Supporting material for article :

C. Tzedakis, M. Crucifix, T. Mitsui and E. Wolff, A simple rule to determine which insolation cycles lead to interglacials, accepted for publication in Nature (reference to be provided)

Directory structure

Data

• caloric_peaks.csv : master data supporting the article containing
  • row index
  • Time.ka.BP : Time in thousands of years BP correponding to Caloric Insolation peaks
  • MIS.or.peak.age : Label (MIS number or peakr age) used throughouth the paper
  • is.0..ig.1..c.ig.2 : index = 0 if interstadial, 1 if interglacial, and 2 if continued interglacial
  • filled.0.or.Open.1 : = 1 if the attribution is considered as less certain and represented as a circle on Figures 1 to 4
  • Caloric.summer.insolation.at.65N.GJm.2 : caloric summer insolation at 65 degrees N in GJ/m2
  • Elapsed.time.ka : Elapsed time since latest insolation peak yielding an interglacial onset
  • Effective.energy.GJm.2 : Effective energy as used on Figure 5
• detrended_LR04_smoothed.csv
• detrended_S05.csv
• insolations.csv
  • Insolations computed based on the Laskar et al. (2004) astronomical solution and obtained using the palinsol R package (see below)
• solstice_peaks.csv
  • same as caloric_peaks.csv but using summer solstice, as used for Extended Data Figure 9.

Note : Microsoft Excel Open XML Format (Xlsx) are also provided in the Xlsx directory, along with the data file ['2016-02-02407A_SI_Tables_S1_and_S2.xlsx'](Data/Xlsx/2016-02-02407A_SI Tables S1 and S2_ew.xlsx') provided as supplementary tables of the Nature article.

R

This R code is provided under MIT Licence (see LICENSE file attached)

• main.R is the master file which load experiment parameters and generate simulation output in the RData directory

• experiment.R contains the MCMC simulation procedure

• analysis_function.R contains supporting functions

• plot_mpt.R loads simulation output in the RData directory to generate Extended Data Figure S10

• plot_frequent_traj loads simualtion output in the RData directory to generate Figure 6

• diag_last_1000k.R generates the data (quantiles_part_1.Rda) as well as a figure similar to Figure 4, but the figure actually published underwent further editing for nice placement of labels.

• diag_last_2500k.R generates the data (quantiles_25Myr_part_3.Rda) as well as a figure similar to Extended Data Figure 5, but the published figure underwent further editing for nice placement of labels.

RData

Contains RData binary files, directly loadable in R, with the output of the Monte-Carlo experiments

Eps

Figures produced directly with the R code. Note that the other figures of the article have been produced based on the different .csv files available in the Data directory.

Software acknowledgements

We are grateful to the developers of R:

R Core Team (2016). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.

we also use the following packages for plotting:

• Erich Neuwirth (2014). RColorBrewer: ColorBrewer Palettes. R package version 1.1-2. https://CRAN.R-project.org/package=RColorBrewer
• Package 'hexbin' by Dan Carr, ported by Nicholas Lewin-Koh, Martin Maechler and contains copies of lattice functions written by Deepayan Sarkar (2015). hexbin: Hexagonal Binning Routines. R package version 1.27.1. https://CRAN.R-project.org/package=hexbin

insolations are obtained using the Package 'palinsol' : M. Crucifix (2016). palinsol: Insolation for Palaeoclimate Studies. R package version 0.94. https://cran.r-project.org/package=palinsol