Sea Surface Height Anomalies of the Arctic Ocean From ICESat‐2: A First Examination and Comparisons With CryoSat‐2

Accurately resolving spatio‐temporal variations in sea surface height across the polar oceans is key to improving our understanding of ocean circulation variability and change. Here, we examine the first 2 years (2018–2020) of Arctic Ocean sea surface height anomalies (SSHA) from the photon‐counting laser altimeter onboard NASA's Ice, Cloud, and land Elevation Satellite‐2 (ICESat‐2). ICESat‐2 SSHA estimates are compared to estimates from ESA's CryoSat‐2 mission, including semisynchronous along‐track measurements from the recent CRYO2ICE orbit alignment campaign. There are documented residual centimeter‐scale range biases between the ICESat‐2 beams (in release‐003 data) and we opted for a single‐beam approach in our comparisons. We find good agreement in the along‐track estimates (spatial correlation coefficient >0.8 and mean differences <0.03 m) as well as in the gridded monthly SSHA estimates (temporal correlation coefficient of 0.76 and a mean difference of 0.01 m) from the two altimeters, suggesting ICESat‐2 adds to the CryoSat‐2 SSHA estimates.

• We present the first (multiyear) examination of Arctic Ocean sea surface height anomalies (SSHA) from the Ice, Cloud, and land Elevation Satellite-2 (ICESat-2) laser altimeter • ICESat-2 SSHA estimates compare well with near-coincident (CRYO2ICE) radar altimetry-derived SSHA estimates from CryoSat-2 • ICESat-2 and CryoSat-2 show good agreement in the seasonal variability in SSHA suggesting ICESat-2 adds to the time-series of Arctic SSHA resolution lidar data that improved lead classification and SSH estimates (Kwok & Morison, 2011), while its orbit inclination resulted in more extensive coverage of the Arctic Ocean. Since 2010, ESA's CryoSat-2 satellite has been acquiring unfocussed synthetic aperture radar (SAR) altimetry data over the polar regions (Parrinello et al., 2018;Wingham et al., 2006). CryoSat-2's high orbit inclination and continuous data collection have enabled basin-scale mapping of seasonal and interannual SSH variability up to 88° latitude. The SSH data from CryoSat-2 have been compared with Arctic tide gauge measurements and ocean mass variations (e.g., GRACE) and basin-scale, monthly estimates of dynamic ocean topography (DOT; Armitage et al., 2016Armitage et al., , 2018Kwok & Morison, 2016) have been produced.
In September 2018, NASA launched the Ice, Cloud, and land Elevation Satellite-2 (ICESat-2) laser altimetry mission, which has since been providing year-round profiling of the Earth's surface up to 88° latitude (Neumann et al., 2019). The novel photon-counting Advanced Topographic Laser Altimeter (ATLAS) on ICESat-2 provides high-resolution surface height measurements across its six-beam configuration. For the polar oceans, the data collected by ICESat-2 are currently being used to produce routine estimates of sea ice height, type (e.g., lead/ice), and freeboard . The ICESat-2 processing algorithms utilize specular returns to discriminate open-water leads from sea ice, and the laser's spatial resolution (∼11 m diameter footprint; Magruder et al., 2020) is significantly higher than that of CryoSat-2 (380 m along-track and 1,650 m across-track pulse limited footprint; Scagliola, 2013). Also, contamination by off-nadir specular returns from up to 15 km across-track can potentially bias CryoSat-2 surface height retrievals (Armitage & Davidson, 2014). New waveform processing techniques have been developed, which could help account for these off-nadir returns and improve lead height retrievals (e.g., Di Bella et al., 2020).
On the other hand, laser altimetry measurements are often hindered by the presence of clouds, which are otherwise penetrated by radar. Measurements of sea ice height and freeboard by ICESat-2 have been validated against coincident laser profiles collected during targeted underflights by NASA's Operation IceBridge (OIB) airborne mission  and the sea ice classification algorithm has been shown to agree well with coincident imagery (Kwok, Petty, Bagnardi, et al., 2021;Petty et al., 2021). At the time of writing, ICESat-2 SSH measurements have yet to be compared against independent height data (e.g., tide gauges, measurements from other airborne or satellite missions).
As of August 2020, the orbit of CryoSat-2 has been modified as part of the CRYO2ICE campaign (https:// earth.esa.int/eogateway/missions/cryosat/cryo2ice), such that every 19 orbits (20 orbits for ICESat-2) the two satellites are aligned for hundreds of kilometers over the Arctic Ocean, acquiring data along near-coincident ground tracks with a minimum time difference of ∼3 h (https://cryo2ice.org/). In this study, we present a first comparison of semisynchronous along-track SSHA retrievals from ICESat-2 and CryoSat-2 from four CRYO2ICE profiles. We examine SSHA from individual ICESat-2 beams and assess interbeam range biases. We produce gridded SSHA composite maps of the Arctic Ocean and examine the relative agreement of the monthly, seasonal, and multiyear SSHA from the two altimeters. Daily/monthly gridded SSHA measurements over both polar oceans are planned to be released as an official ICESat-2 data product (ATL21) in Summer 2021, and this study offers an examination of this type of composite SSHA data over the Arctic.

ICESat-2 Data
The ICESat-2 photon-counting laser altimeter transmits laser pulses split into a six-beam configuration of three beam pairs (each having a strong and a weak beam), where beam numbers 1, 3, and 5 identify the strong beams, and 2, 4, and 6 the weak beams (Neumann et al., 2019). The 10 kHz pulse repetition rate leads to a 0.7 m along-track separation between subsequent laser pulses of the ∼11 m lidar footprint (Magruder et al., 2020). Among the ICESat-2 data products, the Level 3A sea ice products ATL07 (sea ice height and type, https://nsidc.org/data/ATL07) and ATL10 (freeboard, https://nsidc.org/data/ATL10) provide alongtrack measurements for six individual ground tracks (targeted at reference ground tracks, RGTs), and up to 16 satellite passes per day over both the Arctic and the Southern Ocean. The along-track surface heights are generated by aggregating 150 geolocated signal photon heights from the primary science Level 2A ATL03 data product (Neumann et al., 2019). ATL10 data coverage is limited to areas that have an ice concentration >50% (15% for ATL07), as inferred from passive microwave satellite measurements, and up to 25 km distance from land. A full description of the ATL07/10 products can be found in the Algorithm Theoretical Basis Document (ATBD,  and recent changes to the algorithm are further discussed in (Kwok, Petty, Bagnardi, et al., 2021). In this study, we use release 003 (r003) ATL10 data.
In ATL10, the SSHA represents the measured sea surface elevation relative to a multiyear mean sea surface (MSS, see Section 2.3) after various geophysical and atmospheric corrections have been applied (see Table S1). Note that we adjust the solid earth tide correction included in each ICESat-2 segment's SSHA from r003 ATL10 data to correct a discrepancy in the permanent tide system. The adjustment is described in the supporting information (Text S1). The SSHA is provided for each beam at three different length-scales: (a) segments classified as sea surface after radiometric classification as specular returns and height filtering, where SSHA measurements are calculated by fitting impulse-response weighted Gaussian distributions to the height distribution of 150 photons within a segment (∼20 m mean along-track SSH segment resolution for the strong beams); (b) individual leads, where the SSHA is calculated as the weighted mean height from consecutive segments forming an individual lead; (c) ∼10-km along-track sections, where SSHA is calculated as the weighted mean of all leads within a given section for each beam, or linearly interpolated from adjacent sections, and smoothed using a 3-point point smoother. In subsequent analyses, we use (a), height_segmet_height, where ssh_flag = 2, but note that ATL21 data products will be formed using (c) to be consistent with the reference sea surface heights used to calculate freeboards (ATL10 and ATL20). This choice does not introduce significant differences in the gridded SSHA estimates (not shown) but allows us to take advantage of higher spatial resolution and of noninterpolated data when comparing results with CryoSat-2.

CryoSat-2 Data
We use data acquired by the SIRAL K u band SAR altimeter in the SAR mode, one of CryoSat-2's three modes of operation. We use intermediate Level 2 (L2) ice products processed at Baseline-D (Meloni et al., 2020) and available from ESA's CryoSat-2 Science Server (https://science-pds.cryosat.esa.int/). L2 data provide geolocated height measurements above the reference ellipsoid (WGS84) computed from each echo at intervals of ∼300 m. The data are already corrected for instrument effects, propagation delays, measurement geometry, and other geophysical effects (e.g., atmospheric delays and tides, see Table S1). In Table S2 and Figure S1, we provide an assessment of the differences between the ICESat-2 and CryoSat-2 geophysical corrections, estimated from orbit cross-overs (coincident data filtered using a maximum time difference of 10 min and spatial difference of 10 km). Waveform retracking is also already applied in L2 data and determined using a model-fitting method to specular lead waveforms described by Giles et al. (2007). Further details and information can be found in the CryoSat-2 Baseline D Product Handbook (ESA, 2019) and in Meloni et al. (2020). Data coverage is controlled by the operational geographical mode mask (https://earth. esa.int/web/guest/-/geographical-mode-mask-7107) and updated every 2 weeks to account for changes in sea-ice extent.

Mean Sea Surface (MSS)
To consistently compute the SSHA for CryoSat-2, we remove a mean sea surface height from each ellipsoidal elevation from L2 data (height_sea_ice_lead_20_ku, which includes all instrumental and geophysical corrections) by bilinearly interpolating MSS values from a 2.5 km grid , https://zenodo. org/record/4294048) to the interval centroids. The MSS grid and the interpolation approach are the same as those used in the ICESat-2 sea ice data products. The MSS includes the geoid component and is in the mean-tide system (see Text S1), and is derived from CryoSat-2 SSH retrievals during 2011-2015 (Kwok & Morison, 2016) with gaps filled mainly at lower latitudes using the DTU13 global high resolution MSS (data from 10 satellite missions from 1992 to 2012; Andersen et al., 2016).

SSHA Data Binning and Gridding
In along-track comparisons for the CRYO2ICE campaign ( Figure 1, Section 3.1), we first identify measurement overlaps by selecting ICESat-2 SSHA segments from a given beam that fall within the theoretical CryoSat-2 pulse-limited across-track footprint (±825 m across-track from the centroid of each footprint; Scagliola, 2013). We then bin individual SSHA segments for ICESat-2 and SSHA intervals for CryoSat-2 in coincident 10-km sections (following the ATL10 sea ice product and based on the average Rossby radius of deformation for polar latitudes; Chelton et al., 1998) and calculate the simple mean value from all measurements within each bin (shown as stars in Figure 1). For each profile, we calculate the mean (μ) and standard deviation (SD) of the differences from all bins, and the correlation coefficient (R) between the two datasets.  data acquired within a given time period. Finally, we apply to both datasets a mask based on the NSIDC Arctic regional mask, in order to limit our assessment to the Beaufort, Chukchi, East Siberian, Laptev, Kara, Barents, and Greenland seas, and the Central Arctic (see Figure S2 and black dashed outline in maps shown in Figures 2-4).
10.1029/2021GL093155 5 of 10  the last available ICESat-2 r003 ATL10 data set. For some of these alignments, the data products are not available and for many others, SSH data are missing/invalid (e.g., because of cloud cover for ICESat-2). From the subset of available data ( Figure S3), we find four overlaps that extend for at least 400 km with >1,000 valid sea surface height segments/intervals.  Figure S4 together with differences between geophysical corrections (i.e., tides and inverted barometer). Note that applying the geophysical corrections is key when doing these comparisons, as the lack of time-coincidence can cause significant (up to 20 cm) differences ( Figure S4).
The larger (>0.20 m) SSHA excursion shown in both datasets (referenced to the same MSS) in Figure 1b and smaller but still significant short-scale variability in the other profiles may be localized geoid features (e.g., associated to deep ocean ridges) that are not represented properly in the current MSS, and unlikely to be ocean circulation features.

ICESat-2 Beam Comparison
Preliminary analyses by the ICESat-2 Project Science Office (PSO) have suggested that the ATLAS beams have different range biases and that these can vary through time, that is, the height profiles from the six beams are not yet fully calibrated/reconciled and centimeter-level differences between beams remain. To understand the interbeam range variability from SSHA estimates, we calculate the monthly mean SSHA value over the Arctic since the start of the mission for the three strong beams independently (Figure 2a). The monthly SSHA estimate from beam 1 presents the largest differences with respect to the two other strong beams (up to ∼0.07 m in July 2019), while differences between beam 3 and beam 5 are consistently <0.02 m. Correlation coefficients are 0.76, 0.66, and 0.93 for beam 1-beam 3, beam 1-beam 5, and beam 3-beam 5, respectively. In Figures 2b-2d, we show the spatial distribution of the beam-to-beam differences BAGNARDI ET AL.
10.1029/2021GL093155 7 of 10 for a given month (January 2019, gray bar in Figure 2a), which show that differences exhibit no obvious spatial correlation. This remains valid for all months since the start of the mission. The same beam-to-beam differences are also shown as histograms in Figures 2e-2g, further demonstrating the clear interbeam bias associated with beam 1 (mean of −0.03 m when compared to beam 3 and 5) and that differences between beam 3 and 5 are normally distributed around a mean of 0.00 m with a standard deviation of 0.05 m. The significant larger differences with beam 1 are also consistent with the findings of Brunt et al. (2021) estimated over the interior ice sheets of Antarctica (beam 1-3: 0.039 m; 1-5: 0.036 m; 3-5: 0.003 m), suggesting that these are sensor or pointing solution related.
For all of our subsequent analyses (Sections 3.3 and 3.4), and until range differences between beams are fully characterized, we opt to use just a single strong beam when estimating Arctic SSHA. Based on the results presented above, we select the middle strong beam (beam 3) since, despite its lower transmitted energy level (∼80% of beam 1 and 5), the steeper incidence angle results in a stronger backscatter in the presence of highly reflective surfaces (e.g., leads), consistently increasing the number of specular lead returns compared to other strong beams (Kwok, Petty, Bagnardi, et al., 2021). This is currently our recommended strategy for the initial production and release of ICESat-2 ATL21 data.

Monthly and Multiyear SSHA Comparison
In Figure 3a, we compare monthly SSHA means calculated using ICESat-2 beam 3 to those calculated using CryoSat-2 L2 data. We limit this comparison to the Central Arctic, the area outlined by the green dashed line in Figure 3b (from NSIDC Arctic regional mask), where we expect consistent year-round ice cover and to exclude effects introduced by season-dependent changes in sea-ice extent and different data coverage near the coastal regions. Further details for each monthly comparison (mean, number of valid grid cells, number of data points) are provided in Table S3. Differences across all months between the two sensors have a mean of 0.01 m (SD = 0.02 m), and the correlation coefficient from a least squares regression (R) is 0.76 (slope = 0.95, intercept = −0.02 m). We find that up to 0.03 m of the observed monthly SSHA differences, especially during fall/winter, are caused by differences in the inverted barometer correction applied to each data set (see also Table S2 and Figure S1). Our comparisons between heights from ICESat-2 with those from CryoSat-2 show a better agreement than has been shown by Brunt et al. (2021), who compared absolute ice height over the flat interiors of the Antarctic ice sheet and found differences >0.3 m. This larger discrepancy, however, is likely due to the much greater penetration depth of the K u band radar in firn compared to seawater.
We then compare the Arctic SSHA calculated from data spanning the 2-year mission overlap, from November 1, 2018 through October 31, 2020. The ICESat-2 mean 2018-2020 SSHA in shown in Figure 3b and that from CryoSat-2 is presented in Figure 3c. Both maps show a positive SSHA in the southern Beaufort Sea, a strong negative anomaly in the Chukchi/Siberian seas and a weaker negative SSHA in Central Western Arctic, a spatial pattern consistent with recent positive phase in the Arctic Oscillation (Armitage et al., 2018;Morison et al., 2021). In Figure 3d, we show a histogram of the differences between ICESat-2 and CryoSat-2 SSHA, while a map of the SSHA differences is presented in Figure 3e, which shows the ICESat-2 SSHA to be generally higher in the more marginal seas (Barents, Kara, East Siberian, and Chukchi) and slightly lower in the Central Arctic. The marginal seas are areas of large SSH variability where the different acquisition times between the two satellites can capture different parts of these cycles (see Figure S5 for the standard deviation of each data set, showing higher values in the marginal seas) and can therefore explain much of these differences. Increased data acquisition from both missions will enable a more reliable comparison of the mean SSHA from ICESat-2 and CryoSat-2.

Seasonal SSHA Variations From ICESat-2
In Figure 4, we present seasonal maps of Arctic SSHA for 3-month periods starting in mid-October 2018 and ending in September 2020. The top row (Figures 4a-4d) can be directly compared to the bottom row (Figures 4e-4h) to assess year-to-year differences, while from left to right we track the temporal progression during two entire freezing-melting seasons (2018-2019 and 2019-2020). Note that variations in spatial coverage are dictated by variations in sea ice extent since ICESat-2 ATL10 data are only provided for areas that have an ice concentration >50%. Comparisons to CryoSat-2 for each 3-month period are presented in Figure S6, and confirm similar SSHA spatio-temporal variations providing some confidence in the capability of ICESat-2 to produce consistent estimates of Arctic SSHA.
A positive SSHA centered on the Beaufort Sea (a strengthened Beaufort Gyre) is clearly visible during winter months but less apparent in 2020 (see Figures 4c and 4d compared to Figures 4g and 4h). Large variability in the Siberian and Chukchi seas also corresponds to areas characterized by high short-term SSH variability.

Summary and Conclusions
Here, we have presented a first examination of Arctic sea surface height anomalies (SSHA) from NASA's ICESat-2 laser altimeter during the first 2 years of the mission (2018-2020). We analyzed beam-to-beam differences and provided an independent assessment of inter-beam range biases for the ATLAS altimeter. We compared the ICESat-2 SSHA estimates with L2 sea ice data obtained from ESA's CryoSat-2 radar altimeter. We provided a brief description of the necessary steps to compare the SSHA data from the two altimetry missions by imposing the same permanent tide system and MSS. A careful reconciliation of the data (e.g., same geophysical corrections) is needed in future efforts to blend data from ICESat-2 with those from Cry-oSat-2 (and potentially other airborne and space-borne altimetry missions).
The strong agreement between both the semisynchronous along-track estimates from the CRYO2ICE overlaps and basin-scale gridded SSHA estimates between the two sensors suggests that the higher resolution ICESat-2 data can be used to estimate monthly/seasonal SSHA and perhaps resolve 10-km-scale spatial variability in SSHA. The multiyear record of overlap also opens up the potential to produce a new, high-resolution, blended, estimate of the mean sea surface of the Arctic Ocean (and indeed Southern Ocean) which could rectify what we believe to be unphysically large short-scale variations in SSHA shown in the CRY-O2ICE overlaps. Finally, our results provide a first evaluation of the approach used for the production of ICESat-2 SSHA gridded data products for the polar oceans (ATL21). Future work will extend this analysis to the Southern Ocean, pending CRYO2ICE orbit maneuvers for the Southern Hemisphere.