Deep inside "Measuring height of reflection at HF"

[I4MFA W4MFA Eng. Marco Filippi]

I found really interesting the work of Gwyn Griffiths, G3ZIL.
I was wondering about the minimum dH we are able to measure in 120" using 0.1Hz doppler resolution on a 15M 3000Km path, assuming foF2 at 1500Km=8MHz - obviously - and hmF2=300Km.
I believe there is quite a difference (20X) with a 80M/750Km test as the one reported, but I'm not sure my guess is correct.
Answer are welcome!

[Gwyn Griffiths]

Hello Marco

 Thank you for your interest in my article on this topic in RSGB RadCom August 2024. 

BY the way, the RSGB kindly allowed HamSCI to include the pdf in its repository at

https://hamsci.org/publications/measuring-height-reflection-hf

Assuming a spherical Earth.

Taking your example at 21 MHz on a 3000 km path with hmF2 at 300 km, using the equations on page 43 we get the following for a Doppler step of +0.1 Hz:

Initial path length = 3120.952 km

Path velocity = -1.43 m/s

Path length change over 120 seconds = -172 metres

Path 120 seconds later = 3120.780 km

Height 120 seconds later = 299.719 km

Therefore minimum dH observable under these conditions is 281 metres.

Assuming also that all of the Doppler shift is attributable to the change in height.

73

Gwyn G3ZIL

[I4MFA W4MFA Eng. Marco Filippi]

I mean: in a measurement we have to consider the relative error. I know we have an error of 1/10^whatever exponent you set in GPSDO but R has an error of 0.3% that means a 0.8% on what You call H. Please double check my quickly reported values of error, starting from 21Km uncertainty over 6370Km R and the numbers reported above .

That's FINE: a 12Hz (20X) doppler shift means "something interesting" (to me); that's great, an interesting real-time measured alert of a possible iono-iono mode.

But I do not know - You used it - if the s/w and h/w and data field involved are capable of handling such measure range in 2'.

Btw, going from the big picture into details, as the maximum frequency refracted toward the earth (reflected) is foF2(@i)/sen(ia) [ foF2 at reflection point divided by the impact angle sine ] and as Bob NM7M stated (three decades ago) that an higher difference, between used F and such value, lowers (and flatten the arc of real path) the "reflection point", Your Figure 7 seems to me (considering the grey vs cyan graph) a measured demonstration of Bob's study, as we see that it is the increasing of foF2 value (from less than 8MHz to more than 8MHz, accordingly to Australian SWS foF2 map at reported time: we at esWua have no useful data, unfortunately) that has a higher contribute, with respect to hmF2, to the height H of the "reflection point".

I'm busy, due to work, but I'll check asap Your study, thank you for any possible reply about h/w and s/w and data above.

[Gwyn Griffiths]

Hello Marco

Thank you for pressing the point about the effect of radius of the earth. I have now put the maximum equatorial radius (6378 km)  and the minimum polar radius (6357 km) into my calculations and the effect on change of height between two minute intervals was very small, amounting to 2 centimetres in a 160 m height change. 

As I wrote to you in response to your personal message, I have not seen a 12 Hz Doppler shift in HamSCI PSWS data sets. Typical is <1 Hz at 20 or 25 MHz as the band opens on a 2600 km path. Paths across the Auroral Oval will of course show higher, e.g. WWVH to Europe, but we have few PSWS observations in Europe. 

As for my Figure 7 I did not have an explanation for the divergence of the cyan and grey traces. I will have to think carefully about your observation.

73

Gwyn G3ZIL 

[I4MFA W4MFA Eng. Marco Filippi]

Still busy at work, but I want to Thank You for what You shared:

- on 15M with hmF2=300Km and foF2=300MHz, on a 3000Km path, a 120" spaced data sampling reveals a height variation of 0.28Km/0.1Hz doppler shift, with an error of 1/8000 (0.0125%); typical doppler shift values are within 1Hz (change in height about 2.5Km/1%, assuming...) in 15M/12M on a 2600Km path.

As my good friend Spock was used to say, fascinating!

[Terry Bullett]

Gwyn,

Note that a radio wave in a plasma has a group path that is the the measured time of flight of a signal which is what a pulse or FMCW  ionosonde would measure.
But it also has a phase path, and they are not the same, especially in a magnetic plasma where the index of refraction is a tensor and the ray path is not the phase path. 

Observed Doppler shift is the time derivative of the phase path from Tx to Rx. 

For details, check out this book by one of my mentors,  Ken Davies: 

https://nvlpubs.nist.gov/nistpubs/Legacy/MONO/nbsmonograph80.pdf

It's complicated.
Good Luck,

Terry   W0ASP

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Dr. Terry Bullett          WØASP 
NOAA National Centers for Environmental Information (NOAA/NCEI)
Cooperative Institute for Research in Environmental Sciences (CIRES)
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"Life is Complex.  It has a Real part and an Imaginary part." 

[I4MFA W4MFA Eng. Marco Filippi]

Hi Terry, 

referring to

> For details, check out this book 

> by one of my mentors,  Ken Davies

I noted above that imho chap. 4.3 (6 decades ago) has been nicely rewritten by Bob NM7M (3 decades ago) and - I agree - it is really interesting to understand the relationship between hmF2, foF2 and path (apart from any consideration related to O and X waves).

[Gwyn Griffiths]

Thank you, Terry for picking me up on my imprecise use of path length and variation. 

I do have Kenneth Davies book, 1969 edition,  hence I have no excuse.

Forever the student in, as you say, a very complicated subject.

best wishes

Gwyn