Overview

The Mass Balance Module estimates the mass balance of the Greenland Ice Sheet (a future update will include Antarctica) from Earth Observation (EO) data. It is one of the ice-sheet process modules of the ESA Digital Twin Component for Ice Sheets (DTC Ice Sheets, DTC-IS), developed under the ESA Digital Twin Earth (DTE) programme.

The module converts satellite radar-altimetry surface elevation change, together with other EO-derived features such as ice velocity and land surface temperature, into gridded mass balance estimates in gigatonnes per year (Gt yr^-1). In a wider DTC-IS context, this module feeds the Use Case 2: EU Sea-Level Response Fingerprint. There, its output drives the Sea-Level Response EMulator (SELREM), which converts ice-sheet mass change into global and regional sea-level fingerprints, with a focus on European coastlines.

The module also supports what-if scenarios: users can perturb the input forcings (for example scaling ice velocity or applying a temperature offset) and see how the predicted mass balance, and in turn the sea-level response, changes.

Scientific background

The module follows the calibrated radar-altimetry method of Simonsen et al. (2021), which produced a Greenland Ice Sheet mass balance record for 1992–2020. Combining several EO datasets with machine learning makes this a hybrid mass balance estimate.

Surface elevation change from radar altimetry. The module builds on the long record of Ku-band radar altimetry over the Greenland Ice Sheet. This record was first developed in the ESA Climate Change Initiative (CCI) and is now produced operationally by the Copernicus Climate Change Service (C3S). The standard C3S product gives monthly surface elevation change (SEC) on a 25 km grid, from ERS-1, ERS-2, ENVISAT, CryoSat-2 and Sentinel-3A/B (Sørensen et al., 2018). For DTC-IS, DTU runs a modified version of the C3S processing that shortens the CryoSat-2 and Sentinel-3 data window from 3 to 2 years and refines the grid from 25 km to 5 km. This higher-resolution SEC record is hosted on the DTC-IS EO data store and updated as new data become available.

From volume change to mass change. Radar altimetry measures changes in surface height, that is volume change. To convert it to mass change you need to know how firn compaction, radar penetration and changes in acquisition mode affect the measured signal. Following Simonsen et al. (2021), the method learns time-varying calibration fields that convert radar-derived elevation change into ice-equivalent (mass) elevation change. The original model was trained to reproduce the ICESat-derived mass balance (Sørensen et al., 2011) from a set of a priori features. Ten candidate features were tested in 768 combinations. The preferred model was chosen for its agreement with independent IMBIE and GRACE mass balance, its consistency with the static ICESat (2003–2009) calibration field, and the glaciological plausibility of its spatial patterns in the 1990s.

Machine-learning model. The method was originally built on an AdaBoost decision-tree ensemble. The operational implementation in this package uses a pre-trained XGBoost (gradient-boosted decision tree) model. The model is downloaded at run time and its SHA-256 checksum is checked before it is loaded. It predicts the rate of ice-equivalent elevation change (m ice eq. yr^-1) for each grid cell from:

• the observed annual radar elevation change (RAdh),

• radar-altimetry acquisition features from the C3S radar-altimetry product: the acquisition mode (RAmode, LRM vs. SARIn, with CryoSat-2 SARIn starting over Greenland in October 2010) and the distance from the nearest satellite observation to the grid point (RAdist),

• ice surface velocity (iv),

• land surface temperature (LST),

• location (grid X/Y in EPSG:3413, NSIDC Polar Stereographic North).

The prediction provides mass balance in Gt yr^-1. Only the pre-trained model runs inside the digital twin. All input features are retrieved from the DTC-IS EO data store through the Data Download Module (DDM) for the time period the user selects.

Module workflow

The package exposes five command-line entry points that are chained together in the DTC-IS workflow. See Quick Start for example commands and API Reference for the full API.

Entry point	Purpose
mass_balance_enhance_elevation_data_entrypoint	Converts a cumulative, irregularly sampled elevation-change cube into annual (calendar-year) elevation change and rescales windows that are not exactly one year long. The radar-altimetry features (RAdh, RAdist, RAmode) in the feature dataset are then replaced with these updated annual values.
mass_balance_enhance_temperature_data_entrypoint	Replaces the land surface temperature feature with a new temperature dataset (for example the C3S land surface temperature, or projections from the ECMWF Climate Change Adaptation Digital Twin), aggregated to annual means and interpolated onto the model grid.
mass_balance_prediction_entrypoint	Applies the user-defined what-if perturbations, runs the XGBoost model and derives gridded mass balance (Gt yr-1). The grid can optionally be downsampled first.
mass_balance_postprocessing_entrypoint	Compares a predicted mass balance run with a control run and writes totals, grid metadata, input features and the prediction to JSON for the DTC-IS dashboard.
mass_balance_from_thickness_entrypoint	Converts modelled ice thickness, for example ISMIP6 ice-sheet model projections, into gridded mass balance. By default it also reshapes the result into the point time series expected by SELREM, so modelled future mass change can be used alongside the EO-based estimate.

A typical observation-driven run is:

1. Retrieve the feature dataset (GeoZarr) and, optionally, updated elevation change and temperature data through the DDM.

2. Enhance the feature dataset with the updated elevation and/or temperature data.

3. Predict the mass balance, once as a control (no perturbation) and once with the user’s what-if settings.

4. Post-process the results for display, and/or pass the mass balance to SELREM to compute the sea-level response.

Inputs and outputs

The table below outlines the input/output schema of the DTC-IS system design (DTSD) and has been updated to match the current implementation.

I/O	Name	Description	Format
Input	Surface elevation change	Radar-altimetry surface elevation change (C3S-based, 5 km), with the related radar features RAdh, RAmode and RAdist, retrieved from the EO data store through the DDM and subset in time to the user’s selection.	Zarr data cube
Input	Ice velocity	SAR-derived ice surface velocity (iv), retrieved through the DDM.	Zarr data cube
Input	Land surface temperature	EO-derived ice surface temperature (LST), retrieved through the DDM. It can be replaced with other temperature data (for example climate projections) in the temperature enhancement step.	Zarr data cube
Input	Scenario parameters	Multipliers/offsets that perturb the forcings (see What-if scenarios).	Floating-point numbers
Input	Ice thickness (optional)	Modelled ice thickness and, optionally, grounded ice fraction (e.g. ISMIP6), identified by CF standard_name/long_name (land_ice_thickness, grounded_ice_sheet_area_fraction). Used only by the thickness-to-mass-balance entry point.	Zarr data cube
Output	Mass balance	Gridded mass balance (mass_balance, Gt yr-1) together with the predicted ice-equivalent elevation change (prediction, m ice eq. yr-1) on the EPSG:3413 grid, per year.	Zarr data cube
Output	Mass balance from thickness	Gridded mass balance (kg cell-1 yr-1), or by default a point time series ready for SELREM.	GeoZarr
Output	Dashboard summary	Total predicted and control mass balance, grid extent and resolution, years, CRS, input features and the predicted field.	JSON

What-if scenarios

DTC-IS lets users explore how the ice sheet would respond to changed forcing, not just reproduce observations. The prediction entry point applies the following perturbations to the input features before the model runs:

Option	Default	Effect
--ice_velocity_factor	1.0	Multiplies the ice velocity feature (iv).
--land_surface_temperature_offset	0.0	Adds an offset to the land surface temperature feature (LST).
--radar_elevation_factor	1.0	Multiplies the observed radar elevation change feature (RAdh).

The temperature enhancement step also lets you replace observed surface temperature with projected temperature fields. The C3S land surface temperature record and runs driven by the ECMWF Climate Change Adaptation Digital Twin have been used this way to make short-term mass balance forecasts. Running the post-processing step on a control run and a perturbed run gives the change in total mass balance caused by the scenario. Passing the result to SELREM shows how that change affects regional sea level.

Validation and uncertainty

The module has been validated for the Greenland Ice Sheet. The radar-altimetry volume mass balance (radar-VMB) estimate was compared with the following independent datasets:

• satellite gravimetry from GRACE/GRACE-FO (Barletta et al., 2020),

• input–output (mass budget) estimates by Mouginot et al. (2019), Colgan et al. (2019) and Mankoff et al. (2021), and

• the IMBIE reconciled assessment (Otosaka et al., 2023).

Over the 28-year record (1992–2020), the radar-VMB reproduces both the long-term trend and the interannual variability of Greenland mass balance within the uncertainties of these independent estimates. It is strongly correlated with the GRACE mass balance in both timing and size of the fluctuations. Compared year by year with the mass budget record of Mankoff et al. (2021), the root-mean-square error (RMSE) is 86 Gt yr^-1.

The largest discrepancies occur in years of unusually low mass loss (1992, 1995–1998 and 2019), when the model underestimates how much mass the ice sheet retained. This is a known limitation of decision-tree ensembles. They do not capture extreme or non-linear events at the edge of the training data well, such as the cooling after the 1991 Pinatubo eruption. The model can also misinterpret climate extremes, so its results for such years should be interpreted with care.

The independent validation datasets do not always agree with each other within their stated uncertainties (2014, for example). The module therefore reports RMSE against reference datasets as a quantitative measure of performance. Because the model is fast, many feature-perturbation experiments (more than 1000) can be run alongside the mass balance calculation and used to propagate errors from start to finish through the mass balance and SELREM chain. The Antarctic Ice Sheet will be validated against an Antarctic mass balance assessment once the Antarctic model is released.

Limitations and ongoing development

• Spatial coverage. The module currently covers the Greenland Ice Sheet only, on the EPSG:3413 grid. The method can be transferred to Antarctica using the Antarctic C3S elevation-change and ice-velocity products. This extension is ongoing and is considered incremental research with low risk.

• Extreme years. Like other decision-tree ensembles, the model cannot extrapolate far outside the conditions it was trained on (see Validation and uncertainty). Results for anomalous years and for strongly perturbed what-if scenarios should be read with this in mind.

• Future projections. Future mass change from ice-sheet model projections (ISMIP6; Nowicki et al., 2016) can be brought into the same framework through the thickness-to-mass-balance entry point. R&D continues on how best to combine these projections with the EO-driven estimate, so that user-defined what-if scenarios stay within the range of modelled futures.

• Towards hybrid, explainable models. A purely data-driven model offers limited insight into physical processes. In the future, the module could possibly move towards hybrid, explainable models that combine EO data with physical constraints on ice and snow processes. Approaches of interest include symbolic regression (e.g. Qlattice; Wilstrup and Kasak, 2021) and physics-informed neural networks such as PINNICLE (Cheng et al., 2024).

Related DTC-IS components

• Sea-Level Response EMulator (SELREM), in the sea_level_response package: turns mass balance from this module (or from user-supplied or ISMIP6 datasets) into global and local sea-level fingerprints with uncertainties.

• Data Download Module (DDM): retrieves the EO input features from the DTC-IS EO data store and other sources.

• DTC-IS Query API and dashboards: run the module as part of the Use Case 2 workflow. Users can choose a time range and what-if parameters in the interactive dashboard or the accompanying Jupyter Notebook, and export intermediate mass balance datasets.

How to cite

If you use mass balance estimates produced by this module, please cite the underlying method:

Simonsen, S. B., Barletta, V. R., Colgan, W. T., & Sørensen, L. S. (2021). Greenland Ice Sheet mass balance (1992–2020) from calibrated radar altimetry. Geophysical Research Letters, 48, e2020GL091216. https://doi.org/10.1029/2020GL091216

and mention that the estimates were produced with the DTC Ice Sheets Mass Balance Module [date].

Source documents

The scientific description on this page is based on the following DTC Ice Sheets project deliverables (approved 1 May 2026):

• DTU-ESA-DTC-IceSheet-RnDRdv3.00: Research and Development Report, Draft Version 3, §2.1.1 Ice Sheet Mass Balance Module.

• DTU-ESA-DTC-IceSheet-DTSDdv3.00: Design and Technical Specifications Document, Draft Version 3, Ice sheet mass balance module and Use Case 2 workflow.

• DTU-ESA-DTC-IceSheet-VRdv2.00: Validation Report, Draft Version 2, §5.1 Ice Sheet Mass Balance and SELREM.

• DTU-ESA-DTC-IceSheet-RBDdv3.00: Requirement Baseline Document, Draft Version 3, Use Case 2 requirements.

• DTU-ESA-DTC-IceSheet-PR06v1.00: Progress Report 6.

References

• Barletta, V. R., Sørensen, L. S., Simonsen, S. B., & Forsberg, R. (2020). Gravitational mass balance of Greenland 2003 to present v3.0. Technical University of Denmark. Dataset. https://doi.org/10.11583/DTU.12866579.v5

• Cheng, G., Morlighem, M., & Francis, S. (2024). Forward and inverse modeling of ice sheet flow using physics-informed neural networks: Application to Helheim Glacier, Greenland. JGR: Machine Learning and Computation, 1, e2024JH000169. https://doi.org/10.1029/2024JH000169

• Colgan, W., Mankoff, K. D., Kjeldsen, K. K., et al. (2019). Greenland ice sheet mass balance assessed by PROMICE (1995–2015). GEUS Bulletin, 43. https://doi.org/10.34194/GEUSB-201943-02-01

• Mankoff, K. D., Fettweis, X., Langen, P. L., et al. (2021). Greenland ice sheet mass balance from 1840 through next week. Earth System Science Data, 13, 5001–5025. https://doi.org/10.5194/essd-13-5001-2021

• Mouginot, J., Rignot, E., Bjørk, A. A., et al. (2019). Forty-six years of Greenland Ice Sheet mass balance from 1972 to 2018. PNAS, 116(19), 9239–9244. https://doi.org/10.1073/pnas.1904242116

• Nowicki, S. M. J., Payne, A., Larour, E., et al. (2016). Ice Sheet Model Intercomparison Project (ISMIP6) contribution to CMIP6. Geoscientific Model Development, 9, 4521–4545. https://doi.org/10.5194/gmd-9-4521-2016

• Otosaka, I. N., Shepherd, A., Ivins, E. R., et al. (2023). Mass balance of the Greenland and Antarctic ice sheets from 1992 to 2020. Earth System Science Data, 15, 1597–1616. https://doi.org/10.5194/essd-15-1597-2023

• Simonsen, S. B., Barletta, V. R., Colgan, W. T., & Sørensen, L. S. (2021). Greenland Ice Sheet mass balance (1992–2020) from calibrated radar altimetry. Geophysical Research Letters, 48, e2020GL091216. https://doi.org/10.1029/2020GL091216

• Sørensen, L. S., Simonsen, S. B., Nielsen, K., et al. (2011). Mass balance of the Greenland ice sheet (2003–2008) from ICESat data – the impact of interpolation, sampling and firn density. The Cryosphere, 5, 173–186. https://doi.org/10.5194/tc-5-173-2011

• Sørensen, L. S., Simonsen, S. B., Forsberg, R., et al. (2018). 25 years of elevation changes of the Greenland Ice Sheet from ERS, Envisat, and CryoSat-2 radar altimetry. Earth and Planetary Science Letters, 495, 234–241. https://doi.org/10.1016/j.epsl.2018.05.015

• Wilstrup, C., & Kasak, J. (2021). Symbolic regression outperforms other models for small data sets. arXiv:2103.15147. https://arxiv.org/abs/2103.15147