## 5 Discussion  
This study successfully applied an innovative stack processing PSInSAR methodology to monitor and quantify VUG dynamics in Wuhan, China, using a dense, long-term (2012-2020) COSMO-SkyMed dataset. The observed vertical growth patterns, particularly the concentration of high-rise buildings in central districts like Jianghan, Wuchang, and Hanyang, align with previous studies documenting Wuhan's dramatic urbanization and are consistent with the city's strategic development plans focused on enhancing infrastructure and key industries in these core areas [33, 34, 35]. However, the analysis also revealed significant heterogeneity in growth across the city, with peripheral regions exhibiting more modest VUG. This spatial variability echoes broader trends observed in urban expansion globally [3] and underscores the differential development pressures and planning needs across Wuhan.  
A key strength of this research lies in its methodological approach. By adapting PSInSAR through stack processing, we addressed critical challenges inherent in analyzing long-term SAR time series for dynamic VUG, such as data gaps and the appearance/disappearance of PS points due to construction. This overcomes the static stability assumption limiting standard PSInSAR for tracking growth over time [29, 30, 31]. The ability to capture detailed temporal dynamics through time-series analysis and 3D visualization proved invaluable, offering insights beyond traditional 2D remote sensing techniques, which often neglect the crucial vertical dimension [6, 7, 8]. Furthermore, the post-processing steps\(-\)including robust outlier removal using the IQR method, spatial aggregation onto a 50 m grid, and maximum height extraction\(-\)were essential for transforming potentially sparse and noisy PS point data into a coherent, interpretable VUG product suitable for urban analysis.  
The comparison with the GHSL dataset highlighted the value of high-resolution techniques like PSInSAR for accurately characterizing individual structures and local growth patterns, suggesting that while global datasets provide useful context, they may require validation or calibration with localized measurements, especially for tall structures. Validation against high-resolution drone surveys further reinforced the reliability of the PSInSAR height estimations, particularly for buildings exceeding 30 m.  
Despite the demonstrated effectiveness, limitations must be acknowledged. PSInSAR height accuracy is intrinsically linked to PSC presence and distribution, ideally on building tops. Displacement on lower structures can lead to underestimations, while residual noise can cause overestimations, impacting the fine-scale interpretation of VUG. Future research could focus on developing advanced PS selection algorithms specifically designed to identify rooftop scatterers, potentially leveraging machine learning approaches informed by scattering characteristics or geometric analysis incorporating building footprint data. Furthermore, integrating PSInSAR height estimates with complementary datasets, such as high-resolution optical imagery for structural context or LiDAR data where available (even if temporally sparse), could help constrain estimates and mitigate underestimation issues caused by facade or balcony scatterers. Utilizing data from multiple SAR viewing geometries (e.g., combining ascending and descending passes) may also offer improved capabilities for detecting stable points specifically located on building tops. Enhancing noise reduction and gap-filling methods, perhaps using machine learning, could further increase the reliability of VUG time-series analysis. Explicitly integrating socio-economic drivers with the observed spatial VUG patterns also presents a promising avenue for deeper understanding.