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T17 "Warming Can Add Snow" — Findings

Supplied working report; original verdicts not validated.

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

FINDINGS.md

# T17 "Warming Can Add Snow" — Findings

**Date:** 2026-10-30 · **Agent:** research test agent T17 · **Status:** exploratory, not peer reviewed

## Verdict

**NOT SUPPORTED** (primary reading of the pre-registered rule).
Under the alternative "(or vice versa)" reading of the same rule, the label would be
**Conditional** — the substantive conclusion is identical either way:
**the hypothesis's core cold-region prediction fails, and the marginal-region
prediction holds.** See the rule-ambiguity note in hypothesis.md.

## Headline numbers

108 long-record US/Canada stations, 6 088 valid DJF winters 1960–2024 (median 59
winters/station, min 32). Within-station Pearson r between winter mean temperature
and winter total snowfall:

| Group (DJF Tavg) | n | mean r | median r | #neg / #pos | t-test p (neg) | sign-test p (neg) | mean snow trend (OLS, mm/dec) |
|---|---|---|---|---|---|---|---|
| COLD (≤ −10 °C) | 22 | **−0.172** | −0.166 | 18 / 4 | 0.009 | 0.002 | −10.1 (median −1.6; TS −9.4) |
| MID (−10…0 °C) | 51 | −0.444 | −0.481 | 50 / 1 | <0.0001 | <0.0001 | +1.7 (median +7.3; TS −0.2) |
| WARM (> 0 °C) | 35 | −0.360 | −0.424 | 32 / 3 | <0.0001 | <0.0001 | −9.5 (median −6.2; TS −6.0) |
| — extreme COLD (≤ −20 °C) | 5 | **+0.183** | +0.116 | 2 / 3 | — | 0.50 (ns) | — |

- Overall: **100/108 stations have negative r(T, snow)**; only 8 positive.
- COLD mean r 95 % CI = [−0.31, −0.04] — significantly **negative**, i.e. the
  opposite of the prediction; MID [−0.48, −0.40]; WARM [−0.44, −0.28].
- Winter warming is real in these series: DJF T trends +0.42 °C/dec (COLD, 19/22
  warming), +0.38 (MID, 51/51), +0.24 (WARM, 33/35). So the "warming" side of the
  mechanism is present; the "more snow in cold regions" response is not.
- The only stations with positive r(T, snow) among the COLD group are the four true
  Arctic stations: Iqaluit +0.66, Churchill +0.39, Yellowknife +0.12, Sept-Îles +0.13
  (plus Inuvik −0.08, Fairbanks −0.16). The 5-station extreme-cold subgroup
  (≤ −20 °C) averages +0.18 — not significant (sign test p = 0.50), though
  directionally consistent with a moisture-limited Arctic regime.

## Support-rule comparison

| Rule | Requirement | Result | p-values | |
|---|---|---|---|---|
| R1 COLD | mean r POSITIVE, p < 0.05 | **FAIL** — mean r = −0.172 (18/22 negative) | t-test (positive dir) p = 0.991; sign test p = 0.9996 | ✗ |
| R2 WARM | mean r NEGATIVE, p < 0.05 | **PASS** — mean r = −0.360 (32/35 negative) | t-test p < 0.0001; sign test p < 0.0001 | ✓ |

Sensitivity (winter TMIN instead of Tavg, `results/sensitivity_tmin.csv`): COLD −0.17,
MID −0.38, WARM −0.30 — same pattern. Inverse-variance (Fisher-z) weighted group
means: COLD −0.17, MID −0.46, WARM −0.40 — same pattern.

## Interpretation

Warmer winters at the same station are associated with **less** DJF snowfall at
100 of 108 stations, strongest in the MID/WARM groups and weaker but still
significant in the COLD group. The pattern is exactly what a snowline-dominated
response predicts everywhere except the extreme Arctic, where a handful of stations
hint at the moisture-gain regime the hypothesis describes. The hypothesis's
prediction as stated ("snowfall should rise in cold regions") is contradicted for
the cold regions of the US/Canada mid-latitudes, and its refutation clause
("universal snowfall decline would remove the competition") is very close to what
is observed here — the decline is not universal (8 stations positive), but it is
the dominant pattern.

## Limitations

1. **Correlation ≠ attribution.** Within-station winter-to-winter covariance
   conflates temperature's causal effect with shared drivers (storm tracks, ENSO,
   blocking). A warm-winter/snow-poor association can be driven by circulation, not
   thermodynamics.
2. **Station inhomogeneity.** Site moves and instrument changes exist (e.g. Denver
   Stapleton→DIA continuity under one ID, ASOS-era snow measurement changes, 10:1
   depth→water-equivalent convention). Snowfall, not water equivalent, was used.
3. **Truncated Canadian records.** Many Canadian airport SNOW series end 2002–2013
   in GHCNd (task-named cities kept, flagged "relaxed"), so 1960–2024 coverage is
   uneven; the recent warming decades are missing exactly where Arctic positive
   signals live.
4. **US/Canada only** (per brief); no Siberian/Scandinavian stations, where the
   hypothesis might fare differently. Extreme-cold subgroup is tiny (n = 5).
5. **Completeness filters** (≥80 % days, ≥25 winters) dropped Cincinnati and one
   backfill station; results are not sensitive to that.
6. **Station independence.** The sign tests treat stations as independent; spatial
   correlation could inflate significance, but the observed directions are
   overwhelming and the COLD CI is far from the predicted sign.
7. Group mean r is unweighted per the rule; z-weighted means agree (see above).

## What would change the conclusion

- A substantially larger sample of truly Arctic/subarctic stations (≤ −20 °C) —
  the subgroup direction is positive but n = 5; if the extreme-cold regime is the
  intended "cold region", a bigger Arctic sample with records extending past 2013
  could rescue R1.
- Using snowfall water-equivalent and precipitation-controlled (snow fraction ×
  total precipitation) decomposition would isolate the moisture-gain mechanism
  from circulation noise.
- Extending Canadian records to 2024 (or adding ERA5/BEST-style gridded snowfall)
  to remove the truncation bias.
- None of these would change the MID/WARM result, which strongly supports the
  snowline-dominated (marginal-loss) side of the hypothesis.

hypothesis.md

# T17 — "Warming Can Add Snow" — Hypothesis Under Test

**Source:** Incoprea Theory Vol. XXXII #22 "Warming Can Add Snow"
<https://incoprea.com/research-library/original-theories-vol32-20261030/theories/warming-more-snow.html>
Fetched 2026-10-30 ~18:35 UTC via `curl -sL` (sha256 `e363749e180f7d46c94db46c1a25fc360d148f4088faabc496efb567e37092b2`,
raw HTML saved at `workspace/tmp/t17_hypothesis.html`).

## The page's claim, verbatim

> **The claim:** In some regions warming increases snowfall by raising atmospheric
> moisture faster than it raises the snowline.
>
> **01 Mechanism:** Precipitation rises with temperature while the fraction falling
> as snow falls.
>
> **02 Prediction:** Snowfall should rise in cold regions.
>
> **03 Refutation:** Universal snowfall decline would remove the competition.

(Page banner: "Working hypotheses, not findings · Not peer reviewed." Written 30 October 2026.)

## Operational hypothesis (from the test brief, tested here)

In cold regions warming raises snowfall (moisture gain beats snowline rise), while
marginal regions lose snow. Operationally: within-station, warmer winters bring
MORE snow at cold-climate stations and LESS snow at marginal (warm-winter) stations.

## Support rule — written BEFORE analysis, never revised after results

1. **R1 (COLD):** for stations with climatological DJF mean T ≤ −10 °C, the mean
   within-station Pearson correlation between winter mean temperature and winter
   total snowfall must be POSITIVE, p < 0.05 (one-sided t-test on the station
   correlations AND binomial sign test on the count of positive correlations).
2. **R2 (WARM):** for stations with DJF mean T > 0 °C, it must be NEGATIVE
   (same tests, negative direction).
3. **Verdict:** Supported = R1 and R2 both hold; Conditional = exactly one holds;
   Not supported = positive correlation absent in the COLD group.

*Note on rule ambiguity (recorded at write-up):* our outcome (R1 fails, R2 holds)
matches both the "vice versa" parenthetical of "Conditional" and the standalone
"Not supported = positive correlation absent in the COLD group" clause. The
standalone clause is applied as primary (COLD is the hypothesis's core prediction),
so the verdict is **NOT SUPPORTED**; the alternative label would be **Conditional**.
Both labels carry the same substantive conclusion — see FINDINGS.md.

## Test design (fixed before analysis)

- **Data:** GHCN-Daily per-station CSVs, NOAA NCEI public access path
  (`https://www.ncei.noaa.gov/data/global-historical-climatology-network-daily/access/<id>.csv`,
  no token required — verified). 110 long-record US/Canada stations with SNOW,
  TMIN, TMAX: 89 curated cities (task list + group-balancing supplements), 21
  backfill (strict record rule, 80 km spacing). See PROVENANCE.md.
- **Winter:** Dec–Feb, labelled by January year, 1960–2024. Winter valid if ≥80 %
  of its days have SNOW present and ≥80 % have TMIN & TMAX present (trace = present,
  0 mm). Station kept if ≥25 valid winters (108/110 kept).
- **Variables:** winter total snowfall = Σ daily SNOW (mm); winter T = mean of
  (TMAX+TMIN)/2 (GHCNd CSVs report °F-tenths-of-C — converted to °C).
- **Statistic:** within-station Pearson r between winter T and winter snowfall over
  the station's valid winters (computed on anomalies; r is affine-invariant).
  Group mean r tested one-sided by t-test and sign test.
- **Groups:** COLD = DJF Tavg ≤ −10 °C; MID = (−10, 0]; WARM = > 0 °C.
- **Context:** per-station OLS snow trend (mm/decade) and Theil–Sen, averaged by
  group; per-station winter-temperature trend by group.

Included code and results