Opinion ID: 4020089
Heading Depth: 3
Heading Rank: 2

Heading: The Page Memorandum

Text: The Page Memorandum recognized our “concern about the interpretation [we] believed [the] EPA was taking” of the word “average.” Page Mem. 3. It clarified that the Agency “does not interpret the term ‘average’” to mean “the average of a future 3-run compliance test.” Id. (emphasis added) (quoting NACWA, 734 F.3d at 1143). Rather, it explained that the “EPA interprets the average to mean the average emissions over time,” based not only on the “average of all emissions test data from the best performing source or sources” but also on “information regarding the variability of emissions.” Id. (emphasis added). In the EPA’s judgment, “variability is a key factor in establishing” MACT standards because “[e]ach MACT standard is based on limited data from sources whose emissions are expected to vary over their long term Rule. No. 11-1108 Envtl. Pet’rs’ Br. 41. But our NACWA decision did not, as the Petitioners would have it, require the EPA to adopt our belief that the Agency construed “average” to mean “the average of a future 3-run compliance test.” See NACWA, 734 F.3d at 1143. Rather, we asked the EPA to clarify how, in its view, the UPL “represents the ‘average emissions limitation achieved by the best performing 12 percent.’” Id. (emphasis added). Nor do we think that the EPA altered its initial basis for using the UPL, which the EPA has consistently held out as “a statistical formula designed to estimate a MACT floor level that is equivalent to the average of the best performing sources based on future compliance tests.” 2011 Major Boilers Rule, 76 Fed. Reg. at 15,630 (emphasis added). What the EPA failed to do before NACWA was to explain how the UPL functions and why it is a reasonable way to calculate “average” emissions levels. The Page Memorandum does precisely that. 90 performance.” Id. Specifically, “[t]he available emissions data are generally in the form of short term, three-run stack tests, with each test run lasting for between 1 and 4 hours.” Id. For this reason, the EPA concluded that it did not have information “encompass[ing] the emissions performance of a source over time.” Id. (emphasis added). And because the “EPA interprets ‘emissions performance’ . . . to mean the emissions of a source over the long term, rather than just during a short-term stack test,” the EPA found it necessary to “appl[y] a methodology that predicts the actual emissions levels the source is achieving at times other than when stack testing was conducted.” Id. at 3-4 (emphases added). The UPL is the methodology the EPA selected to account for these limitations. Id. at 4. “[A] value derived from widely accepted and commonly used statistical principles,” the UPL “represents the upper end of a prediction interval.” Id. In layman’s terms, the UPL uses an equation that considers (1) the average of the best performing source or sources’ stack-test results (i.e., the mean); (2) the pattern the stack-test results create (i.e., the distribution); (3) the variability in the best performing source or sources’ stack-test results (i.e., the variance); and (4) the total number of stack tests conducted for the best performing source or sources (i.e., the sample size). Id. at 4-5. The UPL, however, cannot demonstrate with absolute certainty the average emissions levels achieved by the best performing sources at all times (indeed, certainty is impossible without continuous monitoring). See id. Instead, the UPL equation produces a range of values that is expected, given the variance in the relevant stack-test data, to encompass the average emissions levels achieved by the best performing sources a specified percentage of the time. Id. at 91 4. To establish the MACT floor, the EPA calibrated the UPL equation to produce a range in which the average emissions levels of the best performing source or sources would be expected to fall 99 per cent of the time, which is referred to as a 99 per cent confidence interval. Id. Once the EPA had this range, it set the MACT floor at the top level of that range— hence, the “upper” in “upper prediction limit”—to arrive at a figure that, 99 out of 100 times, it expected the average emissions levels of the best performing sources to “achieve.” Id. Or, in the EPA’s words, “the 99 percent UPL is the level of emissions that” the EPA is “99 percent confident is achieved by the average source represented in a dataset over a long-term period based on its previous, measured performance history as reflected in short term stack-test data.” Id. One of the equations the EPA used to calculate the UPL is as follows:27 27 The EPA used “one of several equations” to calculate the UPL depending on “certain characteristics of [the] dataset,” including the distribution of data within the dataset. Page Mem. 4. Here, we set out the equation the EPA used for a dataset with a “normal distribution.” Id. at 10. For our review, we need not recount the other, somewhat more complicated equations the EPA used in determining the UPL for datasets with, e.g., a “lognormal distribution.” See id. (“Even though they differ due to separate mathematical properties associated with each distribution, the UPL equations share a common format . . . .”); see generally id. at 11 (describing lognormal distribution equation). 92 NACWA, 734 F.3d at 1139. In this equation:  “x̄ ” is the mean;  “t(0.99, n-1)” is a value called the “t-statistic,” the statistical tool used to set the confidence interval (here, 99 per cent);  “n” is the sample size;  “m” is the number of stack tests that were run to calculate the mean (“x̄ ”); because most stack tests involve 3 “runs,” m usually equals 3;  “s” represents the “standard deviation.” See id.; see also Page Mem. 10-11.