# Application of HY-2B Satellite Data to Retrieve Snow Depth on Antarctic Sea Ice
## 3 Methods  
### Snow Depth Retrieval Model  
The snow layer on the sea ice surface scatters the electromagnetic waves emitted by the sea ice [15; 29]. The energy received by the passive microwave sensor is related to the snow depth and the microwave frequency channel. As snow depth and microwave frequency increase, the radiated energy of the sea ice increases due to the scattering by the snow layer. Based on this physical principle, the difference in the scattering of the snow on sea ice at different microwave frequency channels can be used to retrieve snow depth on sea ice [17; 22]. Snow depth can be calculated as follows:  
\[\mathrm{SD}=a+b\times\mathrm{GR}(f1f2), \tag{1}\]  
\[\mathrm{GR}(f1f2)=\frac{TB(f1)-TB(f2)-k^{-}(1-C)}{TB(f2)+TB(f2)-k^{+}(1-C)}, \tag{2}\]  
\[k^{-}=TB_{\mathrm{ow}}(f1)-TB_{\mathrm{ow}}(f2), \tag{3}\]  
\[k^{+}=TB_{\mathrm{ow}}(f1)+TB_{\mathrm{ow}}(f2), \tag{4}\]  
where, SD is the snow depth (in cm), and \(a\) and \(b\) are the coefficients of the retrieval model. GR represents the gradient ratio of vertical polarization brightness temperature at different frequencies;\(f1\) corresponds to the 37 GHz vertical polarization frequency channel, while \(f2\) corresponds to either the 19 GHz or 7 GHz vertical polarization frequency channel; \(TB\) denotes the vertical polarization brightness temperature received by the passive microwave sensor at different frequencies; \(TB_{\mathrm{ow}}\) represents the mean brightness temperature in open water for different frequencies; and \(C\) represents the sea ice concentration, obtained  
Figure 2: (a) A measured camera fixed on the R/V XueLong used to record sea ice and snow situation during the 35 th Chinese National Antarctic Research Expedition and (b) snow depth estimation involving photogrammetric images. The long red line in (b) denotes the reference ball diameter and the short red lines denote snow depth on sea ice. from the passive microwave brightness temperatures based on the (NT2) NASA Team 2 algorithm [30]. [PERSON] and [PERSON] (1998) pioneered the development of a model for snow depth retrieval using passive microwave SSM/I brightness temperature data, which were derived from SSM/I data spanning 1978-2007 [15]. This model, referred to as the [PERSON] model, has the model coefficients \(a=-2.3\) cm and \(b=-771\) cm. Based on the [PERSON] model, [PERSON] et al. (2003) adapted the algorithm for AMSR-E data and introduced the Comiso03 model, which adjusted the regression coefficients to \(a=2.9\) cm and \(b=-782\) cm [17]. Both the Markus98 and Comiso03 models utilized the 37 and 19 GHz frequencies, which have limited penetration capability with an upper limit 60 cm for the retrieval of snow depth on sea ice. To address the limitations in penetration capability, [PERSON] et al. (2022) employed the lower frequency channel of 7 GHz, which offers better penetration into the snow layer [23]. The resulting retrieval model, referred to as the Shen22 model, has the coefficients \(a=-26.7\) cm and \(b=-411\) cm. This approach demonstrated improved snow depth estimation, particularly in regions with deep snow. Notably, Equations (1)-(4) established a relationship between snow depth on sea ice and the mean open sea water brightness temperature (\(TB_{\text{ow}}\)) at different frequencies, serving as the reference tie point. In this study, a dynamic reference point method [31] was applied instead of a fixed reference tie point, enabling more accurate snow depth estimates. Figure 3 shows that the dynamic tie points used for snow depth retrieval were higher than the traditional fixed tie points used at 19 and 37 GHz for \(TB_{\text{ow}}\). The maximum difference between the dynamic and the fixed tie point for \(TB_{\text{ow}}\) at 19 and 37 GHz was 12.8 and 10.9 K, respectively. The obtained dynamic tie points reflect daily actual changes, thereby benefiting the accuracy of the retrieved snow depth on Antarctic sea ice [32]. Additionally, it is important to consider the effects of day-time melt and nightly freeze of the snow on sea ice.