A fine-scale digital elevation model of Antarctica derived from ICESat-2

Antarctic digital elevation models (DEMs) are essential for human fieldwork, ice topography monitoring and ice mass change estimation. In the past thirty decades, several Antarctic DEMs derived from satellite data have been published. 10 However, these DEMs either have coarse spatial resolutions or vague time stamps, which limit their further scientific applications. In this study, the new-generation satellite laser altimeter Ice, Cloud, And Land Elevation Satellite-2 (ICESat-2) is used to generate a fine-scale and specific time-stamped Antarctic DEM for both the ice sheet and ice shelves. Approximately 4.69 × 109 ICESat-2 measurement points from November 2018 to November 2019 are used to estimate surface elevations at resolutions of 250 m, 500 m and 1 km based on a spatiotemporal fitting method, which results in a 15 modal resolution of 250 m for this DEM. Approximately 74% of Antarctica is observed, and the remaining observation gaps are interpolated using the ordinary kriging method. National Aeronautics and Space Administration Operation IceBridge (OIB) airborne data are used to evaluate the generated Antarctic DEM (hereafter called the ICESat-2 DEM) in individual Antarctic regions and surface types. Overall, a median bias of 0.11 m and a root-mean-square deviation of 8.27 m result from approximately 1.4 × 105 spatiotemporally matched grid cells. The accuracy and uncertainty of the ICESat-2 DEM vary in 20 relation to the surface slope and roughness, and more reliable estimates are found in the flat ice sheet interior. The ICESat-2 DEM is superior to previous DEMs derived from satellite altimeters for both spatial resolution and elevation accuracy and comparable to those derived from stereo-photogrammetry and interferometry. The decimeter-scale accuracy and specific time stamp make the ICESat-2 DEM an essential addition to the existing Antarctic DEM groups, and it can be further used for other scientific applications. 25

All these DEMs provide reasonable elevation estimates for Antarctica; however, some flaws still cannot be totally avoided.
The coverage of the ICESat DEM is limited in ice sheet margins due to its coarse across-track resolution (usually larger than 250 m). Although the ICESat/ERS-1 DEM improves the coverage by combining the measurements from ICESat and ERS-1 45 elevations, the specific time stamp of the DEM is still missing due to the different timespans (1994( -1995( for ERS-1 and 2003( -2008 for ICESat) of these two satellite altimeter datasets. This issue also exists with the REMA DEM and TanDEM-X PolarDEM, where multiyear satellite imageries were used. Different from the abovementioned DEMs, the Slater CryoSat-2 DEM was derived based on a model fitting method by using seven-year CryoSat-2 data (from July 2010 to July 2016). This method can quantify the measured elevation fluctuations due to seasonal variations, and the time stamp is definitive. 50 However, the penetration depth of the CryoSat-2 Ku-band into Antarctic dry snowpack is still unknown, which includes some uncertainties in the elevation estimation. A similar problem also exists with the Helm CryoSat-2 DEM and TanDEM-X PolarDEM (the penetration depth of the X-band into snow may be several meters, Fischer et al., 2020;Dehecq et al., 2016).
A fine-scale Antarctic DEM with a definitive time stamp is still lacking.
The new-generation satellite laser altimeter Ice, Cloud, And Land Elevation Satellite-2 (ICESat-2) of the National 55 Aeronautics and Space Administration (NASA), which was launched on 15 September 2018, provides near-global (up to 88°S) and dense land ice elevation measurements in an accurate repeated cycle of 91 days by using a multibeam (six beams in three pairs that work at 532 nm) laser altimeter (i.e., Advanced Topographic Laser Altimeter System, ATLAS, Neumann et al., 2019). The narrow footprint (approximately 17 m with a spatial interval of 0.7 m) and three pairs of beams (two beams in one pair can determine the local slope) enable a fine-scale measurement of Antarctic surface heights even in steep regions. 60 Hence, ICESat-2 can be expected to provide a new and specific time-stamped Antarctic DEM on a fine scale. Here, we use a one-year time series (from November 2018 to November 2019) of ICESat-2 elevation measurements to generate a new Antarctic DEM that covers both the ice sheet and ice shelves (hereafter called the ICESat-2 DEM). The applied data, DEM generation method and quality control criteria are presented in Section 2. Furthermore, we present the map of the ICESat-2 DEM and construct an accuracy evaluation by comparing it to the spatiotemporally matched elevation 65 measurements from the NASA Operation IceBridge (OIB) airborne mission in Section 3. The performances of the ICESat-2 DEM and six currently available Antarctic DEMs are compared in Section 4, and Section 5 concludes this study.

ICESat-2 data
The ICESat-2 ATL06 land ice elevation product  from November 2018 to November 2019 is used. This 70 product provides land ice elevation measurements at a spatial resolution of 20 m after correcting instrument-specific biases (i.e., corrections for transmit-pulse shape and first-photon bias, Neumann et al. 2019); here, only ATL06 data with good quality (those for which atl06_quality_summary equals zero) are used to generate the DEM. For the data collected over Antarctic ice shelves, corrections for ocean tide and inverse barometer effects are also applied (Padman et al., 2002;Erofeeva, 2002, Egbert et al., 1994). Elevation measurements from all six beams are used to produce the densest surface 75 height coverage. Although the signal energies of strong and weak beams are different, all six beams provide centimeter-scale elevation measurements, and the biases of two beams in one pair are less than 2 cm (Brunt et al., 2019) and 5 cm (Shen et al., 2021) for flat and steep surfaces. Thus, the effect of elevations estimated from weak beams can be negligible.

NASA OIB airborne data
Elevation measurements from the OIB airborne mission in Antarctica are used here to evaluate the accuracy of the ICESat-2 80 DEM on a continental scale, including in the stable ice sheet interior and active marginal ice shelves. Surface heights from OIB airborne missions are measured by the Airborne Topographic Mapper (ATM), a conically scanning laser altimeter (at 532 nm) with a swath width of 140 m and footprint size of 1 to 3 m. The elevation measurement accuracy of ATM is approximately 10 cm or better (Kurtz et al. 2013). Here, the IceBridge ATM L2 Icessn elevation, slope and roughness (V002) product (Studinger et al., 2014) is used, and a data filter is applied to remove abnormal values due to geolocation errors or 85 cloud cover. The local terrain parameters, i.e., slope and roughness, are calculated following Shen et al. (2021). To reduce the effect of seasonal elevation changes on DEM evaluation, the time difference between applied OIB airborne data and ICESat-2 DEM should be less than one year. Thus, OIB airborne data in October and November 2018 and October and
Detailed information concerning these DEMs is provided in

Surface elevation and uncertainty estimation
To generate a definite time-stamped DEM and reduce the effect of seasonal elevation changes, following Slater et al. (2018), a model fitting method is applied. The elevation is estimated using a quadratic function based on the local surface terrain and a time term (Eq. 1). This function is fitted in each grid (the resolutions are listed in the following subsection) by using an iterative least-squares fit to all the elevation measurements. By considering the surface elevation fluctuations and seasonal 120 changes, this method tends to obtain more accurate elevation estimates (McMillan et al., 2014;Flament et al., 2012). Where E is the surface elevations derived from ICESat-2 measurement points, x and y are the local surface terrain respectively, t is the time term, and E is the DEM value in May 2019.
To reduce the effect of any poor fit, a quality control criterion listed in Table 2 is performed, which includes the number of 125 ICESat-2 measurement points used, the time span of the data used, the root-mean-square deviation (RMSD) of the residuals of fitted elevations, the elevation rate of change and its uncertainty. These criteria are constructed for all grid cells, and thus, there are some elevation gasps in the initial DEM. The remaining gaps are filled by using ordinary kriging interpolation, which is widely used for generating previous DEMs (Helm et al., 2014;Slater et al., 2018). During the interpolation process, a search radius of 10 km is applied to obtain neighboring measurement points. This elevation estimation model has been 130 evaluated by previous studies (Slater et al., 2018;Konrad et al., 2017;McMillan et al, 2014;Moholdt et al., 2010;Smith et al., 2009), and the evaluation in Section 3.2 also demonstrates its validity. Table 2. Quality control criteria applied to remove the unrealistic elevations due to the poor fitting performances in each grid cell. 135 Parameters Rules The number of ICESat-2 measurement points ≤ 10 The time span ≤ 2 months RMSD of the residuals of fitted elevations ≥ 10 m Elevation change rate ≥ 10 m/yr The uncertainty of elevation change rate ≥ 10 m/yr The performance of this surface fit method is also affected by the spatial distribution and number of ICESat-2 measurement points. After quality control, 4.69 × 10 9 ICESat-2 measurement points from November 2018 to November 2019 that cover all of Antarctica are used. An adequate number of ICESat-2 measurement points in one grid cell is required to generate valid elevation estimates. Fig. 2 shows the distribution of the numbers of ICESat-2 measurement points used in 140 individual grid cells (at a resolution of 1 km), which indicates a latitude-dependent pattern. Each grid cell contains approximately 418 ± 310 ICESat-2 measurement points. In the ice sheet interior, the large coverage of ICESat-2 measurement points provides a complete surface height observation. In the low-latitude region, the numbers of ICESat-2 measurement points are relatively small, the proportion of observed grid cells is reduced, and the representativeness is also

150
DEM uncertainties are calculated for observed and interpolated grid cells, respectively. The observed grid cell uncertainty is calculated based on the fitting performance, which is provided as the 95% confidence level for elevation estimation. For the interpolated grid cells, uncertainty is calculated from the kriging variance error. In the ICESat-2 DEM uncertainty calculation, the uncertainty from ICESat-2 measurements is not considered because the effect of ICESat-2 measurement bias is limited (< 5 cm, Brunt et al., 2019;< 14 cm, Shen et al., 2021) and no systemic error was found (Shen et al., 2021). 155

Choice of DEM resolution
The selection criterion of DEM resolution is to present the detailed pattern of elevations and ensure enough spatial coverage of observed elevations (a smaller resolution tends to cause more observed elevation gaps). Although a much finer scale (e.g., 250 m) can reveal a more detailed elevation pattern, this contributes to more gaps among observed elevations. To acquire the optimal compromise between the spatial resolution and spatial coverage of observed elevations, we calculate the variations 160 in the spatial coverages of observed grid cells at different latitudes at variable spatial resolutions (250 m, 500 m and 1 km, which are usually applied in the Antarctic DEM, Fig. 3a). The overall spatial coverages of observed elevations when applying 250 m, 500 m and 1 km resolutions are 26%, 46% and 72%, respectively, and high-latitude areas always have The application of three resolutions may include additional effects, i.e., different grid cell resolutions tend to present different elevation estimates. Here, we compare the elevation difference at the regional scale at different spatial resolutions.
The elevation values become lower when a larger spatial resolution is applied, which acts as a 'running mean' (Fig. 3b).
Although applying different spatial resolutions affects the elevation values, this method can increase the coverage of 175 observed elevations, and observed elevations tend to be more reliable than interpolated elevations (as shown in Section 3.2).

DEM evaluation method
Spatiotemporally matched elevation measurements from the OIB airborne mission and ICESat-2 DEM are used to evaluate the ICESat-2 DEM, and one ICESat-2 DEM grid cell usually has several OIB measurement points. In each grid cell, the 185 DEM elevation values are subtracted from the median of all OIB elevations within it, and this difference is chosen as the final bias for each grid cell, which can minimize the effect of abnormal values or outliers.

General attributes of ICESat-2 DEM
The effective time stamp of the ICESat-2 DEM is May 2019, which is halfway between November 2018 and November 2019. The ICESat-2 DEM provides a complete surface elevation reference for Antarctica, which illustrates higher elevations in the ice sheet interior and lower values in marginal ice shelves (Fig. 4). The local slope shows a pattern similar to the DEM, 200 and undulated slopes are found in areas with rugged terrain, such as the Antarctic Peninsula and Transantarctic Mountains (Fig. 5). Both elevation and slope uncertainties show latitude-dependent patterns, and larger values tend to be found at low latitudes, which may be related to the numbers of ICESat-2 measurement points in individual grid cells (Fig. 2).  According to the shaded relief map of Antarctica derived from the ICESat-2 DEM (Fig. 6), obvious topographical patterns and flat terrain can be found in the mountain environments and ice sheet interior, respectively. On the Antarctic Peninsula, good agreement can be found between the grounding line locations determined from ICESat-2 in Li et al. (2020) and the ice shelf limit is visually identified from the shaded relief map (Fig. 6b). Other large-scale terrain features, e.g., subglacial lakes 215 and floating ice shelves, can also be visually detected (Figs. 6c and 6d).  , which is mapped from ICESat-2 data given in Li et al. (2020).
Three spatial resolutions are used in the ICESat-2 DEM, and the distributions of four kinds of grid cells (observed at individual resolutions and interpolated) show obvious latitude-dependent patterns. Regardless of whether at the basin scale 225 or regional scale, more elevations at higher resolutions tend to be located in high-altitude areas, while elevations at lower or interpolated resolutions are mostly located in low-altitude regions (Fig. 7).

Evaluation of ICESat-2 DEM by comparing to OIB airborne data
In total, approximately 6 × 10 9 OIB measurement points that cover both the steep and flat regions (Fig. 1) are chosen to evaluate the ICESat-2 DEM, and one ICESat-2 DEM grid cell generally contains 17 ± 9 OIB measurement points. Generally, the ICESat-2 DEM shows a decimeter-scale bias compared to the OIB surface heights, with a median bias of 0.11 m (Table   3). Ice sheet elevations are more accurate than those estimated for ice shelves. 240 Table 3. Comparisons between the ICESat-2 DEM and spatiotemporally consistent OIB airborne elevation measurements in observed and interpolated areas for individual regions (i.e., the ice sheet and ice shelves).

Region
MeD ( We also evaluate the elevation performance for observed and interpolated grid cells (Table 3). Generally, the bias of 245 observed elevations is obviously smaller than that of interpolated elevations in both ice sheets and ice shelves, which indicates that the observed elevations tend to be more accurate than those estimated from interpolation. Larger biases are included in the ICESat-2 DEM if the coverage of interpolated elevations is high, which demonstrates the reasonability of the three resolutions used for DEM generation from ICESat-2. The accuracy of the ICESat-2 DEM has an obvious relationship with local terrain conditions, and the bias rises when the slope or roughness becomes larger, which is visible for three surface 250 types (Table 4) and three regions with different surface terrains (Fig. 8). The bias in rocks is obviously larger than those for snow/firn and blue ice areas (BIAs), which is mainly due to the local terrain condition, as they are mostly located in the Transantarctic Mountains and the Antarctic Peninsula, while snow/firn and BIAs tend to have flat surface terrain; hence, they have smaller biases. While in the ice sheet interior, the ICESat-2 DEM shows good agreement with the OIB data; in the Pine Island Glacier region and marginal ice sheet, larger biases occur, which is due to the steep terrain conditions there (Fig.  255 8). Table 4. Comparison between the ICESat-2 DEM and spatiotemporally consistent OIB airborne elevation measurements with respect to three surface types, i.e., snow/firn, blue ice areas (BIAs) and rocks. The surface type data are obtained from Hui et al. (2017)   Although OIB airborne data provide an independent evaluation of the generated DEM, they still cannot present a comprehensive comparison. Most of the OIB airborne data were obtained in ice sheet margins or mountain environments, with high slopes and low elevations. Approximately 74% of OIB elevations are less than 1500 m, and 74% of the observed 270 surface slopes from the OIB mission are less than 1° (Fig. 1), while the corresponding percentages from the ICESat-2 DEM are 37% and 89%, respectively. The applied OIB airborne data cannot completely represent the slope/elevation distributions of the Antarctic DEM; hence, the real accuracy of the ICESat-2 DEM is biased and may be higher.

Comparisons with previous published Antarctic DEMs
When compared to the altimeter-derived DEMs, the elevation difference rises when the surface slope becomes larger, 275 especially in mountainous environments (e.g., Transantarctic Mountains and Antarctic Peninsula, Fig. 9). This may be due to https://doi.org/10.5194/tc-2021-204 Preprint. Discussion started: 4 August 2021 c Author(s) 2021. CC BY 4.0 License. their differences in spatial resolution and measurement accuracy; this effect is considerably reduced when the local terrain is flatter (e.g., ice sheet interior).
Compared to the REMA DEM and TanDEM PolarDEM, smaller elevation differences can be found in both the flat ice sheet interior and steep mountains/marginal ice sheets. Usually, DEMs derived from stereo-photogrammetry have a better 280 performance for high-slope regions (Slater et al., 2018); hence, similar elevations indicate the reliability of ICESat-2 DEMs in mountain environments. In particular, the ICESat-2 DEM shows a generally higher surface height than the TanDEM PolarDEM, which is assumed to be caused by the penetration depth of the X-band (TerraSAR-X and TanDEM-X) into snowpack (Fischer et al., 2020;Dehecq et al., 2016). found. The evaluation result shows that the ICESat-2 DEM has a better performance than altimeter-derived DEMs and is comparable to the DEMs derived from stereo-photogrammetry and interferometry (Table 5). 295 The median differences in surface slope and roughness for these five DEMs illustrate that all their elevation biases become 300 more uncertain with increasing slope and roughness (Fig. 10). The ICESat-2 DEM outperforms other altimeter-derived DEMs for all surface conditions. The REMA DEM always has more stable performances than the ICESat-2 DEM, as stereophotogrammetry can generate more consistent elevation estimations at the regional scale than altimetry. A similar situation occurs for the TanDEM PolarDEM under most surface conditions (slopes >1° or roughnesses >5 cm). Nevertheless, the ICESat-2 DEM is comparable to both the REMA DEM and TanDEM PolarDEM when slopes are less than 1°, which 305 occupies 89% of Antarctica north of 88°S. In addition, compared to the REMA DEM, the ICESat-2 DEM can provide an elevation reference with a definite time stamp, which is essential for further ice dynamics and mass change estimation. ICESat/ERS-1 DEM are also included. As surfaces in rocky regions are usually steep, stereo-imagery-derived DEMs show 315 better performance, and the ICESat-2 DEM outperforms all altimeter-derived DEMs (Table 6).

Conclusions
A definite time-stamped (May 2019) DEM for Antarctica with a modal resolution of 250 m is presented based on the surface height measurements from ICESat-2 by using a model fitting method. This DEM has an elevation measurement that accounts for 74% of Antarctica, and the remaining 26% is estimated based on the ordinary kriging method. The accuracy of the ICESat-2 DEM is evaluated by comparing it to the independent airborne data from the OIB mission after spatiotemporal 325 matching. Overall, the ICESat-2 DEM shows a median bias of 0.11 m and an RMSD of 8.27 m, and these accuracies are compromises for DEM values from surface fits and interpolation. A median bias of 0.07 m and an RMSD of 5.25 m are found for areas where elevations are derived from ICESat-2 measurements, and they increase to 0.33 m and 11.70 m for interpolated elevations. The accuracy decreases when the surface slope or roughness increases; thus, larger biases occur for steep rocks, and flat snow/firn and blue ice areas have smaller elevation differences. 330 Compared to DEMs derived from satellite altimeters (i.e., the ICESat DEM, ICESat/ERS-1 DEM, Helm CryoSat-2 DEM, and Slater CryoSat-2 DEM), larger differences are found in regions with high slopes, which is due to their resolution difference, while smaller elevation differences compared to the REMA DEM and TanDEM PolarDEM support the reliability of the ICESat-2 DEM, as DEMs derived from stereo-photogrammetry and interferometry usually have better performances in steep areas. The ICESat-2 DEM shows better performance than altimeter-derived DEMs and is comparable to the fine-335 https://doi.org/10.5194/tc-2021-204 Preprint. Discussion started: 4 August 2021 c Author(s) 2021. CC BY 4.0 License.
scale REMA DEM and TanDEM PolarDEM, which demonstrates the reliability of the ICESat-2 DEM. More importantly, the ICESat-2 DEM has a specific time stamp, which is more valuable for further scientific applications, e.g., land ice height and mass balance estimations.