Determining reliable probability distributions for ice sheet mass change over the coming century is critical to refining uncertainties in sea-level rise projections. Bayesian calibration, a method for constraining projection uncertainty using observations, has been previously applied to ice sheet projections but the impact of the chosen observation type on the calibrated posterior probability distributions has not been quantified. Here, we perform three separate Bayesian calibrations to constrain uncertainty in Greenland Ice Sheet (GrIS) simulations of the committed mass loss in 2100 under the current climate, using observations of velocity change, dynamic ice thickness change, and mass change. Comparing the posterior probability distributions shows that the median ice sheet mass change can differ by 119 % for the particular model ensemble that we used, depending on the observation type used in the calibration. More importantly for risk-averse sea-level planning, posterior probabilities of high-end mass change scenarios are highly sensitive to the observation selected for calibration. Furthermore, we show that using mass change observations alone may result in model simulations that overestimate flow acceleration and underestimate dynamic thinning around the margin of the ice sheet. Finally, we look ahead and present ideas for ways to improve Bayesian calibration of ice sheet projections.

Probabilistic sea-level rise projections are critical for coastal decision-making. The Sixth Assessment Report (AR6) from the Intergovernmental Panel on Climate Change has compiled probabilistic projections, with the contribution from the Greenland and Antarctic ice sheets being quantified, for the first time, by higher-order numerical ice sheet models

One method for conditioning ice sheet projection probabilities on observations is Bayesian calibration

In this study, we explore the effect of different observation types on Bayesian calibrations by using velocity change, dynamic ice thickness change, and mass change observations to perform separate calibrations of a Greenland Ice Sheet (GrIS) ensemble, which simulates Greenland's committed contribution to sea-level change over the current century, from 2015 to 2100. Our study builds upon the work of

We use an ensemble of model simulations that project the committed contribution from the GrIS to sea level over the coming century. The committed contribution captures the mass change of the GrIS in response to current atmospheric and oceanic forcings, independent of future atmospheric or oceanic warming. The committed response can be thought of as the change that is already locked into the ice sheet, which will play out over the coming century. We summarize the model ensemble here and details can be found in

The first observation type that we use for calibration is velocity change. Velocity change observations are computed using the Making Earth System Data Records for Use in Research Environments (MEaSUREs) Greenland Ice Sheet Velocity Map from Interferometric Synthetic Aperture Radar (InSAR) Data, Version 2

The second observation type that we use for calibration is dynamic ice thickness change. This quantity is a useful measure of how out of balance the ice dynamics are with the climate, and, thus, it is a good metric for evaluating the ensemble. Ice sheet surface elevation change time series are obtained from airborne and spaceborne laser altimetry using the Surface Elevation Reconstruction and Change (SERAC) method

We sum the annual dynamic ice thickness change over the time period 2007–2015, only considering those SERAC locations that have an estimate for each year between 2007 and 2015. This results in a set of more than 16 000 data points over the ice sheet in irregularly distributed locations, with higher density around the ice sheet margin where airborne altimetry provides increased spatial sampling beyond the spaceborne altimetry

To assign uncertainties, we combine the approximation errors of ice thickness change from the ALPS and polynomial fits and inflate them to account for errors in the FDM and SMB estimates. We investigate fit errors from ALPS at locations where the magnitude of dynamic ice thickness change is

The third observation type we use for calibration is mass change observations. Mass change observations of the GrIS are derived from the high-spatial-resolution NASA Goddard Space Flight Center (GSFC) global mascon trend solution (release 06), obtained from the Gravity Recovery and Climate Experiment (GRACE) and the Gravity Recovery and Climate Experiment Follow-On (GRACE-FO)

In our Bayesian calibration approach (described in Sect.

Gridded observations and their uncertainties for the 2007–2015 calibration time period. Panels

To calculate model–observation residuals, we must calculate model quantities that match the observed quantities. Velocity is a model state variable and we can compare modeled velocity change directly with observations. Modeled dynamic ice thickness change is calculated by subtracting the SMB anomaly (in units of ice thickness equivalent) from the modeled ice thickness change over 2007–2015. SMB anomaly is calculated by subtracting the mean 1960–1979 SMB from the prescribed SMB forcing for each simulation in the ensemble. The prescribed SMB forcing for the model simulations is obtained from RACMO2.3p2

The modeled quantities are regridded spatially to match the observational quantities. Mean modeled velocity change and dynamic ice thickness change are calculated within the grid cells defined by the same 50 km by 50 km grid used for the observational datasets. Modeled mass change is aggregated within the same drainage basins as used for aggregating the observed mass change

We use a Bayesian calibration approach to refine the spread in simulated GrIS mass change and the uncertainty in model parameters and forcings from our ice sheet model ensemble. A thorough treatment of this approach can be found in

To construct the likelihood, we use model–observation residuals to assign a likelihood score for each ensemble member. We assume that the residuals are independent, are identically distributed, and follow a normal (Gaussian) distribution. Under these assumptions, the score for the

Values for the multiplier

Once the scores,

We perform three separate calibrations using observations of (1) velocity, (2) thickness, or (3) mass change and compare the posterior probability distributions of GrIS committed contribution to GMSL in 2100, as well as model parameters and forcings obtained from all three calibrations.

The calibrated posterior probability distributions of GrIS committed contribution to GMSL and the associated statistics differ between the three calibrations (Fig.

Posterior probability distributions of Greenland's committed contribution to global mean sea level (GMSL) in 2100 from three Bayesian calibrations: velocity (orange), thickness (green), and mass (black) change observations. Prior distribution is shown as a blue curve and the histogram of the prior population is shown as a blue bar graph. Note that the

Statistics for GMSL median (mm), 5th and 95th percentiles (mm), and probability of GMSL larger than 50 and 100 mm (

Posterior probability distributions of model parameters and forcings for all three calibrations are shown in Fig.

Prior and posterior probability distributions of model parameters and forcings: basal friction multiplier

We find that three different ensemble members are scored highest across the three calibrations, with notable differences in the spatial patterns of their model–observation residuals (Fig.

Residuals (modeled minus observed) for the highest-weighted ensemble members from Bayesian calibration using velocity change (column 1), thickness change (column 2), and mass change (column 3) observations. Residuals of velocity (row 1), thickness (row 2), and mass (row 3) change over the calibration time period of 2007–2015 are shown. Note that mass change residuals are shown at the resolution of individual mascons, rather than aggregated within basins, in order to provide additional detail. We provide the root sum of squares (RSS) of the residuals shown below each map.

The choice of observation type strongly affects the results of the calibration. This choice affects the posterior probability distributions of GrIS committed contribution to GMSL in 2100 (Fig.

Basal friction is the most sensitive parameter to choice in observation type (Fig.

Calibration using dynamic ice thickness change results in a posterior probability distribution of GrIS committed contribution to GMSL in 2100 that is quite different from the velocity change and mass change calibrations. Although the spread in the posterior probability distributions of GMSL in 2100 is similar across the three calibrations, as seen from the percentiles in Table

Several factors may contribute to discrepancies seen across the three calibrations. For the dynamic ice thickness change calibration, a potential source for a bias is the estimate of firn thickness change that is used in the calculation of observed dynamic ice thickness change. A bias can be caused by a bias in the estimated trend of firn thickness change either over the 1960–1979 baseline time period or over the 2007–2015 calibration time period; this bias will directly translate to a bias in the observed dynamic ice thickness change and can then bias the posterior probability distribution of ice sheet mass change. Additionally, all three calibrations may be impacted by unique issues related to spatial sampling of the observations. Mass change observations from satellite gravimetry can be affected by “signal leakage”, meaning that mass change of peripheral glaciers and ice caps proximal to the GrIS may contaminate the mass change observations around the ice sheet margin

Differences among the three calibrations in terms of their residuals can provide insight into biases in the model ensemble beyond what can be gleaned from any one of the calibrations alone. For example, the highest-weighted ensemble member from the mass change ensemble overestimates acceleration (Fig.

The ad hoc approach used here and elsewhere

We tested several values for the value of the multiplier,

For our study, we used an ensemble of GrIS committed contribution to GMSL, which quantifies the changes that are locked in to the ice sheet, independent of any additional future atmospheric or oceanic forcing. Greenland's commitment results in a contribution to GMSL that is similar in magnitude to the contribution due to future climate anomalies under the Representative Concentration Pathway (RCP2.6) and Shared Socioeconomic Pathway (SSP1-26) scenarios

Our study presents three calibrations using three different observation types (velocity, thickness, and mass change) of the GrIS over an 8-year time period. The choice of observation type leads to important differences in the posterior probability distributions of GrIS committed contribution to GMSL in 2100. It has been proposed that mass change observations should be used to calibrate ice sheet model projections

Using Bayesian calibration to constrain uncertainty in ice sheet ensembles still has many open questions. We have clearly shown how Bayesian calibration can refine uncertainties in ice sheet projections but future work should explore additional choices, such as the method for specifying model structural uncertainty, the time span over which the calibration is done, the use of time series of observations rather than a snapshot of change, and the use of additional metrics derived from these observations. Additionally, future work can move away from the simplifying assumption that we have made that model-calibration residuals are uncorrelated and, instead, quantify the correlation and incorporate that through a covariance matrix into the calibration procedure. Finally, the modeling community should develop robust methods to quantify structural model uncertainty for velocity change, dynamic ice thickness change, and mass change, which could then be used to perform a multivariate calibration using all three observation types simultaneously. Ultimately, the goal is to make use of all of the observation types to get the best possible calibration, although, as we have shown, utilizing different observation types in separate calibrations can yield additional insight into biases in the model ensemble.

Velocity observations from the Making Earth System Data Records for Use in Research Environments (MEaSUREs) project are available at

The supplement related to this article is available online at:

DF and SN conceptualized the study. IN designed the model ensemble and performed the mass change calibration. DF performed the velocity change and thickness change calibrations and carried out the comparison of the results from the three calibrations. BC and AS prepared the thickness change observations. MC and BL prepared the mass change observations. DF prepared the paper with contributions from all co-authors.

The contact author has declared that none of the authors has any competing interests.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.

This research has been supported by the National Aeronautics and Space Administration (grant nos. NN-H19ZDA001N-SLCST, 80NSSC21K1734, NN-H19ZDA001N-GRACEFO, 80NSSC17K0611, and 80NSSC21K0915).

This paper was edited by Johannes J. Fürst and reviewed by two anonymous referees.