Despite remarkable successes achieved by Differential InSAR, estimations of low tectonic strain rates remain challenging in areas where deformation and topography are correlated, mainly because of the topography-related atmospheric phase screen (APS). In areas of high relief, empirical removal of the stratified component of the APS may lead to biased estimations of tectonic deformation rates. Here we describe a method to correct interferograms from the effects of the spatial and temporal variations in tropospheric stratification by computing tropospheric delay maps coincident with SAR acquisitions using the ERA-Interim global meteorological model. The modeled phase delay is integrated along vertical profiles at the ERA-I grid nodes and interpolated at the spatial sampling of the interferograms above the elevation of each image pixel. This approach is validated on unwrapped interferograms. We show that the removal of the atmospheric signal before phase unwrapping reduces the risk of unwrapping errors in areas of rough topography.