PyRayHF: An open source ray-tracing forward operator for assimilating oblique ionograms

Oblique high-frequency (HF) ionospheric measurements contain valuable information about electron density structure, but remain difficult to assimilate operationally due to the computational cost of ray tracing. PyRayHF is an open-source, fully Python-based framework that addresses such difficulties through the implementation of efficient forward operators for HF propagation and parameter retrieval tailored to data-assimilation (DA) applications. PyRayHF implements magneto-ionic vertical tracing and a hierarchy of two-dimensional oblique ray tracing methods, which are verified against one another for internal consistency and validated through comparative analysis with a full three-dimensional Jones-Stephenson ray tracer. Validation results show that all solvers reproduce key observables, including group path and apex location, with typical errors below 10% when compared to the reference solution. For group path, the primary observable in oblique ionogram interpretation, simple stratified Snell’s-law formulations perform comparably to gradient-based solvers while being several orders of magnitude faster, making them suitable for DA workflows. To enable efficient assimilation, PyRayHF combines a fast vertical forward operator with a midpoint-based oblique-to-vertical transformation. For transmitter–receiver separations of 1,000–2,000 km, midpoint-derived foF2 errors remain below 10%. PyRayHF further provides a parameter-minimization framework that retrieves F2-layer parameters directly from midpoint-converted observations, producing anchor-point measurements suitable for direct assimilation into parametrized systems such as ANCHOR.