Averaging periods & design-value forms

Every air quality standard has two parts people notice — a number and an averaging period — and a third part that decides compliance: the statistical form. Two standards with the same number and averaging period can behave completely differently because their forms differ. This page walks through how each form turns a year of raw measurements (or model output) into the single number that gets compared to the standard: the design value.

From raw hours to a design value

Ambient standards are written against specific statistics of the measured (or modeled) concentration record — not against the single highest value ever seen. The reason is robustness: a one-hour spike during an instrument glitch or a once-in-a-decade inversion should not by itself define an area's air quality. The forms below are exactly as written in 40 CFR Part 50, and AERMOD computes them the same way when it processes model output.

The daily-maximum percentile family (1-hour NO₂ and SO₂)

The 1-hour NO₂ and SO₂ standards use the most involved form. For each day, take the highest 1-hour value; over the year, take a percentile of those daily maxima; then average that percentile across three years:

How the NO₂ 1-hour design value is built: each day's highest hour → rank the year's daily maxima → average 3 years

NO₂ 1-hour (100 ppb): the 98th percentile of the annual distribution of daily maximum 1-hour concentrations, averaged over 3 years. With 365 daily values, the 98th percentile is the 8th-highest day.

Source · 40 CFR §50.11(b), (f) — NO₂ 1-hour primary standard and form; percentile computation per Part 50 Appendix S.

SO₂ 1-hour (75 ppb): the 99th percentile of daily maximum 1-hour concentrations, averaged over 3 years — the 4th-highest day of each year.

Source · 40 CFR §50.17(a), (b) — SO₂ 1-hour primary standard and form; computation per Part 50 Appendix T.

How the SO₂ 1-hour design value is built: each day's highest hour → rank the year's daily maxima → average 3 years

Why the percentile step matters for modeling: a single extreme modeled hour does not set the design value. AERMOD's design-value processing (NO2AVE/SO2AVE ranked output) selects each year's 8th- or 4th-highest daily maximum at every receptor and averages across the modeled years — which is why a compliant demonstration can contain individual hours above the standard's level.

The 24-hour percentile form (PM2.5)

PM2.5's 24-hour standard (35 µg/m³) applies the same idea to daily averages instead of daily maxima: the 98th percentile of 24-hour average concentrations in a year, averaged over 3 years — the 8th-highest day when a full year is measured daily.

Source · 40 CFR §50.20(c) and Part 50 Appendix N — PM2.5 24-hour standard and data interpretation. (§50.18 holds the superseded 2012 standards, retained for reference.)

Two different "annual" rules

"Annual average" hides the biggest trap in the standards. Two annual forms exist, and they answer different questions:

Two different “annual” rules: NO₂ uses the HIGHEST single year; PM2.5 averages three years

Highest single year (NO₂ annual, 53 ppb): the standard is met when the annual arithmetic mean in each calendar year is at or below the level — so the worst individual year of the record governs. Averaging five modeled years together would dilute a bad year and overstate compliance.

Source · 40 CFR §50.11(a), (e) — "met when the annual average concentration in a calendar year is less than or equal to 53 ppb."

Multi-year average (PM2.5 annual, 9.0 µg/m³): the design value is the annual mean averaged over 3 years — here the averaging across years is the form itself.

Source · 40 CFR §50.20(b) and Appendix N (2024 revision) — annual PM2.5 standard and 3-year averaging.

When a multi-year model run reports "ANNUAL", always ask which rule this pollutant uses before comparing to the standard — the difference between the highest year and the mean of years is routinely 10–30%.

The exceedance-count form (PM10)

PM10's 24-hour standard (150 µg/m³) is attained "when the expected number of days per calendar year with a 24-hour average concentration above 150 µg/m³ … is equal to or less than one." In practice, with three years of daily values, the fourth-highest concentration is the compliance metric — three exceedances are allowed across the record.

PM10 24-hour form: not-to-be-exceeded more than ONCE per year — over 3 years the 4th-highest value governs

Source · 40 CFR §50.6(a) — expected-exceedances form per Part 50 Appendix K; the high-fourth-high over 3 years (or high-sixth-high over 5) is the modeling implementation, AERMOD User's Guide §3.2.16.

The remaining simple forms

CO (35 ppm 1-hour · 9 ppm 8-hour): not to be exceeded more than once per year — the second-highest value of the year is compared to the level.

Source · 40 CFR §50.8(a) — carbon monoxide standards.

Ozone (0.070 ppm 8-hour): annual 4th-highest daily maximum 8-hour average, averaged over 3 years. (Ozone is a regional, photochemically formed pollutant — it is not modeled with AERMOD, but its form is included here for completeness.)

Source · 40 CFR §50.19(a), (b) — ozone standard and form.

Lead (0.15 µg/m³): rolling 3-month average, not to be exceeded.

Source · 40 CFR §50.16(a), (b) — "maximum arithmetic 3-month mean concentration for a 3-year period."

Design value vs. modeled concentration

The design value is the statistic the standard defines. A compliance demonstration compares modeled design value + representative background against the standard:

The compliance test: modeled impact + background, compared against the standard

The choice of background monitor, and how background is combined with the modeled result, is its own topic — see Background concentrations & representative monitors.

In PlumeSmart

The platform computes every design value in the form its standard requires — percentile ranks, highest-single-year annual means, exceedance counts — directly from the model output, and labels each reported number with its form and citation. Multi-year NO₂ runs report the annual design value on the highest-individual-year basis automatically.