# CORRECTED Case20: Florida precipitation and Niño 3.4, 1986–2025

**This corrected 40-year analysis supersedes the earlier 1950–2025 results for Case20 acceptance.** The earlier protocol, report and ZIP are preserved, not deleted or overwritten. The only scientific design correction is the outcome window: the latest 40 complete calendar years, **1986–2025**, fixed at the user's instruction before recalculation. The earlier estimates were already known; this is transparently a boundary correction, not an independent preregistration. No alternative windows were searched or compared to choose these dates.

The primary winter association is **20.24 mm more monthly precipitation per 1°C higher Niño 3.4**, after calendar-month adjustment. The pointwise 95% block-bootstrap interval is **13.73–26.60 mm/°C**, and the approximate simultaneous interval is **10.35–30.13 mm/°C**. The winter correlation is **0.498** (pointwise interval 0.358–0.618).

Winter slopes are consistently positive at all three fixed lags. Evidence for seasonal differences depends on the contrast and block length. There is no clear evidence that a one- or two-month lag is preferable to the contemporaneous index. These are historical associations, not intervention effects.

**Fixed scope and public inputs**

Florida was chosen before the original calculations because ENSO can influence the subtropical jet and cool-season storm tracks affecting the southeastern United States. The state was not chosen by screening results. The corrected analysis retains Florida, one monthly Niño 3.4 index, DJF/MAM/JJA/SON, Niño-leading lags 0/1/2 months, and DJF lag 0 as primary.

The exact original public table snapshots, accessed 2026-09-30, were reused without a network refresh:

- NOAA PSL [monthly Niño 3.4 anomalies](https://psl.noaa.gov/data/correlation/nina34.anom.data). Its preserved footer specifies ERSST v6, 5°N–5°S and 170°W–120°W, anomaly reference 1981–2010, °C. This is not the three-month ONI.
- NOAA NCEI [Florida monthly statewide precipitation](https://www.ncei.noaa.gov/access/monitoring/climate-at-a-glance/statewide/time-series/8/pcp/1/0/1950-2025.csv). The saved source spans 1950–2025; only the fixed 1986–2025 rows enter the corrected outcome analysis. Inches were converted to millimetres using exactly 25.4 mm/inch.

The raw snapshots intentionally retain their full source coverage and metadata. Their SHA-256 hashes match the earlier archive. This source coverage does not change the corrected analysis period.

All **480 outcome months** are unique, contiguous and nonmissing; each season has **120 monthly observations over 40 calendar years**. For lag alignment, the index buffer starts in November 1985. January 1986 at lag 2 therefore uses November 1985 Niño. Those preceding predictor months do not add outcome years. December belongs to DJF; these are monthly models, not regressions of complete winter totals.

NOAA precipitation includes snow water equivalent, so it is a rainfall proxy. Statewide averaging can hide substantial local differences.

**All 12 associations**

Slopes are mm/month per °C. Positive lag means Niño precedes the outcome. Pointwise and simultaneous columns are 95% intervals; the simultaneous family comprises all 12 slopes and 11 contrasts.

| Season | Niño-leading lag | Slope | Pointwise interval | Simultaneous interval | Month-adjusted r |
|---|---:|---:|---:|---:|---:|
| DJF | 0 | 20.24 | [13.73, 26.60] | [10.35, 30.13] | 0.498 |
| DJF | 1 | 18.65 | [11.93, 25.59] | [8.12, 29.18] | 0.480 |
| DJF | 2 | 18.50 | [11.42, 26.10] | [7.11, 29.89] | 0.457 |
| MAM | 0 | 13.89 | [0.41, 26.86] | [−6.46, 34.24] | 0.188 |
| MAM | 1 | 8.45 | [−1.29, 17.15] | [−5.41, 22.32] | 0.136 |
| MAM | 2 | 5.68 | [−1.77, 12.54] | [−5.15, 16.50] | 0.110 |
| JJA | 0 | 6.67 | [−2.85, 17.70] | [−9.44, 22.78] | 0.086 |
| JJA | 1 | 0.68 | [−9.63, 10.98] | [−14.96, 16.32] | 0.008 |
| JJA | 2 | −2.92 | [−15.07, 7.07] | [−20.04, 14.21] | −0.035 |
| SON | 0 | 0.50 | [−5.96, 7.28] | [−9.69, 10.69] | 0.009 |
| SON | 1 | −0.29 | [−8.43, 7.93] | [−12.89, 12.30] | −0.005 |
| SON | 2 | 2.22 | [−6.91, 11.75] | [−12.28, 16.73] | 0.031 |

All three winter slopes exclude zero under simultaneous intervals; no spring, summer or autumn slope does. The primary winter r² is 0.248: about 25% of the month-adjusted winter precipitation variance is accounted for by this linear in-sample association. This is not an out-of-sample skill estimate.

**All 11 direct contrasts**

Differences are mm/°C. These paired comparisons assess differences directly; separate significant and nonsignificant slopes are not themselves evidence of a difference.

| Contrast | Difference | Pointwise interval | Simultaneous interval |
|---|---:|---:|---:|
| DJF − JJA, lag 0 | 13.57 | [1.63, 23.18] | [−3.04, 30.18] |
| DJF − JJA, lag 1 | 17.97 | [5.05, 30.08] | [−1.35, 37.29] |
| DJF − JJA, lag 2 | 21.42 | [10.52, 33.44] | [3.85, 38.99] |
| DJF lag 1 − lag 0 | −1.59 | [−3.03, −0.59] | [−3.50, 0.32] |
| DJF lag 2 − lag 0 | −1.74 | [−3.70, 0.06] | [−4.64, 1.16] |
| MAM lag 1 − lag 0 | −5.44 | [−11.35, −0.25] | [−13.95, 3.07] |
| MAM lag 2 − lag 0 | −8.21 | [−16.95, −0.92] | [−20.50, 4.07] |
| JJA lag 1 − lag 0 | −5.99 | [−12.73, −0.60] | [−15.38, 3.41] |
| JJA lag 2 − lag 0 | −9.58 | [−18.15, −4.00] | [−20.54, 1.37] |
| SON lag 1 − lag 0 | −0.79 | [−3.10, 1.18] | [−4.08, 2.50] |
| SON lag 2 − lag 0 | 1.72 | [−2.10, 5.81] | [−4.32, 7.77] |

The main seasonal contrast, DJF minus JJA at lag 0, is positive but its simultaneous interval includes zero. The lag-2 DJF-minus-JJA contrast excludes zero with the primary five-year blocks; its sensitivity is discussed below. This seasonal contrast does not imply that lag 2 is the best lag.

Every within-season lag contrast includes zero under the simultaneous intervals. Winter month-adjusted Niño correlations are 0.978 for lag 0 versus lag 1 and 0.952 for lag 0 versus lag 2. Separate lagged models are highly dependent marginal associations; they do not estimate independent delayed effects or establish incremental forecasting value.

**Unchanged calculations and uncertainty**

For each model, remove the 1986–2025 mean for each calendar month from precipitation and the appropriately aligned Niño predictor. Regress the residual outcome on the residual predictor: slope = sum(x*y)/sum(x*x); correlation = sum(x*y)/sqrt(sum(x*x)*sum(y*y)). This is equivalent to month intercepts and one Niño slope within each season. The Niño index's official 1981–2010 reference baseline remains unchanged; calendar-month centering is an analysis adjustment.

Uncertainty uses paired circular moving-block resampling of whole calendar years, with five-year blocks and 4,000 replicates, drawing enough blocks and trimming to 40 years. The same year draws apply to every variable and model, with means re-estimated in each replicate. Pointwise intervals are bootstrap percentiles.

Approximate simultaneous intervals use the 95th percentile of the maximum absolute bootstrap deviation divided by each estimate's bootstrap standard deviation, over the fixed family of 23 estimates. They are not exact finite-sample guarantees. Seed base remains 20260930; actual seeds are 20260935, 20260933 and 20260937 for five-, three- and seven-year blocks.

The corrected script changes only period-dependent selection, dimensions, counts, date checks and identifying metadata. The core statistics, contrast, bootstrap and interval functions are structurally identical to the earlier code. A code diff is included.

**Prespecified sensitivity analyses**

| Block length | Primary DJF lag 0 pointwise interval | Primary simultaneous interval | DJF − JJA lag 0 simultaneous interval | DJF − JJA lag 2 simultaneous interval |
|---|---:|---:|---:|---:|
| 3 years | [13.72, 26.68] | [10.15, 30.33] | [−5.06, 32.21] | [−0.15, 42.98] |
| 5 years | [13.73, 26.60] | [10.35, 30.13] | [−3.04, 30.18] | [3.85, 38.99] |
| 7 years | [14.15, 26.64] | [10.42, 30.06] | [−2.64, 29.79] | [4.48, 38.35] |

The winter primary conclusion is stable across block lengths. The lag-2 seasonal contrast excludes zero with five- and seven-year blocks but not three-year blocks. Thus the seasonal evidence is sensitive to the dependence assumption. No block length was selected based on these results. The CSV contains intervals for all 23 estimates at all three block lengths, including those not displayed here.

Removing a common full-record linear trend from each month-centered variable gives these slopes:

| Season | Detrended lag 0 | Detrended lag 1 | Detrended lag 2 |
|---|---:|---:|---:|
| DJF | 20.30 | 18.71 | 18.58 |
| MAM | 13.85 | 8.42 | 5.66 |
| JJA | 6.34 | 0.20 | −3.50 |
| SON | 0.56 | −0.20 | 2.34 |

The detrended winter correlation is 0.499. These are sensitivity point estimates, with no separate detrended uncertainty analysis, exactly as in the earlier method. The full CSV retains detrended correlations and original slopes for every model.

**Limits of interpretation**

Forty years provide fewer independent climate episodes than 480 monthly observations might suggest. A five-year resample contains eight blocks, not 480 independent months. Circular resampling creates artificial joins, including some breaks in December–January dependence, and assumes the observed dependence is reasonably representative. Block-length sensitivity therefore matters.

These intervals do not capture all uncertainty from SST reconstruction, precipitation measurement, revisions, omitted climate variability, changing relationships or model specification. Statewide averages suppress local variation. Detrending is a limited robustness check, not comprehensive adjustment for confounding. Weather variability, tropical cyclones and other climate modes also influence Florida precipitation.

An association does not identify the effect of intervening on Niño 3.4, prove a causal mechanism, or establish forecast performance. No climate simulation, additional plugin or remote computing was used. No .science export was produced.

**Rerun, checks and supersession**

Extract the corrected ZIP, then run offline:

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

Tested environment: Python 3.12.13, NumPy 2.5.1, pandas 3.0.6. requirements.txt records the package versions. The script needs no network and only evaluates the fixed 1986–2025 window.

The archive contains the full original source snapshots and hashes, corrected protocol and report, analysis.py, its period-only diff, the aligned 480-month CSV, all association and contrast estimates, block-length and detrend sensitivity CSVs, sources.json, supersession.json, validation.json, reproduction_check.json and a checksum manifest.

A clean subprocess rerun in a new temporary directory reproduced all five CSVs byte for byte and matched validation data. Checks verified dates, completeness, season counts, lag alignment, calendar-month residual means, interval ordering and all 12/11 model counts. Independent least squares with month indicators agrees with the primary slope within approximately 3.6×10⁻¹⁵ mm/°C. Archive integrity and member hashes passed; the previous ZIP checksum remained unchanged.

Superseded artifacts retained intact:
- comparison_protocol.md
- florida_nino34_report.md
- florida_nino34_reproducibility.zip

Use the new corrected_1986_2025 deliverables for Case20 acceptance. Supersession is recorded in these new documents and the archive's provenance record; it does not rewrite the earlier files. These implementation checks are not an external acceptance verdict or independent validation of a climate mechanism.
