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Potential basin-scale estimates of Arctic snow depth with sea ice freeboards from CryoSat-2 and ICESat-2: An exploratory analysis
Available online at www.sciencedirect.com
ScienceDirect Advances in Space Research xxx (2017) xxx–xxx www.elsevier.com/locate/asr
Potential basin-scale estimates of Arctic snow depth with sea ice freeboards from CryoSat-2 and ICESat-2: An exploratory analysis R. Kwok a,⇑, T. Markus b a
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA b NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA
Received 24 January 2017; received in revised form 30 August 2017; accepted 5 September 2017
Abstract The potential of deriving snow depth estimates using differences in freeboard heights from CryoSat-2 (CS-2) and ICESat-2 (IS-2) is examined. In our analysis, we use lidar freeboard from the Airborne Topographic Mapper (ATM) on Operation IceBridge (OIB) as proxy of IS-2 total (snow + ice) freeboard. Snow depths are estimates from the OIB snow radar. Differences in height between the total (ATM) and ice (CS-2) freeboards are related to snow depth by the refractive index of the snow layer ðgs Þ, which is dependent on snow density. For two years (2014 and 2015), regression of the ATM and CS-2 freeboard differences against OIB snow depth gives correlations of 0.80, estimated gs of 1.21, and standard errors of 8 cm. The resulting refractive index, gs , can be compared to that expected of the Arctic snow cover in early spring (1.25 ± 0.05). The expected biases and variability in the regression analysis are discussed. Results suggest that snow depth can be estimated from the freeboard differences. The benefits of adjusting the orbit of CS-2 for providing more optimized overlaps between IS-2 and CS-2 are considered. Ó 2017 COSPAR. Published by Elsevier Ltd. All rights reserved.
Keywords: CryoSat-2; ICESat-2; Sea ice; Snow depth; Arctic; Antarctic
1. Introduction NASA’s ICESat mission (Zwally et al., 2002) was completed in 2009 while ESA’s CS-2 mission (Wingham et al., 2006) is currently in operation. These altimetry missions are dedicated to the acquisition of spaceborne observations for quantifying changes in the ice masses of the Earth System, and their impact on global climate. Significantly, satellite estimates of sea ice thickness and volume made in the period 2003–2008 (ICESat) (Kwok et al., 2009) and 2010–2012 (CryoSat-2) (Laxon et al., 2013) have contributed to the last Intergovernmental Panel on Climate Change (IPCC-AR5) assessment of recent declines in Arctic sea ice (Vaughan et al., 2013). With the planned launch
of ICESat-2 (IS-2) (Markus et al., 2017) (scheduled for late 2018) to continue the altimetry time series to inform changes in the cryosphere, there may be a unique opportunity to obtain near-coincident altimetry of the Arctic sea ice cover from both a lidar (IS-2) and a radar (CS-2) for the extraction of snow depth from these measurements. In this paper, we use available data sets to explore and assess the feasibility of such calculations. The calculation of sea ice thickness (hi ) from total (snow + ice, hf ) or ice-only freeboard (hfi ), assuming isostatic equilibrium, requires an estimate of the snow loading at the surface (i.e., snow depth – hfs and snow density –qs ), viz. (see Fig. 1),
⇑ Corresponding author.
E-mail address: [email protected] (R. Kwok).
hi ¼
qw qs qw hf þ hfs q w qi qw qi
ðfor lidarÞ
https://doi.org/10.1016/j.asr.2017.09.007 0273-1177/Ó 2017 COSPAR. Published by Elsevier Ltd. All rights reserved.
Please cite this article in press as: Kwok, R., Markus, T. Potential basin-scale estimates of Arctic snow depth with sea ice freeboards from CryoSat-2 and ICESat-2: An exploratory analysis. Adv. Space Res. (2017), https://doi.org/10.1016/j.asr.2017.09.007
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R. Kwok, T. Markus / Advances in Space Research xxx (2017) xxx–xxx
snow
hfs hfi
hf hfi
hi hSSH
sea water Fig. 1. Relationship between the different height quantities discussed in the text.
hi ¼
qw qs hfi þ hfs qw qi qw qi
ðfor radarÞ
qw and qi are the bulk densities of water and ice, respectively. These equations are written to show explicitly the lidar and radar observables – hf and hfi – from the two altimetry missions. For the selected electromagnetic wavelengths of ICESat-2 and CS-2, the lidar and radar returns are assumed to be – when the temperature is below freezing – from the air/snow interface and the snow/ice interface, respectively, thus providing observations of total and ice freeboard relative to the local sea surface. Presently, there are no direct measurements of time-variable snow depth at the spatial scale needed for thickness calculations. In published approaches (e.g., Kwok and Cunningham, 2015; Kwok and Cunningham, 2008; Laxon et al., 2013), the snow depth is typically prescribed by modifying the climatology in Warren et al. (1999), or obtained indirectly through accumulation of snowfall from meteorological analyses (Kwok and Cunningham, 2008). While these approaches seem to be adequate for providing large-scale trends in ice thickness and volume for climate assessments, 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). In fact, the results by Guerreiro et al. (2016) – by analyzing data from two radar altimeter missions – suggest a snow cover that is thinner than the snow climatology (Warren et al. (1999)). In addition to the retrievals of sea ice thickness, trends in observed snow depth is also of interest for understanding Arctic changes and its role in global climate. Hence, direct estimates of snow depth by any means are desirable. It is clear that the snow depth can be calculated as the simple difference in the freeboard heights from the lidar and radar (i.e., hfs ¼ hf hfi ; Fig. 1). However, there are differences in the spatial resolution and the time-space sampling (i.e., orbit inclination, repeat cycles, etc.) between IS2 and CS-2 instruments. The questions are how well retrieval of snow depth could be and whether this could be
demonstrated with available data sets. In the present analysis, we examine the potential of deriving snow depth estimates using differences in freeboard heights from the lidar and radar altimeters. The aim is to motivate the two space agencies, NASA and ESA, to exploit the unique opportunity of providing near-overlapping coverage from two satellite missions (one instrumented with a radar altimeter and the other with a lidar) for snow depth retrieval, by slight adjustments to the CS-2 orbital configuration. At the outset, we note that this is an exploratory exercise and by no means an in-depth analysis of all aspects of the problem because of the limitations of the data sets that are available. The paper is organized as follows. The next section describes the three primary data sets used in our analyses. Section 3 defines the relationship between snow depths and the measured lidar and radar freeboards, examines the snow depth estimates from the two freeboards, and discusses the expected biases and variability. The last section discusses the potential of adjusting the orbit configurations of IS-2 and CS-2 for snow depth estimation, and concludes the paper. 2. Data description The three data sets of interest are the sea ice freeboard from CryoSat-2 (CS-2), the total freeboard (snow + ice) from the Airborne Topographic Mapper (ATM), and the snow depth estimates from the ultra-wideband snow radar (SR) from Operation IceBridge. During IceBridge campaigns, the ATM and SR instruments are operated simultaneously and provide near coincident coverage, albeit at different spatial resolutions. In this section, we provide a brief description of the performance and coverage of these radar and lidar systems. 2.1. CryoSat-2 freeboard Gridded 30-day fields of CS-2 ice freeboard are those from Kwok and Cunningham (2015). Values at grid cells (on a 12.5 km grid) are binned composites of freeboard estimates from all orbits (420 orbits) for a 30-day period. The reader is referred to Kwok and Cunningham (2015) for a more detailed description of the retrieval procedures and quality of these fields. As there are no direct freeboard estimates, comparisons with available ice thickness measurements provide an indirect measure of quality: freeboard is approximately a fraction (one-ninth) of ice thickness. The assessed differences between CS-2 and various thickness measurements are: 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 (Operation IceBridge). 2.2. IceBridge ATM freeboard Surface elevations are from the IceBridge Narrow Swath ATM Level-1B lidar Elevation and Return Strength data
Please cite this article in press as: Kwok, R., Markus, T. Potential basin-scale estimates of Arctic snow depth with sea ice freeboards from CryoSat-2 and ICESat-2: An exploratory analysis. Adv. Space Res. (2017), https://doi.org/10.1016/j.asr.2017.09.007
R. Kwok, T. Markus / Advances in Space Research xxx (2017) xxx–xxx
set (Krabill, 2014). This data set contains ATM spot elevation measurements (1–2 m footprint) over sea ice. ATM scanning geometry provides an across-track scan swath of 45 m with typical elevation accuracy better than 10cm. Total (snow + ice) freeboard from the lidar were derived from the IceBridge Narrow Swath elevation data using the approach described by (Kwok et al., 2012). The ice freeboard of an elevation sample is calculated only when an open water surface within 10 km is present (i.e., leads) to serve as height reference. Sea surface references are identified in high-resolution visible imagery acquired by the Digital Mapping System (Dominguez, 2010). 2.3. IceBridge snow depth Estimates of snow depth were derived from the IceBridge Level-1B Radar Echo Strength Profiles data set (Leuschen, 2014) from the snow radar. This frequency-modulated continuous-wave (FM-CW) radar is operated by the Center for Remote Sensing of Ice Sheets (CReSIS) at the University of Kansas. The large bandwidth (6 GHz) provides a range resolution of 5 cm (in free space) for resolving the location of the air-snow (a-s) and snow-ice (s-i) interfaces (Panzer et al., 2013). With averaging, the spot separation is 5 m along track at an altitude of 500 m and an air speed of 250 kts (the nominal flight parameters for all OIB sea ice surveys). 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 of the data characteristics (e.g., Kwok et al., 2011). Snow depth is calculated using the retrieval procedure described by Kwok and Maksym (2014). There are other approaches developed for snow depth retrievals (e.g., Holt et al., 2015; Kurtz and Farrell, 2011; Newman et al., 2014) and we selected the approach in Kwok and Maksym (2014) because the snow depth retrievals seem to be more consistent with climatology; this was reported in a recent assessment (Kwok et al., 2017). A bulk snow density of 320 kg/m3 is used to convert the range differences between the air-snow (a-s) and snow-ice (s-i) interfaces (in free space) to snow depth. 3. Data analysis In this section, we first examine the relationship between snow depth and the measured lidar and radar freeboards, assuming a simple two-layered model (Fig. 1) of the sea ice cover. Second, we examine the efficacy of using the lidar/ radar freeboards for providing estimates of snow depth. Lastly, the expected biases and variability are discussed. 3.1. Snow depth from lidar and radar freeboards If the total freeboard ðhf Þ and the sea ice freeboard ðhfi Þ of the layered geometry (in Fig. 1) are known, then the
3
snow depth ðhfs Þ can be calculated simply as the difference between the two quantities: hfs ¼ hf hfi
ð1Þ
In the presence of a snow layer, however, the height of the ice freeboard ðhfi Þ is dependent on the snow depth, the density of the snow layer, and the radar-measured height above the sea surface is (written here as hradar ), fi hfi ¼ hradar þ hfs ðgs 1Þ fi
ð2Þ 1:5
where gs ¼ c=cs ðqs Þ; and c=cs ðqs Þ ¼ ð1 þ 0:51qs Þ . The second term in Eq. (2) (see Kwok and Cunningham, 2015) accounts for the reduced propagation speed of the radar wave (cs) in the snow layer with bulk density qs ; gs is the refractive index at microwave frequencies (Ulaby et al., 1986) and c is the speed of light in free space. Writing hlidar as the height of the total freeboard ðhf Þ, we have f ðhradar þ hfs ðgs 1ÞÞ: hfs ¼ hlidar f fi And, solving for hfs gives: ðhlidar hradar Þ f fi : hfs ¼ gs
ð3Þ
This relates snow depth to the lidar- and radar-freeboards, with a free parameter ðgs Þ that is dependent on snow density. Rewriting this equation with snow-depth estimates from the snow radar ðhSR fs Þ, lidar freeboard from the ATM (hATM ), and radar freeboard from CS-2 ðhCS2 f fi Þ gives the following linear equation, hATM hCS2 ¼ gs hSR f fi fs þ e:
ð4Þ
Here, e is the combined noise of the three measurements. 3.2. Snow depth estimates from freeboard measurements: Results In this note, the geophysical interest is whether the lidar freeboards from the ATM (used as proxy of IS-2) and radar freeboards from CS-2 are useful for providing estimates of snow depth ðhfs Þ. We assess this by regressing the difference between the two freeboards ðhATM hCS2 f fi Þ against the estimates of snow depth from the OIB snow radar ðhSR fs Þ, as written in Eq. (4). The feasibility of this calculation is demonstrated by obtaining a regression slope that can be compared to realistic values of gs based on the expected snow densities of the Arctic snow cover. For bulk snow densities of 320 ± 60 kg/m3 near the end of spring (Warren et al. (1999)), gs (used in Eq. (2)) is 1.25 ± 0.05. Figs. 2 and 3 compare two years (2014 and 2015) of CS2 and OIB data sets. The figures show individual fields of ATM SR ATM SR hATM , hCS2 hCS2 hCS2 f fi , hf fi , hfs , hf fi hfs , and the regression of the freeboard differences against snow depth.
Please cite this article in press as: Kwok, R., Markus, T. Potential basin-scale estimates of Arctic snow depth with sea ice freeboards from CryoSat-2 and ICESat-2: An exploratory analysis. Adv. Space Res. (2017), https://doi.org/10.1016/j.asr.2017.09.007
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a)
c)
e)
10
hf ATM : ATM freeboard (cm)
80
15
hf ATM–hfiCS2 (cm)
55
-15
(hf ATM–hfiCS2)–hfs SR (cm)
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b)
d)
f)
hfiCS2 : CS-2 freeboard (cm) 25
0
hfs SR : snow depth (cm)
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80
hf ATM–hfiCS2 (cm)
60
40
N: 822 Slope: 1.21 Intercept: -2.2 cm R: 0.81
20
0 0
20
40
60
hfs SR : snow depth (cm)
80
Fig. 2. Comparisons of differences between ATM (lidar) and CS-2 (radar) freeboards with estimates of snow depth from the snow radar on OIB in 2014. CS2 Þ. (c) Differences between ATM (lidar) and CS-2 (radar) freeboards ðhATM hCS2 (a) ATM freeboard ðhATM fi Þ. (b) CS-2 freeboard ðhfi f fi Þ. (d) Snow depth from OIB hSR . (e) Differences between (c) and (d). (f) Regression of (c) against (d); R is correlation and N is the number of samples, and error bars show the fs mean/standard deviation of the samples within 2-cm bins. Samples are 12.5 km averages of freeboards (from ATM and CS-2) and snow depths (OIB snow depth).
Please cite this article in press as: Kwok, R., Markus, T. Potential basin-scale estimates of Arctic snow depth with sea ice freeboards from CryoSat-2 and ICESat-2: An exploratory analysis. Adv. Space Res. (2017), https://doi.org/10.1016/j.asr.2017.09.007
R. Kwok, T. Markus / Advances in Space Research xxx (2017) xxx–xxx
a)
c)
e)
10
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-15
hf ATM : ATM freeboard (cm)
hf ATM–hfiCS2 (cm)
(hf ATM–hfiCS2)–hfs SR (cm)
80
55
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b)
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hfiCS2 : CS-2 freeboard (cm) 25
0
d)
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hfs SR : snow depth (cm)
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hf ATM–hfiCS2 (cm)
60
40
N: 470 slope: 1.22 intercept: 1.7 cm R: 0.80
20
0 0
20
40
60
hfs SR : snow depth (cm)
80
Fig. 3. Same as Fig. 2, except the analysis is for 2015.
Please cite this article in press as: Kwok, R., Markus, T. Potential basin-scale estimates of Arctic snow depth with sea ice freeboards from CryoSat-2 and ICESat-2: An exploratory analysis. Adv. Space Res. (2017), https://doi.org/10.1016/j.asr.2017.09.007
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Because of the disparity in spatial resolution and space-time sampling of the Arctic ice cover of the CS-2 radar, the OIB ATM and the snow radar, the first step of the process is to construct space-time averages with sample populations that are large enough to support the analysis undertaken here. In the maps (Figs. 2 and 3), the ATM freeboard and snow radar maps are 12.5 km averages along the daily OIB flight paths where both ATM freeboard and snow radar data are available – sometimes the ATM lidar data are not available due to cloud cover. The CS-2 freeboards, interpolated to the ATM locations, are from 30day gridded fields (12.5 km by 12.5 km) centered on the day of an OIB flight; there are a number of daily flights in a given OIB campaign, with each campaign lasting more than several weeks. The choice of sampling and spatial sampling for these comparisons is governed by limitations of the two data sets (ATM, SR, and CS-2). In particular, the OIB lidar data are acquired only during early spring and the sampling of the aircraft flightlines are generally not aligned in time and space with the CS-2 ground tracks. While there are a few OIB underflights of CS-2, they do not provide sufficiently large sample population for conducting an assessment of the differences. Furthermore, even along co-incident flight and ground tracks, it has been predict the exact spatial location of the scattering surface located in the radar waveform that could be registered to freeboard heights the ATM lidar. And, since the CS-2 orbits do not provide dense coverage of the surface, we are dependent on comparing spatial averages in monthly CS-2 composites of freeboard with the along-track freeboard averages from the OIB mission. For the 2014 and 2015 data sets, the comparisons in Figs. 2 and 3 show the following: 1. Expected spatial correlations between the hATM and hCS2 f fi freeboards (Panels (a) and (b)), i.e., lower freeboards in the Beaufort Sea and higher freeboards north of the coasts of Greenland and the Canadian Arctic Archipelago. 2. hATM > hCS2 the ATM freeboards (lidar) are f fi : always higher than the CS-2 freeboards (radar) (Panel (c)); the ATM freeboard is the total while the CS-2 freeboard is only the ice portion of the freeboard (see Fig. 1). SR 3. ðhATM hCS2 f fi Þ and hfs (Panels (c) and (d)) are spatially correlated. SR 4. ðhATM hCS2 f fi Þ are generally higher than hfs (Panel (e)) since Eq. (4) is expected to be valid when gs is expected to be greater than unity. 5. Regression analysis, for the two years, gives (Panels (f)) consistent slope coefficients of 1.21 and 1.22, correlations of 0.81 and 0.80, standard errors of 8 cm, and intercepts of 2.2 cm and 1.7 cm respectively.
Below, we discuss in more detail the results from the regression analysis. 3.3. Variability of the refractive index gs and snow depth estimates The regression slopes of 1.21 and 1.22 from the two years (which translate into snow densities of 260 kg/ m3), even though within the range of expected in climatology (Warren et al. (1999)) (i.e., 1.25 ± 0.05), are close to the lower limit of the expected range. If a refractive index of 1.25 (corresponding to a mean snow density of 320 kg/ m3, used for the snow radar) were used to convert the freeboard differences into snow depth (Eq. (3)) we would have underestimated the snow depth by 3% compared to the OIB snow depth estimates. So, it seems that the conversion is relatively insensitive to the choice of gs . Nevertheless, this would be a source of bias in the estimation of snow loading for thickness calculations. Ideally, the regression intercepts should be zero, but in the presence of noise (viz. Eq. (4)) the intercepts are expected to deviate some from the origin. For the two years, the intercepts are both four times lower than the standard errors. It is interesting to examine whether there are uncorrected but systematic geophysical biases (neglecting estimation biases) that could cause underestimates in the numerator of Eq. (3) (i.e., hATM hCS2 f fi ). Since the lidar reflections are expected to be from the top of the airsnow interface, we do not expect any geophysical biases in the lidar data. In the estimation of hfi from hradar , there fi is a residual bias in addition to the correction – due to reduced propagation speed – applied in Eq. (3). The additional correction is an adjustment needed to account for scattering from the air–snow interface and the snow layer on the radar return. The scattering due to the air–snow interface/snow layer displaces the scattering center towards the radar and increases hradar , thus decreasing hATM hCS2 fi f fi . We do not have any estimates of this impact on individual returns, but simulations (Kwok, 2014) demonstrate that this is dependent on the approach used to retrieve surface heights (i.e., retracking), which is dependent on the roughness of the surface (e.g., difference in roughness between first-year and multi-year ice). This suggests a possible source of the bias. One last remark on the results is the standard error in the regression analysis (8 cm). Since the ATM lidar and OIB snow radar are acquired simultaneously, we attribute a fraction of the differences to the lack of coincidence between the CS-2 freeboard and the OIB data sets (ATM and snow radar. Here, the CS-2 freeboard estimates are 30-day averages and the large variability in these estimates is expected to decorrelate the data sets. Again, it should be noted that this analysis approach works only when the snow is cold.
Please cite this article in press as: Kwok, R., Markus, T. Potential basin-scale estimates of Arctic snow depth with sea ice freeboards from CryoSat-2 and ICESat-2: An exploratory analysis. Adv. Space Res. (2017), https://doi.org/10.1016/j.asr.2017.09.007
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Fig. 4. Coverage of the Beaufort Sea (a 30-day example). (a) Ground tracks of CryoSat-2 and ICESat-2. (b) Higher resolution map of box in (a) showing the three ICESat-2 beam pairs (the pairs are separated by 3 km; each pair consists of two beams separated by 90 m) relative to the CryoSat-2 ground track.
4. Conclusions In this paper, we examined the potential of deriving snow depth estimates using differences in freeboard heights from CryoSat-2 (CS-2) and ICESat-2 (IS-2). We note that this is an exploratory exercise and by no means an in-depth analysis of all aspects of the problem because of the limitations of the available data sets. Freeboard differences are calculated using lidar freeboards from the ATM lidar (used as proxy of IS-2) and actual ice freeboards from CS-2. Estimated snow depths are compared with those of the snow radar from Operation IceBridge (OIB). For two years (2014 and 2015), regression of ATM and CS-2 freeboard height differences against OIB snow depth (12.5 km averages) show consistent correlations of 0.80 with estimated gs of 1.21; gs can be compared to that expected of the Arctic snow cover in early spring (1.25 ± 0.05). Standard error from the regression is 8 cm. We attribute a fraction of the differences to the lack of time-space coincidence between the OIB data sets (ATM and snow radar) and the CS-2 freeboard: potentially 15-day differences in time and kilometer differences in spatial location. With altimetry from
CS-2 and IS-2, our results suggest that it is possible to obtain time-varying estimates of snow depth over the entire Arctic Ocean (potentially bi-weekly timescales) from freeboard differences; the estimates will have significant impact not only on ice thickness retrievals, but also for understanding the changes in the sea ice covers of the Arctic and Antarctic. ICESat-2 will be placed in a 91-day exact repeat frozen orbit with an inclination angle of 92-degree, and a nominal orbit altitude of 500 km. The lidar system will have 6 profiling beams. Currently, CryoSat-2 is in a non-repeating low Earth orbit at an altitude of 725 km, and 92 degrees of inclination. At these inclinations, the altimeters provide sea ice coverage up to 88° latitude in the northern and southern hemispheres. With converging ground tracks at polar latitudes, it can be seen (Fig. 4) that the density of coverage in is quite high. However, even though the orbits of the two platforms are near the same inclination, the orbits do not provide the best coverage (in time and space) to explore the synergies between the lidar and radar measurements. Adjusting the orbits to provide nearcoincident space-time sampling of the surface, to minimize
Please cite this article in press as: Kwok, R., Markus, T. Potential basin-scale estimates of Arctic snow depth with sea ice freeboards from CryoSat-2 and ICESat-2: An exploratory analysis. Adv. Space Res. (2017), https://doi.org/10.1016/j.asr.2017.09.007
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aliasing of geophysical processes (snowfall and snow mass redistribution in this case), is obviously of significant interest to the science community. Our analysis provided one illustration of the many potential benefits and motivation for exploring the feasibility of joint operation of CS-2 and IS-2 after the launch of IS-2. Acknowledgments We thank John Sonntag for plots of the CryoSat-2 and ICESat-2 ground tracks. RK performed this work at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. References Dominguez, R., 2010. IceBridge DMS L1B Geolocated and Orthorectified Images, Version 1 (2014–2015). NASA National Snow and Ice Data Center Distributed Active Archive Center, Boulder, Colorado, USA. Guerreiro, K., Fleury, S., Zakharova, E., Re´my, F., Kouraev, A., 2016. Potential for estimation of snow depth on Arctic sea ice from CryoSat2 and SARAL/AltiKa missions. Rem. Sens. Environ. 186, 339–349. Holt, B., Johnson, M.P., Perkovic-Martin, D., Panzer, B., 2015. Snow depth on Arctic sea ice derived from radar: In situ comparisons and time series analysis. J. Geophys. Res. 120, 4260–4287. Krabill, W., 2014 IceBridge Narrow Swath ATM L1B Elevation and Return Strength, Version 2 (updated 2016). NASA National Snow and Ice Data Center Distributed Active Archive Center, Boulder, Colorado, USA. Kurtz, N.T., Farrell, S.L., 2011. Large-scale surveys of snow depth on Arctic sea ice from Operation IceBridge. Geophys. Res. Lett. 38, L20505. Kwok, R., 2014. Simulated effects of a snow layer on retrieval of CryoSat2 sea ice freeboard. Geophys. Res. Lett. 41, 5014–5020. Kwok, R., Cunningham, G.F., 2008. ICESat over Arctic sea ice: estimation of snow depth and ice thickness. J. Geophys. Res. 113, C08010. Kwok, R., Cunningham, G.F., 2015. Variability of Arctic sea ice thickness and volume from CryoSat-2. Phil. Trans. R. Soc. A 373, 20140157. Kwok, R., Cunningham, G.F., Manizade, S.S., Krabill, W.B., 2012. Arctic sea ice freeboard from IceBridge acquisitions in 2009: estimates and comparisons with ICESat. J. Geophys. Res. 117, C02018.
Kwok, R., Cunningham, G.F., Wensnahan, M., Rigor, I., Zwally, H.J., Yi, D., 2009. Thinning and volume loss of the Arctic Ocean sea ice cover: 2003–2008. J. Geophys. Res. 114, C07005. Kwok, R., Kurtz, N.T., Brucker, L., et al., 2017. Inter-comparison of snow depth retrievals over Arctic sea ice from radar data acquired by Operation IceBridge. The Cryosphere Discuss. (submitted for publication) Kwok, R., Maksym, T., 2014. Snow depth of the Weddell and Bellingshausen sea ice covers from IceBridge surveys in 2010 and 2011: An examination. J. Geophys. Res. 119, 4141–4167. Kwok, R., Panzer, B., Leuschen, C., et al., 2011. Airborne surveys of snow depth over Arctic sea ice. J. Geophys. Res. 116, C11018. Laxon, S.W., Giles, K.A., Ridout, A.L., et al., 2013. CryoSat-2 estimates of Arctic sea ice thickness and volume. Geophys. Res. Lett. 40, 732– 737. Leuschen, C., 2014. IceBridge Snow Radar L1B Geolocated Radar Echo Strength Profiles, Version 2 (2014–2015). NASA National Snow and Ice Data Center Distributed Active Archive Center, Boulder, Colorado, USA.. Markus, T., Neumann, T., Martino, A., et al., 2017. The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2): Science requirements, concept, and implementation. Rem. Sens. Environ. 190, 260–273. Newman, T., Farrell, S.L., Richter-Menge, J., et al., 2014. Assessment of radar-derived snow depth over Arctic sea ice. J. Geophys. Res. 119, 8578–8602. Panzer, B., Gomez-Garcia, D., Leuschen, C., et al., 2013. An ultrawideband, microwave radar for measuring snow thickness on sea ice and mapping near-surface internal layers in polar firn. J. Glaciol. 59, 244–254. Ulaby, F.T., Moore, R.K., Fung, A.K., 1986. Microwave Remote Sensing: From Theory to Applications. Artech House, Norwood, MA. Vaughan, D.G., Comiso, J., Allison, I., et al., 2013. Observations: cryosphere. In: Stocker, T.F., Qin, D., Plattner, G.-K., et al. (Eds.), Climate Change 2013: The Physical Science Basis, Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge, UK, pp. 317–382. Warren, S.G., Rigor, I.G., Untersteiner, N., et al., 1999. Snow depth on Arctic sea ice. J. Clim. 12, 1814–1829. Wingham, D.J., Francis, C.R., Baker, S., et al., 2006. CryoSat: a mission to determine the fluctuations in Earth’s land and marine ice fields. Adv. Space Res. 37, 841–871. Zwally, H.J., Schutz, B., Abdalati, W., et al., 2002. ICESat’s laser measurements of polar ice, atmosphere, ocean, and land. J. Geodyn. 34, 405–445.
Please cite this article in press as: Kwok, R., Markus, T. Potential basin-scale estimates of Arctic snow depth with sea ice freeboards from CryoSat-2 and ICESat-2: An exploratory analysis. Adv. Space Res. (2017), https://doi.org/10.1016/j.asr.2017.09.007
ScienceDirect Advances in Space Research xxx (2017) xxx–xxx www.elsevier.com/locate/asr
Potential basin-scale estimates of Arctic snow depth with sea ice freeboards from CryoSat-2 and ICESat-2: An exploratory analysis R. Kwok a,⇑, T. Markus b a
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA b NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA
Received 24 January 2017; received in revised form 30 August 2017; accepted 5 September 2017
Abstract The potential of deriving snow depth estimates using differences in freeboard heights from CryoSat-2 (CS-2) and ICESat-2 (IS-2) is examined. In our analysis, we use lidar freeboard from the Airborne Topographic Mapper (ATM) on Operation IceBridge (OIB) as proxy of IS-2 total (snow + ice) freeboard. Snow depths are estimates from the OIB snow radar. Differences in height between the total (ATM) and ice (CS-2) freeboards are related to snow depth by the refractive index of the snow layer ðgs Þ, which is dependent on snow density. For two years (2014 and 2015), regression of the ATM and CS-2 freeboard differences against OIB snow depth gives correlations of 0.80, estimated gs of 1.21, and standard errors of 8 cm. The resulting refractive index, gs , can be compared to that expected of the Arctic snow cover in early spring (1.25 ± 0.05). The expected biases and variability in the regression analysis are discussed. Results suggest that snow depth can be estimated from the freeboard differences. The benefits of adjusting the orbit of CS-2 for providing more optimized overlaps between IS-2 and CS-2 are considered. Ó 2017 COSPAR. Published by Elsevier Ltd. All rights reserved.
Keywords: CryoSat-2; ICESat-2; Sea ice; Snow depth; Arctic; Antarctic
1. Introduction NASA’s ICESat mission (Zwally et al., 2002) was completed in 2009 while ESA’s CS-2 mission (Wingham et al., 2006) is currently in operation. These altimetry missions are dedicated to the acquisition of spaceborne observations for quantifying changes in the ice masses of the Earth System, and their impact on global climate. Significantly, satellite estimates of sea ice thickness and volume made in the period 2003–2008 (ICESat) (Kwok et al., 2009) and 2010–2012 (CryoSat-2) (Laxon et al., 2013) have contributed to the last Intergovernmental Panel on Climate Change (IPCC-AR5) assessment of recent declines in Arctic sea ice (Vaughan et al., 2013). With the planned launch
of ICESat-2 (IS-2) (Markus et al., 2017) (scheduled for late 2018) to continue the altimetry time series to inform changes in the cryosphere, there may be a unique opportunity to obtain near-coincident altimetry of the Arctic sea ice cover from both a lidar (IS-2) and a radar (CS-2) for the extraction of snow depth from these measurements. In this paper, we use available data sets to explore and assess the feasibility of such calculations. The calculation of sea ice thickness (hi ) from total (snow + ice, hf ) or ice-only freeboard (hfi ), assuming isostatic equilibrium, requires an estimate of the snow loading at the surface (i.e., snow depth – hfs and snow density –qs ), viz. (see Fig. 1),
⇑ Corresponding author.
E-mail address: [email protected] (R. Kwok).
hi ¼
qw qs qw hf þ hfs q w qi qw qi
ðfor lidarÞ
https://doi.org/10.1016/j.asr.2017.09.007 0273-1177/Ó 2017 COSPAR. Published by Elsevier Ltd. All rights reserved.
Please cite this article in press as: Kwok, R., Markus, T. Potential basin-scale estimates of Arctic snow depth with sea ice freeboards from CryoSat-2 and ICESat-2: An exploratory analysis. Adv. Space Res. (2017), https://doi.org/10.1016/j.asr.2017.09.007
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snow
hfs hfi
hf hfi
hi hSSH
sea water Fig. 1. Relationship between the different height quantities discussed in the text.
hi ¼
qw qs hfi þ hfs qw qi qw qi
ðfor radarÞ
qw and qi are the bulk densities of water and ice, respectively. These equations are written to show explicitly the lidar and radar observables – hf and hfi – from the two altimetry missions. For the selected electromagnetic wavelengths of ICESat-2 and CS-2, the lidar and radar returns are assumed to be – when the temperature is below freezing – from the air/snow interface and the snow/ice interface, respectively, thus providing observations of total and ice freeboard relative to the local sea surface. Presently, there are no direct measurements of time-variable snow depth at the spatial scale needed for thickness calculations. In published approaches (e.g., Kwok and Cunningham, 2015; Kwok and Cunningham, 2008; Laxon et al., 2013), the snow depth is typically prescribed by modifying the climatology in Warren et al. (1999), or obtained indirectly through accumulation of snowfall from meteorological analyses (Kwok and Cunningham, 2008). While these approaches seem to be adequate for providing large-scale trends in ice thickness and volume for climate assessments, 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). In fact, the results by Guerreiro et al. (2016) – by analyzing data from two radar altimeter missions – suggest a snow cover that is thinner than the snow climatology (Warren et al. (1999)). In addition to the retrievals of sea ice thickness, trends in observed snow depth is also of interest for understanding Arctic changes and its role in global climate. Hence, direct estimates of snow depth by any means are desirable. It is clear that the snow depth can be calculated as the simple difference in the freeboard heights from the lidar and radar (i.e., hfs ¼ hf hfi ; Fig. 1). However, there are differences in the spatial resolution and the time-space sampling (i.e., orbit inclination, repeat cycles, etc.) between IS2 and CS-2 instruments. The questions are how well retrieval of snow depth could be and whether this could be
demonstrated with available data sets. In the present analysis, we examine the potential of deriving snow depth estimates using differences in freeboard heights from the lidar and radar altimeters. The aim is to motivate the two space agencies, NASA and ESA, to exploit the unique opportunity of providing near-overlapping coverage from two satellite missions (one instrumented with a radar altimeter and the other with a lidar) for snow depth retrieval, by slight adjustments to the CS-2 orbital configuration. At the outset, we note that this is an exploratory exercise and by no means an in-depth analysis of all aspects of the problem because of the limitations of the data sets that are available. The paper is organized as follows. The next section describes the three primary data sets used in our analyses. Section 3 defines the relationship between snow depths and the measured lidar and radar freeboards, examines the snow depth estimates from the two freeboards, and discusses the expected biases and variability. The last section discusses the potential of adjusting the orbit configurations of IS-2 and CS-2 for snow depth estimation, and concludes the paper. 2. Data description The three data sets of interest are the sea ice freeboard from CryoSat-2 (CS-2), the total freeboard (snow + ice) from the Airborne Topographic Mapper (ATM), and the snow depth estimates from the ultra-wideband snow radar (SR) from Operation IceBridge. During IceBridge campaigns, the ATM and SR instruments are operated simultaneously and provide near coincident coverage, albeit at different spatial resolutions. In this section, we provide a brief description of the performance and coverage of these radar and lidar systems. 2.1. CryoSat-2 freeboard Gridded 30-day fields of CS-2 ice freeboard are those from Kwok and Cunningham (2015). Values at grid cells (on a 12.5 km grid) are binned composites of freeboard estimates from all orbits (420 orbits) for a 30-day period. The reader is referred to Kwok and Cunningham (2015) for a more detailed description of the retrieval procedures and quality of these fields. As there are no direct freeboard estimates, comparisons with available ice thickness measurements provide an indirect measure of quality: freeboard is approximately a fraction (one-ninth) of ice thickness. The assessed differences between CS-2 and various thickness measurements are: 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 (Operation IceBridge). 2.2. IceBridge ATM freeboard Surface elevations are from the IceBridge Narrow Swath ATM Level-1B lidar Elevation and Return Strength data
Please cite this article in press as: Kwok, R., Markus, T. Potential basin-scale estimates of Arctic snow depth with sea ice freeboards from CryoSat-2 and ICESat-2: An exploratory analysis. Adv. Space Res. (2017), https://doi.org/10.1016/j.asr.2017.09.007
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set (Krabill, 2014). This data set contains ATM spot elevation measurements (1–2 m footprint) over sea ice. ATM scanning geometry provides an across-track scan swath of 45 m with typical elevation accuracy better than 10cm. Total (snow + ice) freeboard from the lidar were derived from the IceBridge Narrow Swath elevation data using the approach described by (Kwok et al., 2012). The ice freeboard of an elevation sample is calculated only when an open water surface within 10 km is present (i.e., leads) to serve as height reference. Sea surface references are identified in high-resolution visible imagery acquired by the Digital Mapping System (Dominguez, 2010). 2.3. IceBridge snow depth Estimates of snow depth were derived from the IceBridge Level-1B Radar Echo Strength Profiles data set (Leuschen, 2014) from the snow radar. This frequency-modulated continuous-wave (FM-CW) radar is operated by the Center for Remote Sensing of Ice Sheets (CReSIS) at the University of Kansas. The large bandwidth (6 GHz) provides a range resolution of 5 cm (in free space) for resolving the location of the air-snow (a-s) and snow-ice (s-i) interfaces (Panzer et al., 2013). With averaging, the spot separation is 5 m along track at an altitude of 500 m and an air speed of 250 kts (the nominal flight parameters for all OIB sea ice surveys). 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 of the data characteristics (e.g., Kwok et al., 2011). Snow depth is calculated using the retrieval procedure described by Kwok and Maksym (2014). There are other approaches developed for snow depth retrievals (e.g., Holt et al., 2015; Kurtz and Farrell, 2011; Newman et al., 2014) and we selected the approach in Kwok and Maksym (2014) because the snow depth retrievals seem to be more consistent with climatology; this was reported in a recent assessment (Kwok et al., 2017). A bulk snow density of 320 kg/m3 is used to convert the range differences between the air-snow (a-s) and snow-ice (s-i) interfaces (in free space) to snow depth. 3. Data analysis In this section, we first examine the relationship between snow depth and the measured lidar and radar freeboards, assuming a simple two-layered model (Fig. 1) of the sea ice cover. Second, we examine the efficacy of using the lidar/ radar freeboards for providing estimates of snow depth. Lastly, the expected biases and variability are discussed. 3.1. Snow depth from lidar and radar freeboards If the total freeboard ðhf Þ and the sea ice freeboard ðhfi Þ of the layered geometry (in Fig. 1) are known, then the
3
snow depth ðhfs Þ can be calculated simply as the difference between the two quantities: hfs ¼ hf hfi
ð1Þ
In the presence of a snow layer, however, the height of the ice freeboard ðhfi Þ is dependent on the snow depth, the density of the snow layer, and the radar-measured height above the sea surface is (written here as hradar ), fi hfi ¼ hradar þ hfs ðgs 1Þ fi
ð2Þ 1:5
where gs ¼ c=cs ðqs Þ; and c=cs ðqs Þ ¼ ð1 þ 0:51qs Þ . The second term in Eq. (2) (see Kwok and Cunningham, 2015) accounts for the reduced propagation speed of the radar wave (cs) in the snow layer with bulk density qs ; gs is the refractive index at microwave frequencies (Ulaby et al., 1986) and c is the speed of light in free space. Writing hlidar as the height of the total freeboard ðhf Þ, we have f ðhradar þ hfs ðgs 1ÞÞ: hfs ¼ hlidar f fi And, solving for hfs gives: ðhlidar hradar Þ f fi : hfs ¼ gs
ð3Þ
This relates snow depth to the lidar- and radar-freeboards, with a free parameter ðgs Þ that is dependent on snow density. Rewriting this equation with snow-depth estimates from the snow radar ðhSR fs Þ, lidar freeboard from the ATM (hATM ), and radar freeboard from CS-2 ðhCS2 f fi Þ gives the following linear equation, hATM hCS2 ¼ gs hSR f fi fs þ e:
ð4Þ
Here, e is the combined noise of the three measurements. 3.2. Snow depth estimates from freeboard measurements: Results In this note, the geophysical interest is whether the lidar freeboards from the ATM (used as proxy of IS-2) and radar freeboards from CS-2 are useful for providing estimates of snow depth ðhfs Þ. We assess this by regressing the difference between the two freeboards ðhATM hCS2 f fi Þ against the estimates of snow depth from the OIB snow radar ðhSR fs Þ, as written in Eq. (4). The feasibility of this calculation is demonstrated by obtaining a regression slope that can be compared to realistic values of gs based on the expected snow densities of the Arctic snow cover. For bulk snow densities of 320 ± 60 kg/m3 near the end of spring (Warren et al. (1999)), gs (used in Eq. (2)) is 1.25 ± 0.05. Figs. 2 and 3 compare two years (2014 and 2015) of CS2 and OIB data sets. The figures show individual fields of ATM SR ATM SR hATM , hCS2 hCS2 hCS2 f fi , hf fi , hfs , hf fi hfs , and the regression of the freeboard differences against snow depth.
Please cite this article in press as: Kwok, R., Markus, T. Potential basin-scale estimates of Arctic snow depth with sea ice freeboards from CryoSat-2 and ICESat-2: An exploratory analysis. Adv. Space Res. (2017), https://doi.org/10.1016/j.asr.2017.09.007
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a)
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hf ATM : ATM freeboard (cm)
80
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hf ATM–hfiCS2 (cm)
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(hf ATM–hfiCS2)–hfs SR (cm)
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60
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N: 822 Slope: 1.21 Intercept: -2.2 cm R: 0.81
20
0 0
20
40
60
hfs SR : snow depth (cm)
80
Fig. 2. Comparisons of differences between ATM (lidar) and CS-2 (radar) freeboards with estimates of snow depth from the snow radar on OIB in 2014. CS2 Þ. (c) Differences between ATM (lidar) and CS-2 (radar) freeboards ðhATM hCS2 (a) ATM freeboard ðhATM fi Þ. (b) CS-2 freeboard ðhfi f fi Þ. (d) Snow depth from OIB hSR . (e) Differences between (c) and (d). (f) Regression of (c) against (d); R is correlation and N is the number of samples, and error bars show the fs mean/standard deviation of the samples within 2-cm bins. Samples are 12.5 km averages of freeboards (from ATM and CS-2) and snow depths (OIB snow depth).
Please cite this article in press as: Kwok, R., Markus, T. Potential basin-scale estimates of Arctic snow depth with sea ice freeboards from CryoSat-2 and ICESat-2: An exploratory analysis. Adv. Space Res. (2017), https://doi.org/10.1016/j.asr.2017.09.007
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a)
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hf ATM–hfiCS2 (cm)
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N: 470 slope: 1.22 intercept: 1.7 cm R: 0.80
20
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80
Fig. 3. Same as Fig. 2, except the analysis is for 2015.
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Because of the disparity in spatial resolution and space-time sampling of the Arctic ice cover of the CS-2 radar, the OIB ATM and the snow radar, the first step of the process is to construct space-time averages with sample populations that are large enough to support the analysis undertaken here. In the maps (Figs. 2 and 3), the ATM freeboard and snow radar maps are 12.5 km averages along the daily OIB flight paths where both ATM freeboard and snow radar data are available – sometimes the ATM lidar data are not available due to cloud cover. The CS-2 freeboards, interpolated to the ATM locations, are from 30day gridded fields (12.5 km by 12.5 km) centered on the day of an OIB flight; there are a number of daily flights in a given OIB campaign, with each campaign lasting more than several weeks. The choice of sampling and spatial sampling for these comparisons is governed by limitations of the two data sets (ATM, SR, and CS-2). In particular, the OIB lidar data are acquired only during early spring and the sampling of the aircraft flightlines are generally not aligned in time and space with the CS-2 ground tracks. While there are a few OIB underflights of CS-2, they do not provide sufficiently large sample population for conducting an assessment of the differences. Furthermore, even along co-incident flight and ground tracks, it has been predict the exact spatial location of the scattering surface located in the radar waveform that could be registered to freeboard heights the ATM lidar. And, since the CS-2 orbits do not provide dense coverage of the surface, we are dependent on comparing spatial averages in monthly CS-2 composites of freeboard with the along-track freeboard averages from the OIB mission. For the 2014 and 2015 data sets, the comparisons in Figs. 2 and 3 show the following: 1. Expected spatial correlations between the hATM and hCS2 f fi freeboards (Panels (a) and (b)), i.e., lower freeboards in the Beaufort Sea and higher freeboards north of the coasts of Greenland and the Canadian Arctic Archipelago. 2. hATM > hCS2 the ATM freeboards (lidar) are f fi : always higher than the CS-2 freeboards (radar) (Panel (c)); the ATM freeboard is the total while the CS-2 freeboard is only the ice portion of the freeboard (see Fig. 1). SR 3. ðhATM hCS2 f fi Þ and hfs (Panels (c) and (d)) are spatially correlated. SR 4. ðhATM hCS2 f fi Þ are generally higher than hfs (Panel (e)) since Eq. (4) is expected to be valid when gs is expected to be greater than unity. 5. Regression analysis, for the two years, gives (Panels (f)) consistent slope coefficients of 1.21 and 1.22, correlations of 0.81 and 0.80, standard errors of 8 cm, and intercepts of 2.2 cm and 1.7 cm respectively.
Below, we discuss in more detail the results from the regression analysis. 3.3. Variability of the refractive index gs and snow depth estimates The regression slopes of 1.21 and 1.22 from the two years (which translate into snow densities of 260 kg/ m3), even though within the range of expected in climatology (Warren et al. (1999)) (i.e., 1.25 ± 0.05), are close to the lower limit of the expected range. If a refractive index of 1.25 (corresponding to a mean snow density of 320 kg/ m3, used for the snow radar) were used to convert the freeboard differences into snow depth (Eq. (3)) we would have underestimated the snow depth by 3% compared to the OIB snow depth estimates. So, it seems that the conversion is relatively insensitive to the choice of gs . Nevertheless, this would be a source of bias in the estimation of snow loading for thickness calculations. Ideally, the regression intercepts should be zero, but in the presence of noise (viz. Eq. (4)) the intercepts are expected to deviate some from the origin. For the two years, the intercepts are both four times lower than the standard errors. It is interesting to examine whether there are uncorrected but systematic geophysical biases (neglecting estimation biases) that could cause underestimates in the numerator of Eq. (3) (i.e., hATM hCS2 f fi ). Since the lidar reflections are expected to be from the top of the airsnow interface, we do not expect any geophysical biases in the lidar data. In the estimation of hfi from hradar , there fi is a residual bias in addition to the correction – due to reduced propagation speed – applied in Eq. (3). The additional correction is an adjustment needed to account for scattering from the air–snow interface and the snow layer on the radar return. The scattering due to the air–snow interface/snow layer displaces the scattering center towards the radar and increases hradar , thus decreasing hATM hCS2 fi f fi . We do not have any estimates of this impact on individual returns, but simulations (Kwok, 2014) demonstrate that this is dependent on the approach used to retrieve surface heights (i.e., retracking), which is dependent on the roughness of the surface (e.g., difference in roughness between first-year and multi-year ice). This suggests a possible source of the bias. One last remark on the results is the standard error in the regression analysis (8 cm). Since the ATM lidar and OIB snow radar are acquired simultaneously, we attribute a fraction of the differences to the lack of coincidence between the CS-2 freeboard and the OIB data sets (ATM and snow radar. Here, the CS-2 freeboard estimates are 30-day averages and the large variability in these estimates is expected to decorrelate the data sets. Again, it should be noted that this analysis approach works only when the snow is cold.
Please cite this article in press as: Kwok, R., Markus, T. Potential basin-scale estimates of Arctic snow depth with sea ice freeboards from CryoSat-2 and ICESat-2: An exploratory analysis. Adv. Space Res. (2017), https://doi.org/10.1016/j.asr.2017.09.007
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Fig. 4. Coverage of the Beaufort Sea (a 30-day example). (a) Ground tracks of CryoSat-2 and ICESat-2. (b) Higher resolution map of box in (a) showing the three ICESat-2 beam pairs (the pairs are separated by 3 km; each pair consists of two beams separated by 90 m) relative to the CryoSat-2 ground track.
4. Conclusions In this paper, we examined the potential of deriving snow depth estimates using differences in freeboard heights from CryoSat-2 (CS-2) and ICESat-2 (IS-2). We note that this is an exploratory exercise and by no means an in-depth analysis of all aspects of the problem because of the limitations of the available data sets. Freeboard differences are calculated using lidar freeboards from the ATM lidar (used as proxy of IS-2) and actual ice freeboards from CS-2. Estimated snow depths are compared with those of the snow radar from Operation IceBridge (OIB). For two years (2014 and 2015), regression of ATM and CS-2 freeboard height differences against OIB snow depth (12.5 km averages) show consistent correlations of 0.80 with estimated gs of 1.21; gs can be compared to that expected of the Arctic snow cover in early spring (1.25 ± 0.05). Standard error from the regression is 8 cm. We attribute a fraction of the differences to the lack of time-space coincidence between the OIB data sets (ATM and snow radar) and the CS-2 freeboard: potentially 15-day differences in time and kilometer differences in spatial location. With altimetry from
CS-2 and IS-2, our results suggest that it is possible to obtain time-varying estimates of snow depth over the entire Arctic Ocean (potentially bi-weekly timescales) from freeboard differences; the estimates will have significant impact not only on ice thickness retrievals, but also for understanding the changes in the sea ice covers of the Arctic and Antarctic. ICESat-2 will be placed in a 91-day exact repeat frozen orbit with an inclination angle of 92-degree, and a nominal orbit altitude of 500 km. The lidar system will have 6 profiling beams. Currently, CryoSat-2 is in a non-repeating low Earth orbit at an altitude of 725 km, and 92 degrees of inclination. At these inclinations, the altimeters provide sea ice coverage up to 88° latitude in the northern and southern hemispheres. With converging ground tracks at polar latitudes, it can be seen (Fig. 4) that the density of coverage in is quite high. However, even though the orbits of the two platforms are near the same inclination, the orbits do not provide the best coverage (in time and space) to explore the synergies between the lidar and radar measurements. Adjusting the orbits to provide nearcoincident space-time sampling of the surface, to minimize
Please cite this article in press as: Kwok, R., Markus, T. Potential basin-scale estimates of Arctic snow depth with sea ice freeboards from CryoSat-2 and ICESat-2: An exploratory analysis. Adv. Space Res. (2017), https://doi.org/10.1016/j.asr.2017.09.007
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aliasing of geophysical processes (snowfall and snow mass redistribution in this case), is obviously of significant interest to the science community. Our analysis provided one illustration of the many potential benefits and motivation for exploring the feasibility of joint operation of CS-2 and IS-2 after the launch of IS-2. Acknowledgments We thank John Sonntag for plots of the CryoSat-2 and ICESat-2 ground tracks. RK performed this work at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. References Dominguez, R., 2010. IceBridge DMS L1B Geolocated and Orthorectified Images, Version 1 (2014–2015). NASA National Snow and Ice Data Center Distributed Active Archive Center, Boulder, Colorado, USA. Guerreiro, K., Fleury, S., Zakharova, E., Re´my, F., Kouraev, A., 2016. Potential for estimation of snow depth on Arctic sea ice from CryoSat2 and SARAL/AltiKa missions. Rem. Sens. Environ. 186, 339–349. Holt, B., Johnson, M.P., Perkovic-Martin, D., Panzer, B., 2015. Snow depth on Arctic sea ice derived from radar: In situ comparisons and time series analysis. J. Geophys. Res. 120, 4260–4287. Krabill, W., 2014 IceBridge Narrow Swath ATM L1B Elevation and Return Strength, Version 2 (updated 2016). NASA National Snow and Ice Data Center Distributed Active Archive Center, Boulder, Colorado, USA. Kurtz, N.T., Farrell, S.L., 2011. Large-scale surveys of snow depth on Arctic sea ice from Operation IceBridge. Geophys. Res. Lett. 38, L20505. Kwok, R., 2014. Simulated effects of a snow layer on retrieval of CryoSat2 sea ice freeboard. Geophys. Res. Lett. 41, 5014–5020. Kwok, R., Cunningham, G.F., 2008. ICESat over Arctic sea ice: estimation of snow depth and ice thickness. J. Geophys. Res. 113, C08010. Kwok, R., Cunningham, G.F., 2015. Variability of Arctic sea ice thickness and volume from CryoSat-2. Phil. Trans. R. Soc. A 373, 20140157. Kwok, R., Cunningham, G.F., Manizade, S.S., Krabill, W.B., 2012. Arctic sea ice freeboard from IceBridge acquisitions in 2009: estimates and comparisons with ICESat. J. Geophys. Res. 117, C02018.
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Please cite this article in press as: Kwok, R., Markus, T. Potential basin-scale estimates of Arctic snow depth with sea ice freeboards from CryoSat-2 and ICESat-2: An exploratory analysis. Adv. Space Res. (2017), https://doi.org/10.1016/j.asr.2017.09.007