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# Appendix A : South Florida Inland

Flowing Water s— Logistic Regression

Analysis

November 30 , 2012

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# Contents

Appendix A. South Florida Inland Flowing Water—Logistic Regression Analysis

......... A-1

A.1 Introduction

.................................................................................................................. A-1

A.1.1 Data Preparation

............................................................................................... A-1

A.1.2 Binary Logistic Regressio n

.............................................................................. A-2

A.1.3 Frequency of Chl-a Observations Exceeding 30 and 40 μg/L

......................... A-3

A.1.4 Organization

..................................................................................................... A-4

A.2 Binary Logistic Regression Model Runs and Diagnostics with TN and TP

Modeled Together

........................................................................................................ A-4

A.2.1 All Season Model Results with TN and TP as Independent Variables

............ A-7

A.2.2 Dry Season Mo del Results with TN and TP as Independent Variables

........ A-14

A.3 Evaluation of Binary Logistic Regression Model Results

......................................... A-21

A.4 Distributional Statistics

.............................................................................................. A-23

A.4.1 Verified Matched Data

................................................................................... A-24

A.4.2 Verified Matched Data/≤ 10 percent Chl -a Observations > 30 μg/L

............ A-25

A.4.3 All Verified Sites

........................................................................................... A-27

A.4.4 All Verified Sites, Not Impaired for Chl -a, Nutrients, or DO

....................... A-28

A.4.5 All Verified Sites, Not Impaired for Chl

- a or Nutrients

................................ A-29

A.5 Key Results

................................................................................................................ A-30

A.6 References

.................................................................................................................. A-30

A

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# Figures

Figure A -1. Chl-a observations exceeding 30 μg/L as function of annual geometric mean

TN and TP. Open circles and solid triangles indicate “WBID- years” for

which ≤ 10 percent and > 10 percent of chl

- a observations exceed 30 μg/L,

r espectively

. ............................................................................................................. A-4

Figure A

- 2. All season ROC curves; see Table A -3 for model descriptions

............................ A-12

Figure A

- 3. All season geometric mean TN as a function of all season geometric mean

TP. Open circles and solid triangles indicate “WBID

- years” for which ≤ 10

percent and > 10 percent of chl-a observations exceed 30 μg/L, respectively.

Binary logistic regression model for 10 percent frequency represented by

solid and dashed lines for EAA subregion and other subregions grouped

together, respectively. See Table A -4 for regression model.

................................ A-13

Figure A

- 4. All season geometric mean TN as a function of all season geometric mean

TP. Symbols indicate subregion. Binary logistic regression model for 10

percent frequency represented by solid and dashed lines for EAA subregion

and other subregions grouped together, respectively. See Table A- 4 for

regression model

.................................................................................................... A-13

Figure A

- 5. Dry season ROC curves; see Table A -3 for model descriptions

........................... A-19

Figure A -6. Dry season geometric mean TN as a function of dry season geometric mean

TP. Open circles and solid triangles indicate “WBID

- years” for which ≤ 10

percent and > 10 percent of chl-a observations exceed 30 μg/L, respectively.

Binary logistic regression model for 10 percent frequency represented by

solid and dashed lines for West subregion and other subregions grouped

together, respectively. See Table A -5 for regression model.

................................ A-20

Figure A -7. Dry season geometric mean TN as a function of dry season geometric mean

TP. Symbols indicate subregion. Binary logistic regression model for 10

percent frequency represented by solid and dashed lines for West subregion

and other subregions grouped together, respectively. See Table A- 5 for

regression model

.................................................................................................... A-20

Figure A -8. Hypothetical relationship between annual geometric mean TN and annual

geometric mean TP. Black line represents binary logistic regression equation

solved for a frequency of 10 percent. Red dashed lines A) and B) represent

two candidate options for TN and TP criteria. Open circles represent various

“WBID

- year” annual geometric mean TN and TP values.

................................... A-22

Figure A -9. Criteria selection using the all season data and grouped subregions to prevent

algal conditions exceeding 30 μg/L instantaneous chl- a and limiting the

frequency to no more than 10 percent

................................................................... A-22

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# Tables

Table A -1. Number of samples with matched chl-a, TN, and TP; and number and

percentage of samples with chl

- a exceeding 30 μg/L and 40 μg/L using all

data

.......................................................................................................................... A-3

Table A -2. Number of samples with match chl-a, TN, and TP; and number and

percentage of sample s with chl-a exceeding 30 μg/L and 40 μg/L using dry

season data

............................................................................................................... A-3

Table A

- 3. Binary logistic model summaries for models with T N and TP as independent

variables

................................................................................................................... A-5

Table A -4. All season data model for proportion of chl-a observations, p, > 30 μg/L as a

fun ction of annual geometric mean TN (TN GM 

## ), annual geometric mean TP

(TP GM 

## ), and grouped subregions where p = y/(1 + y)

............................................. A-6

Table A-5. Dry season model for proportion of chl-a observations, p, > 30 μg/L as a

function of geometric mean TN (TN GM 

## ), geometric mean TP (TP GM 

## ), and

grouped subregions where p = y/(1 + y)

................................................................. A-6

Table A -6. Descriptions of data sets used for additional distributional statistics

..................... A-23

Table A -7. Verified matched data: mean and standard deviation of WBID- year geometric

mean TN and TP in log

e 

## -transformed space by season and subregion

................. A-24

Table A

- 8. Verified matched data: percentiles of geometric mean TN concentrations

............ A-24

Table A

- 9. Verified matched data: percentiles of geometric mean TP concentrations

............ A-25

Table A

- 10. Verified matched data/≤ 10 percent chl-a observations > 30 μg/L: mean and

standard deviation of WBID- year geometric mean TN and TP in log

e 

## transformed space by season and subregion

.......................................................... A-25

Table A

- 11. Verified matched data/≤ 10 percent chl -a observations > 30 μg/L: percentiles

of geometric mean TN concentrations

.................................................................. A-26

Table A

- 12. Verified matched data/≤ 10 percent chl -a observations > 30 μg/L: percentiles

of geometric mean TP concentrations

................................................................... A-26

Table A -13. All verified sites: mean and standard deviation of WBID- year annual

geometric mean TN and TP in log

e 

## -transformed space by subregion

................... A-27

Table A

- 14. All verified sites: percentiles of annual geometric mean TN concentrations

....... A-27

Table A

- 15. All verified sites: percentiles of annual geometric mean TP concentrations

....... A-27

Table A -16. All verified sites, not impaired for chl-a, nutrients, or DO: mean and

standard deviation of WBID-year annual geometric mean TN and TP in log

e 

## transformed space by subregion

............................................................................ A-28

Table A -17. All verified sites, not impaired for chl-a, nutrients, or DO: percentiles of

annual geometric mean TN concentrations

........................................................... A-28

Table A -18. All verified sites, not impaired for chl-a, nutrients, or DO: percentiles of

annual geometric mean TP concentrations

............................................................ A-28

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## Table A -19. All verified sites, not impaired for chl-a or nutrients: mean and standard

deviation of WBID- year annual geometric mean TN and TP in log

e 

## transformed space by subregion

............................................................................ A-29

Table A -20. All verified sites, not impaired for chl-a or nutrients: percentiles of annual

geometric mean TN concentrations

....................................................................... A-29

Table A -21. All verified sites, not impaired for chl-a or nutrients: percentiles of annual

geometric mean TP concentrations

....................................................................... A-29

Table A -22. Candidate TP criteria from binary logistic regression results and candidate

TN criteria based on TN

- TP ratio where annual geometric mean TP exceeds

corresponding candidate criteria.

.......................................................................... A-30

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# Abbreviations **and Acronyms**

AUC a rea under the curve

Chl-a chlorophyll a

CHLA_GT_30 chl-a > 30 μ g/L

CHLA_GT_ 40 chl-a > 40 μ g/L

confidence interval

Coef c oefficient

DF degrees of freedom

EAA Everglades Agricultural Area

EvPA Everglades Protection Area

Exp e xpected

LN natural logarithm; also log

e



## LN_TN_GM natural logarithm transformed geometric mean total nitrogen ;

a lso LN(TN GM 

## ) or log

e 

## (TN GM 

## )

LN_TP_GM natural logarithm transformed geometric mean total phosphorus ;

also LN(TP GM 

## ) or log

e 

## (TP GM 

## )

Obs observed

P p-value

ROC r eceiver operator characteristic

SE standard error

TN t otal nitrogen

TP total phosphorus

TN_AGM annual geometric mean TN; a lso AGM TN or TN GM



## TP_AGM annual geometric mean TP ; also AGM TP or TP GM



## WBID w ater body identification number

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# Appendix A. **South Florida**  **Inland Flowing Water** 

**— Logistic Regression** 

**Analysis**

**A.1 Introduction** 

This appendix, in support of Volume 3, provides additional information about the methods and

results associated with an alternative approach for computing protective instream TN and TP

criteria for Class I and Class III flowing water s (including canals and streams) using logistic

regression in south Florida.

As an endpoint, EPA has decided to limit the frequency of nuisance algal conditions, measured

with chlorophyll a (chl

- a) , to protect uses. EPA is defining nuisance algal conditions as

> 30 μg/L instantaneous chl -a and limiting the frequency to no more than 10 percent of the

observations, the bases for which are described in the main text. TN and TP criteria were derived

based on empirical regressions between these chlorophyll endpoints and nutrient concentrations

using matched chl -a, TN, and TP water quality data.

**A.1.1 Data Preparation** 

Descriptions of data are provided in the main text. The analyses performed throughout S ections

A.2

, A.3 , and A.4.1 are based on the dataset described here. The analyses were ultimately based

on daily averages, which were first transformed by taking the natural logarithm (LN or log

e 

## ) for

samples for which chl -a , TN

, and TP data were concurrently available

.

Initial data sets were retrieved from Florida’s Impaired Waters Rule ( IWR ) Run 40. Where

available, additional data from DBHydro data were added. Site locations were screened to

include freshwater locations as well as being Class III water. Screening for freshwater included

examination of salinity, specific conductivity, and chloride data, as well as consideration of

existing control structures near the coast. Other data sources utilized in screening for freshwater

sites were the delineations of water body identification numb er ( WBID ) IWR Run 40 water

classifications ( Class III marine and Class II ) as well as the head of salt line (U .S. G eological

Survey ). Water quality site locations and descriptions were evaluated. Descriptions indicating

that sites were from private agricul tural pump stations (an indicator of Class IV waters),

stormwater treatment areas, or marsh were removed. Site locations were also reviewed via

geographic information systems using satellite imagery to confirm their location on Class III

waters in south Florida.

Chl-a, corrected chl -a, TN, and TP data were retrieved from sites passing the above analysis.

Chlorophyll data were consolidated, with preference given to corrected chl -a, and when

unavailable, chl -a was used. TN, TP, and chl -a values were log

e 

## -transformed and averaged to

daily averages. For the binary logistic regression, the analyses were limited to 4,758 daily

averages with matched chl-a, TN, and TP data.

To perform binary logistic regression analyses, the above data were organized by WBID

- ye ar, in

which all nutrient data within a specific year were log

e 

## -transformed and then averaged . Paired

chl -a data were treated as multiple trials for the same average TN and TP geometric mean

A

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## (see binary regression explanation below). All nutrient data were log

e 

## -transformed prior to any

analyses and only back-transformed to present final values.

**A.1.2 Binary Logistic Regression** 

TN and TP criteria for south Florida inland waters were derived using an empirical stressor

response approach (USEPA 2010a) similar to that used to derive numeric nutrient TN a nd TP

criteria for Florida inland lakes as part of the Water Quality Standards for the State of Florida’s

Lakes and Flowing Waters; Final Rule (Final Rule) ( USEPA 2010b) . A logistic regression

equation was derived between chlorophyll, expressed as binary data either greater than (1) or less

than (0) either of the two nuisance bloom condition endpoints, and paired TN and TP data and

solved for the target frequency goal (probability = 0.1 or 10 %). Multiple chlorophyll

observations within any WBID- year were treated as individual trials and paired to the same

WBID

- year average TN and TP data

. Regression modeling was performed using binary logistic

regression functio n in Minitab v16.

The basic form of the logistic regression equation is given by

p Eq

. 1 LN ൬

a + b LN ( T N GM 

## ) + c LN ( T P GM 

## )

1

− p ൰

=

where p is the probability of an instantaneous chl -a observation exceeding the specified threshold

level; a

, b , and c are the regression coefficients; and LN ( TN GM 

## ) and LN ( TP GM 

## ) are the log

e 

## transformed geometric mean TN and TP. After the regression coefficients are estimated, the

value of p can be estimated for various values of TN GM 

## and TP GM 

## using the following equation :

e ( a + b LN ( T N GM ) + c LN ( T P GM ) ) 

## Eq. 2

p = 1 + e ( a + b LN ( T N GM ) + c LN ( T P GM ) )



## Values of TP GM 

## can be estimated for a given value of p and TN GM 

## by

p LN ቀ

1

− p ቁ

− a

− b LN ( T N GM ) 

## Eq

. 3

T P GM 

## = e c



## The regression equations were evaluated using standard regression diagnostics (significance and

fit)

. In addition, receiver operator characteristic (ROC) curves were used to evaluate models

. ROC curves are frequently used to evaluate binary models and reflect the sensitivity (how well a

model pr edicts actual events) and specificity (how well a model predicts non

- events) (Gönen

2006)

. Sensitivity and specificity are also known as the true positive and negative rates,

respectively . ROC curves are plots of model sensitivity as a function of 1- specificity for different

cutoffs of the X variable

. The area under the curve (AUC), estimated with integration, is used as

a measure of overall model discrimination. AUCs < 0.5 show no discrimination, values from

0.7–0.8 are acceptable discrimination, 0.8–0.9 show excellent discrimination, and AUCs of ≥ 0.9

are outstanding albeit e xtremely rare (Hosmer and Lemeshow 2000).

A

- 2Percent of Percent of

Samples w ith

C hl -a Samples w ith

C hl -a S amples w ith

C hl -a S amples w ith

C hl -a

Season Subregion Samples > 30 μg/L > 40 μg/L > 30 μg/L > 40 μg/L

All All Subregions 4

, 75 8 245 139 5.15% 2.92% All 1) Biscayne 1

, 04 5 14 7 1.34% 0.67%

All 2) Palm Beach 1

, 288 109 60 8.46% 4.66%

All 3) EAA 398 37 26 9.30% 6.53%

All 4) EvPA 828 15 4 1.81% 0.48%

All 5) West 1

, 199 70 42 5.84% 3.50%

Percent of Percent of

Samples w ith

C hl -a Samples w ith

C hl -a S amples w ith

C hl -a S amples w ith

C hl -a

Season Subregion Samples > 30 μg/L > 40 μg/L > 30 μg/L > 40 μg/L

Dry 1) Biscayne 532 4 2 0.75% 0.38%

Dry 2) Palm Beach 720 44 25 6.11% 3.47%

Dry All Subregions 2

, 615 130 73 4.97% 2.79% Dry 3) EAA 180 12 8 6.67% 4.44%

Dry 4) EvPA 472 10 2 2.12% 0.42%

Dry 5) West 711 60 36 8.44% 5.06% 

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## A.1.3 **Frequency of C**  **hl -a O**  **bservations E**  **xceeding 30 and 40 μg/L**

Early analysis of a small subset of available data suggested a difference in bloom frequencies

between all season and dry season data . In order to inform decisions about the temporal scale

over which to consider applying numeric criteria, bloom frequencies were compared between the

two season options (all seasons vs. dry season). The number of sampl es with matched chl -a , TN,

and TP were organized by subregion ( see Table A-1). For example, in the Palm Beach subregion

there were 1,288 matched samples with 109 (8.46%) and 60 (4.66% ) samples having chl -a

> 30 μg/L and 40 μg/L, respectively. In all, there were 245 and 139 samples having chl -a

> 30 μg/L and 40 μg/L, respectively. Table A-2 presents the same information for the dry

(November to May) season with a total of 130 and 73 samples having chl -a > 30 μg/L and

40 μg/L, respectively.

Overall, the percent of observations ex ceeding 30 μg/L and 40 μg/L chl -a using all data and dry

season data were the same (test of two proportions, p > 0.7). The same was generally true if the

comparison was conducted subregion- by -subregion , except that the all season percent of

observations in the Palm Beach subregion exceeding 30 μg/L (8.46% ) was greater than the

corresponding dry season percentage (6.11% ), and the all season percent of observations in the

West subregion exceeding 30 μg/L (5.84%) was less than the corresponding dry season

perc entage (8.44%). The overall similarity of these proportions suggests that chl -a values

exceeding the selected nuisance conditions was similar for the entire year as it was within the dry

season alone. This observation, combined with the flexibility of applying a standard throughout

the year, has led EPA to develop criteria based on all season data.

Table A-1 . Number of samples with match ed chl -a , TN, and TP; and number and percentage of samples with

chl -a exceed ing 30 μg/L and 40 μg/L using all data

Table A-2

. Number of samples with match c hl -a , TN, and TP; and number and percentage of samples with chl -a

exceeding 30 μg/L and 40 μg/L using dry season data



## A

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## Figure A-1 displays the percent of chl -a observations > 30 μg/L as a function of annual

geometric mean TN and TP using the all seasons data.

1 0.1 0.01 0.001 10

1

0.1

0.01

Annual Geometric Mean TP, mg/LAnnual Geometric Mean TN, mg/L 1) No

2) Yes Legend



### Figure A-1

. Chl -a observations exceeding 30 μg/L as function of annual geo metric mean TN and TP. Open circles

and solid triangles indicate “ WBID

- year s” for which ≤ 10 percent and > 10 percent of chl

- a observations exceed

30 μg/L, respectively.



## A.1.4 **Organization**

The remainder of this appendix is organized into six sections. Section A.2 presents the results

and diagnostics of the b inary logistic regression analyses where TN and TP were modeled

together using all data (Section A.2.1) and dry season data (Section A.2.2 ). Section A.3 presents

an interpretation of the model results from Section A.2.1. Section A.4 presents selected

distributional statistics that were evaluated

. Section A.5 summarizes the analyses into tables

highlighting the final, selected criteria value w hile Section A.6 lists the references

.



## A.2 **Binary Logistic Regression Model Runs and Diagnostics with TN and TP** 

**M odeled Together** 

The binary regression models considered TN and TP in combination, evaluating their effects

simultaneously using all data (Section A.2.1), dry season data (Section A.2.2), and for various

combinations of subregions. Ten different models were constructed and are summarized in Table

A-3. The first column indicates which section of this appendix provides the output of the logistic

regression model, including regression diagnostics. The season, subregions modeled, and chl -a

co lumns indicate whether all the data or just the dry season data were used, which subregion

A

- 4Regression

Diagnostics Subregion s ROC C urve

( s ee S ection) Season m odeled Chl

- a Nitrogen Phosphorus ( s ee Figure ) Notes

A.2.1.1 All 5 Subregion s > 30 P < 0.05 P < 0.05 Area = 0.8 EAA significantly

Figure A

- 2 A different sub region

A.2.1.2 a All EAA, Other > 30 P < 0.05 P < 0.05 Area = 0.8

Figure A

- 2 B

A.2.1.3 All 5 Subregion s > 40 P = 0.158 P < 0.05 Area = 0.8

Figure A

- 2 C Subregions not

significantly different

A.2.1.4 All

-- > 40 P = 0.98 4 P < 0.05 Area = 0.8

Figure A

- 2 D

A.2.1.5 All

-­ > 40

-­ P < 0.05 Area = 0.8

Figure A

- 2 E

A.2.2.1 Dry 5 Subregion s > 30 P < 0.05 P < 0.05 Area = 0.8 West significantly

Figure A

- 5 A different subregion

A.2.2.2 b Dry West, Other > 30 P < 0.05 P < 0.05 Area = 0.79

Figure A

- 5 B

A.2.2.3 Dry 5 Subregion s > 40 P = 0.119 P < 0.05 Area = 0.81 Subregions not

Figure A

- 5 C significantly different

A.2.2.4 Dry

-­ > 40 P = 0.517 P < 0.05 Area = 0.8

Figure A

- 5 D

A.2.2.5 Dry

-- > 40

-- P < 0.05 Area = 0.8

Figure A

- 5 E

a See also Table A-4

, Figure A-3 , and Figure A-4

b See also Table A-5

, Figure A-6 , and Figure A-7 

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## combinations were modeled, and whether the endpoint was chl -a > 30 or 40 μg/L, respectively.

The nitrogen and phosphorus columns indicate whether the nutrient was st atistically significant

(p < 0.05) or not. No value ( --) in the subregions modeled, nitrogen, or phosphorus column

indicates that variable was not included in the model. The ROC curve column provides a

reference to the corresponding figure showing the ROC curve and the estimate of the area under

the curve. The final column provides comments about the significance of subregions in the

model. For each scenario evaluated, all five subregion s were first evaluated with a variable for

the subregions used to asses s the significance of individual subregion models. Depending on the

significance of the initial five subregion model, subregions were grouped and a new model run

created.

Table A-3 . Binary logistic model summaries for models with TN and TP as independent variables



## For example, the first entry, whose model results are in Section A.2.1.1, shows that proportion of

chl -a observations > 3 0 μg/L was modeled using all seasons data, with both TN and TP as

predictors, and modeled all five subregion s separately. The model indicated a significant effect

of both TN and TP and a ROC curve AUC of 0.8. Of the d ifferent subregional models, only the

Everglades Agricultural Area ( EAA ) subregion was significantly different. As a result, the next

model was identical except that there were only two subregions, EAA and Other (i.e., all other

subregions combined) . Each independent variable was significant and no further options were

considered.

A

- 5Subregion Model (see also Section A.2.1.2 and Figure A-3)

1) Biscayne y = e (1.44621 + 0.23991 × LN(TNGM) + 1.28634 × LN(TPGM))

(1.44621 + 0.23991 × LN(TNGM) + 1.28634 × LN(TPGM)) 2) Palm Beach y = e

3) EAA y = e (0.35664 + 0.23991 × LN(TNGM) + 1.28634 × LN(TPGM))

(1.44621 + 0.23991 × LN(TNGM) + 1.28634 × LN(TPGM)) 4) EvPA y = e

5) West y = e (1.44621 + 0.23991 × LN(TNGM) + 1.28634 × LN(TPGM))

Subregion Model (see also Section A.2.2.2 and Figure A-6)

1) Biscayne y = e (

- 0.09983 + 0.31704 × LN(TNGM) + 0.94255 × LN(TPGM))

(

- 0.09983 + 0.31704 × LN(TNGM) + 0.94255 × LN(TPGM)) 2) Palm Beach y = e

3) EAA y = e (

- 0.09983 + 0.31704 × LN(TNGM) + 0.94255 × LN(TPGM))

(

- 0.09983 + 0.31704 × LN(TNGM) + 0.94255 × LN(TPGM)) 4) EvPA y = e

5) West y = e (0.9437 + 0.31704 × LN(TNGM) + 0.94255 × LN(TPGM)) 

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## All models had a ROC Curve AUC from 0.79–0.81, and the models corresponding to Sections

A.2.1.2, A.2.1.5, A.2.2.2, and A.2.2.5 were the models where all independent variables were

significant.

The resul ting equations for two of the model formulations are provided in Table A-4 and Table

A-5, both of which modeled the proportion of observations > 30 μg/L chl -a and grouped

subregions for the all seasons data and dry season data options, respectively. Note that intercept

values reflect the effect of subregion on the overall model. Corresponding contour p lots that

solved for the 10 percent frequency model solutions are provided in Figure A-3 and Figure A-6,

r espectively.

Table A-4

. All season data m odel for proportion of chl -a observations, p , > 30 μg/L as a function of annual

geometric mean TN (TN

GM 

### ), annual geometric mean TP (TP

GM 

### ), and grouped subregion s where p = y/(1 + y)

Table A-5

. Dr y s eason m odel for proportion of chl -a observations, p , > 30 μg/L as a function of geometric

mean TN (TN

GM 

### ), geometric mean TP (TP

GM 

### ), and grouped subregion s where p = y/(1 + y)



## A

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## A.2.1 **All Season Model Results with TN and TP as Independent Variables** 

A.2.1.1 All Season Data: Chl -a > 30 μg/L Modeled with TN, TP, a nd 5 Subr egion s

Response Information

Variable Value Count

CHLA_GT_30 1 245 (Event)

0 4513

Total 4758

Logistic Regression Table

Odds 95% CI

Predictor Coef SE Coef Z P Ratio Lower Upper

Constant 1.37082 0.517095 2.65 0.008

LN_TN_GM 0.258865 0.122610 2.11 0.035 1.30 1.02 1.65

LN_TP_GM 1.27620 0.106585 11.97 0.000 3.58 2.91 4.42

Region

2) Palm Beach 0.0307394 0.326396 0.09 0.925 1.03 0.54 1.96

3) EAA -1.05400 0.389940 -2.70 0.007 0.35 0.16 0.75

4) EvPA 0.0182849 0.378387 0.05 0.961 1.02 0.49 2.14

5) West 0.0842281 0.336396 0.25 0.802 1.09 0.56 2.10

Log-Likelihood = -817.036

Test that all slopes are zero: G = 296.590, DF = 6, P-Value = 0.000

Goodness-of-Fit Tests

Method Chi-Square DF P

Pearson 664.118 478 0.000

Deviance 540.738 478 0.025

Hosmer-Lemeshow 4.177 8 0.841

Table of Observed and Expected Frequencies:

(See Hosmer-Lemeshow Test for the Pearson Chi-Square Statistic)

Group

Value 1 2 3 4 5 6 7 8 9 10 Total

1

Obs 4 4 8 5 9 14 23 32 62 84 245

Exp 2.5 4.4 5.6 8.0 10.7 15.0 22.2 35.3 57.7 83.6

0

Obs 494 498 469 472 471 463 455 443 451 297 4513

Exp 495.5 497.6 471.4 469.0 469.3 462.0 455.8 439.7 455.3 297.4

Total 498 502 477 477 480 477 478 475 513 381 4758

Measures of Association:

(Between the Response Variable and Predicted Probabilities)

Pairs Number Percent Summary Measures

Concordant 881914 79.8 Somers' D 0.60

Discordant 213596 19.3 Goodman-Kruskal Gamma 0.61

Ties 10175 0.9 Kendall's Tau-a 0.06

Total 1105685 100.0



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## A.2.1.2 All Season Data: Chl -a > 30 μg/L Mo deled with TN, TP, and Grouped Subr egions

Response Information

Variable Value Count

CHLA_GT_30 1 245 (Event)

0 4513

Total 4758

Logistic Regression Table

Odds 95% CI

Predictor Coef SE Coef Z P Ratio Lower Upper

Constant 1.44621 0.273340 5.29 0.000

LN_TN_GM 0.239910 0.105941 2.26 0.024 1.27 1.03 1.56

LN_TP_GM 1.28634 0.0875941 14.69 0.000 3.62 3.05 4.30

Region2

3) EAA -1.08956 0.220694 -4.94 0.000 0.34 0.22 0.52

Log-Likelihood = -817.091

Test that all slopes are zero: G = 296.480, DF = 3, P-Value = 0.000

Goodness-of-Fit Tests

Method Chi-Square DF P

Pearson 666.143 481 0.000

Deviance 540.848 481 0.030

Hosmer-Lemeshow 7.634 8 0.470

Table of Observed and Expected Frequencies:

(See Hosmer-Lemeshow Test for the Pearson Chi-Square Statistic)

Group

Value 1 2 3 4 5 6 7 8 9 10 Total

1

Obs 4 4 8 5 8 15 29 28 60 84 245

Exp 2.5 4.5 5.7 8.2 10.7 15.5 23.5 36.2 55.3 82.9

0

Obs 490 502 474 476 469 477 463 448 424 290 4513

Exp 491.5 501.5 476.3 472.8 466.3 476.5 468.5 439.8 428.7 291.1

Total 494 506 482 481 477 492 492 476 484 374 4758

Measures of Association:

(Between the Response Variable and Predicted Probabilities)

Pairs Number Percent Summary Measures

Concordant 881770 79.7 Somers' D 0.60

Discordant 213162 19.3 Goodman-Kruskal Gamma 0.61

Ties 10753 1.0 Kendall's Tau-a 0.06

Total 1105685 100.0



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## A.2.1.3 All Season Data: Chl -a > 40 μg/L Modeled with TN, TP, and 5 Subr egions

Response Information

Variable Value Count

CHLA_GT_40 1 139 (Event)

0 4619

Total 4758

Logistic Regression Table

Odds 95% CI

Predictor Coef SE Coef Z P Ratio Lower Upper

Constant 0.398446 0.674730 0.59 0.555

LN_TN_GM 0.215643 0.152691 1.41 0.158 1.24 0.92 1.67

LN_TP_GM 1.21312 0.134563 9.02 0.000 3.36 2.58 4.38

Region

2) Palm Beach 0.161837 0.448228 0.36 0.718 1.18 0.49 2.83

3) EAA -0.564848 0.512253 -1.10 0.270 0.57 0.21 1.55

4) EvPA -0.605954 0.630949 -0.96 0.337 0.55 0.16 1.88

5) West 0.277779 0.458948 0.61 0.545 1.32 0.54 3.25

Log-Likelihood = -536.331

Test that all slopes are zero: G = 183.441, DF = 6, P-Value = 0.000

Goodness-of-Fit Tests

Method Chi-Square DF P

Pearson 582.692 478 0.001

Deviance 389.502 478 0.999

Hosmer-Lemeshow 11.031 8 0.200

Table of Observed and Expected Frequencies:

(See Hosmer-Lemeshow Test for the Pearson Chi-Square Statistic)

Group

Value 1 2 3 4 5 6 7 8 9 10 Total

1

Obs 0 2 2 7 8 6 6 18 33 57 139

Exp 1.0 1.7 2.4 3.6 5.0 7.7 12.6 20.9 30.8 53.3

0

Obs 477 483 473 469 471 472 489 464 444 377 4619

Exp 476.0 483.3 472.6 472.4 474.0 470.3 482.4 461.1 446.2 380.7

Total 477 485 475 476 479 478 495 482 477 434 4758

Measures of Association:

(Between the Response Variable and Predicted Probabilities)

Pairs Number Percent Summary Measures

Concordant 517420 80.6 Somers' D 0.62

Discordant 116637 18.2 Goodman-Kruskal Gamma 0.63

Ties 7984 1.2 Kendall's Tau-a 0.04

Total 642041 100.0



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## A.2.1.4 All Season Data: Chl -a > 40 μg/L Modeled with TN and TP

Response Information

Variable Value Count

CHLA_GT_40 1 139 (Event)

0 4619

Total 4758

Logistic Regression Table

Odds 95% CI

Predictor Coef SE Coef Z P Ratio Lower Upper

Constant 0.464971 0.325860 1.43 0.154

LN_TN_GM -0.0021872 0.105922 -0.02 0.984 1.00 0.81 1.23

LN_TP_GM 1.22802 0.111662 11.00 0.000 3.41 2.74 4.25

Log-Likelihood = -541.707

Test that all slopes are zero: G = 172.690, DF = 2, P-Value = 0.000

Goodness-of-Fit Tests

Method Chi-Square DF P

Pearson 628.086 482 0.000

Deviance 400.253 482 0.997

Hosmer-Lemeshow 5.395 8 0.715

Table of Observed and Expected Frequencies:

(See Hosmer-Lemeshow Test for the Pearson Chi-Square Statistic)

Group

Value 1 2 3 4 5 6 7 8 9 10 Total

1

Obs 2 1 3 5 6 8 8 16 41 49 139

Exp 1.3 2.4 3.0 4.1 5.5 8.0 11.7 20.0 33.2 49.7

0

Obs 492 518 476 472 472 474 467 461 446 341 4619

Exp 492.7 516.6 476.0 472.9 472.5 474.0 463.3 457.0 453.8 340.3

Total 494 519 479 477 478 482 475 477 487 390 4758

Measures of Association:

(Between the Response Variable and Predicted Probabilities)

Pairs Number Percent Summary Measures

Concordant 514101 80.1 Somers' D 0.61

Discordant 121587 18.9 Goodman-Kruskal Gamma 0.62

Ties 6353 1.0 Kendall's Tau-a 0.03

Total 642041 100.0



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## A.2.1.5 All Season Data: Chl -a > 40 μg/L Modeled with TP

Response Information

Variable Value Count

CHLA_GT_40 1 139 (Event)

0 4619

Total 4758

Logistic Regression Table

Odds 95% CI

Predictor Coef SE Coef Z P Ratio Lower Upper

Constant 0.462312 0.299284 1.54 0.122

LN_TP_GM 1.22718 0.103893 11.81 0.000 3.41 2.78 4.18

Log-Likelihood = -541.707

Test that all slopes are zero: G = 172.689, DF = 1, P-Value = 0.000

Goodness-of-Fit Tests

Method Chi-Square DF P

Pearson 622.843 464 0.000

Deviance 397.481 464 0.989

Hosmer-Lemeshow 5.600 8 0.692

Table of Observed and Expected Frequencies:

(See Hosmer-Lemeshow Test for the Pearson Chi-Square Statistic)

Group

Value 1 2 3 4 5 6 7 8 9 10 Total

1

Obs 2 1 3 4 7 8 8 16 41 49 139

Exp 1.3 2.4 3.0 4.2 5.5 8.0 11.7 20.0 33.2 49.7

0

Obs 492 518 476 476 468 474 467 461 446 341 4619

Exp 492.7 516.6 476.0 475.8 469.5 474.0 463.3 457.0 453.8 340.3

Total 494 519 479 480 475 482 475 477 487 390 4758

Measures of Association:

(Between the Response Variable and Predicted Probabilities)

Pairs Number Percent Summary Measures

Concordant 514207 80.1 Somers' D 0.61

Discordant 121519 18.9 Goodman-Kruskal Gamma 0.62

Ties 6315 1.0 Kendall's Tau-a 0.03

Total 642041 100.0



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## A.2.1.6 Receiver Operator Characteristic Curves and Model Representation

1.0 0.8 0.6 0.4 0.2 0.0 1.0

0.8

0.6

0.4

0.2

0.0

1 - Specificity (false positive rate)Sensitivity (true positive rate) A) CHLA_GT_30 \ LN_TN LN_TP 5-reg

Area under the curve is approximately 0.8

1.0 0.8 0.6 0.4 0.2 0.0 1.0

0.8

0.6

0.4

0.2

0.0

1 - Specificity (false positive rate)Sensitivity (true positive rate) B) CHLA_GT_30 \ LN_TN LN_TP Grouped

Area under the curve is approximately 0.8



### Figure A-2

. All season ROC curve s; s ee Table A-3 for model descriptions



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1 0.1 0.01 0.001 10

1

0.1

0.01

Annual Geometric Mean Total Phosphorus, mg/LAnnual Geometric Mean Total Nitrogen, mg/L

1) No

2) Yes

EAA

Other Legend



### Figure A-3 . All season geometric mean TN as a function of all season geometric mean TP. Open circles and solid

triangles indicate “ WBID

- year s” for which ≤ 10 percent and > 10 percent of chl

- a observations exceed 30 μg/L,

respectively. Binary logistic regression model for 10 percent frequency represented by solid and dashed lines for

EAA subregion and other subregions grouped together, respectively. See Table A-4 for regression model.

Figure A-4 . All season geometric mean TN as a function of all season geometric mean TP. Symbols indicate

sub region. Bin ary logistic regression model for 10 percent frequency represented by solid and dashed lines for EAA

subregion and other subregions grouped together, respectively. See Table A-4 for regression model.



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## A.2.2 **Dry Season Model Results with TN and TP as Independent Variables**

A.2.2.1 Dry Season Data: Chl -a > 30 μg/L Modeled with TN, TP, and 5 Subr egions

Response Information

Variable Value Count

CHLA_GT_30 1 130 (Event)

0 2485

Total 2615

Logistic Regression Table

Odds 95% CI

Predictor Coef SE Coef Z P Ratio Lower Upper

Constant -0.0073823 0.778410 -0.01 0.992

LN_TN_GM 0.378984 0.140694 2.69 0.007 1.46 1.11 1.92

LN_TP_GM 1.04283 0.134708 7.74 0.000 2.84 2.18 3.69

Region

2) Palm Beach 0.421022 0.569815 0.74 0.460 1.52 0.50 4.65

3) EAA -0.586948 0.657115 -0.89 0.372 0.56 0.15 2.02

4) EvPA 0.628567 0.597789 1.05 0.293 1.87 0.58 6.05

5) West 1.28825 0.560891 2.30 0.022 3.63 1.21 10.89

Log-Likelihood = -441.881

Test that all slopes are zero: G = 150.052, DF = 6, P-Value = 0.000

Goodness-of-Fit Tests

Method Chi-Square DF P

Pearson 447.999 443 0.425

Deviance 344.103 443 1.000

Hosmer-Lemeshow 9.646 8 0.291

Table of Observed and Expected Frequencies:

(See Hosmer-Lemeshow Test for the Pearson Chi-Square Statistic)

Group

Value 1 2 3 4 5 6 7 8 9 10 Total

1

Obs 1 3 1 4 5 14 14 10 34 44 130

Exp 1.1 2.2 3.5 4.3 6.2 10.4 13.1 18.0 26.8 44.4

0

Obs 271 259 270 258 257 271 247 251 233 168 2485

Exp 270.9 259.8 267.5 257.7 255.8 274.6 247.9 243.0 240.2 167.6

Total 272 262 271 262 262 285 261 261 267 212 2615

Measures of Association:

(Between the Response Variable and Predicted Probabilities)

Pairs Number Percent Summary Measures

Concordant 255987 79.2 Somers' D 0.60

Discordant 63648 19.7 Goodman-Kruskal Gamma 0.60

Ties 3415 1.1 Kendall's Tau-a 0.06

Total 323050 100.0



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## A.2.2.2 Dry Season Data: Chl -a > 30 μg/L Modeled with TN, TP, a nd Grouped

Subr egions

Response Information

Variable Value Count

CHLA_GT_30 1 130 (Event)

0 2485

Total 2615

Logistic Regression Table

Odds 95% CI

Predictor Coef SE Coef Z P Ratio Lower Upper

Constant -0.0998278 0.372219 -0.27 0.789

LN_TN_GM 0.317040 0.129961 2.44 0.015 1.37 1.06 1.77

LN_TP_GM 0.942547 0.110959 8.49 0.000 2.57 2.06 3.19

Region2

5) West 1.04353 0.221670 4.71 0.000 2.84 1.84 4.38

Log-Likelihood = -447.197

Test that all slopes are zero: G = 139.419, DF = 3, P-Value = 0.000

Goodness-of-Fit Tests

Method Chi-Square DF P

Pearson 449.926 446 0.439

Deviance 354.736 446 0.999

Hosmer-Lemeshow 8.908 8 0.350

Table of Observed and Expected Frequencies:

(See Hosmer-Lemeshow Test for the Pearson Chi-Square Statistic)

Group

Value 1 2 3 4 5 6 7 8 9 10 Total

1

Obs 1 1 3 2 7 12 13 28 29 34 130

Exp 1.7 2.6 3.1 4.1 6.5 9.2 13.7 19.2 29.6 40.2

0

Obs 280 262 260 259 277 252 256 234 232 173 2485

Exp 279.3 260.4 259.9 256.9 277.5 254.8 255.3 242.8 231.4 166.8

Total 281 263 263 261 284 264 269 262 261 207 2615

Measures of Association:

(Between the Response Variable and Predicted Probabilities)

Pairs Number Percent Summary Measures

Concordant 253618 78.5 Somers' D 0.58

Discordant 66330 20.5 Goodman-Kruskal Gamma 0.59

Ties 3102 1.0 Kendall's Tau-a 0.05

Total 323050 100.0



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## A.2.2.3 Dry Season Data: Chl -a > 40 μg/L Modeled with TN, TP, and 5 Subr egions

Response Information

Variable Value Count

CHLA_GT_40 1 73 (Event)

0 2542

Total 2615

Logistic Regression Table

Odds 95% CI

Predictor Coef SE Coef Z P Ratio Lower Upper

Constant -0.189327 1.03774 -0.18 0.855

LN_TN_GM 0.251358 0.161311 1.56 0.119 1.29 0.94 1.76

LN_TP_GM 1.16302 0.173733 6.69 0.000 3.20 2.28 4.50

Region

2) Palm Beach 0.349359 0.793052 0.44 0.660 1.42 0.30 6.71

3) EAA -0.462409 0.878630 -0.53 0.599 0.63 0.11 3.52

4) EvPA -0.306962 1.00420 -0.31 0.760 0.74 0.10 5.27

5) West 1.17604 0.781090 1.51 0.132 3.24 0.70 14.98

Log-Likelihood = -279.153

Test that all slopes are zero: G = 108.106, DF = 6, P-Value = 0.000

Goodness-of-Fit Tests

Method Chi-Square DF P

Pearson 422.135 443 0.755

Deviance 259.165 443 1.000

Hosmer-Lemeshow 10.633 8 0.223

Table of Observed and Expected Frequencies:

(See Hosmer-Lemeshow Test for the Pearson Chi-Square Statistic)

Group

Value 1 2 3 4 5 6 7 8 9 10 Total

1

Obs 0 0 0 1 7 4 6 10 16 29 73

Exp 0.5 0.7 1.1 1.6 2.6 4.9 7.2 10.7 15.9 27.8

0

Obs 297 272 263 262 254 264 255 251 248 176 2542

Exp 296.5 271.3 261.9 261.4 258.4 263.1 253.8 250.3 248.1 177.2

Total 297 272 263 263 261 268 261 261 264 205 2615

Measures of Association:

(Between the Response Variable and Predicted Probabilities)

Pairs

Concordant Number

152775 Percent

82.3 Summary Measures

Somers' D 0.66

Discordant 30998 16.7 Goodman-Kruskal Gamma 0.66

Ties 1793 1.0 Kendall's Tau-a 0.04

Total 185566 100.0



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## A.2.2.4 Dry Season Data: Chl -a > 40 μg/L Modeled with TN and TP

Response Information

Variable Value Count

CHLA_GT_40 1 73 (Event)

0 2542

Total 2615

Logistic Regression Table

Odds 95% CI

Predictor Coef SE Coef Z P Ratio Lower Upper

Constant 0.459400 0.427139 1.08 0.282

LN_TN_GM -0.0737323 0.113853 -0.65 0.517 0.93 0.74 1.16

LN_TP_GM 1.21314 0.144947 8.37 0.000 3.36 2.53 4.47

Log-Likelihood = -288.105

Test that all slopes are zero: G = 90.202, DF = 2, P-Value = 0.000

Goodness-of-Fit Tests

Method Chi-Square DF P

Pearson 482.970 447 0.116

Deviance 277.069 447 1.000

Hosmer-Lemeshow 6.656 8 0.574

Table of Observed and Expected Frequencies:

(See Hosmer-Lemeshow Test for the Pearson Chi-Square Statistic)

Group

Value 1 2 3 4 5 6 7 8 9 10 Total

1

Obs 0 0 3 1 5 6 5 14 18 21 73

Exp 0.7 1.5 1.7 2.3 3.2 4.8 6.9 11.2 18.5 22.3

0

Obs 261 327 267 262 261 264 256 247 246 151 2542

Exp 260.3 325.5 268.3 260.7 262.8 265.2 254.1 249.8 245.5 149.7

Total 261 327 270 263 266 270 261 261 264 172 2615

Measures of Association:

(Between the Response Variable and Predicted Probabilities)

Pairs Number Percent Summary Measures

Concordant 148236 79.9 Somers' D 0.61

Discordant 35686 19.2 Goodman-Kruskal Gamma 0.61

Ties 1644 0.9 Kendall's Tau-a 0.03

Total 185566 100.0



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## A.2.2.5 Dry Season Data: Chl -a > 40 μg/L Modeled with TP

Response Information

Variable Value Count

CHLA_GT_40 1 73 (Event)

0 2542

Total 2615

Logistic Regression Table

Odds 95% CI

Predictor Coef SE Coef Z P Ratio Lower Upper

Constant 0.377379 0.404615 0.93 0.351

LN_TP_GM 1.18484 0.136485 8.68 0.000 3.27 2.50 4.27

Log-Likelihood = -288.303

Test that all slopes are zero: G = 89.807, DF = 1, P-Value = 0.000

Goodness-of-Fit Tests

Method Chi-Square DF P

Pearson 463.816 406 0.025

Deviance 269.687 406 1.000

Hosmer-Lemeshow 9.950 8 0.269

Table of Observed and Expected Frequencies:

(See Hosmer-Lemeshow Test for the Pearson Chi-Square Statistic)

Group

Value 1 2 3 4 5 6 7 8 9 10 Total

1

Obs 0 0 3 1 5 6 3 16 18 21 73

Exp 0.8 1.5 1.7 2.3 3.2 4.6 6.7 11.2 18.4 22.6

0

Obs 269 314 259 260 267 262 264 248 248 151 2542

Exp 268.2 312.5 260.3 258.7 268.8 263.4 260.3 252.8 247.6 149.4

Total 269 314 262 261 272 268 267 264 266 172 2615

Measures of Association:

(Between the Response Variable and Predicted Probabilities)

Pairs Number Percent Summary Measures

Concordant 147964 79.7 Somers' D 0.61

Discordant 35624 19.2 Goodman-Kruskal Gamma 0.61

Ties 1978 1.1 Kendall's Tau-a 0.03

Total 185566 100.0



## A

- 181.0 0.8 0.6 0.4 0.2 0.0 1.0

0.8

0.6

0.4

0.2

0.0

1 - Specificity (false positive rate)Sensitivity (true positive rate) A) CHLA_GT_30 \ LN_TN LN_TP 5-Reg

Area under the curve is approximately 0.8

1.0 0.8 0.6 0.4 0.2 0.0 1.0

0.8

0.6

0.4

0.2

0.0

1 - Specificity (false positive rate)Sensitivity (true positive rate) C) CHLA_GT_40 \ LN_TP LN_TN 5-Reg

Area under the curve is approximately 0.81

1.0 0.8 0.6 0.4 0.2 0.0 1.0

0.8

0.6

0.4

0.2

0.0

1 - Specificity (false positive rate)Sensitivity (true positive rate) E) CHLA_GT_40 \ LN_TP

Area under the curve is approximately 0.8 1.0 0.8 0.6 0.4 0.2 0.0 1.0

0.8

0.6

0.4

0.2

0.0

1 - Specificity (false positive rate)Sensitivity (true positive rate) B) CHLA_GT_30 \ LN_TN LN_TP Grouped

Area under the curve is approximately 0.79

1.0 0.8 0.6 0.4 0.2 0.0 1.0

0.8

0.6

0.4

0.2

0.0

1 - Specificity (false positive rate)Sensitivity (true positive rate) D) CHLA_GT_40 \ LN_TN LN_TP

Area under the curve is approximately 0.8 

### T echnical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria,

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## A.2.2.6 Receiver Operator Characteristic Curves and Model Representation

Figure A-5

. Dry season ROC curve s ; s ee Table A-3 for model descriptions



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Figure A-6 . Dry season geometric mean TN as a function of dry season geometric mean TP. Open circles and solid

triangles indicate “ WBID

- year s” for which ≤ 10 percent and > 10 percent of chl

- a observations exceed 30 μg/L,

respectively. Binary logistic regression model for 10 percent frequency represented by solid and dashed lines for

West subr egion and other subregions grouped together, respectively. See Table A-5 for regression model.

Figure A-7 . Dry season geometric mean TN as a function of dry season geometric mean TP. Symbols indicate

sub region. Bin ary logistic regression model for 10 percent frequency represented by solid and dashed lines for

West subregion and other subregions grouped together, respectively . See Table A-5 for regression model.



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## A.3 **Evaluation of Binary Logistic Regression Model Results**

EPA developed a series of multivariate binary logistic regressions designed to prevent algal

conditions exceeding 30 or 40 μg/L instantaneous chl- a an d limiting the frequency to no more

than 10 percent of the observations using all season data and dry season data in Sections A.2.1

and A.2.2 , respectively . The frequency of chl-a levels exceeding 30 or 40 μg/L w ere not

significantly different (see Section A.1.3). For this reason, EPA decided to focus further

regression interpretation using the all season data.

Because TN and TP were modeled simultaneously, there are multiple combinations of TN and

TP that can be substituted into the following equation and maintain a frequency, p , of 10 percent

(i.e., p = 0.1):

e ( a+b LN ൫TN GM ൯+c LN ൫TP GM ൯ )



## p =

1+e ( a+b LN ൫TN GM ൯+c LN ൫TP GM ൯ ) 

## Eq. 4

This is depicted in Figure A-8 . The black line represents the binary logistic regression equation

solved for a frequency of 10 percent where higher TN values are associated with lower TP

values. Although it is possible to derive a coupled TN and TP criteria , EPA does not believe that

a coupled criteria would be practical to implement. As a result, EPA selected an optimal set of

TN and TP criteria by maximizing the number of TN and TP observations meeting both criteria.

This is represented with the re d dashed lines A and B . In this example, criteria represented by

line B would encompass observations 5, 6, 7, and 8, whereas line A would encompass

observations 2, 3, 4, 5, 6, and 7. Because line A encompasses more observations, the

corresponding values of TN and TP would be the criteria proposed by EPA. Water bodies with

concentrations outside line A, but still to the left of the black line, might be appropriate for a sitespecific alternative criteria.

Applying this approach to the model results developed in Section A.2.1.2 using the all season

data and grouped subregions to prevent algal conditions > 30 μg/L instantaneous chl- a and

limiting the frequency to no more than 10 percent of the observations is presented in Figure A-9.

The optimal criteria for the Biscayne, Palm Beach, Everglades Protection A rea (EvPA), and

West subregions is represented by the red dashed line, 2 mg/L TN and 0.052 mg/L TP. The

optimal criteria for the EAA subregion range from 3.45 mg/L TN and 0.109 mg/L TP to

4.325 mg/L TN and 0.105 mg/L TP

, represented by a pair of solid red lines in Figure A-9. Note

that the lower TN value is coupled with the higher TP value for the EAA and vice versa. Given

the small percent difference in the range of TP values relative to the TN range for the EAA , EPA

would likely select 4.325 mg/L TN and 0.105 mg/L TP over 3.45 mg/L TN and 0.109 mg/L TP.

A

- 211 0.1 0.01 0.001 10

1

0.1

0.01 

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Annual Geometric Mean Total Phosphorus, mg/LAnnual Geometric Mean Total Nitrogen, mg/L



### A)

B) 1

2 3

4

5

6 7 8 equal to 10%. exceeding 30 μg/L Probability of chl-a



### Figure A-8 . Hypothetical relationship between annual geometric mean TN and annu al geometric mean TP. Black

line represents binary logistic regression equation solved for a frequency of 10 percent. Red dashed lines A) and B)

represent two candidate options for TN and TP criteria. Open circles represent various “ WBID

- year ” annual

geome tric mean TN and TP values

.

Figure A-9 . Criteria selection using the all season data and grouped subregions to prevent algal conditions

exceeding 30 μg/L instantaneous chl

- a and limiting the frequency to no more than 10 percent



## A

- 22Section Section T itle Table Description

A.4.1 Verified Matched See Table A

- 7

, Table Data includes all TN and TP observations from sites that have been

Data A-8 , and Table A-9 verified as a freshwater site on Class III water in the south Florida

nutrient region and that have matched chl

- a, TN, and T P. (Same data as

used throughout Section A.2 and A.3 .)

A.4.2 Verified Matched

Data/≤ 10 percent

Chl

- a Observations > See Table A

- 10

, Table A-11 , and

Table A-12 Same data as Section A.4.1 ; h owever, the data are further screened by

removing data associated with WBID

- years where the percent of chl

- a

observations is > 10%

30 μg/L

A.4.4 All Verified Sites, Not See Table A

- 16

, Same data as Section A.4.3 ; however, the data must come from a WBID

Impaired for Chl

- a,

Nutrients, or DO Table A-17 , and

Table A

- 18 that is not impaired for any of the following: chl

- a, nutrients, and DO A.4.3 All Verified Sites See Table A

- 13

, Table A-14 , and

Table A

- 15 Data includes all TN and TP observations from sites that have been

verified as a freshwater site on Class III water in the south Florida

nutrient region (with no requirement for matched chl

- a data)

A.4.5 All Verified Sites, Not

Impaired for Chl

- a or

Nutrients See Table A

- 19

, Table A-20 , and

Table A

- 21 Same data as Section A.4.3 ; however, the data must come from a WBID

that is not impaired for any of the following: chl

- a and nutrients 

### T echnical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria,

Volume 3 South Florida Inland Flowing Waters



## A.4 **Distributional Statistics**

This section provides a compilation of distributional statistics for various retr ievals of data as

summarized in Table A-6.

Table A-6 . Descriptions of data sets used for additional distributional statistics



## A

- 23Season Subregion Number of

WBID-year

O bservations Total

O bservations Average

WBID-year

LN(TN

GM ) Standard

D eviation

WBID-year

LN(TN

GM ) Average

WBID-year

LN(TP

GM ) Standard

D eviation

WBID-year

LN(TP

GM )

A) Dry

A) Dry

A) Dry

A) Dry

A) Dry

B) All

B) All

B) All

B) All

B) All 1) Biscayne

2) Palm Beach

3) EAA

4) EvPA

5) West

1) Biscayne

2) Palm Beach

3) EAA

4) EvPA

5) West 97

181

37

22

113

119

185

40

24

117 532

720

180

472

711

1045

1288

398

828

1199 - 0.061539

0.296803

0.793659

0.240177

- 0.643558

0.009344

0.271566

0.900271

0.304357

- 0.637727 0.410550

0.352078

0.302649

0.300521

1.219899

0.447709

0.353699

0.333910

0.321106

1.094289 - 4.741048

- 3.371574

- 2.506822

- 4.170031

- 3.205356

- 4.539548

- 3.270395

- 2.449081

- 4.101082

- 3.189833 0.803424

1.030370

0.681320

0.589848

0.844872

0.819902

0.942541

0.593240

0.721794

0.863019

Number of WBID-year Percentiles of A nnual G eometric M ean TN ( mg/L )

O bservations

10 th 25 th 50 th 75 th 90 th Season Subregion ( T otal O bservations)

A) Dry 1) Biscayne 97 (532) 0.56 0.71 0.94 1.24 1.59

A) Dry 2) Palm Beach 181 (720) 0.86 1.06 1.35 1.71 2.11

A) Dry 3) EAA 37 (180) 1.50 1.80 2.21 2.71 3.26

A) Dry 4) EvPA 22 (472) 0.87 1.04 1.27 1.56 1.87

A) Dry 5) West 113 (711) 0.11 0.23 0.53 1.20 2.51

B) All 1) Biscayne 119 (1045) 0.57 0.75 1.01 1.37 1.79

B) All 2) Palm Beach 185 (1288) 0.83 1.03 1.31 1.67 2.06

B) All 3) EAA 40 (398) 1.60 1.96 2.46 3.08 3.77

B) All 4) EvPA 24 (828) 0.90 1.09 1.36 1.68 2.05

B) All 5) West 117 (1199) 0.13 0.25 0.53 1.11 2.15

Note: Percentiles computed as using Microsoft Excel ® formula EXP(NORM.INV(z,x,s)) where x and s are the average and

standard deviation of the WBID

- year annua l geometric mean in log

e - transformed space; z corresponds to the percentile

expressed as a fraction. 

### T echnical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria,

Volume 3 South Florida Inland Flowing Waters



## A.4.1 **Verified Matched Data**

Table A-7 . Verified matched data: mean and standard deviation of WBID

- year geometric mean TN and TP in log

e 

### transformed space by season and subregion

Table A-8

. Verified matched data: percentiles of geometric mean TN concentrations



## A

- 24Number of WBID -year Percentiles of A nnual Geometric M ean TP ( mg/L )

O bservations

10 th 25 th 50 th 75 th 90 th Season Subregion ( T otal O bservations)

A) Dry 1) Biscayne 97 (532) 0.003 0.005 0.009 0.015 0.024

A) Dry 2) Palm Beach 181 (720) 0.009 0.017 0.034 0.069 0.129

A) Dry 3) EAA 37 (180) 0.034 0.051 0.082 0.129 0.195

A) Dry 4) EvPA 22 (472) 0.007 0.010 0.015 0.023 0.033

A) Dry 5) West 113 (711) 0.014 0.023 0.041 0.072 0.120

B) All 1) Biscayne 119 (1045) 0.004 0.006 0.011 0.019 0.031

B) All 2) Palm Beach 185 (1288) 0.011 0.020 0.038 0.072 0.127

B) All 3) EAA 40 (398) 0.040 0.058 0.086 0.129 0.185

B) All 4) EvPA 24 (828) 0.007 0.010 0.017 0.027 0.042

B) All 5) West 117 (1199) 0.014 0.023 0.041 0.074 0.124

Note: Percentiles computed as using Microsoft Excel® formula EXP(NORM.INV(z,x,s)) where x and s are the average and

standard deviation of the WBID -y ear annual geometric mean in log

e - transformed space; z corresponds to the percentile

expressed as a fraction.



### Table A- 10 . Verified matched data/≤ 10 percent c hl

- a ob servations > 30 μg/L: mean and standard deviation of

WBID

- year geometric mean TN and TP in log

e 

### - transformed space by season and subregion

Season Subregion Number of

WBID-year

O bservations Total

O bservations Average

WBID-year

LN(TN

GM ) Standard

D eviation

WBID-year

LN(TN

GM ) Average

WBID-year

LN(TP

GM ) Standard

D eviation

WBID-year

LN(TP

GM )

A) Dry

A) Dry

A) Dry

A) Dry

A) Dry

B) All

B) All

B) All

B) All

B) All 1) Biscayne

2) Palm Beach

3) EAA

4) EvPA

5) West

1) Biscayne

2) Palm Beach

3) EAA

4) EvPA

5) West 97

154

28

21

81

113

140

27

22

88 532

603

133

440

487

1006

971

293

774

925 - 0.061539

0.272248

0.802556

0.239122

- 0.721445

0.008365

0.259279

0.862704

0.283094

- 0.756201 0.410550

0.344750

0.313940

0.307900

1.248559

0.457017

0.356991

0.333325

0.316449

1.134544 - 4.741048

- 3.525786

- 2.593030

- 4.193725

- 3.229954

- 4.592959

- 3.521491

- 2.543251

- 4.177560

- 3.204139 0.803424

1.019832

0.747360

0.593589

0.859188

0.786773

0.901267

0.622502

0.693769

0.835067 

### T echnical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria,

Volume 3 South Florida Inland Flowing Waters

Table A-9 . Verified matched data: percentiles of geometric mean TP concentrations



## A.4.2 **Verified Matched Data/≤ 10 percent Chl**

**- a**  **O bservations > 30 μg/L** 

A

- 25Number of WBID

- y ear Percentiles of A nnual Geometric M ean TN ( mg/L )

O bservations

10 th 25 th 50 th 75 th 90 th Season Subregion (Total O bservations)

A) Dry 1) Biscayne 97 (532) 0.56 0.71 0.94 1.24 1.59

A) Dry 2) Palm Beach 154 (603) 0.84 1.04 1.31 1.66 2.04

A) Dry 3) EAA 28 (133) 1.49 1.81 2.23 2.76 3.34

A) Dry 4) EvPA 21 (440) 0.86 1.03 1.27 1.56 1.88

A) Dry 5) West 81 (487) 0.10 0.21 0.49 1.13 2.41

B) All 1) Biscayne 113 (1006) 0.56 0.74 1.01 1.37 1.81

B) All 2) Palm Beach 140 (971) 0.82 1.02 1.30 1.65 2.05

B) All 3) EAA 27 (293) 1.55 1.89 2.37 2.97 3.63

B) All 4) EvPA 22 (774) 0.88 1.07 1.33 1.64 1.99

B) All 5) West 88 (925) 0.11 0.22 0.47 1.01 2.01

Note: Percentiles computed as using Microsoft Excel® formula EXP(NORM.INV(z,x,s)) where x and s are the average and

standard deviation of the WBID -y ear annual geometric mean in log

e - transformed space; z corresponds to the percentile

expressed as a fraction.

Number of WBID-year Percentiles of Annual Geometric M ean TP ( mg/L )

observations

10 th 25 th 50 th 75 th 90 th Season Subregion ( Total O bservations)

A) Dry 1) Biscayne 97 (532) 0.003 0.005 0.009 0.015 0.024

A) Dry 2) Palm Beach 154 (603) 0.008 0.015 0.029 0.059 0.109

A) Dry 3) EAA 28 (133) 0.029 0.045 0.075 0.124 0.195

A) Dry 4) EvPA 21 (440) 0.007 0.010 0.015 0.023 0.032

A) Dry 5) West 81 (487) 0.013 0.022 0.040 0.071 0.119

B) All 1) Biscayne 113 (1006) 0.004 0.006 0.010 0.017 0.028

B) All 2) Palm Beach 140 (971) 0.009 0.016 0.030 0.054 0.094

B) All 3) EAA 27 (293) 0.035 0.052 0.079 0.120 0.175

B) All 4) EvPA 22 (774) 0.006 0.010 0.015 0.024 0.037

B) All 5) West 88 (925) 0.014 0.023 0.041 0.071 0.118

Note: Percentiles computed as using Microsoft Excel® formula EXP(NORM.INV(z,x,s)) where x and s are the average and

standard deviation of the WBID

- year annual geometric mean in log

e - transformed space; z corresponds to the percentile

expressed as a fraction. 

### T echnical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria,

Volume 3 South Florida Inland Flowing Waters

Table A- 11 . Verified matched data/≤ 10 percent c hl

- a observations > 30 μg/L: percentiles of geometric mean TN

concentrations

Table A- 12

. Verified matched data/≤ 10 percent c hl

- a observations > 30 μg/L: percentiles of geometric mean TP

concentrations



## A

- 26Standard Standard

Number of Number of Average D eviation Average D eviation

WBID-year WBID-year WBID-year WBID-year WBID-year WBID-year

Subregion O bservations TN O bservations TP LN(TN

GM ) LN(TN

GM ) LN(TP

GM ) LN(TP

GM )

1) Biscayne 346 368 0.170232 0.501901

- 5.125960 1.030701

2) Palm Beach 356 366 0.266517 0.314791

- 3.083897 0.840319

3) EAA 175 211 0.757627 0.358001

- 2.804153 0.775932

4) EvPA 194 208 0.472393 0.248973

- 3.880561 0.703899

5) West 230 261

- 0.249670 0.810359

- 3.046594 0.758239

Subregion Percentiles of A nnual G eometric M ean TN ( mg/L )

10 th 25 th 50 th 75 th 90 th

1) Biscayne 0.62 0.85 1.19 1.66 2.26

2) Palm Beach 0.87 1.06 1.31 1.61 1.95

3) EAA 1.35 1.68 2.13 2.72 3.38

4) EvPA 1.17 1.36 1.60 1.90 2.21

5) West 0.28 0.45 0.78 1.35 2.20

Note: Percentiles computed as using Microsoft Excel® formula EXP(NORM.INV(z,x,s)) where x and s are the average and

standard deviation of the WBID

- year annual geometric mean in log

e - transformed space; z corresponds to the percentile

expressed as a fraction.

Subregion Percentiles of A nnual G eometric M ea n TP ( mg/L )

10 th 25 th 50 th 75 th 90 th

1) Biscayne 0.002 0.003 0.006 0.012 0.022

2) Palm Beach 0.016 0.026 0.046 0.081 0.134

3) EAA 0.022 0.036 0.061 0.102 0.164

4) EvPA 0.008 0.013 0.021 0.033 0.051

5) West 0.018 0.028 0.048 0.079 0.126

Note: Percentiles computed as using Microsoft Excel® formula EXP(NORM.INV(z,x,s)) where x and s are the average and

standard deviation of the WBID

- year annual geometric mean in log

e - transformed space; z corresponds to the percentile

expressed as a fraction. 

### T echnical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria,

Volume 3 South Florida Inland Flowing Waters



## A.4.3 **All V**  **erified S**  **ites**

Table A- 13

. All verified sites: mean and standard deviation of WBID

- year annual geometric mean TN and TP in

log

e 

### - transformed space by subregion

Table A- 14

. A ll verified sites: percentiles of annual geometric mean TN concentrations

Table A- 15

. A ll verified sites: percentiles of annual geometric mean TP concentrations



## A

- 27

### Table A- 16 . All verified sites, not impaired for chl

- a, nutrients, or DO : mean and standard deviation of WBID

- year

annual geometric mean TN and TP in log

e 

### - transformed space by subregion

Standard Standard

Number of Number of Average D eviation Average D eviation

WBID-year WBID-year WBID-year WBID-year WBID-year WBID-year

Subregion O bservations TN O bservations TP LN(TN

GM ) LN(TN

GM ) LN(TP

GM ) LN(TP

GM )

1) Biscayne 3 3 0.203588 0.181094

- 6.958087 0.140237

2) Palm Beach 2 2

- 0.023241 1.540546

- 2.621012 0.708166

3) EAA 0 4

-­ -­ - 2.601116 0.121802

4) EvPA 1 0 0.527093

-­ -­ -­

5) West 67 85

- 0.101862 0.492660

- 3.078030 0.588221

Subregion Percentiles of A nnual Geometric M ean TN ( mg/L )

10 th 25 th 50 th 75 th 90 th

1) Biscayne 0.97 1.08 1.23 1.39 1.55

2) Palm Beach 0.14 0.35 0.98 2.76 7.04

3) EAA

-­ -­ -­ -­ -­

4) EvPA

-- -- -- -- -­

5) West 0.48 0.65 0.90 1.26 1.70

Note: Percentiles computed as using Microsoft Excel® formula EXP(NORM.INV(z,x,s)) where x and s are the average and

standard deviation of the WBID -y ear annual geometric mean in log

e - transformed space; z corresponds to the percentile

expressed as a fraction.

Subregion Percentiles of A nnual Geometric M ean TP ( mg/L )

10 th 25 th 50 th 75 th 90 th

1) Biscayne 0.001 0.001 0.001 0.001 0.001

2) Palm Beach 0.029 0.045 0.073 0.117 0.180

3) EAA 0.063 0.068 0.074 0.081 0.087

4) EvPA

-- -- -- -- -­

5) West 0.022 0.031 0.046 0.068 0.098

Note: Percentiles computed as using Microsoft Excel® formula EXP(NORM.INV(z,x,s)) where x and s are the average and

standard deviation of the WBID -y ear annual geometric mean in log

e - transformed space; z corresponds to the percentile

expressed as a fraction. 

### T echnical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria,

Volume 3 South Florida Inland Flowing Waters



## A.4.4 **A ll Verified Sites, Not Impaired for**  **Chl -a**  **, Nutrients, or DO** 

Table A- 17 . All verified sites, not impaired for chl

- a, nutrients, or DO : percentiles of annual geometric mean TN

concentrations

Table A- 18

. All verified sites, not impaired for chl

- a, n utrients, or DO : percentiles of annual geometric mean TP

concentrations



## A

- 28

### Table A- 19 . All verified sites , not impaired for chl

- a or nutrients: mean and standard deviation of WBID

- year

annual geometric mean TN and TP in log

e 

### - transformed space by subregion

Number of Standard Standard

Number of WBID-year Average D eviation Average D eviation

WBID-year O bservations WBID-year WBID-year WBID-year WBID-year

Subregion O bservations TN TP LN(TN

GM ) LN(TN

GM ) LN(TP

GM ) LN(TP

GM )

1) Biscayne 314 337 0.217320 0.473160

- 5.084048 1.017249

2) Palm Beach 145 147 0.274978 0.314045

- 3.460695 0.783614

3) EAA 2 18 0.228898 0.822639

- 2.812306 0.344495

4) EvPA 110 126 0.374796 0.216858

- 4.225245 0.488807

5) West 230 261

- 0.249670 0.810359

- 3.046594 0.758239

Subregion Percentiles of A nnual Geometric M ean TN (m g/L )

10 th 25 th 50 th 75 th 90 th

1) Biscayne 0.68 0.90 1.24 1.71 2.28

2) Palm Beach 0.88 1.07 1.32 1.63 1.97

3) EAA 0.44 0.72 1.26 2.19 3.61

4) EvPA 1.10 1.26 1.45 1.68 1.92

5) West 0.28 0.45 0.78 1.35 2.20

Note: Percentiles computed as using Microsoft Excel® formula EXP(NORM.INV(z,x,s)) where x and s are the average and

standard deviation of the WBID -y ear annual geometric mean in log

e - transformed space; z corresponds to the percentile

expressed as a fraction.

Subregion Percentiles of A nnual Geometric M ean TP ( mg/L )

10 th 25 th 50 th 75 th 90 th

1) Biscayne 0.002 0.003 0.006 0.012 0.023

2) Palm Beach 0.012 0.019 0.031 0.053 0.086

3) EAA 0.039 0.048 0.060 0.076 0.093

4) EvPA 0.008 0.011 0.015 0.020 0.027

5) West 0.018 0.028 0.048 0.079 0.126

Note: Percentiles computed as using Microsoft Excel® formula EXP(NORM.INV(z,x,s)) where x and s are the average and

standard deviation of the WBID -y ear annual geometric mean in log

e - transformed space; z corresponds to the percentile

expressed as a fraction. 

### T echnical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria,

Volume 3 South Florida Inland Flowing Waters



## A.4.5 **All Verified Sites, Not Impaired for Chl**  **-a or Nu**  **trients**

Table A- 20 . All verified sites , not impaired for chl

- a or nutrients : percentiles of annual geometric mean TN

concentrations

Table A- 21

. All verified sites , not impaired for chl

- a or nutrients : percentiles of annual geometric mean TP

concentrations



## A

- 29Binary Logistic Regression Model: 90th Percentile Annual

Designed to prevent algal conditions Geometric Mean:

> 30 μg/L instantaneous chl

- a and limiting the Data screened by removing data associated with

frequency to no more than 10 % of the time WBID -y ears where the percent of chl

- a observations

Method (s ee also Section A.3 ) is more than 10 % (s ee also Section A.4.2 )

Subr egion TN ( mg/L ) TP ( mg/L ) TN ( mg/L ) TP ( mg/L )

1) Biscayne 2 0.052 1.81 0.028

2) Palm Beach 2 0.052 2.05 0.094

4) EvPA *

‒ ‒ ‒ ‒ 3) EAA *

‒ ‒ ‒ ‒

5) West 2 0.052 2.01 0.118

* EPA is not reporting candidate criteria for the EAA and EvPA. 

### Table A- 22

. Candidate TP criteria from binary logistic regression results and candidate TN criteria based on TN

- TP

ratio where annual geometri c mean TP exceeds corresponding candidate criteria

. T echnical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria,

Volume 3 South Florida Inland Flowing Waters



## A.5 **Key Results**

EPA considered a range of options for developing numeric nutrient criteria. For reasons

described in the main body of the document , EPA decided to focus on the grouped region binary

logistic regression model for > 30 μg/L chl -a for 10 percent of the time u sing all the data to

compute TP and TN criteria (see Table A-22). EPA also considered estimating criteria using a

reference condition approach. In one analysis, all data are screened by removing data associated

with WBID

- year s where the percent of chl-a observations is > 10 percent (see Section A.4.2 ).

The 90th percentile concentrations are presented in Table A-22 . Alternatively

, data were

screened by removing all WBIDs that are on the CWA 303(d) listing of impairments for

nutrients, chl-a, or DO as of December 2010 (see Section A.4.4 ).



## A.6 **References**

Gönen, M. 2006. Receiver Operating Characteristic (ROC) Curves. In Thirty -first Annual SAS®

Users Group International Conference , Cary, NC.

http://www2.sas.com/proceedings/sugi31/210-31.pdf . Accessed September 2011.

Hosmer, D.W. and S. Lemeshow. 2000. Applied Logistic Regression . 2nd ed. John Wiley &

Sons, Inc.

USEPA. 2010a. Using Stressor-Response Relationships to Derive Numeric Nutrient Criteria

. EPA -820-S-10-001. U.S. Environmental Protection Agency, Office of Water and Office

of Science and Technology. Washington, D.C.

http://water.epa.gov/scitech/swguidance/standards/criteria/nutrients/upload/finalstressor2

010.pdf . Accessed December 2011.

USEPA. 2010b. Water Quality Standards for the State of Florida’s Lakes and Flowing Waters;

Final Rule . Fed. Regist., Dec. 6, 2010. 75:75762. U.S. Environmental Protection Agency,

Office of Water. http://www.gpo.gov/fdsys/pkg/FR-2010-12-06/pdf/2010-29943.pdf

.

A

- 30