## 2 Materials and Methods  
### Data Source  
The AHI aboard the geostationary Himawari-8/9 satellite in geostationary orbit can provide visible, near-infrared, and infrared observations in 16 spectral channels with high spatial and temporal resolutions. Since the objective of this study is to perform continuous remote sensing of CBH, the algorithm is developed based on the infrared observations of the AHI L1 gridded data with a spatial resolution of 5 km. While attenuation of cloud base signals by optically thick clouds poses challenges for imagers, infrared spectral bands retain considerable capability to derive various cloud parameters [12; 13; 14]. Notably, the solar-independent nature of thermal infrared measurements enables continuous cloud base height estimation throughout diurnal cycles. Therefore, the infrared brightness temperatures in band 8-16 (centering wavelength from 6.2 to 13.3 \(\upmu\)m) and satellite zenith angle (SAZ) from AHI L1 gridded data are used as input features to capture the diurnal variation of clouds [15; 16].  
MODIS, a multispectral imager aboard the Aqua and Terra satellites, observes the Earth at a lower orbit (approximately 705 km). MODIS has 36 visible, near-infrared, and infrared channels, and Terra MODIS collection 6.1 MOD06 products can provide accurate cloud properties with high temporal resolution of 5 min and high spatial resolutions of 5 km for cloud top properties and 1 km for cloud optical properties. It has been demonstrated that MOD06/MYD06 (derived from Aqua MODIS) cloud products have high accuracies in cloud remote sensing retrievals [17; 18]. Therefore, CTH and CWP from MOD06 products are used as labels to establish the CNN model for retrieving cloud optical and microphysical properties [19].  
The Cloud Profiling Radar (CPR, 94 GHz) on the CloudSat and the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP, 532 nm) on the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSOs) operating at distinct wavelengths, enables a comprehensive characterization of cloud vertical profiles through their merged 2B-GEOPROF-LIDAR products [20; 21; 22]. Therefore, the CGT provided by 2B-GEOPROF-LIDAR will be used for the development of the physical model as well as for algorithm validation. However, due to the battery anomaly in 2011, CloudSat-CPR was limited to daytime conditions, which significantly affected its nighttime observing capability [6].  
Launched on 28 May 2024, the Earth Cloud, Aerosol, and Radiation Explorer (Earth-CARE) operates in a sun-synchronous orbit (393 km) and carries two active sensors (cloud profiling radar (CPR) and atmospheric lidar (ATLID)) and two passive instruments (multispectral imager and broadband radiometer) [23]. The CPR onboard EarthCARE, with a larger antenna and lower orbit, provided about 7 dBZ higher sensitivity than CloudSat-CPR and is much better at detecting vertical cloud structures [24; 25]. Specifically, we used the EarthCARE-CPR Level 2A products CPR_TC_2A (version AC) [26] to validate the accuracy of the retrieved AHI CBH in diurnal cycles. In addition, the measurements from four ground-based Ka-band millimeter-wave radar (MMCR) stations are used to evaluate the performance of our AHI CBH retrievals in diurnal cycles [27]. Details of the instruments and data are provided in Table 1.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sensors** & **Products** & **Variables** & **Spatial Resolution** \\ \hline \hline \multirow{4}{*}{AHI} & \multirow{4}{*}{Level 1} & Infrared brightness temperatures & \multirow{4}{*}{0.05\({}^{\circ}\) (5 km)} \\  & & in band 8–16 (centering \\ \cline{1-1}  & & wavelength from 6.2 to 13.3 \(\upmu\)m) & \\ \cline{1-1}  & & Satellite zenith angle & \\ \hline \end{tabular}
\end{table}
Table 1: The data comparison from various sources.