## 5 Conclusions  
This study develops a novel hybrid algorithm designed to estimate single-layer CBH from geostationary infrared observations in diurnal cycles. The method successfully integrates a deep learning model to retrieve cloud properties (i.e., CTH and CWP) with a physical model that uses these properties to infer cloud geometric thickness and, ultimately, the CBH. This study provides an effective approach to obtain large-area and diurmally continuous CBH retrievals from geostationary satellite observations. The results have the  
Figure 9: Four single-layer cloud cases for the intercomparison of the AHI-retrieved CBHs (red dots) and CTHs (blue dots) with Ka-band MMCR measurements (gray shading) at four MMCR stations in November 2022. The white/purple shading indicates the case occurred during daytime/nighttime. potential to improve the estimation of cloud radiative forcing and may also be valuable for aviation guidance. In addition, the algorithm can be applied to other meteorological satellites by retraining the CNN model and reconstructing the ECWC LUT to facilitate the observation of global cloud vertical distributions, which will be important for improving cloud parameterization schemes in general circulation models. Given the limitations of our algorithm in dealing with multi-layer clouds, improvement of the retrieval of CBH for multi-layer clouds will be a topic of future research. Furthermore, deep learning-based nowcasting of cloud vertical distribution will be a prospective study, as the transformative evolution of the low-altitude economy in recent years opens a diverse range of new application scenarios. The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/rs17142469/s1](https://www.mdpi.com/article/10.3390/rs17142469/s1)]([https://www.mdpi.com/article/10.3390/rs17142469/s1](https://www.mdpi.com/article/10.3390/rs17142469/s1)), Figure S1: The look-up table (LUT) of effective cloud water content (ECWC, g/m\({}^{3}\)) constrained by cloud top height (CTH, km) and cloud water path (CWP, kg/m\({}^{2}\)) for clouds (a) over land and (b) over ocean with color scale in log10 units; Figure S2: The probability density functions of the (a) cloud top height and (b) cloud water path for retrieved AHI products and MODIS official measurements; Figure S3: Normalized frequency histograms of cloud top height (CTH) bias (km) for five different latitude bands: (a) 60\({}^{\circ}\)S-30\({}^{\circ}\)S, (b) 30\({}^{\circ}\)S-10\({}^{\circ}\)S, (c) 10\({}^{\circ}\)S-10\({}^{\circ}\)N, (d) 10\({}^{\circ}\)N-30\({}^{\circ}\)N, and (e) 30\({}^{\circ}\)N-60\({}^{\circ}\)N. The red dashed line indicates zero bias; Figure S4: Normalized frequency histograms of cloud water path (CWP) bias (kg/m\({}^{2}\)) for five different latitude bands: (a) 60\({}^{\circ}\)S-30\({}^{\circ}\)S, (b) 30\({}^{\circ}\)S-10\({}^{\circ}\)S, (c) 10\({}^{\circ}\)S-10\({}^{\circ}\)N, (d) 10\({}^{\circ}\)N-30\({}^{\circ}\)N, and (e) 30\({}^{\circ}\)N-60\({}^{\circ}\)N. The red dashed line indicates zero bias. Conceptualization, Z.T. and T.Y. ; methodology, T.Y. ; software, T.Y. ; validation, T.Y., Z.T. and W.A. ; formal analysis, T.Y. and Z.T. ; investigation, T.Y. and S.M. ; resources, X.Z., S.H. and C.L. ; data curation, T.Y. ; writing--original draft preparation, T.Y. ; writing--review and editing, Z.T., W.A. and J.G. ; visualization, T.Y. ; supervision, W.A. ; project administration, S.H. ; funding acquisition, W.A. All authors have read and agreed to the published version of the manuscript. This research was funded by the Fengyun Application Pioneering Project (FY-APP) under Grant FY4(02P)-2024007, the National Natural Science Foundation of China, grant numbers 42305150 and 42325501, and the China Postdoctoral Science Foundation (Certificate Number: 2024T170423).