We present a first examination of Arctic sea ice snow depth estimates from differencing satellite lidar (ICESat-2) and radar (CryoSat-2) freeboards. These estimates cover the period between 14 October 2018 and the end of April 2019. Snow depth is related to freeboard differences by the refractive index/bulk density of the snow layer—the only free parameter in the approach. Area-averaged snow depth ranges from 9 cm (on first-year ice: 5 cm, multiyear ice: 14 cm) in late October to 19 cm (first-year ice: 17 cm, multiyear ice: 27 cm) in April; on average, this snow is thinner over FYI. Spatial patterns and gradients of snow depth estimates compare well with reconstructions using snowfall from ERA-Interim and ERA5, although snowfall from ERA5 is systematically higher. For all months, the results suggest that ~50% of the total freeboard is comprised of snow. Retrievals are within a few centimeters of snow depth data acquired by Operation IceBridge in April 2019. Sources of uncertainties associated with this freeboard-differencing approach are discussed. Further, sea ice thicknesses calculated using the retrieved snow depth and a modified climatology are contrasted. Comparatively, the snow depth and calculated ice thickness using a modified climatology are higher by ~5 cm and 0.33 m, although these differences are not uniform throughout the season. Snow accumulation was slower between October and December but increased between December and January, unlike the modified climatology, which exhibited a monotonic accumulation for all months. Future opportunities for assessment and improvement of these estimates are discussed.
- Our current understanding of snow depth is based largely on climatology developed during last century and from recent airborne surveys
- We present a first examination of Arctic sea ice snow depth estimates from differencing satellite ICESat-2 and CryoSat-2 freeboards
- Sea ice thickness can now be calculated with snow loading from satellite retrievals without resorting to climatology or reconstructions
Plain Language Summary
The snow layer atop Arctic sea ice is an important component of the climate system. In winter, the insulating effects of snow slow the rate of ice growth. In spring, the onset of ice surface melt is delayed until the highly reflective snow layer disappears. During summer, meltwater from snow collects in depressions to form melt ponds, which enhances the absorption of solar radiation leading to more rapid surface warming. Presently, there are no routine measurements of snow depth suitable for assessing the impact of climate changes on the precipitation and accumulation of snow on sea ice. Our current understanding of snow depth is limited and has been based on field measurements conducted in the middle of last century and from airborne surveys conducted over the last decade. In this paper, we combine the measurements from two altimetry missions (ICESat-2 and CryoSat-2) to calculate snow depth over the entire Arctic Ocean. ICESat-2 (a lidar) and CryoSat-2 (a radar) measure the heights to the top and bottom of the snow layer, respectively. Differencing the two heights provides an estimate of the thickness of the snow layer. This paper describes this novel approach and an assessment of the snow depth estimates.
Snow is an integral element of the Arctic and Antarctic sea ice systems and one of the variables that controls the heat and energy balance between the ice, ocean, and atmosphere. Atop Arctic sea ice and its thermal and radiative properties modulate the thickness of the underlying ice cover (Maykut & Untersteiner, 1971). In winter, the insulating effects of snow slow the rate of ice growth (Sturm, Perovich, & Holmgren, 2002). In spring and summer, the onset of surface melt is delayed until the high-albedo snow layer disappears (Petrich et al., 2012). During the melt season, water from snowmelt collects in depressions to form melt ponds, lowering the surface albedo and further enhancing ice melt. This creates a strong positive feedback between increases in absorbed downwelling shortwave radiation and increases in the areal coverage of low-albedo ponds on the ice surface (Kwok & Untersteiner, 2011). The climatic importance of the snow cover in the two sea ice systems is well summarized in a recent paper by Webster et al. (2018). From a remote sensing perspective, estimates of snow loading are critically important for accurate retrievals of ice thickness from sea ice freeboard (e.g., Giles et al., 2007; Kwok & Cunningham, 2008).
Presently, there are no routine measurements of time-variable snow depth at spatial scales needed for freeboard-to-thickness retrievals, but there are numerous investigations of remote sensing techniques for addressing this gap in observations (e.g., Brucker & Markus, 2013; Fons & Kurtz, 2019; Guerreiro et al., 2016; Lawrence et al., 2018). In published approaches for calculating ice thickness (e.g., Kwok et al., 2009; Kwok & Cunningham, 2015; Laxon et al., 2013; Ricker et al., 2014; Tilling et al., 2015), snow depth is typically prescribed by adapting the somewhat dated climatology in Warren et al. (1999) or obtained indirectly through accumulation of snowfall from atmospheric reanalysis products (e.g., Blanchard-Wrigglesworth et al., 2018; Kwok & Cunningham, 2008; Petty et al., 2018). While these approaches seem to be adequate for providing large-scale trends in ice thickness and volume for climate assessments (Vaughan et al., 2013), the lack of snow depth observations limits the usability of the retrieved ice thickness for applications where higher spatial resolutions and improved accuracies are required (e.g., process studies, seasonal forecasts, and navigation). In addition to the retrievals of sea ice thickness, trends in observed snow depth are of broad interest for understanding Arctic changes and their role in global climate. Hence, large-scale time-variable estimates of snow depth by any means are desirable.
The potential of estimating snow depth from ICESat-2 (IS-2, a lidar altimeter) and CryoSat-2 (CS-2, a radar altimeter) freeboards was first examined in Kwok and Markus (2017). The measurement concept is based on differencing the freeboards from IS-2 (which measures the height of the air-snow interface above the local sea surface) and CS-2 (which measures the height of the snow ice interface above the local sea surface) and accounting for deviations in radar path length due to the refractive index of the snow layer (Figure 1). Overall, it is a rather straightforward calculation although there are complexities due to the lack of space-time coincidence of the two freeboard measurements. Presently, the combination of IS-2 and CS-2 satellites now in orbit presents a significant opportunity for examining the efficacy of deriving basin-scale snow depth retrievals from the lidar and radar freeboards using this approach.
In this paper, we provide a first examination of the Arctic snow depth estimates from differencing satellite lidar and radar freeboards for the winter months that span 14 October 2018—the beginning of IS-2 data collection—to the end of April 2019. We note at the outset that these are early results and our analysis does not provide an exhaustive or comprehensive examination of the quality of snow depth retrievals. There are many aspects of data quality, some of which will only be revealed by assessment with snow data acquired and processed by dedicated airborne campaigns (e.g., NASA's Operation IceBridge [OIB], Alfred Wegener Institute's IceBird), field programs (e.g., Multidisciplinary drifting Observatory for the Study of Arctic Climate [MOSAiC]), and when a longer IS-2/CS-2 time series becomes available.
The paper is organized as follows. The next section describes the IS-2 and CS-2 freeboards used to construct the snow depth estimates, the snow depth reconstructions derived from snowfall in ERA-Interim and ERA5 reanalyses, and the snow depth estimates from the snow-radar acquired during OIB. Section 3 discusses the measurement principle and the sampling of the satellite freeboards for calculation of snow depth estimates. Section 4 examines the spatial composites and distributions of the derived snow depth between October and April and compares these estimates to snow depth reconstructions. Section 5 assesses the retrievals with snow depth measurements from the OIB snow radar (SR). Section 6 discusses the uncertainties in the snow depth estimates. Sea ice thickness estimates using our freeboard-derived snow depth estimates are compared with those using a modified snow depth climatology in section 7. The last section concludes the paper.
2 Data Description
The following data sets are used: IS-2 and CS-2 freeboards; snow depth reconstructions derived from snowfall in ERA-Interim and ERA5 reanalyses; and surface heights from the Airborne Topographic Mapper (ATM) lidar and snow depth estimates from snow-radar, both acquired by OIB in April 2019. They are described below.
2.1 CryoSat-2 Freeboards
Along-track radar freeboards (from CS-2, Release C) are derived using the procedure described by Kwok and Cunningham (2015); the reader is referred to this article for a more detailed description of the retrieval approach and assessments of these freeboard estimates. As there are no direct assessments of these freeboard estimates, comparisons with available ice thickness measurements provide an indirect measure of data quality—Freeboard is approximately one-ninth of ice thickness. The assessed differences between CS-2 and various thickness measurements are (Kwok & Cunningham, 2015): 0.06 ± 0.29 m (ice draft from moorings), 0.07 ± 0.44 m (submarine ice draft), 0.12 ± 0.82 m (airborne electromagnetic profiles), and −0.16 ± 0.87 m (OIB) .
2.2 ICESat-2 (IS-2) Freeboards
Lidar freeboards are from the ICESat-2 ATL10 product (Release 002) distributed by the National Snow and Ice Data Center (Kwok, Cunningham, Markus et al., 2019). The ATL10 product provides sea ice freeboard estimates in 10-km segments that contain at least one sea surface reference. The height of a local sea surface reference (href) (i.e., the estimated local sea level) is from available sea ice leads (one or more) within a 10-km segment, and each lead may contain one or more consecutive sea surface height segments. Freeboard heights (hf), in 10-km segments, 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 where the height samples are at least 25 km away from the coast (to avoid uncertainties in coastal tides corrections). More details about the sea ice algorithms can be found in Kwok, Cunningham, Hancock, Ivanoff, and Wimert (2019) and a first assessment of the IS-2 freeboards in Kwok, Kacimi et al. (2019). In the following analyses, freeboards represent gridded (25-km) daily averages of the three strong IS-2 beams; their profiling ground tracks are separated from each other by 3.3 km.
2.3 Reconstructed Fields of Snow Depth
Daily fields of reconstructed snow depths are from two reanalysis products: ERA-Interim (Dee et al., 2011) and ERA5 (C3S, 2017), following the procedures described by Kwok and Cunningham (2008). In the procedure, daily snowfall on drifting ice parcels (100 km × 100 km) is computed on a daily basis. A daily process of accumulation and ice advection is carried out for each drifting Lagrangian parcel to mimic the process of snow accumulation on drifting ice but excludes higher order snow processes, such as blowing snow lost to leads. Ice drift is from optimally interpolated motion fields (described in Kwok et al., 2013). Starting on 1 October, accumulated snowfall on each drifting parcel is recorded through the end of spring. Surface conditions (2-m air temperature and ice concentration) determine whether snow is allowed to accumulate. In the approach, snow accumulates only when the air temperature is below freezing and the ice concentration exceeds 50%. When ice concentration dips below 50%, the accumulated snow is removed. As ice concentrations rarely drop below 50% within the perennial ice pack, this condition is only relevant over seasonal ice during the advancement of the ice cover in the fall. Typically, the snow is thinner where the ice cover is formed later in the season since the sea ice has less time to capture falling snow (Sturm, Holmgren, & Perovich, 2002; Webster et al., 2014). The snow density climatology in Kwok and Cunningham (2008) (a modified version of that used in Warren et al. (1999)) is used to convert the snow water equivalent of the precipitation into snow depth (Figure 2). An initial snow cover (based on the August climatology), representing snow that survived the melt season, is added to the ice at the beginning of the accumulation season.
2.4 Sea Ice Surface Height and Snow Depth From OIB
Surface heights are from the ATM (Studinger, 2019), a conical-scanning lidar system that provides surface profiling swaths at off-nadir scan angles of 15° or 2.5°. ATM data used here are from the 2019 OIB Arctic flights (specifically, 12 and 22 April). The lidar uses a laser wavelength of 532 nm, identical to ATLAS on ICESat-2, and profiles the surface (since 2017) with a 10-kHz pulse repetition frequency, 1.3-ns pulse width (comparable to 1.5 ns for ATLAS), and a scan rate of ~20 Hz. Per-sample height accuracy is ~7 to 10 cm. For a more detailed description of the ATM instrument and data set, the reader is referred to the following publications: Martin et al. (2012), Brunt et al. (2017), and Brunt et al. (2019). For the April 2019 flights (Kwok, Kacimi, Markus, et al., 2019, the system was operated at a flight altitude of 1,000 m (double the nominal flight altitude over sea ice) to allow the wide-scan system to extend the cross-track swath width to ~520 m. ATM freeboards are calculated by differencing the heights with the average heights in leads (openings in the ice cover).
Snow depth is from the OIB “quicklook” sea ice data set, which includes snow depth retrievals from the airborne SR (Kurtz, 2019). The SR on OIB is a frequency-modulated continuous-wave radar operated by the Center for Remote Sensing of Ice Sheets, University of Kansas. The ~6-GHz (2–8 GHz) bandwidth provides a range resolution of ~5 cm (in free space) capable of resolving the location of the air-snow (a-s) and snow-ice (s-i) interfaces (Panzer et al., 2013). The size of the average footprint is ~5–10 m, and the spacing between the processed radar profiles is ~5 m. The reader is referred to the published literature for a more detailed description of the radar system (e.g., Panzer et al., 2013) and the data characteristics (e.g., Kwok et al., 2011). Assessment of the snow depth retrievals (from the radar) in the Arctic with in situ measurements from two field programs shows that they are within a few centimeters, over relatively smooth surfaces, of those obtained with automated snow probes (Kwok et al., 2017).
3 Estimation of Snow Depth From Freeboards
Here, we describe the calculation of snow depth from differencing lidar/radar freeboards, the procedure to sample the freeboards from the two altimeter platforms to construct the monthly composites and discuss the sensitivity of the retrieved snow depths to uncertainties in bulk density.
3.1 Differencing IS-2 and CS-2 Freeboards to Obtain Snow Depth
ρw and ρi are the bulk densities of water and ice, respectively. These two equations are written to show their explicit dependence on the total (hf) and ice (hfi) freeboards.
This equation relates snow depth to the IS-2 and CS-2 freeboard differences (i.e., the observables) with one free parameter, ηs, which is dependent on the bulk snow density. In our calculations below, we use the modified climatological snow density with lower bulk density in the fall, shown in Figure 2 (Kwok & Cunningham, 2008), derived from (Warren et al., 1999).
3.2 Sampling Approach
For differencing freeboards, the two estimates would ideally be coincident in time and space. In our analysis, sampling is restricted to overlaps determined by the orbital configuration of the two different altimeter platforms. ICESat-2 was inserted into a 91-day exact repeat orbit with an inclination angle of 92° and a nominal orbit altitude of ~500 km. CryoSat-2 is in a 369-day repeat orbit at an altitude of 725 km, and ~92° of inclination. At these inclinations, both altimeters provide sea ice coverage to 88° latitude in the Northern and Southern hemispheres. With converging ground tracks at high polar latitudes, the density of crossovers is quite high. But even though the two instruments are near the same inclinations, the orbits are not aligned in time and space. And since neither the IS-2 nor the CS-2 surface profiles provide dense coverage of the surface, we are dependent on comparing near-coincident spatial averages of along-track freeboards from the two altimeters.
In the following, differences are calculated using gridded (25-km grids) daily fields of IS-2 and CS-2 freeboards. As noted earlier, the IS-2 freeboards are gridded averages (25-km) of the three strong IS-2 beams and thus provide a better sampling of the spatial mean. At each IS-2 grid cell, we calculate freeboard differences using samples with time separations |ΔT| < 15 day and CS-2 freeboards in neighboring grids cells that are within a 75-km box. We find that this sampling strategy provides the best sampling coverage without sacrificing precision. The selection of this sampling approach is based on a sensitivity analysis shown in section 6.
3.3 Sensitivity to Bulk Density
At 0.32 g/cm3 and an uncertainty in density Δρs of ±0.07 g/cm3 (average size of error bars in Warren et al., 1999), the uncertainty in the snow depth is ~4% of the difference in freeboard. For a 30-cm freeboard difference, this translates into ~1-cm uncertainty in snow depth. The sign in the above equation indicates that the snow depth will be underestimated if the density is overestimated. This analysis suggests that snow depth is relatively insensitive to uncertainties in the bulk density.
As above, at 0.32 g/cm3 and an uncertainty in density Δρs of ±0.07 g/cm3, the uncertainty in thickness is ~70% of the freeboard difference. For a 30-cm freeboard difference, the uncertainty in density translates into ~0.2-m uncertainty in thickness. As expected, for a fixed freeboard, an overestimation in density leads to an underestimation in snow depth (above) and an overestimation of ice thickness since a larger fraction of freeboard is now assigned to the higher density ice instead of snow. If a Δρs of ±0.07 g/cm3 is indeed realistic, the above values provide bounds on density-induced errors in snow depth and sea ice thickness estimates. In any case, the above provides guidance on the expected sensitivity to the one free parameter in our simple model to convert freeboard differences to snow depth.
4 Snow Depth Estimates
In this section, we first compare the spatial patterns and distributions of the monthly snow depth composites with snow depth reconstructions from ERA-Interim and ERA5 reanalysis products. Then, we examine the relationship between snow depth and total freeboard. Here, the Arctic Ocean is defined as the region bounded by the gateways into the Pacific Ocean (Bering Strait), the Canadian Arctic Archipelago (CAA), and the Greenland (Fram Strait) and Barents Seas (Figure 3).
4.1 Monthly Composites of Snow Depth and their Distributions
Figure 3 shows the monthly composites of all IS-2 and CS-2 freeboards and snow depth from differencing the two altimeter freeboards (hΔf) and reconstructions using estimates of ERA-Interim (hERA - I) and ERA5 (hERA5) snowfall. The composite fields are on a 25-km grid, and the displayed fields are smoothed with a 25-km Gaussian kernel. The hERA - I and hERA5 composites are subsampled averages of their daily fields: to better mimic the incomplete spatial sampling by the daily hΔf fields in the monthly composites, we first mask the daily fields of hERA - I and hERA5 with the daily fields of hΔf. That is, we retain the values of hERA - I and hERA5 only if there exists a corresponding estimate of hΔf; this is so that the sampling is matched in resulting monthly composites. The associated freeboard and snow depth distributions are shown in Figure 4.
The spatial patterns in the hΔf, hERA - I, and hERA5 fields, during the early winter months of October, November, and December, agree well qualitatively. While it is difficult to argue that the data sets (hΔf, hERA - I, and hERA5) by themselves are physically realistic, the correlations of the large spatial features provide corroborative evidence and lend credence that the first-order changes in snow depth are being reproduced by these approaches. Over the Arctic Ocean, there is a distinct gradient in snow depth across the ice cover from Greenland to Siberia, and the development of the tongue of thicker snow on multiyear ice (MYI) is definitely captured in all the fields (see tongue in MYI distribution in Figure 9).
Distinctive modes can be seen in the snow depth distributions in Figure 4. Between October and December, the hΔf distributions (Figure 4b) are distinctly bimodal. The first mode of the October distribution consists of samples of thinner snow over young seasonal ice (modal peak ~2 cm) with low freeboards (dark blue in the composite) characteristic of an advancing ice cover. The higher secondary peak of ~11 cm is snow on older ice at high Arctic latitudes north of the CAA and Greenland coast. Deeper snow in this region may be from snowfall early in the growth season (i.e., after late September) and/or residual snow from the previous season. Anecdotally, however, snow is no longer expected to survive the summer as ponds due to snowmelt are pervasive throughout the Arctic; this has yet to be confirmed on a broader scale. As the area of the ice cover advances in November and December, the snow depth only grows to ~9.6 cm. In the distribution plots, the increasing coverage of the seasonal snow cover can be seen in the growth of first-year ice (FYI) population compared to the relatively static MYI population.
Past December, the snow depth in both the hERA - I and hERA5 monthly composites are thicker than those in the hΔf fields, even though the spatial patterns remain similar. This is expected as there are no loss terms in our reconstruction algorithm. The treatment of the daily snow estimates does not account for the wind redistribution of snow, losses into open leads, or changes due to divergence/convergence of the ice cover, and deposition and sublimation are assumed to be negligible. Thus, in the reconstructions, the snow accumulates and snow depth increases over time. Over MYI, the snow depth is the total accumulation since the start date of the reconstruction. On seasonal ice, the first date of snow accumulation is variable. After the initial creation of that ice parcel, the age of seasonal ice due to ice deformation within a grid cell is not resolved. Also, it can be seen that hERA - I > hERA5; the ERA5 reanalysis products have been shown to report higher snowfall when compared to ERA-Interim (Wang et al., 2019).
One other spatial feature of note is the development of the snow cover in the Chukchi Sea which began in January. The correspondence in the hΔf, hERA - I, and hERA5 composites as well as the IS-2 and CS-2 freeboard composites suggests that this regional increase in snow depth is due to enhanced snow accumulation. To investigate snowfall conditions for this season, we examined the number, strength, and snowfall of cyclones, which is the primary source of snow accumulation in the Chukchi region (Webster et al., 2019). Using the Melbourne University Cyclone Tracker (Simmonds et al., 2008), we found heightened cyclone frequency, intensity, and cyclone-associated snowfall in the western Chukchi region for the 2018–2019 winter period relative to the 1979–2019 climatological mean (Figure 5). Collectively, these results indicate that the localized area of deep snow in the Chukchi Sea is likely a geophysical feature and further demonstrates the utility of hΔf for investigating the first-order processes that drive snow depth heterogeneity in this region (Webster et al., 2014).
Figure 6 summarizes the seasonal evolution of the Arctic snow cover. The snow depth (hΔf) ranges from an average of ~9 cm (FYI: ~5 cm; MYI: ~14 cm) during the second half of October to ~19 cm (FYI: ~18 cm; MYI:~27 cm) in April. The numerical values are shown in Table 1. The results show a relatively slow buildup of the snow cover between October and December with a larger increase between December and January, followed by slower growth for the remainder of the winter. The retrieved snow depth can be compared to those from reconstructions. In general, the growth in the two reconstructed fields is more monotonic and does not exhibit the features seen in the retrieved data. The hERA - I reconstructions are closer to hΔf, while the hERA5 reconstructions are expected to be higher (Wang et al., 2019).
4.2 Relationship Between Freeboard and Snow Depth
The large-scale relationship between snow depth and total freeboard is of geophysical interest as it provides a broad connection between the two parameters. Such a relationship, if reliable, could be potentially useful for providing rough estimates of snow depths where there are gaps in observation. Figure 7 shows the monthly scatterplots of hΔf and IS-2 total freeboard for November to April. At the length scale here, the regression analysis (regression slope, intercept, and standard error in each plot) shows that the two values are highly correlated (with the freeboard explaining >80% of the variance in snow depth). The negligible intercepts (<1.6 cm) also make geophysical sense as one should expect zero snow depth at near zero freeboard.
The slopes vary between 0.51 and 0.55 between November and April and tell us the fraction of the total freeboard that is composed of snow. For this winter at least, these regression results suggest that approximately half of the total freeboard could be made up of snow. And, the standard errors of <3 cm throughout the season suggest skills that would be useful for predicting snow depth where only total freeboards are available.
5 Comparison With Snow Depths From OIB Data
To assess the quality of snow depths derived from satellite freeboard differences, we compare the retrievals with snow depth estimates from the SR and the OIB instruments. First, we examine the temporally coincident along-track snow depths derived from the IS-2 and ATM lidar freeboards (i.e., by differencing with CS-2 freeboards); these results serve to demonstrate the efficacy of the differencing approach using near-coincident data sets. Second, we show the relationship between gridded mean snow depths in the monthly composites and those from the OIB SR. The OIB data set used here was acquired during the Arctic campaign in April 2019.
5.1 Comparisons With Retrieval Along the SR Track and the IS-2 Track
In a recent study (Kwok, Kacimi, Markus, et al., 2019), the ATM and the IS-2 data were coregistered from four under flights during the 2019 OIB Arctic deployment to assess IS-2 height retrievals. These results showed that, for a total of 99 10-km segments where there was coincident coverage, the average correlation between the profiles were >0.95. In particular, on 12 and 22 April, there were clearly identifiable leads in both the IS-2 ATL07 product and OIB optical imagery (CAMBOT) that allowed the estimation of local sea levels for calculation of the two lidar freeboards. From these freeboards, independent snow depth estimates from both the ATM and IS-2 instruments were calculated (by differencing with CS-2 radar freeboards). In all the calculations below, radar freeboard is the closest CS-2 freeboard that is within a ±15-day time window and a distance of 25 km. Here, we focus on snow depths calculated over two 80-km long segments from the two days. The coregistered profiles are averaged to ~2-km resolution, with 1-km postings.
First, we compare snow depths from freeboard differences (i.e., IS-2 minus CS-2 and ATM minus CS-2 freeboards) along the IS-2 track. Figures 8a and 8b (top panels) compare the retrievals of two 80-km segments. The ATM-derived snow depths were 22.0 cm (12 April) and 28.0 cm (22 April). Because the ATM and IS-2 heights are highly correlated, the two derived snow depths similarly correlated as well (~0.98). The mean difference between the IS-2- and ATM-derived snow depths are 0.3 cm (12 April) and 3.7 cm (22 April).
Second, we compare the ATM-derived snow depths along the IS-2 track (from above) with ATM-derived snow depths along the SR tracks. The SR tracks are not in general coincident with the IS-2 tracks even though they were within the 420-m ATM swath; i.e., they are displaced across track. For this, ATM freeboards were first calculated at the SR footprints along the 80-km segment and then, as above, averaged to 2-km resolutions with 1-km postings. The mean snow depths of the ATM-derived freeboards (along the SR track) were 22.7 cm (12 April) and 28.6 cm (22 April). Compared to the ATM-derived freeboards (along the IS-2 track) above, the differences were −0.7 cm (12 April) and −0.6 cm (22 April). The cross-track separation between the IS-2 and SR tracks was ~12 m on 12 April and ~155 m on 22 April. This suggest that within this range of separation, the variability in mean snow depths (at the 80-km scale) is small.
Third, freeboard-derived snow depths (above) were compared with snow depths from the OIB SR. Along the SR track, there are gaps (up to 40%) in the SR retrievals. As well, the bandwidth of the radar system imposes a lower limit on the resolvable snow depth to ~10 cm. Thus, along-track averages without accounting for these gaps in observations are typically overestimated compared to the true value. The means of the SR estimates were 18.1 cm (12 April) and 30.9 cm (22 April). This results in differences of 4.7 cm (12 April) and −2.3 cm (22 April) when compared with snow depths along SR tracks. As mentioned above, these results serve to demonstrate the efficacy of the differencing approach for obtaining snow depths.
5.2 Comparison With Composite Means
The snow depths from the OIB SR can be compared with estimates in the monthly composites. We note here that the SR snow depths are representative of neither the time mean of a grid cell nor the spatial mean of that cell (at a given time) in the gridded monthly composite because the sampling of the SR tracks provides only limited coverage of the 25-km grid at a specific time. That is, the SR sample statistics represent but one realization of an underlying distribution. Hence, correspondence between the SR estimates at a point in time and the monthly mean is not expected. Instead of direct comparison of the two values, we show the SR snow depths in the population of derived IS-2/CS-2 estimates (at the SR grid cell) for that month. Figures 9b and 9c show the time-variable IS-2/CS-2 snow depths from the three IS-2 strong beams that were used to estimate the composite mean for April. As a reminder, the strong beams are separated from one another by ~3.3 km.
First, as expected, on the two days where we had near coincident IS-2 and ATM (on 12 and 22 April), the results are as above (i.e., differences were within a few centimeters). Second, the correlations between the strong beams are higher at the 12 April grid cell compared to 22 April. In terms of spatial variability, 22 April is located in a region where there is a high fraction of rougher MYI (see Figure 9a) suggesting one source of local variability in the beam-to-beam retrievals. Last, for both grid cells, the time variability over the month is likely due to the advection of regions of different snow depths through the grid cell or due to sampling issues (discussed in the next section). The time-variable retrievals over a month provide a measure of the grid level variability, which is 6.0 and 4.9 cm for the two grid cells. From the three strong beams at latitudes above 80oN where orbits converge, there can potentially be a large population of independent observations that contributes to the monthly average. For the locations here, there were 77 and 25 on 12 and 22 April grid cells, respectively.
6 Sources of Uncertainty
In this section, we first examine the sensitivity of the snow depth calculations to space-time sampling differences because the two satellite freeboards are not measured simultaneously. Second, we discuss briefly the likely impact of ice deformation. Last, we address the potential impact of biases in CS-2 freeboards due to scattering within the snow layer.
6.1 Sampling Considerations
The variability in retrieved snow depth and coverage due to space-time sampling is examined here. The results in earlier sections are based on differencing freeboard samples with time separations |ΔT| < 15 day and using CS-2 freeboards that are within a 75-km box. To examine the sensitivity to space-time sampling, we obtain retrievals with time separations |ΔT| < 1, <10, and < 15 days. And, for each of the three time separations, we use available CS-2 freeboards at the collocated grid cell and in eight neighboring grids cells (i.e., within a 75-km box). This gives us six space-time combinations for assessing the snow depth sensitivity of the retrievals to spatiotemporal sampling differences.
For the six sampling combinations, the standard deviations of the differences in calculated snow depths are all less than 1 cm, which suggests that the spatial variability of the CS-2 freeboards is low. At larger spatial scales (averages), low spatial variability in CS-2 freeboards is expected; since during winter, in the absence of ice deformation, the spatial variation is dominated by basal growth and snow loading. In fact, these two processes act against each other although at different time scales: Basal growth increases freeboard while snow accumulation depresses freeboard. Physically, thermodynamic growth is a temporally slow process (seasonal time scale) and less than ~10% of the growth in thickness adds to freeboard. Precipitation is a more episodic process but only ~3% of any change in snow depth adds to changes in ice freeboard. This can be seen in the IS-2 and CS-2 freeboard distributions with considerably greater variability in the IS-2 freeboard distributions (Figure 4). Given the low variability of CS-2 freeboard, the larger variability in IS-2 freeboards is primarily due to spatial variability in the distribution of snow—the parameter of interest of this analysis. Indeed, the variability of the area-averaged IS-2 freeboard between October and April (18.9–34.0 cm) is more than double the range of the CS-2 freeboards (8.5–10.3 cm).
The low spatial variability of ice freeboards allows us to extend the boundaries of space-time sampling of the CS-2 freeboards. The advantage of longer time separations and looking over longer distances for CS-2 freeboards is the added coverage for constructing full composites at the basin scale. In fact, increasing the time-separation tolerance to 10 days provides the best gain in coverage of more than 40% (Table 2).
|Space/time||25 km/1 day||25 km/10 day||25 km/15 day||75 km/1 day||75 km/10 day||75 km/15 day|
6.2 Ice Deformation
Ice deformation is an episodic and localized process. For a material element on the ice cover, while ice volume is conserved, total freeboard increases with convergence (ridging and rafting) and decreases with divergence (open water formation). Since the sampling of the satellite freeboards for snow depth calculations is not simultaneous, variability would be introduced when processes are not sampled at the same time. Furthermore, the impact of asymmetric sampling in time would depend on the time order of satellite observations. If the CS-2 freeboards were sampled at an earlier time than the IS-2 freeboards, a convergence (divergence) event that occurred in the interim would cause the snow depth to be overestimated (underestimated). If the CS-2 freeboards were sampled after the IS-2 freeboards and a convergence (divergence) event occurred between sampling, the snow depths would be underestimated (overestimated). In practice, the sampling of the CS-2 freeboards is centered around the time of the IS-2 freeboards. Thus, if the events were random, they would increase the snow depth variance but have a small impact on the average monthly snow depth. The above analysis (section 6.1) shows, however, that, in all of the six combinations of space-time sampling, the standard deviations in retrieved snow depths were less than a centimeter. These results suggest that the effect of sea ice dynamics in biasing the results may be small.
6.3 Radar Freeboards and Location of the Snow-Ice Interface
This works out to be −0.37 m for a 7-cm adjustment and can be compared to the FYI thickness estimates discussed in the next section. While the physical basis of a displacement of the RP due to brine wicking is sound, we do not believe that we understand the prevalence of this process over Arctic sea ice and the life cycle of brine that has been wicked into the snow layer, i.e., whether it is persistent throughout the season once present, to warrant implementation at this time.
In our approach, we assume that the radar derived surface is from the snow-ice interface. Hence, snow depths in some instances may be underestimated if the snow processes described above occur regularly. And, the assessments in section 5 are limited to regions over the MYI cover. We do not have a way at this point in time to address the realism of the suggested adjustment and the implication of this issue in our retrieval algorithm, but anticipate that coordinated field and remote sensing observations like those from the MOSAiC expedition will prove useful in understanding the ubiquity of these processes such that corrections can be applied appropriately.
7 Ice Thickness Using Satellite Snow Depth and a Modified Climatology
Here, the aim is to examine the spatial and temporal differences for the 2019 winter (October 2018 through April 2019). The sea ice thickness composites using freeboard-derived and climatological snow depths and their differences and distributions are shown in Figure 10, and the monthly values are shown in Figure 11. The monthly plots show the development of the snow and ice covers. The ice thickness values are in Table 3. Briefly, the mean freeboard-derived snow depths ranges from 8.1 cm in October to 18.6 cm in April, while the mean KC15 snow depths ranges from 13.6 to 22.6 cm for the same two months. This is a difference of 5.5 cm in October and 4 cm in April. Similarly, the mean Arctic Ocean ice thickness using freeboard-derived snow depths ranges from 1.15 m (FYI: 0.6 m; MYI: 1.66 m) in October to 2.07 m (FYI: 1.85 m; MYI: 3.23 m) in April. This can be compared to 1.45 m (FYI: 0.9 m; MYI: 2.17 m) and 2.23 m (FYI: 1.96 m; MYI: 3.76 m) for the same two months in the KC15 fields. This gives a difference in mean thickness of 0.30 m (FYI: 0.30 m; MYI: 0.51 m) in October and 0.15 m (FYI: 0.10 m; MYI: 0.53 m) in April.
|Thickness (m)||Freeboard-derived||Modified climatology||Differences|
Broadly, it can be seen that (1) both snow depth and ice thickness are higher in the KC15 fields compared to the freeboard-derived fields; (2) the differences decrease after January; and (3) there are larger differences over the MYI regions north of the CAA and Greenland coast. The thicker ice in the KC15 fields (Figure 10), using CS-2 freeboards, is due to higher prescribed snow depth and therefore higher snow loading. Over the entire 6.5-month growth season, the average difference in monthly mean thicknesses is 0.33 m (FYI: 0.23 m; MYI: 0.58 m). The monthly differences are, however, not uniform throughout the season; they are higher between October and December. The reduced difference after January (Figure 8b, Table 1) is a consequence of the larger increase in freeboard-derived snow depth in December and January. If the freeboard-derived snow depths (Figures 4a and 8a) were indeed a more realistic depiction of the monthly variability in 2019, then the prescribed climatology is inadequate for understanding seasonal variability even though the end-of-season differences are only ~0.15 m. While it is clear that a fixed climatology does not capture the interannual variability in the development of the snow cover, the results here highlight the seasonal variability associated with potentially more realistic snow depths. Over MYI, the thicker ice is due to the deeper snow prescribed by equation 14.
In this paper, we provide an examination of Arctic snow depth from differencing satellite lidar (ICESat-2) and radar (CryoSat-2) freeboards. These snow depths represent the first time-variable basin-scale estimates from satellite altimetry. The present analysis covers the period between 14 October 2018 and the end of April 2019. The derived snow depth was assessed with snow depth reconstructions and available snow depth measurements from the SR on OIB. Arctic sea ice thickness calculated with these snow depth estimates were compared with estimates from a modified snow climatology. Below, we highlight some of the results and discuss future opportunities for validation and assessment of this retrieval approach.
Over one Arctic growth season, the retrievals show that area-average snow depth ranges from ~8 cm (FYI: ~4 cm; MYI: ~12 cm) in late October to ~19 cm (FYI: ~17 cm; MYI: ~27 cm) in April. Similar to ice thickness, higher snow depths are found over the thicker ice north of the CAA and Greenland coasts. Seasonally, results show a relatively slow buildup of the snow cover between October and December, a larger increase between December and January, followed by slower growth for the remainder of the winter. Spatial patterns of snow depth estimates compare well with reconstructions with snowfall from ERA-Interim and ERA5, although the ERA5 reconstructed snow depths are systematically higher. April retrievals are within a few centimeters of snow depths acquired by the SR on OIB.
Estimates of sea ice thickness using the retrieved snow depths are compared with estimates (from CS-2 freeboards) from a modified snow climatology. Overall, the area-averaged snow depth and sea ice thickness from the modified climatology are higher by ~5 cm and 0.33 m, although these differences vary over the season. The seasonal cycle in snow depth in 2019, specifically thinner snow between October and December followed by higher growth in the snow cover between December and January, was not captured by the monotonic increase in snow depth of the somewhat dated snow depth climatology developed using field data from the last century. Consistent sea ice thickness can now be calculated, using snow depth estimates constrained by satellite retrievals, without resorting to climatology or reconstructions.
As a first examination, the results are potentially useful even though the sampling of the two freeboards is not simultaneous and coincident. At short time scales (days), the variability of CS-2 freeboards is low, and the results suggest that the variability in snow depth is explained largely by variability in IS-2 freeboard. At the grid scale considered here (25 km) and in the absence of ice deformation, CS-2 freeboards are primarily affected by basal growth and snow loading. Less than ~10% of the growth in sea ice thickness adds to the ice freeboard, whereas only ~3% of any increase in snow depth contributes to ice freeboard. Thus, the freeboard differences should be relatively robust, but the potential biases in CS-2 freeboards due to the presence of brine near the snow-ice interface in seasonal ice remain an issue to be addressed (Nandan et al., 2017).
The present analysis, however, is only a first step in understanding the approach and does not constitute a comprehensive evaluation of its efficacy. There are many aspects of data quality, some of which will only be revealed by assessment with data acquired and processed by dedicated airborne campaigns (e.g., NASA's OIB, and AWI's IceBird), upcoming field programs (e.g., MOSAiC), and when a longer IS-2/CS-2 time series become available.
An important data set for assessment of our approach will be the field data collected by the MOSAiC program (https://mosaic-expedition.org). The year-long MOSAiC observatory embarked on its journey on 20 September 2019. At this writing, the observatory has been frozen into the ice in the eastern Arctic Ocean, and the drift track is expected to take it across the Arctic exiting the Fram Strait in mid-2020. Along the drift track, the sea ice team plans to make detailed measurements of snow (e.g., density, depth, and salinity profiles) and ice properties and their evolution over the course of the year. Since the MOSAiC drift will mostly be above 80°N, there will be dense satellite (IS-2 and CS-2) coverage of the area around the observatory. The combination of the satellite data and the continuous measurements from MOSAiC on the development of the snow environment will provide an invaluable seasonal-cycle data set (a once in a blue moon opportunity) for validating and improving our understanding of the fields of snow depths derived here. Importantly, the MOSAiC sampling plan will provide measurements at a length scale suited for comparisons with satellite retrievals.
From the remote sensing perspective, improving the near space-time coincidence of IS-2 and CS-2 freeboards is also crucial for assessment of methodology described herein. ICESat-2 was inserted into a 91-day exact repeat frozen orbit with an inclination angle of 92°, and CryoSat-2 is in a 369-day repeat orbit with the same inclination. Both altimeters provide sea ice coverage up to 88° latitude in both hemispheres, and the converging ground tracks at polar latitudes provide high density of crossovers. However, even though the orbits of the two platforms are near the same inclination, the orbits do not offer the best coverage (in time and space) to explore the synergies between the lidar and radar measurements. Adjusting the orbits to provide improved coincidence in space-time sampling of the surface, to minimize aliasing of geophysical processes (snowfall and snow mass redistribution in this case), is obviously of significant interest to the science community. This motivated the formation of a Joint NASA-ESA working group to explore this opportunity, while there is an overlap in the IS-2 and CS-2 missions, to “tune” the CS-2 orbital parameters slightly to improve the time separation between near coincident IS-2 and CS-2 measurements (crossovers and along-track sampling). A study is being prepared by the working group to provide inputs on potential benefits to improvements of snow depth estimates and recommendations for adjusting the CS-2 orbit. If the CS-2 orbit was adjusted, it will provide a crucial data set for not only understanding the current retrievals but also the design of future instruments for the measurement of Arctic Ocean snow depth.
ERA-Interim data sets are available at https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era-interim. ERA5 data sets are available on the Copernicus Climate Change Service (C3S) Climate Data Store (https://cds.climate.copernicus.eu/#!/search?text=ERA5&type=dataset). The OIB Airborne Topographic Mapper data used here are available at http://nsidc.org/data/ILPATM1B/versions/1. The OIB CAMBOT data are available at http://nsidc.org/data/IOCAM1B/versions/2. The OIB sea ice freeboard, snow depth, and thickness “quicklook” data can be found at https://daacdata.apps.nsidc.org/pub/DATASETS/ICEBRIDGE/Evaluation_Products/IceBridge_Sea_Ice_Freeboard_SnowDepth_and_Thickness_QuickLook/. The ICESat-2 data used herein are available at https://nsidc.org/data/icesat-2/data-sets. The monthly snow depth composites derived here will be made available on pangaea.de prior to publication. M.A.W. acknowledges support by the National Aeronautics and Space Administration's New Investigator Program in Earth Science. R.K. and S.K. carried out this work at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.
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