Extended Data Fig. 1: Improvement of NAO matching over variance adjustment.

a, Time series of observed (black curve) and variance-adjusted model forecast (years 2–9; red curve, mean of the 676-member lagged ensemble; red shading, 5%–95% confidence interval diagnosed from the forecast ensemble-mean error variance) 8-yr running-mean December-to-March AMV index. b, As in a, but for the NAO-matched forecast (see Methods). c, d, As in a, b, but for northern European rainfall. ACC for the forecast ensemble mean, ACC for a forecast made by persisting the latest observed 8-yr mean available before each start date and RPC are indicated. Indices are defined in Methods. Time series are anomalies relative to the average of all year-2–9 hindcasts. Variance adjustment does not affect the correlation skill, but the uncertainties (red shading) capture the observations better, especially for northern European precipitation (compare c with Fig. 2e). However, NAO matching clearly improves predictions of the timing of the AMV minimum in the late 1980s and the subsequent rapid warming. It also captures the observed increase in northern European precipitation from the 1960s to late 1980s and decrease thereafter.