A study of O/X wave data assimilation and inversion for ionospheric vertical electron density profiles

Longlong Niu ^1* Chen Zhou ² Na Wei ^1* Zhong-Xin Deng ^1* Yun Ning ^1* Rong Chen ^1* Wen Liu ^1*

• ¹ Xiangtan University, Xiangtan, China
• ² Wuhan University, Wuhan, Hubei Province, China

The ionospheric vertical sounding yields ionograms, which are curves reflecting the relationship between virtual height and frequency. Through the inversion of these ionograms, it is possible to obtain the electron density profile of the ionosphere. Existing methods for inverting ionograms rely on modelbased approaches. However, such methods exhibit poor stability, when the ionogram tracing data are subject to interference or the loss of multiple frequency points, this can lead to significant errors in the model solutions. Influenced by the geomagnetic field, radio waves propagating through the ionosphere split into the ordinary wave (O-wave) and the extraordinary wave (X-wave). Both characteristic waves provide valuable insights into the structural information of the ionosphere. In this study, we introduce the X-wave into the parameter inversion of the ionosphere. Utilizing a data assimilation method, we enhance the stability of the inversion process by incorporating more physical measurement information. Specifically, we use the trace data of the X-wave from the ionogram as observational values. Simultaneously, based on the trace data of the O-wave from the ionogram, we employ a multi-quasiparabolic (QPS) model to invert and obtain the electron density profile, which serves as the background value. Subsequently, a Kalman filter assimilation method is adopted to continuously integrate the observational information into the background information, thereby refining the background electron density profile. Finally, we selected several typical ionograms to validate and analyze the assimilation algorithm, comparing the results with those obtained using the Reinisch inversion algorithm. The findings indicate that the profiles derived from the joint inversion of O-wave and X-wave data show a better agreement between the calculated virtual height and the measured virtual height. This approach notably reduces the fitting error between the synthesized ionogram traces and the X-wave traces, demonstrating that the profiles inverted using data assimilation methods are closer to the true electron density profiles.