Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria, 

Volume 3 South Florida Inland Flowing Waters 

Appendix A: South Florida Inland

Flowing Waters—Logistic Regression

Analysis 

November 30, 2012
 
 

Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria, 

Volume 3 South Florida Inland Flowing Waters 

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 Regression .............................................................................. 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 Model 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-i 
 

 

Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria, 

Volume 3 South Florida Inland Flowing Waters 

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, 

respectively.............................................................................................................. 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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Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria, 

Volume 3 South Florida Inland Flowing Waters 

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 samples 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 TN 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
 

function of annual geometric mean TN (TNGM), annual geometric mean TP
 

(TPGM), 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 (TNGM), geometric mean TP (TPGM), 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 loge-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 logetransformed 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 loge-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 logetransformed 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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Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria, 

Volume 3 South Florida Inland Flowing Waters 

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 logetransformed 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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CI 

Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria, 

Volume 3 South Florida Inland Flowing Waters 

Abbreviations and Acronyms 

AUC area under the curve 

Chl-a chlorophyll a 

CHLA_GT_30 chl-a > 30 μg/L 

CHLA_GT_40 chl-a > 40 μg/L 

confidence interval 

Coef coefficient 

DF degrees of freedom 

EAA Everglades Agricultural Area 

EvPA Everglades Protection Area 

Exp expected 

LN natural logarithm; also loge 

LN_TN_GM natural logarithm transformed geometric mean total nitrogen; 

also LN(TNGM) or loge(TNGM) 

LN_TP_GM natural logarithm transformed geometric mean total phosphorus; 

also LN(TPGM) or loge(TPGM) 

Obs observed 

P p-value 

ROC receiver operator characteristic 

SE standard error 

TN total nitrogen 

TP total phosphorus 

TN_AGM annual geometric mean TN; also AGM TN or TNGM 

TP_AGM annual geometric mean TP; also AGM TP or TPGM 

WBID water body identification number 

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Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria, 

Volume 3 South Florida Inland Flowing Waters 

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 waters (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 Sections 

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 loge) 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 number (WBID) IWR Run 40 water 

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

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

that sites were from private agricultural 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 loge-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-year, in 

which all nutrient data within a specific year were loge-transformed and then averaged. Paired 

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

A-1 
 

 

 

 

 

 

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Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria, 

Volume 3 South Florida Inland Flowing Waters 

(see binary regression explanation below). All nutrient data were loge-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 stressorresponse approach (USEPA 2010a) similar to that used to derive numeric nutrient TN and 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 function in Minitab v16. 

The basic form of the logistic regression equation is given by 

p Eq. 1 LN ൬ a + b LN(TNGM) + c LN(TPGM) 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(TNGM) and LN(TPGM) are the logetransformed geometric mean TN and TP. After the regression coefficients are estimated, the 

value of p can be estimated for various values of TNGM and TPGM using the following equation: 

e(a+b LN(TNGM)+c LN(TPGM)) Eq. 2

p = 

1 + e(a+b LN(TNGM)+c LN(TPGM)) 

Values of TPGM can be estimated for a given value of p and TNGM by 

p LNቀ

1−pቁ− a−b LN(TNGM) Eq. 3 

TPGM = 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 predicts 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 extremely rare (Hosmer and Lemeshow 2000). 

A-2 
 

 

 

 

Percent of Percent of 

Samples with 

Chl-a 

Samples with 

Chl-a 

Samples with 

Chl-a 

Samples with 

Chl-a 

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

All All Subregions 4,758 245 139 5.15% 2.92% 

All 1) Biscayne 1,045 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 with 

Chl-a 

Samples with 

Chl-a 

Samples with 

Chl-a 

Samples with 

Chl-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% 

Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria, 

Volume 3 South Florida Inland Flowing Waters 

A.1.3 Frequency of Chl-a Observations Exceeding 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 samples 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 exceeding 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 

percentage (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 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 

Table A-2. Number of samples with match chl-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 

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Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria, 

Volume 3 South Florida Inland Flowing Waters 

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. 

0.001 0.01 0.1 1

10 

1 

0.1 

0.01 

Annual Geometric Mean TP, mg/L 

Annual Geometric Mean TN, mg/L 

1) No 

2) Yes 

Legend 

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, 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 binary 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 while Section A.6 lists the references. 

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

Modeled 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 

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

A-4 
 

Regression 

Diagnostics Subregions ROC Curve 

(see Section) Season modeled Chl-a Nitrogen Phosphorus (see Figure) Notes 

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

Figure A-2A different subregion 

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

Figure A-2B 

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

Figure A-2C 

Subregions not 

significantly different 

A.2.1.4 All -- > 40 P = 0.984 P < 0.05 Area = 0.8 

Figure A-2D 

A.2.1.5 All -­ > 40 -­ P < 0.05 Area = 0.8 

Figure A-2E 

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

Figure A-5A different subregion 

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

Figure A-5B 

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

Figure A-5C significantly different 

A.2.2.4 Dry -­ > 40 P = 0.517 P < 0.05 Area = 0.8 

Figure A-5D 

A.2.2.5 Dry -- > 40 -- P < 0.05 Area = 0.8 

Figure A-5E 

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 

Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria, 

Volume 3 South Florida Inland Flowing Waters 

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 statistically 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 subregions were first evaluated with a variable for 

the subregions used to assess 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 > 30 μg/L was modeled using all seasons data, with both TN and TP as 

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

of both TN and TP and a ROC curve AUC of 0.8. Of the different 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-5 
 

 

 

 

 

 

 

Subregion 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)) 

Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria, 

Volume 3 South Florida Inland Flowing Waters 

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 resulting 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 plots that 

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

respectively. 

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

geometric mean TN (TNGM), annual geometric mean TP (TPGM), and grouped subregions where p = y/(1 + y) 

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

mean TN (TNGM), geometric mean TP (TPGM), and grouped subregions where p = y/(1 + y) 

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Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria, 

Volume 3 South Florida Inland Flowing Waters 

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, and 5 Subregions 

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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Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria, 

Volume 3 South Florida Inland Flowing Waters 

A.2.1.2 All Season Data: Chl-a > 30 μg/L Modeled with TN, TP, and Grouped Subregions 

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 

A-8 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria, 

Volume 3 South Florida Inland Flowing Waters 

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

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 

A-9 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria, 

Volume 3 South Florida Inland Flowing Waters 

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 

A-10 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria, 

Volume 3 South Florida Inland Flowing Waters 

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 

A-11 
 

 

 

 

 

 

Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria, 

Volume 3 South Florida Inland Flowing Waters 

A.2.1.6 Receiver Operator Characteristic Curves and Model Representation 

0.0 0.2 0.4 0.6 0.8 1.0 

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 

0.0 0.2 0.4 0.6 0.8 1.0 

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 curves; see Table A-3 for model descriptions 

A-12 
 

 

 

Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria, 

Volume 3 South Florida Inland Flowing Waters 

0.001 0.01 0.1 1

10 

1 

0.1 

0.01 

Annual Geometric Mean Total Phosphorus, mg/L 

Annual 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-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. 

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 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria, 

Volume 3 South Florida Inland Flowing Waters 

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 Subregions 

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 

A-14 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria, 

Volume 3 South Florida Inland Flowing Waters 

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

Subregions 

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 

A-15 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria, 

Volume 3 South Florida Inland Flowing Waters 

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

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 

A-16 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria, 

Volume 3 South Florida Inland Flowing Waters 

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 

A-17 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria, 

Volume 3 South Florida Inland Flowing Waters 

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-18 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.0 0.2 0.4 0.6 0.8 1.0 

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 

0.0 0.2 0.4 0.6 0.8 1.0 

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 

0.0 0.2 0.4 0.6 0.8 1.0 

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 

0.0 0.2 0.4 0.6 0.8 1.0 

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 

0.0 0.2 0.4 0.6 0.8 1.0 

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 

Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria, 

Volume 3 South Florida Inland Flowing Waters 

A.2.2.6 Receiver Operator Characteristic Curves and Model Representation 

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

A-19 
 

 

Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria, 

Volume 3 South Florida Inland Flowing Waters 

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. 

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 
 

Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria, 

Volume 3 South Florida Inland Flowing Waters 

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 and 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 were 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 LN൫TNGM൯+c LN൫TPGM൯)

p = 

1+e(a+b LN൫TNGM൯+c LN൫TPGM൯) 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 red 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 Area (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-21 
0.001 0.01 0.1 1

10

1

0.1

0.01

 

Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria, 

Volume 3 South Florida Inland Flowing Waters 

Annual Geometric Mean Total Phosphorus, mg/L 

Annual 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 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. 

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 
 

 

 

 

 

Section Section Title 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 TP. (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; however, 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 

Technical 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 retrievals of data as 

summarized in Table A-6. 

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

A-23 
 

Season Subregion 

Number of 

WBID-year 

Observations 

Total 

Observations 

Average 

WBID-year 

LN(TNGM) 

Standard 

Deviation 

WBID-year 

LN(TNGM) 

Average 

WBID-year 

LN(TPGM) 

Standard 

Deviation 

WBID-year 

LN(TPGM) 

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 Annual Geometric Mean TN (mg/L) Observations 

10th 25th 50th 75th 90th Season Subregion (Total Observations) 

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 annual geometric mean in log e-transformed space; z corresponds to the percentile 

expressed as a fraction. 

Technical 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 logetransformed space by season and subregion 

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

A-24 
Number of WBID-year Percentiles of Annual Geometric Mean TP (mg/L)Observations 

10th 25th 50th 75th 90th Season Subregion (Total Observations) 

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-year 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 chl-a observations > 30 μg/L: mean and standard deviation of 

WBID-year geometric mean TN and TP in loge-transformed space by season and subregion 

Season Subregion 

Number of 

WBID-year 

Observations 

Total 

Observations 

Average 

WBID-year 

LN(TNGM) 

Standard 

Deviation 

WBID-year 

LN(TNGM) 

Average 

WBID-year 

LN(TPGM) 

Standard 

Deviation 

WBID-year 

LN(TPGM) 

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 

Technical 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 Observations > 30 μg/L 

A-25 
Number of WBID-year Percentiles of Annual Geometric Mean TN (mg/L)Observations 

10th 25th 50th 75th 90th Season Subregion (Total Observations) 

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-year 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 Mean TP (mg/L)observations 

10th 25th 50th 75th 90th Season Subregion (Total Observations) 

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. 

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

concentrations 

Table A-12. Verified matched data/≤ 10 percent chl-a observations > 30 μg/L: percentiles of geometric mean TP 

concentrations 

A-26 
Standard Standard 

Number of Number of Average Deviation Average Deviation 

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

Subregion Observations TN Observations TP LN(TNGM) LN(TNGM) LN(TPGM) LN(TPGM) 

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 Annual Geometric Mean TN (mg/L) 

10th 25th 50th 75th 90th 

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 Annual Geometric Mean TP (mg/L) 

10th 25th 50th 75th 90th 

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. 

Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria, 

Volume 3 South Florida Inland Flowing Waters 

A.4.3 All Verified Sites 

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

loge-transformed space by subregion 

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

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 loge-transformed space by subregion 

Standard Standard 

Number of Number of Average Deviation Average Deviation 

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

Subregion Observations TN Observations TP LN(TNGM) LN(TNGM) LN(TPGM) LN(TPGM) 

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 Annual Geometric Mean TN (mg/L)

10th 25th 50th 75th 90th 

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-year annual geometric mean in log e-transformed space; z corresponds to the percentile 

expressed as a fraction. 

Subregion 

Percentiles of Annual Geometric Mean TP (mg/L)

10th 25th 50th 75th 90th 

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-year annual geometric mean in log e-transformed space; z corresponds to the percentile 

expressed as a fraction. 

Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria, 

Volume 3 South Florida Inland Flowing Waters 

A.4.4 All 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, nutrients, 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 loge-transformed space by subregion 

Number of Standard Standard 

Number of WBID-year Average Deviation Average Deviation 

WBID-year Observations WBID-year WBID-year WBID-year WBID-year 

Subregion Observations TN TP LN(TNGM) LN(TNGM) LN(TPGM) LN(TPGM) 

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 Annual Geometric Mean TN (mg/L)

10th 25th 50th 75th 90th 

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-year annual geometric mean in log e-transformed space; z corresponds to the percentile 

expressed as a fraction. 

Subregion 

Percentiles of Annual Geometric Mean TP (mg/L)

10th 25th 50th 75th 90th 

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-year annual geometric mean in log e-transformed space; z corresponds to the percentile 

expressed as a fraction. 

Technical 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 Nutrients 

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-29 
 

 

 

 

 

 

 

 

Binary 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-years where the percent of chl-a observations 

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

Subregion 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 geometric mean TP exceeds corresponding candidate criteria. 

 

Technical 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 using 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-years 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