## 2 Datasets and Methods
### Direct Comparison Using Collocated Measurements  
This method is based on the comparison of \(\sigma^{0}\) data measured by two of the HSCAT scatterometers over the same area with a short time lag in order to limit geophysical changes to the scenes (in particular ocean wind speed and direction). The collocation constraints are: (1) the maximum spatial distance between pairs of \(\sigma^{0}\) is 25.0 km; (2) the maximum temporal distance is 60 min; (3) and the maximum difference in antenna azimuth angle is 5\({}^{\circ}\). In this study, the observing incidence angle is not a concern, since all the HSCAT instruments operate at the same fixed incidence angle. Figure 2 shows the global distribution of collocated HY-2B and HY-2D measurements in three months. The collocations are over land and oceans, and a few of them may be over sea ice. Besides, it is clear that there are more collocations near the latitude of 60\({}^{\circ}\) N or 60\({}^{\circ}\) S. This is because the HY-2D satellite only reaches latitudes within \(\pm\)60\({}^{\circ}\).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Scatterometer**} & \multirow{2}{*}{**Products**} & \multicolumn{2}{c}{**Initial Corrections**} & \multirow{2}{*}{**Time Period**} \\ \cline{3-3} \cline{5-5}  & & **HH** & & & \\ \hline HY-2B & L1B V20 & +0.5 dB & \(-\)0.7 dB & December 2018–August 2021 \\ HY-2C & L1B V20 & \(-\)1.3 dB & \(-\)1.4 dB & October 2020–August 2021 \\ HY-2D & L1B V22 & \(-\)0.6 dB & \(-\)0.5 dB & June 2021–August 2021 \\ QuikSCAT & L2A V2 & / & / & January 2000–December 2008 \\ ISS & L2A V1.1 & / & / & October 2014–August 2015 \\ \hline \hline \end{tabular}
\end{table}
Table 1: A brief description of datasets.  
Based on the collocations, histograms of \(\sigma^{0}\) values for each polarization can be generated. Then the probability density function (PDF) and cumulative distribution function (CDF) of \(\sigma^{0}\) data for each polarization can be further made. Figure 3 provides the histogram of \(\sigma^{0}\) data for the case of HY-2B and HY-2D, in which the \(\sigma^{0}\) interval (horizontal axis) is 0.1 dB. It is clear that the curves of HY-2B and HY-2D are almost overlapping, and the histogram of corresponding differences is shown in Figure 3 for each polarization.  
Based on the collocated backscatter measurements, the intercalibration result of the direct comparison method can be derived by two ways: (1) taking the average of differences between the collocated \(\sigma^{0}\) data, i.e., the overall bias for each polarization; (2) and using a CDF matching technique to calculate \(\sigma^{0}\) dependent calibration in dB units (i.e., corresponding to a nonlinear calibration for \(\sigma^{0}\) in linear units).  
Figure 3: Histogram of the matched \(\sigma^{0}\) for each polarization of HSCAT-B or HSCAT-D (**a**), and the corresponding \(\sigma^{0}\) differences (**b**). The histograms are counted with interval of 0.1 dB.  
Figure 2: Global distribution of collocated HY-2B and HY-2D measurements for three months (June 2021 to August 2021). The color stands for the number of matchups in each \(1^{\circ}\times 1^{\circ}\) grid.  
The CDF matching method was applied in the derivation of the C-band model version 7 (CMOD-7) for sea surface wind retrieval, in which the CDF is for wind speed [8]. In this study, it will be applied to the CDF of \(\sigma^{0}\) data. Two CDFs of \(\sigma^{0}\) data can be matched in this way: one CDF is set as a reference and the other one is calibrated nonlinearly with respect to the reference. To each original (un-calibrated) data point \(\sigma^{0}_{\rm o}\) a calibrated data point \(\sigma^{0}_{\rm r}\) is associated, such that the original CDF value at \(\sigma^{0}_{\rm o}\) equals the reference CDF value at \(\sigma^{0}_{\rm r}\). Thus, the calibration value at \(\sigma^{0}_{\rm o}\) is \(\sigma^{0}_{\rm o}-\sigma^{0}_{\rm r}\).