Ionospheric delay is now recognized as a major error source for satellite navigation systems. ICAO SBAS (satellite-based augmentation system), the operational standard WADGPS (wide-area differential GPS) system, has a capability to make a correction to the ionospheric delay effects on GNSS in addition to satellite clock and orbit. According to the error analysis for the SBAS, ionospheric correction has a large uncertainty due to improper modeling of the ionosphere. In fact, the ionosphere is modeled as the thin shell in the SBAS message. This simple model might fit the actual ionosphere during quiet ionospheric condition but could not represent the large-scale structure of the ionosphere during daytime including the equatorial anomaly. The SBAS broadcasts vertical ionospheric delays in meters at the grid points (IGP; ionospheric grid point) located at every five degrees of latitude and longitude when using the message defined by the current standard. User receivers convert them to the slant delay using socalled obliquity factor derived under an assumption of the thin shell ionosphere as well as bilinear interpolation between IGPs. It is, however, known that the ionosphere has a certain vertical structure. Therefore, the authors have considered some ionospheric models for single-frequency WADGPS and compared their capabilities. The first model examined is 'Variable Height Shell'; This model still treats ionosphere as a thin shell, but the shell height is variable, not fixed at 350 km. In general, the peak height of the ionospheric density becomes low during daytime while high during nighttime. Based on this model, the SBAS broadcasts the shell height in addition to the contents of the current message to reflect the actual peak height. This model implicitly involves slab thickness as well as various peak height of the ionosphere. Another possible model is 'Multi-Layer Shell' including double- or triple- layer thin shell models. Based on this model, multiple layers of the thin shell are defined at the fixed heights and they share the vertical ionospheric delay. According to the past study, triple-layer model tended to be unstable and sometimes produced negative delays which never be observed. At this time the residual optimization algorithm proposed by the authors is applied and works well so to separate the vertical ionospheric delay into each layer. In this paper, vertical structure of the ionosphere is briefly described and the proposed model is explained. The results can be applied to the single-frequency wide-area differential GPS systems including the ICAO SBAS with some modification or addition of ionospheric correction messages.