Overview

Radar altimeters measure ice-sheet surface height along the satellite ground track. On this portal those measurements are converted into three families of product on a common polar-stereographic grid:

Processing chain

1. Input data

1.1 Altimetry Level-2 products

The primary input is Ku-band radar altimetry from a series of overlapping ESA missions, spanning the early 1990s to the present day.

Full instrument parameters and source-dataset details for each mission:

1.2 Auxiliary data

2. Elevation change

Surface elevation change is derived with the CPOM land-ice surface-fit (plane-fit) method.

2.1 Single-mission processing

Gridding

Along-track L2 elevations, and associated parameters such as backscatter, are binned into a regular grid archive organised by mission cycle.

Surface fit

In each grid cell a recursive least-squares plane fit separates spatial slope and anisotropy from temporal change. A backscatter (power) correction reduces radar penetration and surface-condition artefacts. The residual time series is the height change (dH) at that cell.

Surface model function:

• h = heading (ascending = 1, descending = 0)
• t = time in years since the reference time 1 January 2000
• x, y = cartesian coordinates from the centre of the grid cell, in m

The surface components of the modelled elevation are removed from the measured elevation, leaving the temporal change plus residuals:

For the backscatter correction, a model of the power is fitted as a function of time and heading:

The gradient m of dz/dp is calculated over a limited time interval (for example 60 months), and the component of elevation change due to changes in backscatter power is removed:

Finally, dH/dt is calculated recursively from the gradient b of a linear fit of dz with time:

Epoch averaging and GIA

Irregular dH samples are averaged into fixed epochs, typically 140 days. A glacial isostatic adjustment (GIA) correction from the IJ05 R2 model (Ivins et al., 2013) is applied so that the reported dH reflects ice-sheet surface change rather than solid-Earth motion. The output is one epoch-averaged dH time series per mission on the common grid.

2.2 Gap fill

Before missions are merged, remaining temporal and coverage gaps in the single-mission (or pre-merge) dH records are filled by triangulation (Shepherd et al., 2019), so that the time series used for cross-calibration are as complete as possible. Observed values are preserved where data exist; filled cells carry additional uncertainty.

2.3 Multi-mission cross-calibration

Single-mission epoch averages are combined into one continuous record. In each grid cell a multiple regression on time and mission terms estimates and removes inter-mission biases. Missions need not overlap, as gaps can be bridged by the temporal model. The result is a cross-calibrated multi-mission dH stack with an associated cross-calibration uncertainty.

2.4 Pole-hole fill

Altimetry coverage is incomplete near the South Pole, in mission-dependent “pole holes”. After cross-calibration these polar gaps are filled by extrapolating from surrounding observed rates and heights, by region and ice/snow regime, following Shepherd et al. (2019), so that ice-sheet-wide integrals are spatially complete.

2.5 Elevation rates

Linear dH/dt maps are computed from the filled elevation time series over fixed or sliding windows for selected periods.

import numpy as np
from scipy.optimize import curve_fit

def linear(t, a, b):
    return a * t + b

# time: 1D decimal-year array
# dh_stack: 3D array with shape [time, y, x]
start_year = 2010.0
end_year = 2020.0
interval_mask = (time >= start_year) & (time < end_year)

dh_dt = np.full(dh_stack.shape[1:], np.nan)

for i in range(dh_stack.shape[1]):
    for j in range(dh_stack.shape[2]):
        series = dh_stack[:, i, j]
        valid = interval_mask & np.isfinite(series)
        if np.sum(valid) < 6:
            continue
        popt, _ = curve_fit(linear, time[valid], series[valid])
        dh_dt[i, j] = popt[0]  # slope in m/yr

3. Density assignment

A time-varying density mask (Shepherd et al., 2019) assigns to each grid cell and epoch either:

• Ice density (917 kg m⁻³) where elevation change is dominated by ice dynamics, or
• Surface snow / firn density elsewhere,

so that volume change is converted to mass with an appropriate density.

The working product for mass conversion is a filled, cross-calibrated dH stack on the 5 km grid, typically starting from the mid-1990s for published series.

4. Mass change

4.1 Height to mass

Per grid cell and epoch, mass change is computed as:

where ρ is the density mask value and A is the cell area (5 km × 5 km). Results are aggregated from kilograms to gigatonnes (Gt) for ice-sheet and basin products.

4.2 Spatial aggregation

Time series are formed for:

• Individual drainage basins (Rignot / IMBIE-style numbering; Rignot et al., 2016)
• IMBIE regions: AIS, WAIS, EAIS and APIS
• The full grounded ice sheet

Basin and region height series use spatial means of dH; mass series use spatial sums of dM (or the equivalent).

4.3 Rates

dH/dt and dM/dt are estimated per grid cell by a linear fit to the filled time series over a chosen interval, optionally after light temporal smoothing. The slope uncertainty combines the fit covariance with propagated measurement uncertainty. Regional rates follow from the same trends aggregated over basins or IMBIE regions.

5. Uncertainty

Height and mass uncertainties are built from several independent contributions combined in quadrature. Typical components are:

For mass, the density uncertainty is also propagated. Time series shown on the portal display a cumulative uncertainty that grows with record length in a controlled way, as accumulated epoch errors scaled by elapsed time.

6. Products for the data portal

Notes for portal users

• Coverage and uncertainty vary in space and time: early missions, steep coastal terrain and polar gaps are less well constrained.
• GIA (IJ05 R2) is removed from the elevation record used for mass conversion, so that reported mass change is attributable to the ice sheet and not to solid-Earth rebound.
• Published time series in this configuration commonly start after ~1995 and report change relative to the first retained epoch.

References

1. Ivins, E. R., James, T. S., Wahr, J., Schrama, O., Ernst, J., Landerer, F. W., and Simon, K. M. (2013). Antarctic contribution to sea level rise observed by GRACE with improved GIA correction. Journal of Geophysical Research: Solid Earth, 118(6), 3126–3141.
2. Rignot, E., Mouginot, J., and collaborators (2016). Antarctic drainage basin and ice-sheet definitions used within IMBIE.
3. Shepherd, A., Gilbert, L., Muir, A. S., Konrad, H., McMillan, M., Slater, T., Briggs, K. H., Sundal, A. V., Hogg, A. E., and Engdahl, M. E. (2019). Trends in Antarctic Ice Sheet elevation and mass. Geophysical Research Letters, 46, 8174–8183.
4. van Dalum, C. T., van de Berg, W. J., van den Broeke, M. R., and van Tiggelen, M. (2025). The surface mass balance and near-surface climate of the Antarctic ice sheet in RACMO2.4p1. The Cryosphere, 19, 4061–4090.