An Assessment of Fecal Indicator
Bacteria-Based Water Quality
A N D R E W D . G R O N E W O L D , *, †
M A R K E . B O R S U K ,‡
R O B E R T L . W O L P E R T ,† , §A N D
K E N N E T H H . R E C K H O W†
Nicholas School of the Environment, Duke University,
Durham, North Carolina 27708, Thayer School of
Engineering, Dartmouth College, Hanover, New Hampshire
03755, and Department of Statistical Science, Duke
University, Durham, North Carolina, 27708
Received December 16, 2007. Revised manuscript received
April 1, 2008. Accepted April 4, 2008.
Fecal indicator bacteria (FIB) are commonly used to assess
Unlike most measures of pollutant levels however, FIB
concentration metrics, such as most probable number (MPN)
and colony-forming units (CFU), are not direct measures of
the true in situ concentration distribution. Therefore, there is
water quality assessments, such as those used in the Total
Maximum Daily Load (TMDL) program. To address this problem,
we present an innovative approach to assessing pathogen
contamination based on water quality standards that impose
limits on parameters of the actual underlying FIB concentration
distribution, rather than on MPN or CFU values. Such
concentration-based standards link more explicitly to human
employed, and are consistent with the outcomes of most
with concentration-based standards can be inferred from
traditional MPN values using a Bayesian inference procedure.
This methodology, applicable to a wide range of FIB-based
data from shellfish harvesting waters in the Newport River
Estuary, North Carolina. Results indicate that areas determined
to be compliant according to the current methods-based
standards may actually have an unacceptably high probability
of being in violation of concentration-based standards.
Section 303(d) of the United States Clean Water Act requires
that states assess the condition of surface waters and report
those which fail to meet ambient water quality standards
(1, 2). These are added to the United States Environmental
Protection Agency (USEPA) list of impaired waters (3) and
can only be removed after the performance of a Total
Maximum Daily Load (TMDL) assessment (4, 5) followed by
sample-based verification that the standards are being met.
and natural sources, including a margin of safety (MOS),
which can be discharged into a receiving water without
violating water quality standards (2, 4). Such predictive
body concentrations (6, 7).
The latest official assessment of U.S. water quality data
(8) indicates that pathogens are the leading cause of coastal
shoreline standard violations (275 total miles impaired) and
the second leading cause of violations in rivers and streams
(82,100 total miles impaired). Fecal indicator bacteria (FIB),
These are typically reported as either the most probable
of FIB form the basis of numeric water quality standards for
several designated uses including drinking water supply (9),
recreational use (10), and shellfish harvesting (11).
Unlike most measures of pollutant levels, the probability
the true in situ concentration distribution. The true FIB
concentration at a fixed point over time is typically believed
distribution (12, 13). The probability distributions of cor-
responding MPN and CFU values for the same monitoring
location, however, are discrete and, in the case of the MPN,
often multimodal. In addition, MPN and CFU variability
depends on the number and volume of sample aliquots.
Accurately predicting MPN- or CFU-based standard
violations from FIB loading levels should therefore involve
water concentration translates into an MPN or CFU value,
and then how frequently those MPN and CFU values violate
standards (5, 14). A review of current modeling practice,
however, indicates that such an approach is seldom, if ever,
impairment from model-based predictions of FIB concen-
the frequency with which a model-generated distribution of
violate shellfish harvesting area water quality standards.
Second, we identify the distributional parameters of c
that these parameters be used as the basis for FIB-based
standards because they do not depend on the analytical
body concentration, and are consistent with the outcomes
of most water quality models. In the third part, we dem-
onstrate how compliance with such concentration-based
standards can be inferred from traditional MPN and CFU
values using a Bayesian approach. We demonstrate this
procedure using data from the most recent assessment of
shellfish harvesting waters in the Newport River Estuary of
Eastern North Carolina.
1.1. Background on Current FIB-Based Water Quality
Standards. Model Ordinance in the Guide for the Control of
Molluscan Shellfish, prepared by the National Shellfish
Sanitation Program (NSSP), includes recommended water
limits on MPN- and CFU-based measures of fecal coliform
* Corresponding author e-mail: email@example.com.
†Nicholas School of the Environment, Duke University.
‡Thayer School of Engineering, Dartmouth College.
§Department of Statistical Science, Duke University.
Environ. Sci. Technol. 2008, 42, 4676–4682
46769ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 42, NO. 13, 200810.1021/es703144k CCC: $40.75
2008 American Chemical Society
Published on Web 05/22/2008
concentration (11). States which participate in the NSSP,
and which are also members of the Interstate Shellfish
Sanitation Conference, enforce the Model Ordinance as a
minimum requirement for sanitary control of shellfish (11).
in surface waters with other designated uses, such as
recreational use (10) and drinking water supply (9), we
standards as an example.
While several MPN- and CFU-based FIB analysis proce-
dures are in common use (for a wide range of water body
designated uses), the three cited in NSSP-recommended
standards for shellfish growing waters (see ref (11), Chapter
(MTF), the 3-tube MTF, and the membrane filtration (MF)
procedure for fecal coliform bacteria. Here, we explore only
the 5-tube MTF and the MF procedures because they are far
5-tube MTF procedure involves diluting a water quality
sample into 3 sets of 5 tubes, with each set of 5 containing
either 10 mL, 1 mL, or 0.1 mL of the original sample
concentration of the sample (15)). The MPN is then the
concentration based on the number of positive tubes
observed in each dilution series after a period of incubation
(15–18). A positive tube is one containing visible gas, which
MF procedure involves filtering a water quality sample and
counting the number of bacteria colonies emerging from
the filter on a growth plate after a period of incubation. The
number of colonies is divided by the sample aliquot volume
and reported as the CFU (19–23).
to additional uncertainty arising from minor variations in
experimental protocol. NSSP criteria address MPN and CFU
variability by recommending that a water body assessment
be based on a minimum number n of MPN or CFU values,
and by recommending separate numeric standards for the
(Table 1). For example, the NSSP criteria for MPN values
from a standard 5-tube MTF decimal dilution analysis state
of 30 of the most recent randomly collected samples” have
an MPN median and geometric mean no greater than 14
no greater than 43 organisms per 100 mL (11). Ninetieth
percentiles are calculated from a log-normal distribution
parametrized by the mean and variance of the natural
logarithm of the n MPN or CFU values (11).
A common goal of model-based TMDL assessments is to
evaluate pollution loading mitigation strategies which will
result in compliance with water quality standards. Despite
a growing body of research on the role of models and model
uncertainty in water resources management (7, 14, 24), we
know of no water quality models which explicitly acknowl-
attempt to fill this gap.
Most water quality standards, including those based on FIB
concentrations, imply that long-term pollutant concentra-
tions at a monitoring station are adequately characterized
(6, 13). The 30 fecal coliform samples required by NSSP
guidelines, however, are usually collected at bimonthly
assessments may take 4-5 years to complete. Changes in
fecal coliform sources and delivery routes during that time
are likely to translate into changes in the fecal coliform
coliform concentration probability distribution at a moni-
toring station throughout the assessment period. While we
recognize this is a potentially restrictive assumption, it is
results to be easily compared with recommended water
quality criteria. Developing strategies for assessing a water
distribution is an area for additional research (25).
We also assume that water quality samples are either
simulated (as in the case of a model forecast) or collected
based on a systematic random sampling program. In other
words, we assume that the 30 samples (as required by NSSP
guidelines) are collected under environmental conditions
(such as rainfall and tide, for example) indicative of long-
term distributions. Furthermore, we presume that the NSSP
criteria for an “Approved” classification implies compliance
guidelines, Chapter 2, subsection 02F (“Standards for ap-
MPN- and CFU-Based Standard Compliance. As a starting
point, we assume that uncertainty in a water quality model
or variability in the environment leads to a probability
distribution on the fecal coliform concentration c (in organ-
isms per 100 mL) that is log-normal, LN(µc, σc), where µcand
σcare the mean and standard deviation, respectively, of the
natural logarithm of c . Therefore, we began our analysis by
simulating 300,000 concentrations drawn at random from
this distribution. We then randomly grouped the 300,000
simulations into 10,000 “samples” of size 30. We repeated
the simulation for values of µcevenly spaced between 0 and
3.5 in log(organisms per 100 mL) (at intervals of 0.05), and
The ranges of values for µcand σcwere selected based on a
preliminary analysis of MPN values from the Newport River
values, we randomly drew an MPN and a CFU value from
the conditional sampling distribution. For the MPN values,
where pi) probability of a positive tube in dilution series
i, c ) fecal coliform concentration (in organisms per 100
mL), vi) volume of original sample in dilution series i (mL),
tubes in dilution series i (i ? [1,. . .,d]), and mi) number of
tubes in dilution series i (often 5).
TABLE 1. NSSP Shellfish Harvesting Area Fecal Coliform Water
Quality Standards Based on a Minimum of 30 Randomly
basis for standardq50
n MPN observations from 5-tube
n CFU observations from MF
VOL. 42, NO. 13, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY 9 4677
CFU values were generated using a Poisson Po(λ) prob-
ability model (32):
where y ) number of identifiable colony forming units, and
V ) sample aliquot volume.
Previous authors have suggested that the Poisson distri-
bution underestimates the variability of microorganisms in
both natural waters and sample aliquots and recommend
using the negative binomial distribution instead (32–37).
However, the Poisson probabilities in our eqs 1 and 3
and CFU values given the true fecal coliform concentration
c . Because we also assume a log-normal distribution on c,
the marginal distributions of positive tubes and CFU values
are very similar to the negative binomial. It is possible,
however, that the conditional distributions represented by
eqs 1 and 3 may also be more widely dispersed than Poisson
due to departures in laboratory procedure from standard
We explored probability models more dispersed than the
Poisson and found that our analysis would only change
significantly if the methodological variability (e.g., measure-
that described by the Poisson distribution (see Supporting
Information for details). We believe that variability of this
magnitude is highly unlikely when standard laboratory
procedures are carefully followed.
For each (µc, σc) pair, we recorded the proportion of the
10,000 simulated size-30 samples which violated the geo-
metric mean standard, the median standard, the 90th
percentile standard, or any of the three standards for both
MPN and CFU values (see Table 1). Simulations and
software program R (39).
Guidelines prepared by USEPA for assessing water quality
impairment suggest that a waterbody does not support its
use criteria (40, 41). NSSP guidelines for shellfish harvesting
waters address this provision by setting numeric limits on
statistics of a set of at least 30 consecutive water quality
samples. According to NSSP guidelines, any size-30 sample
which violates any of the standards (i.e., geometric mean,
standards no more than 10% of the time for purposes of
FIGURE 1. Combinations of the mean µc and standard deviation σc of the log-transformed fecal coliform concentration distribution
which yielded MPN (solid lines) or CFU (dotted lines) samples in violation of the NSSP median standard (panel a), geometric mean
standard (panel b), 90th percentile standard (panel c), or any standard (panel d) with a frequency of either 0.005 or 0.1. The zone of
violations is in the upper right of each panel.
4678 9 ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 42, NO. 13, 2008
To formulate our results in the form of a more readily
by fitting a regression model to points on the violation
boundary (see Supporting Information for details).
2.3. Translation of MPN and CFU Values to Concentra-
tion-Based Standard Compliance. Assessing compliance
with concentration-based standards from traditional MPN
and CFU observations requires “reversing” the logic of the
probabilistic expressions given in eqs 2, 3, and 4 through a
process of Bayesian inference (42, 43). This involves using
these equations, together with the log-normal distribution
on c, as the likelihood functions for µc and σc and then
σc. Following approaches of refs 44–47, we use diffuse prior
distributions for µc and σc in the model of J independent
observations of the concentration c at a given monitoring
LN(cj|µc, σc),j)1,. . .,J
Normal(µ0)0,σc)1 000 000)
distribution using the Bayesian software package WinBUGS
(48). Posterior distributions used in our analysis are based
on 1000 MCMC samples collected after convergence, as
indicated by a potential scale reduction factor Rˆ) 1.0 (44).
Although we used very diffuse priors in this analysis,
the Bayesian approach is still preferable to a frequentist
method because it yields a full posterior distribution for
the distributional parameters, rather than mere point
estimates. This allows us to express our results in terms
of both “confidence of compliance” (6, 31) and in terms
of the posterior probability of a sample of size n revealing
a violation. We define confidence of compliance (CC) in
this case as the posterior probability that the actual values
of µcand σcare below our proposed violation boundaries.
We estimated CC by integrating the joint (µc, σc) posterior
probability density function over all possible µc and σc
values that fall below these boundaries. The posterior
probability of a sample revealing a violation is estimated
distribution to generate samples of fecal coliform con-
centration from the log-normal distribution. These con-
centrations are then propagated through eqs 1 and 2 to
generate size-30 sample sets of MPN values, from which
violation probabilities can be calculated.
2.4. Application to the Newport River Estuary. We
based (µc, σc) standards to water quality monitoring data
collected from the Newport River Estuary, NC, during the
most recent assessment period (2000-2005). The NC De-
partment of Environment and Natural Resources, Shellfish
(and other shellfish harvesting waters throughout North
Carolina) at roughly bimonthly intervals and analyzes each
Estuary is historically a productive shellfish harvesting area.
However, all of its segments and tributaries are either
permanently or conditionally closed to shellfishing based
on poor water quality or proximity to known or potential
sources of fecal contamination. As a result, the estuary and
its tributaries comprise 28 of the designated shellfish
harvesting areas in North Carolina which are currently
included in the USEPA 303(d) list and therefore require a
TMDL assessment. Our goal in analyzing these data is to
have yielded a different impairment decision than that
obtained using the MPN-based standard, and therefore
whether water quality data provide quantitative support for
3.1. Data Simulations. Simulation results indicate that (for
a given µc and σc) samples will violate NSSP water quality
standards at different frequencies depending on whether
of the two standards will depend on the value of σc.
Specifically, application of the 5-tube MTF procedure (and
to lead to a violation than application of the MF procedure
(and CFU standard) when σc is greater than 0.65, and
more likely to lead to a violation when σcis less than 0.65
the range of those collected at the Newport River shellfish
harvesting area monitoring stations are more likely to be in
violation of the NSSP 90th percentile standards (Figure 1c)
1a and b).
3.2. Concentration-Based Standards. Our regression-
based estimation of the lines that divide violating from
nonviolating values in the joint (µc, σc) space reveals that
0.5% of the time) are defined by the following inequalities
for the MPN procedure:
and by the following inequalities for the CFU procedure:
Thus, with point estimates of µc and σc determined for a
particular site from either a simulation model or sample-
status of that site can be established in a straightforward
way. Of course, when there is uncertainty about µcand σc,
then, rather than a binary compliance determination, a CC
is the result, as demonstrated in the next section.
3.3. Newport River Estuary Assessment. Application of
Newport River Estuary resulted in eight stations having an
or CFU standard (Table 2). Samples collected between 2000
and 2005 actually revealed MPN standard violations at all
eight of these stations. While violations were not found at
any of the other stations during this period, our Bayesian
inference procedure indicates a low CC with the MPN
standard (less than 25%) at four other stations as well (Stns.
8, 8A, 25, and 84). This reflects the stringency of the NSSP
guideline that no violations, ever, will be tolerated (which
Thus, a station such as station 25, which did not actually
reveal a violation during the 2000-2005 assessment period,
still has a pattern of MPN values that indicate it would be
for σc> 0.65
for σce 0.65
for σc> 0.65
for σce 0.65
VOL. 42, NO. 13, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY 9 4679
a violation, even with the collection of many more samples.
The marginal probability that a water quality sample
of size 30 (the minimum required by NSSP) will reveal an
MPN violation at a particular location can be assessed by
knowledge of uncertainty about the concentration at that
location, (ii) the log-normal distribution of c capturing
environmental variability, and (iii) the Poisson/binomial
a violation actually did violate at least one of the three
period. All of the remaining stations have a probability of
violation less than 33%, and samples from these stations
did not show a violation.
Given the inherent differences between actual in situ FIB
water quality standard compliance in response to TMDL
levels should involve a two-step process. First, water body
FIB concentrations are predicted from changes in loading,
presumably using a water quality model. Then, these
concentrations are translated into laboratory results corre-
sponding to a particular method and compared to relevant
and pathogen TMDL assessment treat the predicted in situ
concentration as if it were equivalent to the corresponding
laboratory result (49–51). Thus, an important source of
In an effort to address the above problem, we have
outlined the probabilistic expressions required to translate
FIB concentrations into either MPN- or CFU-equivalent
NSSP fecal coliform standards corresponding to these two
of actual water body concentrations may be found to be in
standard. This is clearly an undesirable situation.
Rather than recommend a revision to the numeric limits
of the existing MPN- and CFU-based standards, we suggest
that FIB standards be based on the actual in situ concentra-
tion. The various laboratory analysis techniques would then
be explicitly understood to be imperfect measures of this
have a number of important benefits. First, and foremost,
such standards would have an explicit connection to the
protection of human health. This is because impairment
conditions in the water body, rather than on the uncertain
outcome of a laboratory analysis.
Second, a focus on in situ concentrations would lead to
a single set of universal standards which are independent of
the analytical procedure used. We demonstrated how the
distribution of the actual fecal coliform concentration in
could be performed on any laboratory method, for any
designated use category, by incorporating method-specific
measures of uncertainty and designated use-specific stan-
dards of quality. In fact, by estimating the “second-order”
uncertainty in the concentration distribution itself, in the
form of uncertainty in µcand σc(see Figure 2), the Bayesian
approach provides an incentive for states to employ or
that have a lower measurement error will lead to a greater
“confidence of compliance” at a nonviolating site than
methods that are more uncertain.
a more consistent and accurate treatment of FIB concentra-
tion data in models forming the basis for TMDL determina-
tions. In addition to precluding the need for modelers to
or CFU, a focus on concentration would facilitate proper
loading specification and model calibration. Currently, FIB
loading rates in models are often expressed in units of MPN
or CFU per unit volume (52). However, the discrepancy
between MPN- and CFU-based determinations of FIB
concentration coming from a particular loading source and
as FIB loading rates will lead to model predictions that
represent neither the true FIB concentration nor MPN- or
using MPN or CFU determinations to calibrate a FIB water
are correct MPN or CFU values. The concentration-based
perspective adopted here provides a potential solution to
these common, but flawed, FIB water quality modeling
Our results show that a new concentration-based FIB
standard can be conveniently expressed in terms of the
concentration distribution. We gave examples of such a
standard that are compatible with the stringency imposed
by the present MPN or CFU standards. Of course, rather
method-based standards, it would be more logical for the
NSSP to select an in situ concentration threshold that
should not, in theory, be exceeded more than a specified
TABLE 2. Estimated Confidence of Compliance (CC), Posterior
Probability of Violating any MPN Standard, and Observed
Violations for Monitoring Stations in the Newport River
Estuary during the 2000-2005 Assessment Period
of size-30 sample
violated any MPN
standard during the
4680 9 ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 42, NO. 13, 2008
analysis technique would then provide an estimate of this
exceedance frequency, together with the uncertainty in
NSSP would therefore also need to specify the level of
confidence required to avoid shellfish harvesting area
that requiring a CC of 50% or greater would not be
unreasonable. All stations with a CC greater than or equal
50% according to the MPN standard were determined to
be in compliance according to samples collected during
the 2000-2005 assessment period. A CC threshold also
protects against possible inconsistencies in the current
standards under which a water body may have an
unacceptably high (e.g., greater than 10%) probability of
violating existing NSSP standards yet, because of the
inherent limitations in using only 30 samples, yield a
compliant water sample set (e.g., stations 8, 8A, 16A, 25,
Water quality models used for TMDL assessment should
as those applied to monitoring programs. An approach to
uncertainty has been presented previously (6), and is
consistent with the approach taken here. This allows for
straightforward translation between concentration-based
standards, water quality analysis techniques, and model
predictions, accounting for the variability and uncertainty
characteristics of each.
Division of Water Quality (Contract EW05049) through the
USEPA 319 program, and through grants from the National
Science Foundation (NSF Grants DMS-0112069 and DMS-
0422400). M.E.B. was partially supported by a grant from
USEPA Office of Research and Development’s Advanced
(Global Earth Observation System of Systems). In addition,
the North Carolina Association of Environmental Profes-
sionals (NCAEP), and Quantitative Environmental Analysis
(particularly Patti Fowler, Andy Haines, Shannon Jenkins,
and J.D. Potts) for making their water quality monitoring
data available, and for answering questions throughout the
suggestions, as did two anonymous reviewers.
Supporting Information Available
Supporting Information is available for the analysis of
alternative probability models (Section 2.1), and regression
models (Section 3.2). This information is available free of
charge via the Internet at http://pubs.acs.org.
FIGURE 2. Joint posterior probability density contour lines (solid lines) for four monitoring stations in the Newport River Estuary.
Dashed and dotted lines indicate combinations of the mean µc and standard deviation σc of the log-transformed fecal coliform
concentration distribution which violate our concentration-based standards no more than 0.5% of the time using MPN or CFU
standards as the reference. Confidences of compliance (CC) are given in the lower left of each panel for both MPN- and CFU-based
VOL. 42, NO. 13, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY 9 4681
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