## 1. Introduction

[2] Numerous effects of GNSS signal scintillations on transionospheric paths of propagation have been studied employing the St. Petersburg-Leeds-Newcastle Hybrid Scintillation Propagation Model. The initial version of the model [*Gherm et al.*, 2000] was solely based on Rytov's approximation and was therefore limited to weak and moderate scintillation conditions. To account for the case of strong scintillation, it was further extended as a combination of Rytov's method and the classical random screen technique [*Gherm et al.*, 2005]. The extended model was termed the Hybrid Scintillation Propagation Model (HSPM).

[3] Various scenarios of propagation have been studied utilizing the HSPM. In particular, in the work by *Maurits et al.* [2008]some typical properties of scintillations relevant to transionospheric paths of propagation at high latitudes have been studied including that from polar patches. In this case the University of Alaska Fairbanks Eulerian Parallel Polar Ionosphere Model was used to model the background high-latitude ionosphere.*Zernov et al.* [2009] also investigated the scintillation effects due to the bubbles occurring in the equatorial ionosphere. In this paper a very good agreement of the model results with the experimental data was reported in modeling the time dependence of the scintillation index S_{4} as a group of bubbles traversed the signal paths from two satellites of the GPS constellation to a receiver at the Earth's surface in Cameroon. The most recent update of the HSPM [*Gherm et al.*, 2011a] enabled investigation of the scintillation effects of the GNNS signals at two different frequencies (as for the dual-frequency mode of operation) for the same satellite to receiver path. In particular, the effects of correlation/decorrelation of the field phases at different frequencies were studied, and the contribution of the diffraction into the range error in the dual-frequency method was assessed. To allow for the description of the two-frequency effects, the state-of-the-art version of the HSPM was developed, which, when generating the two physical random screens and then determining the appropriate times series of the fields, also takes into account the effects of mutual correlation of the fields at the different frequencies.

[4] In the present paper, we further employ the HSPM in order to address a number of the effects of scintillation on GNSS signals for transionospheric paths of propagation, specifically, for the case of strong scintillation. In section 2 the dependence of a number of the indices and other statistical moments of scintillation of the transionospheric field are studied as a function of the severity of the signal fluctuations. These include the time correlation radius of the field intensity, *τ*_{I} and of the complex amplitude of the random field *τ*_{C} and the spectral indices of the phase and log amplitude fluctuations (*p*_{a} and *p*_{ϕ}, respectively).

[5] In section 3 the effect of the full cycle phase accumulation is considered. In the conditions of strong scintillation, the deep amplitude fades frequently occur. This is likely to be accompanied by fast phase changes, which may lead to full 2*πM* radians (where *M* is a positive, or negative integer) phase accumulation. The probability of this effect is studied for the conditions of strong scintillation.

[6] Finally, section 4 is devoted to a discussion of the problem of the consistency/inconsistency of the equivalent phase screen model for the interpretation of the scintillation effects on the transionospheric paths of propagation. Comparison is also made of the results of modeling scintillation effects utilizing HSPM and the technique of the random screen approximation.