Single-frequency Satellite-based Augmentation Systems (SBASs) compute and broadcast estimates of vertical ionospheric delays and integrity bounds on the estimates called the Grid Ionospheric Vertical Errors (GIVEs) at Ionospheric Grid Points (IGPs). The dominant contribution of the GIVE comes from the undersampled ionospheric irregularity threat model. This paper presents a methodology for the undersampled ionospheric threat parameterization to reduce the magnitude of the GIVE. A threat model metric that measures the uniformity of angular separation of measurements was designed and incorporated into the current metric set, the fit radius and the relative centroid metric (RCM), such that threat geometries were parameterized rigorously based on the extended metric set. An undersampled threat model was constructed with the proposed three-dimensional metric set and historical ionospheric storm data from the global navigation satellite system stations in South Korea. We also simulated SBAS availability in the Korean region to demonstrate the benefit of the presented threat model methodology. In our preliminary assessment, the implementation of the proposed method was found to improve the 99.9% availability of the approach procedure with vertical guidance I by up to 12% when the approach was applied to the GIVE monitor algorithm.