With the increasing number of high-resolution gravity observations, which became available in the recent years, global Earth gravity models can be regionally refined. While global gravity models are usually represented in spherical harmonic basis functions with global support, a very promising option to model the regional refinements is the use of spherical radial basis functions with quasi-compact support. These functions are not necessarily orthogonal on a sphere, and usually, more functions are used in regional modelling than minimally needed from a global point of view. This makes the modelling more difficult. Furthermore, no techniques or choices of radial basis functions and other parameters in the regional modelling approach are established so far, as it is the case for global gravity modelling in spherical harmonics. In this article, a closed-loop simulation is used to investigate the mathematical modelling accuracy of different radial basis functions, which are compared to each other. Furthermore, artificial effects, which occur in the modelling results with very low levels of noise on the observations, are investigated. The whole study is performed on synthetic observations of a residual gravitational potential signal for the Himalaya area with different levels of noise. Spherical radial basis functions are a compromise between spatial and frequency localization, which are mutually exclusive. We show that spatial localization properties are even more important than frequency localization in the regional case, even though a band-limited signal is modeled.