Global Positioning System (GPS) data for phase delay differential between Ll and L2 frequencies are analyzed by a model in which the combined effect of hardware and phase ambiguity terms is represented by a constant for each receiver-satellite path and the ionospheric contribution is represented by the RIBG model (ray trace through the combined ICED (ionospheric conductivity and electron density), Bent, and Gallagher ionospheric models). RIBG contains a detailed global empirical climatological ionospheric model of the electron density versus height profile (EDP) from 80 km up to the plasmapause, which is combined with a full three-dimensional ray trace propagation model. Discrete inverse theory (DIT) is used to fit the driving parameters of RIBG to about 2 hours worth of data from a single GPS receiver at various geographical locations. Validity is demonstrated by the ability of the GPS-updated RIBG model to predict independent measurements of (1) vertical total electron content (TEC) over the ocean out to substantial distances from a GPS receiver, often in excess of 2000 km at midlatitudes, and (2) the electron density versus height profile (EDP). Performance variation with magnetic latitude is noted. Flexibility in RIBG to adjust different driving parameters for different parts of the EDP, in order to obtain a best fit of GPS data, benefits the EDP prediction. Implications of this approach for GPS navigation and other radio system applications are discussed.