Tropospheric delays are still the main error source of satellite-based Interferometric Synthetic Aperture Radar (InSAR) mapping of Earth’s surface movements. Recent studies have demonstrated the potential of global atmospheric models (GAMs) in reducing InSAR tropospheric delays. However, the importance of appropriate interpolation and weighting strategies in GAM corrections has largely been overlooked. Here we present a new GAM-based tropospheric correction method that incorporates spatial stochastic models of the troposphere into the weighting strategy of the correction. The method determines the correlation between a pixel of interest and neighboring GAM grid locations (3D) according to the spatial variability of the tropospheric random field, instead of subjectively using an inverse distance method, a local spline function, or other standard interpolation scheme. Also, our new method considers horizontal heterogeneities of the tropospheric field by estimating the integral of the tropospheric delays along the satellite line-of-sight (LOS) direction, instead of calculating projected zenith-delays. The method can be used with any GAM, but we here implement it with the latest ECMWF (European Center for Medium-Range Weather Forecasts) ERA5 reanalysis products. We validate the new method with hundreds of Sentinel-1 images from 2015 to 2020 over the island of Hawaii, a location with variable topography, surface conditions, local climate, and deformation, and explore the tropospheric corrections for both interferograms and time-series analysis products (deformation velocities and time-series solutions). Compared with other GAM corrections (PyAPS, d-LOS, and GACOS), our new method yields a larger reduction of the average standard deviation of the corrected interferograms, i.e., from 2.55 to 1.91 cm, instead of 2.47 cm (PyAPS), 2.44 cm (d-LOS), and 2.10 cm (GACOS). Also, a larger fraction of 87% of the interferograms (243 out of 280) is improved, compared with 52%, 53%, and 66% for the other GAM corrections, respectively. These results demonstrate the importance of considering (1) tropospheric stochastic models in GAM corrections, (2) horizontal heterogeneities when estimating the LOS delays, and (3) tropospheric delays when mapping long-wavelength or small-magnitude deformations using InSAR.