# Niño 3.4 and Florida monthly precipitation, 1950–2025

Florida winter precipitation is positively associated with Niño 3.4 in this fixed observational comparison. The prespecified primary estimate is **18.9 mm more precipitation per month per 1°C higher Niño 3.4**, after calendar-month adjustment (95% pointwise block-bootstrap interval **13.9–24.1 mm/°C**; approximate simultaneous interval **11.0–26.8 mm/°C**). The month-adjusted winter correlation is **0.454** (pointwise 95% interval 0.350–0.556).

The estimates suggest a stronger winter relationship than in summer or autumn, but the direct seasonal differences are uncertain. None of the 11 seasonal or lag contrasts excludes zero under the joint simultaneous intervals. There is no convincing evidence here for a preferred 1- or 2-month delay over the same-month index.

**Why this comparison was chosen**

Florida was selected before calculating associations because ENSO can influence the subtropical jet and cool-season storm tracks affecting the southeastern United States. This is the physical rationale for a hypothesis, not evidence obtained from screening states. The protocol fixed four outcome-month seasons—DJF, MAM, JJA, SON—and Niño-leading lags of 0, 1, and 2 months. DJF at lag 0 was designated primary. No other state, lag, outcome window, or transformation was searched for a stronger result.

**Data and definitions**

The two public monthly tables were accessed on 2026-09-30:

- NOAA PSL [Niño 3.4 monthly anomalies](https://psl.noaa.gov/data/correlation/nina34.anom.data). The saved table identifies ERSST v6, 5°N–5°S and 170°W–120°W, anomalies relative to 1981–2010, in °C. This is the monthly Niño 3.4 series, not the three-month Oceanic Niño Index. The file includes later observations, which the analysis excludes.
- NOAA NCEI [Florida statewide monthly precipitation](https://www.ncei.noaa.gov/access/monitoring/climate-at-a-glance/statewide/time-series/8/pcp/1/0/1950-2025.csv). The response identifies Florida and inches. Values were converted to mm using exactly 25.4 mm/inch.

Precipitation is a rainfall proxy: the NOAA measure also includes the water equivalent of snow. It is a statewide aggregate, not a station or local rainfall series.

All 912 outcome months from January 1950 through December 2025 are present, unique, and nonmissing. Each season contains 228 monthly observations over 76 calendar years. Niño observations from November 1949 onward support the lagged predictors. For example, January 1950 precipitation at lag 2 uses November 1949 Niño 3.4. No future Niño values are used to explain earlier rainfall. December is classified as winter; these are monthly regressions, not regressions of complete three-month winter totals.

**All prespecified associations**

Each entry is a slope in mm/month per °C, followed by its pointwise 95% interval. Positive lag means Niño precedes precipitation.

| Outcome season | Lag 0 | Lag 1 month | Lag 2 months |
|---|---:|---:|---:|
| DJF | 18.9 [13.9, 24.1] | 17.4 [12.5, 22.8] | 17.5 [12.7, 23.0] |
| MAM | 16.2 [6.6, 28.2] | 13.7 [5.7, 23.1] | 11.0 [4.6, 18.4] |
| JJA | 8.8 [−0.02, 19.2] | 3.3 [−6.9, 13.8] | 1.5 [−8.2, 10.8] |
| SON | 4.3 [−0.4, 9.2] | 3.3 [−2.2, 8.6] | 5.0 [−0.9, 10.2] |

The contemporaneous correlations are DJF 0.454, MAM 0.221, JJA 0.125, and SON 0.082. The winter correlation squared is 0.206: an in-sample linear fit accounts for about 21% of the calendar-month-adjusted winter precipitation variance. This is not out-of-sample forecast skill.

Pointwise intervals do not protect against examining the whole table. The full CSV also gives approximate simultaneous intervals for a family of 23 slopes and contrasts. All winter slopes remain positive under those intervals. Spring lag 0 includes zero; spring lags 1 and 2 have lower bounds only slightly above zero (0.035 and 0.179 mm/°C). Those borderline results should not be used to choose a lag.

**Do seasons or lags differ?**

The main seasonal contrast, DJF minus JJA at lag 0, is **10.0 mm/°C**, with pointwise interval **−0.3 to 19.8** and simultaneous interval **−5.4 to 25.5**. Thus a clear winter association and a less certain summer association do not, by themselves, establish that their slopes differ.

Winter lag 1 minus lag 0 is −1.44 mm/°C (pointwise −2.51 to −0.53; simultaneous −2.99 to 0.11). Winter lag 2 minus lag 0 is −1.36 mm/°C (pointwise −3.02 to 0.28; simultaneous −3.90 to 1.18). All remaining lag contrasts also include zero in their simultaneous intervals. The paired contrasts are provided in full, including DJF–JJA at each lag.

Winter month-centered Niño predictors have correlations 0.969 between lags 0 and 1 and 0.936 between lags 0 and 2. The lagged regressions are separate marginal associations. They neither isolate independent delayed effects nor show that a lagged predictor improves a contemporaneous model.

**Calculations and uncertainty**

For each of the 12 models, subtract the 1950–2025 calendar-month mean from precipitation and the aligned Niño predictor. Regress centered precipitation on centered Niño. The slope is sum(x*y)/sum(x*x); correlation is sum(x*y)/sqrt(sum(x*x)*sum(y*y)). This is equivalent to a regression with three calendar-month intercepts and one Niño slope within each season. Correlations refer to month-adjusted variables, not unadjusted monthly levels.

The main uncertainty calculation resamples paired contiguous blocks of five whole calendar years, circularly wrapping at the record ends, until 76 years are obtained. All variables and models share the same sampled years, and calendar-month means are re-estimated in every replicate. There are 4,000 replicates. This respects temporal dependence within blocks and supports paired contrasts; it does not treat 228 seasonal months as independent observations.

Pointwise intervals are bootstrap percentiles. Simultaneous intervals use the 95th percentile of the maximum absolute bootstrap deviation, standardized by each estimate's bootstrap standard deviation, across all 12 slopes and 11 contrasts. These are approximate joint intervals, not exact finite-sample guarantees. The recorded seed 20260930 is the base; actual seeds are base + block length (20260935, 20260933, 20260937).

Prespecified three- and seven-year block checks give primary winter pointwise intervals of 13.9–23.7 and 14.2–24.2 mm/°C. The primary conclusion is stable. The winter-minus-summer pointwise interval crosses zero with three- and five-year blocks but not seven-year blocks; its simultaneous interval includes zero for all three. This sensitivity reinforces caution about seasonal differences.

Removing a common full-record linear time trend from each variable, in addition to month means, changes the primary winter slope from 18.9 to 19.2 mm/°C and correlation from 0.454 to 0.459. Full detrended point estimates for all 12 models are included; no separate uncertainty analysis was run for those sensitivity estimates.

**Interpretation limits**

ENSO persistence, other climate modes, weather variability, tropical cyclones, possible long-term nonstationarity, and spatial averaging all matter. Detrending is only a limited robustness check, not control for all confounding. Circular blocks introduce artificial joins, break some December–January dependence at joins, and assume the observed dependence structure is sufficiently representative. Only 76 years are observed; a five-year block length corresponds to roughly 15 blocks per resample. Neither resampling nor those approximate intervals captures all uncertainty from SST reconstruction, precipitation measurement, data revisions, or model specification.

These are historical associations. They do not estimate the effect of an intervention that changes tropical SST, identify a causal pathway, prove a preferred lag, or establish operational forecasting performance. Statistical resampling was used, but no climate simulation, extra plugin, or remote computing was used.

**Reproducibility and verification**

The accompanying archive contains the UTF-8 snapshots of both retrieved tables, their SHA-256 checksums and URLs, the pre-analysis protocol, analysis.py, all five result CSVs, validation.json, and an independent rerun check. The file hashes refer to the preserved decoded UTF-8 snapshots. The raw table footers remain intact.

Extract the archive and run:

```text
python analysis.py --input-dir . --output-dir rerun
```

No network access is needed. Tested versions were Python 3.12.13, NumPy 2.5.1, and pandas 3.0.6; requirements.txt records the analysis packages. The CSVs retain more precision than the report.

Checks cover date continuity, duplicates, missing-value sentinels, units, season counts, lag-date boundaries, zero calendar-month residual means, interval ordering, and the number of comparisons. The primary slope agrees with an independent least-squares fit using raw data and month indicators to about 1.4×10⁻¹⁴ mm/°C. The archived command-line script was rerun in a clean temporary directory, and its five output CSVs and validation data matched the packaged results. These checks verify implementation consistency; they do not independently validate the climate hypothesis.
