Extended Data Fig. 10: Reconstruction skill and methods agreement in years 1 ad and 1000 ad.

a, Density of CRPS_RE values in PCR reconstructions based on: the full proxy network (dark yellow, the same as the PCR boxplot in Extended Data Fig. 9); proxy records extending at least to 1000 ad (green); and the records covering the full Common Era (blue). Numbers besides the curves indicate the percentage of grid cells with positive values. b, c, Maps showing the spatial distribution of CRPS_RE for the years 1000 ad (b) and 1 ad (c). Proxy locations are indicated with grey circles. d–f, As for a–c but for the CRPS_CE. g–i, As for a–c but for the RMSE. j–l, As for a–c but for the correlation coefficient. In general the spatial patterns between the time periods we analysed remain similar over time, but with areas of lower skill naturally extending backwards in time (see also the red line in Fig. 1). The largest decrease in skill generally occurs in the first millennium ad. m–o, Average correlation of ensemble median reconstructions accross all methods over the periods 1900–1999 ad (m), 1000–1099 ad (n) and 1–99 ad (o). More than 99% of correlations are positive in all three periods. Respectively 97%, 76% and 73% of correlations in the twentieth, eleventh and first centuries ad are above 0.28, which is the average α = 0.05 significance level given the autocorrelation in the reconstructions. In all periods the method agreement is larger in the Northern Hemisphere, particularly in the North Pacific and European domains, than in the Southern Hemisphere. Lowest agreement is found over tropical South America and Africa and over the Southern Ocean, the same areas that also exhibit the largest errors in the reconstructions.