Calculations Performed in Developing the Proposed 2012 RWQC Values:

This memo presents the calculations and process of rounding values 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 Method 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 mL are based on the EPA's analysis 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 mL for a GM of 35 cfu per 100 mL
   * Assuming a log10 standard deviation 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= antilog10 [log10(GM)+Z90*log10SD]			(1)

where Z90=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.
   
STV = 110 cfu per 100 mL for 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 110 cfu per 100 mL.

E. coli (fresh waters)
GM = 126 cfu per 100 mL
   * Based on the results of the 1986 freshwater analyses 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 NGI per 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)):
   
Swimming associated HCGI illness = − 11.74 + 9.397 (mean log10 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 analyses presented in section 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 NGI per 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 HCGI per 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 mL for a GM of 126 cfu per 100 mL
   * Using Equation (1) and assuming a log10 standard deviation of 0.40, the STV is 410 cfu per 100 mL.
   
STV = 320 cfu per 100 mL for a GM of 100 cfu per 100 mL
   * Using Equation (1) and assuming a log10 standard deviation of 0.40, the STV corresponding to the GM of 100 cfu per 100 mL is 325 cfu per 100 mL. EPA rounded down to 320 cfu per 100 mL.  





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 mL for a GM of 35 cfu per 100 mL
   *    Assuming a log10 standard deviation of 0.44, the 75[th] percentile of the distribution is given by Equation (1), where Z75=0.675 is the one-sided standard normal z statistic for a 75% CI.
   
   *    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 Z75=0.675 and log10 standard deviation of 0.44, the BAV is 59 cfu per 100 mL. EPA rounded up to 60 cfu per 100 mL. 

E. coli (fresh waters)
BAV of 235 cfu per 100 mL for a GM of 126 cfu per 100 mL
   * Using Equation (1) with a Z75=0.675 and log10 standard deviation of 0.40, the BAV is 235 cfu per 100 mL.  
   
BAV of 190 cfu per 100 mL for a GM of 100 cfu per 100 mL
   * Using Equation (1) with a Z75=0.675 and log10 standard deviation of 0.40, the BAV is 186 cfu per 100 mL. EPA rounded up to 190 cfu per 100 mL


Enterococcus qPCR (fresh and marine waters)
BAV of 1,000 cce per 100 mL for a GM of 470 cce per 100 mL
   * Using Equation (1) with a Z75=0.675 and log10 standard deviation of 0.49, the BAV is 1,007 cce per 100 mL. EPA rounded down to 1,000 cce per 100 mL.
   
BAV of 1,000 cce per 100 mL for a GM of 300 cce per 100 mL
   * Using Equation (1) with a Z75=0.675 and log10 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
     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

                                      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 470 cce per 100 mL and 300 cce per 100 mL
   * Using EPA's NEEAR combined relationship between swimming-associated illness (Equation (3) below) 
 
Swimming associated NGI = -27.31 + 23.73 (mean log10 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 470 cce per 100 mL.

qPCR-based STV values of 2,000 and 1,280 cce per 100 mL
   * Using Equation (1) with a Z90=1.28 and assuming a log10 standard deviation of 0.49,
         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 1,272 cce per 100 mL. EPA rounded up to 1,280 cce per 100 mL. 
