25 Pa. Code § 88.513

Current through Register Vol. 54, No. 50, December 14, 2024

Section 88.513 - 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 § 88.512(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 S_n.

(5) Obtain the critical value (C) from Table 1.

(6) Compare C to S_n. If S_n 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)

nm	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))

25 Pa. Code § 88.513

The provisions of this § 88.513 adopted October 21, 2016, effective 10/22/2016, 46 Pa.B. 6780.

The provisions of this § 88.513 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).