Within-winter NAO spread had a positive mean link to monthly rain concentration in three British countries in 1951-2025

We tested whether variation in the North Atlantic Oscillation (NAO) within winter was linked to uneven monthly rainfall. We used 75 complete winters in England, Wales and Scotland from fixed Met Office and NOAA data. For each country, we fit monthly rain concentration to NAO spread with controls for time, winter mean NAO, its square and winter rainfall total. The equal-country mean slope was 0.0361 concentration units per NAO spread unit. The 95% paired five-winter block interval was 0.0049 to 0.0700. Scotland had a positive country interval; England and Wales did not. The mean interval stayed above zero with separate monthly NAO controls, with no rainfall-total control, and with monthly climate adjustment. It included zero in both time halves and for the largest-month rain share. In a secondary 1981-2025 reconstruction test, adding NAO spread gave 7.07% mean error reduction, with an interval of -5.42% to 16.28%. Thus the fitted association did not give clear added reconstruction accuracy. The result is an association in three country averages, not a causal test, a lead forecast, or evidence about daily flood peaks. The package gives source hashes, monthly inputs, code, all checks, resampling draws and an independent numerical audit.

NAO · winter rainfall · monthly concentration · Great Britain · paired block bootstrap · seasonal aggregation