# Retrieval of Cloud Ice Water Path from FY-3F MWTS and MWHS
## 3 Description of Cloud Ice Water Algorithm
For a scatter-free, isothermal atmosphere, where \(\Delta T=0\), the brightness temperature at microwave frequencies can be approximately represented using Equation (10) [29] as follows:  
\[T_{b}=T_{s}[1-(1-\varepsilon)\gamma^{2}] \tag{10}\]  
In this context, \(\gamma\) can be further expressed as:  
\[\gamma=\exp[-(\tau_{0}+\tau_{v}+\tau_{l})/\mu)] \tag{11}\]  
where \(\tau_{0}\) is parameterized as a function of surface temperature, \(\tau_{l}\) is derived as a function of cloud liquid water and cloud layer temperature, and \(\tau_{v}\) is parameterized as a function of water vapor path [7]. Due to the complexity and variability of land surface types and the non-uniformity of background radiation, the application of the radiative transfer equation to estimate the brightness temperature at the base of ice clouds over land is limited. [PERSON] and Weng \begin{table}
\begin{tabular}{c c c c c} \hline
**Parameters** & **Thresholds** & \(\mathbf{b_{0}}\) & \(\mathbf{b_{1}}\) & \(\mathbf{b_{2}}\) \\ \hline \(\Omega_{N}\) & \(D_{e}<1.2\) mm & \(-1.74663\) & \(1.90711\) & \(-0.73029\) \\  & \(D_{e}\geq 1.2\) mm & \(-1.58571\) & \(1.52230\) & \(1.52230\) \\ \hline \end{tabular}
\end{table} 
Table 2: The parameter used in the calculation of \(\Omega_{N}\). derived the brightness temperature at the base of ice clouds by utilizing observed brightness temperature data from the Advanced Microwave Sounding Unit (AMSU) under non-scattering conditions, combined with data from the Advanced Very High Resolution Radiometer (AVHRR), and applying an empirical relationship between low- and high-frequency channels [8]. After validation, the results showed errors comparable to those obtained over the ocean. This study uses brightness temperature data from the 23.8 GHz and 31.4 GHz channels on MWTS-III, along with data from the 89 GHz and 166 GHz channels on MWHS-II, to establish an empirical relationship between the brightness temperatures of low- and high-frequency channels. The empirical relationships used in this study are presented in Equations (12) and (13). \[T_{b\_89}=122.85+1.08T_{b23}-0.54T_{b31} \tag{12}\]  
\[T_{b\_166}=313.20+1.32T_{b23}-1.70T_{b31} \tag{13}\]  
Figure 3 presents scatter plots illustrating the statistical relationship between the calculated brightness temperatures at the 89 GHz and 166 GHz channels, derived using Equations (12) and (13), in conjunction with brightness temperature data from the 23.8 GHz and 31.4 GHz channels of MWTS-III, and the corresponding observed brightness temperatures. As shown in Figure 3a, there is a strong correlation between the 89 GHz brightness temperatures obtained from the 23.8 GHz and 31.4 GHz channel data and the observed brightness temperatures, with \(R^{2}=0.942\) and \(RMSE=4.561\). As illustrated in Figure 3b, although the accuracy of the 166 GHz brightness temperatures obtained using the 23.8 GHz and 31.4 GHz channel data is slightly lower than that of the 89 GHz brightness temperatures, they still exhibit a high correlation with the observed brightness temperatures. This indicates that, despite the complexity of land surface types, high-precision brightness temperature data at the 89 GHz and 166 GHz channels can still be obtained, thereby facilitating the acquisition of more accurate IWP retrieval data.