A probabilistic ice-sheet parameterization for Antarctic ice-sheet evolution

Published Jul 09, 2026 on Dryad. https://doi.org/10.5061/dryad.sbcc2frkt

Data files

Jul 09, 2026 version files 13.12 MB

Gen2025-Final_v3_Gernon-ppr_FINAL_AUG2025.R

52.95 KB
LR-SL16lagged-unpadded.txt

10.07 KB
README.md

4.04 KB
tcurr.txt

450.90 KB
VA-rA-hA-BRAcha_Submission.csv

10.09 MB
WHprob-limY65m_age_SL_SLm_tforw_dOc.txt

2.51 MB

Abstract

The model is updated from Rohling et al. (2024) and now includes dynamic ice-aspect ratios (h/radius) in response to (a) duration of ice cover over a location (the longer, the less regolith influence), duration of ice-free conditions once bedrock is exposed (the longer, the more regolith is built up again); and (b) mean bedrock slope from ice-sheet centre to margin (dependent on initial continent slope and cumulative GIA). The model is now probabilistic and uses a generous set of monotonic random perturbations to the d18Oc:SL input function (spanning the entire width of the Milankovitch variability in the Spratt and Lisiecki regression, Climate of the Past 2016). Propagation of all uncertainties and their co-variations is evaluated using a Monte Carlo assessment. The number of iterations is set in line 54 to N = 500. It was found that no substantive changes occurred in the output once N > 100. Care must be taken that outcome probability envelopes are not simply additive, as uncertainties in several cases are drawn from a closed sum (when one goes up, others must go down). Hence all probability envelopes must be separately resolved because they cannot be obtained from standard addition routines. Ice altitude and bedrock changes are now plotted properly including the initial bedrock elevations ("peakX"). A plot has been added of the percentage of Monte Carlo simulations that exceeds a radius of 0m, for each time slice. At the end, an animation has been added that shows the simple modelled Antarctic ice extent changes over time on a map, with its reconstructed 68 % probability envelope (based on the 16^th and 84^th percentiles).

Dataset DOI: 10.5061/dryad.sbcc2frkt

Description of the data and file structure

The data were collected to develop and test an improved model of past ice-sheet dynamics (updated from Rohling et al. (2024) - see "Access Information"). Specifically, the work refines the relationship between benthic foraminiferal δ¹⁸O and sea-level anomalies through a Monte Carlo approach, and introduces a dynamic treatment of ice-sheet aspect ratios that respond to both bedrock slope and basal friction. These experimental efforts allow reconstruction of Antarctic ice-sheet volumes and their variability within probabilistic uncertainty bounds, providing a more realistic framework than previous constant-aspect-ratio models.

Files and variables

File: Gen2025-Final_v3_Gernon-ppr_FINAL_AUG2025.R

(See Code/Software for Details)

File: VA-rA-hA-BRAcha_Submission.csv

Variables

Modelstep – Time-stepping of the model (in ka)
Age – Age in kiloyears ago (ka)
VA – Reconstructed Antarctic ice volume (in m sea-level equivalent, m_seq)
rA – Reconstructed Antarctic ice-sheet radius (circular, in km)
hA – Reconstructed Antarctic ice-sheet thickness at summit (in m)
BRAcha – Reconstructed bedrock elevation change below the summit of the Antarctic ice sheet (in m)
…median – Median of reconstructed property
…q16 – 16th percentile of reconstructed property
…q84 – 84th percentile of reconstructed property

Code/software

Software and workflow needed to view and run the data

The dataset and code can be accessed and run using the free, open-source R statistical environment (https://www.r-project.org/), tested with R version ≥ 4.3.0. The main script, “Gen2025-Final_v3_Gernon-ppr_FINAL AUG2025.R”, implements the 2025 UPDATED probabilistic ice-sheet model from Rohling et al. (2024).

Required R packages (all open-source) include:

library(foreach)
library(doParallel)
library(parallel)
library(scales)
library(scam)
library(dplyr)
library(data.table)
library(ggplot2)
library(sf)
library(tibble)
library(rnaturalearth)
library(gganimate)
library(ggtext)

Workflow:

Ensure the input files "tcurr.txt", "WHprob-limY65m_age_SL_SLm_tforw_dOc.txt", and "LR-SL16lagged-unpadded.txt" are present in the same working directory as the R script.
Create an empty folder named "MCresults" within the working directory.
Update the working directory paths in lines 73–74 of the script to match the user’s system.
Run the R script, which performs Monte Carlo simulations (default N=500) of ice-sheet aspect ratios and δ¹⁸O–sea-level relationships, generates probability-resolved outputs, and plots ice altitude, bedrock changes, and Antarctic ice extent.
Figures are exported as PNG files, and the animation of ice extent is saved as a standard MP4 file (antarctica_ice_radius.mp4).

All analyses, figures, and the animation can be reproduced using only the R environment with the listed packages and the provided input files.

Access information

Other publicly accessible locations of the data:

The analysis here (fully described in Gernon et al., under consideration) has been updated from Rohling et al. (2024):
Rohling, E. J., Gernon, T. M., Heslop, D., Reichart, G. J., Roberts, A. P., & Yu, J. (2024). Reconciling the apparent discrepancy between Cenozoic deep-sea temperatures from proxies and from benthic oxygen isotope deconvolution. Paleoceanography and Paleoclimatology, 39, e2024PA004872. https://doi.org/10.1029/2024PA004872
The model updates are described in the summary above, and in a paper by Gernon et al. (inc. Rohling, E.J.) entitled "Continental breakup-driven uplift instigated East Antarctic Ice Sheet formation" (under consideration).