Quantitative evidence
Why our method is better
Four pieces of evidence in order, strongest first. All of them draw on the same candidate pool — the 50,813 areas that pass the installation eligibility filter — so the rival strategies were never handed worse options.
Evidence 1
Adding sensors at our recommended sites genuinely improves the model
Only our strategy consistently reduces model error. But with 8 repetitions, the direction of the effect is clear while its magnitude cannot yet be claimed with confidence.
| Strategy | Error reduction | Runs improved | Error after |
|---|---|---|---|
| Our method | +2.1% ± 5.4 | 5/8 | 20.75 |
| Most populated cities | +0.7% ± 6.4 | 4/8 | 21.01 |
| Random placement | -0.7% ± 7.8 | 4/8 | 21.29 |
Result of each run
One dot per repetition. The spread is wide, and we show it precisely because of that.
How this was tested
The 16 independent locations are shuffled into three roles: 3 are hidden to measure error, 4 become candidate sites for new sensors, and the remaining 9 form the training data. Each strategy picks 2 of the 4 candidates, the model is retrained, and error is measured again on the 3 hidden locations. The whole process repeats 8 times with different splits.
The standard deviation is still ±5.4 across only 8 repetitions, so this result is not statistically significant. The direction is consistent; the magnitude is not established. We report it as it stands.
Evidence 2
Our sensors do not overlap each other
Nearly every one of our sensors measures a different body of air. Under the most-populated-cities strategy, only 2 of 20 stand alone — the rest re-measure air another sensor already covers.
| Strategy | Stand alone | Wasted | Area types | Closest pair | Population |
|---|---|---|---|---|---|
| Our method | 18/20 | 10% | 10 | 94.6 km | 561,912 |
| Random placement | 17.6/20 | 12.2% | 7.9 | 53.0 km | 156,059 |
| Most populated cities | 2/20 | 90% | 2 | 4.6 km | 8,659,761 |
The definition used
Two sensors count as overlapping when they sit closer than 104.4 km, the spatial range of influence we measured from the data ourselves. Effective clusters is the number of groups left after nearby sensors are merged into one.
Our method against 30 random runs
Each bar is one random run, sorted. The red line marks where our method lands.
27/30 random runs scored lower than our method.
One figure that does not flatter us
The city-based strategy wins decisively on population covered: 8.66 million people against our 561,912. We show it because cherry-picked numbers are not evidence.
But that is exactly the problem. 2 of its 20 sensors pile into the same metropolitan area and measure much the same thing over and over. Its population coverage looks large on paper; the new knowledge it buys is close to zero.
Evidence 3
Without spatial spreading, the result is far worse
Spreading sensors out does not cost population coverage — it raises it by 45%.
| Top scores only | With spatial damping | |
|---|---|---|
| Area types reached | 3 | 8 |
| Overlapping pairs | 70 | 0 |
| Closest pair | 5 km | 333 km |
| Population covered | 412,418 | 598,201 |
Had we simply taken the top 20 scores with no distance damping, they would bunch together: 70 of 190 site pairs overlapping, and area-type coverage collapsing to 3.
Evidence 4
The effect of the regime swap
We deliberately swapped the three lowest-scoring sites for candidates from area types that have never been measured. Coverage doubled at the cost of a 6% drop in population — a trade-off we made knowingly.
| Before the swap | After the swap | |
|---|---|---|
| Area types reached | 8 | 10 |
| Never-measured types | 3 | 6 |
| Population covered | 598,201 | 561,912 |
| Closest pair | 333 km | 94.6 km |
The minimum-distance threshold does not drive the result
We tested the minimum-distance threshold at 8 different values, from 0 to 300 km. All of them produced 20 identical sites with exactly the same total score. The distance rule works purely as a safety net, not as a parameter tuned to flatter the outcome.