The IS-2 sea ice height product (ATL07) contains profiles of surface heights and surface type of individual height segments along each of the six ground tracks (Kwok et al., 2020a). Individual height estimates in ATL07 are derived from height distributions constructed using a fixed aggregate of 150 geolocated photons from the ATLAS Global Geolocated Photon Data product (ATL03) (Neumann et al., 2019). Individual ATL10 freeboard estimates are derived from ATL07 surface. A local sea surface reference (href) (i.e., the estimated local sea level) is derived from the heights of available lead segments (one or more) within a 10 km along-track section (for each beam). Each lead may contain one or more consecutive sea surface height segments. The derived sea surface references are interpolated to obtain estimates between gaps of <50 km in length and extrapolated to adjacent 10 km sections where gaps are >50 km. Within each 10 km section, individual freeboard heights (hf) are calculated as the difference between the surface heights (hs) and the local sea surface reference (i.e., hf=hs-href). In ATL10, freeboards are provided only where the ice concentration is higher than 50 % and the height samples are at least 25 km away from the coast (to avoid uncertainties in coastal tide corrections). The ATL07 and ATL10 products (currently R002 and R003) are available from the National Snow and Ice Data Center (Kwok et al., 2020a).

Of special note here is that, in this paper, we address only the sea surface references from individual strong beams. Previous releases (Releases 001 and 002) of sea ice freeboards in ATL10 included swath-wide (multibeam) freeboard estimates by combining and using available sea surface references across all strong beams. Due to residual range biases (centimeter level) between the three IS-2 strong beams, these swath-wide freeboard estimations should not have been provided in ATL10. Until successful inter-beam range calibrations are satisfactorily achieved, these multibeam estimates will no longer be provided to users in upcoming releases. The release of the multibeam estimates was due to an error in software implementation (see https://nsidc.org/sites/nsidc.org/files/technical-references/ICESat2_ATL07_ATL10_Known_Issues_v003_Nov2020.pdf, last access: 1 November 2020).

We use CAMBOT imagery obtained during the spring 2019 OIB Arctic campaign. CAMBOT is a nadir-looking digital camera system operated by the ATM instrument team that provides georeferenced and orthorectified imagery with a spatial resolution of ∼9 cm at the nominal flight altitude of 500 m. The CAMBOT data are available through the NSIDC (Studinger and Harbeck, 2019). The spring 2019 OIB Arctic campaign surveyed the thicker multiyear ice north of Ellesmere Island and was designed to optimize spatial and temporal coincidence with IS-2 (see Fig. 1 in Kwok et al., 2019b). Winds (and thus sea ice drift) were reported to be low throughout these flights, increasing coincidence; however the presence of leads in this highly consolidated sea ice regime was limited. Manual inspection of the CAMBOT imagery and ATL07 data identified ∼10 examples of misclassified dark leads. We include two example scenes here (Sect. 4) which had the best spatial and temporal coincidence with IS-2. Scene 1 was obtained by CAMBOT on 12 April at 13:23:48–13:24:45 UTC (86.6∘ N, 127.5∘ W), where IS-2 (RGT 218, Beam 2) passed at 13:03–13:05 UTC (with a time difference of ∼20 min). Scene 2 was from 22 April at 14:07:15–14:08:12 UTC (81.6∘ N, 118.2∘ W), where IS-2 (RGT 371, Beam 2) passed at 13:29–13:33 UTC (time difference of ∼40 min). RGTs (reference ground tracks) are imaginary lines centered on the six beams used to identify distinct IS-2 orbits within a given IS-2 repeat cycle of 91 d.

Each height segment in ATL07 is assigned a surface type (specular, dark lead (smooth), dark lead (rough), gray ice, snow-covered ice, rough, shadow). These surface types were chosen as they are expected to broadly represent the typical surfaces encountered over the polar oceans – a detailed description of the classification approach can be found in Kwok et al. (2016). The primary use of surface types is for determining, together with local height statistics, whether a given height segment is suitable for use as a sea surface height sample in computing freeboards in ATL10. The surface-type classifier uses three attributes derived from the photon distribution of a height segment; they are photon rate (rsurf), width of photon distribution (ws) and background rate (rbkg).

The surface photon rate (photons / shot) is the average number of detected surface photons (photoelectrons) divided by the number of laser shots required to construct a 150-photon aggregate. In the absence of clouds, it provides a measure of the brightness or apparent reflectance of the surface. Open leads of smooth open-water or thin ice surfaces at near-nadir incidence angles can be specular or quasi-specular (i.e., high photon rates) but can also have low photon rates characteristic of surfaces with low surface reflectance or albedo. Specular returns are relatively common in IS-2 sea ice returns, and these returns are especially useful as large numbers of photons over very short length scales (i.e., small number of shots with inter-pulse spacing of 70 cm) are ideal for resolving very narrow leads (tens of meters) within the ice cover. Unlike the higher signal-to-noise returns from specular surfaces, the classification of low-albedo surface is more prone to errors due to cloud effects (Sect. 4). Clouds can attenuate the strength of the surface returns because the transmitted or reflected energy is scattered away (atmospheric scattering) from the narrow field of view of the ATLAS instrument (more on this below). Between the two extremes, the surface types are of ice or snow surfaces but may be of geophysical interest for the general understanding of surface and cloud conditions. The Gaussian width (ws) of the photon height distribution provides a measure of the surface roughness; the width is useful in further partitioning the height segments into different surface types (e.g., a specular surface with a relatively wide Gaussian width is classified as sea ice and not a lead).

Prior to surface finding, background photons are separated from surface photons based on their distance from the mode of the height distribution (Kwok et al., 2019a). Photon events that are not classified as surface returns are designated as background or noise photons. Background photon events could be associated with noise in the lidar instrument (e.g., stray light, detector dark counts) or scattered sunlight at the laser wavelength. Specifically, the solar background count rate (Bs) is the solar zenith radiance due to solar energy scattered by the surface or atmosphere and provides a useful reflectance measure for surface identification. But the latitudinal, seasonal and daily variability of the solar zenith makes Bs more challenging to use. Under clear skies, the surface returns from Lambertian surfaces are approximately linearly related to the solar background rate. Deviations from a linear relationship are indicative of shadows (cloud shadows or ridge shadows), specular returns or atmospheric scattering. In the case of quasi-specular returns from a dark lead, for example, the behavior of background vs. photon rate is not positively correlated: that is, while the surface photon rate is high for quasi-specular returns, the solar background rate is low due to a low-reflectance smooth surface. When the sun is up in the polar regions, the availability of solar background provides another proxy of surface reflectance and adds to the confidence level in our surface-type classification. The reader is referred to the procedure described in Kwok et al. (2019a) for further details.

When a sea surface sample is present locally, it is typically the lowest height along a height profile. Since sea surface samples designated by the classifier (specular and smooth dark leads) are not always unambiguous (i.e., subject to classification errors) and their heights are noisy estimates, the lowest point may not be the optimal estimate. In the IS-2 sea ice algorithm, we bracket the candidate samples in the surface height distribution selected to calculate our sea level reference. From the population of smooth surfaces (Hsmooth; i.e., with ws<0.13 m), we define the upper and lower limits of the height bracket (hUB, hLB) to select the candidate samples, as follows:

hLB is the lowest height in Hsmooth.

Estimates from individual leads are then combined to obtain a sea level reference (h^ref) for a 10 km along-track section as below (weighting is based on the error variance of each lead σlead(i)2): h^ref=∑i=1Nlαih^lead(i)i and σ^ref2=∑i=1Nlαi2σ^lead(i)2, where αi=1σlead(i)2∑j=1Nl1σlead(i)2. For each valid ice segment along the given beam, the freeboard and associated error variance are then given as hf=hi-h^ref and σf2=σi2+σ^ref2.

Figure 1 shows the distribution photon rates (photon / shot) and lead lengths of the sea surface height samples (strong beams). The mean photon rates of the entire height population (between ∼6–8, Fig. 1 – left panel) are dominated by the expected returns from a mixture of snow-covered sea ice of different roughness. The distributions are remarkably consistent for the 3 months (January, June and October 2019) shown here. As expected, Beam 3 has consistently weaker surface returns. This is due to the lower transmitted laser energy (transmitted energy of Beam 3 is ∼0.81 % of Beam 1 and 5) and thus lower return for this beam, which is consistent with pre-launch expectations and is attributable to the custom construction of the optical component used to split the laser energy into the six IS-2 beams (Neumann et al., 2019). A consequence of this is that it takes more pulses (longer along-track distance) to construct a 150-photon aggregate for surface finding – hence the longer lead lengths seen in Fig. 1.

Because a fixed number of photons are used in surface finding, photon rates are determined by the number of shots, or along-track distance, needed to construct these 150-photon aggregates. That is, the segment length adapts to changes in photon rates from surfaces of different reflectance: height segment lengths are longer when the returns are lower, and vice versa. The distributions of lead lengths (aggregate of sea surface segments described above) – used in reference height calculations – are bi-modal (Fig. 1 – right panel); the modes are determined by leads that are specular or quasi-specular and by leads with very low reflectance. The lead lengths vary between ∼10 and 150 m, with modes at ∼27 m (specular leads) and ∼60 m (dark leads). The upper bound in segment length (∼150–200 m) is controlled by a setting in the surface-finding procedure that restricts the distance over which photons are aggregated and serves to reduce the number of noise and background photons accumulated in long-distance aggregates. The consequences of a longer integrating distance for estimating surface heights of dark leads are (1) the likelihood that there is a mixture of surface types in the height segment and (2) the higher number of accumulated noise photons in the larger number of shots used.

For estimating the reference surface heights, the specular and dark-lead heights (in R001 and R002) are mixed in the weighting process above.

In the presence of clouds, the photon rates are unreliable proxies of brightness or apparent surface reflectance of the surface. In the first CAMBOT–IS-2 scene (Fig. 2a), the attenuation effects of atmospheric moisture are evident in the coincident coverage of a “dark” lead detected by the surface-type classifier (Fig. 2a). A clear indication of the presence of clouds is the concurrent along-track decreases in IS-2 photon rate (from ∼6 to ∼2 photons / shot) and increases in background rate (from ∼3 to 4 MHz), followed by a recovery of both parameters to close to their expected levels. Since a dip in the recorded levels of the CAMBOT data is not seen, the clouds are likely present in the atmospheric column above the altitude of the IceBridge platform, which was ∼1000 m for this flight line. Because of the attenuated photon rates, the IS-2 samples within the linear feature (refrozen lead) in the CAMBOT image were mislabeled as a dark lead by the surface classifier. In the absence of the attenuation effects (dip in photon rates), these samples would not have been classified as a dark lead. Even though the post-classification height filter ensured that the surface height of those samples was the lowest in the neighborhood, the sampled heights are unlikely indicative of the sea surface (i.e., they are higher than the actual sea surface).

The second example shows gaps in IS-2 surface retrievals near the center of the CAMBOT image. Gaps in IS-2 data are present when the software on board the IS-2 observatory determines, by an onboard analysis of the photon density in that atmospheric column, that surface returns are unlikely to be present; thus no data are telemetered or downlinked to the ground station. This suggests the presence of clouds in the neighborhood of the gaps. In fact, large variability in photon rates and CAMBOT data is seen away from the gaps. Since this type of surface variability is unlikely from the sea ice cover in an area north of Ellesmere Island on 22 April, both the IS-2 and CAMBOT data are affected by the atmosphere. Again, there is a misclassified lead near the center of the image – with a distinct dip in the surface height – even though a correct surface classification would have removed those samples as candidate sea surface segments. These two examples highlight the potential effects of clouds in surface-type classification.

Why are cloud flags not used? The crucial element in freeboard retrieval is the accurate identification of the height samples that are suitable for estimation of the local sea surface, largely because of the low density of these samples on the ice cover, and errors in reference heights affect freeboard estimates over 10 km length scales, unlike the impact of errors in individual ice surface height estimates. The cloud flags in IS-2 are sampled every 400 m and not compatible with the size of the leads used here (27–80 m). Also, we find that the cloud flags are quite conservative: our understanding to date is that a large number of leads would be removed if the cloud flags were used to filter the returns. The IS-2 cloud flags, as they are currently designed, are thus currently ineffective for addressing the cloud issue at the length scale of the leads in the sea ice data.

In first and second releases of the IS-2 sea ice products (R001 and R002), both specular and dark leads were used in the determination of the local (10 km) sea surface references. Here, we examine the height distributions of the population of specular and dark leads used in reference surface estimation to assess whether the distributions of dark leads introduce biases in the freeboard calculation. The height distributions of the two surface-type categories in the Arctic and Antarctic for 3 months in 2019 (January, June and October) are shown in Fig. 3. We summarize the results as follows:

The height distributions overlap even though the mean of the height distribution of dark leads is higher by up to 10 cm: the modes of the distributions are skewed relative to each other, and the differences in the negative tail of the distribution are more distinct. This provides further, albeit indirect, evidence that the height distribution of the dark leads is contaminated by incorrect classification of the surface as discussed above.

We have examined a simple approach to identifying the fraction of dark leads that may be affected by clouds (for possible implementation in future data releases but not R003). In the approach, the photon rate of a dark lead (PRlead) is compared to the height segment with the highest photon rate (PRmax) in the neighborhood of the dark lead. As a simple diagnostic, we calculate the contrast ratio: R=PRmaxPRlead. Under cloud-free and ideal conditions, we expect the contrast to be between 8 and 9; i.e., the albedo of snow-covered sea ice is >0.8 compared to the lower albedo (reflectance) of smooth open leads of ∼0.1. In less-than-ideal conditions (e.g., cloudy conditions), however, we expect this contrast to be lower.

Figure 4 shows the percentage of the dark-lead population with contrasts <2, <3 and <4 within a ±20 km neighborhood of the dark lead. It is evident that 70–80 % of the population (for the months shown here) have a contrast ratio <4 and are potentially misclassified if clouds were not considered in the surface-type analysis. This preliminary analysis suggests that this local contrast ratio diagnostic could provide a useful filter to address the cloud misclassification issue. However, the effectiveness and the implementation of this approach need to be examined in more detail if this is to be incorporated into the next IS-2 sea ice product generation.

In R001 and R002, candidate height segments that were selected to estimate reference heights for freeboard calculations included, as discussed above, two primary surface types: specular and smooth dark leads. Given the likelihood of the mislabeling of dark-lead segments as suggested by the results presented here, a simple revision to the algorithm for production of R003 has been implemented. Instead of using two surface types for reference height calculation, only the specular surface returns are used to derive the reference sea surface. This is a simple change in the software system, chosen to enable continued sea ice product generation while a more sophisticated filtering approach (as highlighted in the previous section) is tested. The overall impact of this change in the freeboard estimates is shown in the next section.

Here, we compare the retrievals from R002 and R003 for the months of January, June and October 2019. The consequence of this change can be seen in the freeboard composites and distributions of the Arctic and Antarctic sea ice covers (Figs. 5 and 6), and Table 1 summarizes the freeboard statistics of the distributions. The differences are summarized below:

In the monthly composites of the Arctic and Antarctic, area coverage has decreased by ∼10–20 % because, due to excluding the dark leads, there are fewer estimates of the local reference sea surface for freeboard calculations.

The increased freeboards correspond to an increase in ice thickness and snow depth estimates from ICESat-2 first examined in Petty et al. (2020) and Kwok et al. (2020b). These are not addressed in this paper because the present focus is on the publicly available ICESat-2 sea ice freeboard product distributed by the ICESat-2 mission. The impact on sea ice thickness and snow depth will be addressed in forthcoming papers.