# On-Orbit Calibration Method for Correction Microwave Radiometer of the HY-2 Satellite Constellation
## 5 Inversion and Verification  
The better way to fit the retrieval model is to use BT data from the radiometer and synchronously observed atmospheric parameters, but at present there are no sufficient on-site observation datasets from the atmosphere. This experiment used ECMWF reanalysis atmosphere data to match the second group dataset (see Table 2) from the HY-2B satellite and obtain coefficients. The new retrieval models are of the form [33]:  
\[AWV=a_{0}+a_{187}ln(280-TB_{18.7})+a_{238}ln(280-TB_{23.8})+a_{37}ln(280-TB_{37}) \tag{7}\]  
\[WPD=c_{0}+c_{187}ln(280-TB_{18.7})+c_{238}ln(280-TB_{23.8})+c_{37}ln(280-TB_{37}) \tag{8}\]  
Ordinary least squares can determine the coefficients; \(TB_{18.7}\), \(TB_{23.8}\) and \(TB_{37}\) represent BT, respectively, from the three channels of the CMR; the fitted coefficients are given in Table 3. Both AWV and WPD are products of CMR, AWV is the most important contribution to WPD, and there is a specific mathematical relationship between them [34]. Different retrieval algorithms are built for AWV and WPD in this study, in order to verify the reliability of the on-orbit calibration method for two groups of results. After on-orbit calibration, BT values of the first dataset (see Table 2) were reprocessed and compared. The operational algorithm for the HY-2 satellite constellation processes the BT dataset before and after calibration. Compared results are shown in Table 4. Both mean bias and RMS decrease significantly between the HY-2C or HY-2D satellite and the HY-2B satellite after calibration. With the new retrieval algorithm for Equations (7) and (8), the BT datasets are processed and compared again; there are similar changes in the differences between satellite products. The operational algorithm and new algorithm are respectively used for the BT datasets of the HY-2B satellite; the difference between the two products is relatively small. According to the above compared results, it can be seen that similar algorithms from different data sources have little impact on products, while BT values are the key factor in determining the accuracy of products. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & **Content** & **Reference** & **Compared** & \
\begin{tabular}{c} **Mean Bias (mm)** \\ **Before/After** \\ \end{tabular} &
\begin{tabular}{c} **RMS (mm)** \\ **Before/After** \\ \end{tabular} \\ \hline \multirow{3}{*}{Operational} & HY-2C & \multirow{3}{*}{HY-2B} & AWV & \(-0.320/-0.274\) & \(1.447/0.932\) \\  & & WPD & \(-1.849/-1.722\) & \(8.451/5.877\) \\  & & AWV & \(-0.731/0.451\) & \(1.980/1.346\) \\  & HY-2D & & WPD & \(-4.361/2.807\) & \(11.832/7.521\) \\ \hline \multirow{3}{*}{HY-2B (operational vs new)} & AWV & \(-0.189\) & \(0.780\) \\  & & WPD & \(-1.214\) & \(4.832\) \\ \hline \multirow{3}{*}{New} & HY-2C & \multirow{3}{*}{HY-2B} & AWV & \(0.509/0.378\) & \(1.632/1.218\) \\  & HY-2D & & WPD & \(3.172/2.212\) & \(9.831/7.427\) \\ \cline{1-1}  & & AWV & \(-0.802/0.461\) & \(2.040/1.422\) \\ \cline{1-1}  & & WPD & \(-4.577/2.857\) & \(12.028/8.764\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Cross-checking for CMRs before and after on-orbit calibration. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Product** & \multicolumn{4}{c}{**Coefficient**} \\ \hline  & \(a_{0}\) & \(a_{187}\) & \(a_{238}\) & \(a_{37}\) \\ AWV & \(20.9824976853874\) & \(91.5293174061542\) & \(-129.146718974558\) & \(33.5602960484433\) \\ \hline \multirow{3}{*}{WPD} & \(c_{0}\) & \(c_{187}\) & \(c_{238}\) & \(c_{37}\) \\  & \(0.08414570\) & \(0.57683177\) & \(-0.78380061\) & \(0.19110949\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Coefficients in the retrieval algorithm of atmospheric water vapor (AWV) and wet path delay (WPD). In the distribution of crossovers (see Figure 5), it can be seen that the density of crossovers at high latitudes is significantly greater than that at low latitudes.