This paper proposes a simple and fast method to estimate Atmospheric Phase Screens (APSs) by jointly exploit a stack of Synthetic Aperture Radar (SAR) images and a dataset of GNSS-derived atmospheric product. The output of this processing is conceived to be ingested by Numerical Weather Prediction Models (NWPMs) to improve weather forecasts. In order to provide wide and dense area coverage and to respect requirements in terms of spatial resolution of ingestion products in NWPMs, both Permanent Scatterers (PSs) and Distributed Scatterers (DSs) are jointly exploited. While the formers are by definition stable targets, but unevenly distributed, the latter are ubiquitous but stable only within a certain temporal baseline that can vary depending on the operational frequency of the radar. The proposed method is thus particularly suited for C, L, and P band missions with low temporal baseline between two consecutive acquisitions of the same scene: these conditions, that are both necessary to provide the dense space-time coverage required by meteorologists, allow for a reliable and robust estimation of APSs thanks to the intrinsic limitation of temporal decorrelation. The proposed technique integrates Zenith Total Delay (ZTD) products computed on a very sparse grid from a network of GNSS stations to correct for SAR orbital errors and to provide the missing phase constant from the derived APS map. In this paper, the complete workflow is explained, and a comparison of the derived APSs is performed with phase screens derived from state-of-the-art SAR processing workflow (SqueeSAR®).