Radar altimeters are the most widely used sensors for measuring the surface elevation of the polar ice sheets (Remy et al., 1999; Allison et al., 2009). It is a valuable tool for monitoring and quantifying the volume change of the Antarctic Ice Sheet (AIS) (Zwally et al., 2005; Wingham et al., 2006; Flament and Rémy, 2012; Helm et al., 2014). However, altimetric observations are affected by several errors: error due to atmospheric or ionospheric propagations, slope error and error due to the radar wave penetration into the cold and dry snow (Ridley and Partington, 1988). The first two errors are usually corrected with good accuracy (Remy et al., 2012; Nilsson et al., 2016), while the last one is the most critical and the most challenging problem to tackle (Remy et al., 2012) as it results in an overestimation of the observed distance between the satellite and the target, leading to a negative bias in the surface elevation estimation. The magnitude of the penetration error on the estimated surface elevation is between a few tens of centimeters and few meters (Remy and Parouty, 2009). For instance, Michel et al. (2014) have found a surface elevation difference of -0.5 m between ENVIronment SATellite (ENVISAT) and ICESat crossover points over Antarctica. Authors relate this negative bias to the difference in the penetration depth between the radar altimeter wave that penetrates within the snowpack and the laser altimeter beam that does not penetrate within the snowpack. The temporal variation in the penetration error is therefore critical for accurate interpretation of ice sheet volume changes (Remy et al., 2012).

Radar altimeter measures the power level and time delay of the radar echoes reflected by the snowpack. The signal recorded by radar altimeters, namely the waveform, is processed by an algorithm called the “retracker” to determine several characteristics such as the range, the backscattering coefficient, the leading edge width and the trailing edge slope from the waveform shape. Various methods of waveform retracking exist, yet none adequately corrects for the effect of radar penetration (Arthern et al., 2001; Brenner et al., 2007). To reduce the effect of the spatially varying radar penetration bias on the estimated surface elevation changes, Zwally et al. (2005) used an empirical linear relationship between the surface elevation residuals and the backscattering coefficient residuals at a crossover points of the satellite tracks (data points where satellite tracks cross). A similar method had been described by Wingham et al. (1998). Flament and Rémy (2012) used a linear relationship between time series of the surface elevation and the all waveform parameters: the range, the backscattering coefficient, the leading edge width and the trailing edge slope (computed with the ICE-2 retracker; Legresy et al., 2005) on the along tracks of the satellite. Both approaches are based on changes in the backscattering coefficient, which varies with time, reflecting changes in the snowpack properties (Legresy and Remy, 1998; Lacroix et al., 2007). A more precise understanding of the annual and interannual variations of the backscattering coefficient is a prerequisite for improving the estimation accuracy of the surface elevation trend over the AIS. In addition to measuring the surface elevation, the radar wave when interacting with the snowpack provides information on the snow properties (surface roughness and density, temperature, grain size, and stratification). Indeed, the backscattering coefficient is a combination of two components, the “surface echo” and the “volume echo” (Brown, 1977; Ridley and Partington, 1988; Remy et al., 2012). The former mainly depends on surface roughness and density of near-surface snow while the latter mainly depends on snow temperature, grain size and snowpack stratification (Remy and Parouty, 2009; Li and Zwally, 2011) over a certain depth that mainly depends on the radar frequency (e.g., less than 1 m at Ka band and less than 10 m at Ku band; Remy et al., 2015).

The radar wave interaction with snow provides information on the snowpack surface and subsurface properties, but it complicates the altimetric signal interpretation because the latter would be sensitive to many more snow parameters than if the signal only came from the surface. To clarify the impacts of snow parameters on the backscattering coefficient, this paper investigates the spatial and seasonal variations of the radar backscattering coefficient at the S, Ku and Ka bands. To this end, electromagnetic models are used to assess the backscattering coefficient sensitivity to snow properties at the three frequencies. The aim of this paper is to determine the prevailing snow parameters that drive the seasonal cycle of the observed backscattering coefficient at different radar frequencies and locations over the AIS.

The ENVISAT carries two radar altimeter sensors (RA-2) that operate at 13.6 GHz (Ku band ∼ 2.3 cm) and 3.2 GHz (S band ∼ 9.4 cm). The S band was originally intended for ionospheric corrections while the Ku band provides more accurate surface elevation due to the lower penetration depth. Comparison of the altimetric waveform characteristics between the Ku and S bands revealed different seasonal variations over the AIS (Lacroix et al., 2008b). The dual-frequency information can therefore be useful for retrieving information on snowpack properties. The launch in March 2013 of the radar altimeter Satellite for ARgos and ALtiKa (SARAL)/AltiKa that operates at the Ka band (37 GHz ∼ 0.8 cm) and had the same 35-day phased orbit as ENVISAT until March 2016 allowed comparisons with much higher frequencies for the first time. Temporal variations of the estimated surface elevation with respect to the backscattering coefficient are 6 times lower at the Ka band than that of the Ku band, which implies that the volume echo at the Ka band comes from the near subsurface (< 1 m) and is mostly controlled by ice grain size and temperature (Remy et al., 2015).

The sensitivity of the volume echo to snow temperature shown in Fig. 8b implies that the volume echo is maximum in winter at the Ku and Ka bands and constant at the S band. This sensitivity is explained by the fact that increasing snow temperature increases absorption, resulting in a decrease of the radar wave penetration in the medium and thus limiting the volume echo. Also, increasing snow grain size increases the scattering coefficient, which in turn increases the radar wave extinction in the medium. This results in a decrease of the radar wave penetration and therefore may limit the volume echo. Moreover, the positive lag observed between the Ku and Ka bands in the WP in Fig. 4 can be explained by the difference of the radar wave penetration depth between the Ku (∼ 10 m) and Ka (> 1 m) bands in the snowpack. This lag is related to the propagation of the temperature gradient from the surface into the snowpack. As the temperature controls the snow grain metamorphism and the radar wave penetration depth, the variation in the volume echo would be predominantly driven by the seasonal variations of snow temperature.

Snow density is involved in both the surface and volume echoes. The magnitude of these echoes increase with increasing surface snow density, and thus similar seasonal cycle of σ0 would be expected at any frequency if snow density were the main driver. This is in contrast to the observations (Fig. 3). Therefore, the seasonal cycle of σ0 cannot be explained solely by snow density. Being insensitive to snow temperature and grain size (Fig. 8b, c), the observed seasonal cycle of σ0 at the S band cannot be explained by the volume echo. This implies that snow surface properties (surface snow density and roughness) are the main factors driving the seasonal cycle of σ0 at the S band.

From the S to Ka band, the radar wavelength decreases by a factor of 12 from 9.4 to 0.8 cm corresponding to a scale change from centimeter to millimeter. The scale at which the surface roughness plays a role in radar backscattering coefficient depends on the radar wavelength (Ulaby et al., 1982). On a rough surface, the surface scattering consists of two components: the coherent and incoherent scattering (Ulaby et al., 1982). The former is the scattered component in the specular direction while the latter is the scattered component in all directions. As the radar wavelength is shortened to less than a centimeter, the surface appears rougher and the surface coherent component vanishes (Ulaby et al., 1982). The surface incoherent component magnitude is small and thus is concealed by the volume scattering, which consists of only incoherent scattering. The backscattering coefficient at a smaller wavelength or on a rougher surface consists of only incoherent components and therefore appears as a volume-scattering medium. Simulations in Fig. 8 emphasize this contention, showing a greater amplitude of the volume echo at higher frequencies. We can therefore argue that the seasonal cycle of the observed σ0 at the Ka band is governed by the volume echo. This explains the peak of the observed σ0 in the winter at the Ka band over the AIS.

Several observations show that sastrugi (10 cm to 1 m height) are the main contributors to surface roughness (Kotlyakov, 1966; Inoue, 1989; Lacroix et al., 2007). Since the biggest features (hectometer to kilometer scales) change little over time, it is likely that the most influential roughness scale in the seasonal cycle of the surface echo is the sastrugi (Lacroix et al., 2008a). Despite the increase in magnitude of the surface and volume echoes with surface snow density, evidence from Fig. 3 suggests that the seasonal cycle of σ0 cannot be explained by the seasonal cycle in surface snow density. Therefore, it is likely that the seasonal cycle of the observed σ0 at the S band, predominantly driven by the surface echo, stems from the seasonal cycle of the snow surface roughness. There is no field observation that confirms this fact, but our findings suggest that such information would help to understand the altimetric signal in the future. However, in this study it is difficult to differentiate with certainty between the surface snow density and the snow surface roughness, which drives the seasonal cycle of the surface echo. There are three main reasons for this: (i) The snow surface roughness is poorly known, in particular its seasonal variability; (ii) surface snow properties evolve rapidly with the wind; and (iii) the relation between the surface snow roughness and density is complex because both variables are interdependent. The denser the snow surface, the larger the effect of surface roughness. This amplification is due to the increase of the effective dielectric discontinuity with density (Fung, 1994).

Considering that σ0 at the Ku band shows two opposing seasonal cycle patterns over the AIS and its wavelength is between that of the S and Ka bands, we suggest that σ0 at the Ku band is dominated by the seasonal cycle of the surface echo, similar to the S band in the SP, and by the seasonal cycle of the volume echo, similar to the Ka band in the WP. We support this hypothesis with ancillary data and by modeling. By overlaying the Antarctica RADARSAT mosaic with the SP boundaries (Fig. 9), we find that the WP matches regions of large heterogeneous backscatter from RADARSAT, where megadunes (Frezzotti et al., 2002) and wind-glazed surfaces (Scambos et al., 2012) have been observed. The seasonal cycle of σ0 at the Ku band is maximum in the winter in heterogeneous RADARSAT backscatter regions while it is maximum in the summer in the other regions. In fact, areas of megadunes are characterized by slightly steeper regional slope and the presence of highly persistent katabatic winds (Frezzotti et al., 2002) and wind-glazed surfaces have been formed by persistent katabatic winds in areas of megadunes (Scambos et al., 2012). There exists therefore a relationship between the wind and the seasonal cycle of σ0. To further investigate this point, we used ERA-Interim reanalysis wind speed data supplied by ECMWF (European Centre For Medium-Range Weather Forecasts) on the period 2002 to 2010, corresponding to that of the Ku band. Equation (1) is used to compute the seasonal characteristics of the wind speed by replacing σ0 with the wind speed. A visual inspection shows a high spatial coherence of the seasonal amplitude of the wind speed (Fig. 10a) patterns with the date of maximum σ0 over the seasonal cycle at the Ku band (Fig. 2b). Wind speed average (8.2 ± 1.6 m s-1) and seasonal amplitude (1.7 ± 0.4 m s-1) are higher in the WP than in the SP (6.6 ± 1.58 m s-1 and 1.0 ± 0.3 m s-1, respectively).

The striking similarity in the spatial distribution of the seasonal amplitude of σ0 at the Ka band (Fig. 5c) and the seasonal date of maximum σ0 at the Ku band (Fig. 2b), which is itself correlated to the seasonal amplitude of the wind speed (Fig. 10a), suggests that the wind plays a significant role in the spatial distribution of the seasonal amplitude of σ0 at the Ka band. Although the wind effects on the snowpack are numerous and complex, we retained two for which we simulated the impacts on the volume echo (Fig. 8): a.

Wind may smash snow grains so that the surface snow density increases with wind speed (Male, 1980); this leads to an enhancement of the volume echo at the three frequencies as shown in Fig. 8a. Surface snow density is a good candidate for explaining the spatial distribution of the seasonal amplitude of σ0 at the Ka band because snow compaction can occur at different times of the year depending on the snow accumulation rate and the temperature gradient (Li and Zwally, 2002, 2004).

This study, using 35-day repeat radar altimetry data, carries out spatial and temporal comparative analysis of the seasonal amplitude and date of maximum σ0 at the S, Ku and Ka bands. We used an 8-year time series of σ0 for the Ku band, a 5-year time series of σ0 for the S band and a 3-year time series of σ0 for the Ka band, covering the time period of 2002 to 2010 for ENVISAT sensors and 2013 to 2016 for the SARAL/AltiKa sensor. The backscattering coefficient shows seasonal variations with varying amplitude and phase over the AIS and with a marked dependence on radar frequency. In general, it is maximum in winter at the Ka band and maximum in summer at the S band. At the Ku band, both behaviors are found with a maximum in the winter in the so-called WP and a maximum in the summer in the SP.

We investigated snow properties that dominate the seasonal changes in the volume echo with electromagnetic models of the backscattering coefficient. As a result, we showed that variations in snow properties, such as temperature and grain size, cannot explain the seasonal cycle of σ0 observed at the S band due to its small sensitivity to those parameters. In contrast, the temperature cycle reasonably explain the seasonal cycle of the observed σ0 at the Ka band. We explain that the contrasted seasonal cycle of the observed σ0 at the Ku band is due to its high sensitivity to the volume echo in the WP and to the surface echo in the SP. The geographical patterns of the WP and SP are related to the seasonal amplitude of the wind speed. This is a result of the presence or lack of wind-glazed surfaces, induced by strong and persistent winds in the megadune areas.

This investigation provides new information on the Antarctic Ice Sheet surface seasonal dynamics and provides new clues to build a robust correction of the altimetric surface elevation signal. Multi-frequency sensors are the key for improving the understanding of the physics of radar altimeter measurements over the AIS. An important limitation of this study is the lack of information on the seasonal variability of the snow surface roughness in Antarctica, which will be the topic of future work.