Comparison of CryoSat-2 and ENVISAT radar freeboard over Arctic sea-ice : Toward an improved Envisat freeboard retrieval

During the past decade, sea-ice freeboard has been monitored with various satellite altimetric missions with the aim of producing long-term time series of ice thickness. While recent studies have demonstrated the capacity of the CryoSat-2 mission (2010-) to provide accurate freeboard measurements, the current estimates obtained with the Envisat mission (2002-2012) still require some large improvements. To improve Envisat freeboard retrieval, we first compare CryoSat-2 and Envisat radar freboard estimates during the common 5 flight period (2010/11 and 2011/12 sea-ice growth seasons). The along-track analysis shows that unlike for CryoSat-2, the sea level as retrieved by Envisat is systematically located above the level of sea-ice floes. Consequently, Envisat radar freeboard estimates display unrealistic negative values during the entire ice growth season and all over the circumpolar region. This result is attributed to the sensitivity of pulse-limited waveforms to ice surface properties (surface roughness and snow volume scattering) and to the use of a threshold retracker. 10 The analysis of the gridded radar freeboard difference together with the corresponding Envisat pulse peakiness maps suggests that the discrepancy between the two sensors is also related to the surface properties of sea-ice floes. This strong linkage is, here as well, attributed to the higher sensitivity of pulse-limited waveform echoes to the variability of ice surface properties (surface roughness and snow volume scattering) and to the use of a threshold retracker. Based on the relation between the Envisat pulse-peakiness and the radar freeboard difference between Envisat and CryoSat-2, 15 we produce a monthly CryoSat-2-like version of Envisat freeboard (Envisat/PP). The Envisat/PP freeboard displays a similar spatial distribution as CryoSat-2 (RMSD = 1.5 cm) during the two ice growth seasons and for all month of the period of study. The comparison of the altimetric datasets with in situ ice draft measurements during the common flight period shows that the Envisat/PP dataset (RMSE = 12 28 cm) is as accurate as CryoSat-2 (RMSE = 15 21 cm) and highly more accurate than the uncorrected Envisat dataset (RMSE = 178 179 cm). 20 The comparison of the improved Envisat radar freeboard dataset is then extended to the rest of the Envisat mission to demonstrate the validity of PP-correction out of the calibration period. The good agreement between the Envisat/PP and the in situ ice draft dataset (RMSE = 13 32 cm) demonstrates the potential of the PP-correction to produce accurate freeboard estimates over the entire Envisat mission lifetime.


Introduction
Sea ice is one of the most sensitive indicators of Arctic climate system changes.Satellite observations have demonstrated that the Arctic sea-ice extent has decreased at an average rate of 4 % per decade from 1978 to 2010 and at an accelerated rate of 8.3 % over the 1996-2010 period (Comiso, 2012).In addition to the sea-ice cover reduction, it has been shown that Arctic sea ice is also thinning (Rothrock et al., 1999;Kwok and Rothrock, 2009).Based on submarine ice draught measurements, Rothrock et al. (1999) reported a decrease of ∼ 1.3 m in the 1990s relative to ice thickness measurements obtained over the 1958-1976 period.However, Holloway and Sou (2002) show that local submarine measurements can be impacted by large-scale displacement of perennial ice and that sea-ice thickness should be monitored at basin scale to accurately estimate sea-ice volume changes.
Over the past decade, satellite radar altimeters have been used to estimate basin-scale sea-ice thickness.It is generally assumed that over snow-covered sea ice, the main scattering horizon of the  GHz) radar signal is located at the snow-ice interface (Beaven, 1995).Hence, Ku-band radar altimeters have been used to monitor the height of sea ice above sea level, generally referenced as sea-ice freeboard.By assuming the hydrostatic equilibrium between the ocean and the snow-covered sea ice, freeboard can be converted to ice thickness (Laxon et al., 2003).Following this methodology, sea-ice thickness has been estimated with the pulselimited altimeters RA on board ERS-1 and RA-2 on board ERS-2 and Envisat (Laxon et al., 2003;Giles et al., 2008).While the Envisat ice thickness estimates are promising, the current prototype product (http://icdc.cen.uni-hamburg.de/1/projekte/esa-cci-sea-ice-ecv0.html) has a positive bias of 0.5 to 1.5 m and does not reproduce accurately the seasonal cycle of ice growth (Kern et al., 2015).It is the goal of the European Space Agency (ESA) Sea Ice Climate Change Initiative project (SI-CCI) to improve RA-2 freeboard retrievals and to provide accurate time series of ice thickness over the Envisat mission lifetime (Ridout et al., 2012).More recently, sea-ice thickness was estimated with the Ku-band Synthetic Aperture Radar (SAR) Interferometric Radar Altimeter (SIRAL) on board CryoSat-2.Unlike for Envisat, CryoSat-2 ice thickness estimates are in good agreement with in situ measurements and display a realistic seasonal cycle (Laxon et al., 2013;Kwok and Cunningham, 2015;Tilling et al., 2015).
The difference between Envisat and Cryosat-2 ice thickness estimates poses an important question: why does CryoSat-2 provide more realistic estimates of ice thickness than Envisat while both sensors operate at the same central frequency?
First of all, the bias in Envisat ice thickness estimates could be caused by an inaccurate conversion of freeboard to ice thickness.However, the study by Kern et al. (2015) shows that even when using a similar parameterisation of snow depth and ice density as in CryoSat-2 studies (Laxon et al., 2013;Kwok and Cunningham, 2015), the Envisat ice thickness estimates remain relatively inaccurate.In particular, the authors do not succeed in reproducing the seasonal ice growth cycle.This result suggests therefore that the bias in Envisat ice thickness estimates is driven by a bias in the freeboard fields rather than by an inaccurate conversion of freeboard to ice thickness.
The common flight period of Envisat and CryoSat-2 (November 2010-March 2012) represents an unique opportunity to analyse the bias in the Envisat freeboard fields.In Schwegmann et al. (2016), Envisat and CryoSat-2 radar freeboard data sets are compared over Antarctic sea ice.While the spatial and temporal distributions are consistent, it is shown that CryoSat-2 radar freeboard is thicker (thinner) for thick (thin) freeboard values.The authors conclude that the discrepancy between the two data sets is likely to be related to the difference in footprint characteristics between pulselimited and SAR altimetry.
Over sea ice, conventional pulse-limited altimeters such as Envisat have a typical footprint of 2-10 km (Connor et al., 2009).Unlike pulse-limited altimetry, the SAR technology and the Doppler post-processing allow the along-track position of each scatterer to be identified and offer SIRAL an along-track footprint of ∼ 300 m (the across-track being unchanged).The reduction of the footprint size of the SAR mode mainly has two consequences for the monitoring of sea ice.First of all, it allows the impact of bright off-nadir reflections in the along-track direction to be minimised and thus improves the range estimation over ice floes.In addition, the Doppler post-processing allows the surface response of the radar signal to be sharpened, which reduces the impact of surface roughness and snow volume scattering on the retrieval of the altimetric range (Raney, 1995).
It is therefore very likely that the better results obtained with CryoSat-2 over sea ice are related to the reduced impact of off-nadir reflections and diffuse scattering effects on the radar signal.Following this theoretical basis, we seek to analyse the discrepancy of radar freeboard between CryoSat-2 and Envisat and its link with the ice surface properties.In particular, we seek to analyse the impact of surface specularity on the freeboard retrieval.
In Sect.2, we introduce the data sets used in the present study as well as the freeboard retrieval algorithms.Then, we compare CryoSat-2 and Envisat waveform echoes (Sect.3.1), along-track freeboard estimates (Sect.3.2) and gridded freeboard estimates (Sect.3.3).In Sect.3.4, we build a Cryosat-2-like version of the Envisat freeboard based on the relation between the freeboard discrepancy of Envisat and CryoSat-2 and the Envisat pulse peakiness (PP).Finally, in Sect.3.5, we convert CryoSat-2, Envisat and the corrected Envisat freeboard data sets to ice draught fields and compare each data set to in situ measurements.

Envisat
Envisat was launched in 2002 by ESA and was set on the same orbit as the ERS-1/2 satellites, providing coverage of the Arctic Ocean up to 81.5 • N. The RA-2 altimeter on board Envisat includes a Ku-band pulse-limited radar altimeter with a bandwidth of 320 MHz.To derive the Envisat freeboard fields, we use the Sensor Geophysical Data Record (SGDR) product from ESA (https://earth.esa.int/web/guest/-/ra-2-sensor-data-record-1471) that is converted to NetCDF files by the Centre of Topography of Oceans and Hydrosphere (CTOH).The netcdfs contain geolocated 20 Hz waveform echoes, orbit parameters, ionospheric (model) and tropospheric (model) corrections.In addition to the parameters provided in the ESA sgdr product, the CTOH product also provides the DTU15 mean sea surface correction (Andersen and Knudsen, 2015) as well as the FES14 tide correction (Carrere et al., 2015).Envisat freeboard is estimated from November 2010 to April 2011 for the first common winter and from November 2012 to March 2012 for the second common winter season.The reduced period during winter 2011/2012 is due to the end of the Envisat mission at the beginning of April 2012.

CryoSat-2
CryoSat-2 was launched by ESA in 2010 and was primarily designed for the observation of ice over land and ocean surfaces (Wingham et al., 2006).Although the highly inclined orbit of CryoSat-2 allows for the monitoring of sea-ice freeboard up to 88 • N, we only make use of observations below 81.5 • N in the present study (maximum latitude of Envisat orbit).Below this latitude and over the Arctic ocean, CryoSat-2 operates mostly in SAR mode except for observations close to the coastline and for a narrow patch located between 130 and 150 • W and north of 80 • N, where it is set in SAR interferometry mode.As the purpose of the present study is to analyse the difference in radar freeboard between pulselimited and SAR altimetry, we only consider freeboard observations in SAR regions and discard observations in SARIn regions for both CryoSat-2 and Envisat.The SIRAL altimeter on board CryoSat-2 operates at the same central frequency (Ku-band) and with the same bandwidth (320 MHz) as Envisat.
In the present study, we produce freeboard fields from the CryoSat-2 Baseline-C l1b product, which is also converted to NetCDF files by CTOH.The netcdfs contain geolocated 20 Hz waveform echoes, orbit parameters, ionospheric (model) and tropospheric (model) corrections, mean sea surface correction (DTU15, Andersen and Knudsen, 2015) and tide corrections (FES14, Carrere et al., 2015).The atmospheric and oceanic corrections are identical for the Envisat and CryoSat-2 products.As for Envisat, CryoSat-2 freeboard is estimated from November 2010 to April 2011 for the first common winter and from November 2012 to March 2012 for the second common winter season.

Ancillary data
Daily sea-ice extent and multiyear ice (MYI) age fields are available at a 12.5 km resolution from the National Snow and Ice Data Center (NSIDC) and are derived from AMSR-E and SSMIS passive microwave observations (Anderson et al., 2014).
The Beaufort Gyre Exploration Project (BGEP) moorings provide high-frequency (0.5 Hz) measurements of seaice draught since August 2003 due to a network of two to four moorings located in the Beaufort Sea (http://www.whoi.edu, Melling et al., 1995).The buoys are equipped, along with other instruments, on an upward-looking sonar (ULS), which measures the distance from the mooring to the bottom of the ice with a 420 kHz beam sonar.Sea-ice draught is then estimated by removing the depth of the mooring that is deduced from pressure measured every 40 s.The accuracy of each 0.5 Hz measurements is ±5 cm.
To provide simultaneous analysis of ice types with radar observations, we use Landsat-7 and Landsat-8 optical imagery.The georeferenced "natural colour" images distributed by the USGS (http://earthexplorer.usgs.gov/)are obtained from a combination of visible (bands 6, 5, 4) and thermal (band 10) images and have a general resolution of 30 m. Due to technical issues of the Landsat-7 imager, there are no usable images during the common flight period of CryoSat-2 and Envisat.We therefore use images out of the common flight period.
The Landsat-7 image used to collocate Envisat observations was acquired on 16 April 2004 in the Beaufort Sea and the Landsat-8 image used to collocate CryoSat-2 observations was acquired on 1 May 2015 in the Beaufort sea as well.
In both examples used in the present study, the time latency between the Landsat images and the altimetric observations is shorter than 24 h in order to minimise the impact of sea-ice drift on the correlation of both data sets.

Freeboard retrievals
In this section we describe the methodology that is applied to CryoSat-2 and Envisat to derive radar freeboard.While the different measurement modes (pulse limited and SAR) are expected to cause differences in the radar freeboard estimates, we try to keep the retrieval algorithms as similar as possible between the two sensors in order to reduce the impact of the processing chain on each data set.
The procedure we apply to retrieve Envisat and CryoSat-2 radar freeboard is described in detail in the ESA SI-CCI project (Ridout et al., 2012) and is based on the already published method used for ERS-2 (Peacock and Laxon, 2004;Laxon et al., 2003).
Radar freeboard is obtained by measuring the difference in range between the ocean and sea-ice floes.The discrimination between sea-ice and ocean observations is performed through the analysis of the radar waveform shape.Radar echoes over open water in sea-ice fractures (leads) are generally highly specular due to the presence of a thin and smooth layer of ice and/or of a flat ocean surface.On the contrary, radar returns over sea-ice floes are relatively rough due to the impact of sea-ice deformation and snow accumulation.Consequently, the discrimination between leads and ice floes can be performed with the analysis of the PP.In the present study, the PP is defined as follows:  where WF represents the echo and N WF is the number of range bins.
To distinguish lead from ice floe observations, the common methodology consists of using thresholds on the PP (Peacock and Laxon, 2004).In order to determine the appropriate thresholds, we collocate Landsat images with Envisat and CryoSat-2 PP observations as explained in the previous section.In Fig. 1, we show typical on-track Envisat (left) and CryoSat-2 (right) PP observations plotted over Landsat images.
The collocated analysis displays similar results for Envisat and CryoSat-2.Over sea-ice leads, the PP is always higher than 0.3 and can reach 0.6 (not visible due to the colour bar saturation).Based on this result and other similar visual observations, we define leads as observations with PP higher than 0.3.
In most freeboard retrievals, a threshold on the PP is also applied to identify mixed echoes found in the neighbouring of sea-ice leads (see Fig. 1) and to only keep unambiguous ice floe observations (Laxon et al., 2003;Peacock and Laxon, 2004;Giles et al., 2008;Ricker et al., 2014).Based on visual observations of collocated Landsat images with PP values such as the one shown in Fig. 1, we define sea-ice floes as observations with a PP lower than 0.10.
To estimate the surface elevation of ocean and sea-ice floes from the waveform echoes, several methodologies are used in the literature.In the ESA SI-CCI project, two different retracker algorithms are employed to take into account the difference in the waveform shape over specular leads and rough ice floes (Ridout et al., 2012), while in Ricker et al. (2014), the authors use a single retracker for leads and ice floe observations.Following the latter study, we only use a single retracker and make no extra correction.This choice is made to limit the potential bias driven by the use of different algorithms and to fully understand the discrepancies between Envisat and CryoSat-2 radar freeboard measurements.However, the difference in waveform shape between the two radar altimeters is likely to cause a difference in the radar freeboard fields.
Over surfaces with an heterogeneous reflectivity such as sea ice, basic retracking algorithms based on the waveform maximum power can be easily biased by off-nadir reflections.For this reason, we use the more robust Threshold First-Maximum Retracker Algorithm (TFMRA) to estimate the surface level position (Helm et al., 2014).For both Envisat and CryoSat-2 and for both leads and ice floes observations, the TFMRA retracker is parameterised similarly: waveform echoes are first oversampled by a factor 10.Then, the first waveform echo maximum is identified by calculating the first derivative of the power echo using a 3-point Lagrangian and finally, the echo position is estimated at 50 % of the first waveform echo maximum.
The next step of freeboard retrieval consists of interpolating the sea level underneath sea-ice floes and estimating the height of ice floes above the interpolated sea level.As the sea level interpolation can result in large errors due to uncertainties in estimates of ocean tide, barometer tide and mean sea surface height, we argue that the sea level should only be interpolated within sections of 25 km around each lead.Once the sea level is interpolated, single freeboard measurements are calculated and smoothed along the altimeter track with a 25 km window median.As in Schwegmann et al. (2016), we then discard freeboards smaller than 1 m or larger than 2 m to avoid the presence of unrealistic values.
Finally, monthly freeboard observations are gridded onto a 12.5 km × 12.5 km polar stereographic grid using a median filter with a radius of 100 km.Similarly to the freeboard maps, the Envisat along-track PP is also converted to monthly gridded maps.

Freeboard-to-thickness conversion
To convert the freeboard (fb) height to sea-ice thickness (SIT), we assume the hydrostatic equilibrium between the snow-covered sea ice and the ocean and we use the following expression: where h s represents snow depth, ρ i is ice density, ρ s is snow density and ρ w is sea water density.
To operate the freeboard-to-thickness conversion, several snow-depth data sets have been employed.For instance, Laxon et al. (2003) and Giles et al. (2008) use the time and space-varying snow depth climatology (hereafter W99) from the study by Warren et al. (1999).However, recent in situ observations have demonstrated that snow depth has thinned by 50 % over first-year ice relative to the W99 climatology (Kurtz et al., 2013;Guerreiro et al., 2016).Following this result, Kwok and Cunningham (2015) estimate snow depth according to the following equation: where h s (X, t, f MY ) represents the time-(t) and space-(X) varying W99 climatology, and f MY is the MYI fraction that they derive from the Advanced Scatterometer (ASCAT) following the study by Kwok (2004).In the present study, we use a similar methodology to estimate snow depth except that we use a different data set to derive MYI ratio.Indeed, the methodology based on ASCAT observations assumes a direct link between ice age and ice roughness, which is not necessarily true in any case.To overcome this issue, we use the National Snow and Ice Data Center (NSIDC) ice age data set (http://nsidc.org/data/docs/daac/ nsidc0611-sea-ice-age/, Anderson et al., 2014).In this product version, the ice age is calculated by tracking the ice by comparing adjacent passive microwave images as well as using wind forcing and buoy displacement information.In addition to not making the assumption of a constant correlation between ice age and ice roughness, this product has the advantage of being available over the entire Envisat mission (2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012).In the present study, monthly snow depth fields are therefore derived as follows: first, each ice pixel with ice older than 1 year is considered as MYI and pixels with ice younger than 1 year is considered FYI.Then, we apply an average filter with a radius of 100 km (similarly to the freeboard data sets) and estimate the ratio of MYI observation within the filtering area to build MYI concentration maps.Finally, we use the resulting MYI ratio fields, the W99 climatology and Eq. ( 3) to determine monthly snow depth fields.
Based on the results by Alexandrov et al. (2010), recent studies attribute a lower density to MYI (882 kg m −3 ) than to FYI (917 kg m −3 ).To account for the difference in ice density between MYI and FYI, we use the same definition for ice density as in Kwok and Cunningham (2015): where ρ MY i and ρ FY i are respectively set to 882 and 917 kg m −3 and where f MY is the MYI concentration derived from the NSIDC MYI age data set.
Regarding snow and sea water densities, we use the same parameterisation as in Kwok and Cunningham (2015).More precisely, the snow density follows the monthly average prescribed by Warren et al. (1999) and the sea water density is set to 1024 kg m −3 .
Another important step for the freeboard-to-thickness conversion is the correction of the slower wave propagation effect in the snow pack.Indeed, the radar signal propagates slower in snow than in the atmosphere, which causes an underestimation of the freeboard estimates.To correct this bias, we add the factor α (see Eq. 5) to correct the freeboard measurements as operated in Kwok and Cunningham (2015). (5) 3 Results

Comparison of CryoSat-2 and Envisat waveform echoes
As a first analysis, we compare mean CryoSat-2 and Envisat waveforms echoes for observations originating from leads, MYI and FYI.Leads and ice floes are identified as described in Sect.2.4 and MYI and FYI observations are distinguished using the NSIDC ice age data set.More specifically, ice floes echoes located in areas with more than 70 % of MYI are classified as MYI and ice floes located in areas with less than 30 % are classified as FYI.
To average CryoSat-2 and Envisat waveform echoes, we use the same methodology as in the study by Zygmuntowska et al. (2013).All waveform echoes are normalised and shifted so their maximum power is located in the same sampling bin (the 67th bin here).Then, all waveform echoes are averaged to produce a mean echo.To produce average echoes, we use all waveforms available during the November 2010-April 2011 period and in the common under-flight area.Results are presented in Fig. 2.
First of all, CryoSat-2 waveforms clearly display a narrower leading edge width (LEW) than Envisat waveforms.This difference is mostly caused by the smaller SAR footprint (Raney, 1995).For both sensors, the difference in ice surface type tends to modify the shape of the leading edge.In particular, the LEW is much wider for MYI and FYI than for lead observations.This phenomenon is generally attributed to an increase of surface roughness and/or of volume scattering.As suggested by Fig. 2, the LEW widening displayed by MYI waveforms is larger for Envisat than for CryoSat-2 waveforms.Considering that MYI is generally rougher and covered by a thicker snow layer than FYI, this result suggests that SAR waveforms are less sensitive to the variations of surface properties than pulse-limited waveforms.The lower sensitivity of CryoSat-2 waveforms to surface properties is mostly due to the Doppler post-processing that allows a reduction of the widening of the effective footprint related to the increase of surface roughness and/or volume scattering (Chelton et al., 2001;Raney, 1995).
The deformation of waveform echoes related to changes of surface properties is likely to cause biases on the altimetric range retrieval.In particular, the LE widening is likely to cause an underestimation of the surface level position over rough surfaces (Chelton et al., 2001).This is particularly true when using empirical threshold retrackers that do not take into account the modification of the waveform shape (Kurtz et al., 2014).
Considering the seemingly lower impact of ice surface properties on CryoSat-2 waveform echoes, our results suggest that CryoSat-2 ranges estimates should be less impacted by surface roughness and/or snow volume scattering changes.Hence, the better freeboard estimates obtained with CryoSat-2 are likely to be related to a lower sensitivity of waveform echoes to the variability of ice surface properties.

Comparison of along-track radar freeboard estimates
As CryoSat-2 and Envisat have a different orbit configuration, it is unfortunately not possible to compare the radar freeboard over the exact same track.Thus, all one can do is to compare the radar freeboard within the same Arctic region.In Fig. 3, we show ground tracks of Envisat and CryoSat-2 missions used to analyse typical along-track freeboard estimates.Both tracks are located in the in the western part of the Arctic Ocean and were acquired on 24 February 2011.
The ice type classification (grey tons) shows that both MYI and FYI observations are found below each track.Figure 3b and c shows the elevation of floes (grey) and leads (black) for each satellite mission.The first striking difference between the two data sets is the dispersion of surface elevation.Over sea-ice leads, CryoSat-2 displays a relatively low standard deviation of surface elevation (4.2 cm) when compared to Envisat (7.8 cm).This result clearly demonstrates that CryoSat-2 provides more consistent sea level estimates than Envisat.The standard deviation of the floes surface elevation is also lower for CryoSat-2 (8.6 cm) than for Envisat (18.6 cm).This discrepancy between the two data sets is most likely to be related to the larger footprint size of Envisat radar altimeter and to its higher sensitivity of sea-ice properties.This result will be further discussed in the following section.
Surprisingly, the elevation of Envisat leads is found above the average elevation of sea-ice floes, which causes the radar freeboard to be negative (Fig. 3d).In the literature, this phenomenon is attributed to the large difference between leads and ice floes waveform echoes (Laxon, 1994;Giles et al., 2008;Laxon et al., 2013).This effect was also observed when comparing sea level observations obtained over flat leads and over rough open ocean (Giles et al., 2012).
As surface roughness and snow volume scattering increase, radar waveform echoes become more diffuse.As threshold retrackers do not take into account the modification of the waveform shape, this phenomenon causes a bias in the range retrieval.More specifically, altimetric ranges estimated with relatively specular echoes appear shorter than altimetric ranges estimated with diffuse echoes.
Unlike for Envisat, the average elevation of CryoSat-2 seaice floes is found above the sea level.As already shown in the study by Ricker et al. (2014), this result suggests that CryoSat-2 allows realistic freeboard estimates to be retrieved with the use of a single retracker and without applying any constant correction.As suggested in the previous section, this difference between the two sensors is mainly related to the difference in altimetric mode (SAR and pulse limited).In SAR altimetry, the Doppler post-processing allows the surface response to be sharpened and minimise the sensitivity of the waveform shape to surface roughness and volume scattering (Raney, 1998).Consequently, SAR altimetry is less impacted by the variability of ice surface properties than pulselimited altimetry, which enables realistic (positive) freeboard estimates to be retrieved.
In most studies, the bias related to the difference in specularity is artificially corrected by applying a different retracking algorithm to leads and ice floes and/or by applying an empirical constant correction (Giles et al., 2008;Laxon et al., 2013).As we seek to fully understand the impact of ice surface properties on CryoSat-2 and Envisat freeboard retrievals, we do not apply such a correction at this stage of the freeboard retrieval.

Comparison of gridded radar freeboard estimates
As mentioned in the previous section, the difference in surface properties between leads and ice floes is generally expected to result in a constant bias in the freeboard estimates.In addition to this constant bias, the study by Kurtz et al. (2014) demonstrates that the variability of surface properties within ice floes (especially roughness variability) also causes a variable bias in the freeboard estimates when us-ing a threshold retracking algorithm.Based on this result, we seek to analyse the impact of sea-ice surface properties on CryoSat-2 and Envisat radar freeboard estimates in detail.
As the along-track observations do not allow the same regions to be strictly compared, we now compare monthly gridded freeboard data sets.In Fig. 4a, we show monthly maps of the radar freeboard difference ( fb) for the 2010/2011 ice growth season between Envisat and CryoSat-2 (Envisat -CryoSat-2).We show the corresponding figure for the 2011/2012 ice growth season in Fig. S1 in the Supplement.
For every Arctic region and for each month of the period of study, CryoSat-2 is always thicker than Envisat ( fb < 0).This result is mostly due to the unrealistic negative Envisat freeboard estimates described in the previous section.
During the entire ice growth season, small fb observations are located over FYI in marginal regions such as in the Bering Strait, north of the Atlantic Ocean and in coastal regions.Small fb are also particularly present at the beginning of the ice growth season.Conversely, large fb observations are mainly located over MYI areas at the Canadian Arctic Archipelago and are mostly visible at the end of winter.The evolution of the fb all along the winter season as well as its spatial distribution suggest that the discrepancy between CryoSat-2 and Envisat radar freeboard estimates is related to the ice surface properties.In particular, variations of waveform shape driven by changes in ice roughness and snow accumulation are likely to be responsible for the observed variations of fb.To further analyse the link between the variability of the ice surface properties and the radar freeboard discrepancy between Envisat and CryoSat-2, the waveform pulse peakiness (PP) can be analysed.For nadir-looking radar altimeters such as Envisat and CryoSat-2, high values of PP indicate the presence of flat and specular FYI while low values of PP indicate the presence of rough and snow-covered MYI (Zygmuntowska et al., 2013).This phenomenon is also visible on the waveform echoes shown in Fig. 2.
In Fig. 4b, we show monthly maps of Envisat PP for the 2010/11 ice growth season.To build these maps, PP observations corresponding to leads have been removed.In November, most Arctic regions display a PP larger than 0.1.These relatively high values are mainly explained by the presence of specular young sea ice.Only rough MYI areas display PP observations lower than 0.1 during this period of the year.The average Envisat PP decreases progressively from 0.14 in November to 0.07 in April due to the ice growth, ice deformation and snow thickening that increase the ice surface diffusion.Only coastal regions keep displaying relatively high values of PP during the entire ice growth season.
Considering Fig. 4a and b, it is striking how the PP and the fb maps are correlated.This relation between the two parameters is particularly visible in marginal and coastal regions where the PP and the fb are both relatively high.
To further demonstrate the link between the PP and the fb, we show in Fig. 5 the relation between the fb and the Envisat PP for November 2010-April 2011 (blue) and November 2011-March 2012 (red) as well as the polynomial regression obtained with the entire set of observations (dark dashed line).As suggested by the visual observations of Fig. 4, there is a clear correlation between the PP and the fb (R = 0.82).The radar freeboard difference varies from −33 cm for low PP to −18 cm for high PP.Between the two ice growth seasons, the relation between the PP and the fb is fairly similar despite a slight discrepancy for low PP values (< 0.08).The relatively high dispersion observed for low PP values between the two winter seasons is mostly driven by an insufficient sampling of thick freeboard/low PP estimates due to the relatively low amount of thick ice below 81.5 • N over the period of study.
The linkage between the PP and the fb shown in Figs. 4 and 5 demonstrates that the discrepancy of radar freeboard between CryoSat-2 and Envisat is related to the impact of surface properties on the radar signal.Considering that CryoSat-2 provides relatively accurate freeboard estimates and that SAR waveforms are less sensitive to ice surface properties, the linkage between the fb and the Envisat PP is most likely driven by a higher impact of ice surface properties on pulse-limited altimetry.This result is nothing more than an extension of the conclusions made in the previous section: Envisat waveform echoes are more impacted by the variability of ice surface properties than SAR waveform echoes (see Fig. 2).The higher sensitivity of pulse-limited waveforms to ice surface properties tends to create a variable bias in the altimetric range and thus on the freeboard estimates.In particular, Fig. 5 suggests that Envisat radar freeboard is more underestimated over ice characterised by a low PP than over ice characterised by a high PP.In other words, the freeboard height is underestimated over thick and rough sea ice and/or underestimated over thin and specular sea ice.This finding is similar to the results shown in the study by Schwegmann et al. (2016).3.4 Toward an improved Envisat freeboard: Envisat/PP Section 3.2 and 3.3 show that the current Envisat freeboard estimates should be corrected from (1) the constant elevation bias existing between leads and ice floes and (2) from the variable bias caused by the variability of ice surface properties (surface roughness and volume scattering) found within ice floes.While (1) can be reduced by using an empirical correction as operated in previous studies (Giles et al., 2008;Laxon et al., 2013), (2) requires a more sophisticated methodology.
A first approach could consist of developing a retracking algorithm model that takes into account the variability of ice surface properties as operated in Kurtz et al. (2014) instead of using threshold retrackers.While such a model could provide accurate measurements of sea-ice freeboard, it requires accurate knowledge on sea-ice characteristics such as mean surface slope (diffusion), angular backscattering efficiency (specularity) and snow volume scattering properties, which are currently hardly measurable parameters.
Another approach to improve the Envisat freeboard retrievals would consist of correcting the Envisat radar freeboard from both (1) and (2) with the results obtained in the present study.In particular, the regression function y(PP) shown in Fig. 5 can be used to build a CryoSat-2-like version of Envisat freeboard, which should considerably improve the current estimates.Following this approach, in Fig. 6c we show the Envisat freeboard corrected as follows: where fb pp is the corrected Envisat radar freeboard (hereafter Envisat/PP), PP is the Envisat pulse peakiness, fb is the uncorrected Envisat radar freeboard and y(PP) is the average relationship between PP and fb shown in black in Fig. 6.Note that we fit y(PP) relation with the entire set of observations (November 2010-April 2011 and November 2011-March 2012) in order to minimise the impact of radar freeboard uncertainties.Unlike for Envisat (Fig. 6a), the Envisat/PP data set displays realistic positive freeboard estimates during the entire winter.Considering Fig. 6b and c, the Envisat/PP radar freeboard is very similar to the results obtained with CryoSat-2, with thick freeboard estimates over MYI and thinner estimates over FYI.As shown in Table 1, the RMSD between Envisat/PP and CryoSat-2 (∼ 1.5 cm) is clearly better than the average RMSD between Envisat and CryoSat-2 (∼ 23 cm).Note that we show the corresponding results for the 2011/2012 ice growth season in Fig. S2 in the Supplement.
To further assess the capacity of the PP correction to provide a CryoSat-2-like version of Envisat freeboard, we show in Fig. 6d the probability distribution function (PDF) of the Envisat/PP (blue) and CryoSat-2 (black) radar freeboard estimates.We also provide the average bias and average root mean square difference between the two data sets in Table 1.For each month of the period of study, the distribution of the Envisat/PP and CryoSat-2 data sets are relatively similar to similar mean/modal values.Only November and, to a lesser extent, December show a discrepancy between the two data sets with an overestimation of Envisat radar freeboard estimates.This result could be due to a lower accuracy of the native Envisat radar freeboard estimates and/or to a lower performance of the PP correction during this period for which the amount of specular scattering is relatively high.
In addition to the spatial variability, the Envisat/PP and CryoSat-2 data sets display relatively similar seasonal variations with an increase of respectively 3.4 and 2.1 cm between November 2010 and April 2011 and of 3.0 and 3.3 cm between November 2011 and March 2012 (see Table 1).This result suggests that unlike for the native Envisat radar freeboard estimates (Kern et al., 2015), the Envisat/PP should allow a realistic seasonal ice growth cycle to be derived.
The relatively good match between CryoSat-2 and Envisat/PP radar freeboard demonstrates that the PP correction allows a robust CryoSat-2-like version of Envisat freeboard to be built during each month of the common flight period of Envisat and CryoSat-2 missions.

Comparison to BGEP ice draught measurements
To assess the potential of the PP correction approach in producing accurate ice thickness estimates, we now convert the CryoSat-2, Envisat and Envisat/PP radar freeboard data sets to sea-ice draught (thickness -freeboard) fields and compare the results to BGEP ice draught measurements.For www.the-cryosphere.net/11/2059/2017/The Cryosphere, 11, 2059-2073, 2017 this purpose, we estimate the monthly median altimetric ice draught within a radius of 50 km around each available mooring, which we compare to the corresponding monthly median mooring ice draught.In Fig. 7, we show the monthly CryoSat-2 and Envisat/PP ice draught estimates as a function of the corresponding monthly BGEP ice draught.In colour, we represent the MYI fraction for each observation.We also provide statistical parameters (mean bias, RMSE and correlation coefficient) in Table 2 for each data set.
CryoSat-2 ice draught estimates display a relatively low RMSE (15 cm) with in situ measurements during the 2010/11 ice growth season (Fig. 7a) and a higher RMSE (21 cm) during the 2011/12 ice growth season (Fig. 7b).The higher RMSE observed in Fig. 7b is mainly driven by a few values characterised by a low MYI fraction.This result suggests that the higher RMSE obtained during 2011/12 might be caused by an inaccurate snow depth and/or ice density parameterisations rather than by an error in the freeboard fields.
The comparison of the Envisat/PP and Envisat data sets during the 2010/12 period clearly shows the improvement brought by the PP correction (see Table 2).The lower mean bias and RMSE is mostly due to the correction of the average bias between leads and ice floes (labelled (1) above) while the improved correlation coefficient is mostly due to the cor- The Cryosphere, 11, 2059-2073, 2017 rection of the variable bias existing within ice floes (labelled (2) above).
The correlation between the Envisat/PP data set and the BGEP ice draught measurements displays a low RMSE (12 cm) during winter 2010/11 (Fig. 7j) and a relatively higher RMSE (28 cm) during winter 2011/12 (Fig. 7k).As for CryoSat-2, we attribute this difference to a potential inaccurate freeboard-to-thickness conversion.
To further assess the potential of the PP correction, it is necessary to verify whether the Envisat/PP data set is also valid in the cross-calibration period.As the BGEP ice draught measurements are available from August 2003, the accuracy of the PP correction can be evaluated over most of the Envisat mission lifetime.The Envisat and Envisat/PP ice draught estimates are therefore computed over the 2003-2010 ice growth seasons and are compared with the corre-sponding mooring observations.Results are presented in Table 2 and in Fig. 7c-i.
As during the 2010-2012 period, the Envisat/PP ice draught data set displays a good agreement with the buoy observations (RMSE = 13 to 32 cm) relative to the uncorrected Envisat data set (RMSE = 165 to 186 cm).This good agreement between the Envisat/PP and the BGEP ice draught estimates demonstrates therefore that the Envisat/PP data set provides accurate estimates of sea-ice draught during the entire Envisat mission.
The largest improvements brought by the PP correction are particularly visible for winter seasons occurring right after the low sea-ice summer extent (2007/08, 2008/09, 2010/11 and 2011/12).As displayed in Fig. 7, these winter seasons are characterised by mixed FYI and MYI and thus by heterogeneous sea-ice conditions (surface roughness, snow depth, etc).This result confirms therefore that the PP corrections al- lows the impact of ice properties on the freeboard estimates to be reduced and that it enables more accurate ice thickness estimates to be retrieved.

Discussion
In Sect.3.1, we show that the variability of ice surface properties has a stronger impact on Envisat waveforms than on CryoSat-2 waveforms (especially between FYI and MYI).Based on this observation, we conclude that CryoSat-2 radar freeboard should provide estimates of radar freeboard relative to Envisat with relative accuracy.Nevertheless, one can still observe a variability of CryoSat-2 waveform echoes depending on the ice type.This result suggests that while the sensitivity of CryoSat-2 waveforms is relatively low, the radar freeboard derived from CryoSat-2 is also likely to be biased by the ice surface properties.In the study by Kurtz et al. (2014), the authors demonstrate that the variability of the ice surface properties between ice floes (mainly ice roughness) causes a bias in CryoSat-2 freeboard estimates when using a threshold retracker.However, the comparison of our CryoSat-2 ice draught estimates with in situ measurements as well as preliminary studies (Laxon et al., 2013;Kwok and Cunningham, 2015;Tilling et al., 2015) demonstrate that CryoSat-2 freeboard estimates are fairly accurate despite the use of a threshold retracker.Consequently, the impact of CryoSat-2 freeboard uncertainty on the Envisat/PP estimates should be minor.The exercise operated in the present study could nevertheless be repeated with better CryoSat-2 estimates to derive a more accurate PP correction, which could further improve the Envisat freeboard estimates.
While the PP correction allows most of the bias between CryoSat-2 and Envisat freeboard data sets to be removed, other sources of inconsistencies could explain the remaining difference between the two data sets.For instance, bright off-nadir reflections have a higher impact on Envisat than on CryoSat-2.The reduced footprint of CryoSat-2 allows bright off-nadir reflections in the along-track direction to be filtered out, which enables more accurate estimates of surface level position to be produced than with Envisat.As this discrepancy between the two radar altimeters is not corrected by the PP correction, the Envisat/PP freeboard is therefore likely to be less accurate than CryoSat-2's.Another source of discrepancy between SAR and pulse-limited altimetry is the size of the sampled ice floes.Thanks to the Doppler post-processing, the SAR mode of CryoSat-2 allows smaller ice floes to be sampled than Envisat.As small ice floes are generally thinner than large ice floes, this difference could cause a sampling bias between the two sensors.More specifically, Envisat freeboard is likely to overestimate regional freeboard height.The only thing one can do to reduce this sampling bias would be to estimate freeboard height when sea ice is as compact as possible (in the middle of winter, for example).

Conclusions
In this study we investigate the inconsistency between CryoSat-2 and Envisat radar freeboard estimates during the common flight period (November 2010-April 2011and November 2011-March 2012).The analysis of the alongtrack surface elevation estimates shows that the average Envisat ice floes elevation is always found below the sea level.This unrealistic result is attributed to the high difference in waveform shape acquired over smooth and rough surfaces and to the use of a threshold retracker.Unlike Envisat, the average CryoSat-2 elevation of ice floes is mostly found above the sea level, which allows the retrieval of realistic freeboard estimates.The better results of CryoSat-2 are attributed to the SAR post-processing that allows the radar response to be sharpened and reduces the impact of ice surface properties on waveform echoes.
The analysis of the gridded freeboard height difference between CryoSat-2 and Envisat shows that the discrepancy between the two sensors is larger over ice characterised by a low PP than over specular and young ice characterised by a high PP.Here as well, this discrepancy is attributed to the higher sensitivity of Envisat waveform echoes to sea-ice surface properties (surface roughness and snow volume scattering).
While the average difference in waveform shape between leads and ice floes is generally corrected by the use of a different retracking algorithm for leads and ice floes in freeboard retrieval processing, the bias due to the variability of sea-ice surface properties has yet never been taken into account in Envisat freeboard studies.To correct these two biases, we built an improved Envisat freeboard data set (Envisat/PP) based on the relation between the freeboard difference between Envisat and CryoSat-2 and the Envisat PP.The resulting Envisat/PP freeboard estimates display similar patterns to CryoSat-2 over the entire period of study (RMSD = ∼ 1.5 cm) and offers a more realistic seasonal cycle (∼ 2.0 to 3.0 cm) than the uncorrected Envisat freeboard.
The comparison of each altimetric data set with in situ ice draught observations during the common flight period reveals that Envisat/PP ice draught is much more accurate (RMSE = 12-28 cm) than the uncorrected Envisat data set (RMSE = 178-179 cm) and as accurate as CryoSat-2 (RMSE = 15-21 m).
To further assess the potential of the PP correction, the Envisat and Envisat/PP ice draught data sets are extended to the 2003-2010 period and are similarly compared to BGEP ice draught measurements.As for the 2010-2012 period, the agreement with in situ measurements is higher for Envisat/PP (RMSE = 13-32 cm) than for Envisat (RMSE = 165-186 cm), which demonstrates the potential of the PP correction to provide accurate freeboard estimates over the entire Envisat mission lifetime.
The result obtained in the present study should therefore allow circumpolar sea-ice thickness to be derived over more than a decade by combining Envisat and CryoSat-2 data sets and should help to improve our understanding of the undergoing Arctic sea-ice changes.

Figure 1
Figure 1.(a) PP spatial variability along the Envisat track (16 April 2003) plotted over a Landsat-7 LandsatLook Image acquired on the same day and (b) PP spatial variability along CryoSat-2 track (1 May 2015) plotted over a Landsat-8 LandsatLook Image also acquired on the same day.For both figures, each dot represents a 20 Hz PP measurement.

Figure 2 .
Figure 2. (a) Envisat and (b) CryoSat-2 mean waveform echoes for leads (blue), FYI (green) and MYI (red) calculated during the 2010/11 winter and for the entire common flight region.

Figure 3 .
Figure 3. (a) Map of the Envisat (red) and CryoSat-2 (blue) tracks (both monitored on 24 February 2011) selected for the along-track analysis of the radar freeboard.The light shading shows MYI regions (defined as sea ice with a MYI fraction above 0.7) and the dark grey shading shows FYI regions (defined as sea ice with a MYI below 0.7).(b) CryoSat-2 and (c) Envisat leads (grey dots) and ice floes (black dots) surface elevation corresponding to the tracks shown in panel (a).(d) Envisat (red) and CryoSat-2 (blue) freeboard corresponding to the tracks shown in panel (a).

Figure 4 .
Figure 4. (a) Monthly freeboard difference ( fb) between Envisat and CryoSat-2 and (b) monthly Envisat pulse peakiness (PP) shown for the November 2010-April 2011 period.The dark lines represent the isoline MYI fraction equal to 0.7.

Figure 5 .
Figure 5. Relation between the monthly freeboard difference between Envisat and CryoSat-2 ( fb) and the monthly Envisat pulse peakiness (PP) shown for winter 2010/2011 (blue) and 2011/2012 (red).The error bars show the corresponding standard deviation for each value and the dark tilted line represents the linear fit of all monthly observations (November 2010-April 2011 and November 2011-March 2012).The fitting equation is given by fb = 6.9.PP 3 + 5.3PP 2 + 1.6.PP − 0.4.