§ 87.213. Procedure for calculating and applying an annual trigger.
(a) This section contains two alternative methods for calculating the annual trigger. One method shall be proposed by the applicant to be approved and applied by the Department for a remining permit.
(b) Method 1 for calculating and applying an annual trigger (T) is accomplished by completing the following steps:
(1) Calculate M and M1 of the baseline loading data as described under Method 1 for the single observation trigger in § 87.212(b) (relating to procedure for calculating and applying a single-observation (monthly) trigger).
(2) Calculate M-1 as the median of the baseline data which are less than or equal to the sample median M.
(3) Calculate the interquartile range, R = (M1 - M-1).
(4) The annual trigger for baseline (Tb) is calculated as
Tb=M+(1.815*R)/SQRT(n)
where n is the number of baseline loading observations.
(5) To compare baseline loading data to observations from the annual monitoring period, repeat the steps in paragraphs (1)—(3) for the set of monitoring observations. Label the results of the calculations M' and R'. Let m be the number of monitoring observations.
(6) The subtle trigger (Tm) of the monitoring data is calculated as
Tm=M'-(1.815*R')/SQRT(m)
(7) If Tm › Tb, the median loading of the monitoring observations has exceeded the baseline loading.
(c) Method 2 for calculating and applying an annual trigger (T) is accomplished by completing the following steps:
(1) Let n be the number of baseline loading observations taken, and let m be the number of monitoring loading observations taken. To sufficiently characterize pollutant loadings during baseline determination and during each annual monitoring period, it is required that at least one sample result be obtained per month for a period of 12 months.
(2) Order the combined baseline and monitoring observations from smallest to largest.
(3) Assign a rank to each observation based on the assigned order: the smallest observation will have rank 1, the next smallest will have rank 2 and so forth, up to the highest observation, which will have rank n + m. If two or more observations are tied (have the same value), then the average rank for those observations should be used.
(4) Sum all the assigned ranks of the n baseline observations, and let this sum be Sn.
(5) Obtain the critical value (C) from Table 1.
(6) Compare C to Sn. If Sn is less than C, then the monitoring loadings have exceeded the baseline loadings.
(7) Critical values for the Wilcoxon-Mann-Whitney test are as follows:
(i) When n and m are less than 21, use Table 1. To find the appropriate critical value, match column with correct n (number of baseline observations) to row with correct m (number of monitoring observations).
Table 1—Critical Values (C) of the Wilcoxon-Mann-Whitney Test (for a one-sided test at the 0.001 significance level)
m n 10 11 12 13 14 15 16 17 18 19 20 10 66 79 93 109 125 142 160 179 199 220 243 11 68 82 96 112 128 145 164 183 204 225 248 12 70 84 99 115 131 149 168 188 209 231 253 13 73 87 102 118 135 153 172 192 214 236 259 14 75 89 104 121 138 157 176 197 218 241 265 15 77 91 107 124 142 161 180 201 223 246 270 16 79 94 110 127 145 164 185 206 228 251 276 17 81 96 113 130 149 168 189 211 233 257 281 18 83 99 116 134 152 172 193 215 238 262 287 19 85 101 119 137 156 176 197 220 243 268 293 20 88 104 121 140 160 180 202 224 248 273 299 (ii) When n or m is greater than 20 and there are few ties, calculate an approximate critical value using the following formula and round the result to the next larger integer. Let N = n + m.
Critical Value=0.5*n*(N+1)-3.0902*SQRT(n*m(N+1)/12)
(iii) When n or m is greater than 20 and there are many ties, calculate an approximate critical value using the following formula and round the result to the next larger integer. Let S be the sum of the squares of the ranks or average ranks of all N observations. Let N = n + m.
Critical Value=0.5*n*(N+1)-3.0902*SQRT(V)
In the preceding formula, calculate V using:
V=(n*m*S)/(N*(N-1)-(n*m*(N+1)2/(4*(N-1))
Authority The provisions of this § 87.213 issued under section 5 of The Clean Streams Law (35 P.S. § 691.5); sections 4(a) and 4.2 of the Surface Mining Conservation and Reclamation Act (52 P.S. § § 1396.4(a) and 1396.4b); and section 1920-A of The Administrative Code of 1929 (71 P.S. § 510-20).
Source The provisions of this § 87.213 adopted October 21, 2016, effective October 22, 2016, 46 Pa.B. 6780.
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