v>EPA
United States	Office of Water	EPA-822-R-21-005
Environmental Protection	A .
Agency	Mail code 4304T	August 2021
Ambient Water Quality Criteria to Address Nutrient
Pollution in Lakes and Reservoirs
Office of Science and Technology
Office of Water
U.S. Environmental Protection Agency
Washington, DC

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Notices
This document has been drafted and approved for publication by the Health and Ecological
Criteria Division, Office of Science and Technology, Office of Water, United States Environmental
Protection Agency, and is approved for publication. Mention of trade names or commercial
products does not constitute endorsement or recommendation for use.
Cover photo by Dana Thomas, 2019
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Contents
Executive Summary	viii
1	Introduction and Background	1
2	Problem Formulation	3
2.1	Management Goals	3
2.2	Assessment Endpoints and Risk Metrics	4
2.2.1	Aquatic Life Use	5
2.2.2	Recreational Use	8
2.2.3	Drinking Water Source	9
2.3	Risk Hypotheses	9
2.4	Analysis Plan	10
3	Analysis	11
3.1	Data	11
3.1.1	Biological Data	13
3.1.2	Chemical Data	14
3.1.3	Dissolved Oxygen and Temperature Profiles	14
3.1.4	Mapped Data	15
3.2	Stressor-Response Models	15
3.2.1	Zooplankton Biomass	16
3.2.2	Deep Water Hypoxia	23
3.2.3	Microcystin Concentration	40
3.2.4	Phosphorus-Chlorophyll a	48
3.2.5	Nitrogen-Chlorophyll a	58
3.3	Duration and Frequency	62
4	Characterization	65
4.1	Other Measures of Effect and Exposure	65
4.2	Incorporating State Data	67
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4.3	Existing Nutrient-Chlorophyll a Models	67
4.4	Limitations and Assumptions	68
4.5	Deriving State-Specified Criteria	70
5 References	71
Appendix A: State Case Study: Chlorophyll o-Microcystin	A-l
A.l Data	A-l
A.2 Statistical Analysis	A-l
A.3 Results	A-3
A.4	Criteria Derivation	A-7
Appendix B: State Case Study: Chlorophyll o-Hypoxia	B-l
B.l	Data	B-l
B.2 Statistical Analysis	B-l
B.3 Results	B-2
B.4	Criteria Derivation	B-5
Appendix C: State Case Study: Total Nitrogen-Chlorophyll a	C-l
C.l	Data	C-l
C.2 Statistical Analysis	C-l
C.3 Results	C-2
C.4 Criteria Derivation	C-3
Appendix D: Operational Numeric Nutrient Criteria	D-l
Appendix E: Example Workflow for Deriving Lake Nutrient Criteria	E-l
E.l Identify Designated Uses	E-l
E.2 Compile Data	E-l
E.3 Management Decisions	E-2
E.4 Accounting for Interannual and Sampling Variance	E-6
E.5 Incorporating State Data in National Models	E-7
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Figures
Figure 1. Conceptual model linking increased nutrients to aquatic life use (Source: US EPA
2010a)	5
Figure 2. Conceptual model linking increased nutrient concentrations to public health
endpoints	9
Figure 3. Simplified conceptual model showing pathways selected for analysis	10
Figure 4. Schematic of network of relationships for modeling zooplankton biomass	16
Figure 5. Relationships between measured biovolume, Chi a, and estimated seasonal mean
phytoplankton biovolume	20
Figure 6. Estimated relationships between zooplankton and Chi a for lakes > 8 m deep	21
Figure 7. Locations of NLA lakes used to fit the DOm model. These lakes were designated as
dimictic and were stratified at the time of sampling	24
Figure 8. Illustrative examples of depth profiles of temperature, temperature gradient, and
DO	25
Figure 9. Schematic of hypoxia model	26
Figure 10. Chi a vs. DOm. DOm values	29
Figure 11. Demers and Kalff (1993) predicted stratification day vs. model mean estimate	30
Figure 12. Relationships between individual predictors and DOm, holding other variables
fixed at their mean values	31
Figure 13. Model predicted DOm vs. observed DOm. Open circles: individual samples; solid
line: 1:1 relationship	31
Figure 14. Contours of modeled mean lake temperature computed at the overall mean
elevation and mean sampling day	33
Figure 15. Relationship between lake temperature and sampling day (left panel) and
elevation (right panel)	33
Figure 16. Days of the year that mixed layer temperatures decrease below the critical
temperature for cool-water species	35
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Figure 17. Days of the year that mixed layer temperatures decrease below the critical
temperature for cold-water species	35
Figure 18. Simplified DO profile used to compute threshold for DOm. Open circle: the
targeted condition of DO at 5 mg/L, 30 cm below the thermocline	37
Figure 19. Effects of other predictors on Chi a criteria	38
Figure 20. Schematic showing relationship between different variables predicting
microcystin	41
Figure 21. Modeled relationships for the microcystin model	44
Figure 22. Example of derivation of Chi a criterion to protect recreational uses based on
targeted microcystin of 8 ng/L and exceedance probability of 1%	45
Figure 23. Probability of the indicated number of excursions observed in 10-day assessment
windows during a 100-day season for different single day exceedance probabilities.... 48
Figure 24. Schematic representation of compartment model for TP. PdiSS: dissolved P; Chi:
Chi a; Turb: total turbidity; Turbnp: turbidity attributed to nonphytoplankton
sources	49
Figure 25. Turbidity vs. Chi a. Solid line: the limiting relationship between Chi a and
turbidity when contribution of allochthonous sediment is negligible	53
Figure 26. Relationship between Turbnp, Pdiss, and lake depth. Open circles: mean estimate
of parameter value in each of 30 lake depth classes	53
Figure 27. Ecoregion-specific values of loge(di), P bound to nonphytoplankton suspended
sediment	54
Figure 28. TP versus Turbnp and Chi a	55
Figure 29. Example of deriving TP criteria for a Chi a target of 10 ng/L for data from one
ecoregion (Southeastern Plains)	56
Figure 30. Variation in the concentration of N bound in phytoplankton among Level III
ecoregions at the overall mean Chi a = 9.3 ng/L. Gray scale shows N concentrations
in M-g/L	59
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Figure 31. Variation in DON among Level III ecoregions at an overall mean DOC = 5.6 mg/L.
Gray scale shows N concentrations in ng/L	60
Figure 32. TN-DIN vs. Chi a and DOC	61
Figure 33. Illustrative example of deriving TN criteria for a Chi a target of 10 ng/L for one
ecoregion (Southeastern Plains)	62
Figure 34. Variation in the relationship between Chi a and cyanobacterial-relative
biovolume among states	A-4
Figure 35. Comparison of Chi o/cyanobacterial-relative biovolume relationships in Iowa	A-5
Figure 36. Comparison of predicted relationship between Chi a and microcystin for the
state-national model (left panel) and a model using only Iowa state data (right
panel)	A-6
Figure 37. Microcystin and Chi a measurements in Iowa	A-7
Figure 38. Observed DOm vs. Chi a, sampling day, DOC, and depth below the thermocline	B-3
Figure 39. Estimated first day of stratification for Missouri lakes (left panel) and NLA lakes
(right panel)	B-4
Figure 40. Model coefficients estimated for models for Missouri data, NLA data, and
combined data	B-4
Figure 41. Relationships between day of year and DOm for six Missouri lakes	B-5
Figure 42. Relationship between Chi a and DOm in an illustrative lake with depth below
thermocline at 10m, DOC at 1.6 mg/L, and 130 days after spring stratification	B-6
Figure 43. Chi a vs. TN-DIN in Iowa	C-2
Figure 44. Chi a vs. TN-DIN in Beeds Lake, Iowa	C-3
Figure 45. Lake-specific criteria derivation using combined Iowa-NLA model for two
different lakes in Iowa	C-4
Figure 46. Example distribution of 10 TP measurements	D-2
Figure 47. Example of defining an operational criterion magnitude	D-4
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Executive Summary
Excess nutrients can degrade the condition of water bodies worldwide; in lakes and reservoirs
(hereafter, referred to only as "lakes" unless noted otherwise), the effects of excess nitrogen (N)
and phosphorus (P) may be particularly evident. High levels of nutrient loading commonly
stimulate excess growth of phytoplankton, which can limit the recreational use of lakes.
Overabundant phytoplankton also increase the amount of organic matter in a lake, which, when
decomposed, can depress dissolved oxygen (DO) concentrations below the levels needed to
sustain aquatic life. In extreme cases, the depletion of DO causes fish kills. Nutrient pollution can
stimulate the excess growth of nuisance phytoplankton, such as cyanobacteria, which can
produce cyanotoxins that are toxic to animals and humans. Elevated concentrations of
cyanotoxins can reduce the suitability of a lake for recreation and as a source of drinking water.
Numeric nutrient criteria provide an important tool for managing the effects of nutrient
pollution by providing nutrient goals that ensure the protection and maintenance of designated
uses. The United States (U.S.) Environmental Protection Agency (EPA) published recommended
numeric nutrient criteria for lakes and reservoirs in 2000 and 2001 for 12 out of 14 ecoregions of
the conterminous United States. Those criteria were derived by analyzing available data on the
concentrations of total nitrogen (TN), total phosphorus (TP), chlorophyll a (Chi a), and Secchi
depth.
Scientific understanding of the relationships between nutrient concentrations and deleterious
effects in lakes has increased since 2001, and standardized, high-quality data collected from
lakes across the United States have become available. In this document, EPA describes analyses
of these new data and provides models from which numeric nutrient criteria can be derived. The
criterion models replace the recommended numeric nutrient criteria of 2000 and 2001 and are
provided in accordance with the provisions of Section 304(a) of the Clean Water Act (CWA) (Title
33 of the United States Code [U.S.C.]  1314(a)) for EPA to revise ambient water quality criteria
from time to time to reflect the latest scientific knowledge. CWA Section 304(a) water quality
criteria serve as recommendations to states and authorized tribes for defining ambient water
concentrations that will protect against adverse effects to aquatic life and human health. The
ecological and health protective responses on which the criterion models are based were
selected by applying a risk assessment approach to explicitly link nutrient concentrations to the
protection of designated uses.

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The criterion models are nonregulatory, and this document describes the models and their
inputs. States may use the recommended models to derive candidate nutrient criteria for each
applicable designated use and, after demonstrating that the criteria protect the most sensitive
designated use, adopt the criteria into their state standards. States may also modify the criteria
to reflect site-specific conditions or establish criteria based on other scientifically defensible
methods (Title 40 of the Code of Federal Regulations [CFR] 131.11(b)). The updated
recommended CWA Section 304(a) nutrient criteria for lakes do not compel a state to revise
current EPA-approved and adopted criteria, total daily maximum load nutrient load targets, or N
or P numeric values established by other scientifically defensible methods. As part of their
triennial review, if a state uses its discretion to not adopt new or revised nutrient criteria based
on these CWA Section 304(a) criterion models, then the state shall provide an explanation when
it submits the results of its triennial review (40 CFR 131.20(a)).
Following the risk assessment paradigm, EPA first defined water quality management goals for
numeric nutrient criteria, and then defined assessment endpoints and metrics that are
associated with achieving these goals and are sensitive to increased nutrient concentrations.
The water quality management goals are articulated as designated uses in Section 101(a)(2) of
the CWA (33 U.S.C.  1251) (i.e., the protection and propagation offish, shellfish, and wildlife
[aquatic life] and recreation in and on the water). Another common designated use for lakes is
to serve as drinking water sources. Excess loads of nutrients can lead to excessive growth of
phytoplankton that can adversely impact designated uses in different ways, described below as
assessment endpoints and metrics. EPA modeled stressor-response relationships using these
endpoints and metrics to derive recommended numeric nutrient criterion models (Table 1).
Table 1. Summary of designated uses and associated measures of effect and exposure
Designated use
Assessment endpoint
Risk metric
Applicability


Rate of change of zooplankton

Aquatic life
Zooplankton biomass
biomass relative to
phytoplankton biomass
All lakes
Aquatic life
Cool- and cold-water fish
Daily depth-averaged DO
below the thermocline
Seasonally stratified
lakes with cool- or
cold-water fish
Recreation
Human health
Microcystin concentration to
prevent liver toxicity in children
All lakes
Drinking water
Human health
Microcystin concentration to
prevent liver toxicity in children
All lakes
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For aquatic life, EPA identified two assessment endpoints. The first endpoint is zooplankton
biomass, and the risk metric is the slope of the relationship between zooplankton and
phytoplankton biomass, which quantifies the degree to which energy produced by
phytoplankton at the base of the food web is transferred to zooplankton and subsequently to
higher trophic levels. When excess nutrients are available, phytoplankton biomass can increase
at rates that exceed the capacity of zooplankton to consume. The threshold for the risk metric is
one in which the rate of change of zooplankton biomass relative to phytoplankton biomass is
approximately zero. This condition describes a lake in which the biomass of grazing biota (i.e.,
zooplankton) does not increase with increases in food (i.e., phytoplankton), and primary
production at the base of the food web is weakly linked to production at higher trophic levels.
This endpoint applies to all lakes in the conterminous U.S.
The second aquatic life endpoint is health and survival of cool- and cold-water fish, and the risk
metric is the DO concentration in deep water that protects against mortality of these fish. Excess
nutrients typically increase primary productivity, which then increases the amount of organic
matter in a lake. Then, in the deep waters of a lake, DO is consumed as this organic matter is
decomposed, leading to hypoxic and anoxic conditions. The risk metric is defined more
specifically as the daily DO concentration, calculated as a depth-averaged value below the
thermocline, which can be reduced to concentrations insufficient to support some fish species
during the critical period of the summer when they require deep, cold waters to escape high
temperatures at shallower depths. This endpoint applies to seasonally stratified lakes harboring
cool- and cold-water fish.
For recreational uses and drinking water sources, the assessment endpoint is human health.
For recreational uses, EPA selected the threshold for the risk metric as the concentration of
microcystin associated with adverse effects on children (specifically, liver toxicity) from
incidental ingestion of water during recreation. When excess nutrients are available,
phytoplankton communities can shift toward a greater abundance of cyanobacteria that can
release cyanotoxins, and microcystins are the most commonly monitored and measured
freshwater cyanotoxin in the U.S. The threshold for the risk metric is 8 micrograms per liter
(Hg/L), based on recently published national recommendations for human health recreational
water quality criteria and swimming advisories for cyanotoxins (US EPA 2019). For the drinking
water use, EPA selected the threshold for the risk metric as the concentration of microcystins
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associated with adverse effects on children resulting from oral exposure to drinking water
(0.3 ng/L), consistent with the health advisory for microcystins (US EPA 2015b). The
microcystin concentration from the health advisory applies to finished drinking water;
however, EPA is aware that states and authorized tribes express water quality standards for
protecting drinking water sources as either protecting the ambient source water before
treatment or after treatment. The ability of treatment technologies to remove microcystin is
too variable for EPA to set a national recommendation for an ambient source water
concentration that would yield a protective concentration after treatment. If a state or
authorized tribe applies the health advisory standard to drinking water after treatment, then
they can account for the expected treatment in their facilities and select a higher microcystin
concentration in the ambient source water that would result in the targeted microcystin
concentration in the finished drinking water.
Data used in this analysis were collected in EPA's National Lakes Assessment (NLA), which
sampled lakes across the conterminous U.S. in 2007 and 2012. Most of the sampled lakes were
selected randomly so the resulting data represent the characteristics of the full population of
lakes in the conterminous U.S. At each lake, standardized protocols were used to collect
extensive measurements of biotic and abiotic characteristics.
This document describes statistical stressor-response models that relate Chi a concentrations to
each of the risk metrics and that relate TN and TP concentrations to Chi a. A hierarchical
Bayesian network is specified for each model to represent the effects of different variables on
the relationship of interest. For example, microcystin is related to cyanobacteria biovolume,
which is then linked to Chi a concentration. The models directly represent the processes that
govern the relationships of interest and facilitate the use of other data sets in conjunction with
data from EPA's NLA. When coupled with the targets for each response, the models provide
candidate Chi a, TN, and TP criteria recommendations that states may then use with state risk
management decisions to demonstrate they are protective of different designated uses. For
lakes with multiple use designations, the states shall adopt criteria from these candidate criteria
that protect the most sensitive use.
Models provided in this document are based on national data, but states often collect extensive
data during routine monitoring. Incorporating local data into the national models can refine and
improve the precision of the stressor-response relationships. In the appendices of this
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document, EPA describes three case studies in which state monitoring data have been combined
with national data, yielding models that can be used to derive recommended numeric nutrient
criteria that account for both unique local conditions and national, large-scale trends.
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1 Introduction and Background
Nutrient pollution, or the excess loading of nitrogen (N) and phosphorus (P), can degrade the
conditions of water bodies worldwide, and in lakes the effects of nutrient pollution are often
most evident. One visible consequence of nutrient pollution in lakes and reservoirs (hereafter,
referred to only as "lakes" unless noted otherwise) is cultural eutrophication, an increase in
primary productivity and algal abundance that increases the amount of organic matter in a
water body (Smith et al. 2006, Smith and Schindler 2009). Decomposition of organic matter
reduces dissolved oxygen (DO) concentrations in the water column, especially in deeper waters
under stratified conditions. These hypoxic conditions are inhospitable to most aquatic species
and reduce their ability to survive within a particular lake (Jones et al. 2011, Scavia et al. 2014).
Nutrient pollution also favors the growth of undesirable, nuisance phytoplankton (e.g.,
cyanobacteria), some of which produce cyanotoxins (Paerl and Otten 2013). Many species of
cyanobacteria are superior competitors for light compared to other phytoplankton. Hence, in
lakes with nutrient pollution, cyanobacteria can dominate by reducing the light available to
other phytoplankton (Carey et al. 2012). A number of other mechanisms, including superior
uptake rates for carbon dioxide and an ability to migrate vertically in the water column, also
may explain the frequent occurrence of cyanobacteria dominance in eutrophic systems (Dokulil
and Teubner 2000). Cyanobacteria dominance can interfere with the designated uses of a lake
because cyanobacteria not only can form unsightly and odorous surface scums (reducing the
aesthetic appeal of the lake for recreation) (Paerl and Ustach 1982), but also can produce
cyanotoxins that can limit the use of the lake as both a source of drinking water and for
recreation (Cheung et al. 2013). Many species of cyanobacteria are also less palatable than
other phytoplankton to grazing organisms, and so, increases in cyanobacterial abundance can
alter lake food webs and reduce the efficiency with which energy from primary production is
transferred to higher trophic levels (Elser 1999, Filstrup et al. 2014a, Heathcote et al. 2016).
Nutrient pollution in lakes and resulting adverse environmental effects are widespread in the
United States (U.S.). Nutrient pollution occurs in lakes of different sizes, in catchments with
varying land uses, and in different climates. The U.S. Environmental Protection Agency (EPA) has
long recognized the effects of nutrient pollution and has recommended that states and
authorized tribes (hereafter, "states"), acting under their Clean Water Act (CWA) authorities,
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adopt numeric nutrient criteria as one way to facilitate the management of these effects. A
state's numeric nutrient criteria (1) provide nutrient goals to protect and maintain the
designated uses of a water body (Title 33 of the United States Code [U.S.C.]  1313(c)),
(2) provide thresholds that allow the state to make accurate water quality assessment decisions
(33 U.S.C.  1313(d)), and (3) provide targets for restoration of water bodies that can guide
waste load allocation decisions (33 U.S.C.  1313(d)). To assist states and authorized tribes in
deriving numeric nutrient criteria, EPA has published a series of technical support documents on
methods for deriving criteria for lakes and reservoirs (US EPA 2000a), streams and rivers (US EPA
2000b), wetlands (US EPA 2008), and estuaries and coastal waters (US EPA 2001). A technical
support document on using stressor-response relationships for deriving numeric nutrient
criteria has also been published (US EPA 2010a). In 2000 and 2001, under its authority described
in Section 304(a) of the CWA (33 U.S.C.  1314(a)), EPA issued 12 documents that provided
recommended numeric nutrient criteria for lakes, streams, and rivers in different ecoregions of
the U.S. These criteria were derived by using available monitoring data to estimate the
concentrations of total nitrogen (TN) and total phosphorus (TP) that were expected to occur in
least-disturbed reference water bodies in different nutrient ecoregions.
In accordance with the provisions of Section 304(a) of the CWA, which directs EPA to revise
ambient water quality criteria from time to time to reflect the latest scientific knowledge, EPA is
issuing revisions to numeric nutrient criteria recommendations for lakes based on analyses of
newly available, national-scale data and reflecting advances in scientific understanding of the
relationship between excess nutrients and adverse effects in lakes. The criterion
recommendations are models that generate numeric nutrient criteria based on national data
and state risk management decisions. State data, if available, can be incorporated into the
national criterion models to compute relationships that more accurately represent local
conditions. In deriving these models, EPA uses a risk assessment framework (Norton et al. 1992;
US EPA 1998, 2014) to identify assessment endpoints that relate directly to the water quality
management goals for U.S. lakes specified by the CWA and that are sensitive to increased
concentrations of N and P. Then, EPA uses stressor-response analysis to estimate relationships
between increased N and P (estimated by measurements of TN and TP) and different risk
metrics directly linked to the assessment endpoints (US EPA 2010a). National criterion models
are provided for both TN and TP as the simultaneous control of both nutrients provides the
most effective means of controlling the deleterious effects of nutrient pollution
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(US EPA 2015a, Paerl et al. 2016). These stressor-response criterion models replace the
ecoregion-specific nutrient criteria recommended previously for lakes/ which were derived
using a reference distribution approach.
The remaining sections of this document are organized broadly according to the steps of risk
assessment: (1) problem formulation, (2) analysis, and (3) characterization. The purpose of this
document is to provide the technical details underlying the estimation of relationships between
increased nutrient concentrations and different responses, as well as details regarding the
derivation of numeric nutrient criterion recommendations using the national models. States
may use these criterion models to derive candidate nutrient criteria and, after demonstrating
that the criteria protect designated uses, adopt the criteria into their state water quality
standards. States may also modify the criteria to reflect site-specific conditions or establish
criteria based on other scientifically defensible methods (40 CFR 131.11(b)). For waters with
multiple use designations, the state shall adopt criteria from the candidate criteria that support
the most sensitive designated use (40 CFR 131.11(a)(1)). Water quality standards adopted by
states are subsequently subject to review by EPA, pursuant to Section 303(c) of the CWA
(33 U.S.C.  1313(c)).
2 Problem Formulation
Problem formulation is the first step in a risk assessment, in which "...the problem is defined,
and a plan for analyzing and characterizing risk is determined" (US EPA 1998). More specifically,
during problem formulation, the management goals are articulated, assessment endpoints and
risk metrics are selected, and conceptual models are specified that link stressors with
assessment endpoints.
2.1 Management Goals
EPA focused on protecting uses that reflect management goals articulated in Section 101(a)(2)
of the CWA (33 U.S.C.  1251), which include maintaining conditions so different water bodies
support aquatic life use (i.e., providing for the protection and propagation of fish, shellfish, and
1 Ecoregional nutrient criteria for lakes and reservoirs (EPA 822-B-00-007, EPA 822-B-01-008, EPA 822-B-
01-009, EPA 822-B-01-010, EPA 822-B-00-008, EPA 822-B-00-009, EPA 822-B-00-010, EPA 822-B-00-011,
EPA 822-B-00-012, EPA 822-B-00-013, EPA 822-B-00-014, and EPA 822-B-01-011)
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wildlife), recreation (i.e., providing for recreation in and on the water), and use of the water
body as a source of drinking water. Under the CWA, it is a state's responsibility to designate uses
for its waters, and many states have designated uses that provide for aquatic life and recreation
uses. Some states have also designated waters as sources of drinking water. EPA focuses on
aquatic life, recreation, and drinking water source because they represent uses that are
particularly sensitive to increased concentrations of N and P. States can derive candidate
nutrient criteria for each of the applicable designated uses in their lakes and, by comparing
these criteria, identify the most sensitive use. Water quality criteria adopted by states for waters
with multiple use designations must support the most sensitive use (40 CFR 131.11(a)).
2.2 Assessment Endpoints and Risk Metrics
The next step in problem formulation is to define assessment endpoints that can be used to
quantify attainment of the management goals. Each of the management goals expressed in
terms of different designated uses was associated with different assessment endpoints.
Protection of recreational uses and drinking water sources pertains to public health rather than
ecological health, and hence, the assessment endpoint is human health for these two
designated uses. For aquatic life, the procedures of ecological risk assessment were followed to
select assessment endpoints defined as "explicit expressions of the actual environmental values
that are to be protected" (US EPA 1998). Three considerations guided the selection of these
endpoints: ecological relevance, susceptibility to the stressor of interest (i.e., increased nutrient
concentrations in the present case), and relevance to management goals.
After selecting the assessment endpoints, EPA developed conceptual models that represented
current understanding of the linkages between increased N and P concentrations and effects on
the assessment endpoint and management goals (Figure 1). The conceptual models were used
to select specific risk metrics that quantified key steps along the causal path linking increased N
and P concentrations to deleterious effects on aquatic life and public health. The final selections
for the criterion recommendations were also influenced by the availability of data at the
continental spatial scales considered in this analysis. These risk metrics were used as the
response variables in stressor-response analysis. For a narrative description of the conceptual
model, refer to Using Stressor-Response Relationships to Derive Numeric Nutrient Criteria (US
EPA 2010a).
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Nutrients
Hydrology-Geology;
Natural Vegetation
Lake Morphology;
Retention Time
Primary Production
Color
Temperature
Aquatic Macrophytes
Phytoplankton
Suspended
Sediment
Nuisance
Algae
HABs
Respiration
Organic Matter
Food Quality
Food Quantity
Dissolved
Oxygen
Water Clarity;
Light Availability
Biological Communities
Zooplankton
SAV
Benthic
Communities
Fish
Aquatic Life Support
Figure 1. Conceptual model linking increased nutrients to aquatic life use (Source: US EPA 2010a).
2.2.1 Aquatic Life Use
Nutrient pollution and eutrophication can affect the health of the lake biological community via
many pathways (see Figure 1). As discussed earlier, increased nutrients typically stimulate
primary productivity and increase the amount of organic matter in a lake. Decomposition of the
organic matter depletes the DO in the water, reducing the suitability of deeper waters as habitat
for fish and invertebrates (Cornett 1989). Increased production and respiration also can increase
the range of acidity throughout the day-night cycle in some lakes (Schindler et al. 1985),
reducing the suitability of shallow waters as habitat for certain species. Increased algal biomass
also reduces water clarity, and the reduction in light availability limits the depths at which
submerged aquatic vegetation can persist (Phillips et al. 2016). Reduced water clarity can also
shift fish assemblage composition away from species that depend on sight for foraging
(De Robertis et al. 2003). Further, high nutrient concentrations favor the growth of
cyanobacteria, which are less palatable to grazing species than other phytoplankton, altering the
food web of the lake (Haney 1987).
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EPA selected two assessment endpoints to characterize the health of aquatic life in lakes:
(1) zooplankton biomass, which is applicable to all lakes, and (2) the survival and growth of cool-
and cold-water fish in seasonally stratified lakes. For the second endpoint, EPA selected depth-
averaged DO concentration as the risk metric. In seasonally stratified lakes with cool-water fish,
criteria based on zooplankton biomass and DO can be compared, and the more stringent
criterion is applied to ensure that aquatic life is protected. Collectively, the two assessment
endpoints provide a broad assessment of the health of the lake biological community. Data
were also available for each endpoint, and each endpoint quantified well-studied effects of
nutrient pollution.
2.2.1.1 Zooplankton biomass
The rate of change of zooplankton biomass compared to the rate of change of phytoplankton
biomass quantifies changes in the shape of biomass pyramids in lakes (Elton 1927). Biomass
pyramids provide a graphical depiction of the amount of biomass at different trophic levels, and
typically, the biomass of primary producers (at the bottom of the pyramid) exceeds the biomass
of herbivores and carnivores at successively higher levels of the pyramid. In lakes, the ratio of
herbivore biomass (i.e., zooplankton) to primary producer biomass (i.e., phytoplankton) (Z:P)
has been observed to decrease along eutrophication gradients (Leibold et al. 1997). Reasons for
the decreasing trend in Z:P have been the subject of some debate, much of which centers on the
relative importance of top-down versus bottom-up food web effects. For zooplankton, top-
down forces consist mainly of the effects of planktivore fish consuming zooplankton biomass
(Jeppesen et al. 2003) and bottom-up forces include changes in the quantity and quality of the
phytoplankton assemblage on which zooplankton feed (Filstrup et al. 2014a). With excess
nutrients, one particularly important bottom-up mechanism is the decrease in the edibility of
the phytoplankton assemblage associated with the increased dominance of cyanobacteria with
increasing levels of eutrophication. Laboratory studies demonstrate that the lack of highly
unsaturated fatty acids in cyanobacteria negatively affects the growth rates of a common
zooplankton species (Daphnia) (Demott and Miiller-Navarra 1997, Persson et al. 2007). Field
observations (Miiller-Navarra et al. 2000) and microcosm experiments (Park et al. 2003) have
added further support for this finding. Many cyanobacteria also present physical challenges to
grazers, collecting in colonies or filaments that are too large to be consumed (Bednarska and
Dawidowicz 2007), or surrounding themselves with gelatinous sheaths (Vanni 1987). Altered
6

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elemental stoichiometry and, hence, nutritional quality of phytoplankton under different levels
of eutrophication may also influence zooplankton biomass (Hessen 2008).
The rate of change of zooplankton biomass with respect to increasing phytoplankton biomass
(AZ/AP) provides an informative measure of the effects of eutrophication on food web function
for the purposes of informing the derivation of numeric nutrient criteria (Yuan and Pollard
2018). This rate of change can be thought of as the slope of the relationship between Z and P. In
most lake food webs, any increase in the basal resources (i.e., phytoplankton biomass) would be
expected to be associated with a corresponding increase in the biomass of consumers of those
resources (i.e., zooplankton biomass), and the slope between Z and P would be positive. In
eutrophic lakes, however, increases in phytoplankton biomass often are not associated with an
increase in zooplankton biomass, and the slope (AZ/AP) approaches zero (Leibold et al. 1997,
Hessen et al. 2006, Heathcote et al. 2016). Based on this observation, EPA used the rate of
change in zooplankton biomass relative to changes in phytoplankton biomass (AZ/AP) as a
measure of the effect of excess nutrients on lake food webs.
2.2.1.2 Dissolved oxygen
Excess nutrients typically increase primary productivity, which increases the amount of organic
matter in a lake. Then, DO is consumed as the organic matter is decomposed, leading to hypoxic
and anoxic conditions (see Figure 1). Low concentrations of DO limit the extent to which habitat
is available to fish and zooplankton (Colby et al. 1972, Tessier and Welser 1991, Vanderploeg et
al. 2009), and oxygen availability is a key determinant of the quality and quantity of habitat
available to aquatic biota in many lakes (Evans et al. 1996). Although hypoxia occurs naturally in
a small number of systems (Diaz 2001), anthropogenic nutrient loads have greatly increased the
occurrence of hypoxia worldwide (Jenny et al. 2016). Deoxygenation of lake water typically
begins near the lake bottom and proceeds to shallower depths over the summer, especially in
stratified, relatively deep lakes, where the replenishment of DO from surface mixing is restricted
(Cornett 1989, Wetzel 2001). Therefore, an increasing proportion of the deeper waters of a lake
can become uninhabitable for certain organisms over the course of the summer (Molot et al.
1992). Exclusion of deeper waters as viable habitat, in particular, can disproportionately affect
particular species of adult and juvenile fish (Lienesch et al. 2005).
Another strong determinant of the available habitat for fish and zooplankton is water
temperature. Summer brings a longer photoperiod and more intense solar insolation, which
7

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increases water temperatures near the surface of many lakes to levels harmful to certain species
(Ferguson 1958, Eaton and Scheller 1996). The viable habitat for cool- and cold-water species, in
particular, can be restricted by surface warming (Jacobson et al. 2010, Arend et al. 2011). In
contrast to deoxygenation, warming starts at the surface of the lake and proceeds to deeper
depths over the course of the summer. Therefore, certain species offish are "squeezed"
between increasing temperatures at shallow depths and decreasing DO at deeper depths
(Coutant 1985, Stefan et al. 1996, Lee and Bergersen 1996, Plumb and Blanchfield 2009),
requiring them to choose between suboptimal temperatures or oxygen (Arend et al. 2011).
Under those conditions, the metalimnion and the upper edge of the hypolimnion can provide an
important refuge, and even a thin layer of cool water with sufficient DO can provide an
important habitat for supporting fish health through the warmest summer days. Because they
often can tolerate lower DO concentrations than fish, zooplankton can retreat to deeper depths
of the hypolimnion to escape fish predation, but are also limited ultimately by low DO
concentrations (Tessier and Welser 1991, Stemberger 1995).
Based on these considerations, the mean concentration of DO below the thermocline was
identified by EPA as an appropriate metric for assessing risks to cool- and cold-water fish in
seasonally stratified lakes. In those lakes during the summer, the availability of cool-water
habitat is constrained by deep water DO concentrations, and so, this risk metric links increased
nutrient concentrations to deleterious effects affecting the survival of fish and zooplankton in
deep lakes.
2.2.2 Recreational Use
EPA selected the concentration of cyanotoxins as the risk metric linking increased nutrients to
the suitability of lake water for primary and secondary contact recreation. Increased nutrient
concentrations and an attendant increase in cyanobacterial abundance can increase
concentrations of cyanotoxins (Figure 2), which cause adverse effects on the health of people
exposed to the water (US EPA 2019). One of the most commonly occurring types of cyanotoxins
in freshwaters is microcystins (based on available data). To protect recreational uses of lakes,
EPA identified microcystin concentration as the best risk metric because of the availability of
National Lakes Assessment (NLA) data (US EPA 2010b) and because microcystin thresholds for
recreational exposures have recently been published (US EPA 2019).
8

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Color
Taste and
Odor
Drinking Water Supply
Recreation
Suspended
Sediment
Hydrology-Geology;
Natural Vegetation
Water Clarity;
Light Availability
Lake Morphology;
Retention Time
Aquatic Macrophytes
Temperature
HABs
Phytoplankton
Nuisance
Algae
Organic Matter
Nutrients
A
Primary Production
f Algal
I Toxins J
Figure 2. Conceptual model linking increased nutrient concentrations to public health endpoints.
2.2.3 Drinking Water Source
Increased nutrient concentrations and an attendant increase in cyanobacteria can increase
concentrations of cyanotoxins, which are toxic when consumed at certain concentrations and
quantities (see Figure 2) (Chorus 2001, Stewart et al. 2008, US EPA 2015b). As was done for
recreational use, EPA selected microcystin in lake source water as the risk metric for the
drinking water use.
2.3 Risk Hypotheses
EPA specified risk hypotheses for each of the selected assessment endpoints. Based on a survey
of available literature, EPA concluded that increased concentrations of N and P increase the risk
to both ecological and human health (Figure 3). For aquatic life, the risk hypotheses consist of
the pathway in which increased nutrient concentrations increase phytoplankton biovolume
(measured as chlorophyll a [Chi a]). Then, as phytoplankton biovolume and associated biomass
increase, the relationship between zooplankton biomass and phytoplankton biomass (AZ/AP)
9

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changes so that increases in phytoplankton biomass are no longer associated with increases in
zooplankton biomass, and increases in primary production at the base of the lake food web are
not transferred to higher trophic levels. For the case of deep water DO concentrations,
increased phytoplankton biomass increases organic matter in the lake, which, when
decomposed, consumes DO (Walker 1979). The decreased concentrations of DO then affect lake
aquatic life. The risk hypotheses for both recreation and drinking water source designated uses
state that increased nutrient concentrations increase the biovolume of cyanobacteria and
concentrations of microcystin.
Nutrients
Primary Production
Phytoplankton (Chi o)
Cyanobacteria
Organic material
Deep water
dissolved oxygen
Food quality
Biologica I CommunRjes
a n ktori^v
pi ^
Drinking water
source
Fish
Recreation
Aquatic life use
Figure 3. Simplified conceptual model showing pathways selected for analysis.
2.4 Analysis Plan
An analysis plan outlines the scope, approaches, and methods to be used in the risk assessment.
Here, the analysis plan consists of acquiring appropriate data and estimating relationships
between phytoplankton biovolume and each of the risk metrics as well as between N, P, and
phytoplankton biovolume. The critical measurement in all these relationships is Chi a, which is
closely associated with phytoplankton biovolume. Stressor-response analysis was applied to
available data to estimate relationships between nutrient concentrations and different risk
metrics. Because Chi a concentration is the critical parameter for all risk metrics, EPA developed
10

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different stressor-response models associating Chi a concentration with each of the risk metrics
(i.e., zooplankton biomass (AZ/AP), deep water DO concentration, and microcystin). The models
then yielded candidate criteria for Chi a corresponding to each of the risk metrics (and their
associated endpoints). A candidate Chi a criterion is defined as a protective concentration
associated with a particular risk metric and/or with a particular designated use. The final
criterion for a lake is then derived by comparing candidate criteria and selecting the criterion
that protects the most sensitive use. N and P are estimated in field measurements as TN and TP,
and so, EPA developed models relating TN and TP concentrations to Chi a concentrations that
can translate each of the different Chi a criteria into recommended TN and TP criteria.
Because different risk metrics have been identified for each of the three designated uses, these
risk metrics lead to the derivation of different recommended numeric nutrient criteria. In
general, a state's water quality criteria for any single lake would need to protect the most
sensitive use (i.e., the state should select the most stringent numeric nutrient criteria across all
relevant uses and endpoints) (40 CFR 131.11(a)(1)).
3 Analysis
Because stressor-response analyses for each of the risk metrics differed substantially from one
another, most of this section is organized by models for the different risk metricszooplankton
biomass, deep water hypoxia, and microcystinfollowed by models relating TN, TP, and Chi a.
Because the same data were used to fit each of these models, all the data used in the analyses
are discussed first.
3.1 Data
EPA analyzed data collected in the NLA in the summers (May-September) of 2007 and 2012 to
support the derivation of recommended numeric nutrient criteria. The NLA data were collected
from a random sample of lakes from the continental U.S. In 2007, lakes with surface areas larger
than 4 hectares and, in 2012, lakes larger than 1 hectare were selected from the contiguous U.S.
using a stratified random sampling design (US EPA 2012c). The final data set was supplemented
by a small number of hand-picked lakes identified as being less disturbed by human activities
(US EPA 2010b). The additional lakes were included to increase the number of least-disturbed
lakes for which data were available, and by helping ensure the full range of conditions was
11

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sampled, data from the additional lakes were expected to improve the accuracy of the
estimated stressor-response relationships. The overall sampling design of the NLA was synoptic,
but 10% of sampled lakes were randomly selected and resampled on a different day after the
initial visit. The timing of the second visit varied among lakes, but on average, the second
sample was collected approximately 46 days after the first. Approximately 20% of the lakes were
sampled in both 2007 and 2012. The sampling day of the year was recorded for each visit and
used in subsequent analyses to account for temporal changes in deep water DO concentration.
Overall, data from approximately 1,800 different lakes are included in the data set, but the
specific number of samples used to estimate each stressor-response relationship varies slightly
based on data available at each lake. The specific number of samples is provided in the
subsequent discussion of each model. Quality assurance project plans for the NLA are available
in separate publications (US EPA 2009, 2012b).
During each visit to a selected lake, an extensive suite of abiotic and biological variables was
measured. Only brief details on sampling protocols are provided here regarding the parameters
used to derive these criterion models; more extensive descriptions of sampling methodologies
are available in the NLA documentation (US EPA 2007, 2011). A sampling location was
established in open water at the deepest point of each lake (up to a maximum depth of 50
meters [m]) or in the mid-point of reservoirs. In 2012, an additional sampling location for
collection of microcystin, algae, and Chi a data was established in the littoral zone
approximately 10 m away from a randomly selected point on the shoreline.
At the open water site, a vertical, depth-integrated methodology was used to collect a water
sample from the photic zone of the lake (to a maximum depth of 2 m). Multiple sample draws
were combined in a rinsed, 4-liter (L) cubitainer. When full, the cubitainer was gently inverted to
mix the water, and an aliquot was taken as the water chemistry sample. That subsample was
placed on ice and shipped overnight to the Willamette Research Station in Corvallis, Oregon. A
second aliquot was taken to use in characterizing the phytoplankton community and was
preserved with a small amount of Lugol's solution. A Secchi depth measurement was also
collected at this site. Two zooplankton samples were collected with vertical tows for a
cumulative tow length of 5 m using fine- (50-micrometer- [-nm-]) and coarse- (150-nm-) mesh
Wisconsin nets. In lakes at least 7 m deep, one 5-m deep tow was collected with each mesh. In
12

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shallower lakes, vertical tows over shorter depths were combined to reach the cumulative tow
length of 5 m.
At the littoral zone site, two grab water samples were collected 0.3 m below the surface where
the lake was at least 1 m deep using a 2-L brown bottle. The first sample was split into two
subsamples: one subsample for quantifying algal toxin concentration and the second subsample
preserved with a small amount of Lugol's solution and used to characterize the phytoplankton
community. The second grab sample collected with the 2-L bottle was used to quantify Chi a
concentration.
3.1.1 Biological Data
Phytoplankton biovolume from the field samples was measured in the laboratory. Samples
collected from both open water and littoral zone locations were examined by taxonomists, who
identified at least 400 natural algal units to species under l,000x magnification. Observations
were aggregated and abundance was calculated as cells per milliliter. In each sample, the
dimensions of the taxa that accounted for the largest proportion of the observed assemblage
were measured and used to estimate biovolume. Biovolumes of the most abundant taxa were
based on the average of measurements from at least 10 individuals, while biovolumes of the
less abundant taxa were based on somewhat fewer measurements. The biovolume was
reported as cubic micrometers per milliliter (nm3/mL) (US EPA 2012a), which was converted to
cubic millimeters per liter (mm3/L). Approximately 5% of the phytoplankton samples were
randomly selected and reidentified and measured by a second taxonomy laboratory. These
reidentified samples provided a basis for estimating laboratory measurement error. Biovolume
measurements were converted to biomass using a density of 1 gram per milliliter (g/mL)
(Holmes et al. 1969).
Zooplankton samples from the coarse- and fine-mesh net tows were processed separately. In
each sample, zooplankton specimens were examined and counted under 100-1,000x
magnification in discrete subsamples until at least 400 individuals were identified. In the coarse-
mesh net samples, all taxa were identified and enumerated. In the fine-mesh net, only "small"
taxa were identified and enumerated (Cladocera less than 0.2 millimeters [mm] long, copepods
less than 0.6 mm long, rotifers, and nauplii). Zooplankton abundance was estimated based on
the volume of sampled lake water used to identify the targeted count of 400 individuals.
Measurements of at least 20 individuals were collected for dominant taxa (i.e., taxa
13

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encountered at least 40 times in the subsample); at least 10 individuals were measured for taxa
encountered from 20 to 40 times; and at least 5 individuals were measured for rare taxa
(encountered less than 20 times in the subsample). Zooplankton biomass estimates were based
on existing length and width relationships (Dumont et al. 1975, McCauley 1984, Lawrence et al.
1987). Estimates from the coarse- and fine-mesh samples were added to yield a single
zooplankton sample per lake visit.
3.1.2	Chemical Data
For both 2007 and 2012 data, TN, nitrate-nitrite (NOx), ammonia, and TP concentrations; true
color, dissolved organic carbon (DOC) concentration, turbidity, and acid-neutralizing capacity
(ANC) were measured in the laboratory from the open water sample at prespecified levels of
precision and accuracy (US EPA 2012a). Typical laboratory methods included persulfate
digestion with colorimetric analysis for TN and TP, nephelometry for turbidity, comparison to a
calibrated color disk for true color, and automated acidimetric titration for ANC. To measure
Chi a concentration, 250 mL of lake water was pumped through a glass fiber filter in the field
and quantified in the laboratory to prespecified levels of precision and accuracy. Examples of
lower reporting limits include 20 ng/L for TN, 4 ng/L for TP, and 0.5 ng/L for Chi a.
Microcystin sample processing began with three sequential freeze/ thaw cycles to lyse
cyanobacteria (Loftin et al. 2008). Processed samples were filtered using 0.45 pim polyvinylidene
difluoride membrane syringe filters and stored frozen until analysis. The concentration of
microcystin in the filtered water sample was measured with an enzyme-linked immunosorbent
assay (ELISA) using an Abraxis kit for Microcystin-ADDA, which employs polyclonal antibodies
that are unique to microcystins and other similar compounds. The binding mechanism of the
Microcystin-ADDA assay is specific to the microcystins, nodularins, and their congeners;
therefore, results from that assay could include contributions from any compound within the
ADDA functional group (Fischer et al. 2001). The minimum reporting level for the assay was 0.1
ju,g/L as microcystin-LR.
3.1.3	Dissolved Oxygen and Temperature Profiles
At the deepest point of each lake (or in the midpoint of reservoirs), a multiparameter water
quality meter was used to measure profiles of DO concentrations, temperature, and pH at a
minimum of 1-m depth intervals (see Section 3.2.2 for an examples of depth profiles). Profiles in
14

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lakes less than 3 m deep were sampled at 0.5-m depth intervals. Water temperatures were
converted to estimates of water density (Jones and Harris 1992), and density gradient was
estimated between all available depths below 0.5 m as the difference in density between two
successive measurements divided by the difference in the depths of the two measurements.
Temperature gradients were computed with the same approach. Samples collected in the
uppermost 0.5 m were excluded to limit the effects of surface warming on the gradient
calculations.
3.1.4 Mapped Data
Lake physical characteristics, including lake surface area, geographic location (latitude and
longitude), elevation, lake catchment area, and lake perimeter, were estimated from mapped
data. From these characteristics, the following composite variables were calculated: (1) the
drainage ratio, which is defined as the ratio of catchment area to lake surface area and
characterizes the degree to which the lake catchment influences the lake; (2) the shoreline
development, which is defined as the ratio between the perimeter of the lake and the perimeter
of a circle with the same area as the lake and characterizes the geometric complexity of the lake
shore; and (3) the lake geometry ratio, which is defined as area0 25/depth, or the ratio between
fetch and lake maximum depth, and has been shown to differentiate lakes that stratify
seasonally (low values of the geometry ratio) from lakes that are polymictic (Gorham and Boyce
1989, Stefan et al. 1996). Variables quantifying the mean annual precipitation and mean annual
air temperature at the lake location were extracted from 30-year averaged climatic data (Daly et
al. 2008).
3.2 Stressor-Response Models
Stressor-response models estimate relationships between environmental stressors
(e.g., increased nutrient concentrations) and responses, or risk metrics. In this section, stressor-
response models for zooplankton biomass, deep water hypoxia, and microcystin concentration
are described. The stressor in these models is phytoplankton biovolume, quantified as Chi a.
Models estimating relationships between TN, TP, and Chi a are also described.
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3.2.1 Zooplankton Biomass
Zooplankton occupy a key link in the lake food web, and the relationship between
phytoplankton biovolume and zooplankton biomass provides insights into changes in the food
web as lake productivity increases.
3.2.1.1 Statistical analysis
EPA specified a Bayesian network model to estimate the relationship between summer mean
phytoplankton and zooplankton biomasses (Figure 4). A Bayesian network provides a unified
framework for modeling the cascading relationships between different measurements and
propagates estimation errors and model uncertainty correctly throughout the model (Qian and
Miltner 2015; Yuan and Pollard 2018).
Summer mean
phytoplankton biovolume
(6)

Summer mean
zooplankton abundance
15)
UU2}
Observed
phytoplankton
biovolume
Summer mean
zooplankton biomass
(sy-
Observed Chi a
Observed
zooplankton
abundance
Observed
zooplankton
biomass
Figure 4. Schematic of network of relationships for modeling zooplankton biomass. Gray-filled ovals:
available observations; other nodes: modeled parameters; numbers in parentheses refer to equation
numbers in the text.
The first set of relationships in the network estimated seasonal mean phytoplankton biovolume
based on measurements of Chi a concentration and of phytoplankton biovolume. The two
measurements provided independent estimates of phytoplankton biovolume, each with
different sources of error. Chi a is measured precisely from field samples, but the Chi a content
of phytoplankton can vary depending on environmental conditions and species composition
(Kasprzak et al. 2008), so that a measured Chi a concentration in one sample might indicate a
slightly different phytoplankton biovolume than the same Chi a measured in another sample.
Hence, Chi a concentration is modeled as being directly proportional to the seasonal mean
phytoplankton biovolume in lake j (Pj), but the constant of proportionality, b, (i.e., the Chi a
16

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content of phytoplankton in a sample) is allowed to vary among samples. The log-transformed
version of this model equation is as follows:
log(C7iZ[) = log(%j) + logObj)	(1)
log(bj) ~Normal([ib,ob)	(2)
where the value of b, for each sample, /', is drawn from a single log-normal distribution
characterized by a mean, /Ub, and a standard deviation, Ob. The mean value, /Ub, accounts for
differences in the measurement units of Chi a and phytoplankton biovolume; however, in the
model, both Chi a and phytoplankton biovolume measurements are standardized by subtracting
their observed mean values and dividing by their standard deviation, so /Ub is zero. The multilevel
expression of the model equation allows the mean Chi a content of phytoplankton cells
estimated for each sample to vary, but imposes the constraint that estimates of phytoplankton
Chi a content for each sample must be drawn from a common log-normal distribution (Gelman
and Hill 2007). Measurements collected at the same lake on different days and collected on the
same day in the littoral zone and in the middle of the lake were used to estimate seasonal mean
phytoplankton biovolume.
Direct measurements of phytoplankton biovolume provide an unbiased estimate of true
phytoplankton biovolume. These direct measurements, however, are obtained by summing
contributions from measurements taken from many different individual phytoplankton, each of
which includes measurement error. Hence, the summed estimate of total biovolume includes a
substantial amount of measurement error. That measurement error was explicitly modeled, and
a second estimate of the seasonal mean phytoplankton biovolume was expressed as follows:
log(P0bs,i) ~Normal(log(Pjli]), st)	(3)
where P0bsj is the observed phytoplankton biovolume in sample /'. Final model estimates of PjW
were consistent with both Chi a and observed phytoplankton biovolume, and by combining the
two measurements, the accuracy of the final estimate was maximized.
Zooplankton abundance (A) and biomass (Z) were modeled as increasing functions of seasonal
mean phytoplankton biovolume (or biomass, using the conversion factor of 1 g/mL). Previous
studies in oligotrophic lakes found that zooplankton biomass increased as a constant proportion
of phytoplankton biomass (Rognerud and Kjellberg 1984, del Giorgio and Gasol 1995). That is,
17

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after log-transforming, the relationship between P and Z should approach the following at low
concentrations of P:
where the slope of the relationship between log(Z) and log(P) approaches 1. In contrast, in
eutrophic lakes, minimal changes in Z were observed with changes in P, and the slope between
log(Z) and log(P) approached zero (Yuan and Pollard 2018). Those patterns guided the selection
of the following functional form for modeling the relationship between log(Z) and log(P):
where, in general, E[.] indicates the expected value of the variable enclosed in the square
brackets. The coefficients fi,f2,f3, cp, and q were estimated from observations of Zj and the
estimated seasonal mean phytoplankton concentration, Pj, estimated from measurements of
phytoplankton biovolume and Chi a. The slope of this function approaches f2 at large values of P
and approaches a slope of f2 +fs at low values of P. A prior distribution for/2 +f3 was specified as
a normal distribution centered at 1 with a standard deviation of 0.2, expressing the prediction
(stated above) that, at low levels of phytoplankton (oligotrophic lakes), zooplankton biomass
should increase as a constant proportion of phytoplankton biomass.
A similar model was specified for zooplankton abundance (A) as follows:
where the parameters, alr a2, a3, and r were estimated from the data, and the third term on the
right side of the equation again introduces curvature in the fitted relationship. The change point
for zooplankton abundance, cp, was estimated as being the same as for zooplankton biomass
because of the strong influence of abundance on total biomass. In the case of zooplankton
abundance, no a priori assumptions about the slope of the relationship at high or low levels of
phytoplankton guided the choice of parameter values.
Observed values of zooplankton abundance and biomass were then related to the estimated
expected values as follows:
log(Z) = log(fc) + log (P)
(4)
[log(Zj)] = A + f2log (Pj) - f3qlog 1 + exp
(5)
[log (Aj)] = a1 + a2 log (Pj) + a3 log [1 + exp (_'g(y c''j]
(6)
log(4
obs,i
) -Normal(E[log(^m)], s2)
log (Z
obs,i
) -Normal(E[log(Z;m)],s3)
(7)
(8)
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Similar to the model equations for phytoplankton, variability in the observations of zooplankton
abundance and biomass relative to estimated mean values were modeled as log-normal
distributions with standard deviations of s2 and s3. These error terms included contributions
from temporal, sampling, and measurement error.
Because the strength of the interaction of the zooplankton assemblage with benthic resources
was expected to differ between shallow and deep lakes (Benndorf et al. 2002, Scheffer and van
Nes 2007) and exploratory data analysis indicated that lake depth was an important covariate
(Yuan and Pollard 2018), different parameter values for ai, a2, a3,fi,f2, f3, and cp were estimated
for each of three classes of lakes defined by depth. The curvature parameters q and r were fixed
at 1. The number of lake classes was specified to balance between accounting for differences in
lake depth and maintaining enough samples within each class to estimate relationships. Depth
thresholds defining each class were selected to ensure that a similar number of samples was
assigned to each class, yielding the following thresholds: less than 3.8 m, 3.8-8.0 m, and more
than 8.0 m.
All model equations were fit simultaneously to data collected at each lake, including revisits on
different days, and littoral and mid-lake samples for phytoplankton. Weakly informative priors
were specified for all model parameters except for/2 +/s (Gelman 2006). Weakly informative
prior distributions constrain parameter estimates away from extreme values, while allowing the
data to determine the estimate for each parameter. All other statistical calculations were
performed with R, an open-source statistical modeling software (R Core Team 2017).
Hierarchical Bayesian models were fit using the rstan library, which implements the No-U-Turn
sampler, a variant of a Hamiltonian Monte Carlo sampling approach (Duane et al. 1987, Stan
Development Team 2016).
3.2.1.2 Results
Data collected at a total of 1,096 lakes were available for analysis, with approximately 330 lakes
assigned to each depth class. Estimated mean phytoplankton biovolume within each sample was
much more strongly associated with Chi a concentration than with measured phytoplankton
biovolume, because of the high variability associated with measured phytoplankton biovolume
(Figure 5).
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	I	I	I	I		I	"I	I	I
0.1	1	10 100	0.1	1	10 100
Mean biovolume (mm3/L)	Mean biovolume (mm3/L)
Figure 5. Relationships between measured biovolume, Chi a, and estimated seasonal mean phytoplankton
biovolume. Solid lines: 1:1 relationship (left panel), proportional relationship (right panel).
Estimated relationships between phytoplankton biomass (as quantified by Chi a) and
zooplankton abundance and biomass matched trends observed in the data (see Figure 6 for an
example for lakes deeper than 8 m in left and middle panels, respectively). The relationship
between zooplankton biomass and phytoplankton biomass also was consistent with the initial
assumption that, in oligotrophic lakes with low levels of phytoplankton biomass, the slope
approached 1, and in eutrophic lakes with high levels of phytoplankton biomass, the slope
approached zero (right panel, Figure 6).
The models show the gradual change in the shape of the biomass pyramid along the
eutrophication gradient. In oligotrophic lakes, the slope of the relationship between zooplankton
and phytoplankton biomass is near 1, indicating that small increases in phytoplankton biomass
are reflected in a proportional increase in zooplankton biomass. As Chi a increases, however,
the slope decreases, and the increase in zooplankton biomass per unit of increase in
phytoplankton biomass [log(AZ)/log(AP)] approaches zero. In eutrophic lakes, increases in
phytoplankton biomass do not result in comparable changes in zooplankton biomass. These
changes along the eutrophication gradient are consistent with other similar studies, as reviewed
in Yuan and Pollard (2018).
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 		I' I	I'  """I' ' """I
1	1	10	100	1000
Chi a (j-ig/L)	Chi a	Chi a
Figure 6. Estimated relationships between zooplankton and Chi a for lakes > 8 m deep. Left panel: Chi a vs.
zooplankton abundance; middle panel: Chi a vs. zooplankton biomass; right panel: Chi a vs. slope of the
relationship between zooplankton biomass and Chi a. Solid lines: mean relationships; shaded areas (left
and middle panels): 90% credible intervals (bounded by the 5th and 95th percentiles of the distribution of
possible mean relationships; dashed lines (right panel): 90% credible interval; open circles (left and middle
panels): average of five samples nearest the indicated Chi a concentration; dotted horizontal line (right
panel): one example value of threshold for deriving a Chi a criterion.
3.2.1.3 Chi a criterion derivation
Calculating candidate criteria for Chi a based on this response requires the specification of two
parametersthe value of the slope between log(Z) and log(P) and the certainty level, as
quantified by the credible interval (i.e., the Bayesian analog to a confidence interval).
Considerations: Slope between log(Z) and log(P). The threshold slope of zero between log(Z)
and log(P) is the limit beyond which changes in zooplankton biomass are not associated with
changes in phytoplankton biomass. This threshold identifies the point at which a disconnect
between phytoplankton and zooplankton production begins and increasing primary productivity
in the lake escapes zooplankton grazer control, a condition which can exacerbate blooms. EPA
therefore recommends a threshold of zero as the minimum value for this parameter. Higher
threshold slopes may be selected for certain types of lakes in which a higher proportion of
phytoplankton is expected to be consumed by zooplankton (e.g., oligotrophic), but quantifying
the appropriate value for this slope requires the collection of additional data from these lakes.
Graphically, this threshold defines the horizontal line on which the Chi a criterion will be based
(see Figure 6).
Considerations: Certainty level. The certainty level, as quantified by the credible interval,
expresses the statistical uncertainty about the position of the mean relationship and is
comparable to a confidence interval used in frequentist statistics. The percentile value selected
as the certainty level (e.g., the 90% certainty level) specifies the probability that the mean
21

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relationship is located within the estimated bounds of the corresponding credible interval (e.g.,
there is a 90% probability that the actual mean relationship is located within the bounds
associated with the 90% credible interval). In practice, the bounds of the credible interval are
calculated from percentiles of the posterior distribution of the mean relationship. For example,
at any Chi a concentration, the criterion model provides a distribution of possible values of the
slope between zooplankton and phytoplankton biomasses. The credible interval is centered at
the median value of this distribution of slopes, and the bounds of the 90% credible interval are
calculated as the 5th and 95th percentiles of this distribution.
Basing the criterion value on the lower bound of the selected credible interval provides
additional assurance that the calculated criterion is protective, given the data and model
uncertainty. That is, more protective criteria are based on lower percentiles of the distribution
of possible mean relationships (i.e., lower bounds of the credible interval). For example, if one
selects a certainty level of 90%, the corresponding bounds for the 90% credible interval are
computed as the 5th and 95th percentiles of the distribution of estimated mean relationships.
Therefore, basing a criterion on the lower bound of the 90% credible interval implies there is a
5% chance that the actual slope between log(Z) and log(P) is less than the selected threshold.
That is, there is a 5% chance that the derived criterion value is greater than the concentration
needed to achieve the desired condition, and therefore, a 5% chance that the criterion is under-
protective. More certainty on the criterion value is achieved by selecting greater certainty levels.
For example, there is a 1% chance that a criterion based on the 98% certainty level would be
under-protective. In statistical hypothesis testing, convention suggests that p-values of 1% or 5%
are statistically significant results, which can also inform the selection of the certainty level.
Selection of the certainty level as the basis for the criteria is a management decision, and a
range of certainty levels (and associated credible intervals) from 50% to 99% is provided in the
associated interactive tool (see below). The ecological effects of reduced grazer control of
phytoplankton biomass associated with a slope threshold value of zero can be substantial and
difficult to reverse; and therefore, conservative certainty levels (i.e., 90% - 99%) are
recommended for this response.
Chi a criterion derivation: Illustrative criteria for Chi a for different management decisions are
shown in Table 2. The interactive tool, which uses posterior simulation with the estimated
parameter distributions, computes candidate criteria for different combinations of the slope
22

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threshold and the certainty level (https://nsteps.epa.gov/apps/chl-zooplankton). With this tool,
a user can specify the value of the slope between log(Z) and log(P), lake depth, and the certainty
level, and the associated criteria and stressor-response relationship are updated to reflect those
selections. The tool provides transparent information regarding the effects of different levels of
certainty and can provide a useful means of engaging with stakeholders regarding the risk
management decisions underlying criterion development.
Table 2. Illustrative Chi a criteria (ng/L) for different certainty levels and a slope threshold value of 0 for
A(log Z)/A(log P). Values shown for each lake depth class.


Depth class

Certainty level
< 3.8 m
3.2-8 m
> 8 m
90%
51
21
13
99%
34
15
9
3.2.2 Deep Water Hypoxia
EPA specified a model for deep water DO that represents the temporal decrease in DO during
summer stratification, while accounting for differences among lakes in eutrophication status,
depth, and DOC concentrations (Yuan and Jones 2020a).
3.2.2.1 Data
EPA first restricted analysis to data collected from seasonally stratified lakes because hypoxic
and anoxic conditions occur more consistently during stratified conditions. Lakes were identified
that were likely to be seasonally stratified by computing the lake geometry ratio. This metric
approximates the relative effects of lake fetch and depth on stability of stratification, and lakes
with a geometry ratio less than 3 m"05 exhibit seasonal stratification (Gorham and Boyce 1989).
Therefore, EPA restricted NLA data to lakes with geometry ratios less than that threshold. Lakes
likely to be dimictic (i.e., mixing fully in the spring and in the fall and ice-covered in the winter)
were also identified based on latitude and elevation. This classification approach adjusts the
lake latitude by elevation, and then identifies lakes with adjusted latitudes greater than 40 N as
dimictic (Figure 7) (Lewis 1983). Restriction to dimictic lakes allowed EPA to use a simple
relationship based on annual mean temperature in the model to more accurately predict the
first day of stratification, and thus, more accurately estimate model parameters (see below).
The location of dimictic lakes also roughly corresponded with lakes that were likely to harbor
23

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cool- and cold-water fish. Finally, data were restricted to samples in which temperature profiles
exhibited evidence of stratification (defined as a temperature gradient of at least 1 degree
Celsius per meter [C/m]).

Figure 7. Locations of NLA lakes used to fit the DOm model. These lakes were designated as dimictic and
were stratified at the time of sampling.
Mean deep water DO concentrations (DOm) in the selected NLA lakes were computed from
temperature and DO profiles. First, measurements collected at depths less than or equal to
0.5 m were excluded to minimize the effects of surface warming. In some profiles, duplicate
measurements of DO and/or temperature were collected at each depth, and in these cases, the
average was used in computations. EPA used only profiles with measurements collected from at
least half of the possible 1-m increments in the final analysis.
The upper boundary of the metalimnion was identified as the shallowest depth at which the
temperature gradient exceeded 1 C/m (excluding the surface layer) (Figure 8) (Wetzel 2001).
DOm for each lake profile was computed as the mean of DO measurements estimated at all 1-m
increments deeper than the upper boundary of the metalimnion. That estimate of DOm
necessarily includes some measurements in the metalimnion, which might increase the
estimates of DOm relative to studies that can focus only on the hypolimnion. In the NLA data set,
the upper boundary of the metalimnion could be determined for most profiles. In contrast,
many lakes in the NLA data set were too shallow to maintain a hypolimnion with small vertical
temperature gradients (Jones et al. 2011), and therefore, no approach for consistently defining
the hypolimnion for all lakes was available (Quinlan et al. 2005). Furthermore, inclusion of the
24

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metalimnion was consistent with the assumption that taxa can use this transitional region as a
refuge from warmer temperatures in the mixed layer (Klumb et al. 2004). The depth of water
below the thermocline was computed as the difference between the maximum depth recorded
for each lake and the mean depth of the upper boundary of the metalimnion. Chi a and DOC
measurements from each lake were also used in the analysis. Prior to statistical analysis, all
measurements were standardized by subtracting their overall mean values and dividing by the
standard deviation. This standardization had no effect on the final model results, but helped the
Bayesian models converge more efficiently (Gelman and Hill 2007).
5 10 15 20	012345	2468
Temperature (C)	Temperature gradient (C/m)	qq (mg/L)
Figure 8. Illustrative examples of depth profiles of temperature, temperature gradient, and DO. Dashed
horizontal line: estimated depth of the bottom of the epilimnion.
3.2.2.2 Statistical analysis
EPA modeled the decrease in DOm as a linear function, an approximation that is appropriate for
DOm concentrations higher than approximately 2 milligrams per liter (mg/L) (Burns 1995). This
threshold reflects experimental evidence indicating that the rate of decrease of hypolimnetic DO
is constant at relatively high ambient concentrations of DO, but can be affected by DO
concentrations near zero (Cornett and Rigler 1984). The linearly decreasing function also
precludes the possibility of episodic mixing events that transport DO from shallow waters to
deeper depths of the lake. In some lakes, those mixing events are rare, but in other lakes (e.g.,
cold polymictic lakes), they might occur frequently. In the latter group of lakes, the model
predicts DOm during extended periods of still weather, and the associated criteria would protect
25

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aquatic life in those scenarios. Below, the statistical model is first described followed by a
description of the approach for addressing DOm measurements less than 2 mg/L.
Dissolved organic
carbon (DOC)
Depth below
thermocline (D)
Air temperature
(Temp)
Eutrophication
(Chi a)
First day of
stratification (t0)
Oxygen demand
(VOD)
Sampling
day (t)
Figure 9. Schematic of hypoxia model. Numbers in parentheses refer to equation numbers in the text.
NLA data were fit to the following model equation:
E[DOm,i\ = D0j[(] + VODj[q(ti - t0,fcp])	(9)
where DO0,j[i] is the value of DOm at the start of spring stratification in lake j corresponding to
sample /', and volumetric oxygen demand (VODj) is the net imbalance in the volumetric oxygen
budget for lake j, expressed as mg/L/day of DO (Burns 1995). That is, VOD estimates the rate of
decrease in DOm per day. t, is the date that sample i is collected, and t0,k[i] 's the date of the
beginning of stratification for the lake-year k corresponding to sample /'. Observed values of
DOm,i were modeled as being normally distributed about the expected value, with a standard
deviation of Oi.
The first day of stratification (t0) was not measured for any of the lakes, and the precise day on
which stratification occurs for a given lake and year depends on local wind speeds,
temperatures, and lake morphology (Cahill et al. 2005). Previous work in northern temperate
dimictic lakes found that the first day of stratification could be modeled as a function of mean
annual temperature (Demers and Kalff 1993), so EPA specified the following relationship for t0:
to,k = b1 + bzTempm + ek	(10)
where Temp^i is the mean annual air temperature at the location for lake j corresponding to
lake-year k, and bi and b2 are coefficients that are fit to the data. The published relationship in
26

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Demers and Kalff (1993) provided initial estimates for bi and b2, which were used to specify
prior distributions for the two parameters. The error term ek is included in the model because
the first day of stratification varies substantially in different years for a given lake because of
differences in weather. Data published by Demers and Kalff (1993) indicated that the standard
deviation of residual error for this relationship was approximately 12 days, so this value was
used to specify the prior distribution for the standard deviation of ek.
The initial concentration of DO at the time of stratification, DO0, was also not measured for any
of the lakes. Deep water temperatures in many seasonally stratified lakes are determined by
temperatures prior to initiation of stratification (Hondzo and Stefan 1993), and so, deep water
lake temperatures at the time of stratification were approximated as the minimum annual air
temperature at the lake location. Then, the saturated DO concentration at the minimum annual
air temperature provided an estimate for DO0. Minimum air temperatures less than 4 degrees
Celsius (C) were set to 4 C, corresponding to water temperatures when the lake surface begins
to freeze (Demers and Kalff 1993).
Lake trophic status affects VOD because increased phytoplankton production in the epilimnion
increases the quantity of organic material available for decomposition in the hypolimnion and in
lake sediments (Hutchinson 1938). In many lakes, allochthonous sources also provide organic
matter that fuels bacterial respiration and depletes oxygen in deep lake waters (Pace et al. 2004,
Kritzberg et al. 2004). VOD has also been observed to decrease with increasing hypolimnion
depth, a phenomenon attributed to a weaker overall influence of sediment oxygen demand as
the volume of the hypolimnion increases (Cornett and Rigler 1980, Muller et al. 2012). Based on
these mechanisms, EPA modeled VOD as a linear function of the long-term mean Chi a
concentration and depth below the thermocline in the lake. To account for the effect of
allochthonous organic matter, DOC was also included as a third predictor variable for VOD
(Hanson et al. 2003, Cole et al. 2011). The model equation for VOD can then be written as
follows:
E[VODj] = d-t + d2 log(ChlmnJ) + d3DmnJ + d4log (DOCmnJ)	(11)
where di, d2, d3, and d4 are model coefficients estimated from the data; log(Chlmn,j) is the long-
term mean of the log-transformed Chi a concentration lake, j; Dmnj is the mean depth of the lake
below the thermocline; and log(DOCmn,j) is the seasonal mean of log-transformed DOC
concentration in the lake. Variability in VOD across individual lakes about the mean value
27

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estimated from the predictor variables was modeled as a normal distribution. Because Chi a
concentrations can vary substantially over the summer in a lake, the modeling approach used
with the zooplankton model provided a distribution of possible long-term mean log(Chlmn)
values for each lake, given one or more instantaneous measurements of Chi a concentration.
More specifically, seasonal mean log(Chlmn) values for different lakes were modeled as a normal
distribution as follows:
log(ChlmnJ) ~NormalQichl,schlil)	(12)
Then, individual log-transformed measurements from each lake were assumed to be drawn
from a normal distribution with a mean value equal to the long-term mean as follows:
log(CWi) -Normal^log (ChlmnJ[q), schl2)	(13)
where Chi, is the Chi a concentration measured in sample, /', associated with the mean log(Chlmn)
concentration in lake j[i], (Note that Equations (12) and (13) are not shown in Figure 9.) Within-
year variability of DOC and depth below the thermocline were substantially less than observed
for Chi a, so long-term means for each of those parameters were estimated as the mean value
of all available data for each lake. Weakly informative prior distributions were assigned to all
parameters except for those that are noted above. Weakly informative prior distributions
constrain parameter estimates away from extreme values, while allowing the data to determine
the estimate for each parameter.
As noted earlier, DOm approaches zero asymptotically over time and modeling that relationship
with the linear model described above would introduce biases to the model. To account for the
asymptotic relationship, EPA modeled samples with DOm less than 2 mg/L with methods used
for measurements that are below a known detection limit. That is, the samples were modeled as
if their "true" DOm values were unknown but their maximum values were 2 mg/L (Gelman and
Hill 2007). This approach retained some information inherent in a sample with DOm less than 2
mg/L (i.e., Chi a, lake depth, DOC, and sampling day are consistent with low DOm), but allowed
the use of linear relationships in the model to estimate the rate of DO depletion. More
specifically, the model fits a linear trend in time to DOm observed from lakes with similar Chi a,
DOC, and depth. By assuming that measurements of DOm less than 2 mg/L are unknown, the
estimates of the linear relationship are more strongly determined by the higher DOm
concentrations, and samples with DOm less than 2 mg/L exert a weak influence that is still
consistent with the overall relationship. Retaining samples with DOm less than 2 mg/L in the
28

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model prevents biases that would be introduced by considering only lakes with relatively high
DOm.
3.2.2.3 Results
A total of 477 samples collected at 381 lakes were available for analysis. DOm concentrations in
165 samples were less than 2 mg/L and were modeled as unknown values that were less than
2 mg/L The asymptotic relationship can be seen in the plot of Chi a versus DOm (Figure 10), in
which DOm decreases steadily up to a Chi a concentration of about 4 ng/L. At higher Chi a
concentrations, the magnitude of the slope of the relationship between DOm and Chi a
decreases and approaches zero.
m
_i
U)
E
o0

o
Q
m
co
o
1
10
Chi a Oig/L)
Figure 10. Chi a vs. DOm. DOm values. Gray-filled circles: values < 2 mg/L; solid line: non para metric fit to
the data shown only to highlight the asymptotic relationship.
The majority of the estimates for the first day of stratification ranged from day 30 to day 120
(Figure 11). In most lakes, the Demers and Kalff (1993) estimate for the first day of stratification
was later than the value of t0 estimated by the model. This systematic difference is consistent
with the fact that most of the lakes considered in Demers and Kalff (1993) were located north of
the mean latitudinal location of the NLA lakes. The strong association between the Demers and
Kalff (1993) estimates and the current estimates indicates that the overall formulation of the
model, in which stratification day is a function of mean annual temperature, is valid.
29

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>* o
CD 10
"D t-
c
o
OO
(/)
c
03
0
 
Z. 10
o
o CO
Q)
(n
o
0- o
80
100 120 140 160 180
D & K predicted stratification day
Figure 11. Demers and Kalff (1993) predicted stratification day vs. model mean estimate. Solid line: the 1:1
relationship.
Relationships estimated between DOm and different predictors were consistent with the
hypothesized effects of each of the predictors (Figure 12). DOm decreased strongly with
increases in DOC and Chi a, reflecting the increased organic material available in lakes with high
concentration of the two parameters. Conversely, DOm increased with increasing depth below
the thermocline, consistent with observations in other studies. Substantial uncertainty is
associated with the relationship between DOm and day of the year, reflecting the inherent
uncertainty in estimating the first day of stratification for different lakes.
The root mean square (RMS) error on model predictions for samples with DOm higher than
2 mg/L was 1.5 mg/L. RMS error is defined as the square root of the average squared difference
between predicted and observed values. Slightly greater residual variability in the observations
about the mean predictions were observed at high values of DOm (Figure 13).
30

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DOC (mg/L)
i	1	1	1	1	1	r
0 10 20 30 40 50 60
Depth below thermocline (m)
Figure 12. Relationships between individual predictors and DOm, holding other variables fixed at their
mean values. Solid line: mean relationship; gray shading: 90% credible intervals.
CD
	I
CD
E
o,
 O
O ^
~
IS
2
8> 
-Q
O
c>
CN
0
2
6
8
10
12
4
Predicted DOm (mg/L)
Figure 13. Model predicted DOm vs. observed DOm. Open circles: individual samples; solid line: 1:1
relationship.
The statistical model described for DOm is consistent with the mechanisms of DO depletion in
the deep waters of a lake, in which available DO below the thermocline is progressively depleted
after the initiation of spring stratification. The estimated effects of eutrophication, DOC, and
31

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lake depth on the rate of oxygen depletion were consistent with trends observed in other
studies.
3.2.2.4 Chi a criteria derivation
As described earlier, warm temperatures in the shallow mixed layer of a lake act together with
deep water hypoxia to constrain the available habitat for cool- and cold-water taxa. Therefore,
to derive criteria based on deep water hypoxia, estimates of changes in water temperature over
the course of the summer are required to identify periods of time during which mixed layer
temperatures are too high for different taxa. Those periods of time then determine when deep
water DO concentrations need to be sufficiently high to support different organisms.
Water temperature in the lake mixed layer depends on a variety of factors, including the local
climate, solar insolation, lake morphology, and the day of the year (increasing in the spring and
summer and decreasing in the fall). To identify temperatures in different lakes that were likely
to limit available habitat for different fish, EPA first developed models to predict temperature in
the shallow, mixed layer of different lakes. NLA data collected at all lakes in the conterminous
U.S. were used to fit the model. At each lake, maximum temperature (excluding the top 0.5 m of
the surface layer) observed in vertical profiles collected in each lake were modeled as a function
of lake geographic location, elevation, and sampling day of the year with a generalized additive
model (Wood 2006) of the following form:
ElTi\ = fi + fiElevm + s(ydayi, df = 7) + s(Latm, Lonm,df = 30)	(14)
where E[T,] is the expected value of the maximum temperature in the lake observed in sample /'.
EleVj[i]\s the elevation of the lake, j, corresponding to sample /'. The variable yday, is the day of
the year that the sample was collected, and Latjtf and Lonjy are the latitude and longitude of the
lake. The relationship between temperature and elevation was modeled as a simple linear
relationship, characterized by two regression coefficients, fi, and f2. Relationships between lake
temperature and sampling day and between lake temperature and location were modeled as
nonparametric splines, represented in Equation 14 as s(.), with the maximum degrees of
freedom, df, as indicated. Observed values of T, were assumed to be normally distributed about
the modeled expected value.
Lake temperature generally decreased with increased latitude, as would be expected (Figure
14), but deviations from that latitudinal pattern were observed on the west coast of the U.S.,
32

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where lake temperatures were substantially lower than lakes at a similar latitude in the eastern
U.S. This trend likely arises from the moderating influence of the coastal waters on air
temperatures. Lake temperatures in eastern Texas and Louisiana were warmer than lake
temperatures at the same latitudes elsewhere. Lake temperatures decreased with elevation, as
expected, and exhibited a unimodal pattern with sampling day, with maximum temperatures
occurring on average on Day 204, or July 22 (Figure 15). Overall, the model predicted lake
temperature with an RMS error of 1.9 C.
>5
Figure 14. Contours of modeled mean lake temperature computed at the overall mean elevation and
mean sampling day.
00
CNI
CNI
Q)
3
CNJ
CNJ
CNJ
CNJ
CO
CD
0
1000
2000
3000
CNJ
Q)
CNJ
3
CNJ
CN
O
CNJ
CO
150
200
250
Day of year	Elevation (m)
Figure 15. Relationship between lake temperature and sampling day (left panel) and elevation (right
panel). Variables that are not plotted are fixed at their mean values. Gray shading: 90% confidence
intervals; solid lines shows the mean relationships.
33

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The pattern of temperature changes with time (see Figure 15) provides insight into the critical
period during which the severity of deep water hypoxia can influence aquatic life in lakes. For
most lakes, mixed layer temperatures increase in the spring and exceed critical temperatures for
different species, at which point cool- and cold-water obligate species must move to deeper
depths. Then, in the fall, decreasing mixed layer temperatures allow those species to move back
to shallower waters. Models for DOm indicate that, in dimictic lakes after the onset of spring
stratification, DOm decreases monotonically over time until fall turnover (see Figure 12).
Therefore, the length of time between spring stratification and when mixed layer temperatures
decrease below the critical temperature thresholds in the fall is a key factor for deriving a
protective Chi a criterion.
EPA used documented temperature thresholds defined for cool- and cold-water fish as
examples of critical mixed layer temperatures (Coker et al. 2001). For cool-water species, EPA
identified an illustrative temperature threshold of 24 C. Walleye, striped bass, and yellow perch
are examples of lake fish that are members of that group (McMahon et al. 1984). For cold-water
species, EPA identified an illustrative temperature threshold of 18 C. Lake trout and cisco are
examples of cold-water obligate species (Marcus et al. 1984, Jacobson et al. 2008). (Note: These
references are only examples of the types of information that can be used to inform decisions
regarding the critical temperature for different fish species and different fish life stages.) Then,
given a lake's location and elevation, the lake temperature model predicts the day of the year
that the mixed layer temperature would decrease below the critical temperatures. For cool-
water species, mixed layer temperatures decreased below the critical temperature of 24 C on
days 210-260 (Figure 16), taking into account the fact that the dimictic lakes considered in this
analysis are located in the northern half of the country (see Figure 7). Lakes in which mixed layer
temperatures increased above 24 C at some point during the year were predominantly located
in the eastern U.S., as high elevations and climate in the western U.S. moderate lake
temperatures. For cold-water species, mixed layer temperatures decreased below the critical
temperature of 18 C on days 220-280 (Figure 17). Temperatures in many lakes in the southeast
part of the U.S. rarely decrease below the critical threshold in the summer, but those lakes also
generally do not harbor cold-water fish.
34

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(
^	
>260		^
220-
;220'
270'
oo(
o 0
Figure 16. Days of the year that mixed layer temperatures decrease below the critical temperature for
cool-water species. Small dots: lakes in which mixed layer temperatures never exceed 24 C.
250'
C" -
260'
CO o

230;
270'


Figure 17. Days of the year that mixed layer temperatures decrease below the critical temperature for
cold-water species. Small dots: lakes in which mixed layer temperatures do not decrease below 18 C
during the summer; contours: effects of large differences in elevation across lakes in the western U.S.
Criterion values for Chi a are calculated from the model equation for DOm, rewritten here:
DOm = DO, + [di + d^2 log(Chlmn) + d^D + d4 log(DOCmn)](t - t0)	(15)
Deep water DO concentrations depend not only on Chi a concentration, but also on the depth of
the lake below the thermocline (D), DOC concentration (DOCmn), and length of time that has
elapsed since the establishment of stratification (t - to). A procedure for computing the day of
the year, tcr/t/ at which mixed layer habitat is cool enough for different species to move to
shallower water is also described above, highlighting the influence of lake location and elevation
35

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as additional factors to consider. Based on these models, Chi a criteria for different lakes vary
considerably depending on each lake's specific characteristics.
Prior to calculating a Chi a criterion, a threshold value for DOm must be selected. Existing EPA
recommendations specify that the 7-day mean minimum DO concentration should be at least
5 mg/L to support cold-water fish (US EPA 1986). This threshold is also consistent with DO
concentrations that fish have been observed to avoid in field studies (Coutant 1985, Plumb and
Blanchfield 2009). A thin layer of cool water with sufficient DO provides a critical refuge for fish
during the warmest periods of the year, and fish have been observed to seek out those cool
water refuges. Observations of fish in warm lakes during the summer have indicated that they
will congregate in cold water refuges as shallow as 30 centimeters (cm) (Coutant and Carroll
1980, Snucins and Gunn 1995, Baird and Krueger 2003, Mackenzie-Grieve and Post 2006).
Hence, maintaining a DO concentration of at least 5 mg/L at a depth of 30 cm below the
thermocline can provide a sufficient refuge for certain fish species and be protective of aquatic
life. To convert this condition to a value of DOm, EPA considered a simplified case in which DO
linearly decreases from saturated conditions above the thermocline (DO = 8.4 mg/L at 24 C) to
a concentration of zero at some deeper depth (Figure 18). The linear decrease in DO is
consistent with a steady-state solution of the diffusion equation, assuming a constant eddy
diffusivity (Stefan et al. 1995). Based on this DO profile and the requirement that DO is 5 mg/L at
30 cm below the thermocline, an illustrative threshold value for DOm can be computed as
1.6 mg/L for a lake that is 2 m deep below the thermocline. That is, when the temperature
profile is as depicted in Figure 18, depth-averaged DO computed for the water column below
the thermocline is 1.6 mg/L. Other thresholds for DOm specific to different species of fish and
different depths can also be calculated. For example, the threshold value for DOm for a lake that
is 10 m deep below the thermocline would be 0.3 mg/L.
36

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E
B co
Q.
a)
Q
Thermocline
0 2 4 6 8
DO (mg/L)
Figure 18. Simplified DO profile used to compute threshold for DOm. Open circle: the targeted condition of
DO at 5 mg/L, 30 cm below the thermocline.
The influence of different factors on Chi a criterion can be visualized by computing criteria at
median values of all covariates and then examining changes in criteria that occur with the
change in a single covariate. The relationship between Chi a and DOm at median values for all
other covariates are shown as solid lines in each panel of Figure 19. Lakes in which covariate
values differ from the medians of the data set cause changes in the candidate Chi a criteria. For
cool-water species, using the illustrative threshold temperature, the median number of days
between spring stratification and release of the temperature constraint in the mixed layer was
135 days. The 75th percentile of this day range, corresponding to lakes in warmer climates, was
151 days, whereas the 25th percentile, corresponding to lakes in cooler climates, was 116 days.
When the critical window for maintaining sufficient DO in the deeper waters decreases to 116
days, the corresponding Chi a criterion increases to 11 ng/L, whereas in lakes in which the
critical window is 151 days long, the Chi a criterion is 2 ng/L (left panel, Figure 19).
37

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oo
Depth below thermocline

E
o
O
CM
O
Days since stratification
E
O
Q
o
DOC

E
o
O
CM
O
1
Figure 19. Effects of other predictors on Chi a criteria. Solid lines: relationship between Chi a and D0m at
median values for all other variables; dashed line: D0m = 0.3 mg/L; dotted lines: 25th and 75th percentiles
of days elapsed since stratification (left panel), 25th and 75th percentiles of mean DOC concentrations
(middle panel), and depth below thermocline of 4 m and 20 m (right panel).
Similar ranges of criteria can be calculated for changes in DOC and the lake depth below the
thermocline. The median concentration of DOC in the available data was 5 mg/L, but in lakes in
which DOC is 3 mg/L (the 25th percentile of observed DOC in the data), the Chi a criterion
increases to 8 ng/L; and in lakes in which DOC is 7 mg/L (the 75th percentile), the Chi a criterion
decreases to 2 ng/L (middle panel, Figure 19). Finally, the median lake depth below the
thermocline was 9 m. In a deeper lake, with 20 m of water below the thermocline, the Chi a
criterion increases to 7 ng/L; but in a shallower lake, with only 4 m of water below the
thermocline, the Chi a criterion decreases to 3 ng/L (right panel, Figure 19).
To better illustrate the possible range of criteria, EPA computed illustrative Chi a criteria for
each of the dimictic lakes sampled in the NLA. Because those lakes represent a random sample
of the population of lakes in the U.S., the resulting Chi a criteria are a representative distribution
of criteria, providing insight into likely criteria for different types of lakes. For dimictic lakes
harboring cool-water species (again, using the illustrative temperature threshold), the median
Chi a criteria is 3.4 ng/L, and the range defined by the 25th and 75th percentiles is 1.3-10.6
Hg/L. For lakes harboring cold-water species, using the illustrative temperature threshold, the
median Chi a criterion is 1.8 ng/L, with a range of possible values extending from 1-7.6 ng/L.
In states where measurements of profiles of DO are available, these data can be readily
modeled in conjunction with the national data (see Appendix B). In the example shown in
Appendix B, modeling temporally resolved DO profiles from one state with the national data
improved the precision of estimates of the first day of stratification. Because of this
38

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improvement in model precision, the results of the combined state-national model are provided
in the interactive criterion derivation tool.
The interactive tool used for estimating candidate Chi a criteria is provided at
https://nsteps.epa.gov/apps/chl-hypoxia. With this tool, the user can specify lake physical
characteristics that influence the relationship between Chi a and DOm as well as management
decisions about targeted conditions that affect the criterion.
Considerations: Lake physical characteristics. Lake physical characteristics that are specified
include the lake location (latitude and longitude) and lake elevation. That information is
converted to an estimate of mean annual air temperature and, coupled with the model results,
these data provide an estimate of the date of spring stratification. Note, though, that this
estimate applied most accurately to dimictic lakes, and estimates of the first day of stratification
for other type of lakes (e.g., polymictic) are more uncertain and may require additional data.
Other lake physical characteristics that are specified are lake depth below the thermocline and
average lake DOC concentration, factors that influence DOm.
Water quality management decisions that influence the calculated criterion include parameters
that define fish habitat (i.e., the critical maximum temperature for fish species in the lake, the
threshold DO concentration, and the depth of the summer refugia) and the certainty level.
Considerations: Fish habitat. The critical maximum temperature for fish species in the lake is
used to calculate the average day of the year that temperature constraints are released in the
epilimnion. That is, the annual temperature model (see Figure 15) is used to identify the date
that fish can potentially move to oxygen-rich shallower waters. The threshold DO concentration
for the fish (e.g., a DO concentration of 5 mg/L for cold-water fish) and the desired minimum
thickness of the refugia (e.g., 30 cm) are used to compute the targeted condition for DOm. That
targeted value of DOm is the minimum concentration required on the days prior to the release of
temperature constraints.
Considerations: Certainty level. The certainty levels, as with other criteria, provide additional
assurance that the calculated criterion is protective, based on the data and model uncertainty.
For example, selecting the 50% certainty level implies that, at the estimated Chi a criterion, only
25% of predicted mean values of DOm, based on the data, were less than targeted value. In
statistical hypothesis testing, convention suggests that p-values of 1% or 5% are statistically
significant results, which can also inform the selection of the percentile, but selection of the
39

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certainty level as the basis for the criterion is ultimately a water quality management decision.
More conservative certainty levels (e.g., higher percentiles) may be appropriate when applying
this response in non-dimictic lakes in which the first day of stratification is more uncertain.
The interactive tool uses posterior simulation with model parameter distributions to predict the
DOm on the critical day prior to a release from temperature constraints in the surface layer for
different Chi a concentrations. These model results can be used to help derive criteria for a
specified threshold DOm. Samples with covariate values similar to those selected by the user are
highlighted in the provided plots in the app.
3.2.3 Microcystin Concentration
The model for microcystin relates Chi a concentration to a distribution of microcystin
concentrations. By specifying different targets for microcystin concentration, this model can
inform the derivation of criterion values for the protection of drinking water uses or recreational
uses.
3.2.3.1 Statistical analysis
A network of relationships can be specified that reflects current understanding of the linkage
between lake eutrophication (as represented by Chi a) and increased concentrations of
microcystin in individual samples (Figure 20). At the bottom of the diagram, cyanobacterial
biovolume is directly associated with microcystin. Cyanobacterial biovolume is then expressed
as the product of total phytoplankton biovolume and the proportion of the biovolume that is
cyanobacteria (i.e., the relative biovolume of cyanobacteria), which clarifies the nature of the
relationship between Chi a and cyanobacterial biovolume. More specifically, Chi a is directly
proportional to phytoplankton biovolume (repeating the relationship used in the zooplankton
model) (Kasprzak et al. 2008), and, as Chi a increases, the relative biovolume of cyanobacteria
has been observed to increase (Downing et al. 2001).
40

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(16)
(20)
(21)
Microcystin
Chi a
Cyanobacterial biovolume
Phytoplankton biovolume
Cyanobacterial relative
biovolume
Figure 20. Schematic showing relationship between different variables predicting microcystin. Numbers in
parentheses: refer to equation numbers in the text.
Each of the relationships in the network described above is expressed mathematically in the
Bayesian network. First, phytoplankton biovolume, P is modeled as being directly proportional
to Chi a concentration (Chi), in sample /':
Pi = kCiiChk	(16)
The reciprocal of the parameter kc,i is the average amount of Chi a per unit biovolume of
phytoplankton. Because the Chi a content of phytoplankton can vary with environmental
conditions and assemblage composition, different values of this parameter are estimated for
each sample, /'. The overall distribution of the set of values for kc,i is assumed to be log-normal
with a mean value of /Uk and a standard deviation of Ok.
Exploratory analysis indicated that a quadratic function provided a reasonable representation of
the relationship between the expected relative biovolume of cyanobacteria, pc, and Chi a as
follows:
E[logit(pci)] = A + f2chli + f2chl2t (17)
wherefi,f2, and f3 are coefficients estimated from the data.
Because laboratory replicates of P, and pC;, were available, uncertainty associated with measuring
phytoplankton and relative biovolume of cyanobacteria was estimated as follows:
log{Brrij) ~Normal(\og{Bi^j]), sx)	(18)
logit(jpmc j)~N ormal(logit(p c s2)	(19)
41

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where Bmj and pmCJ are the laboratory measurements of phytoplankton biovolume and
proportion cyanobacteria, respectively, and the index j maps replicate measurements to the
corresponding estimate of the true value of the measurement for sample /'. These laboratory
replicates are assumed to be normally distributed about their respective estimates of the
transformed sample means, with standard deviations of Si and ss, respectively.
Cyanobacterial biovolume (C) can then be expressed as the product of the relative biovolume of
cyanobacteria and total phytoplankton biovolume. After log-transforming, the expression is as
follows:
log(Cj) = log(fcCji) + log(pc [) + log(Chli)	(20)
where cyanobacterial biovolume in sample i is the sum of a log-transformed parameter kc, the
log-transformed cyanobacterial relative biovolume in the sample, and the log-transformed Chi o
concentration.
The final component of the model relates cyanobacteria biovolume to microcystin. Initial
exploration of the data indicated that microcystin increases at a rapid rate relative to
cyanobacterial biovolume at high levels of cyanobacteria. At low levels of cyanobacteria,
however, microcystin increases at a somewhat lower rate. To account for this change in rate,
microcystin was modeled with a piecewise linear model as follows:
log fcc,i) = 9(log (Q))	(21)
where the response variable in this relationship is Hmcj, the estimated mean concentration of
microcystin in sample /'. The function g(.) is the piecewise linear function, which is characterized
by four parameters: the intercept, di, and slope, d2, of the first segment; the point along the
gradient at which the slope changes, cp; and the slope of the second segment, d3.
The distribution of observed microcystin concentrations about the mean value was then
modeled as a negative binomial distribution as follows:
MCi~NB(nMCi,(p)	(22)
where MC, is the microcystin observed in sample i and NB(.) is a negative binomial distribution
with overdispersion parameter, cp. Because the negative binomial distribution specifies only
nonnegative integer outcomes, before fitting the model, EPA multiplied microcystin
measurements by 10 and rounded to the nearest integer. Microcystin measurements below the
42

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detection limit of 0.1 ng/L were set to zero (Yuan and Pollard 2017). Weakly informative prior
distributions were assigned to all parameters in the model.
3.2.3.2 Results
A total of 2,352 observations of microcystis cyanobacterial and phytoplankton biovolume, and
Chi a were available from the NLA data set for analysis. Those measurements were collected
from 1,116 different lakes spanning the conterminous U.S. An additional 112 samples of
laboratory replicates of phytoplankton and cyanobacterial biovolume measurements were
available to quantify measurement variability.
Three different relationships were estimated in the national model: (1) Chi a and phytoplankton
biovolume, (2) Chi a and cyanobacterial relative biovolume, and (3) cyanobacterial biovolume
and microcystin. (The relationship between phytoplankton biovolume, cyanobacterial relative
biovolume, and cyanobacterial biovolume required no statistical estimation.) The observed
relationship between Chi a and phytoplankton biovolume was accurately represented as a line
with a slope equal to 1 on log-log axes (left panel, Figure 21), similar to the relationship
estimated in the zooplankton model.
Cyanobacterial relative biovolume exhibited an increasing relationship with Chi a (middle panel,
Figure 21). The quadratic functional form allowed the model to represent the steepening of the
relationship at higher concentrations of Chi a. Mean microcystin increased with cyanobacterial
biovolume (right panel, Figure 21). The slope of the relationship increased at a cyanobacterial
biovolume of 1.9 mm3/L, but the 90% credible interval on the location of this changepoint
ranged from 0.5 to 5 mm3/L. At cyanobacterial biovolumes greater than the changepoint, the
slope of the mean relationship was statistically indistinguishable from 1, whereas at
cyanobacterial biovolumes less than the changepoint, the slope was 0.61, with the 90% credible
interval ranging from 0.51 to 0.69. Overall, the credible interval about the cyanobacteria-
microcystin relationship was narrow compared to those estimated for the Chi o-cyanobacterial
relative biovolume relationship as shown.
43

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_J
O)
=-
O
2
o
o
o
0.001
0.01
0.1
1
10
o
TJ
c
3
X!
as
o
o
o
O
o
o
o
1000
1
10
100
Chi a (jig/L)	Chi a (ng/L)	Cyano biovolume (mm3/L)
Figure 21. Modeled relationships for the microcystin model. Left panel: relationship between Chi a and
phytoplankton biovolume; open circles: observed measurements of Chi a and phytoplankton biovolume;
solid line: has a slope of 1. Middle panel: relationship between Chi a and cyanobacterial relative
biovolume; open circles: average cyanobacterial relative biovolume in ~20 samples at the indicated Chi a
concentration; solid line: estimated mean relationship; gray shading: 5th and 95th percentiles of the
distribution of possible mean relationships (i.e., the 90% credible interval); vertical axis: has been logit-
transformed. Right panel: relationship between cyanobacterial biovolume and microcystin; open circles:
average microcystin in ~20 samples at the indicated cyanobacterial biovolume; solid line: estimated mean
relationship; gray shading: 90% credible intervals about the mean relationship; small filled circles: Chi a
bins in which microcystin in all samples was zero.
3.2.3.3 Chi a criteria derivation
Chi a criteria to protect recreational uses and drinking water sources can be derived from the
estimated network of relationships by combining the model equations for total phytoplankton
biomass, cyanobacterial-relative biovolume, and microcystin and the uncertainty inherent in
each of the relationships (Figure 22). More specifically, based on a threshold concentration for
microcystin and an allowable exceedance frequency of that threshold, Equation (22) can be
used to compute the mean predicted microcystin that would be associated with these values.
Then, Equations (20) and (21) can be used to calculate the Chi a concentration associated with
this mean microcystin. This model is based on instantaneous measurements of Chi o,
cyanobacterial biovolume, and microcystin. To relate instantaneous Chi a concentrations to a
seasonal mean Chi a concentration, EPA computed the variance of Chi a concentrations within
lakes over the summer sampling season using repeat visits included in the NLA data set. Then,
the variance was used to estimate the probability of exceeding an instantaneous Chi a
concentration, based on the seasonal mean Chi a concentration.
Threshold concentrations for microcystin have been published, and those targeted conditions
can guide the use of the models to derive Chi a criteria. To protect sources of drinking water, the
EPA uses a health advisory that recommends a threshold concentration for microcystin of
0.3 |a,g/L for preschool children less than 6 years old (US EPA 2015b). This short-term health
44

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advisory does not include consideration of exposure to other sources (i.e., a relative source
contribution term). Typically, EPA would use an ambient water quality criterion (developed
under Section 304(a) of the CWA) as the endpoint for the protection of human health. The
criterion would include consideration of exposure through drinking water and fish consumed, if
both are designated uses for a waterbody. The criteria also provide estimates for only fish
consumption. Because human health criteria are not available for microcystins, EPA
recommends using the drinking water health advisory, recognizing that this threshold is an
underestimate of risk for water bodies where consumption of fish is an important route of
exposure.
O
O
o
o
o
Oo
o
o
o
o
c o
c o) <9
O "D O
OO
Q_ c CM
o
0.1	1	10	100	1000
Chi a (ng/L)
Figure 22. Example of derivation of Chi a criterion to protect recreational uses based on targeted
microcystin of 8 |jg/L and exceedance probability of 1%. Top panel-open circles: observed values of
microcystin and Chi a for samples in which microcystin was greater than the detection limit; solid line:
predicted microcystin that will be exceeded 1% of the time for the indicated Chi a concentration; gray
shading: 25th and 75th percentiles of the distribution of possible mean relationships (i.e., the 50%
credible interval); solid vertical and horizontal line segments: candidate Chi a criterion based on targeted
microcystin. Bottom panel: proportion of samples for which microcystin was not detected in ~100 samples
centered at the indicated Chi a concentration.
45

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The drinking water health advisory applies to finished drinking water, but national ambient
water quality criteria are designed to protect sources of drinking water. Human health criteria
focus on water sources prior to treatment for two main reasons. First, the ability of treatment
technologies to remove microcystin is too variable (Hoeger et al. 2005, Westrick et al. 2010, US
EPA 2015c) for EPA to set a national recommendation for a protective ambient source water
concentration that would yield a protective concentration after treatment. Second, consistent
with the core statutory objective of the CWA Section 101(a) " to restore and maintain the
chemical, physical, and biological integrity of the Nation's waters", the criteria are premised on
the position that ambient waters should not be contaminated to a level where the burden of
achieving health objectives is shifted away from those responsible for pollutant discharges and
placed on downstream users such as drinking water utilities to bear the costs of upgraded or
supplemental water treatment. EPA is aware that states or authorized tribes express water
quality standards for protecting drinking water sources as either protecting the ambient source
water before treatment or after treatment. If a state or authorized tribe applies the health
advisory standard to drinking water after treatment, then they can account for the expected
treatment in their facilities and select a higher microcystin concentration in the ambient source
water that would result in the targeted microcystin concentration in the finished drinking water.
Doing so will result in a concentration of Chi a in the ambient source water that will protect
human health from the effects of microcystin in the finished drinking water. To protect
recreational uses, EPA recommends a threshold concentration for microcystin of 8 ju,g/L to
protect children (US EPA 2019). This threshold was based on incidental ingestion of water during
recreation.
After selecting the designated use of interest, calculating the corresponding Chi a criterion
requires two additional management decisions: selection of the allowable exceedance
probability of the threshold and selection of a certainty level. These decisions are combined with
a posterior simulation using the estimated distributions of the model parameters to estimate
Chi a criteria.
Considerations: Allowable exceedance probability. The allowable exceedance probability can
be interpreted directly in terms of environmental outcomes as the probability of observing a
specified microcystin in a sample for a given seasonal mean Chi a concentration. For example,
after accounting for model uncertainty by selecting a 50% certainty level, microcystin in lakes
46

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with a seasonal mean Chi a concentration of 22 ng/L would be expected to exceed a threshold
of 8 ng/L in 1% of samples (Table 3) (solid vertical line in Figure 22). With daily sampling, one
interpretation of this result is that on average, microcystin would exceed the threshold 1 day
out of every 100, so 1 day during the swimming season for many states would not support
recreational use of the lake.
The frequency component of the recreational cyanotoxin criteria is specified in terms of
excursions of the criterion magnitude during 10-day assessment windows (US EPA 2019), in
which a water body is considered impaired for recreation when more than three excursions
occur in 1 year. If we assume initially that daily samples are independent events, we can
calculate the probability of at least one exceedance of the criterion magnitude in a 10-day
window, and then compute a seasonal probability associated with greater than three excursions
within all 10-day windows during a 100-day season. For example, if our single day exceedance
probability is 0.05, there is a 62% chance that we will observe greater than three excursions
during a 100-day season (Figure 23).
The initial assumption that daily samples of microcystin are independent from one another is
conservative, as we would expect that a day with a high concentration of microcystin would be
more likely to be followed by another day with high concentrations. That is, cyanobacterial
blooms and the associated increases in microcystin concentration are likely to be clumped in
time. This tendency for temporal autocorrelation may lower the computed seasonal
probabilities, as we would expect somewhat fewer excursions during 10-day assessment
windows if daily observations of elevated microcystin occur in groups. Overall, this information,
or similar calculations tailored to conditions within a particular lake can further inform the
selection of exceedance probability when deriving the candidate criterion.
47

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o
>>
lQ 
-------
differences in phytoplankton biomass among lakes can be associated with differences in both
Chi a and TP, yielding a strong correlation between the two (Lewis and Wurtsbaugh 2008). In
other lakes, high concentrations of suspended sediment can contribute to TP and affect
observed TP-Chl a relationships (Jones and Knowlton 2005). When TP-Chl a relationships are
being estimated, lakes with high concentrations of suspended sediment show low Chl:TP ratios
relative to the average pattern (Hoyer and Jones 1983, Jones and Knowlton 2005).
EPA modeled the relationship between TP and Chi a by explicitly accounting for the
contributions of different compartments to observed TP, resulting in the positions of TP and
Chi a in the model equation being reversed from the typical model formulations. The model
explained variations in TP in various compartments, rather than explaining variation in Chi a
(Yuan and Jones 2020b).
3.2.4.1 Statistical analysis
EPA specified a model that estimates contributions to TP from different compartments, where
TP is modeled as the sum of contributions from dissolved P, P bound to nonphytoplankton
sediment, and P bound in phytoplankton (Figure 24).
Chi
Turb
(23,24)
diss
Turb
(28,29)
np
TP
Figure 24. Schematic representation of compartment model for TP. PdiSS: dissolved P; Chi: Chi o; Turb: total
turbidity; Turbnp: turbidity attributed to nonphytoplankton sources. Shaded box for Turbnp: a variable
inferred by the model; numbers in parentheses: refer to equation numbers in the text.
Direct measurements of nonphytoplankton sediment were not collected during the NLA.
Instead, turbidity measurements were available that are associated with total suspended solids
and include contributions from both nonphytoplankton and phytoplankton components.
Because an estimate of nonphytoplankton sediment is needed to model TP, turbidity is modeled
as the sum of two components: (1) turbidity that is directly associated with phytoplankton
biomass, or autochthonous suspended sediment (Turbaut) and (2) turbidity associated with all
49

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other sources, or nonphytoplankton turbidity (Turbnp). The second component of turbidity
includes turbidity associated with allochthonous sediment and sediment resuspended from the
lake basin (Hamilton and Mitchell 1996). EPA modeled Turbaut as being directly proportional to
Chi a (Jones et al. 2008), a measure of algal biomass and, therefore, the components of turbidity
were expressed as follows:
E[Turb] = Turbnp + Turbaut = Turbnp + fChl	(23)
where E[Turb] indicates that the model applies to the expected value of turbidity (Turb). The
amount of Turbaut associated with each unit of Chi a is expected to vary with algal composition.
For example, small phytoplankton species would tend to scatter light differently than larger
species. Assuming that algal composition changes with trophic conditions (Godfrey 1982), the
change in algal composition can be modeled by expressing the coefficient/as an unknown
function of Chi a. Also, assuming that f(Chl) can be modeled as a power function (f= bChlm), the
product of f(Chl) and Chi a can be written as follows as bChlk without any loss of generality:
E[Turb\ = Turbnp + f(Chl)Chl = Turbnp + bChlk	(24)
where the exponent, k, is equal to m+1.
Exploratory analysis indicated that concentrations of Turbnp varied with different lake
characteristics, but the predictor that accounted for the most variability was lake depth.
Therefore, 30 classes of lakes based on maximum depths were defined, and the value of Turbnp
within each of the classes was modeled as a log-normal distribution about a mean value specific
to that depth class as follows:
\og(Turbnp)~Normal(jiaii, oa)	(25)
where jua /is the mean value of log(Turbnp) for depth class /', and oa is the standard deviation of
the distribution of individual measurements of Turbnp. The set of values for ^a,, was then
assumed to be drawn from a single normal distribution as follows:
Hai~Normal(n,	(26)
where ^ and a^ are the mean and standard deviation of this distribution. The mean distribution
loosely constrains the possible values of iua i, while allowing lakes with smaller amounts of data
to "borrow information" from lakes with larger amounts of data (Gelman and Hill 2007).
50

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Finally, sampling variability for Turb was assumed to be log-normally distributed as follows:
log(Turb) ~Normal(E[log(Turb)], aT)	(27)
where E[log(Turb)] is the expected value of log(Turb) expressed in Equation (24).
EPA used results from the model for turbidity simultaneously to estimate contributions to
different components of TP. Recall that TP is modeled as being composed of contributions from
dissolved P (Pdiss), P bound to suspended sediment, and P bound to phytoplankton. Based on this
assumption, the following model equation can be written:
E[TP] = Pdiss + g-^Turbnp + g2Chl	(28)
where the concentration of P bound to nonphytoplankton suspended sediment is modeled as
being directly proportional to Turbnp, and P bound to phytoplankton is modeled as being directly
proportional to Chi a. The coefficient gi quantifies the P content of Turbnp, while the coefficent
g2 expresses P concentration relative to Chi a concentration. P content is expected to vary with
the level of turbidity and the composition of the phytoplankton assemblage, so, similar to the
model for turbidity, the coefficients gi and g2 were allowed to vary as power functions of Turbnp
and Chi a, respectively. So, the final model equation can be written as follows:
E[TP] = Pdiss + djurb + d2Chln	(29)
Exploratory analysis indicated that dissolved P was associated with lake depth, so, similar to
Turbnp, different values of Pdiss were estimated for each of 30 lake depth classes as follows:
log(Pdiss,mn,i) ~ Normal^
iss> Gdiss )	(30)
where Pdiss,mnjis the mean dissolved P concentration in lake depth class i, and the overall mean
value of \og(Pdiss,mn,i) is /Udiss with a standard deviation of Odiss-
Exploratory analysis also indicated that the P associated with each unit of Turbnp and Chi a (i.e.,
the values of the coefficients di and d2) varied most strongly with geographic location. Because
of that trend, different values for these coefficients were estimated for different Level III
ecoregions. Ecoregion-specific values for these parameters were assumed to be drawn from log-
normal distributions as follows:
\og(du) ~ Normal(ndl, adl)
log(d2~ Normal(jj.d2, ad2)	(31)
51

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where the index, /', refers to values of each parameter for different ecoregions.
Finally, sampling variation for TP was assumed to be log-normally distributed as follows:
log(7T) ~ Normal(E[\og(TP)], aTP)	(32)
All the relationships described in this section on statistical analysis were fit simultaneously to
the available data with a hierarchical Bayesian model (Stan Development Team 2016). Prior
distributions for all model parameters were assumed to be weakly informative.
3.2.4.2 Results
Observations of turbidity were correlated with Chi a, and a distinct lower boundary in the
scatter of data was evident (Figure 25). The model relationship defining this lower boundary can
be computed by setting Turbnp to zero in Equation (24). Then, after log-transforming, the
equation can be written as log(Turb) = log(b) + klog(Chl). In other words, when Turbnp is
negligibly small, the relationship between Turbaut and Chi a is a straight line in the plot of
log(Chl) vs. log(Turb) (solid line in Figure 25). Deviations in sampled values above that line show
the contribution of Turbnptothe overall turbidity measurement. Mean values of fa and k
estimated from the model were 0.67 (0.62, 0.73) and 0.67 (0.65, 0.69) (90% credible intervals
shown in parentheses). Based on the functional form that was assumed for the relationship
between turbidity and Chi a, the contribution of phytoplankton to turbidity (i.e., Turbaut/Chl a)
was estimated as being proportional to Chi"033. That is, as Chi a increases, the amount of
turbidity associated with each unit of Chi a decreases, a trend that is consistent with a shift from
small-bodied, diatom-dominated assemblages to colonies of cyanobacteria cells (Scheffer et al.
1997).
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9) o
111111ii 1111111ii 1111111ii 1111111ii 1111111
0.1	1	10 100
Chi a (ng/L)
1000
Figure 25. Turbidity vs. Chi a. Solid line: the limiting relationship between Chi a and turbidity when
contribution of allochthonous sediment is negligible.
Estimates of Turbnp and mean dissolved P both exhibited decreasing relationships with increasing
depth (Figure 26). Turbnp decreased from approximately 1.4 nephelometric turbidity units (NTU)
in shallow lakes to nearly zero in deep lakes, while Pdiss varied from approximately 2.6 ng/L in
shallow lakes to 1.6 ng/L in deep lakes. Both of these relationships are consistent with a
mechanism by which fine sediment from the lake bottom is likely to be collected in surface
water samples in shallow lakes. In the case of Pdiss, the trend indicates that measurements of
dissolved and particulate components of TP are determined by filter size and P bound to
sediment fine enough to pass through the filter contributes to estimates of dissolved P.
CO
o
o
o
oou
TT-rr
1
-1	1	1IIn-|
10
Depth (m)
oooo o o o
I	1	1	1
CD
c\i
c\i
CM
C\j
O
c\i
O Cfc
o o
CP
t-^t
1
O o
O o
o o
-1	1	1III I I I
10
Depth (m)
Figure 26. Relationship between Turbnp, Pdiss, and lake depth. Open circles: mean estimate of parameter
value in each of 30 lake depth classes.
53

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The quantity of P bound to nonphytoplankton suspended sediment expressed by the coefficient
di exhibited substantial geographic variation (Figure 27). Coherent spatial patterns could be
discerned in the variation of di among different states, with relatively high levels of P content in
the upper Midwest region of the country (e.g., Montana, North Dakota, and South Dakota) as
well as in parts of the western mountains. Comparatively lower levels of P content were
observed in the northeast region of the U.S. Mechanisms for these large-scale variations in P
content are likely related to the underlying geology of soils in each region (Olson and Hawkins
2013). Values of d2, the amount of P within phytoplankton, spanned a much narrower range
than estimated for di, only ranging from 1.6 to 4.5 per unit of Chi a. The relative difference in
regional variability in the coefficients indicates that spatial differences in the amount of P bound
to nonphytoplankton suspended sediment account for more of the variability in TP-Chl a
relationships than spatial differences in P within phytoplankton, and the amount of P residing in
phytoplankton is relatively constant. The effects of differences in the amount of P bound to
nonphytoplankton sediment can be taken into account by computing ecoregion-specific TP
criteria.
log(d1)
2	3	4	5
Figure 27. Ecoregion-specific values of loge(c/i), P bound to nonphytoplankton suspended sediment.
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Limiting relationships that estimate the P content of phytoplankton biomass and Turbnp can also
be calculated (Figure 28), For phytoplankton biomass, the limiting relationship is calculated by
setting PdiSs and Turbnp in Equation (29) to zero, yielding the following log-transformed
relationship: log (TP) = log(d2) + n log (Chi). Different values of d2 were estimated for each
ecoregion, but the distribution of those values is characterized by an overall mean value of 2.5
(2.0, 3.1), while the mean value of the parameter n was 0.87 (0.82, 0.92). The straight line based
on the two parameter values represents P associated with phytoplankton biomass, as quantified
by Chi a, and it tracks the lower limit of the observed data (solid line, right panel, Figure 28). As a
limiting relationship, one would expect that the majority of values of TP would be greater than
this line indicates, but variability associated with the value of d2 causes some values of TP to fall
below the limit.
For Turbnp, setting Pdiss and Chi a to zero yields the following relationship: log(TP) = log(d1) +
rnlog (Turbnp). The mean value of the coefficient ch was 31 (23, 40), and the value of the
exponent m was 0.35 (0.32, 0.40) (left panel, Figure 28). Overall, the RMS error for predicting
loge(TP) was 0.52 for the model.
Figure 28. TP versus Turbnp and Chi a. Solid lines: the limiting relationship between the indicated variable
and TP; gray shaded areas: the 90% credible intervals about the mean relationship.
3.2.4.3 Phosphorus criteria
Two relationships between Chi a and TP that can be inferred from the TP model inform the
derivation of TP criteria. First, the limiting relationship between Chi a and TP estimated from the
model quantifies the amount of P that is bound to phytoplankton (see Figure 28). This
relationship predicts TP concentration in samples in which suspended sediment and dissolved P
0.001 0.1 1 10 100
Turbnp (NTU)
0.1
10 100 1000
Chi a (ng/L)
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concentrations are very low and defines the minimum value of TP that is associated with a
targeted Chi a concentration. This limiting relationship can also be interpreted as the Chi a yield
of P (Yuan and Jones 2019) and could be used to predict the change in Chi a that would
potentially result from a change in the amount of biologically available P in the water column
(Reynolds and Maberly 2002).
A second relationship between TP and Chi a accounts for contributions from P bound to
nonphytoplankton sediment. If lake depth is specified, then the relationship estimated between
lake depth and nonphytoplankton sediment can be used to estimate an average contribution to
TP from these other compartments in the water column (see Figure 26). The resulting
relationship then provides an estimate of the ambient TP concentration one would expect to
observe as a function of Chi a, and therefore, provides a TP criterion value.
The prediction of ambient TP that accounts for contributions from nonphytoplankton sediment
provides an estimate of the mean TP concentration that one would expect to observe for a
given Chi a (Figure 29). As such, this ambient TP concentration provides a criterion. (Illustrative
examples for TP criteria are shown in Table 4.) Note that contributions of Pdiss are not included in
predictions of ambient TP criteria. In many lakes PdiSS is composed of more biologically available
forms of P (e.g., soluble reactive P), and so, concentrations of Pdiss should be near zero in lakes in
which reductions in P loading would be expected to influence phytoplankton abundance.
1	10
Chla(ng/L)
1000
Figure 29. Example of deriving TP criteria for a Chi a target of 10 ng/L for data from one ecoregion
(Southeastern Plains). Open circles: all data; filled circles: data from the ecoregion; solid line: limiting TP-
Chl a relationship from compartment model; dashed line: ambient TP-Chl a relationship taking into
account contributions from nonphytoplankton sediment for a 3-m deep lake; solid horizontal and vertical
line segments: Chi a target and associated TP criterion; shaded areas: 80% credible intervals.
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Table 4. Illustrative example of TP criteria corresponding to data shown in Figure 29. Example TP criteria
for illustrative Chi a targets. TP criteria calculated for a 3-m deep lake.
Chi a target
80% certainty level
50% certainty level
10 Hg/L
21
22
15 Hg/L
28
30
The interactive tool for computing different TP criteria associated with Chi a is available at
https://nsteps.epa.gov/apps/tp-tn-chl. This tool allows the user to specify the targeted Chi a
concentration and the physical characteristics of the lake.
Considerations: Targeted Chi a concentration. The targeted Chi a concentration is the final
criterion value derived for the lake(s) of interest after consideration of the different designated
uses.
Considerations: Lake characteristics. Users can select the lake depth to be used when
computing TP criteria. The coefficients di and d2 characterize the amount of P associated with
nonphytoplankton suspended sediment and phytoplankton, respectively, and these coefficients
vary among ecoregions (Figure 27). Therefore, users also can select an ecoregion for computing
TP criteria. Data selected for an ecoregion are highlighted in the provided plots.
Considerations: Certainty level. Users can select a certainty level (as quantified by the credible
interval) to account for the effects of model uncertainty on the calculated criteria. Basing
criteria on the lower bound of the credible interval provides additional assurance that the
calculated criterion is protective, given the data and model uncertainty. For example, selecting a
certainty level of 50% dictates that the 25th percentile of the distribution of mean relationships
is used to compute the lower bound of the envelope of possible relationships. A criterion based
on this lower bound implies that only 25% of predicted TP concentrations at the selected Chi a
concentration were less than the criterion value. In statistical hypothesis testing, convention
suggests that p-values of 1% or 5% (corresponding to certainty levels of 99% and 95%,
respectively) are statistically significant results. Those practices can also inform the selection of
the percentile, but selection of the certainty level as the basis for the criterion is ultimately a
water quality management decision.
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3.2.5 Nitrogen-Chlorophyll a
Similar to the model for TP, each TN measurement is composed of N contained within three
compartments: N bound in phytoplankton, dissolved inorganic N (i.e., nitrate, nitrite, and
ammonia), and dissolved organic N (DON). Unlike the TP model, exploratory analysis indicated
that the N content of inorganic suspended sediment was negligible (Yuan and Jones 2019).
3.2.5.1	Statistical analysis
Field measurements of the difference between TN and dissolved inorganic nitrogen (DIN = NOx +
ammonia) were modeled as follows:
E[TN - DIN] = ftChlkl + DON = fcCM"1 + f2DOC	(33)
where variations in the observations of total N minus dissolved inorganic N (TN-DIN) are
attributed to two compartments: N bound in phytoplankton, modeled as fiChlkl and DON.
Exploratory analysis indicated that DON was closely associated with DOC, as they often originate
from the same watershed sources (Berman and Bronk 2003), so the concentration of DON was
modeled as being directly proportional to DOC.
As with the TP model, exploratory analysis indicated that the parameters fi and f2 varied most
strongly with geographic location. Because of those trends and to facilitate the use of this model
with local data sets, different values of fi, and f2 were specified for each Level III ecoregion:
lg(/i,i) ~ Normal(iin, afl)
lg(/2,i) ~ Normal{jif2, af2)	(34)
where the parameters jifi and jif2 estimate the mean values of the distribution of fi and f2 while
Ofi and Of2 estimate the standard deviations.
The sampling distribution of TN-DIN was assumed to be log-normally distributed as follows:
log(7W - DIN) ~Normal(E[log (TN - DIN)], aTN)	(35)
where oTn is the standard deviation of observed values of log(TN-DIN) about their expected
value.
3.2.5.2	Results
A total of 2466 samples collected from 1875 lakes were available for analysis. Values for the
coefficient, fi, quantifying phytoplankton N content ranged from 11 to 43 in different ecoregions
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with an overall mean value of 18.3 (14.9, 22.3). The values estimated for f2 spanned a greater
range among ecoregions with a minimum value of 35 and a maximum value of 103. The overall
mean value of f2 was 64.9 (61.0, 68.9). The broad range in values of f2 indicates that strong
differences exist among different locations regarding the nature of the relationships between
DOC and DON. The mean value of the exponent, kl, was 0.90 (0.86, 0.94).
To visualize the variability in phytoplankton N among ecoregions, the concentration of N bound
in phytoplankton at the overall mean Chi a concentration of 9.3 ng/L is mapped (Figure 30).
With the exception of one high value of 320 ng/L estimated for the Sand Hills, Nebraska
ecoregion, N-content of phytoplankton exhibited only small variations among ecoregions. N
content ranged from 83 - 185 ng/L with a median value of 136 ng/L. Coherent spatial patterns
in the N-content of phytoplankton were not evident.
Phytoplankton N
T	I	I
100	150	200	250	300
Figure 30. Variation in the concentration of N bound in phytoplankton among Level III ecoregions at the
overall mean Chi a = 9.3 ng/L. Gray scale shows N concentrations in ng/L.
Estimated DON concentrations at the overall mean DOC concentration of 5.6 mg/L ranged from
194 - 570 ng/L with a median concentration of 365 ng/L (Figure 31). Variations in DON among
ecoregions were substantially greater than observed for phytoplankton N. Spatial patterns were
I
59

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also evident, with higher concentrations of DON in the upper Midwest regions of the U.S. and
lower concentrations in the mountains in the western and eastern regions of the country.
DON
500
Figure 31. Variation in DON among Level III ecoregions at an overall mean DOC = 5.6 mg/L Gray scale
shows N concentrations in ng/L.
EPA calculated limiting relationships that estimate the N content of phytoplankton biomass with
a procedure identical to that used for TP (Figure 32). In this case, the limiting relationship was
calculated by setting the contribution from DON in Equation (33) to zero, yielding the following
log-transformed relationship: log(TN  DIN) = log^) + k log(Chl). The straight line based
on those two parameter values represents N associated with phytoplankton biomass, as
quantified by Chi a, and it tracks the lower limit of the observed data (solid line, left panel Figure
32).
Similarly, setting DIN and Chi a to zero in Equation (33) yields the following limiting relationship
for DON: log(7W) = log(/2) + log (DOC) (solid line, right panel Figure 32). The mean value of f2
indicates that, on average, the concentration of DON was 0.065 times that of DOC. Overall, the
RMS prediction error for loge(TN-DIN) was 0.37.
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o O
o
o
OcO
I
-	o
U)	o
=L	O
z
I-
oor
o
1
10
100
oo
o
o
I
^	o
O)	o
=L	O
z
H
oo
o
CO
Chi a (jj-9/L)	DOC (mg/L)
Figure 32. TN-DIN vs. Chi a and DOC. Solid lines: the limiting relationship between each variable and TN-
DIN; shaded area: the 95% credible intervals about this mean relationship.
3.2.5.3 Nitrogen criteria
The prediction for the ambient concentration of TN-DIN accounts for the increase in TN-DIN one
would expect with increased Chi a, but also includes contributions from DON (as estimated by
DOC) in the lake. Mean predictions for TN-DIN can be computed for different values of Chi a that
include average contributions from other sources of N in the water column. The value of this
ambient TN-DIN concentration that is associated with a targeted Chi a concentration then
provides a criterion for TN-DIN (Figure 33, Table 5).
Criteria for N concentrations are commonly expressed in terms of TN rather than TN-DIN. To
convert a criterion for TN-DIN to a criterion for TN, the availability of DIN for phytoplankton
uptake can be considered. More specifically, the components of DIN (NOx and ammonia) are
easily assimilated by phytoplankton and, when excess concentrations of DIN are observed in a
lake, it may indicate that factors other than N availability are limiting phytoplankton growth.
Therefore, controlling phytoplankton growth by reducing available N would first require that
DIN concentrations are reduced to near zero and, when that occurs, criteria expressed for TN-
DIN would be the same as those for TN. Furthermore, examination of NLA data indicated that
DIN concentrations were below the detection limit in 72% of samples, so TN-DIN was equivalent
to TN in most samples. Hence, in most cases TN monitoring data can be assessed relative to TN-
DIN predictions from the criterion models.
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0.1	1	10	100	1000
Chi a (ng/L)
Figure 33. Illustrative example of deriving TN criteria for a Chi a target of 10 ng/L for one ecoregion
(Southeastern Plains). Open circles: all data; filled circles: data from selected ecoregion; solid line: limiting
TN-DIN vs. Chi a relationship from compartment model; dashed line: mean ambient TN-DIN vs. Chi a
relationship taking into account mean DOC observed within the selected ecoregion: shaded area: 80%
credible intervals; horizontal and vertical solid line segments: Illustrative Chi a target and associated TN
criterion.
Table 5. Illustrative example of TN criteria corresponding to data shown in Figure 33.
Chi a target
80% certainty level
50% certainty level
10 Mg/L
380
390
15 Hg/L
440
450
The same interactive tool for computing different TP criteria also provides TN criteria associated
with Chi a (https://nsteps.epa.gov/apps/tp-tn-chl). This tool allows the user to specify the
targeted Chi a concentration, DOC concentration, and an ecoregion of interest. Finally, users can
select the certainty level (or, credible interval) to account for the effects of model uncertainty
on the calculated criteria. Data selected for an ecoregion are highlighted in the provided plots.
3.3 Duration and Frequency
The duration component of a water quality criterion is the length of time over which discrete
water samples are averaged to assess the condition of the water body. The frequency
component defines the number of times over a given time period that the specified magnitude
of the criterion can be exceeded while the water body is still assessed as being in compliance
with the criterion and maintaining designated uses. In conjunction with the magnitude of the
criterion, these additional components define a water quality criterion.
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Specification of duration and frequency components of numeric nutrient criteria is complicated
by the fact that the ecological effects of elevated nutrient concentrations usually arise from a
sequence of events. For example, higher nutrient concentrations increase the abundance of
phytoplankton. Over time, higher abundances of phytoplankton then increase the amount of
organic material in the deeper waters of a lake, and decomposition of the stored organic
material can reduce the concentrations of DO. In this case, the duration and frequency of
exceedance of a Chi a concentration in the mixed layer of the lake is related only indirectly to
the ecological effect of decreased DO and the ultimate reductions in the amount of habitat for
cool- and cold-water species. Contrast this example with the specification of duration and
frequency of toxic pollutants, for which the length of time and frequency of exposure to the
pollutant can be directly linked to effects on different organisms (e.g., mortality). A second
consideration arises from the variability of environmental measurements, for which estimates of
mean concentrations of Chi a, TN, and TP can only be estimated from a finite number of
samples. So, when specifying duration and frequency components of the recommended
numeric nutrient criteria, EPA considered both the timescale of the ecological responses and the
statistical uncertainty in estimating mean values.
The recommended duration for Chi a criteria derived from the models described in this
document is a growing season (typically summer) geometric mean value, consistent with the
summary statistic used for Chi a in the stressor-response analyses. The geometric mean was
selected to account for the fact that Chi a measurements are frequently log-normally
distributed. EPA used seasonal mean Chi a concentrations integrated over the photic zone for
analysis because timescales of ecological responses to increased nutrient concentrations are
long. For example, as described earlier, some of the increase in deep water oxygen demand
arises from accrual of organic material over long time periods while other oxygen demand arises
from recently created organic matter that settles through the water column. Mean Chi a
concentration in the lake is associated with mechanisms acting at both timescales, providing a
measure of the average amount of organic material supplied by the photic zone. Similarly,
systematic changes in zooplankton composition would be expected to occur at longer, seasonal
timescales. For the microcystin model, the basic unit of analysis was an individual sample, in
which the model predicted the probability of different microcystin concentrations in a sample,
given the sample's Chi a concentration. When estimating the relationship for computing criteria,
however, EPA computed probabilities of different individual Chi a concentrations as a function
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of seasonal mean Chi a concentration, again linking seasonal mean Chi a concentration to the
probability of deleterious effects. The long timescale of ecological response also supports the
use of other durations that characterize average Chi a over long period of time. For example, in
lakes with very long growing seasons, annual average Chi a may also be appropriate.
The unit of analysis for models relating Chi a to TN and TP concentrations was also the individual
sample, in that TN and TP concentrations measured within a water sample were described as
the sum of phytoplankton-bound N and P and other compartments in the sample containing
those nutrients. Because the models are expressed as simple sums of components, each one
remains applicable even if expressed in terms of seasonal averages. Hence, seasonal geometric
mean Chi a criteria can be converted to seasonal geometric mean TN and TP criteria using the
same model, and the recommended durations for TN and TP criteria are also seasonal mean
values.
EPA recognizes that seasonal geometric mean concentrations of Chi a, TN, and TP calculated in
different years can vary about their long-term means, and the frequency components of the
criteria can be used to account for this variability. For example, in a year with particularly high
precipitation one might observe higher than average loads of TP to downstream lakes. Similarly,
in a year with longer than average periods of sunshine one might observe higher rates of
accumulation of phytoplankton biomass and higher concentrations of Chi a. Sampling variability
and within-year temporal variability also can cause large variations in estimated seasonal
averages. Hence, in lakes in which long-term mean concentrations of Chi a, TN, and TP are
below the criteria, some seasonal mean concentrations might still exceed the criterion
magnitude. Variability in estimated seasonal mean concentrations can be addressed by
estimating interannual and sampling variability and incorporating it into the expression of the
criteria or in the assessment methods. More specifically, states may calculate adjusted criterion
magnitudes that are associated with allowable frequencies of exceedance based on the
observed variability of nutrient concentrations. For example, seasonal mean concentrations of
TP would be expected to exceed a criterion magnitude that is equal to the long-term mean in
approximately 50% of the years, whereas less frequent exceedances of a higher criterion
magnitude would be expected. Appendices D and E provide examples of calculations that
identify different combinations of criterion magnitudes and frequencies.
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4 Characterization
In an ecological risk assessment, during the risk characterization phase, the results from the
analysis are evaluated and the risk to ecological endpoints is described. In this section, general
issues associated with applying the criterion models are considered, so a broader scope of topics
is considered than is typically addressed during risk characterization. The topics include a
discussion of other measures of effect and exposure that were not used in the criterion models,
comparisons of current models with past models linking nutrients to Chi a, and limitations of the
criterion models. Specific topics associated with deriving criteria in states and authorized tribes
are also considered, including methods for incorporating local monitoring data into the national
models, methods for developing statewide criteria, and the specification of duration and
frequency components for the criteria.
4.1 Other Measures of Effect and Exposure
A variety of other measures of effect and exposure could be used for deriving nutrient criteria
associated with each of the pathways described in Figure 1 and Figure 2. In selecting the
responses for analysis, EPA considered (1) available data, (2) the current state of scientific
understanding of each pathway, and (3) the degree to which a pathway and a response could be
applied broadly to most lakes. For many possible measures of effect and exposure, data
availability was a key consideration. For aquatic life, direct measurements of fish assemblage
composition and biomass were not collected during the NLA, and the lack of those data limited
the potential for considering several pathways such as evaluating alterations in fish assemblage
composition because of reduced visibility. Lake benthic communities also exhibit changes along
a eutrophication gradient (Vadeboncoeur et al. 2003), but none of those data were available.
For recreational and drinking water source uses, the effects of other cyanotoxins (e.g.,
cylindrospermopsin, saxitoxin, anatoxin) might be important for certain lakes, but continental-
scale data for those other cyanotoxins were not available at the time of this analysis. In certain
lakes, cyanobacterial blooms have also been observed at depths below the surface layer
(Jacquet et al. 2005), but observations of phytoplankton at those depths were not available.
Similarly, organic matter generated by increased primary productivity can increase the
concentrations of disinfection by-products during the drinking water treatment process
(Graham et al. 1998, Galapate et al. 2001), and chemicals produced during blooms of certain
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algal species can introduce unpleasant taste and odors to drinking water (Graham et al. 2010).
However, continental-scale data pertaining to disinfection by-product precursors or taste and
odor chemicals were not available.
Insufficient scientific understanding of a causal pathway also limited consideration of certain
measures of effect and exposure. For example, scientific consensus is currently lacking on the
precise level of cyanobacteria that is harmful to aquatic life. That information gap limited the
utility of using cyanobacterial abundance as a final response measurement, despite the fact that
increased cyanobacterial abundance occurs frequently with nutrient pollution (Dolman et al.
2012). (Note, however, that cyanobacterial abundance measurements quantify a key step in the
model linking Chi a to microcystin.) Similarly, increased levels of cyanobacteria can cause rashes
on people who contact the water (Pilotto et al. 1997, Zhang et al. 2015, US EPA 2015b),
potentially affecting the use of a lake for recreation. However, precise quantitative relationships
between the occurrence of rashes and cyanobacterial abundance are not currently available.
For certain measures of effect or exposure, data were available, but other factors limited the
degree to which the response could be applied. For example, Secchi depth data were available
in the NLA data set, and that measure of transparency could have informed an assessment of
the aesthetic appeal of different lakes for recreation. That is, increased nutrient concentrations
cause increases in the abundance of phytoplankton that reduce water clarity and decrease the
aesthetic appeal of a lake (Carvalho et al. 2011, Keeler et al. 2015). Aesthetic considerations
have been used by others as a basis of water quality criteria (Heiskary and Wilson 2008) and
may be recommended for oligotrophic lakes in which maintaining historically high levels of
water clarity is a management objective (see, for example, https://www.epa.gov/tmdl/lake-
tahoe-total-maximum-daily-load-tmdl). However, the aesthetic expectations for the national
population of lakes depends on geographic location (Smeltzer and Heiskary 1990), and user
perception survey data at the continental scale of this analysis were not available. Similarly,
reducing the frequency of phytoplankton blooms has been cited as a motivation for controlling
nutrient loads (Bachmann et al. 2003), but aesthetic expectations regarding bloom frequency
were not available at the national scale.
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4.2	Incorporating State Data
State water quality managers are often interested in exploring relationships between
environmental factors and biological responses using locally collected monitoring data. In many
cases, leveraging knowledge from broader regional scales (e.g., national scale) can enhance local
understanding. This document describes recommended numeric nutrient criterion models
based on national data that link designated uses to Chi a, TN, and TP. The NLA data set provided
a comprehensive set of measurements collected from large numbers of sites with identical
protocols (US EPA 2011, Pollard et al. 2018), and the availability of consistent measures from
lakes spanning broad gradients facilitated the calculation of accurate national estimates of
relationships of interest. However, the number of samples is limited within the national data set
that is available to estimate relationships within any single state, and uncertainty in estimating
relationships specific to a single state is higher than that associated with the national models. In
contrast, monitoring conducted by state agencies can yield more intensive temporal sampling
over more sites, and hence, relationships estimated from those data can assist local
management decisions within that state. Data collected at the state level, however, can be
limited in the parameters that are measured, and the range of environmental conditions
sampled is limited by conditions occurring within the state boundaries.
All the recommended criterion models described in this document are formulated to facilitate
consideration of state data. State-specific values for certain coefficients in each model (e.g.,
Figure 34 in Appendix A) have been estimated, and local state, monitoring data can be used to
refine the estimates of state-specific coefficients, while remaining consistent with national
trends. Appendices A, B, and C discuss three examples of case studies in which state monitoring
data have been combined with national data to refine recommended criteria. State monitoring
data sets are each unique, and EPA is available to assist states in combining their monitoring
data with the national models.
4.3	Existing Nutrient-Chlorophyll a Models
Empirically estimated relationships between TP and Chi a concentrations have provided a basis
for lake water quality management for over four decades. This relationship was initially
identified in Connecticut and Japanese lakes (Deevey 1940, Sakamoto 1966), and subsequently
extended to a broad range of temperate lakes in the mid-1970s (Dillon and Rigler 1974, Jones
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and Bachmann 1976, Carlson 1977). Those early analyses regressed Chi a on TP concentrations
and reported similar coefficients showing the ratio of Chl:TP increased with lake trophic state.
Over time, many studies have explored the veracity of that relationship and assessed sources of
residual variation, testing the limits of applicability to different regions and lake types (Prairie et
al. 1989, McCauley et al. 1989, Jones and Knowlton 2005, Filstrup et al. 2014b). Variations in the
relationship have been attributed to differences in lake depth (Pridmore et al. 1985), TN:TP ratio
(Smith 1982, Prairie et al. 1989, Molot and Dillon 1991), grazing by zooplankton and mussels
(Mazumder 1994, Mellina et al. 1995), landscape characteristics (Wagner et al. 2011), and light
limitation (Hoyer and Jones 1983, Knowlton and Jones 2000, Havens and Niirnberg 2004).
Regional studies have evaluated the relationship as influenced by edaphic and climatic factors in
locations such as Canada (Prepas and Trew 1983), Argentina, (Quiros 1990), the United Kingdom
(Spears et al. 2013), and Europe (Phillips et al. 2008). Recently, lake classifications have
improved the precision and accuracy of this relationship (Yuan and Pollard 2014).
As described in Sections 3.2.4 and 3.2.5, EPA reformulated the nutrient-chlorophyll models to
account for variations in TP and TN, rather than in Chi a. The new models better account for
variability in measurements of TP and TN and are consistent with an understanding of the
components of TP and TN in the water column. The reformulated models cannot be directly
compared with earlier studies, including those cited previously. Estimates of N and P content of
phytoplankton, however, are consistent with values reported elsewhere (Yuan and Jones 2019).
4.4 Limitations and Assumptions
The recommended models for deriving numeric nutrient criteria are limited by the nature of the
data that underlie the analysis. First, nutrient data for each lake consisted of samples collected
at a single point, resulting in no information on within-lake spatial variability in nutrient
concentrations being included in the analyses. Nutrient concentrations within particular lakes
can vary considerably across different locations (Perkins and Underwood 2000), resulting in
criteria based on samples collected at the deepest point or midpoint of the reservoir that might
not be applicable to samples collected elsewhere. When deriving their criteria, states may
specify assessment methodologies to collect samples from different locations in the same lake
to address this issue and analyze those local data to account for spatial variability.
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Similarly, nutrient and response data used in the current analysis were collected only in the
summer, so monitoring data assessed with respect to these recommended criteria may also be
limited to summer data. Nutrient concentrations in some lakes can vary considerably between
summer and winter (S0ndergaard et al. 2005), and states may specify assessment protocols to
ensure that only data collected in the summer are compared with criterion concentrations. In
other locations, much longer growing seasons exist, and annual average nutrient and Chi a
concentrations are comparable to summer averages.
As noted earlier, most of the statistical criterion models described here combine the effects of
spatial, temporal, and sampling variability and estimate a single value for each model that is
applicable to all lakes in the data set. The components of variability, however, might differ
across lakes and affect the resulting criteria. For example, spatial variability in complex, dendritic
reservoirs can be much greater than in simple, circular lakes (Gloss et al. 1980). In most cases,
local monitoring data can inform and potentially improve the parameter estimates both for
specific locations and for groups of lakes. Segmenting lakes with complex morphology into
discrete, more homogeneous areas may also help address issues with spatial variability.
The uncertainty estimated for each modeled relationship is associated with the number of
samples used in the model, and consideration of sample size can affect the interpretation of the
resulting criteria. For example, the number of NLA samples within a single Level III ecoregion can
be small. The hierarchical structure of the model does improve the precision of model estimates
in those ecoregions, but the precision of TP and TN criteria specific to ecoregions with small
amounts of data could be further improved by including state monitoring data. Additional
national-scale data such as that from the 2017 NLA may also be incorporated as they become
available to improve model precision.
Recommended criteria based on the drinking water health advisories for microcystin
incorporate some conservative assumptions that affect the final values. The recommended
criteria are intended to reflect the ambient water quality conditions that protect a drinking
water use before treatment. They do not, however, account for the varying levels of treatment a
drinking water facility can implement to remove microcystin before generating finished drinking
water, the condition of the water to which the cyanotoxin health advisories apply. As a
precautionary step, a drinking water facility may implement treatment protocols that minimize
the breakage of cyanobacteria cells (Chow et al. 1999, Westrick et al. 2010) which, in turn,
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would minimize the release of intracellular microcystin into the treated water. EPA based the
recommended models on the total microcystin present in the NLA samples, both dissolved in
the water and within cyanobacterial cells, which necessitated the lysis of cyanobacterial cells
prior to microcystin quantification. In contrast, breakage of cyanobacterial cells is a process that
some drinking water treatments for cyanotoxins are designed to limit. Criteria based on the
national models provide protective water quality conditions in the source water, but
concentrations of microcystin that slightly exceed health advisory values can be further reduced
in the finished drinking water through carefully engineered and operated source water
treatment processes.
Recommended criteria derived using the models described here provide concentrations that,
when exceeded, are associated with a loss of support for designated uses, but the models do
not provide information regarding appropriate remediation actions. Indeed, among lakes in
which the criteria are exceeded, appropriate remediation actions will likely differ. In some lakes,
the magnitude of N loading from anthropogenic sources is small, while P loading is large, and
cyanobacteria supply N to the system via fixation (Schindler et al. 2008). In those lakes,
reductions in P loading might be the appropriate water quality management action. In other
lakes, ample supplies of N from anthropogenic sources are available, and management actions
might need to focus on reducing both N and P loading (Ferber et al. 2004). In some lakes, excess
N in the form of inorganic nitrogen (NOx or ammonia) is abundant, and the presence of high
concentrations of DIN might provide insights into the effects of different management
interventions. For example, DIN is readily taken up by phytoplankton, so the presence of large
concentrations of DIN might indicate that other factors, such as light availability, limit
phytoplankton growth. In those cases, initial reductions of N loading to reduce NOx might be
necessary before the effects of N control can be observed.
4.5 Deriving State-Specified Criteria
Criteria derived from the recommended national models vary with differences in lake
characteristics (e.g., depth and ecoregion), and specifying a single set of criteria applicable to all
lakes in a state might not account for those variations. Methods for deriving criteria that
account for natural variations among water bodies are already available, and these methods can
be applied to ensure that appropriate criteria are applied to different types of lakes. First, states
can classify water bodies and derive different criteria for each class of water body. The
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recommended national models facilitate the classification of lakes by providing specific insights
into the factors that most affect the derivation of protective numeric nutrient criteria.
Furthermore, the national models can be used to compute criteria for different lakes in a state
to provide information about the types of lakes for which criterion magnitudes are most similar.
For example, different recommended criteria for TP and TN are associated with different Level
III ecoregions; however, among the ecoregions within one state, the difference in criterion
magnitudes might be small enough to specify a single set of criteria applicable to multiple
ecoregions. Second, site-specific criteria can be specified for a small number of lakes with
characteristics that differ substantially from the rest of the lakes in a state. Here, too, the
recommended national models provide the means of deriving these criteria for individual lakes.
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Appendix A: State Case Study: Chlorophyll a-Microcystin
This case study in Iowa describes chlorophyll a (Chi a) and microcystin data collected by the
Iowa Department of Natural Resources (IDNR) that are combined with national data to estimate
a stressor-response relationship for the state (Yuan and Pollard 2019).
A.l Data
Chl a measurements in Iowa were collected as part of an ambient lake monitoring program
conducted by IDNR. Water samples were collected with an integrated water column sampler
above the thermocline, when present, to a maximum depth of 2 meters (m) at the deepest
point of each lake. Lake water samples were collected in the summer (May-September). An
aliquot of the water sample was analyzed for Chl a in the laboratory by non-acidified
fluorometry after filtering water samples through GF/C filters. In a separate IDNR monitoring
program, microcystin concentrations are sampled regularly at swimming beaches in Iowa during
the summer. This sampling effort includes state park beaches and locally managed beaches
across the state. Microcystin was quantified in composite water samples collected at nine
different locations on three transects spanning the swimming beach. On each transect, samples
were collected at depths of 0.15, 0.5, and 1.0 m. Chl a and microcystin samples were matched
by lake and sampling date for use in the analysis. To maximize the available data, microcystin
and Chl a measurements collected within 1 day of each other were included as matched
samples.
A.2 Statistical Analysis
The structure of a statistical model that accommodates data collected at different spatial scales
must be defined to ensure that the available data appropriately inform model estimates.
Consider the case of a large national data set of approximately 1,000 samples and a state data
set of approximately 50 samples. If the two data sets were pooled, the national data would
dominate the state data simply because of the larger sample size, and the state data would
exert a weak influence on the model. In any single state, however, only about 20 samples from
the national data might be available, and we would expect the state data to dominate
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estimates. Defining a hierarchical structure in the model helps ensure that each data set exerts
the appropriate influence on the model results (Gelman and Hill 2007).
A second issue that arises from combining data sets is that different measurements are often
collected in the different data sets. This problem is addressed in the national models by
modeling a comprehensive network of relationships between different parameters to take
advantage of the many different measurements available in the National Lakes Assessment
(NLA) data (Qian and Miltner 2015). Then, state data sets in which only a subset of
measurements were collected could still be feasibly modeled by informing specific aspects of
the network.
State data from Iowa were included in the national model and inform estimates of relationships
in the same network. As mentioned earlier, however, only Chi a and microcystin measurements
were available in the Iowa state data set. To prevent over-specifying the model, EPA selected
one of the relationships in the network that could be refined with data from the state. The
relationship between Chi a and the relative biovolume of cyanobacteria relied most heavily on
empirical calibration, so it was selected for refinement with state data. More specifically, the
national model was revised so that model coefficients specific to each state were estimated
(Equation (17)).
E[logit(pCii)] = fim + f2,mchli + f3ikli]chlf	(36)
where different values of each of the coefficients were estimated for each state in the United
States, k. The values of the coefficients for each state were constrained by normal distributions
defined by the parameters, and Of. For example, the set of state-specific coefficients for/j
were drawn from a single normal distribution as follows:
/1~WormaZ(Ju^i,oyi)	(37)
Identical expressions can be written for the set of f2 values and f3 values. These distributions
constrained the range of possible values so estimates of those parameters computed with
relatively small sample sizes within individual states can "borrow" information from estimates
computed from other states (Gelman and Hill 2007).
Iowa state data were included in the model by noting that the data should inform estimates of
the coefficients only in the state of Iowa. That is, estimates of fi,f2, and f3 from Equation (36) in
Iowa are based on both the Iowa state data set and NLA data collected in Iowa. In other states,
A-2

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estimates of the coefficients are based only on NLA data. The influence of Iowa state data on the
national distributions of the coefficients (as characterized by /Uf and Of) is limited because the
data affect only one element of the overall distributions of coefficients. Within the state of Iowa,
however, the coefficients can be fit to maximize the predictive accuracy of the overall
relationship linking Chi a to microcystin for both Iowa data and NLA data collected in Iowa, while
remaining consistent with the range of possible values observed across all states.
One final difference in fitting the Iowa state data is that several sources of variability modeled
separately in the national model (e.g., Si and s2 in equations (18) and (19)) are combined into
one estimate of residual variability. This combination of error terms reflects the data available
from Iowa, in which no laboratory replicates or direct measurements of cyanobacterial
biovolume were available. Hence, one lumped source of variability was estimated.
For comparison, a simple bivariate model was fit using only IDNR data, in which microcystin
concentration was modeled as a quadratic function of Chi a.
A.3 Results
A total of 556 samples of Chi a were measured at 28 lakes in Iowa. In some lakes, microcystin
concentrations were sampled at different beaches, so 686 observations of microcystin were
matched to the Chi a measurements.
In the revised national model with state-specific relationships between Chi a and the relative
biovolume of cyanobacteria, coefficients varied substantially among states. Because coefficient
values for quadratic relationships are not easily interpreted, the predicted mean cyanobacterial-
relative biovolume at a Chi a concentration of 20 microgram per liter (ng/L) is plotted to
visualize the range of variation among states (Figure 34). For comparison, among all the national
data, mean cyanobacterial-relative biovolume was 0.18 at Chi a concentration of 20 ng/L.
Systematic changes in cyanobacterial-relative biovolume with latitude or longitude were not
evident, but some regional differences were observed. For example, cyanobacterial-relative
biovolume for a Chi a concentration of 20 ng/L in Northeast states was generally lower than
elsewhere, whereas in Midwest states, it was somewhat higher.
A-3

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PropCyano
-120	-100	-80
Longitude
Figure 34. Variation in the relationship between Chi a and cyanobacterial-relative biovolume among
states. PropCyano: predicted mean relative biovolume of cyanobacteria at an illustrative Chi a = 20 ng/L.
As described previously, the relationship between Chi a and cyanobacterial relative biovolume
in Iowa was adjusted to maximize the accuracy of the predicted microcystin. Inclusion of Iowa
data reduced the magnitude of the slope of the relationship between Chi a and cyanobacterial-
relative biovolume but increased the intercept (Figure 35). So, higher values of cyanobacterial-
relative biovolume were observed at Chi a concentrations less than about 10 ng/L. At higher Chi
a concentrations, inclusion of Iowa state data did not substantively change the predicted
cyanobacterial-relative biovolume. Overall, in Iowa, the estimated relationship between
cyanobacterial-relative biovolume and Chi a was statistically indistinguishable from a constant
value (Figure 35). The addition of the state data also narrowed the range of the credible
intervals, as would be expected.
A-4

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1	10	100
Chi a (ng/L)
Figure 35. Comparison of Chi o/cyanobacterial-relative biovolume relationships in Iowa. Filled gray: 90%
credible intervals for estimate of relationship using only NLA data collected in Iowa; solid and dashed
lines: mean and 90% credible intervals for estimate of relationship using both Iowa state and NLA data.
The predicted mean relationship between Chi a and microcystin in Iowa from the state-national
model closely followed the observed data (left panel, Figure 36), exhibiting a slight increase in
slope as Chi a concentration increased. The 90% prediction intervals shown in the plot were
based on the mean values of repeated random draws of 15 samples from the predicted
distribution to replicate the plotted observed data. The intervals were broad and included most
of the estimated mean values. The curvature observed in the simple bivariate fit between Chi a
and microcystin using only Iowa data was opposite of that observed from the state-national
model, predicting that the rate of increase in microcystin was lower at high Chi a concentrations
than at low Chi a concentrations (right panel, Figure 36). The 90% prediction intervals of this fit
also included most of the observed mean values, but qualitatively, the simple bivariate model
did not match the observed data as closely as did the state-national model.
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1	10	100
Chi a (ug/L)
1	10	100
Chi a (ug/L)
Figure 36. Comparison of predicted relationship between Chi a and microcystin for the state-national
model (left panel) and a model using only Iowa state data (right panel). Open circles: average microcystin
concentration computed in ~15 samples at the indicated Chi a; solid lines: mean relationship; dashed
lines: 5th to 95th percentiles of distribution of means of 15 samples drawn from predicted distribution.
Three features inherent to the model combining state and national data are likely responsible
for the improved predictions of observations in the Iowa data set. First, the network of
relationships specified in the national model define a nonlinear function linking Chi a to
microcystin that yielded a curved mean response (left panel, Figure 36). When only Iowa data
are available, no information regarding the functional form of the relationship between Chi a
and microcystin is known. Hence, it is difficult for the model to identify the correct shape of the
curve. Indeed, the concavity of the mean relationship identified by the model using only Iowa
data (right panel, Figure 36) was opposite of that estimated in the combined state-national
model. Second, the network of relationships in the state-national model provided information
regarding unobserved variables and relationships that could be used in lieu of direct
observations. In this example, the relationships between Chi a and total phytoplankton
biovolume and between cyanobacterial biovolume and microcystin were supplied by the
national model. The Iowa-only model lacked the benefit of the additional information, and
hence, for this model a direct relationship between Chi a and microcystin had to be estimated
that aggregated the different causal linkages. Finally, the hierarchical structure of the national
model placed constraints on the range of possible values for parameters estimated within each
state. These constraints limited model parameters for the state data set to values that were
generally consistent with national parameters.
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A.4 Criteria Derivation
Derivation of a recommended Chi a criterion based on decisions such as allowable exceedance
rate, targeted microcystin, and model uncertainty follows an identical process as described for
the national model. The model based on both IDNR data and NLA data yields a slightly different
relationship from the model estimated from only the national data (Figure 37). Slightly greater
uncertainty accompanies the estimate of the mean relationship in the Iowa-NLA model than the
estimate in the NLA-only model (see Figure 22), and that uncertainty is reflected in a broader
range of possible Chi a criteria. In the example shown in Figure 37, to maintain a maximum
exceedance rate of 1% of microcystin of 8 ng/L, the Chi a criterion associated with the bound of
the 50% credible interval was 14 ng/L.
O
O
o
o
o
o
=	O
O	Q)
'tl	0 ^
O	"D o
Q_ C= C\J
OO O
1	10	100
Chi a (ng/L)
Figure 37. Microcystin and Chi a measurements in Iowa. Top panel-open circles: observed values of
microcystin and Chi a for samples in which microcystin was greater than the detection limit; solid line:
predicted microcystin that will be exceeded 1% of the time for the indicated Chi a concentration; gray
shading: 50% credible interval about mean relationship; horizontal and vertical line segments: candidate
Chi a criteria based on targeted microcystin. Bottom panel: proportion of samples for which microcystin
was not detected in ~100 samples centered at the indicated Chi a concentration.
A-7

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Appendix B: State Case Study: Chlorophyll a-Hypoxia
This case study in Missouri describes national and state data that are combined to refine
estimates of the relationship between chlorophyll a (Chi a) and deep water hypoxia. As
described in Section 3.2.2, mean concentrations of dissolved oxygen below the thermocline
(DOm) decrease with time during the period of summer stratification. The sampling design of the
NLA allowed for one visit to most of the lakes, so estimating temporal changes in deep water
DOm in the national model required a space-for-time substitution. State monitoring data
collected during multiple visits to a smaller number of lakes provided an opportunity to directly
estimate temporal changes in DOm and to compare the relationship between eutrophication and
the rate of oxygen depletion with estimates from NLA data.
B.l Data
The Missouri data considered in this case study were collected an average of 3-4 times per year
by the University of Missouri (MU) from 1989 to 2007 as part of a statewide monitoring effort.
Samples were collected near the dam for each reservoir (herein referred to as lakes for
simplicity), where vertical profiles for temperature and DO concentration were measured (YSI
model 51B or 550A meters). Composite water samples from a depth of approximately 0.25
meter (m) were transferred to high density polyethylene containers, placed in coolers on ice,
and transported to the MU Limnology Laboratory. There, a 250-milliliter aliquot was filtered
(Pall A/E) for determination of total Chi a via fluorometry following pigment extraction in heated
ethanol (Knowlton et al. 1984, Sartory and Grobbelaar 1984). A total of 198 measurements of
DOm were available for analysis, collected at 20 different lakes over 62 unique lake-year
combinations.
B.2 Statistical Analysis
The same model equations used in the national model were applied to data collected in
Missouri:
(38)
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where DO0 is the value of D0m at the start of spring stratification, volumetric oxygen demand
(VOD)k is the net imbalance in the volumetric oxygen budget for lake k corresponding to sample
/' expressed as milligrams per liter per day of DO (Burns 1995), t, is the date that sample /' is
collected, and t0j- is the date of the beginning of stratification for lake-year j. Observed values of
DOm were assumed to be normally distributed with a standard deviation of about the
expected value. Note that, like the national model, VOD is assumed to be constant for each lake,
but the date of the beginning of stratification varied by year and lake. The model equation
specifying the relationship between Chi a, dissolved organic carbon (DOC), and lake depth and
VOD was the same equation used in the recommended national model (see Equation (11)). As
with the national model, saturation DO concentrations at the minimum temperature in Missouri
were used to set the value of DO0.
The treatment of DO measurements less than 2 milligrams per liter (mg/L) in the Missouri data
differed from the approach used in the NLA. From 2 to 14 measurements of DOm greater than
2 mg/L were available in the Missouri data set for each of the lake-years included in the model,
so data were available to directly estimate temporal changes in DOm. Because data were
available at each lake before DOm approached zero, measurements of DOm that were less than
2 mg/L could be excluded without biasing the model results.
Two models were run to explore the effects of combining Missouri data with the national
model. In the first model, only Missouri data were used, and in the second model, both Missouri
and NLA data were used to estimate the parameter values.
B.3 Results
The range of values spanned by each of the covariates differed between the two data sets.
Missouri measurements were collected over a broader range of days than the NLA, whereas
lakes sampled by the NLA covered a broader range of Chi a concentrations (Figure 38).
Variations in DOC concentrations and depths below the thermocline were also narrower in the
Missouri data than in the NLA data. Those differences in the range of observations were
reflected in the strength of correlation between each covariate and DOm. For Missouri, sampling
day was most strongly correlated with DOm, whereas for the NLA, sampling day exhibited the
weakest correlation with DOm. Instead, in the NLA data, Chi a, DOC, and the depth below the
thermocline were all more strongly correlated with DOm.
B-2

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o
Q
O
Q
OO^Oo
I2e 8
rrTT~
0.1
1	'1 1 T
1	10
Chi (ug/L)
8 o
n O
Or
O qqO
0Oc5P.c
o 0 S *
 o?.f
O 00 &o  fc  o 
-IS?
X)0 O
& 8)
n	1	1	1	1	!	r
0	10 20 30 40 50 60
Depth below thermocline (m)
Figure 38. Observed DOm vs. Chi a, sampling day, DOC, arid depth below the thermocline. Open circles:
NLA data; filled circles: Missouri.
The first day of stratification for Missouri lakes was generally earlier than for most of the
dimictic lakes considered in the national model (Figure 39), a finding that is consistent with the
fact that Missouri is located at the southern end of the geographic distribution of dimictic lakes
(see Figure 7). Both the Missouri-only model and the NLA-only model yielded similar estimates
of the relationship between Chi a and VOD [d2 in Equation (11)) (Figure 40), and the estimate
based on the combined data sets improved further on the precision. Estimates of coefficients
characterizing the relationship between VOD and depth below the thermocline (d3) and DOC (d4)
were much more precise in the NLA-only data set than in the Missouri-only data set. Hence, the
estimate based on the combined data set mainly reflects the trends in the NLA data.
B-3

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o
"=fr
o
>> 
o
c
> 
o
c

-------
150
Day of year
200	250
Day of year
140 160 180
Day of year
T	1	1	T~
140	160	180	200
Day of year
"I	1	1	1	1	1	1	r
80 100 120 140 160 180 200 220
Day of year
"I	1	T
80 100 120 140 160 180 200
Day of year
Figure 41. Relationships between day of year and DOm for six Missouri lakes. Different line and symbol
colors in each panel correspond to data collected within different years with at least three samples. Open
gray circles: other samples collected at each lake.
B.4 Criteria Derivation
The utility of combining Missouri and NLA data to inform decision-making is evident when one
considers the predicted relationship between Chi a and DOm calculated using parameter
estimates from the Missouri data and from the combined Missouri-NLA data set (Figure 42). In
the example shown, the relationship is calculated based on illustrative values for other
covariates (depth below thermocline at 10 m, DOC at 1.6 mg/L, and time between spring
stratification and sampling at 130 days). Because use of both data sets improves the precision of
model parameters, the resulting mean relationship is also estimated with increased precision
and a targeted Chi a concentration can be identified with greater confidence. In this example,
the 50% credible interval for the targeted Chi a concentration corresponding to an illustrative
threshold of DOm = 0.1 extends from 5.5-8.9 ng/L when the combined model is used. When
using only Missouri data, the interval expands to 4.5-9.7 ng/L.
B-5

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3 4 5
Chi (ng/L)
,n
910
Figure 42. Relationship between Chi a and DOm in an illustrative lake with depth below thermocline at
10m, DOC at 1.6 mg/L, and 130 days after spring stratification. Gray shading: 50% credible intervals about
mean relationship from combined Missouri-NLA model; dashed line: 50% credible intervals about mean
relationship from Missouri-only model; dotted line: DOm = 0.1 mg/L
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Appendix C: State Case Study: Total Nitrogen-Chlorophyll a
This case study in Iowa examines how combining locally collected measurements of total
nitrogen (TN) and chlorophyll a (Chi a) with the national models can refine predictions
calculated from these local data sets.
C.l Data
Data used for this case study were collected by the Iowa Department of Natural Resources
(IDNR) as part of their routine monitoring program. For each lake in the data set, TN, nitrate-
nitrite, Chi a, and dissolved organic carbon (DOC) values were measured. A total of 968
observations collected at 31 different lakes were available for analysis.
C.2 Statistical Analysis
The same model formulation provided in Equation (33) was applied to the IDNR data, expressing
TN-dissolved inorganic nitrogen (-DIN) as the sum of a phytoplankton compartment, modeled as
fiChlk, and a dissolved organic nitrogen (DON) component, modeled as f2DOC:
E[TN - DIN] = fcCM" + DON = fcCM" + f2DOC	(39)
DOC measurements were available only at a small proportion of Iowa lakes, so EPA simplified
the national model to the following form for modeling Iowa data:
E[TN - DIN] = fcCM" + u	(40)
where u is a lake-specific constant representing the contributions of DON in each lake to
observed values of TN-DIN. Recall also that, in the national model, the coefficient fi varied
across states. With the IDNR data set, multiple samples were collected from each lake, so the
model could be refined further to estimate a value of/i for each lake as follows:
lg(/ij) ~ Normal{nfl IA, ofl)	(41)
where the index, j, refers to different lakes, and the mean value iXfijA is computed for data
collected in Iowa.
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To examine the effects of considering local state data in the context of the national model, two
models were fit. In the first model, only IDNR data were used to estimate the coefficients. In the
second model, relationships were fit to both the IDNR data and NLA data simultaneously. The
exponent k was modeled as being the same in both the IDNR and NLA data, while the
coefficients fi for each lake were estimated with IDNR data and NLA data collected within Iowa,
and the value of iXfijA was constrained by the national distribution among all the states in the
NLA data.
C.3 Results
Data collected during the NLA in Iowa and by IDNR spanned similar ranges of Chi o, TN-DIN, and
DOC (Figure 43). The limiting relationship between Chi a and TN-DIN estimated using only IDNR
data approximated the lower edge of the cloud of points (gray shading) but were estimated with
more uncertainty than when estimated using both IDNR and NLA data (solid lines). The mean
limiting relationships between Chi a and TN-DIN estimated with the two models were
statistically indistinguishable from one another.
Figure 43. Chi a vs. TN-DIN in Iowa. Open circles: data collected by Iowa DNR -filled circles: data collected
by NLA in Iowa; solid lines: 95% credible intervals for limiting relationships between Chi a and TN-DIN
estimated using both NLA and IDNR data; shaded gray area: 95% credible intervals for limiting
relationships estimated using only IDNR data.
The root mean square (RMS) prediction error of log(TN-DIN) measurements in the IDNR data
was the same for the models using only IDNR data (RMS = 0.27) and the combined Iowa - NLA
data (RMS = 0.27), indicating that imposing national constraints on the parameter values did not
improve the accuracy of predictions at the scale of the local state data. Uncertainty about
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estimates of the relationship between TN-DIN and Chi a for individual lakes was very similar
(example shown in Figure 44), indicating that a sufficient number of samples was available for
each lake to estimate the relationship without the information provided by the national model.
/ /
_l
z
o o
1 8
z
H
10	100
Chi a (|ig/L)
Figure 44. Chi a vs. TN-DIN in Beeds Lake, Iowa. Open circles: observed data; gray shading: 90% credible
intervals for predicted relationship based on only IDNR data; solid lines: 90% credible intervals for
predicted relationship using both IDNR and NLA data.
C.4 Criteria Derivation
Because of the higher number of samples collected within each lake in the IDNR data set, unique
relationships between TN-DIN and Chi a for each lake could be calculated, and those
relationships, in turn, can be used to derive numeric nutrient criteria (Figure 45). Variations
across lakes in DON and in the coefficients of the modeled relationship yield differences in the
estimated relationship between TN-DIN and Chi a. Then, resulting TN ambient criterion differ as
well. For an illustrative target Chi a concentration of 15 micrograms per liter (ng/L), the mean
ambient TN criterion for the lake shown in the left panel of Figure 45 was 750 ng/L, while the TN
criterion for the lake in the right panel was 1260 ng/L.
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T
30 40 60 80
10
Chi a (ng/L)
30 40 60 80
10
Chi a (ng/L)
100
Figure 45. Lake-specific criteria derivation using combined Iowa-NLA model for two different lakes in
Iowa. Open circles: observed values of TN-DIN and Chi a in Iowa for each lake; gray shading: 50% credible
intervals about the mean relationship; solid line: mean relationship calculated using mean DOC
concentration in lake; horizontal and vertical line segments: TN criterion calculation for illustrative Chi a
target of 15 ng/L.

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Appendix D: Operational Numeric Nutrient Criteria
Operationally, chlorophyll a (Chi a), total nitrogen (TN), and total phosphorus (TP) criteria can be
specified to account for the effects of sampling and temporal variability on observed mean
concentrations (Barnett and O'Hagan 1997). In most cases, the condition of a lake will be
assessed by examining a small number of samples and the uncertainty in the estimation of the
true seasonal mean value from those data will be determined by the number of samples, the
temporal variability of nutrient concentrations in the lake, and the inherent sampling variability
of the measurement. By examining historical data from many different lakes, sampling
variability associated with Chi a, TN, and TP can be estimated and "operational" criteria can be
specified to account for this variability with adjusted criterion magnitudes and by adopting a
frequency component that allows for some excursions of the specified magnitude.
Ambient monitoring of nutrient concentrations provides the basis for determining whether a
lake complies with the specified numeric nutrient criteria. Because of logistical and resource
restrictions, the number of water quality samples available at different lakes can vary from a
single grab sample to weekly or monthly samples throughout the sampling season. Statewide
monitoring designs also vary in how often a lake is visited in different years. For example, a
typical rotating basin design might sample the same lake once every 5 years, whereas other
lakes might be sampled every year. Because of the differences in the frequency of sample
collection, a statistical analysis of available monitoring data might be necessary to accurately
assess compliance with the numeric nutrient criteria. This appendix describes a statistical
approach for deriving operational or realizable criteria magnitude, duration, and frequency
components.
This document provides tools to compute numeric nutrient criteria expressed as seasonal mean
values. Those criteria implicitly assumed that a large number of samples are available for
characterizing the condition of each lake and that the uncertainty in the computation of the
mean value is small (Barnett and O'Hagan 1997), a condition that is usually not satisfied by
routine monitoring data. Operational criteria incorporate statistical uncertainty in estimating
environmental conditions from a much smaller number of samples. The statistical approach
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recommended here requires that one estimate the sampling and temporal variability of nutrient
concentrations within lakes for which criteria are specified.
A variety of approaches are available that account for within-lake variability when defining
operational criteria, but they should all be designed to consider that nutrient concentrations
vary in space (e.g., at different points on a lake) and in time. Both sources of variability account
for a distribution of nutrient concentrations that will arise when a lake is repeatedly sampled.
For example, if a single sample of TP was collected from one lake every year, over 10 years, the
distribution of values might be as shown in Figure 46, in which observed concentrations range
from 30 to 80 micrograms per liter (ju,g/L). Given this example, the water quality management
question is whether the lake complies with its specified numeric nutrient criteria. Here, if the
criterion is 60 ju,g/L, a methodical approach for assessing compliance can enhance the utility of
the criterion. This section provides one example of an approach for accounting for sampling
variability and defining "operational" nutrient criteria.
o
c
a>
D
a~
(D
o 1 		1	1	1	
I	1	1	1	1	1	1
20	40	80	160
TP(ng/L)
Figure 46. Example distribution of 10 TP measurements. Note that the horizontal axis is log-scaled.
Estimates of variability of measurements within lakes are needed to inform decisions on
operational criteria, and those estimates can be computed from historical data. For this
example, EPA analyzed TP data extracted from the Storage and Retrieval Data Warehouse
(STORET) that had been collected in the summers from 1990 to 2011. From those data, lakes
were identified in the United States with at least 5 years of nutrient data, yielding 25,056
samples collected from 846 different lakes. In this illustrative example, all available data were
used, but screening data to identify lakes with relatively lower levels of anthropogenic nutrient
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loading may be advisable. A statistical model was then used to estimate variance in nutrient
measurements across different samples collected in the same year and from the same lake
(within-lake variability). A model was fit to TP measurements that explicitly estimated intra-
annual and interannual variability as follows:
log (TPt) = am + bm + rt	(42)
where TP, is measured in sample i at site j and in year k. So, observed TP in a sample is modeled
as being log-normally distributed about a mean value that is the sum of an overall site mean (ay)
and a random effect of year (bk). The random effect of year is assumed to be normally
distributed with a mean value of 0 and a standard deviation of syeor, and the intra-annual
variance (r,) is modeled as a normal distribution with a mean of 0 and a standard deviation of
Ssampie Intra-annual variance not only includes contributions from traditional sources of sampling
variability (e.g., measurement uncertainty), but also includes variability that could be attributed
to differences in TP concentrations among different locations in a lake and differences in TP
concentrations one might observe over the course of a single sampling season. Hence, intra-
annual variance was expected to differ among different lakes, so, the overall distribution of
different values of sSamPie was modeled as a half-Cauchy distribution (Gelman 2006).
Fitting this model to the TP data collected from STORET yielded a mean estimate of 0.15 for the
standard deviation of intra-annual variability of log(TP). Among different lakes in the data set,
this value ranged from 0.10 to 0.27, so sampling variability varied substantially among the lakes
in the data set. Estimating intra-annual variability from local data collected in the lake of interest
would help ensure that the estimate correctly reflects variability in the lake. The mean standard
deviation of inter-annual variability was 0.11.
Once intra- and inter-annual variability for the lake or lakes of interest has been estimated, this
information can be combined with the criterion for that lake to estimate a distribution of
nutrient concentration values that would be observed if the lake complied with the criterion. For
example, if the standard deviation of the intra-annual variability of log(TP) in a particular lake is
estimated as 0.15 and the inter-annual variability is estimated as 0.11, the combined variability
is the square root of 0.152 + 0.112, or 0.19. For illustrative purposes, if we assume the TP
criterion for the lake is 60 ng/L, we can infer the characteristics of the cumulative distribution of
single observations of TP that would be observed at the lake if it were exactly complying with its
criterion (Figure 47). Then, based on this distribution, operational criteria can be derived. For
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example, one might define an operational criterion that corresponds with the 10th percentile of
the distribution (TP = 34 ng/L) and assert that a single TP observation below that value indicates
the probability that the mean TP concentration in the lake is greater than 60 ng/L is less than
10%. That is, a lake with an observation below that threshold is likely in compliance with the
criterion. Conversely, one might define a criterion at the 90th percentile of the distribution (TP =
105 ng/L) and assert that a single TP observation that exceeds that value indicates the
probability that the mean TP concentration is lower than 60 ng/L is less than 10%. That is, any
lakes with an observation that exceeds that threshold is likely to be out of compliance with the
criterion. Different water quality management outcomes (e.g., additional sampling) could be
triggered at different threshold concentrations. Also, different operational criteria can be
developed depending on probabilities of error that are acceptable to environmental managers.
o

00
o
CD
Q. <=>
(U
~ ^
Jo o
Is
O 
o
o
20
30
40 50 60
80
200
100
TP (ng/L)
Figure 47. Example of defining an operational criterion magnitude. Solid line: the cumulative probability of
observing a single sample TP lower than or equal to the indicated value if the true annual mean was
exactly equal to the criterion (TP = 60 |ag/L); dashed line: the cumulative probability for the average of
four samples; black arrows: operational criteria for one sample; gray arrows: operational criteria
associated with the mean of four samples.
This analysis also highlights the relative benefits of collecting additional samples from each lake.
More specifically, the combined standard error (s.e.) on the estimate of a summer mean
concentration is as follows:
Sample 2	[43|
-J m	interannual	\^~>l
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where N is the number of samples collected, ssampie is the sampling variability of the nutrient
concentration (estimated as an intra-annual standard deviation), and Siterannuai is the inter-
annual standard deviation. Hence, additional samples increase the precision with which the
annual average nutrient concentration can be estimated by reducing the effect of intra-annual
variability. In Figure 47, the dashed line shows the cumulative probability distribution of mean
values computed using four samples. Because of the reduction in the standard error,
assessments for compliance can be made with much greater confidence. The same 10%
probabilities used above for single samples yield operational criteria of 41 ng/L and 89 ng/L,
when applied to the case of the mean of four measurements (gray arrows in Figure 47).
Information and procedures regarding the use of operational criteria in assessment might be
described in a state's assessment methodology to accompany criteria specified in the water
quality standards.
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Appendix E: Example Workflow for Deriving Lake Nutrient
Criteria
To further assist states and authorized tribes, an example workflow for deriving numeric
nutrient criteria for a lake or reservoir is illustrated in this appendix by working through the case
for a hypothetical Lake XYZ. The location of the lake is selected for illustrative purposes only,
and the characteristics of Lake XYZ (e.g., depth, ecoregion, location, elevation) do not
correspond to an actual location in the United States. Frequently Asked Questions (FAQs) are
also included in each of the steps.
E.l Identify Designated Uses
Designated uses for Lake XYZ are aquatic life protection and recreation. For aquatic life, a
reproducing population of cool water fish are present. For recreation, swimming in the lake is a
common summer activity.
E.2 Compile Data
The maximum depth of Lake XYZ is 10 meters (m), and on average, the thermocline in the
summer is located 3 m below the surface. Mean dissolved organic carbon (DOC) concentration is
5 milligrams per liter (mg/L). The lake is located at 42.5 N, 83.5 W at an elevation of 1500 m.
The lake is located in Ecoregion 55, the Eastern Cornbelt Plains. Cool-water fish species in the
lake can tolerate temperatures up to 19 Celsius (C) and dissolved oxygen (DO) down to 4 mg/L.
FAQs:
1.	How do I measure depth below the thermocline?
Depth below the thermocline is best estimated by examining vertical profiles of
temperature and estimating the depth of the thermocline as the shallowest depth
where the temperature gradient exceeds 1 C/m. Depth below the thermocline can then
be calculated as the difference between maximum depth and thermocline.
2.	What do I do with multiple measurements of depth?
Lakes vary in depth depending on location, but to be consistent with measurements
collected by the National Lakes Assessment, depth can be recorded as the maximum
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depth in natural lakes and the midpoint of reservoirs. Thermocline depth varies with the
day of sampling, so if data from different days are available, a seasonal average
thermocline depth can be used in the models.
3.	How do I develop statewide criteria from lake-specific numbers?
The models provide a way to calculate criterion values based on factors that may vary
among lakes in a state (e.g., depth, ecoregion, DOC). Different options are available for
computing statewide criteria depending on how much these factors vary within a state,
ranging from lake-specific criteria to a single set of criterion values that applies to all
lakes. Analysis to examine the range of nutrient criteria associated with different lakes
in a state can inform these decisions. For example, if a large range of lake depths are
found in a state, and criterion values differ widely among those lakes, then specifying
criteria by depth class may be appropriate. The criterion models provide a tool for
directly quantifying the effects of differences in lake characteristics on criterion values.
4.	How do I derive criteria when data needed by the models are missing?
Data for specific parameters (e.g., DOC) may not be available for every lake, but often
information regarding the distribution of parameter values within a state or ecoregion
can be estimated. For example, if the mean and standard deviation of DOC in a state or
ecoregion can be computed, then this distributional information can be used to specify
a range of lake nutrient criteria.
E.3 Management Decisions
For comparison, criterion values were calculated at three certainty levels: 50%, 80%, and 90%.
Decisions were also required to determine the desired allowable probability of microcystin
exceeding the recreational threshold of 8 micrograms per liter (ng/L), the size of the cool-water
refuge, and the zooplankton slope threshold. A value of 1% was selected for the probability of
exceeding the microcystin threshold, the cool-water refuge size was set at 0.3 m, and the
zooplankton slope threshold was set at 0. The resulting candidate criteria are shown in the
tables below (Table 6).
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Table 6. Illustrative candidate Chi a criteria (ng/L) for Lake XYZ.
Certainty level
Aquatic life
Zooplankton biomass
Hypoxia
Recreation
50%
21
15
22
80%
14
12
9
90%
13
11
6
The tabulated values provide insights into both the most sensitive use in the lake and the
uncertainty in chlorophyll a (Chi a) criteria associated with protecting that use. The candidate
Chi a criterion for hypoxia is the lowest among uses at a certainty level of 50%, whereas
candidate Chi a criteria for recreation are the lowest among uses for certainty levels of 80% and
90%. Among certainty levels, the range of Chi a criterion values is greatest for recreation,
indicating that the sensitivity of certainty level to different criterion values is low relative to the
other responses and uses. That is, small changes in the Chi a criterion are associated with small
changes in the certainty level for this response. For hypoxia, the range of criterion values is
narrow, indicating higher sensitivity. Here, small changes in the Chi a criterion are associated
with relatively large changes in certainty level. Finally, the food web implications associated with
lakes in which Chi a exceeds the level at which log(Z)/log(P) = 0 over the long term may be
substantial and difficult to reverse, and therefore, the use of the 90% certainty level is
recommended for this response to provide assurance that the candidate Chi a criterion for this
response is protective. Based on these considerations, a final Chi a criterion of 12 ng/L might be
selected. This value is slightly less than the 90% certainty level for the zooplankton biomass
endpoint and corresponds to the 80% certainty level for the hypoxia endpoint. The value also
corresponds with the 72% certainty values for recreation. This Chi a criterion value is used to
compute the total phosphorus (TP) and total nitrogen (TN) criteria in Table 7.
Table 7. Criteria for TP and TN corresponding to a Chi a criterion of 12 ng/L
Certainty level
TP (Hg/L)
TN (ng/L)
50%
25
560
80%
24
540
90%
36
570
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More generally, criteria could also be derived that are protective of different designated uses
and applied to different lakes depending on the applicable uses, while ensuring that, for each
lake, the most sensitive use is protected.
FAQs
1.	How do I select the certainty level?
The certainty level, or credible interval, specifies a range of possible criterion values
within which the actual value lies with the specified probability. For example, the 50%
certainty level implies that there is a 50% chance that the actual value is within the
specified bounds (i.e., the 50% certainty level is bounded by the 25th and 75th percentiles
of distribution of possible criteria). In other words, the selection of 50% certainty level
indicates that 25% of possible criterion values lie on either side of the model's best
prediction. Because the criterion is based on the lower bound of the 50% certainty level,
there is a 25% chance that the derived criterion value is greater than the concentration
needed to achieve the desired condition. That is, there is a 25% chance that the criterion
is under-protective. More certainty on the criterion value is achieved by selecting
greater certainty levels. For example, there is only a 5% chance that a criterion based on
the 90% certainty level would be under-protective. The R Shiny apps provide
transparent information regarding the effects of different levels of certainty and can
provide a useful means of engaging with stakeholders regarding the risk management
decisions underlying criterion development.
2.	How do I select a slope threshold for the zooplankton model?
A value of zero for the slope threshold for the zooplankton model identifies the point at
which changes in zooplankton biomass are not associated with changes in
phytoplankton biomass. In other words, on average there is no increase in zooplankton
biomass given a corresponding increase in their food source, phytoplankton. At this
point the food web in a lake may be out of balance, an indication that aquatic life use
may not be supported. States and authorized tribes may opt to select a higher threshold
to provide additional assurance that aquatic life is protected in their lakes.
3.	How do I select a refuge depth for the hypoxia model?
Limited data are available on the refuge depth that is necessary to protect cool- and
cold-water fish from the combined effects of hypoxia and increased temperature. The
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studies cited in the criterion document include studies conducted in lakes with both
deep water hypoxia and warm surface layer temperatures, and studies conducted in
lakes with cool water inflows where fish have been observed to congregate. A minimum
refugia depth of 0.3 m is identified in some of these studies. But the final selection for
the refuge depth may also consider other factors, including the likelihood of a prolonged
stable stratification in a lake with no mixing events and the likelihood of elevated
temperatures in the surface layer through the end of the summer. States and authorized
tribes may opt to select a larger refuge depth to provide additional assurance that
aquatic life is protected in their lakes.
4.	How do I select the exceedance probability for microcystin ?
The exceedance probability for microcystin can be interpreted directly in terms of the
environmental outcome. That is, if mean Chi a concentration in a lake is maintained at
the calculated criterion value, then the exceedance probability can be expressed in
terms of the number of days of exceedance. For example, a 1% exceedance probability
suggests that on average, microcystin will exceed the threshold concentration 1 day out
of 100, so on average, 1 day in the swimming season for most states would not support
recreational use of the lake. Furthermore, in Section 3.2.3.3, a method is described for
translating the 1-day exceedance probability to a seasonal probability for a specified
number of excursions during 10-day assessment windows [as specified in the
recreational cyanotoxin criteria, (US EPA 2019)], and this information can further inform
selection of the exceedance probability. As with the certainty level, the R Shiny app
provides a transparent means of communicating the effects of different exceedance
probabilities to interested stakeholders.
5.	How do I interpret slider values that do not yield criterion values?
Certain combinations of slider selections do not yield numeric criteria in the R Shiny
apps and instead will return an error message. An example of this scenario occurs in the
zooplankton model when a high slope threshold is selected with a high certainty level.
When a desired slider combination does not yield a criterion value, consult with EPA to
refine the model and possibly incorporate site-specific information.
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E.4 Accounting for Interannual and Sampling Variance
Criterion values can account for sampling and temporal variability to increase the accuracy of
compliance monitoring and to account for allowable exceedance frequencies of the criteria for
Chi a, TN, and TP. Appendix D describes the statistical calculations for deriving operational
criterion magnitudes and examples of those computations are shown below for the Chi a
criterion. Based on the comparison of criterion values above, 12 ng/L was selected as the Chi a
criterion. Intensive monitoring data at lakes similar to Lake XYZ indicate that the within-year
standard deviation of loge(Chl a) in Lake XYZ is 0.8, while among-year standard deviation is 0.2.
Given this information, the criterion magnitude can be adjusted to account for an allowable
exceedance frequency. Here, to illustrate the approach, criterion magnitudes are calculated that
can be exceeded once every 3 years.
To assess whether the lake is in compliance with a criterion value, we adjust the criterion
magnitude as follows. First, calculate the combined standard deviation of Chi a measurements:
For a once in 3 years exceedance frequency, calculate Chi a concentration that will be exceeded
one-third of the time, assuming that Chi a measurements are log-normally distributed, with a
mean value equal to the log-transformed criterion value, and a standard deviation equal to the
combined standard deviation calculated above:
Where Cnn3 is the criterion value adjusted to an allowable one exceedance every 3 years, C is
the criterion value of 12 ng/L, sCOmb is computed above, and z0.67 is the 67th percentile of the
standard normal distribution (i.e., a 1 in 3 year frequency of exceedance). This calculation yields
a value of 17 ng/L that is exceeded once every 3 years (assuming that a single sample of Chi a is
collected each year and the mean Chi a concentration in the lake is equivalent to the criterion
value of 12 ng/L). That is, if Lake XYZ was conforming exactly with the applicable criterion, then
we would expect to see Chi a concentrations exceeding 17 ng/L in one-third of the years.
If several samples are combined to estimate each seasonal mean, the calculation for sCOmb is
adjusted to account for this averaging as follows:
^comb
'within-year
among-year
(44)
log (Ci in 3) = log (C) + Z0 67scomb = log(12) + 0.44(0.82) (45)
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Scomb
N
?2
within-year l 2
77	r Samong-year
M
0.82	,AC-\
	+ 0.22 = 0.6 (46)
Note: the numerical example shows the computation when four samples are averaged. Based
on this adjustment, Cn3for seasonal means computed as the average of four samples is 16
Hg/L-
E.5 Incorporating State Data in National Models
Regular monitoring has been conducted at Lake XYZ and other lakes, in which a variety of water
quality measurements are collected, and the state agency is interested in determining whether
the state monitoring data can be combined with the national models to improve the accuracy
and precision of the derived criteria. Several factors should be considered when making this
decision:
1.	National models provide applicable criteria.
The criteria provided by the national criterion models apply to most lakes and reservoirs
of the United States. The criterion models estimate relationships between
measurements (e.g., Chi a and microcystin) that do not vary strongly with geographic
location, and therefore, incorporation of state data may not appreciably change
criterion values.
2.	Assess the inventory of observed data.
The measurements that are available in a state or tribal dataset should be compared
with the variables that are included in the national models. Measurements of endpoint
variables (i.e., microcystin, depth-averaged DO, zooplankton biomass, TP, and TN) and
measurements of variables that account for large proportions of variability in these
endpoints (i.e., Chi o, DOC, phytoplankton biomass, turbidity) need to be available for
combining state and national data.
3.	Consider the likelihood of changes to national models.
Several factors determine the degree to which state data influence national
relationships. Of these, two can be evaluated a priori. First, the number of samples
collected for each parameter in the state data set should be no less than approximately
10% of the size of the national dataset. Second, relationships among variables can be
more or less precise relative to the national data, depending on factors such as
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differences in sampling protocols; however, state data that feature more precise
relationships among variables of interest are more likely to influence the national
model.
4. Consult with EPA on statistical techniques for incorporating local monitoring data with
national models.
Due to wide variations in the types of data that are collected, sampling protocols, and
database formats, the process of combining state and national data is unique for each
dataset. Therefore, EPA is ready to provide technical assistance to any state or
authorized tribe that is interested in combining their data with the national criterion
models as resources allow. Please contact your regional nutrient coordinator to request
technical support through EPA's Nutrient Scientific Technical Exchange Partnership and
Support (N-STEPS) program.
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