SUPPLEMENTARY INFORMATION

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1 SUPPLEMENTARY INFORMATION DOI: /NCLIMATE2336 Stormiest winter on record for Ireland and UK Here we provide further information on the methodological procedures behind our correspondence. First, the automated identification routine used to detect and characterise cyclones is outlined (Section 1), before we show the agreement between intensity calculated by the algorithm, and an independent assessment of cyclone severity derived from reanalysis wind speeds (Section 2). We then explain the methods used to bridge cyclone metrics between reanalysis datasets in reconstructing I-UK storminess and assess correspondence with gale indices (Section 3). Finally, we provide statistical interpretation of W2013/14 as the stormiest on record (Section 4) and test the homogeneity of the I-UK storminess series (Section 5). 1) Cyclone Identification The automated detection algorithm 1 identifies cyclones based on sea level pressure minima and has been used by the National Oceanic and Atmospheric Administration (NOAA) to diagnose storm tracks from 6-hourly reanalysis data. The algorithm was applied to winter (December to February, DJF) 6-hourly sea level pressure data obtained from the NCEP1 2 and CR 3 archives for the years 1948/49 to 2013/14 and 1871/72 to 2011/12, respectively. Due to uncertainty in extrapolating measured air pressure to sea level 4, data from grid cells >1000 m elevation according to the NCEP1 model topography were omitted from the analysis (areas shaded white in Fig. 1a in the main text and in Supplementary Figure 1). To detect a cyclone centre we used the threshold condition that a pressure gradient of at least 1 hpa 250 km -1 must be apparent between the tested grid point and its neighbouring cells. Arc lengths along great circles were used to calculate these gradients from the regular lat-lon grids. Consistent with previous studies 1,4,5 cyclone intensity was defined as the local Laplacian of sea level pressure. For each 6-hourly pressure map, the detection routine stores the resulting cyclone intensity, as well as date/time and position (latitude/longitude). DJF cyclone metrics were then summarised for each domain (main text, Fig. 1a). 2) NCEP1: Cyclone Intensity and Extreme Wind Speeds over the North Atlantic Mean DJF cyclone intensity measures for the entire North Atlantic (NA) region were significantly correlated with the 95 th percentile of NCEP1 10-metre wind speeds across the domain (r = 0.74, p<0.05), corroborating results from the cyclone identification routine. This agreement extends to trends, as according to the Mann Kendall test 6,7, significant (p<0.05) upward trends are apparent in both series over the period of analysis. NATURE CLIMATE CHANGE 1

2 Supplementary Figure 1 Trends in DJF 95 th percentiles of NCEP1 10-metre wind speeds and mean cyclone intensity averaged over the North Atlantic (see Figure 1 main text for details of domains). Slopes, whose values are annotated on the plot, were calculated using the Theil-Sen estimation method 8,9. 3) Reconstructing I-UK cyclone metrics from 20CR The 20CR was employed to gain a longer-term perspective of I-UK storminess. We applied the cyclone identification algorithm to each of the 56 20CR constituent ensemble members and then averaged the resulting series to generate ensemble mean cyclone statistics. To view W2013/14 NCEP1 storminess in a 143-year context, it was necessary to bridge between NCEP1 and 20CR cyclone metrics using linear regression. First, we re-calculated NCEP1 cyclones for I-UK after bilinearly interpolating the 2.5 NCEP1 sea level pressure data to the 2 grid used by 20CR. This step maintains consistency in grid resolution and I-UK domain boundaries and improves the correspondence in cyclone counts and storminess between reanalysis datasets (p<0.05 according to t-test on the difference in correlation coefficients between native and interpolated girds across 20CR ensemble members: Supplementary Figure 2). The regression adjustment was formulated with 20CR as the independent variable and NCEP1 as the dependent variable for the overlapping period (W1948/49 to W2011/12; n = 64). Regression adjustments were fitted and applied to both the ensemble mean cyclone metrics, and to each of the 56 constituent ensemble members. The regression coefficients (Supplementary Table 1) were then used to adjust the 20CR record for the years 1872/73 to 2011/2012. The regression adjusted (RA) ensemble mean (EM) cyclone metrics are referred to as RA-20CR-EM in the main text and hereafter, while the RA-20CR constituent members (CMs) are referred to as RA-20CR-CMs. Following adjustment NCEP1 W2012/13 and W2013/14 were appended to generate 143-year records of cyclone metrics, referred to as reconstructed series hereafter and in the main text. 2

3 Supplementary Figure 2 Comparison of I-UK cyclone metrics from the 20CR and NCEP1 2.5 (native) and 2 (interpolated) datasets. Correlation coefficients in the top left of plots give the correspondence between 20CR ensemble mean (EM) and NCEP1 (interpolated/native) cyclone metrics; ± gives one standard deviation of the correlation coefficients across 20CR constituent ensemble members (CMs). Supplementary Table 1 Diagnostics for regression models used to bridge interpolated NCEP1 and 20CR-EM metrics. Coefficients and goodness-of-fit measure (r 2 ) quantify the regression function for cyclone counts, mean cyclone intensity and storminess index. Slopes are dimensionless and intercepts have units of counts/4 (cyclone counts) and Laplacians of sea-level air pressure ( 2 p: hpa 10-5 Km -2 for intensity and storminess). Bracketed numbers correspond to ± one standard deviation of the respective diagnostic when the regression function was fitted to 20CR-CMs. Cyclone metric Slope Intercept r 2 Counts (0.020) (1.024) (0.010) Mean intensity (0.026) (0.604) (0.021) Storminess (0.015) (18.089) (0.010) 3

4 3.1) Reconstructed RA-20CR-EM cyclone metrics and gale events We show correlations between reconstructed RA-20CR-EM cyclone metrics and longrunning precipitation series in the main text. Comparable wind speed datasets are not available due to the practical difficulties in maintaining consistent measurement practices. However, the UK Jenkinson Gale Index 10 computed using NCEP1 and 20CR 11 allows comparison of our cyclone metrics with a methodologically-distinct, threshold-based index of storminess. Significant associations are observed between most combinations of gale counts and our cyclone metrics (supplementary Table 2). Mean cyclone intensity correlates most strongly with counts of the stronger, presumably because it requires intense storms to generate such winds. The weakest correlations are observed for cyclone counts, which is unsurprising as this metric contains no information regarding cyclone intensity. We note that our cyclone counts correlate more strongly with than do totals of cyclonic Lamb Weather Types (LWTs) 11. Correlations between gale counts and storminess are all significant, but more modest than for cyclone intensity, which is explained by the composite nature of the storminess metric itself. We note that the severity of W2013/14 ranks top in the reconstructed RA-20CR-EM storminess series and counts of very severe. This supports our interpretation of the unprecedented nature of W2103/14 storminess. Supplementary Table 2 Correlations between reconstructed RA-20CR-EM cyclone metrics/lwts and the Jenkinson Gale Index 10,11. Correlations significantly different from zero at p < 0.05 are marked*. RA-20 CR-EM Metric severe very severe + severe + very severe severe + very severe Counts * * 0.12 Intensity 0.43* 0.52* 0.45* 0.52* 0.50* 0.60* 0.56* Storminess 0.21* 0.26* 0.43* 0.25* 0.29* 0.38* 0.31* + severe + very severe LWTs Hybrid * Pure ) The unprecedented nature of I-UK W2013/14 To further assess the extreme nature of W2013/14 we estimated the likelihood of exceedance for individual winters within the 143 year reconstructed storminess series by considering uncertainty in the regression adjustment and the spread in storminess metrics between 20CR-CMs. Assuming the regression residuals follow a Gaussian distribution, the probability that storminess in any year of the RA-20CR-CMs exceeded that of W2013/14 can be estimated by evaluating the cumulative standard normal distribution function, with a z- score given by: Eq. 1 4

5 where is RA-20CR storminess in year y for constituent 20CR ensemble member m, is W2103/14 storminess and is the standard deviation of the regression prediction, given by: Eq.2 In which indicates non-adjusted 20CR storminess, whilst n, over-bar and V denote the sample length (64), mean and variance of used to fit the regression function; is the standard deviation of the residuals from this regression. The 95% prediction bounds shown in the main text Fig. 2a correspond to ±2, in which the index refers to the ensemble mean series. We evaluated the standard normal cumulative distribution using the Matlab statistics toolbox. We found that across all RA-20CR-CMs the second stormiest year (W1914/15) had a median likelihood of exceeding W2013/14 of 1.37%. Therefore, we conclude that after accounting for both the spread in storminess across all RA-20CR-CMs and sampling uncertainty in individual regression adjustments, it is very unlikely that W2013/14 storminess was exceeded in the full 143-year period for I-UK. 5) Homogeneity Testing Non-homogeniety within RA-20CR may result from changes in the amount of observations assimilated 4. We assessed the homogeneity of all reconstructed storminess series using the non-parametric Pettitt change point test 12 with the null hypothesis (no change) and alternative hypothesis (a single upward or downward change point in a given year) evaluated at the 5% significance level. We found that reconstructed RA-20CR-EM storminess does not have a significant change point (the most likely year is 1909: p=0.07). However, 23% of the reconstructed RA-20CR-CMs storminess series do record a change-point (p-value < 0.05) for this year. If this change point (for which there is only weak evidence) is indeed an indication of lower data quality, it suggests that storminess may be systematically underestimated prior to However, we emphasise that even if all pre-1909 reconstructed RA-20CR storminess indices are revised upward by an amount equal to the maximum difference in means between all ensemble members (pre-and post-1909), W2013/14 remains the stormiest on record (Supplementary Figure 3). 5

6 Supplementary Figure 3 Sensitivity of reconstructed storminess series to pre-1909 adjustment. Top shows reconstructed storminess series with piece-wise means for the periods separated by the apparent 1909 change point (differentiated by background colour). Bottom illustrates the effect of adjusting all pre-1909 reconstructed RA-20CR-CMs upward by an amount equal to the maximum difference between pre/post change point across constituent members. Note that the green line highlights W2013/14 storminess. References 1. Serreze, M.C. & Barrett, A.P. J. Climate 21, (2008). 2. Kalnay, E. et al. B. Am. Meterol. Soc. 77, (1996). 3. Compo, G.P. et al. Q.J.R. Meteorol. So. 137, 1-28 (2011). 4. Wang, X.L. et al. Clim. Dynam. 40, (2013). 5. Pinto, J. G., Spangehl, T., Ulbrich, U., & Speth, P. Meteorol. Z. 14, (2005). 6. Mann, H. B. Econometrica 13, (1945). 7. Kendall, M. G. Rank correlation methods, (Charles Griffin, 1975). 8. Theil, H. A. Nederlands Akad. Wetensch. Proc. 53, (1950). 9. Sen, P. K. J. Am. Stat. Assoc. 63, (1968). 10. Jenkinson, A.F. & Collison, F.P. Synoptic Climatology Branch Memorandum 62, (1977). 11. Climatic Research Unit (June, 2014); Pettitt, A.N. J. Roy. Stat. Soc. C 28, (1979). 6