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H659 — Recharge happens in extremes

Supplied working report; original verdicts not validated.

Review status: Needs review. This is an archival source note, not a passed proof.

README.md

# H659 — Recharge happens in extremes

**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.

| Model | Predictors | Within R² | CV R² | AIC |
|---|---|---:|---:|---:|
| 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.

hypothesis.md

# Test 06 — Recharge happens in extremes (H659)

Published at https://incoprea.com/research-library/original-theories-vol3-20261030/

## Claim, verbatim

> "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."

## Predictions

- **P1** Annual recharge is predicted better by the count of extreme precipitation
  days than by the annual precipitation total.
- **P2** Adding event counts to annual totals improves out-of-sample prediction.
- **P3** A disproportionate share of recharge follows top-decile storms.

## Design fixed before computation

### Well selection

The NWIS site service was queried with

```
https://waterservices.usgs.gov/nwis/site/?format=rdb&parameterCd=72019&siteType=GW
  &hasDataTypeCd=dv&stateCd=NJ&siteStatus=all&seriesCatalogOutput=true
```

For the New Jersey sample only rows with `data_type_cd=dv`, `parm_cd=72019`,
`stat_cd=00003` (the **mean** of the daily values — `00001` and `00002` are the
daily maximum and minimum, different sensors, verified against the JSON time
series) were eligible. The 17-state census that motivates the state choice counts
the longest 72019 daily series per site regardless of `stat_cd`, because some
states publish only one statistic (Nebraska publishes `00001` with 12,461 daily
values); in New Jersey the longest series is always the mean. A well was eligible
if its record overlapped 1990-01-01–2024-12-31 by at least 15 years and its
prorated observation count implied at least 80 % of days present (a well with
sparse measurements cannot lose more than 20 % of days *and* retain years).

New Jersey was chosen before any recharge value was computed, on three grounds:
107 eligible wells (fewer than California's 130, Georgia's 144 or Ohio's 137, but
among the largest of the 17 states surveyed), a network of dedicated observation
wells rather than production wells, and a dense GHCN-Daily network. Of the 44
highest-ranked wells examined, 4 had no station passing the 30-year test within
40 km and were skipped; all 40 selected wells paired. The larger states were not
analysed, which is a limitation of breadth, not a result.

Each well was paired with the nearest GHCN-Daily station within 40 km that has
**at least 30 years in 1990-2024 with at least 329 valid PRCP days** (90 % of days).
The 329-day test is applied to the downloaded daily values, not to the station
inventory: several New Jersey co-operative stations have a century-long inventory
but only a handful of complete years in the study window (Ocean City has four).
Wells with no qualifying station within 40 km were ineligible. Eligible wells were
ranked by in-window observation count (descending, site number as tie-break) and the
first 40 that survived the download and the 15-analysable-year rule were used. If a
site had been refused by the daily-values service it would have been dropped and the
next ranked well substituted; the number dropped is reported.

**Result of the selection: 40 wells, 16 stations** (see `data/selected_wells.csv`).

### Well-year construction

For each well-year (calendar year, 1990–2024):

1. Keep the year if it has at least 292 valid daily depth-to-water values (80 % of
   365; 293 in a leap year, but 292 is applied uniformly, so leap years are
   marginally permissive).
2. Recharge `R = Sy * sum(max(0, d[t-1] - d[t]))` over consecutive calendar days with
   both values present, `Sy = 0.10` (sensitivity 0.05 and 0.20). A day whose
   predecessor is missing contributes no rise; rises are never bridged across gaps.
3. Require the paired station to have at least 329 valid PRCP days in the same
   calendar year; otherwise the well-year is dropped.

`72019` is depth to water in feet below land surface, so a **decrease** in depth is a
rise in water level.

### Predictors

- `P_ann` — annual precipitation total, mm (GHCN PRCP is tenths of mm).
- `N95` — count of days in the year with PRCP strictly greater than the station's
  95th percentile of **all** valid days 1990–2024 (zeros included), a fixed
  station-level threshold.
- `N99` — the same at the 99th percentile.
- `coolshare` — share of annual precipitation falling in November–April, the
  recharge season in New Jersey (seasonality control).

### Models (pooled well-years, well fixed effects by within-well demeaning)

- **A**: `R ~ P_ann`
- **B**: `R ~ N95`
- **C**: `R ~ P_ann + N95`
- **D**: `R ~ P_ann + N99 + coolshare`

Reported: n wells, n well-years, in-sample within-well R², AIC
(`n ln(RSS/n) + 2k`, `k` = well intercepts + slopes + 1), and 5-fold
cross-validated R² with folds by **contiguous blocks of years** (1990–96, 1997–2003,
2004–10, 2011–17, 2018–24). Held-out predictions use training-fold well means and
coefficients.

**Decisive statistic:** `dCV = CV_R2(C) - CV_R2(A)` and `dAIC = AIC(A) - AIC(C)`.

### P3

"Top-decile storm days" are days above the 90th percentile of **wet days**
(PRCP > 0) at the station, 1990–2024, a fixed station threshold. For each event day
the window is the event day plus the following 29 days (30 days total); overlapping
windows are unioned and restricted to the calendar year. For each well, pooled over
its analysable years:

- `frac_R` = recharge on window days / total recharge
- `frac_P` = precipitation on window days / total precipitation
- `ratio` = `frac_R / frac_P`

The well-level median ratio is the P3 statistic.

### Verdict rules (pre-specified)

- **Support** the claim only if **all three** hold:
  `dCV > 0.10`, `dAIC > 10`, and median P3 ratio ≥ 1.5.
- **Refute** if annual totals predict as well:
  `max(CV_R2(C) - CV_R2(A), CV_R2(D) - CV_R2(A)) < 0.02`, i.e. neither the raw
  extreme count nor the 99th-percentile count with seasonality adds 0.02.
- Anything else is **neither** (report the numbers, do not re-specify).

Per-prediction verdicts:

- P1 supported if `CV_R2(B) - CV_R2(A) > 0.02`; refuted if ≤ 0; weak otherwise.
- P2 supported if `dCV > 0.10`; partial if 0.02 < `dCV` ≤ 0.10; refuted if < 0.02.
- P3 supported if median ratio ≥ 1.5; not supported otherwise.

### Inference and correction family

Two confirmatory tests, Benjamini–Hochberg across the family of two:

- **T1** — partial association of `N95` with `R` in model C. Seeded within-well
  residual permutation (N95 residualised on `P_ann` within well, residuals permuted
  within well, 2,000 draws): two-sided p for the standardised coefficient.
- **T2** — P3 excess. Seeded paired sign-flip permutation on the 40 well-level
  log ratios (20,000 draws), two-sided p for mean log ratio ≠ 0 (geometric mean ratio ≠ 1).

`dCV` and `dAIC` are effect-size criteria fixed above; they are reported with a
cluster bootstrap (1,000 resamples of wells) 95 % CI, not a p-value. No second
correction is applied.

### Sensitivity (pre-specified)

1. Drop the five well-years with the largest `R` and rerun.
2. `Sy = 0.05` and `0.20` — `R` scales by a constant, so R², CV R², dAIC and P3
   ratios are invariant; report the implied recharge volumes.
3. **Post-hoc, labelled:** `N95`/`N99` defined over wet days instead of all days;
   60-day P3 windows.

### What this design cannot see

It observes water-table fluctuation, not infiltration: pumping, evapotranspiration,
lateral flow and changes in storage below the screen all enter `R`. A well screened
in a confined unit can show a precipitation response without local recharge. The
design is observational and cannot identify a causal threshold; "associated with"
is the strongest verb used.

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This test was designed and executed with AI assistance (DeepSeek, via its coding
agent) and is not peer reviewed.

Included code and results