The confidence interval incorporates two sources of uncertainty. The first one derives from the the method of translating information in the proxies into temperatures. Seven different peer-reviewed methods are employed and all considered equally likely in the figure. The methods range from a simple linear method where proxies sensitivities are fitted to the observational to determine past temperature, to more complicated methods in which information about spatial patterns is taken into account, or information about natural forcing is taken into account.
The second type of uncertainty is in the selection of proxies. Some proxies might not be entirely reliable and their inclusion might slightly bias the reconstruction. By randomly selecting a subset of proxies, this uncertainty can be quantified.
Code to create the figure is adapted from the Nature Geosciences paper[1] and can be found on https://figshare.com/collections/Global_mean_temperature_reconstructions_over_the_Common_Era/4507043. The figure is a simplification of Fig 1a from this paper. Individual reconstruction methods are not shown.
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