EPA’s New Ozone Rule: Part 6

Let’s look at EPA’s proposed ozone rule to see exactly what it entails. Unlike previous ozone rules, it has two distinct parts1:

  • A primary standard to protect human life and health.
  • A secondary standard to protect property, agriculture, and the environment.

Technically speaking, EPA rules always had primary and secondary standards, but up to now, the ozone primary and secondary standards were identical2. This is the first time that the two standards were made distinct, done at the urging of EPA’s Clean Air Scientific Advisory Committee (CASAC)3.

The two standards are different in character. The primary standard is based solely on averages4. If the average ozone concentration rises above a certain level, that location is in non-attainment. The secondary standard is based on cumulative exposure to ozone1. It is more focused on the effects caused by long-term exposure to ozone.

The new rule is making an interesting statement: it appears that with regards to human health we are more interested in the acute effects of high exposure. With property and agriculture, we seem more concerned with ozone’s long term effects. Yet the EPA is aware of that long-term exposure to ozone can degrade human health over time.

Now if a locale is to be in attainment, it presumably must meet both the primary and secondary standards. Sometimes one standard will be more stringent, sometimes the other. Consider locales which meet one standard and not the other. In one locale, ozone levels are usually very low. Occasionally, they peek to high levels, just often enough so that the locale does not meet the primary standard, yet the cumulative exposure to ozone remains low. In another locale, ozone levels are consistently high causing large cumulative exposure, but they fall just shy of breaking the primary standard. State and Federal authorities will need to keep track on two sets of numbers for each locale to enforce both standards.

The primary standard in the proposed rule is actually the same as in current rule, just a little stricter, the maximum concentration lowered from 75 ppb in the current rule to 70 ppb. The air is sampled frequently at a measuring station, and readings are averaged out over an eight-hour period. This yields 1,095 such averages in a calendar year (1,098 in a leap year). The three highest averages are thrown out and the fourth-highest average is used to represent the year’s maximum. The maximums from three consecutive years are then averaged together. If this composite average exceeds 70 ppb, that locale is considered in nonattainment1.

The secondary standard is a little more complicated but easily understandable if you remember your high school algebra. The values to be summed are not the ozone concentrations themselves but a calculation based on each reading of ozone concentration, called the W126 index5. To determine, the cumulative index, hourly readings of ozone concentrations are taken at an individual station 12 hours a day, starting at 8 a.m. and finishing at 7 p.m. A value Wi is then calculated as follows:

                                     Wi =        Ci                 
1 + 4403e –ACi


Ci (read as “C sub i”) is the reading of ozone concentration measured in parts per million (ppm) taken at hour i. Because the W126 index is cumulative, Ci is in units of ppm-hours.

e is the base of natural logarithms, approximately equal to 2.71828.
A is a constant equal to 126/ppm-hour.

For example, suppose at 2:00 in the afternoon we measured an ozone concentration of .083 ppm. We would then calculate a W value for 2 pm this way:

             W2pm =                              .083 ppm-hours                   
                                1 + (4403)(e – (126/ppm-hour)(.083 ppm-hours))

This can easily be calculated with the help of a scientific calculator6 (note that the ppm-hours units cancel in the exponent as they should), yielding a value of 0.74 ppm-hours. This means that the ozone concentration at 2 pm will contribute slightly less to the cumulative total than if we did not use the formula (.074 ppm-hours versus .083 ppm-hours).

The Wi values are summed each day, giving a daily cumulative total:

Wdaily = ΣWi

summed from the first reading of the day at 8 am to the last reading at 7 pm.

The Wdaily values are themselves summed over a three-month period. As I understand it, these are running totals: January-February-March, February-March-April, March-April-May, and so on.

W126 = ΣWdaily

summed from the first day of each three-month period through the last day.

Thus, each calendar year produces ten W126 values, from January-February-March through October-November-December. The highest W126 value for the year is selected. This process is carried out for three consecutive years, producing three yearly maximum W126 values. The average of these three values is the final W126 value. If it is higher than 13 ppm-hours, then the area where the readings were taken is declared to be in non-attainment5.

For example, the following are fictitious highest W126 totals summed up during each of 2008, 2009, and 2010. All values are in ppm-hours:

Year Highest Value Period Summed
2008 15.2 Apr-May-Jun
2009 14.3 May-Jun-Jul
2010 12.9 Mar-Apr-May

The average of these three values is 14.1 ppm-hours. Since this is above the standard of 13 ppm-hours, the area from where these readings were taken is in non-attainment.

Why is the W126 index used? To quote A.S.L. & Associates, a Montana company whose founder developed the W126 index:

The W126 index is a cumulative exposure index that is biologically based. The W126 ozone index focuses on the higher hourly average concentrations, while retaining the mid- and lower-level values. By applying a continuous weighting, the W126 index has the advantage of not utilizing an artificial “threshold.”

In 1985, A.S. Lefohn proposed the use of the W126 ozone exposure index for predicting vegetation effects. The cumulative W126 exposure index uses a sigmoidally weighted function (i.e., “S” shaped curve) as described by Lefohn and Runeckles (1987) and Lefohn et al. (1988). The W126 index is a cumulative exposure index and not an “average” value. It is a biologically based index, which is supported by research results (i.e., under both experimental and ambient conditions) that show that the higher hourly average ozone concentrations should be weighted greater than the mid- and lower-level values. The W126 index is accumulated over a specified time period.7

Let’s look again at the equation that defined the individual hourly W126 values, designated as Wi:

                                     Wi =        Ci                 
1 + 4403e –ACi

Let’s plot the Wi values on a graph as a function of the original hourly ozone concentrations that generated them, Ci:

Graph of Wi values plotted against the ozone concentrations used to calculate the values.

As the graph shows, when the ozone concentration Ci is less than .035 ppm-hour, Wi values are negligible. As Ci increases, the Wi values quickly climb, but are still always less than Ci. As Ci increases beyond about .085 ppm-hour, the growth rate of Wi subsides somewhat until about .10 ppm-hour, when Ci nearly equals Wi (within 1%), and the graph becomes linear. This shows that for ozone concentrations less than 0.035 ppm, the W126 values contribute almost nothing to the cumulative total. For concentrations greater than than .100 ppm, the W126 values are almost identical to the ozone concentrations. In between 0.035 ppm and .100 ppm, the contribution varies, with larger concentrations contributing much more to the cumulative total than smaller concentrations.

You can also see this in a table that I prepared of oxygen concentrations in increments of .010 ppm and their corresponding W126 values:

Ozone   Percent of Ozone
Concentration (ppm) W126 Value Concentration
0.01 0.0000 0.08%
0.02 0.0001 0.28%
0.03 0.0003 0.99%
0.04 0.0014 3.39%
0.05 0.0055 11.01%
0.06 0.0182 30.36%
0.07 0.0424 60.59%
0.08 0.0675 84.42%
0.09 0.0855 95.03%
0.10 0.0985 98.54%


  1. U.S. Environmental Protection Agency, National Ambient Air Quality Standards, 2010, pg. 1 and pg. 6
  2. U.S. Environmental Protection Agency website, Ozone (O3) Standards – Table of Historical Ozone NAAQS. To view, click here.
  3. U.S. Environmental Protection Agency, National Ambient Air Quality Standards, 2010, pg. 17.
  4. ibid., pg. 34
  5. ibid., pg. 193.
  6. It is even easier using Microsoft Excel® or similar spreadsheet program. If an ozone concentration in ppm is in cell A1, then this formula typed in cell B1 will give the corresponding W126 value:

    = A1 / (1 + 4403 * EXP(-126*A1))

  7. A.S.L. & Associates website, How the W126 Ozone Exposure Index Was Developed. To view, click here.

2 responses to “EPA’s New Ozone Rule: Part 6

  1. Pingback: EPA’ s New Ozone Rule: Part 15 | Michael Klein's Environmental Essays

  2. Pingback: EPA’s New Ozone Rule: Part 24 | Michael Klein's Environmental Essays

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