For the work on HF TDoA a realistic method for the signal delay is needed. Up to now, the great-circle distance divided by the speed of light is used which of course is incredibly naive. Nevertheless it seems to work, at least to some degree.

Rather than attempting a full-fledged ray-tracing simulation one can use the theorems of Breit and Tuve and Maryn's theorem for obtaining the signal propagation delay from virtual vertical height profiles, see, e.g,

arXix:1104.2248 and

here.

In order to evaluate this technique let us use the

oblique ionograms measured by the University of Twente web SDR (thanks to PA3FWM for making these available! and for him and G3PLX for explanations):

The plots below show the time delay vs. UTC for two days in June at two different frequencies. Overlaid are time delays obtained by

- VOACAP: all propagation modes with probability>0.3 are shown,
- simulations explained above using electron density profiles obtained from the international reference ionosphere model IRI2016.

(For this comparison the oblique ionograms have been corrected for a time offset of ~0.3ms whose origin is not yet clear)

All plots are generated using octave and this

octave binding of the IRI2016 model.

As the IRI model is a climatological model (as is VOACAP), the agreement between model calculation and data is not expected to be perfect. Only the general features of these backscatter ionograms are reproduced, such as the 2-hop E-layer reflection for lower frequencies during mid-day but, e.g., not sporatic E-layer reflections in the late afternoon/evenings.

Note also that this simple method does not take into account magneto-ionic effects which become important for lower frequencies (and at local night-times).