Hydrology
The claim that aquifer recharge is carried by a minority of high-intensity storms, so storm counts should beat rainfall totals.
Does recharge come from extreme storms?
Claim (verbatim, Original Theories, volume III): "Aquifer recharge is carried by a minority of high-intensity storms that cross an infiltration threshold, so recharge tracks the count of extreme events better than annual or seasonal rainfall totals."
Result
The claim fails all three predictions on 40 USGS observation wells and 1,336 well-years (1990–2024). Recharge estimated by water-table fluctuation was not predicted better by extreme-day counts than by annual precipitation, and extreme-day counts alone were worse.
Five-fold cross-validated R² for annual precipitation alone was 0.0093. Adding the count of days above the station's 95th precipitation percentile moved it to 0.0094, a gain of +0.0001 (cluster-bootstrap 95% CI −0.0040 to +0.0027). AIC moved the wrong way: the combined model was 0.6 worse. Extreme days alone reached a CV R² of 0.0038. The pre-specified refutation criterion — an added CV R² below 0.02 — is met, and the claim is refuted.
| A | annual precipitation | 0.0123 | 0.0093 | −293.90 |
|---|---|---|---|---|
| B | extreme-day count (N95) | 0.0050 | 0.0038 | −284.09 |
| C | annual P + N95 | 0.0133 | 0.0094 | −293.30 |
| D | annual P + N99 + seasonality | 0.0131 | 0.0058 | −291.04 |
This is not a power failure. Giving each well equal weight raises the annual-precipitation CV R² to 0.134; extreme counts then add only 0.0014. The rainfall signal is present; the extreme-count signal is not.
P3 fails in the opposite direction. Recharge in the 30 days after top-decile storm days was a median 0.629 of annual recharge, while those days carried 0.756 of annual precipitation: a median ratio of 0.836 (IQR 0.793–0.928), with 0 of 40 wells reaching 1.5×. Windows cover 58.4% of days; a 60-day window gives 0.923.
Design
Wells are NWIS parameter 72019 daily means, 1990–2024. Of 107 New Jersey wells with eligible records (≥15 years, ≥80% of days present), the 40 highest-ranked by in-window observations with a GHCN station within 40 km (≥30 complete years) were used; 4 of 44 examined lacked one; no site was refused. Sixteen stations were used (median 14.7 km, maximum 36.6 km).
Recharge is R = Sy × Σ max(0, d[t−1] − d[t]) over consecutive days, Sy = 0.10. Well-years with fewer than 292 depth values or 329 precipitation days were rejected. Models A–D are pooled with well fixed effects (within-well demeaning); CV R² is five-fold with contiguous year blocks. P3 uses the 90th percentile of wet days at each station and 30-day windows from those days.
Two confirmatory tests form one Benjamini–Hochberg family: T1, the N95 coefficient in model C, gives a standardised −0.0548 (permutation p = 0.244, q = 0.244); T2, the P3 log ratio, gives −0.1533 (sign-flip p = 0.00005, q = 0.0001). The decisive CV and AIC comparisons are effect-size criteria fixed in advance, with a 1,000-resample cluster bootstrap.
Prediction verdicts
P1 — refuted. Extreme-day counts predict annual recharge worse than annual precipitation: CV R² 0.0038 against 0.0093 (−0.0055).
P2 — refuted. Adding N95 to annual totals changes CV R² by +0.0001 and worsens AIC by 0.6, nowhere near the 0.10 support threshold.
P3 — not supported. The median recharge share after top-decile storms is below the precipitation share, not 1.5× above it: 0.836, with 0 of 40 wells above 1.5.
Sensitivity checks do not move it. Dropping the five largest recharge well-years gives a CV gain of 0.0000 and a ratio of 0.836. Rises above 0.05 ft give −0.0002 and 0.839; above 0.10 ft, −0.0005 and 0.847. Wet-day extremes give +0.0009. Wells with median depth ≤30 ft give −0.0009 and 0.950. Changing Sy to 0.05 or 0.20 scales the volumes (347.0 and 1,387.8 mm yr⁻¹) but leaves every R², AIC difference and ratio unchanged.
Limits
The recharge proxy is noisy. Mean annual recharge is 693.9 mm, 57.5% of mean annual precipitation (1,207.3 mm) — too high for New Jersey — and the sum of positive daily rises is 2.42× the annual water-level range. It therefore counts pumping recovery, evapotranspiration and measurement reversals as well as recharge. This is a test of water-table fluctuation, not of infiltration.
Response depends on depth: median within-well r(R, P) is 0.781 in wells 0–15 ft deep (11 wells) and 0.160 below 100 ft (15 wells); the correlation between depth and response is −0.621. Deep, probably confined wells dilute the pooled estimate. Even the shallow subgroup shows no extreme-count gain.
The design is annual: 35 years, five year-blocks, one common slope. It cannot see event-scale threshold behaviour, and precipitation comes from the nearest qualifying station up to 36.6 km away. Thresholds are station climatologies estimated over the same years. Observational data: "associated with" is the strongest verb.
What would change the answer
A proxy that isolates infiltration — lysimeters, tracers, soil moisture — rather than water-table fluctuation; unconfined wells with pumping excluded; a drier climate where the top decile of wet days is genuinely rare rather than 58% of the calendar; and an event-scale (1–7 day) response model instead of annual aggregation.
Files and disclosure
run.py reruns everything from the network and writes data/.csv, results.json and figures/.png; SOURCE.md lists every URL, query, count and SHA-256. This test was designed and executed with AI assistance (DeepSeek's coding agent) and is not peer reviewed.
Figures
