Previous-month NAO gave no clear added winter rainfall forecast gain in England and Wales in 1981-2025

We tested whether previous-month North Atlantic Oscillation (NAO) improves monthly winter rainfall forecasts beyond recent local rainfall in England and Wales. Separate linear models used earlier winters only. The test covered 45 winters in 1981-2025 and 270 country-month targets. Added lag NAO gave 1.41% equal-country mean skill. The conditional 95% five-winter block interval was -1.69% to +4.38%. All planned lag-model checks had intervals that included zero. A diagnostic model with target-month NAO gave 12.10% skill (1.47% to 21.75%), but it used information unavailable at forecast time. Its gain was larger in Wales and weaker in the later test period. Two model checks left diagnostic gain uncertain. The test leaves added lag forecast value uncertain. It does not reject the known circulation-rainfall link or test dynamical forecasts. Two country averages, revised data, simple models and conditional uncertainty limit inference. We supply source subsets, hashes, forecasts, code, block draws, a figure and an independent audit.

NAO · rainfall · England · Wales · forecast · chronological validation · null result