A tompgraphic model is developed to reconstruct the 3D refractivity structures of the troposphere from ground-based Global Positioning System (GPS) measurements. The refractivity is a function of temperature, pressure, and humidity or water vapor of the atmosphere. The reconstruction is possible because a ground network of many GPS receivers that record integrated slant water along ray paths of the electromagnetic waves provide the required information. To validate the developed tomographic model, a reference state of the atmosphere is obtained by using measured temperature, pressure, and water vapor profiles observed by a multi-channel microwave radiometer. That is, the 3D wet refractivity structure is derived from the known temperature, pressure, and water vapor profiles, and hence serves as reference or "ground truth". In this study, a 5 by 5 GPS network is simulated. Distance between any two consecutive GPS receivers is 4 km. The atmosphere is divided into 11 layers whose thickness is one km. The atmosphere of interest is hence divided into 275 (=5 by 5 by 11) cubes. The GPS signals that pass through the 275 cubes intersect all over during a certain time interval of interest, and permit the reconstruction. The reconstructed wet refractivity structure is very good with errors ranging between 5 and 10% below 4 to 5 km altitude compared with the ground truth. Its assimilation into numerical weather prediction models is potentially help to improve especially short-term forecasting.