# Investigations into Frost Flower Physical Characteristics and the C-Band Scattering Response
## 3 Results and Discussion
### Stage 2: Initial Frost Flower Formation and Spatial Proliferation
[17] (21.5 to 62.5 PSU), and [PERSON] et al. [37] (95 \(\pm\) 42 PSU). In this experiment, we observe that the frost flower salinity was twice as large as the surface salinity during frost flower growth. This can be observed in our experimental data as well as data sets from Reference [19] and Reference [20] while [PERSON] et al. [16] noted that the salinity of the sea ice surface brine skim layer was around 1.4 times smaller than their observed frost flower salinity. Scatterometer measurements during the period of significant frost flower spatial proliferation through the morning and early afternoon on 13 January indicate that the observed physical changes in the surface caused substantial increases in backscatter for all polarizations and incidence angles (Figure 6) with more pronounced increases at lower incidence angles. As the frost flowers grew and spatially covered the sea ice, NRCS increases by 14.8 dB (VV), 11.7 dB (HH), and 6.0 dB (HV) and were measured at 25\({}^{\circ}\). Similar increases were observed for co-polarized signals at higher incidence angles. However, the cross-polarized trend lagged temporally. Liquid brine (first observed on the sea ice surface at 08:40 and then throughout this stage of the experiment) had a higher dielectric constant than the previously observed dry sea ice surface. The increase in permittivity results in an increase of the co-polarization ratio (VV/HH). This effect is more pronounced at higher incidence angles (Figure 6). Minimum backscatter occurred around 12:30 for co-polarized signals at 25\({}^{\circ}\). Similar inflections were observed at other incidence angles and polarizations. However, they were not distinct minima similar to the 25\({}^{\circ}\) case. For comparison, at 25\({}^{\circ}\) incidence, [PERSON] et al. reported an initial sea ice backscatter of \(-\)26 dB (VV), \(-\)28 dB (HH), and \(-\)34 dB (HV) before observing a substantially smaller increase of about 5 dB for VV and HH polarizations during frost flower growth and spatial proliferation. For HV, [PERSON] et al. observed an initial decrease of 4 dB with a subsequent increase of 9 dB [20]. Figures 7 and 8 show images of the frost-flower-covered sea ice surface from a top view and an oblique view, respectively. LiDAR measurements at 14:30 on 13 January near the end of Stage 2 are shown in Figure 9 underlying the scatterometer scan footprint on the SERF pool surface and processed for the areas of the surface corresponding to scatterometer swaths at each incidence angle (Table 1). All aspects of the surface roughness (including the autocorrelation function (ACF) and anisotropy in \(L_{c}\) with the azimuth angle have been characterized with the LiDAR data [32]. The average RMS height (\(h\)) for individual incidence angles ranged from 0.23 cm to 0.26 cm and the correlation length (\(L_{c}\)) ranged from 0.57 cm to 0.99 cm. Maps of the correlation length and RMS height are given in Figure 9a,b. RMS height showed very little variation (\(\leq\)0.3 mm) between scatterometer incidence angles. \(L_{c}\) exhibited some variation with a maximum value of 0.99 cm at 40\({}^{\circ}\) and a minimum value of 0.68 cm at a 20\({}^{\circ}\) scatterometer incidence angle. The surface is, therefore, electromagnetically rough (per the Rayleigh roughness criteria), which indicates that surface scattering will be present in the backscattering signatures. Figure 9 emphasizes that, in spite of similarities between RMS height at each incidence angles, there was inhomogeneity in the surface roughness that can be linked to the frost flower coverage. The roughness values we measured are in agreement with our previously reported values in Reference [19], which means that the geometric properties of the frost flowers were similar in both experiments. The LiDAR's capability for characterizing the frost flower roughness parameters is consistent between experiments. Figure 8: Oblique view of the sea ice surface during the mid-afternoon. Bare ice patches are visible between frost flowers (14:40 on 13 January).