## 2 Materials and Methods
### Methods
#### 2.3.2 Physical Model  
According to the physical model developed by [PERSON] et al. [8], CGT can be effectively estimated using CWP via a LUT of ECWC constrained by cloud properties and environmental conditions. The definition of ECWC is used to represent the vertical variation of cloud water content. Considering the difference between the CTH and CWP retrieved from AHI infrared observations and those from AHI operational products, the LUT of ECWC needs to be reconstructed using a spatiotemporally collocated AHI-CPR-CALIOP dataset. Specifically, the retrieved AHI CTH and CWP were firstly collocated with CGT detected by CloudSat-CALIPSO, which is shown in Figure 1c. Using the relationship in Equation (2), this dataset allowed us to calculate a large sample of ECWC values. After that, we strati  
Figure 1: Schematic flowchart of the research framework. Panel (**a**) shows the multi-source data collocation and preprocessing. Panel (**b**) illustrates the training process of the CNN-based retrieval model, with the numbers indicating the kernel size of each layer. Panel (**c**) represents the construction of the physical model (ECWC LUT) using the CloudSat-CALIPSO cloud profiles, and finally retrieved AHI CBH from AHI infrared observations based on the CNN model and ECWC LUT. In all subplots, warmer colors (e.g., yellow, red) indicate higher values, while cooler colors (e.g., purple, blue) represent lower values. fied these ECWC by two cloud properties (i.e., CTH and CWP) and three environmental variables (i.e., surface type, latitude, and season). Specifically, the CTH constraint ranges from 0 to 20 km with an interval of 1 km, and the CWP constraint ranges from 0 to 2 kg/m\({}^{2}\) with inhomogeneous intervals due to its highly nonlinear distribution. Among the three environmental variables, surface type constraint includes land and ocean, latitude constraint refers to 60\({}^{\circ}\)S-30\({}^{\circ}\)S, 30\({}^{\circ}\)S-10\({}^{\circ}\)S, 10\({}^{\circ}\)S-10\({}^{\circ}\)N, 10\({}^{\circ}\)N-30\({}^{\circ}\)N, and 30\({}^{\circ}\)N-60\({}^{\circ}\)N, and season constraint refers to spring (March-April-May, MAM), summer (June-July-August, JJA), autumn (September-October-November, SON), and winter (December-January-February, DJF). Based on these constraints, the ECWC LUT is composed of 40 sub-tables (2 surface types \(\times\) 5 latitude zones \(\times\) 4 seasons), with each sub-table containing 200 pieces of data. Each cell within a sub-table stores the mean ECWC values for that specific set of conditions. Figure S1 provides the established LUT of ECWC, which clearly shows distinction between ocean and land surfaces. This difference arises from the fundamental dissimilarities in their surface radiative properties. The ocean surface acts nearly as a blackbody in the thermal infrared channels, while land surfaces exhibit significantly lower and more spectrally variable emissivity. By developing surface-dependent LUTs, our algorithm can better account for the varying background conditions, leading to a more accurate retrieval of CBH. Following the physical model developed by [PERSON] et al. [8], CGT is calculated through Equation (3) using the CWP retrievals and ECWC. Here, the ECWC for each AHI pixel is searched from the LUT based on its CTH and CWP as well as corresponding environmental variables (i.e., surface type, latitude, and season). Subsequently, CBH can be inferred using the CTH and CGT estimates via Equation (4). \[ECWC=\frac{\int_{\mathrm{C}BH}^{CTH}CWC(z)dz}{CTH-CBH}=\frac{CWP}{CGT} \tag{2}\]  
\[\mathrm{CGT}=\frac{CWP}{ECWC} \tag{3}\]  
\[\mathrm{CBH}=\mathrm{CTH}-\mathrm{CGT} \tag{4}\]  
To conclude, by organically combining a CNN model that retrieves CWP and CTH from infrared observations and a physical model that estimates CBH based on CGT using a LUT of ECWC, a novel algorithm for retrieving CBH based on geostationary satellite infrared observations is developed.