Quantifying Errors in the Midpoint Transform Applied to Oblique Ionograms

It is important to specify the state of the ionosphere for Over‐the‐Horizon communications and surveillance. Both vertical and oblique ionograms provide valuable data to this end. Oblique ionograms can probe the ionosphere in locations where it would be impractical to build a vertical ionosonde, but their measurements are not straightforward to assimilate. There are essentially two assimilation methods: the first is to transform the oblique ionogram to the corresponding vertical ionogram and assimilate it at the link midpoint. There are a few different ways to perform this transform, all of which introduce errors. The second method is to ingest the oblique ionogram directly. This method does not make these assumptions, but is more computationally expensive and is currently only implemented in the GPS Ionospheric Inversion data assimilation model. This paper quantifies the errors in the first method. This is done by simulating oblique ionograms as well as vertical ionograms at the oblique link midpoint using numerical raytracing. The oblique ionograms are transformed and compared to the verticals. Differences in the critical frequency and the height at which it occurs are studied as a function of latitude, local time, oblique link direction, and mode (O or X). This is done for ground ranges of 2,500, 1,250, 600, 300, 150, and 75 km. For 2,500 km links, we find Root Mean Square Errors for critical frequency of 0.4 MHz (9.9%), and 22 km (9.3%) for hmF2. Shorter links are less affected, but still have significant errors for ground distances over 300 km.