Measurement report: Quantifying the trade-off between station number and spatial layout in sparse GNSS networks for calibrating all-weather FY-4A precipitable water vapor

Integrating satellite-derived precipitable water vapor (PWV) provides data with high spatiotemporal resolution, which is crucial for monitoring and forecasting extreme weather. However, current fusion and calibration methods typically relies on dense GNSS networks, hindering application in data-sparse regions. It remains unclear whether improving calibration under sparse conditions depends more on increasing station numbers or optimizing their spatial placement. To address this, we developed a machine learning-based calibration framework for FY-4A all-weather PWV and conducted controlled experiments across China. Our key finding is that for a fixed station budget, a spatially random layout consistently outperforms clustered or geographically biased distributions, reducing RMSE by up to 27 %. While increasing station density improves spatial generalization, with RMSE at independent stations dropping from 3.24 mm to 2.28 mm and bias converging near zero, performance gains saturate beyond approximately 120–160 stations. Spatially, errors under sparse, non-uniform networks concentrate in regions with strong humidity gradients or complex terrain; a uniform layout distributes errors more evenly. Temporally, all calibrated models capture seasonal cycles, with residual errors peaking in summer due to convective activity. This study demonstrates that in sparse network design, maximizing spatial coverage uniformity is more critical than simply adding stations. We thus provide a transferable framework and a quantitative principle for generating reliable satellite PWV products where GNSS observations are limited.