Assimilating VLF Transmitter Observations With an LETKF for Spatial Estimates of the ${D}$ -Region Ionosphere

The <inline-formula> <tex-math notation="LaTeX">${D}$ </tex-math></inline-formula>-region ionosphere plays an important role in coupling the neutral atmosphere to denser ionospheric plasma above. Practically, it impacts long-range radio communications between extremely low frequencies (ELFs), where communications are enabled by the layer, and high frequencies (HFs), which are attenuated by the layer. A combination of its altitude and extremely low electron density means that it is difficult to make measurements of the region using typical ionospheric remote sensing techniques, and our knowledge of the <inline-formula> <tex-math notation="LaTeX">${D}$ </tex-math></inline-formula>-region is limited as a result. This article presents the development of an ensemble Kalman filter method to spatially map <inline-formula> <tex-math notation="LaTeX">${D}$ </tex-math></inline-formula>-region electron density profiles over the continental United States using an array of very low frequency (VLF) radio transmitters and receivers. Data assimilation has previously been used to estimate higher altitude regions of the ionosphere, but its application to VLF radio measurements and the <inline-formula> <tex-math notation="LaTeX">${D}$ </tex-math></inline-formula>-region is new. The technique has several favorable features, including statistical confidence measures with every estimate, the ability to localize the influence of measurements, inclusion of physically realistic spatial correlations, relatively fast convergence, and the ability to add observations to the estimate as they become available. We describe the filter and present results for day, night, and terminator ionospheres using simulated data. We also present a study on the robustness of the filter when initialized with a prior that is far from the true ionosphere. The method shows promise for application to real data in the near future, especially for estimating the characteristics of large-scale features in the <inline-formula> <tex-math notation="LaTeX">${D}$ </tex-math></inline-formula>-region.

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