Evaluating Airborne Ku-Band Radar Altimetry over Landfast First-Year Sea Ice

Recent studies have challenged the assumption that Ku-band radar used by the CryoSat-2 altimeter fully penetrates the dry snow cover of Arctic sea ice. There is also uncertainty around the proper technique for handling retracker threshold selection in the Threshold First-Maxima Retracker (TFMRA) method which estimates the ice surface elevation from the radar echo waveform. The purpose of this study was to evaluate the accuracy and penetration of the TFMRA retracking method applied 5 to the Airborne Synthetic Aperture Radar and Interferometric Radar Altimeter System (ASIRAS), an airborne simulator of the CryoSat-2, to investigate the effect of surface characteristics and improve accuracy. The ice surface elevation estimate from ASIRAS was evaluated by comparing to the snow surface measured by aggregating laser altimetry observations from the Airborne Laser Scanner (ALS), and the ice surface measured by subtracting ground observations of snow depth from the snow surface. The perceived penetration of the ice surface estimate was found to increase 10 with the retracker threshold and was correlated with the value of surface properties. The slope of the relationship between penetration and threshold was greater for a deformed ice surface, a rough snow surface, a deeper snow cover, an absence of salinity and a larger snow grain size. As a result, the ideal retracked threshold, one that would achieve 100% penetration, varies depending on properties of the surface being observed. Under conditions such deep snow or a large grain size, the retracked elevation sr was found in some cases to not penetrate fully the snowpack. This would cause an overestimation of the sea ice 15 freeboard and as a consequence, the sea ice thickness. Results suggest that using a single threshold with the TFMRA retracking method will not yield a reliable estimate of the snow-ice interface when observed over an area with diverse surface properties. However, there may be potential to improve the retracking method by incorporating knowledge of the sensed surface physical characteristics. This study shows that remotely sensed surface properties, such as the ice deformity or snow surface roughness, can be combined with the waveform shape to 20 select an ideal retracker for individual returns with an additional offset to account for the incomplete penetration of Ku-band over appropriate surface characteristics. 1 https://doi.org/10.5194/tc-2020-283 Preprint. Discussion started: 5 November 2020 c © Author(s) 2020. CC BY 4.0 License.


Field measurements
Field measurements were collected by ECCC over a 46km path following the CryoVEx flight line (King et al., 2015). Snow 85 depth measurements were collected using Snow-Hydro Magnaprobes supported with Global Positioning System (GPS) sensors with a horizontal accuracy of 2m (Sturm and Holmgren, 2018). A total of 37,320 collocated measurements were obtained at a spacing of approximately 2m along the flight track, with transects branching out orthogonally at random intervals at lengths of up to 100m. Bulk measurements of snow density were obtained using a ESC30 gravimetric snow sampler at 174 points along the track, with an average separation of 550m. Approximately 10km of the collection path was coincident with airborne 90 observation track (within the 20m x 3m footprint). The coincident segments of the path ranged in size from 100m to 2860m, with at least 10 segments being over 500m in length. Since a large number of segments are greater than the reported lengthscale of snow depth variability on sea ice (King et al., 2015), and span a distance that covers multiple ice floes, the data are likely representative of mid-March conditions on first-year sea ice in the Canadian Arctic Archipelago.
An additional 20,440 measurements were collected from three sites situated approximately 1km, 18km and 31km North of 95 the start of the CryoVEx track. Each site contained a measurement grid of 21 lines covering 500m along the track and 14 lines covering 250m across-track. An additional 54 density measurements were obtained at each site in grids of 3 lines along and 6 lines across-track.
Vertical profiles of the snowpack properties were collected by excavating 37 pits along the course of the track, 14 of which were within 14 meters of a radar altimeter nadir. A YSI EcoSense EC-300A sensor was calibrated in a control solution of saline 100 water and used to measured snow salinity with an accuracy of ± 0.2PSU. Each pit stratigraphy was manually determined by inspecting the snow pit face with a finger hardness test. Grain size and classifications were determined by selecting 3 grains deemed to be representative of the layer and measuring their minimum and maximum diameter with a 2mm compactor card and a field microscope. Nandan et al. (2017b) identified that the snowpack parameters which had the most impact on the Kuband microwave penetration were the snow salinity and snow grain size. These properties were measured along vertical profiles 105 in the snow pits. Ideally, the profile layers were to be aligned with radar altimeter echoes acquired coincidentally with the snow pit measurements. Due to uncertainties in determining the sensor offset, such an alignment was not feasible. Therefore, the snowpack properties were summarized per pit as a layer weighted average.

Radar Processing
The ASIRAS return can be described by measuring the pulse peakiness (PP) which is generally calculated as the ratio between 110 the maximum echo return power and either the sum or the mean of the total echo power. The PP value can be used to indicate a specular surface scatter (high PP) or a diffuse surface scatter (low PP), and is commonly used to distinguish between open ocean, leads and sea ice (Peacock and Laxon, 2004;Ricker et al., 2014). While the study only covers landfast first-year sea ice, the parameterization of the measurements' waveform may be beneficial due to the known effect of surface roughness on the shape of the waveform (Makynen and Hallikainen, 2009).

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The radar waveform was retracked to estimate elevation of the interface within the echo. Estimated elevation was then compared to the observed elevation of the ice surface, which was obtained by subtracting the field measured snow depth from the snow surface elevation. A common method for retracking Ku-band sea ice altimeter waveforms to obtain sea ice freeboard is the threshold first maxima re-tracker algorithm (TFMRA) (Xia and Xie, 2018;Ricker et al., 2014). This method finds a point on the echo with a value equal to a given percentage (threshold) of the maximum echo value that is the closest such point on 120 the leading edge of the waveform, which is the left side of the first instance of the echo's maximum value (Helm et al., 2014).
The threshold percentage can vary from 40% to 80% (Ricker et al., 2014), with recent studies suggesting that 70% is the most effective (Xia and Xie, 2018). To evaluate the effect of the TFMRA threshold selection on the error, thresholds of 20% to 100% at a 10% interval were applied.
The aircraft carrying the sensor is subject to variations in pitch and roll, causing the target to deviate from the nadir. These Due to the positioning and structure of the platform, the ALS and ASIRAS sensors have a relative offset that needs to be calibrated against a common surface elevation. An offset compensation is applied to the ASIRAS radar to align the snow surface return with the ALS measured surface. In the case of CryoVEx, the offset is calibrated over runways (Hvidegaard et al., 2014), using corner reflectors (Willatt et al., 2011), or over open water (King et al., 2018). Since none of these options 135 were available for this study, the sensor offset was calibrated using the distance between the estimated and observed snow-ice interfaces in returns over an area of shallow snow and flat ice. To reduce the effect of snowpack volume scattering on the radar waveform, only returns with an average observed snow depth of less than 10cm within the radar footprint over level ice were considered during calibration.
The elevation of a snow-covered ice surface can be underestimated by radar altimetry due to the the reduced speed of 140 electromagnetic waves in snow (Mallett et al., 2019;King et al., 2020). The retracked elevation is adjusted by applying a correction factor such that the speed of light through the snow is given by where p s is the density of the snow in gcm −3 (Kurtz et al., 2013).
The retracked elevation s r for each ASIRAS return is compared to the elevation of the snow and ice surface within the 145 footprint of that return. The snow surface s a s is obtained from the average elevation of ALS points within the footprint, while the ice surface s s i is calculated by subtracting the average of ground-based snow depth observations within the footprint from the snow surface. To evaluate the ability of the Ku-band radar altimeter to measure the elevation of the snow-ice interface, penetration (P ) and the accuracy of the interface estimate (E) are calculated. Estimates of P are retracked elevation relative to the snow surface elevation, with positive being below and negative being above. Quantities of E are retracked elevation 150 relative to the ice surface elevation, with positive being above and negative being below. The penetration can also be expressed as a proportion of the observed snow depth, which yields the percentage of the snowpack penetrated P r or proportion of the snowpack as error E r . To measure the magnitude of error over a group of returns, the absolute values of E and E r are expressed as E a and E ra respectively.
The sensor used in the ASIRAS radar altimeter is based on the SIRAL sensor design used in Cryosat 2, so its footprint can 155 be estimated using the same principles (Mavrocordatos et al., 2004). For the tracks used in this study, the ASIRAS altimeter was flown in single-antenna SAR, low-altitude mode. Due to the nadir-facing orientation of the sensor, the footprint is pulsedoppler-limited (PDL), and based on its flight parameters has an approximate size of 2 meters in the along-track and 20 meters in the across track direction (Scagliola, 2013). Measurement of the surface such as snow depth, surface elevation and ice deformity classification are aggregated to the footprint for each return to estimate the surface characteristics observed by the 160 radar altimeter. To evaluate the best method for aggregating measurements, circular areas with radii ranging from 8 to 40 meters at 2-meter intervals are also used as aggregation footprints.

Results and Analysis
To evaluate the accuracy of the retracker-estimated ice surface elevation, the footprint used to aggregate measured snow surface properties must represent the area of the surface observed by ASIRAS. Ideally, this is the pulse-doppler limited (PDL) footprint, 165 but rough surfaces can increase the distance from nadir at which features appear in the radar signal (Newman et al., 2014). In the past larger circular footprints have been used to represent the ASIRAS footprint and compensate for off nadir influence (King et al., 2018).
In Figure 3, the mean and standard deviation of the error E ra of all ASIRAS returns is plotted for multiple footprint radii.
It shows the magnitude and variability of the error E ra change with the radius of a circular footprint, reaching a minimum at 170 approximately 14 meters. The error of E ra for the circular footprint (blue line) is lower for almost all radii than for the PDL (black line at 44.9% and 34.7% respectively). Since the number of surface observations aggregated by a footprint increases with radius, it is expected that the error decreases with size. The increasing error beyond 14 meters suggests that the footprint covers almost all of the surface features that contribute to the signal, and that any features beyond are not correlated to the return.
This effect may be due to the roughness of the ice surface, where ice features that are elevated above the surface at the nadir 175 can appear in the radar signal at distances proportional to their height, but can also be affected by the spatial autocorrelation of surface properties. A 14-meter radius footprint is used henceforth in this analysis to improve the reliability of the snow and ice surface reference elevations, and as a best-case scenario when evaluating the retracker accuracy, to reduce the contribution the footprint size to the retracker error.
In Figures 4 and 5, the penetration as a proportion of the snow depth P r is used to demonstrate the retracked elevation in 180 relation to the snow and ice surfaces, but the same effect is seen in the penetration P and error E measurements. The position of the retracked elevation relative to the snow and ice surfaces follows a normal distribution whose mean and variability are affected by the retracker threshold (Figure 4). Selecting a larger retracker threshold increases the penetration of the retracked https://doi.org/10.5194/tc-2020-283 Preprint. Discussion started: 5 November 2020 c Author(s) 2020. CC BY 4.0 License.  elevation into the snowpack, with the lowest retracker threshold (20%) having a P r of 42% and the highest (100%) having a value of 59%. A higher threshold not only moves the retracked elevation distribution closer to the ice surface, but also increases 185 its variability, resulting in more retracked elevations to appear below the ice surface (from 8% to 16%) and fewer to appear within the snowpack (from 77% to 73%).
8 https://doi.org/10.5194/tc-2020-283 Preprint. Discussion started: 5 November 2020 c Author(s) 2020. CC BY 4.0 License. Mean penetration P r increases with retracker threshold in a relationship that approximates the logit function ( Figure 4B), which is an expected result given that leading part of the radar altimeter waveform can be fitted using a Gaussian curve (Zygmuntowska et al., 2013). An ideal threshold would be one where the average retracked elevation has 100% penetration 190 through the snowpack, but Figure 4B shows that the average penetration does not exceed 56%, even at the waveform peak (100% threshold).
To investigate how surface properties can affect the penetration (P r ) and its relationship with the retracker threshold, penetration is shown for categories of ice deformed type, snow depth, h topo , pulse peakiness, snowpack salinity and snow grain size in figure 4. The value of these surface properties appears to affect both the average penetration and the slope of the penetration-195 threshold relationship. The P r for all categories of h topo starts at approximately 50% (20% threshold), but the high h topo returns gain a 50% penetration (to the 100% threshold), while the low h topo returns only gain 20% (Figure 5c). In contrast, the shallowest snow depth category only gains 15% compared to the other categories' 25%, but the average penetration increases by 10% to 15% across progressively shallower categories. Among the returns that had a snow pit within their footprint, those with no snowpack salinity showed a strong increase of penetration with threshold, while those with salinity had an almost 200 constant penetration at 60 to 70% ( Figure 5). A smaller grain size from 0.949mm to 1.93mm showed a consistent penetration, but larger grain sizes had the only observed negative penetration-threshold slope.
The primary issue highlighted by the analysis is that a TFMRA retracker alone could not be used to obtain an accurate estimate of the ice surface elevation for FYI near Eureka. The method used to calibrate the ALS-ASIRAS sensor offset uses 205 snow-covered ice, which should underestimate the offset, resulting in a lower retracked elevation and an overestimate of the penetration. Given that systematic errors of the analysis favour a higher penetration, the peak penetration P r of 57% through the snowpack suggests that the Ku-band radar signal is not consistently returning from the ice surface, but from within the snowpack. Since the sea ice thickness is estimated from the sea ice freeboard and snow depth using a hydrostatic equilibrium model (Tilling et al., 2016;Li et al., 2020), the error between the retracked elevation and the actual ice surface would be mag-210 nified in the ice thickness error by a proportion relative to the ratio of the sea water density to the snow density. To accurately measure the ice surface elevation under the conditions of this study, the TFMRA retracker would need to be augmented with an offset that would correct for the distance between the retracked elevation and the ice surface.
A method that extends the penetration of the retracked elevation would also need to account for the difference the in penetration-threshold between observations with different surface properties. The ideal retracker threshold for a surface with a 215 high surface roughness or deformed ice surface might be lower than one for a low-h topo surface or an undeformed surface. In this case there is potential to improve the radar altimetry by incorporating surface properties measured by other remote sensing platforms (Landy et al., 2020). The ice deformity type was extracted from the C-band RADARSAT-2 while the h topo calculated from ALS observations. CryoSat-2 observations may then be assisted by measurements from the RADARSAT Constellation Mission (RCM), ICESat-2 or by other platforms which can give insight into characteristics of the Arctic snowpack and ice 220 surface.
The shape of the radar waveform may also have potential in augmenting the TFMRA method, as it is correlated with differences in the penetration-threshold relationship. At the leading edge of the waveform peak, the strength of the return signal increases with distance from the sensor. A point along the leading edge at a higher threshold of the peak will be closer to the peak, and will have penetrated further (deeper) into the snowpack, resulting in a positive relationship between retracker 225 threshold and penetration. A higher threshold-penetration slope, as seen in Figure 5, is likely caused by a wider and flatter return signal with a lower pulse peakiness. In Figure 5d, the pulse peakiness has an effect on the relationship slope similar to that of h topo and an effect on the average penetration similar to that of show depth. It is possible, therefore, that the pulse peakiness can act as a proxy for a combination of the surface roughness and snow depth, and can be used to approximate the effect of those characteristics on the penetration.

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The results of this study are consistent with the findings of Nandan et al. (2017a), who determined that snow depth and salinity can impact the penetration of Ku-band radar through snow, potentially overestimating the ice surface elevation and reducing the accuracy. They suggested that a correction factor based on distributed measurements of snow depth and salinity can be applied to the freeboard to improve accuracy. Although Guerreiro et al. (2017)  12 https://doi.org/10.5194/tc-2020-283 Preprint. Discussion started: 5 November 2020 c Author(s) 2020. CC BY 4.0 License.