991. Guidance for Water Quality-based
Decisions: The TMDL Process. Office of Water. EPA 440/4-91-001.
Washington, D.C.
U.S. Environmental Protection Agency. March 1991. Technical Support Document for
Water Quality-based Toxics Control. Office of Water. EPA 505/2-90-001.
Washington, D.C.
U.S. Environmental Protection Agency. 1986. Ambient Water Quality Criteria for
Bacteria-1986. Office of Water. EPA-440/5-84-002. Washington, D.C.
EPA 841-B-07-006 68 August 2007
------- |