A complete reference for the formula, components, weights, and design decisions behind the Air Exposure Severity Index.
AERSI is a multiplicative composite index. Each component amplifies the others — a station with heavy pollution, frequent exceedances, and volatile swings does not score the sum of those problems, but their product.
How polluted is the air today, across all pollutants combined?
Each pollutant is normalized against its WHO guideline limit, then combined with epidemiologically-derived weights.
A normalized value of 1.0 means exactly at the safe limit. A value of 4.0 means four times the danger threshold.
How often is this station's air unsafe, and how confident are we?
EPF counts how many days in the rolling window the AQI exceeded 100 — the CPCB threshold between satisfactory and moderate — then applies a confidence weight based on how much data is available.
With only 7 days of data, EPF is shrunk toward neutral (1.0) — we can't yet be confident a pattern has emerged. At 30 days it reaches full strength.
| Days Collected | Confidence | EPF if 50% exceeded |
|---|---|---|
| 7 days | 0.23 | 1.115 |
| 15 days | 0.50 | 1.250 |
| 30 days | 1.00 | 1.500 |
How wildly does the air quality swing day to day?
Volatile air is dangerous in a specific way — people cannot predict or adapt to swings they cannot anticipate. Sudden acute spikes cause health events that consistent (even bad) air does not.
The tanh function squishes any positive number into the range 0 to 1 — it grows fast initially, then flattens. This means VSF is always between 1.0 and 2.0 regardless of how extreme the volatility gets. It also depends only on the absolute swing in AQI, not on the mean — so a heavily polluted city with stable readings correctly scores VSF ≈ 1.0.
| Std Dev (σ) | tanh(σ/100) | VSF | Interpretation |
|---|---|---|---|
| 0 | 0.00 | 1.00 | Perfectly stable, no penalty |
| 30 | 0.29 | 1.29 | Mild swings |
| 60 | 0.54 | 1.54 | Moderate variation |
| 100 | 0.76 | 1.76 | Large, significant swings |
| 200 | 0.96 | 1.96 | Extreme volatility, near ceiling |
The reference baseline is built into the formula itself. A station sitting exactly at WHO limits for all pollutants, with zero exceedances and zero volatility, scores:
AERSI = 1.0 is the WHO safety threshold. Every point above it represents compounding exposure beyond safe limits.
| AERSI | Category | Meaning |
|---|---|---|
| < 0.8 | Very Low | Cleaner than WHO guidelines |
| 0.8 – 1.2 | Low | Near the safety threshold |
| 1.2 – 2.0 | Moderate | Concerning cumulative exposure |
| 2.0 – 3.0 | High | Significant exposure risk |
| > 3.0 | Extreme | Persistent, intense, volatile pollution |
Population density does not modify AERSI. A remote station with extreme scores is flagged with the same severity as a dense urban one. AERSI measures exposure severity, not public health burden — those are different questions.
The EPF confidence weight prevents overconfident conclusions in the early days of data collection. As snapshots accumulate, scores stabilize and gain full statistical weight automatically.
Both EPF and VSF are bounded between 1.0 and 2.0. AERSI has a natural baseline of 1.0. There is no arbitrary normalization step — the meaning is built into the math.
The index is explicitly designed to be early-stage. With 30+ days of consistent data, EPF and VSF gain their full voice. The pipeline runs daily and commits new data automatically.
Air quality data is sourced from the Central Pollution Control Board (CPCB) via the Government of India's open data platform, data.gov.in.
WHO guideline limits are from the WHO Global Air Quality Guidelines (2021). Pollutant weights are informed by the Global Burden of Disease study and related epidemiological literature.