ATL07 provides along-track sea ice height, including surface types and the height profiles of sea ice and open water leads, where ice concentration > 15 % . In ATL07, 150 consecutive photons along a beam are aggregated to form a segment. The location/time of each segment is denoted as the average location/time of all photons within that segment. Based on the height histogram of these photons (fit into Gaussian), as well as surface and background photon rates and lidar parameters, the height and type of a segment are determined. Segment surface types are classified into clouds, ice/snow, and specular/dark leads. We only analyze segments that are marked as “good” in height segment quality, which was determined by the fitting of the observed histogram to a Gaussian distribution. Given that segments with bad height quality are often associated with rough/ridged surfaces, whereas lead detection is done on smooth surfaces, we don't expect the quality fit flags to cause issues with the lead detection. Generally, low surface rates (caused by low reflectance) indicate water/thin ice in leads, whereas high surface rates imply ice/snow. However, very high surface rates have also been observed from smooth open-water/thin ice surfaces. Therefore, leads are further classified into specular (with very high surface rates) and dark (with low surface rates) leads. Some specular leads are selected and marked to be sea surface height candidates that are used to derive sea surface reference in ATL10 (detailed in the next subsection). As dark leads are sometimes misclassified as clouds, they are not used as sea surface references in ATL10, and we will only show results of specular leads from ATL07.

As each segment consists of 150 photons, segment lengths vary across different surface types with various reflectance (Fig. a). Segment lengths are generally inversely related to surface photon rates: specular lead segments are shortest with very high surface rates, followed by ice/snow segments. Given that surface type is designated for each segment, segment lengths indicate the resolution of ATL07 in different surface types. ATL07 strong beams can resolve ice/snow surface in a resolution of ∼ 12 to 14 m (±5.5 m, half of the footprint size), and specular leads down to only ∼ 7.5 m (±5.5 m, Fig. a). We note that the detection of specular leads in ATL07 is very strict to avoid possible other surface types (mostly ice) to be classified as specular leads. Therefore, specular leads detected in ATL07 are likely a conservative estimate of total lead extent.

Total segment number in ATL07 in November–April of 2018–2024 is on the order of 6×106 (Fig. b), besides regions near coasts and ice edge, where total segment number reduces to ∼ 10⁶. The dense samplings of ICESat-2 indicate the statistical robustness of lead characterization.

(P21) assessed ICESat-2 ATL07 surface types product, and validated the along-track lead fraction in the first winter of the mission (2018–2019) with Sentinel-2 images. Several new releases of ICESat-2 ATL07 product have been published since P21, with longer records and improved algorithms, allowing improved characterization of lead statistics, such as sizes in addition to the areal fraction.

ATL10 provides freeboard estimates using the same segments as ATL07, including those identified as leads, over regions with ice coverage > 50 %. For each 10 km distance along all beams, a single value of sea surface reference is first derived from all sea surface height candidates marked in ATL07. A specular lead segment is selected to be a sea surface reference candidate when its segment height is smaller than the lead threshold maximum height calculated from all segments over the 10 km distance. The lead threshold maximum height is the maximum of the two quantities: 2 % of valid heights within the 10 km track and the minimum value of a subset of valid heights where the segment is not on the edge of a data gap and the fitted Gaussian width is less than 0.13 m see ATBD;. Freeboard is then calculated as the difference between the segment height and the sea surface reference. In cases where no sea surface height candidates are available in the 10 km distance, or the tilts in these candidates are larger than 20 cm per 10 km, the reference sea surface will be interpolated between two valid sea surface references if the time gap and height difference between the two sea surface references are small see ATBD;. There will be cases where the estimated freeboard is negative because the derived sea surface reference is not local to each individual segment or a result of subsurface scattering in snow-free thin ice ; these negative values are truncated to zero in ATL10. A case study suggests that only ∼ 0.2 % of all segments are truncated to zero. Quality flags that describe the quality of the along-track Gaussian fit are also provided. We only use segments marked as valid in the quality flag.

In ATL10, we define a segment as lead segment when its freeboard is smaller than 3 cm. These lead segments include both open-water leads, as well as newly-closed ones, which represents a maximum ice and snow thickness in the lead of ∼ 30 cm. The choice of 3 cm is arbitrary to some degree, based on the representative uncertainty of ∼ 1–2 cm in ATL10 freeboard . We will discuss the sensitivity of lead properties to the freeboard criterion in Sect. 5. ATL10 strong beams can resolve lead segment lengths to as small as 7.5 m (±5.5 m), same as ATL07 (Fig. a). The lengths of the lead segments in ATL10 range from 7.5 to ∼ 19.5 m (±5.5 m), as newly-freezing ice (moderate reflectance) and dark leads (low reflectance) are also identified as leads in ATL10. Total number of segments in ATL10 is comparable with those in ATL07 as expected, since ATL10 segments are based on the same segments in ATL07, with differences arising from ice concentration filters and quality flags.

For each product, we first combine consecutive lead (ice) segments to form a single lead (ice floe). The size of a lead is then calculated as the distance between the first and last segment centers, plus half of the first and last segment length, given that the location of a segment is assigned to be the middle position of the segment. As introduced earlier, the footprint size (11 m) characterizes the uncertainty in lead (ice floe) sizes. We use “size” (equivalent to the term “apparent lead width” used in ) instead of the commonly used “width”, as ICESat-2 tracks are not always perpendicular to leads to measure the actual “width”. Such orientation problems will be discussed later in the paper.

Within a given grid cell (or region), lead fraction (Lf) is calculated as the total length of all leads divided by the length of all leads and ice floes defined in the previous section: 1Lf=∑i=1nLi∑i=1nLi+∑j=1NLj, in which Li is the size of a given lead, n is the total number of leads, Lj is the size of a given ice floe, and N the total number of ice floes.

A lead/ice segment that crosses two grid cells (or regions) is assigned to the cell (region) encompassing its center. Given the meter to tens-of-meter scale of a single segment, we assume that the impact of such region-crossing segments is small.

We characterize uncertainties in lead fraction by two quantities: (1) their formal standard errors, and (2) lead fraction after accounting for footprint size. In (1), the formal standard errors in lead fraction are given by the ratio of their standard deviations to the square root of sampling size: 2σf=∑i=1Nb(Lfbi-Lfb‾)2Nb/Nb, where Lfbi is the lead fraction in an individual beam, Lfb‾ is the averaged lead fraction over all beams within a given cell (region), and Nb represents the total number of beams. In (2), we calculate the lead fraction by adding (subtracting) the footprint size to (from) each individual lead and subtracting (adding) the footprint size from (to) each individual ice floe in equation (1) as: 3Lflow=∑i=1n(Li-11)∑i=1n(Li-11)+∑j=1N(Lj+11),4Lfhigh=∑i=1n(Li+11)∑i=1n(Li+11)+∑j=1N(Lj-11), in which Lflow and Lfhigh are the lower and upper estimates of the lead fraction.

The two quantities described above quantify different aspects of uncertainties. Standard errors suggest the representativeness of the cell-mean lead fraction calculated by equation (1). The lower and upper estimates of the lead fraction indicate the uncertainties associated with the geolocation of photons.

The spatial patterns of lead fraction, number, and power-law exponents are generally consistent with ice thickness: ice edges are more prone to breaking due to wind stress or ocean circulation, leading to larger leads. Specifically, a band of high lead fraction (> 1 % in ATL07 and > 5 % in ATL10) from ∼ 90° E to ∼ 120° W is present following the coastline. This stripe appears to co-locate with coastal shelf waves , likely driven by the cross-shelf Ekman transport from local winds . These constantly generated waves could result in more ice breaking, preconditioned by the thinner ice near the coast, likely yielding the observed high lead fraction. The ratio of the lead fraction in ATL10 to that in ATL07 is smaller in the Barents Sea and Baffin Bay area compared to the Central Arctic. An explanation could be that open leads are quickly refrozen in the Central Arctic compared to ice edges, resulting in more newly closed leads that are considered as leads in ATL10 but not in ATL07.

The power-law distribution of the sea ice leads reflects the fractal nature and nonlinearity in sea ice fracturing, which exhibit self-similar behavior that is often generated by repeated physical growth process . Many other variables exhibit the same fractal nature that follows a power-law distribution of their sizes, including the complementary solid component of the ice cover – sea ice floes e.g.,. Here, we find evidence that the power-law exponent increases with lead size and varies across regions and time, likely reflecting differences in winds e.g., and ocean forcing like waves e.g., acting on varying sea ice conditions that modulate its resistance to deformation . Lead refreezing rate under different thermodynamic and dynamic processes may also contribute to the scale-dependent power-law exponent.

An increasing power-law exponent has been theorized and observed for sea ice floes. Regional and temporal variability in floe size exponents has likewise been linked to the growth–melt cycle and ice precondition e.g.,. Collectively, our results, and those for sea ice floes, suggests that assumptions of a (constant) power-law distribution could potentially give rise to the misrepresentation of sea ice simulations see. In the future, taking into consideration the size-, region-, and time-varying exponent could be useful for the parameterization of lead effects in models.

As noted previously, ICESat-2 measurements are not sufficient to determine the orientation of leads; however, previous studies using MODIS and AMSR-E found that leads greater than 1 km are anisotropic: more leads are found to align closer to the north-south direction (< 60° or > 120° east of north) than the west–east direction, although regional variations are present e.g.,.

The pan-Arctic spatial distribution of the climatological lead fraction in our study is qualitatively consistent with that from other satellites like MODIS , Envisat and CryoSat-2 . However, a quantitative comparison is challenging, given the different time periods in these studies and the different definitions in the lead fraction. For example, lead frequency, the ratio of lead counts over the total number of counts per pixel and month/year, is used to characterize sea ice occurrence in MODIS , while the percentage of lead waveforms are used in Envisat and CryoSat-2 work . We note that lead fraction reported here from ATL07 is likely substantially lower than those derived from the satellites mentioned above e.g.,, because ATL07 lead detection algorithm identifies only reliable specular leads.

As outlined in Sect. 2.2, we classify segments with freeboard height smaller than 3 cm as leads. Raising this threshold would result in the inclusion of more thin ice as recently closed leads, and vice versa. The impact of a large threshold is especially pronounced in regions of newly formed sea ice, where thin ice may be erroneously classified as leads.

To assess the influence of the freeboard height criterion on ATL10-derived lead detection, we select two ATL10 tracks across the Arctic in different time periods, one on 30 November 2018 during the growth season, and the other on when ice is near its seasonal maximum (1 March 2019; Fig. a, b). We then identify leads based on varying freeboard thresholds from 1 to 4 cm. The two freeboard snapshots on part of the tracks over thinner ice (Fig. c, d) and thicker ice (Fig. e, f) reveal a larger difference in lead detection in November over thinner ice with varying threshold values, compared to that in March and to regions with thicker ice during November. Indeed, the along-track lead fraction over thinner (< 80° N) and thicker (> 80° N) ice (Fig. g, h) exhibits the greatest relative increase in November south of 80°N, by 511 % when using a freeboard threshold of 4 cm instead of 1 cm. Despite the difference in the magnitude of lead fraction using varying thresholds, excluding November from our calculations does not qualitatively change the climatological and interannual variations in lead fraction (not shown). In fact, no perfect threshold can be selected, as ice grows quickly in new leads during winter. Therefore, instead of pursuing a perfect threshold, we use 3 cm, equivalent to the ice and snow thickness of ∼ 30 cm, regardless of seasons and sea ice states, to distinguish leads from pack ice and characterize the near pan-Arctic winter ice leads.

Another source of uncertainty in ATL10 lead detection arises from the reference sea surface used to derive freeboard height. As described in Sect. 2.2, the reference sea surface is not locally defined but instead represents the average sea surface height along a 10 km segment. In addition, if no reference surface can be determined due to lack of data, it is obtained through interpolation of adjacent surfaces. The uncertainties associated with the reference sea surface propagate to the freeboard estimates and, consequently, affect the lead detection.

Although our work used officially released ICESat-2 products to characterize the pan-Arctic lead fields in the ICESat-2 era, lead properties are dependent on the processing method, for example, the removal of dark leads in ATL07 and the freeboard threshold used in ATL10. Our study suggests that, despite the limitation in perfectly identifying the “true” leads, ICESat-2 is capable of representing lead characteristics in climatological and annual scales.

Ongoing efforts continue to improve the algorithm to detect leads from ICESat-2 measurements. These advances include, but not limited to, machine learning approaches developed by and , and improved photon aggregation and height filtering criteria introduced by . These new techniques were validated using coincident Sentinel-2 imagery, and are thus limited to specific times and locations. Extending the application of these new methodologies to the full record of ICESat-2 measurements over the entire Arctic could potentially reduce the uncertainties in lead statistics.

Our analyses focus on the winter season to minimize the effects from other open-water features such as melt ponds and polynyas. A new two-month ICESat-2-derived melt pond characteristics in the melting season has been published based on the density-dimension algorithm . A better quantification of the role of leads in the Arctic climate system over the melting season could be possible when a longer record of melt pond data becomes available.