## Methods  
### SAR Image and Waveform Parameters  
Comparison of SAR imagery and altimeter waveform data requires the spatial overlap of both data sets. Consecutive SAR images of the same orbit were assembled into one single image and corresponding altimeter tracks located using the geolocation information of the product. Rectangular polygons with a length of 300 m in along-track and 1.5 km in across-track direction were calculated around each altimeter track point. This size resembles the footprint size of the altimeter associated with the first peak of the return [22]. The mean value of backscatter intensity \(\sigma^{0}\) at co- and cross-polarization of this polygon is calculated for comparison with parameters describing the shape of the altimeter waveform.  
SAR instruments and altimeters perceive sea ice surface information differently because of their viewing geometry, e.g., side-looking for SAR imagery and nadir-looking for distance measuring altimeters [24; 25]. Smooth surfaces, i.e., flat open water or thin ice, have a low backscatter intensity in SAR imagery while altimeter waveforms show a narrow peak with high power. With increasing roughness of the surface, SAR backscatter intensities increase, and altimeter waveforms become more diffuse with lower peak power and larger power values in the tail of the waveform. Figure 2 shows examples of typical waveforms for leads, first-year and multiyear sea ice. Note the differences of the scaling of the y-axis.  
In this study, we used pulse peakiness (PP), scaled inverse mean power (IMP) and stack standard deviation (SSD) as parameters to characterize the shape of the waveform. The first two are derived from the waveform while SSD is a stack parameter that is provided as auxiliary information with the data set. The maximum peak power is a helpful parameter for visual waveform interpretation but contains similar information as PP. PP is used in the quantitative analysis whereas peak power is used for qualitative description of spatial waveform evolution.  
Figure 2: Example waveforms for different surface types. (**a**) Lead, (**b**) first-year and (**c**) multiyear sea ice. Note the difference in the scaling of the y-axis.  
PP is a measure for how much power is contained in the maximum power compared to the mean power of the waveform and is calculated according to [26]:  
\[\mathrm{PP}=\frac{max(WF_{i})}{\sum_{i}WF_{i}}\cdot 256 \tag{1}\]  
where \(WF_{i}\) is the waveform and 256 is the number of bins of the waveform. PP is high for returns from smooth surfaces and decreases with surface roughness. SSD describes the angular variation in power for the stacked waveforms [10] and is low for cases of specular surface scattering and increases for rougher surfaces where returns from larger incidence angles contribute significantly to the signal. We also introduced a new parameter, scaled inverse mean power IMP that reflects the total power contained in a waveform and is calculated as follows:  
\[\mathrm{IMP}=\frac{256}{\sum_{i}WF_{i}}\cdot 2\cdot 10^{-13}. \tag{2}\]  
This parameter is scaled by \(2\cdot 10^{-13}\) to avoid too small values and hence increase readability. IMP shows a similar behavior as SSD but enhances the contrast when waveforms become more similar in terms of peak power. Leads are expected to have a high PP and low values of IMP and SSD because of the specular nature of the nadir return. First-year sea ice has an increased surface roughness but is smoother than multiyear sea ice, which decreases PP but increases IMP and SSD. Multiyear sea ice or rough surfaces therefore have the lowest PP but the highest IMP and SSD values.