## 3 Unique Contributions of Ka-Band Information in AltiKa Data
### Complementarity between Ku and Ka Measurements over Ice Sheet Surfaces  
Exploiting Ka frequency properties over land ice or sea ice is of particular interest to better assess the level of surfaces covered by ice or snow. Comparing measurements in Ku and Ka frequencies allows us to understand and quantify the penetration properties of the radar waves. Over water surfaces, Ku and Ka signals reflect at the air/water interface. It is commonly understood that in presence of snow or ice, the radar wave penetrates the ice pack if its wavelength is larger than the snow grain size (typically 0.5 mm but grain size depends on the temperature (snow metamorphism) and snow accumulation). According to [34], higher temperatures cause the snow grains to grow quickly, whereas higher accumulation rate causes them to slowly grow. Ku- and Ka-band wavelengths are respectively 2.21 cm and 0.84 cm. The factors between signal wavelength and grain size are respectively 44 and 17 in Ku- and Ka-bands. For a given wavelength, according to Mie theory [35], the scattering coefficient is conversely proportional to the radar wavelength at a power of 4. From Ku- to Ka-band, the scattering coefficient consequently increases by a factor 55. This leads to a penetration depth over  
Figure 14: The power spectra of sea surface heights from SARAL/AltiKa and Jason-2 in Bay of Bengal. Green line represents (1/50 km). Figure 15: SWH from Jason-2 PISTACH product (**left**) and SAC coastal product (**right**) based on AltiKa data. snow surface between 0.1 m and 0.3 m in Ka-band [36]. Analysis performed on the altimeter signal acquired in Ku- and Ka-bands over the Antarctic ice sheet are consistent with this assumption. To illustrate this theoretical introduction, we represent in Figure 16, the different penetration effects in Ku- and Ka-bands by comparing mean waveforms computed over ocean (SWH = 1 m \(\pm\) 20 cm and similar epochs) and at a cross-over over Lake Vostok [37]. This lake in Antarctic is known to be quite perfectly flat, avoiding all effects induced by surface slopes (that can be different in Ku- and Ka-bands due to the different antenna gain patterns of the two missions). Over ocean, for SARAL/AltiKa (Ka-band) and Sentinel-3A (Ku-band in Pseudo-Low Resolution Mode), 1498 and 377 individual waveforms have been aggregated. Over Lake Vostok, for SARAL/AltiKa and Sentinel-3A, 1763 and 359 individual waveforms have been aggregated. We must note that waveforms have been artificially aligned to be compared. It appears on the left plot of Figure 16 that ocean and land ice leading edges are quite identical except for the very last points of the leading edge. Additional energy appears on the trailing edge samples for ice returns. This clearly indicates that the radar signal has been backscattered in the snow pack. However, considering that the distribution of energy in the leading edge is similar over ocean and over land ice, we can assume that an unique reflective surface is responsible for the main reflection (as for ocean) and that a retracking processing will provide the range corresponding to the distance between the satellite and this reflective surface. This surface can be assumed to be at the air/snow interface. The plot on the right of Figure 16 shows that in Ku-band, returns are completely different over ocean and land ice. Clearly, the red echo can be considered as the summation of different contributions coming from different layers inside the snow pack, each contribution being attenuated depending on the absorption characteristics of each layer. In these cases, determining a range indicating the position of the main reflection (its distance from the radar) is very hard. If a threshold empirical retracker is used, the value of the threshold arbitrarily determines the reflective surface inside the snowpack. For a better comparison of Ku and Ka measurements over Lake Vostok, waveforms in both bands are superimposed in Figure 17. The waveform acquired in Synthetic Aperture Radar (SAR) mode (Sentinel-3A, Ku-band) has been added (in red).