## 3 Results
### Validation of CBH Using Spaceborne Cloud Radar and Lidar Measurements  
With the CTH and CWP retrievals derived from the CNN-based model, the CBH can be estimated from satellite observations using the physical model based on the LUT of ECWC. Here, we extensively evaluate the CBH estimates through comparison with the active measurements of CloudSat-CALIPSO and EarthCARE, which are some of the most powerful means to measure the vertical structures of clouds. Figure 4 shows an example of CTH, CWP, and CBH retrievals based on the AHI infrared observations, with a comparison to the CloudSat-CALIPSO measurements. To provide a direct comparison, we also include the CTH product from the MODIS instrument aboard the Aqua satellite (MYD06). This choice is due to the fact that the CALIPSO flies in formation with Aqua in the A-Train satellite constellation, lagging by only 1-2 min, which ensures optimal spatiotemporal collocation. It is important to note that while the MYD06 product is used here for synergistic validation with CloudSat-CALIPSO, our model training and other analyses primarily utilized the MOD06 product. Figure 3: Pixel-by-pixel comparison of (**a**) retrieved AHI CTH and (**c**) retrieved AHI CWP against their corresponding MODIS labels. Panels (**b**,**d**) show the corresponding error distributions for CTH and CWP, respectively. In (**a**,**c**), the color scale represents the number of matchups on a logarithmic scale. The black solid line is the 1:1 line, and the red solid line represent the linear regression. The vertical red dashed line in (**b**,**d**) is the zero-error line. N represents the total number of points, R is the correlation coefficient, BIAS is the mean deviation, and RMSE is the root mean squared error. The CTH, CWP, and CBH retrieval results cover a broad region spanning from 60\({}^{\circ}\)S to 60\({}^{\circ}\)N and 80\({}^{\circ}\)E to 200\({}^{\circ}\)E. In contrast, the CloudSat-CALIPSO measurements are limited to the nadir pixels, as indicated by the red lines in Figure 4a-c. A cross-section comparison between the AHI CTH (blue circles) and CBH retrievals (red circles) with the MYD06 CTH (black crosses) and the vertical cloud structures detected by CloudSat-CALIPSO (gray shading) at 03:00 UTC on 1 March 2017 is shown in Figure 4d. We selected the specific track segment from 145\({}^{\circ}\)E to 175\({}^{\circ}\)E for this cross-section because it features a complex cloud system, whereas the preceding section (i.e., 140\({}^{\circ}\)E-145\({}^{\circ}\)E) was predominantly clear sky and thus less informative for algorithm evaluation. The comparison between AHI-retrieved CTH and the MYD06 CTH product shows that our algorithm shows a relatively high accuracy. Furthermore, the results demonstrate that the AHI CBH retrievals are typically in agreement with those from CloudSat-CALIPSO when the AHI CTHs are reliably retrieved. For optically thin cirrus (e.g., pixels near 159\({}^{\circ}\)E), the AHI CTH retrievals are notably underestimated, resulting in an underestimation of the CBH for these pixels. Such significant biases in the CTH retrievals of thin and high clouds have also been observed in the operational cloud property products of both AHI and MODIS through comparison with ground-based cloud radar measurements [27; 32]. It should be noted that the retrieval model based on the ECWC LUT can partially reduce the effects introduced by CTH errors. In specific, as shown in Figure S1, the ECWC in the LUT tend to decrease with increasing CTH, leading to overestimated ECWC when the CTH is underestimated. Subsequently, the overestimated ECWC will lead to underestimated CGT, thus reducing the influence of CTH errors on the estimation of CBH. As illustrated in Figure 4d, between 150\({}^{\circ}\)E and 160\({}^{\circ}\)E, the AHI CTH retrieval values differ from the CloudSat-CALIPSO-detected CTH by 2-4 km. However, the retrieved CBH remains reasonably close to those detected by active remote sensing.