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The anomalous propagation conditions, particularly the tropospheric ducts, severely impact the regular operation and performance evaluation of radio devices in the atmospheric boundary layer. Therefore, it is necessary to provide the regional distribution of tropospheric ducts for utilizing or avoiding these abnormal propagation phenomena. As significant uncooperative signal sources, the global navigation satellite systems (GNSS) have been widely applied in the remote sensing of the ocean and atmosphere due to the greater convenience and lower cost. With the completed deployment of the BeiDou Navigation Satellite System (BDS) in 2020, an additional source can be chosen in the relevant studies. Taking the BDS as an example, since the scattered signals from the ocean surface at low satellite elevation angles can be effectively trapped by tropospheric ducts, we propose a method to invert for the regional distribution of tropospheric ducts using the received power of ocean-scattered signals in this paper. Firstly, the propagation model was built to calculate the received power, and a suite of simulations was made in various atmospheric environments. The results suggested that the received power is more sensitive to the surface duct without a base layer. Then, we made a preliminary estimation of the tropospheric ducts on the ocean nearby Qingdao utilizing the Weather Research and Forecasting (WRF) model as well as the echo data measured by a Doppler weather radar. Before the inversion, the actual satellite azimuth and elevation angles should be obtained to evaluate the bistatic scattering coefficients and the received powers of the selected satellite signals. Finally, we presented an inversion example using the proposed method. In absence of the actual measurements, the received powers pre-estimated at different SNRs served as the inputs of the inversion process and the estimated duct parameters were used to verify the validity of the proposed inversion method. For both the received power and modified refractivity profile, the fitness between the values pre-estimated using the estimated duct parameters and calculated by the inverted duct parameters gets better as the elevation angle decreases and the SNR increases. The variation of the fitness between the estimated and inverted values is slightly different for each duct parameter. Moreover, the calculation of inversion errors further explained the above behaviors, including the mean absolute error (MAE) and the root mean square error (RMSE). Despite some certain errors, the inversion results maintain the overall tendencies and most characteristics of the estimated values, thus proving the validity of the inversion method.

Inversion for Inhomogeneous Surface Duct without a Base Layer Based on Ocean-Scattered Low-Elevation BDS Signals