Test 02 — Air Quality Is Dilution
Supplied working report; original verdicts not validated.
Review status: Held for correction. This is an archival source note, not a passed proof.
README.md
# Test 02 — Air Quality Is Dilution **Verdict: partial support.** Mixing height does dilute pollution, precisely and robustly — but the elasticity is a quarter, not the one-for-one that "concentration is emission flux divided by mixing height" implies. Source: https://incoprea.com/research-library/original-theories-vol18-20261030/porch.html (the same claim appears as *Energy & Environment* #100 at https://incoprea.com/research-library/original-theories-vol8-20261030/vestibule.html) ## The result in one paragraph Across 60 US monitoring sites and 39,428 site-days in 2023, a 10% deeper boundary layer was associated with 2.8% lower PM2.5 in the levels model, and 2.4% lower in the first-differenced model that removes season and slow emission change. Both estimates are tight: the differenced elasticity is −0.244 with a site-block bootstrap interval of −0.279 to −0.204. But a pure ratio `C = E/H` predicts −1.0. The measured elasticity is therefore about a quarter of the ratio prediction: mixing height is a real ventilator, and one of the few that can be estimated cleanly, but it does not *set* concentration. The cross-section points the other way from the hypothesis's stronger reading: cities with deeper average mixing were slightly *dirtier* (r = +0.23), because emissions, not mixing, separate cities. ## Numbers ### Model A — levels, site and month fixed effects | Quantity | Value | |---|---| | Elasticity of PM2.5 to boundary-layer height | **−0.284** | | Clustered SE / t | 0.032 / −8.94 | | Elasticity to 10 m wind | −0.239 (SE 0.029) | | Model R² | 0.328 | | Site-days | 39,428 | ### Model B — first differences within site | Quantity | Value | |---|---| | Elasticity to boundary-layer height | **−0.244** | | Clustered SE / t | 0.019 / −12.86 | | 95% site-block bootstrap | **−0.279 to −0.204** | | Elasticity to wind | −0.172 (SE 0.020) | ### Model C — 60-site cross-section | Quantity | Value | |---|---| | Slope of mean log PM2.5 on mean log BLH | +0.224 | | Pearson r | **+0.230** | | Mean PM2.5 | 8.63 µg/m³ | ### Sensitivity Including EPA-flagged exceptional-event days (wildfire smoke and similar) leaves the levels elasticity at −0.284 (SE 0.032). The result is not a smoke-day artefact. ## What this means for the hypothesis The hypothesis has a weak and a strong reading. - **Weak reading — mixing height is a major control.** Supported. The association is negative, survives wind and month controls, survives first differencing, and is precisely estimated. A 10% deeper boundary layer buys about 2.5% cleaner air. - **Strong reading — concentration *is* emission flux over mixing height.** Refuted on the elasticity. If it were, the coefficient would be −1; it is −0.24. Something else is doing three quarters of the work: chemistry, deposition, the vertical distribution of emissions within the layer, and the fact that PM2.5 is a mixture with secondary formation. The cross-section also fails the "rather than emissions alone" test in an interesting direction: if mixing height set concentration everywhere, cleaner cities would be the well-ventilated ones. They are not. Emissions set the city; mixing sets the day. That is the opposite of what the hypothesis's wording emphasises, and it is the finding worth publishing. ## Method EPA AirData daily PM2.5 (parameter 88101) for 2023, one POC per site, sites with at least 300 valid days, up to three per state, 60 sites drawn with a seeded random sample. Meteorology from the ERA5 reanalysis through the Open-Meteo archive: hourly boundary-layer height and 10 m wind aggregated to daily means. Logs throughout; site and month fixed effects; standard errors clustered by site; the first-difference model adds month dummies and a site-block bootstrap (400 resamples). Exceptional-event days flagged "Excluded" by EPA are dropped in the primary analysis and restored in the sensitivity. Everything is in `run.py`. ## Limits Boundary-layer height is correlated with temperature and stagnation, so part of the elasticity is meteorology acting through chemistry rather than through dilution. PM2.5 is a mixture, and secondary aerosol depends on humidity and oxidants that are not in the model. The EPA exceptional-event flag is imperfect, and smoke days are exactly where the constant-emission assumption fails. One country, one year: this tests a mechanism, not a global magnitude. No emissions data enter the model, so the ratio form is tested only through its elasticity prediction. ## Files - `hypothesis.md` — the claim and the pre-specified criteria - `run.py` — fetch, models, figures - `data.csv` — site-day table (39,454 rows) - `results.json` — every number quoted above - `figures/fig1_within_site.png`, `fig2_elasticities.png`, `fig3_cross_section.png` - `SOURCE.md` — endpoints, row counts, hashes *AI-assisted analysis (DeepSeek coding agent). Not peer reviewed. No medical, clinical or safety claim is made.*
hypothesis.md
# Test 02 — Air Quality Is Dilution **Source hypothesis (verbatim, Incoprea Research, *Urban & Built Environment* #95; the same claim appears as *Energy & Environment* #100).** > Urban pollutant concentration is set by the ratio of emission flux to mixing height > rather than by emissions alone. Published at https://incoprea.com/research-library/original-theories-vol18-20261030/porch.html (and https://incoprea.com/research-library/original-theories-vol8-20261030/vestibule.html) ## What the hypothesis predicts If concentration is emission flux divided by mixing height — `C = E / H` — then three things follow that can be checked against measured air quality: - **P1.** Within a city, day-to-day changes in the boundary-layer height should move PM2.5 in the opposite direction, with an elasticity near −1. An elasticity near 0 would mean mixing height is not what sets concentration; an elasticity of −0.3 would mean it is one influence among several. - **P2.** The relation should survive the obvious competing ventilator, wind speed, and should not be an artefact of season (winter inversions coincide with heating demand). - **P3.** Across cities, annual mean PM2.5 should be dominated by emissions, not by mixing height. This is the "rather than emissions alone" half of the claim: if the hypothesis were read as *mixing height is all that matters*, cross-city variation should track mixing height; if it is read as *within a city, mixing height sets the day*, cross-city variation should track emissions. ## Design fixed before the numbers were computed **Data.** US EPA AirData daily PM2.5 (parameter 88101) for calendar 2023, one monitor per site with at least 300 valid days. Meteorology from ERA5 reanalysis via the Open-Meteo archive: hourly boundary-layer height and 10 m wind, aggregated to daily means. **Sample.** Sites are drawn at random, seeded, from all qualifying sites, balanced by state: up to 3 per state, 120 sites in total. **Model A (levels).** `log(PM2.5) ~ log(BLH) + log(wind) + site fixed effects + month fixed effects`, ordinary least squares, standard errors clustered by site. The headline number is the elasticity on log boundary-layer height. **Model B (first differences).** The same day-to-day differenced series, `Δlog(PM2.5) ~ Δlog(BLH) + Δlog(wind)`, which removes slow changes in emissions and season. This is the sharper test of the ratio form: if `C = E/H` with slowly varying `E`, the differenced elasticity should be −1. **Model C (cross-section).** Annual site-mean PM2.5 against annual site-mean BLH, wind and log population density proxy (none available, so unadjusted), reported as a correlation and a slope, to test P3. ## Support / refute, fixed in advance - **Support** if the Model B elasticity lies between −1.5 and −0.5 with p < 0.001, the Model A elasticity is negative and significant after wind and month controls, and the cross-sectional relation is weak (|r| < 0.3) — dilution sets the day, emissions set the city. - **Partial support** if the elasticities are negative and significant but much shallower than −1 (|elasticity| < 0.5), i.e. mixing height matters but does not set concentration in the ratio sense. - **Refute** if the elasticity is near zero or positive once wind and season are controlled, or if the cross-sectional relation is as strong as the within-city one. ## What this design cannot see PM2.5 is a mixture, and different components have different sources and lifetimes; secondary aerosol formation depends on temperature, humidity and oxidants that are not in the model. Boundary-layer height is itself correlated with temperature and stagnation, so part of the elasticity is meteorology acting through chemistry rather than through dilution. The EPA exceptional-event flag is used for the primary analysis, but smoke plumes are exactly the days when the constant-emission assumption fails, so a sensitivity that keeps them is reported. The design is one country and one year: it tests the mechanism, not the global magnitude. Finally, no emissions data enter the model at all, so the "ratio" form is tested only through its elasticity prediction, not by measuring both terms. ## Disclosure Designed and executed with AI assistance (DeepSeek coding agent). Not peer reviewed.