EPA/600/A-94/236
August 1991
COMPUTING TMDLs FOR URBAN RUNOFF AND OTHER
POLLUTANT SOURCES
by
Lewis A. Rossman
Water and Hazardous Waste Treatment Research Division
Risk Reduction Engineering Laboratory
Cincinnati, Ohio 45268
RISK REDUCTION ENGINEERING LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
CINCINNATI, OHIO 45268

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Abstract
Under the Gean Water Act, states are required to compute Total
Maximum Daily Loads (TMDLs) for their priority water bodies. A TMDL
determines the maximum pollutant loading from both point and nonpoint
sources that a receiving water can accept without exceeding an allowable
frequency of water quality excursions. Computing a TMDL is difficult because
point source loadings are continuous in time while nonpoint source loadings
occur only intermittently. A framework for determining a TMDL and its
allocation among sources is developed, based on a modified form of continuous
simulation. The approach is applied to an example problem of lead toxicity
control within an urban catchment. Results show that it is possible to define
the TMDL in an operationally useful way for simple receiving water systems,
that the computed TMDL value depends on the level of nonpoint source
control selected, and that multiple combinations of equally effective point and
nonpoint source control levels are possible.
Introduction
The U.S. Environmental Protection Agency (EPA) has established the
"TMDL process" to satisfy the requirements of section 303(d) of the Gean
Water Act (Guidance for Water Quality, 1991). A TMDL> or Total Maximum
Daily Load, establishes the allowable loadings from all pollutant sources (both
point and nonpoint) to a waterbody so that water quality standards are
attained. Developing a TMDL typically involves the following kinds of
activities: (1) selecting the type of water quality impact to analyze, (2)
identifying the pollutant loadings from all types of sources that affect the
selected water quality impact, (3) determining the total amount of pollution
that the waterbody can accept without exceeding water quality standards, (4)
allocating this allowable pollutant load to the various sources.
These activities mirror the commonly accepted approach to water quality
management as described in textbooks (Pavoni, 1977) and even in federal
guidance issued two decades ago (Guidelines, 1971). What makes the TMDL
process especially pertinent today is the programmatic emphasis it places on
coordinated control of both point and nonpoint pollution sources, including
urban runoff. This emphasis is enforced through EPA's Water Quality Planning
and Management Regulation (40 CFR Part 130) which requires that States
develop TMDLs for their priority water bodies and submit these for EPA
approval.
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Planning for coordinated control of both point and nonpoint pollution
sources is made difficult by the fundamentally different nature of the two
sources. Point sources discharge continuously while most nonpoint pollution
occurs only intermittently. Pollution loads from nonpoint sources, such as
urban runoff, are influenced greatly by rainfall and other stochastic phenonema
(e.g., the effectiveness of street sweeping) and are therefore not predictable in
any deterministic sense. The receiving water impacts of both types of sources
are affected by many other stochastic factors as well. These include stream
flow, temperature, pH, alkalinity, hardness, and light intensity. Thus a
fundamental question to ask is how can the statistical variability of all these
factors be taken into account so that a TMDL and its allocation among sources
reliably meets water quality standards.
This paper illustrates one approach for making the TMDL an
operationally useful concept. It demonstrates how the TMDL should be
interpreted in light of the various sources of variability that affect receiving
water impacts. And it shows how a TMDL can be quantified and allocated
between point and nonpoint sources so that water quality standards are met.
Background
EPA guidance (Guidance for Water Quality, 1991) defines the TMDL
for a waterbody segment with the following equation;
TMDL = WLA + LA + MOS	(1)
where WLA (wasteload allocation) is the portion of the TMDL allocated to
existing or future point sources, LA (load allocation) is the portion allocated
to existing or future nonpoint sources or to natural background sources, and
MOS (margin of safety) is a portion that accounts for the uncertainty in the
relationship between pollutant loads and receiving water quality (or a portion
reserved for future growth within the watershed).
The TMDL itself is the maximum pollutant loading that a water body
can receive without violating water quality standards. It can be expressed in
units of mass per time, toxicity, or other appropriate measures that relate to a
State's water quality standard (Guidance for Water Quality, 1991). EPA
guidance does not address the issue of how the loadings from both continuous
(point sources) and episodic (nonpoint sources) can be reconciled into a single
number nor does it recognize the fact that when interpreted literally, as an
allowable daily load, the TMDL varies from day to day as a receiving water's
capacity to accept pollutant loads varies.
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EPA recommends that numeric water quality standards be stated in
terms of magnitude, duration and frequency, i.e., a standard is a receiving water
concentration occuring over a given averaging period allowed to be exceeded
with a specified frequency (Technical Support Document, 1991). In theory, the
standard can be stated in terms of some quantitative measure of water quality
impact that can be related to pollutant source loading. These include limits on
specific chemical concentrations (e.g., lead), ambient toxicity (e.g., a dilution
necessary to achieve a specific endpoint for an aquatic species in a toxicity
test), and biological criteria (biological community indices, amount of suitable
habitat). We will focus on chemical-specific standards because the predictive
linkages between loadings (and pollution reduction measures such as BMPs)
and aquatic toxicity and biological indicators are not as well developed.
Viewing water quality standards in these terms, a TMDL could be set
to a water body's loading capacity whose frequency of not being exceeded
equals the allowable excursion frequency of the water quality standard. For
example, if one excursion above water quality limits were allowed every 3 years,
then the TMDL would equal the daily water body loading capacity whose
frequency of not being exceeded is once in 3 years. Taking this concept one
step further, suppose the magnitude of the water quality standard is a constant
concentration CWQS, and the x-day average stream flow is Q, where x is the
averaging period used in the water quality standard. Then for any x-day period,
the water body loading capacity is Q • and a TMDL could be found by
solving the following equation for TMDL:
FreqfQ-CwQs < TMDL} = E 	(2)
where Freq{X} is the frequency at which condition X occurs and E is the
allowable excursion frequency of the water quality standard. This concept is
displayed visually in Figure 1.
Because stream flow is the only quantity that varies in Eq. 2, the TMDL
can be set to QdesQ^Qs where Qdes is a design flow, equal to the flow whose
frequency of not being exceeded is E. This has been the traditional approach
used for simplified waste load allocations for point sources (which ignores
background and nonpoint sources) wherein
WLA = QdesCwQs	(3)
and
Cps = WLA/Qpj	(4)
with Cre = point source effluent concentration limit and Qps = point source
flow rate.
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LOADING
CAPACITY
TMDL
EXCURSION
1
t
a
o
TME, YRS
Figure 1. One Possible Interpretation of the TMDL
When background sources and nonpoint sources (such as urban runoff)
are included the picture becomes more cloudy. First, the argument above
assumes that the TMDL is a constant load that the waterbody sees every day.
This might be true for point sources (if variability in discharge flow and
treatment efficiency were ignored) but certainly would not be the case with
intermittent nonpoint source loadings. Second, nonpoint source controls, such
as detention basins or porous pavement, will alter runoff flow and therefore
change the stream flow statistics. Thus the TMDL and any design flow will
become a function of the nonpoint source control program chosen. Finally,
there are many other sources of variability, besides stream flow, that can affect
a TMDL. For example, CWQS could be a function of other water quality
parameters, such as hardness in the case of heavy metals or pH and
temperature in the case of ammonia (Quality Criteria, 1986). These
parameters will vary, both seasonally and randomly, over time. Likewise,
background source levels of a pollutant might display a random variation as
would effluent levels of a pollutant being discharged from a point source's
treatment process. How might these additional sources of variability be taken
account of when computing a TMDL?
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Computational Approach
Figure 2 illustrates the nature of the problem being addressed. Given
a time-varying, uncontrollable source of background pollutant loading,
determine the mixture of controls on point and nonpoint pollutant sources and
the corresponding TMDL whose resulting frequency of water quality excursions
meets the limit set in the standard. The following questions seem particularly
relevant: (1) what are the relative contributions of different source categories
to the TMDL, (2) which type of source most influences water quality
excursions, (3) as nonpoint source loads are reduced, how much can point
source loads be increased, and (4) what is the most cost-effective mix of point
and nonpoint source controls?
BACKGROUND
--i: isotiricfiir
'-s'jVZ:
POINT 80URCE
—-As
Load
' TVr»
Load
A A h A
Twrm
NONPOINT
SOURCE
WATEfl
QUALITY
Concur.
Figure 2. Definitional Sketch of a Receiving Water System
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We have shown that a direct determination of a TMDL based on the
concept of loading capacity will not allow us to find a meaningful allocation of
this load between point and nonpoint sources. An alternative approach is to
use continuous simulation modeling (Singh et al., 1982). A set of point and
nonpoint control actions is specified and a long-term record of all pertinent
flows, source loadings, and supplemental water quality input variables are
accumulated, either from historical measurements or from statistical models.
A water quality response model is then used to' predict a time series of water
quality conditions. A frequency analysis of these conditions is made to
determine the frequency of water quality excursions. Based on these results,
source loadings are adjusted and the simulation process is repeated until the
desired excursion frequency is acheived.
An alternative way for computing TMDLs is available that avoids the
need to do repetitive continuous simulation. The approach is best suited for
screening level analyses on free-flowing rivers where point sources and runoff
outfalls are in close proximity to one another. It does not consider fate and
transport phenomena within the receiving water, but focuses instead on meeting
water quality standards at the edge of a mixing zone between all source inputs.
This makes it only applicable to situations where the water quality conditions
at a mixing point are determined only by source loadings occuring during the
averaging period used to evaluate water quality standards. Examples would be
episodic events, such as heavy metal toxicity or bacteriological contamination,
and algal bloom problems which can be correlated with annual or seasonal
loadings of nutrients. Sediment deposition, transport and resuspension or
nutrient recycling within benthic deposits are problems which cannot be
handled at this time.
This alternative approach can accommodate several complicating factors.
Water quality standards can be functions of supplementary parameters, such as
temperature and pH. Speciation of materials at the point where sources mix
can be considered. Statistical variability of all relevant factors can be
accounted for, using a variety of different distributional assumptions. Lastly,
the method can show how for a given allowable excursion frequency, different
nonpoint source control actions give rise to different levels of point source
controls.
As we noted earlier, runoff controls can alter stream flow statistics and
therefore the frequency of water quality excursions. We account for this by
analyzing candidate nonpoint source control strategies one at a time. For each
strategy, we determine what the long-term mean point source loading must be
so that water quality excursion frequencies are met From this we can establish
a TMDL and, as each nonpoint control option is examined, generate a trade-off
curve between point and nonpoint control efforts.
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In general terms, the steps of the approach go as follows:
1.	Select a nonpoint source control option.
2.	Simulate a long-term daily record of:
a.	background stream flows (0^), contaminant concentrations (C^),
and, where relevant, supplementary water quality variables (such as
temperature, PH, or hardness)
b.	nonpoint source flows (Q^s) and pollutant concentrations (CNTS)
c.	point source discharge flows (Ore), variations in point source
treatment efficiency (V), and, where relevant, supplementary water
quality variables.
3.	If water quality standards (C^qs) are functions of supplementary water
quality variables, then compute these standards for conditions occurring
over each day of the record.
4.	For each x-day period of the record (where x is the duration specified
in the water quality standards), use a rearrangement of the simple mass
balance equation to compute the point source discharge concentration
(Cps) that just meets water quality standards:
< ^WQS > * * * " < Qnps^-nps/Q>i
Cps 		 (5)
x
where Q = Qbs+Qps+Qnps an(J „ denotes the x-day average of the
quantity X.
5.	From the collection of computed values, find C'pg, the value whose
frequency of not being exceeded equals the allowable water quality
excursion frequency.
6.	Evaluate the following quantities:
WLA = C*PSLTA(QPSV)
LA = LTA(QbsCbs + Qjs-psQ^ps)
TMDL = WLA + LA
where LTA(X) is the long-term average value of X over the simulation.
7.	Evaluate the costs and any other criteria associated with the point and
nonpoint source controls used in the analysis (such as land requirements
and implementability) and repeat the analysis for another choice of
nonpoint source control.
In step 6 we interpret the TMDL as the sum of the long-term average
loadings from each source category that achieves water quality standards, with
the understanding that the variability associated with each source loading has
been taken into account to insure compliance with water quality standards.
This allows us to add together quantities (long term average loads) defined
over equivalent time frames. This view of the TMDL differs from that in the
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previous section, where it was interpreted as a water body loading capacity with
a certain frequency of not being exceeded. Also note that the third element of
a TMDL as defined in Eq. 1, the MOS (margin of safety), is not explicitly
considered here. One way to include it in the calculations is to reduce C^QS by
a given amount.
A computer program was written to implement steps 1-6 of this TMDL
procedure. Some notable features of the program are:
1.	Water quality standards for heavy metals can be functions of stream
hardness while standards for ammonia can be functions of pH and
temperature.
2.	Any external rainfall-runoff model can be used to generate runoff events
as long as its output includes the start time, duration, flow, and
contaminant concentration for each event generated.
3.	Daily background stream flow is taken from historical flow records.
This avoids the problem of having to identify a statistically correct
stream flow probability distribution, including the proper autocorrelation
structure between successive daily flows.
4.	Daily concentrations of background water quality parameters are
generated by an equation containing two terms: The first term is a daily
deterministic seasonal pattern that repeats each year; the second term
adds randomly generated perturbations to the annual pattern. A similar
equation is used to generate daily point source flows and supplemenatry
water quality variables (pH, temperature, etc.).
5.	The V factor in Eq. 5 is computed by modeling the daily variability in
contaminant concentration discharged from the point source as a
lognormally distributed, first order Markov time series. It can be fully
described by means of a coefficient of variation and an auto-correlation
coefficient.
Example Application
We present an example TMDL analysis that illustrates how the
questions asked at the beginning of the previous section can be answered. The
problem involves controlling acute aquatic toxicity caused by lead discharges
within an urban catchment area. The data are summarized in Table 1. Note
that the lead standard increases with increasing water body hardness and can
only be exceeded once every three years. Historical stream flow data from the
Quinnipiac River in Connecticut are used along with rainfall statistics from
Boston. We assume that no lead is present from background sources and that
its mean concentration in uncontrolled runoff is 100 ug/L. A simple statistical
rainfall-runoff model (Areawide Assessment, 1976) is used to generate runoff
events.
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Table 1, Data Used in Example TMDL Calculation
Data Category
	"	-—		——|
Value
Water Quality Standards
Type
Averaging Period
Concentration Limit
Excursion Frequency
US EPA CMC (Acute)
1 day
34 ug/L at 50 mg/L Hardness
82 ug/L at 100 mg/L Hardness
137 ug/L at 150 mg/L Hardness
1 in 3 years
Stream Flow
River
Period of Record
Mean Flow
7-day, 10-year Low Flow
Quinnipiac near Wallingford CT
1932 - 1978
205 cfs (6 m3/sec)
32 cfs (1 m3/sec)
Background Source
Lead Concentration
Hardness
0 ug/L
87-SF + 15 -N(0,1)
0.86 < SF < 1.15
Point Source
Flow
Hardness
Lead Variability
3 cfs (0.08 m3/sec)
100 mg/L
CV = 0.7
Nonpoint Source
Rainfall Statistics
Catchment Area
Runoff Coefficient
Lead Concentration
Hardness
Boston, MA
1310 acre (531 ha)
0.38
Mean = 100 ug/L
CV = 0.7
Mean = 100 mg/L
CV = 0.5
Notes: CV = coefficient of variation; N(0,1) is a normally distributed random
variable with zero mean and unit variance; SF = seasonality factor.
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Table 2 presents TMDL results for the case of no runoff controls. The
mean point source lead limit (C'ps) must be 54 ug/L to achieve the 1 in 3 year
excursion frequency. On a long-term average basis, the receiving water can
accept 687 g/day of lead of which 58 percent comes from the point source and
the rest from urban runoff. Table 3 shows during what periods of the historical
record excursions of the lead standards would have occurred under the
assumptions of our simulation. Note that every excursion is caused primarily
by runoff.
Table 2. TMDL Results for No Runoff Control
Mean Point Source Concentration
54 ug/L
Total Maximum Daily Load
687 g/day
Point Source Waste Load Allocation
392 g/day
Background/Nonpoint Source Load Allocation
295 g/day
A second run was made using 15 acre-ft (18450 m3) of detention storage
runoff control. Table 4 shows the TMDL that results under this scenario. The
allowable point source discharge limit has increased more than three-fold, the
nonpoint load has almost halved, and the TMDL has more than doubled. An
excursion table like Table 3 would show that there are just as many events as
before, because the allowable excursion frequency has not changed. But now
the point source becomes the dominant cause in 20 percent of the events.
It is interesting to compare the magnitudes of the point loads, nonpoint
loads, and load capacities over time for these two runs. Figures 3 and 4 do this
for a portion of 1944, a year containing several water quality excursions. These
excursions show up very clearly in the figures where the sum of the two loads
exceeds the load capacity curve. The figures also show that runoff storage has
reduced the magnitude of all but the highest runoff loads and has permitted a
higher level of point source loading to occur.
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Table 3, Water Quality Excursions Under No Runoff Control
Date
Duration

% Caused by

(Days)
Magnitude1
Runoff
09/24/31
1
1.78
99.2
10/23/31
1
1.22
95.1
07/16/35
1
1.61
98.8
07/20/44
2
1.06
95.5
09/08/44
1
1.30
91.6
08/01/47
1
1.56
98.3
06/27/49
1
2.59
99.2
08/24/56
1
1.46
98.2
07/29/57
1
1.14
98.3
12/18/62
1
1.56
99.4
10/27/63
1
2.92
96.6
04/03/66
1
1.76
99.2
01/21/67
1
2.57
99.4
10/28/77
1
1.45
99.8
'Ratio of actual load to load capacity.
Table 4, TMDL Results for 15 Acre-Ft of Detention Storage
Mean Point Source Concentration
174 ug/L
Total Maximum Daily Load
1439 g/day
Point Source Waste Load Allocation
1281 g/day
Background/Nonpoint Source Load Allocation
158 g/day
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I. ¦. .1 Nonpoint
Load
Point
Load
Load
Capaolty
>»
1?
!
TJ C
3
so
1S
12
nJ.W n.
¦ -I - -«l »¦ i.J - In .L. ¦ I
J. J
Day
Figure 3. Lead Loadings for Portion of 1944 - No Nonpoint Controls
I I Nonpoint
Load
Point
Load
Load
Capaolty
!,
;i

20
16
12
¦JiB.Hn.iln.

JlAfaL
Day
Figure 4. Lead Loadings for Portion of 1944 - 15 Acre-Ft of Storage
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Table 5 shows the results of computing TMDLs for a variety of different
storage levels. As additional increments of storage are added, the TMDLs and
point source loads rise at a diminishing rate. Figure 4 compares detention
storage with treatment as a nonpoint source control. A 50 percent lead
removal in the runoff is equivalent to 30 acre-ft (36900 m3) of storage and
allows a fourfold increase in the point source lead loads. By computing the
costs of these various allocations of lead between point and nonpoint sources
we could determine the most cost-effective mix of controls that meets our water
quality objective.
Table 5. TMDLs for Different Volumes of Detention Storage
Storage
acre-ft1
TMDL
g/day
Point WLA
g/day
Nonpoint LA
g/day
% Nonpoint
Excursions2
0
687
392
295
100
3 ,
895
627
268
100
6
1269
1028
241
100
15
1439
1281
158
80
22.5
1689
1588
101
40
30
1725
1659
66
20
Percentage of excursions caused primarily from runoff.
Conclusions
This paper has provided an operational meaning to the TMDL concept.
The TMDL is contingent upon the method of nonpoint source control used and
should be calculated as the sum of long-term average loads. A modified form
of continuous simulation was developed to compute its value and its allocation
between pollution sources for simple receiving water systems. In general, the
TMDL will increase as tighter levels of nonpoint source control are applied.
Many different combinations of point and nonpoint source controls that meet
water quality standards can be generated. Further economic analysis could
then determine the most cost-effective combination of controls. These ideas
were illustrated through a numerical example involving the control of acute
lead toxicity.
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100
no -
i
I too -
g lfO -
100
to
10
0
10
40
•0
NonpoM 8torfto* lAo-fO or lUmoval (1U
Figure 5. Effect of Runoff Controls on Point Source Discharge Limits
Several questions remain regarding the computation of TMDLs. Can
the concepts used here be extended to consider larger scale watersheds where
considerable distances exist between discharge points? How can more complex
water quality impact phenomena, such as interactions between sediments and
overlying waters, be handled? In these situations the effects of settleable solids
in runoff may not be observed until months later, after sediment processes have
released nutrients or created an oxygen demand in the overlying waters
(Novotny and Bendoricchio, 1989), Finally we need to explore how the
approach would work with alternative ways of defining water quality impacts
and protection, such as ambient toxicity, biological indices, physical habitat
protection, and riparian restoration.
Acknowledgement
Although the work described in this paper has been funded wholly or in
part by the U.S. Environmental Protection Agency, it has not been subject to
the agency's review and therefore does not necessarily reflect the views of the
agency, and no official endorsement should be inferred.
14

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Appendix. References
Areawide Assessment Procedures Manual. (1976). EPA-600/9-76-014, Municipal
Environmental Research Laboratory, U.S. Environmental Protection Agency,
Cincinnati, OH.
Guidance for Water Quality-based Decisions: The TMDL Process. (1991). EPA
440/4-91-001, Office of Water, U.S. Environmental Protection Agency,
Washington, D.C
Guidelines • Water Quality Management Planning. (1971). Water Quality Office,
U.S. Environmental Protection Agency, Washington, D.C.
Novotny, V. and Bendoricchio, G. (1989). "Linking Nonpoint Pollution and
Deterioration." Water Environment & Technology, 1(3), 400-407.
Pavoni, J.L (editor) (1977). Handbook of Water Quality Management Planning.
Van Nostrand Reinhold, New York, NY.
Quality Criteria for Water - 1986. (1986). EPA 440/5-86-001, Office of Water
Regulations and Standards, U.S. Environmental Protection Agency,
Washington, D.C.
Singh, U.P., Scholl, J.E., and Wycoff, R.L. (1982). "Computer-Optimized
Stormwater Treatment (COST) Program: Philadelphia Case Study." Water
Resources Bulletin, 18(5), 769-778.
Technical Support Document for Water Quality-based Toxics Control. (1991).
EPA/505/2-90-001, Office of Water, U.S. Environmental Protection Agency,
Washington, D.C.
15

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TECHNICAL REPORT DATA
-i (Please read tnsirucr.ens on the reverse before comph
	
1. REPORT NO, 2.
EPA/600/A-94/236
3.
4. TITLE ANDSU8T1TLE
Computing TMDLs for Urban Runoff and Other
Pollutant Sources
5. REPORT DATE ~ ~ 		
August 1991
6. PERFORMING ORGANIZATION CODE
7. AUTHORtS)
Lewis A. Rossman
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
U.S. Environmental Protection Agency
Risk Reduction Engineering Laboratory
26 W. Martin Luther King Drive
Cincinnati, OH 45268
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
In-house Project
12. SPONSORING AGENCY NAME AND ADDRESS
Same as above
13. TYPE OF REPORT AND PERIOD COVERED
Conference Proceedings
14. SPONSORING AGENCY CODE
EPA/600/14
15. SUPPLEMENTARY NOTES
To appear in Conference Proceedings, Effects of Urban Runoff on Receiving Systems ..
p:1-15 •
16. ABSTRACT
	 Under the Clean Water Act, states are required to compute Total Maximum Daily
Loads (TMDLs) for their priority water bodies. A TMDL determines the maximum
pollutant loading from both point and nonpoint sources that a receiving water can
accept without exceeding an allowable frequency of water quality excursions.
Computing a TMDL is difficult because point source loadings are continuous in time
while nonpoint source loadings occur only intermittently. A framework for determining
a TMDL and its allocation among sources is developed, based on a modified form of
continuous simulation. The approach is applied to an example problem of lead toxicity
control within an urban catchment. Results show that it is possible to. define the
TMDL in an operationally useful way for simple receiving water systems, that the
computed TMDL value depends on the level of nonpoint source source control selected,
and that multiple combinations of equally effective point and nonpoint source control
levels are possible.--':—
17. KEY WORDS AND DOCUMENT ANALYSIS
a. DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS
c. COSATI Field/Croup
Water Qua!ity
Pollution
Runoff
Modeling
Computers
Total Maximum Daily Load
Urban Runoff
Nonpoint Pollution
Waste Load Allocation

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,?M7
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