Synthetic time series generators of signal attenuation due to rain are an important tool for radio-communication system simulations. These generators must reflect both the long- and short-term dynamics of signal attenuation due to rain, and have to rely on prolonged experimental observations of attenuation time series. Such prolonged observations are not always feasible, especially if a large number of different climates have to be covered. Fortunately, rain attenuation is well correlated with the rain rate above all when long term statistics are considered. Only for particular events the correlation may be lower in some cases, especially for intense rain events which have a limited spatial expansion. The advantage of using rain rate data instead of rain attenuation data as a basis for synthetic time series generators of signal attenuation is the following: there exist consistent sets of rain rate time series from numerous locations around the globe. In this paper, enhancements to an existing synthetic rain rate generative model are presented and discussed. These enhancements include (1) the modeling of fast variations of rain rate, (2) the grouping of rain events into episodes, and (3) the extension to the spatial domain (space-time model).