Ionospheric scintillations can not only reduce the accuracy of GPS/SBAS receiver pseudorange and carrier phase measurements but also result in a complete loss of lock on a satellite. Thus it is important to be able to investigate, model and mitigate scintillation effects. Thus, a trans ionospheric propagation model has been developed which can calculate frequency spectra (power spectra) of the phase and level (log-amplitude) fluctuations in a trans ionospheric channel of propagation containing time-varying electron density irregularities (which produce the scintillations) and which is valid even for strong scintillation conditions. The strongest amplitude scintillation occurs due to bubbles in the low latitude ionosphere. These have also been modelled and their effect on transionospheric GPS paths determined. Calculated power spectra of these processes can be used to produce random time sequences of the log-amplitude anaphase of the field. Examples of simulations and their use are presented for high and low latitudes and scintillation mitigation for GPS receivers is discussed.