Changes in the North Atlantic Oscillation over the 20th century

. The North Atlantic Oscillation explains a large fraction of the climate variability across the North Atlantic from the eastern seaboard of North America across the whole of Europe. Many studies have linked the North Atlantic Oscillation to climate extremes in this region, especially in winter, which has motivated considerable study of this pattern of variability. However, one overlooked feature of how the North Atlantic Oscillation has changed over time is the explained variance of the pattern. Here we show that there has been a considerable increase in the percentage of variability explained by the North Atlantic Oscillation (NAO) over the 20th century from 32 % in 1930 to 53 % by the end of the 20th century. Whether this change is due to natural variability, a forced response to climate change, or some combination remains unclear. However, we found no evidence for a forced response from an ensemble of 50 Coupled Model In-tercomparison Project Phase 6 (CMIP6) models. These models did all show substantial internal variability in the strength of the North Atlantic Oscillation, but it was biased towards being too high compared to the reanalysis and with too little variation over time. Since there is a direct connection be-tween the North Atlantic Oscillation and climate extremes over the region, this has direct consequences for both the long-term projection and near-term prediction of changes to climate extremes in the region.

1. Figure S1: Percentage variability explained by the first mode of EOFs in the CMIP6 models and reanalyses.
2. Figure S2: Percentage variability explained in the first mode of the CBF of CMIP6 models for two 30-year periods.
3. Figure S3: Spatial pattern correlation between the first mode of CBF of CMIP6 models and EOF of ERA-20C reanalysis for two 30-year periods.5 4. Figure S4: Taylor skill score between the first mode of CBF of CMIP6 models and EOF of ERA-20C reanalysis for two 30-year periods.
5. Figure S5: Absolute variability explained by the first mode of EOFs in the CMIP6 models and reanalyses.

Figure S1 .
Figure S1.Percentage of variance explained by the first mode of EOF in the reanalyses and EOF in the CMIP6 models in a moving 30-year period.ERA20C and NOAA20c reanalyses are shown in bold in blue and orange respectively.CMIP6 models are shown by thin lines in grey, except for NorESM2-LM (red) and NorESM2-MM (blue).Multi-model ensemble mean is shown in thick black line.Individual models are only shown when the projected pattern correlates to the projected pattern of the first mode of EOF in the ERA-20C reanalysis at or above the 80% level.

Figure S2 .
Figure S2.Percentage of variability explained by the first mode from the Common Basis Function for each of the models in 30-year periods at the start and end of the full time series, 1900-1929 (top) and 1981-2010 (bottom).Models are ordered in both plots by the amount of variability explained for the initial period of 1900-1929.The horizontal black line in both plots gives the amount of variability explained by the first mode of EOF in ERA 20th Century reanalysis, upon which the CBFs are based.CMIP6 models are shown in grey, except for NorESM2-LM (red) and NorESM2-MM (blue).

Figure S3 .
Figure S3.Correlation of the spatial pattern of the first mode from the Common Basis Function and the first mode of EOF from the ERA-20C reanalysis for each of the models in 30-year periods at the start and end of the full time series, 1900-1929 (top) and 1981-2010 (bottom).Models are ordered in both plots by the pattern correlation for the initial period of 1900-1929.CMIP6 models are shown in grey, except for NorESM2-LM (red) and NorESM2-MM (blue).

Figure S4 .
Figure S4.Taylor skill score between the first mode from the Common Basis Function and the first mode of EOF from the ERA-20C reanalysis for each of the models in 30-year periods at the start and end of the full time series, 1900-1929 (top) and 1981-2010 (bottom).Models are ordered in both plots by the skill score for the initial period of 1900-1929.CMIP6 models are shown in grey, except for NorESM2-LM (red) and NorESM2-MM (blue).

Figure S5 .
Figure S5.Absolute variance explained by the first mode of EOF in the reanalyses and EOF in the CMIP6 models in a moving 30-year period.This is a combination of the percentage variance explained as shown in Supplemental Figure S1 and the total variance in the sea level pressure, shown in Figure 5 in the main paper.ERA20C and NOAA20c reanalyses are shown in bold in blue and orange respectively.CMIP6 models are shown by thin lines in grey, except for NorESM2-LM (red) and NorESM2-MM (blue).Multi-model ensemble mean is shown in thick black line.Individual models are only shown when the projected pattern correlates to the projected pattern of the first mode of EOF in the ERA-20C reanalysis at or above the 80% level.