Since many years, civil aviation has identified GNSS as an attractive mean to provide navigation services for every phase of flight due to its wide coverage area. However, GPS standalone cannot meet ICAO requirements in terms of accuracy, integrity, availability and continuity, particularly in the case of precision approaches. To achieve improved level of performance, different augmentation systems have been developed aiming at enhancing and monitoring the quality of the Signal-In-Space (SIS). In particular GBAS, for Ground Based Augmentation System, allows guarantying a very high level of performance in a given coverage area surrounding an airport for example. Currently, GBAS is foreseen as an important source of innovation for civil aviation since it has already been certified for CAT I precision approaches and may allow reaching ICAO requirements down to CAT II/III minima, then providing an alternative to ILS. This possibility is actively investigated and ICAO and Industry standardization bodies are currently deriving requirements for GBAS CAT II/III. Autoland simulations for CAT II/III certification require numerous simulations to assess statistically the aircraft capability to autoland. Therefore, it is necessary to identify the GBAS GLS (GPS Landing System) behavior with sufficient fidelity, taking into account physical phenomenon affecting accuracy, continuity and integrity, but still, with adequate limited representativeness, assuming that it will feed an autoland simulator dedicated to airworthiness demonstration of aircraft guidance laws. A model has been proposed in the past but the evolution of CAT II/III requirements and the lack of information on the validation methods used make it necessary to investigate further this subject. The goal of this paper is to provide the steps to the development of a model of GBAS L1 C/A depicting the behavior of the outputs of the system with sufficient fidelity for CAT II/III autoland simulations. Our study is based on the previously proposed model. We focused here on the nominal and steps error models which so far appears to be an adequate representation of GBAS behavior for autoland simulations. However, we propose some improvements to update this model so as to reflect the evolution of the requirements and enhance its representativeness while meeting its primary objective to serve airworthiness demonstration. Moreover, additional simulations have been run to extend this model to Cat III airports all over the world since it has been first developed only for North America.