Modeling of radio wave propagations under sporadic-E influence at low and middle latitudes

The sporadic-E (Es) layer is a thin layer of several kilometers existing at an altitude around 100 km and features extremely dense ionized irregularities, which can reflect or scatter high frequency (HF) and very high frequency (VHF) radio waves. The most popular theoretical explanation for mid-latitude Es formation is the wind shear theory. Measurements by rocket souding have shown that Es has high electron density and relatively sharp density gradient in the vertical direction. The one-hop propagation of VHF signal in Es can even reach as far as 2000 km. In this paper, we consider incident radio waves influenced by Es via both reflecting and scattering processes at low and middle latitudes, the coefficients of which are related to and vary with the critical frequency of Es (f(oEs)). Firstly, with a supposed parabolic density distribution and the autocorrelation function of the electron density given by Booker, HF and VHF radio wave propagations in Es are analyzed according to the reflection and scattering theory. Secondly, a numerical model for the combined reflecting and scattering processes is developed in the form of piecewise function, the contribution of which can be distinguished by the portion factor of reflection (k(r)). According to the model, there are two threshold ratios of the critical frequency to the wave frequencies f(r) and f(s) respectively. The incident radio waves are totally reflected by Es when f(oEs)/f is higher than f(r) and mostly scattered when f(oEs)/f is lower than f(s). A transition zone exists between two critical points, with the combined processes working together. Thirdly, HF/VHF radio wave propagations in low and middle latitudes of Es are are in the north-southern direction and east-western direction separately. The experiment link in the north-southern direction is from Kunming to Xi'an at distance of 1065 km, and the ionosonde used for Es observation is located at Chongqing. Two east-west links are arranged, one of which is from Dehong to Huaihua and the other is from Dehong to Chenzhou, with the ionosonde located at Kunming and the ground distance as far as 1240 km and 1590 km respectively. The measurement data are treated and parameters of the above mentioned model for wave propagation in Es are experimentally determined. Finally, our model is verified by comparing with ITU-R model. Our results are consistent with the results from the ITU-R model when the f(oEs)/f is high (i.e., the reflecting process plays a main role). When the scattering process dominates, the attenuation value of VHF signal is far less than that predicted by the ITU-R model, which is closer to actual measurements. It is concluded that our model is more preferable for HF and VHF radio wave propagations in Es at low and middle latitudes.