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### Calculations Performed in Developing the Proposed 2012 RWQC V**alues :**  This memo presents the calculations and process of rounding value s performed by EPA in the process of developing the 2012 RWQC values. **1. The Recommended 2012 RWQC values Table 1.**  **Recommended 2012**  **RWQC. Criteria**  **Elements Estimated Illness Rate (NGI): 36** 

**per 1,000 primary contact recreators**  OR **Estimated Illness Rate (NGI): 32 per 1,000 primary contact** 

**recreators Magnitude**  **Magnitude** Indicator GM

(cfu/ 100 mL) **a** STV

(cfu/ 100 mL) **a** GM (cfu/ 100 mL) **a** STV

(cfu/ 100 mL) **a** Enterococci

– marine and fresh 35 130 30 110 OR E. coli

– fresh 126 410 100 320 **Duration and Frequency** : The waterbody GM should not be greater than the selected GM magnitude in any 30 - day

interval. There should not be greater than a ten percent excursion frequency of the selected STV magnitude in the same 30
- day interval. **a** EPA recommends using EPA Metho d 1600 (U.S. EPA, 2002a) to measure culturable enterococci, or another equivalent method that measures culturable enterococci and using EPA Method 1603 (U.S. EPA, 2002b) to measure culturable E. coli , or any other equivalent method that measures culturable E. coli. **Enterococci (fresh and marine**  **waters )**  Culturable enterococci GMs of 30 and 35 cfu per 100 mLare b ased on the EPA’s anal ys is of the 1986 epidemiological data and the NEEAR combined fresh and marine water quality data as described in the 2012 RWQC document. STVs for those GMs were calculated as follows: STV = 130 cfu per 100 mLfor a GM of 35 cfu per 100 mL  Assuming a log 10 standard deviation 1 of 0.44, the 90 th percentile of the distribution with a GM of 35 cfu per 100 mL is given by Equation (1) : STV= antilog 10 [log 10 (GM)+Z 90 *log 10 SD] (1) where Z 90=1.28 is the one
- sided standard normal z statistic for a 90% confidence interval (CI).  The STV is **128 cfu per 100 mL**  . EPA rounded up to 130 cfu per 100 mL .

1 The standard deviations are based on water quality data from EPA epidemiological studies. Standard deviations based on: the 1986 freshwater E. coli studies was 0.4 0; the NEEAR studies, using the marine and freshwater beaches combined (not including Surfsi de or Boquerón) for culturable enterococci was 0.44; and the NEEAR studies, using the marine and freshwater beaches combined (not including Surfside or Boquerón) for Enterococcus qPCR Method 1611 was 0.49.2

STV = 110 cfu per 100 mLfor a GM of 30 cfu per 100 mL  Using Equation (1) and a log10 standard deviation of 0 .44, the STV for a GM of 30 cfu per 100 mL is **1 1**  **0 cfu per**  **100 mL** . **E. c oli**  **(fresh water**  **s )**  GM = 126 cfu per 100 mL  Based on the results of the 1986 freshwater anal ys es and the analyses presented in section 3.2.4 of the 2012 RWQC , EPA assumes that 35 cfu per 100 mL culturable enterococci corresponds to 36 NGIper 1 , 000 primary contact recreators (8 HCGI per 1,000 primary contact recreators).  Using the 1986 fresh water relationship between swimming
- associated illness (Equation (2 ) ) 2 : Swimming associated HC GIillness = − 11.74 + 9.397 (mean l og 10 E. coli per 100 mL) (2) EPA computed that 8 HCGI per 1,000 primary contact recreators corresponds to an E. coli density

of **126 cfu per**  **100 mL**  . GM = 100 cfu per 100 mL  Based on the anal ys es presented in secti on 3.2.4 of the 2012 RWQC , EPA estimated that 30 cfu per 100 mL culturable enterococci corresponds to an estimated illness range of 27
- 36 NGIper 1 , 000 primary contact recreators (Figure 4 in the 2012 RWQC document). EPA used the midpoint of this range (31.5 NGI per 1,000 primary contact recreators ) as the estimated illness corresponding to 30 cfu per 100 mL . The illness rate of 31.5 NGI per 1,000 primary contact recreators corresponds to 7 HCGIper 1,000 primary contact recreators.  Using the 1986 fresh water relationship between swimming
- associated illness (Equation (2) ) , 7 HCGI per 1,000 primary contact recreators corresponds to an E. coli density of **99 cfu per**  **100 mL** . EPA rounded up to 100 cfu per 100 mL . STV = 410 cfu per 100 mLfor a GM of 126 cfu per 100 mL  Using E quation (1) and assuming a log10 standard deviation of 0.4 0 , the STV is **410 cfu per**  **100 mL**  . STV = 320 cfu per 100 mLfor a GM of 100 cfu per 100 mL  Using E quation (1) and assuming a log10 standard deviation of 0.4 0 , the STV cor responding to the GM of 100 cfu per 100 mL is **32 5**  **cfu per 100**  **mL** . EPA rounded down to 320 cfu per 100 mL .

2 U.S. EPA 1986. EPA’s Ambient Water Quality Criteria for Bacteria

– 1986. U.S. Environmental Protection Agency: Washington, DC. EPA440/5
- 84 - 0023

**2. Beach Action Values (BAV)**  **Table 2**  **. Beach Action Values (BAV)**  **.**

**Indicator Estimated Illness Rate** 

**(NGI): 36 per 1,000 primary contact**  **recreators**

**OR Estimated Illness Rate**  **(NGI): 32 per**  **1,000 primary contact**  **recreators BAV**  **(Units per 100 mL) BAV**  **(Units per 100 mL)**  Enterococci

– culturable (fresh and marine) **a** 70 cfu 60 cfu E. coli

– culturable (fresh) **b** 235 cfu 190 cfu Enterococcus spp. – qPCR (fresh and marine) **c** 1,000 cce 640 cce **a** Enterococci measured using EPA Method 1600 (U.S. EPA, 2002a), or another equivalent method that measures culturable enterococci. **b** E. coli measured using EPA Method 1603 (U.S. EPA, 2002b), or any other equivalent method that measures culturable E. coli. **c** EPA Enterococcus spp. Method 1611 for qPCR (U.S. EPA, 2012b). See section 5.2. 2012 RWQC. **Enterococci ( marine**  **and fresh waters**  **)** BAV of 70 cfu per 100 mLfor a GM of 35 cfu per 100 mL  Assuming a log 10 standard deviation of 0.44 , the 75 th percentile of the distribution is given by Equation (1), where Z 75 =0.675 is the one
- sided standard normal z statistic for a 75% C I.

 The BAV is **69 cfu per 100 mL**  . EPA rounded up to 70 cfu per 100 mL . BAV of 60 cfu per 100 mL for a GM of 30 cfu per 100 mL  Using Equation (1) with a Z 75 =0.675 and log 10 standard deviation of 0.44, the BAV is **5 9**  **cfu per 100 mL**  . EPA rounded up to 60 cfu per 100 mL . **E. c** **oli (fresh**  **waters )**  BAV of 235 cfu per 100 mLfor a GM of 126 cfu per 100 mL  Using Equation (1) with a Z 75 =0.675 and log 10 standard deviation of 0.4 0 , the BAV is **235 cfu per**  **100 mL** . BAV of 190 cfu per 100 mLfor a GM of 100 cfu per 100 mL  Using Equation (1) with a Z 75 =0.675 and log 10 standard deviation of 0.4 0 , the BAV is **186 cfu per**  **10 0 mL**  . EPA rounded up to 190 cfu per 100 mL **Enterococcus qPCR**  **( fresh and marine**  **waters )**  BAV of 1,00 0 cce per 100 mLfor a GM of 470 cce per 100 mL  Using Equation (1) with a Z 75 =0.675 and log 10 standard deviation of 0.49 , the BAV is **1,0 0**  **7 cce**  **per 100 mL**  . EPA rounded down to 1,000 cce per 100 mL .4

BAV of 1,000 cc e per 100 mLfor a GM of 300 cce per 100 mL  Using Equation (1) with a Z 75 =0.675 and log 10 standard deviation of 0.49 , the BAV is **642 cfu per**  **100 mL** . EPA rounded down to 640 cce per 100 mL **3. Equivalent Enterococcus**  **qPCR Method 1611**  **values (fresh and marine waters**  **) Table**  **3 . Values for qPCR** **.**

**Element E**  **stimated Illness Rate (NGI): 36 per**  **1,000 primary contact**  **recreators** OR **Estimated Illness Rate (NGI): 32**  **per 1,000**  **primary contact recreators**  **Magnitude Magnitude**  **GM (cce per**  **100 mL) STV** 

**(cce per 100 mL)**  **GM**

**(cce per 100 mL)**  **STV**

**(cce per 100 mL)**  qPCR**a** 470 2,000 300 1,280 **Duration and Frequency** : The waterbody GM should not be greater than the selected GM magnitude in any 30 - day interval. There should not be greater than a 10 percent excursion frequency

of the selected STV magnitude in the same 30
- day interval. **a** EPA Enterococcus spp. Method 1611 for qPCR (U.S. EPA, 2012b). **Enterococcus**
**– qPCR**  **Method 1161 (fresh and marine**  **waters )**  qPCR
-based GM values of 47 0 cc e per 100 mL and 300 cce per 100 mL  Using EPA’s NEEAR combined relationship between swimming
- associated illness (E quation (3) below) Swimming associated NGI =
- 27.3 1 + 2 3.73 (mean l og 10 qPCR cce per 100 mL) (3)

 31.5 NGI per 1,000 primary contact recreators corresponds to a qPCR GM of **301 cce per**  **100 mL** .  36 NGI per 1,000 primary contact recreators corresponds to an exact qPCR GM of **466 cce per**  **100 mL** .  EPA rounded 301 to 300 cce per 100 mL, and 466 to 47 0 cce per 100 mL . qPCR
-based STV values of 2,000 and 1,280 cce per 100 mL  Using E quation (1) with a Z 90=1.28 and assuming a log10 standard deviation of 0.4 9 , o The STV value for a GM of **470 cce per**  **100 mL**  is **1,992 cce per**  **100 mL**  . EPA rounded up to 2,000 cce per 100 mL. o The STV value for a GM of **300 cce per 100**  **mL** is **1,27 2**  **cc e**  **per 100**  **mL** . EPA rounded up to 1,280 cce per 100 mL.