Elevation changes of the Antarctic Ice Sheet (AIS) related to surface mass balance and firn processes vary strongly in space and time. Their subdecadal natural variability is large and hampers the detection of long-term climate trends. Firn models or satellite altimetry observations are typically used to investigate such firn thickness changes. However, there is a large spread among firn models. Further, they do not fully explain observed firn thickness changes, especially on smaller spatial scales. Reconciled firn thickness variations will facilitate the detection of long-term trends from satellite altimetry; the resolution of the spatial patterns of such trends; and, hence, their attribution to the underlying mechanisms. This study has two objectives. First, we quantify interannual Antarctic firn thickness variations on a

The global mean sea level rose by

The mass balance of a grounded ice sheet is commonly separated into three components: surface mass balance (SMB), ice discharge, and basal mass balance. SMB comprises total precipitation (snowfall, rainfall), total sublimation (from surface and drifting snow), drifting snow erosion, and meltwater runoff

The mass loss of the AIS is dominated by ice discharge from outlet glaciers of the West Antarctic Ice Sheet (WAIS)

To date, regional climate models (RCMs) have been commonly used to simulate the SMB for the entire ice sheet

Besides modelling tools, satellite measurements provide the only possibility of inferring ice-sheet-wide changes in SMB and firn thickness. Observations from satellite altimetry provide a high spatial resolution of several kilometres and go back to the year 1992 for covering most of the AIS

Using SMB and firn modelling outputs alone to quantify interannual variations in SMB and firn thickness introduces large uncertainties: the intermodel spread is large, and the model outputs also differ from satellite observations

This study focuses on the interannual variations in firn thickness on a regional to local scale. Knowledge of interannual variations is required to isolate long-term trends in ice volume or mass changes. To identify the underlying glaciological processes and separate SMB and firn signals from ice dynamics, the spatial patterns of interannual variations and long-term trends need to be resolved. As the analysis of basin integrals is not sufficient for this purpose, we work at a

We use the altimetry products from

To derive a continuous time series of elevation changes, intermission and intermode calibration offsets must be solved. While

Since we focus on the interannual to decadal timescales, we fit and remove the offset, linear, quadratic, and seasonal signals from the monthly elevation changes for every

We use the firn thickness changes from the firn models IMAU-FDM v1.2A of

The firn model from

Both firn models use the same semi-empirical equation of

We subtract the offset, linear, quadratic, and seasonal signals from the modelled firn thickness changes in the same way as we do for the altimetric time series, except that we assume constant seasonal amplitudes for the entire period. The subtracted parameters are presented in Figs. S1–S4. This leaves us with firn thickness variations on interannual timescales, which we refer to as modelled firn thickness variations,

We jointly analyse the interannual elevation changes from satellite altimetry and firn modelling results. Figure

Workflow of the analysis. Grey boxes are the results, their notation, and the section where they are first presented. White boxes are the main methodological steps to derive these results and the sections where they are explained.

Basin-mean time series of modelled firn thickness variations from

We identify dominant temporal patterns in firn thickness variations by principal component analysis (PCA). PCA, also called empirical orthogonal function (EOF) analysis, is applied to identify dominant modes of variability, represented by pairs of a principal component (PC) and an EOF, which represent the temporal and spatial patterns, respectively

The PCA is performed on the modelled firn thickness variations,

Drainage basins of the EAIS and WAIS used in this study (thick black lines), slightly modified from the definition of

We separately apply the PCA to

For each

We define a combined product by the linear combination of Eq. (

We use different weights for the observations from different time periods. As results from the older altimetry missions generally have a higher noise level

To assess the goodness of fit, we calculate the values of

We derive two different sets of

Names of the four different versions of regression results derived by applying the regression approach of Eq. (

In Appendix

We assess the impact of the choice of data sets and thus the influence of different errors in the adjusted firn thickness variations,

We refer to the differences between adjusted and modelled firn thickness variations as “the adjustments” (

We analyse the time series of altimetric residuals,

The altimetric residuals,

The first PCA is applied to the four versions of standardised residuals (

We can explain at least

PCA results of basin 3: dominant patterns in firn thickness variations identified from standardised firn modelling data (Ma).

Figure

Regression results for the grid point P1 (Fig.

The SD of altimetric residuals,

The scaling factors,

Scaling factors for basin 3.

In general, the spatial patterns of the rms of the adjusted firn thickness variations,

Root mean square (rms) of the times series of

To evaluate the sensitivity of

Histograms of the temporal rms, assessed at each grid cell, of differences between various versions of firn thickness variations. Vertical lines in the box indicate median values. Corresponding rms maps of differences are displayed in Figs. S15–S17.

Overview of the comparison between various versions of firn thickness variations, as detailed in Fig.

The differences between the various versions of

The altimetric residuals are used to calculate the goodness of fit or

After the individual calculation of

Explained variance or

The impact of methodological changes to the regression approach (E1, E2, and E3 as summarised in Sect.

So far, the presented

However, on the level of individual grid cells the altimetric residuals,

We find a stronger autocorrelation for the time series of

The first three dominant modes explain

PCA results of standardised altimetric residuals for the period after 2003.

PCA results of standardised altimetric residual differences for the period after 2003.

In general, adjusted firn thickness variations,

The adjusted firn thickness variations,

In the following, we compare how much variance of altimetric variations (for the period after 2003) can be explained according to the applied approach and the two different spatial considerations used previously, namely, first, the percentages assessed from grid cell time series and then averaged over the entire area, and second, the percentages from time series averaged over the entire area (“mean Antarctic” time series, Fig.

Mean Antarctic interannual elevation changes depending on the applied approach. Modelled firn thickness variations (

Our regression approach (Eq.

The adjusted firn thickness variations,

To assess the combined influence of firn model and altimetry errors on

We assess the robustness of

Histograms of the temporal rms of differences between various versions of firn thickness variations assessed at each grid cell of basin 3.

Firn model errors arise from firn signals that are not simulated or not correctly represented by the firn model or its input from RCMs and reanalysis data. They are partly reflected in the differences of

The spatial patterns of absolute differences within

The modelled SMB components and their uncertainties have a direct impact on the modelled firn thickness. By assessing the spread of an ensemble of modelled firn thickness changes,

In a relative sense, the adjustments (e.g. Fig.

In basin 4, towards the boundary with basins 1 and 3, the large relative adjustments (Fig. S17e–h) indicate disagreement between the models and altimetry, whereas the four versions of altimetry agree (Fig. S15i–l) and the two models agree (Fig. S16d). The reasons for this are not yet clear. Basin 8 is characterised by large megadune fields

Discrepancies within the adjustments (i.e. within versions of

The differences between any version of

A further limitation in radar altimetry is that measurements refer to the local topographic maxima within their footprints. Especially at the margins over complex topography, this can lead to sampling issues, as the elevation changes acquired there cannot capture the larger changes often found in the valleys. Laser altimeters are not affected by this sampling issue. However, since ICESat operated in the campaign mode

Discrepancies within the adjustments (i.e. within versions of

Uncertainties due to a different analysis of the altimetry measurements are reflected by the differences in

The differences between

The following features may likely be quite clearly attributed to a difference in intermission and intermode calibration between the two altimetry products. The mode change of CryoSat-2 (see e.g. Fig. 5 in

In regions of a low signal-to-noise ratio the regression approach has a limited capability to distinguish between signal and error. This applies in particular to the interior of the EAIS (basin 8 and parts of basins 1 and 4). In these areas, the regression of the altimetry data to

We included altimetry measurements only over the period May 1992 to December 2017 as this represents the common period of both altimetry products (Sect.

The stochastic model in the regression approach does not include temporal error covariances in altimetry (Sect.

We do not aim here to compare our results with in situ data, as the ground-based SMB observations are mostly single-point measurements and have a very sparse spatial and temporal coverage

To improve firn model outputs, it is important to refine the horizontal spatial resolution of RCMs and to simulate surface processes at a higher spatial resolution

To improve altimetry products, noise in the altimetry measurements and correlated altimetry errors related in particular to time-variable radar signal penetration and scattering effects need to be reduced.

Future developments in firn modelling, satellite altimetry analysis, and altimetry mission sensors will allow for identifying interannual firn signals and, thereby, better isolating and quantifying long-term trends. This will improve long-term estimates and reduce their uncertainties

We developed a new approach that combines satellite altimetry and firn modelling results to resolve Antarctic firn thickness variations at a high temporal and spatial resolution, namely by monthly

Our guiding question was as follows: how well can satellite altimetry and firn models resolve Antarctic firn thickness variations? Well, it depends. This study shows that firn models and altimetry products provide complementary information on firn thickness variations. The combined data set,

How well

We identified regions of discrepancy between the firn models and the altimetry products and within the models or altimetry and discussed the underlying errors in both the models and the altimetry. These results shall help modellers and altimetry data processors to improve their simulations and processing methods (Sect.

Differences between the

To investigate the impact of methodological changes on determining adjusted firn thickness variations,

In the first experiment, E1, we simply subtract the modelled firn thickness variations,

We consider the regression method whose

The impact of methodological choices on the goodness of fit is tested based on the three experiments, E1–E3 (Sect.

Explained variance or

For every grid cell, Fig.

The simple scaling factor,

The altimetry products from

The supplement related to this article is available online at:

MTK: conceptualisation, data curation, formal analysis, investigation, methodology, software, visualisation, writing (original draft). MH: conceptualisation, funding acquisition, methodology, supervision, writing (review and editing). EB: formal analysis, writing (review and editing). MOW: data curation, writing (review and editing). LS: funding acquisition, writing (review and editing). SBMV, PKM, MRvdB: resources (provision of the firn model data), writing (review and editing).

At least one of the (co-)authors is a member of the editorial board of

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.

We thank the editor Louise Sandberg Sørensen, the referee Peter L. Langen, and an anonymous referee for their detailed and constructive reviews, which helped to improve and shorten the paper. Maria T. Kappelsberger and Eric Buchta were funded by the Deutsche Forschungsgemeinschaft (DFG) as part of Special Priority Programme (SPP) 1158 Antarctic Research with Comparative Investigations in Arctic Ice Areas (grant no. HO 4232/10-1, project no. 442929109; grant nos. SCHE 1426/26-1 and 1426/26-2, project no. 404719077). Matthias O. Willen was funded by the DFG as part of SPP 1889 Regional Sea Level Change and Society (SeaLevel) (grant no. HO 4232/4-2, project no. 313917204). Sanne B. M. Veldhuijsen acknowledges funding by the Netherlands Organisation for Scientific Research (NWO) (grant no. OCENW.GROOT.2019.091).

This research has been supported by the Deutsche Forschungsgemeinschaft (grant no. HO 4232/10-1, project no. 442929109; grant nos. SCHE 1426/26-1 and SCHE 1426/26-2, project no. 404719077; grant no. HO 4232/4-2, project no. 313917204) and the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (grant no. OCENW.GROOT.2019.091).This open access publication was financed by the Saxon State and University Library Dresden (SLUB Dresden).

This paper was edited by Louise Sandberg Sørensen and reviewed by Peter L. Langen and one anonymous referee.