Separate monthly NAO terms gave no clear winter rainfall reconstruction gain in Scotland in 1981-2025

We tested whether separate December, January and February NAO terms improve reconstruction of winter rainfall totals beyond winter mean NAO. We used 75 winters from fixed Met Office and NOAA snapshots. Earlier-year fits reconstructed 45 winters in 1981-2025. Scotland was the primary country. Added monthly terms raised mean squared error by 3.79%; RMSE rose from 92.11 to 93.84 mm. The conditional 95% five-winter block interval for error reduction was -18.47% to +4.98%. England and Wales also had negative point scores with intervals across zero. Removing time or using 30-year training did not give clear gain. The test leaves the value of these monthly linear terms uncertain. It does not imply equal physical response across months or assess advance forecasts. Revised records, country averages, model choice and 45 test winters limit inference. Code, source hashes, aggregate evidence, numerical checks and a figure are included. External record tables remain outside the publication and can be rebuilt.

NAO · winter rainfall · seasonal aggregation · Scotland · chronological reconstruction · null result