# Retrieval of Cloud Ice Water Path from FY-3F MWTS and MWHS
## 2 Satellite Data and ERA5 Data
### Cross-Calibration  
The IWP retrieval algorithm used in this study was originally developed based on observational data from MHS and AMSU-A onboard satellites operated by NOAA and METOP polar-orbiting satellites of Europe [7; 8; 13]. However, the microwave observations in this study are derived from the MWTS-III and MWHS-II instruments onboard the FY-3F satellite. Variations in instrument characteristics and observational environments across different satellite systems can significantly affect IWP retrieval results. To address these discrepancies and improve the reliability and accuracy of retrievals, this study applies China's Advanced Radiative Transfer Modeling System (ARMS) and employs the double-difference method to cross-calibrate the FY-3F observations with those from METOP satellites. This approach effectively mitigates systematic errors caused by platform differences, providing a robust data foundation for subsequent IWP retrievals. The ARMS was officially released in late 2020. This system introduced an accurate and efficient scheme for calculating atmospheric transmittance and developed a comprehensive atmospheric spectral dataset. Its effectiveness in assimilation and retrieval applications for meteorological satellites has been extensively validated. Moreover, its performance is comparable to internationally recognized radiative transfer models, such as Radiative Transfer for TOVS (RTTOV) and Community Radiative Transfer Model (CRTM) [25; 26]. The double-difference method, a widely used technique for satellite data cross-calibration, effectively reduces systematic biases between instruments, enhancing the consistency and reliability of observational data. Variations in design principles and orbital characteristics among sensors on different satellites can introduce systematic errors, complicating direct comparisons of satellite observations. To address this issue, the double-difference method utilizes third-party data to establish a consistent reference framework. This reference is then used to calculate and correct observation errors across satellites, ensuring accurate calibration. In this study, the ARMS was employed to generate simulated values as third-party data for calibrating FY-3F satellite observations to align with METOP-C satellite data. Accurate atmospheric and surface parameters are crucial for obtaining reliable satellite observation simulations from ARMS. Accordingly, ERA5 data under clear-sky conditions were spatially and temporally matched to provide input parameters for theARMS system, producing simulated satellite observation values consistent with actual observational conditions. The first step in applying the double-difference method to correct FY-3F observation data involves calculating the differences between satellite observation values and their corresponding simulated values, as expressed in Equations (1) and (2):  
\[D_{F}=O_{F}-B_{F} \tag{1}\]  
\[D_{M}=O_{M}-B_{M} \tag{2}\]  
In Equations (1) and (2), \(O_{F}\) and \(O_{M}\) represent the observation values from the FY-3F and METOP-C satellites, respectively. \(B_{F}\) and \(B_{M}\) denote the corresponding simulated values for these satellites, derived using the ARMS model. \(D_{F}\) and \(D_{M}\) signify the differences between the observation values and their respective simulated values. Since \(B_{F}\) and \(B_{M}\) are simulated values obtained from the ARMS system under identical atmospheric and surface conditions, they can be assumed equal (\(B_{F}=B_{M}\)). Using Equations (1) and (2), the double difference between the two satellites is calculated, as shown in Equation (3):  
\[D_{D}=O_{F}-O_{M} \tag{3}\]  
The double-difference value derived from Equation (3) is used to correct the FY-3F satellite observation data, ensuring alignment with the METOP-C satellite data. This method is applicable to similar instruments on different satellites and effectively addresses inconsistencies in observation data between satellite platforms.