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Doppler effect measurements around 4/12/2021 total eclipse


Aim

Measure the doppler effect (deviation) between RWM transmitter at Moscow (MSK), Russia and receiver at Lochem (Lc), The Netherlands. This will be measured between December 1st 2021 and at least December 20th 2021. This is part of the research around Antarctic Eclipse Festival (see also https://hamsci.org/doppler-instructions).
The total eclipse was broadcasted by NASA.
04122012 Total
        eclipse (c) NASA
(c) NASA, 2021, It looks to have a solar flare!

Equipment

Locations

Total eclipse on Antarctic

Total eclipse is at: 76.7833° N 46.1983° W
The Dec. 4th total eclipse will be between 05:29 and 09:37UTC. Totality at 07:34UTC.
Totality happens in the middle of the continuous carrier of RWM between 07:30 and 07:38UTC.

Transmitter at RWM Moscow (MSK), Russia

RWM is at: 55.7228° N 38.2049° E
MSK Sun rise is around 05:39UTC and MSK Sun set is around 12:59UTC.

Transmitter at CHU Ottawa, Canada

CHU is at: 45° 17' 47" N, 75° 45' 22" W

Midway CHU

Midway CHU (in Atlantic) is around: 49.7° N 41.1° W
Midway CHU Sun rise is around 10:40UTC and Midway CHU Sun set is around 18:42UTC.

Midway RWM

Midway RWM (in Poland) is around: 53.5° N 21.9° E
Midway RWM Sun rise is around 06:32UTC and Midway RWM Sun set is around 14:12UTC.

Receiver at Lochem (Lc), The Netherlands

Lc is at: 52.1614° N, 6.4156° E
Lc Sun rise is around 07:25UTC  and Lc Sun set is around 15:24UTC.
The total eclipse happens close to the moment of Lc Sun rise.

Proces around measurements

A few steps were involved in the measurements:

Qualitative modeling

The critical frequency (fo) and height of the layers during the day can be seen in below illustrative pictures (so not necessarily correct for the location in this eclipse research, but the form/behavior is similar).

An height and foE plot for the E-layer is below (Verhulst&Stankov, 2017, Fig. 4B):
E-layer heigth and Fc
A height and foF2 plot for the F-layer is here (Smith, 1951, page 257):
Fc
        and critical height of leayer during day

Here is an almost real time view of the fo and height of the F2-Layer: IRTAM and GAMBIT
D-layer's absorption has similar (symmetrical) diurnal behavior as the E-layer (Smith, 1951, page 260), but it is of course about absorption (instead of reflection).

Reflection

A vertical beam with critical frequency (fo) will just be reflected at the mentioned layer (beams of higher frequency will pass through).
In case the beam is not vertical a higher reflective higher frequency (MUF: Maximum Usable Frequency) can be reached. This is related to the MUF-factor.
MUF = fo * MUF-factor

<Poole (2004, page 44) looks to have a typo: instead of the '*' it has wrongly a '/'>

For a path of some 2250km (which is the when looking at RWM and Lc); the E-layer has a MUF-factor of 4.8 and the F-layer a MUF-factor of 3.2 (Poole, 2004, page 44).
So 4,996kHz might just use the E- and F2-layer behavior and the 9,996kHz and 14,996kHz will most likely only use the F-layer behavior (for our case: DEC. 1936/left plot in above picture).

Frequency deviation

A height plot over the day for the E-layer and F2-layer can be seen above. Winter time curves are important for this particular eclipse research.
The frequency deviation (doppler effect) will depend on the height change. So one needs to differentiate these plots.

The speed (black line) of the E-layer after differentiating is (Sun rise @ 07:40 and Sun set @ 15:40):

Speed of E-layer
Before Sun rise and after Sun set the E-layer has vanished.

The speed (yellow line) of the F2-layer after differentiating is (Sun rise @ 07:15 and Sun set @ 16:45):

Speed of F-layer

Sun's dip angles

What does 'Sun rise/set' mean at the E/F-layers of 110/250km: towards sea level (around 10/18° which are the Sun's visible light dip angles as used by Verhulst&Stankov, 2014) or smaller (related to UV) dip angles? A large dip angle would provide too much absorption of the Sun's far/extreme UV rays through the air below E-layer.
<Sun's dip = - Sun's altitude>

See also the below picture for the penetration of far/extreme UV rays around 90/150km (which determines the effective horizon for these rays):
pentration of UV
Picture from
Windows to the Universe® (http://windows2universe.org) © 2010, National Earth Science Teachers Association. Creative Commons License

So a Sun's dip angle closer to 4° is more likely when interpretating the observations of Verhulst&Stankov (2014, Figure 5). The following picture (the purple and green dotted lines follow the first/last observability of the E-layer) shows this:
E-layer first
      observations
Based on the E-layer (at 110km): the layer gets enough Sun rays from a Sun's dip angle of around 4°, which is equivalent to a distant effective horizon of 90km. 90km is the bottom (this might be close the Kármán line [Verhulst&Stankov, 2014, page 7]) where the far-ultraviolet rays can reach (up to which the influence of the E-layer ionisation ends).

The extreme-ultraviolet that causes the F-layer has a bottom of influence around 150km. This would result in a approximate 10
° dip angle for the Sun, when assuming an F-layer at 250km. This would be around 1 hour earlier that Sun rise at sealevel, which maps somewhat the behavior seen in the above F-layer height graph.
<
IMHO, a Sun's dip angle of around 10/18° due to visible light, as used by Verhulst&Stankov (2014), does not look correct. Let me know your ideas>

Simulation

We need to combine, the time of day, the speed of the E- or F-layer, MUF of E- of F-layer, the Sun's dip angle and the absorption of D-layer, to provide a theoretical frequency deviation over the day. The below is all about the qualative behavoir.

An attempt has been made to simulate the behavior at the three frequencies:
Simulated
        frequency deviation
This has been derived from the above Layer-Heights, Layer-fo, dHeight/dTime, D-layer absorption, dip angle and adjusting for the Sun's position @ Midway. The deducted MUF-factors are around the expected 3.2 (for F-layer) and 4.8 (for E-layer).
The simulation in general looks to follow the timing of the measurements more or less. The F2-layer downward's trough just before Sun rise is not visble in the 4,996kHz curve as that F2-trough is partly in de 'shadow' of the E-layer (remember the radio waves are under an angle of some 12°/18° when reaching the E/F-layer).

The F2-layer height (hmF2) has been traced from GAMBIT for 16-12-2021 at Midway RWM (red curve). To get the speed one needs to differentiate the height (purple curve),

Heigth and speed of
        F-layer

This speed can be transformed into a frequency deviation (black curve in below graph) by using:
Frequency deviation [Hz] (doppler effect) = ((<light speed [km/sec]> + <speed of layer [km/sec]>)/(<light speed [km/sec]> - <speed of layer [km/sec]>) - 1) * <Station frequency [Hz]> * MUF-factor

<the MUF-factor [3.2] is included, as the radio waves do not fall perpendicular on the F-layer>

This gives the following picture:

speed
      of F2 layer height change
This black curve looks to correlate with the frequency deviation measured with the FLEX-1500. 4,996kHz measurements (green dots) deviate near Sun rise/set, as that frequency is influenced during those periods by the E-layer instead of F-layer.
Need to check if this matching can be matched on other dates!

I think there migth be a different behavior when we swap the receiver and transmitter locations; as the layers are 'illuminated' differently.

Influence of eclipse

The total eclipse in Antarctic is far away, does this have an influence on the ionosphere around middle Europe?

Perhaps this can be compared with the 21 August 2017 total eclipse and the related results. The influence on the ionosphere of a total eclipse looks to be around 45° (from the centre of the eclipse), as the Dec 2021 eclipse is at around latitude 76° S, its influence might extend to 30° S, so quite far away from Midway RWM (53° N).
From above measurements, no real effect can be seen in The Netherlands from the total eclipse. But perhaps statistical analysis (by the Antarctic Eclipse Festival) could proof differently. The measurements have been shared with that group and Zenodo.

Conclusions

During two weeks the RWM continous carriers has been measured using the SDR FLEX-1500. The radio frequency is not 100% the station frequency. To get to hear the RWM station signals at 1kHz, we need to put the radio on a slightly different frequency. But this difference does not seem to change over time, so the frequency stability of the FLEX-1500 looks to be good. It is unlikley due to the height of the indoor aerial, but it could difference in room temperature. Need to investigate further.

The E- and F-layers at the midway location between transmitter and receiver is determining the effects of these layers.
The E- and F-layer are illuminted by the far/extreme UV rays and this starts with Sun's dip angle of respectively 4° and 10° (so not the same Sun dip angle if it were visible rays, which would be 10° and 18°).
At a qualitative level we can simulate the freqeuncy deviation (due to the doppler effect) of radio ways based on modeled E- and F-layers (by looking at [change of] fo/MUF, change of layer-height, absorption in D-layer, time of day and location).

The measured frequency deviation did not really change significant during the day of the eclipse. This is perhaps also not expected so far away from the total eclipse location (distance between Poland and Antarctic).

When results of Antarctic Eclipse Festival are available; a reference to them will be included.

Acknowledgments

I would like to thank the following people for their help and constructive feedback: Kristina Collins, Tobias Verhulst and all other unmentioned people. Any remaining errors in methodology or results are my responsibility of course!!! If you want to provide constructive feedback, let me know.

Literature

Collins, Kristina et al.: Citizen scientists conduct distributed Doppler measurement for ionospheric remote sensing. In: IEEE Geoscience and Remote Sensing Letters (2021), pp. 1-5.
Poole, Ian D.: Radio propagation: Principles and practice Radio Society of Great Britain 2004.
Smith, Newbern: Influence of the Sun upon the ionosphere. In: Proceedings of the American Academy of Arts and Sciences 79  (1951), issue 4, pp. 254-265.
Reijs Victor. (2021). Frequencty deviations seen in RWM carrier wave (Version 1) [Data set]. Zenodo. https://doi.org/10.5281/zenodo.5774050
Verhulst, Tobias G.W. and Stanimir M. Stankov: Height-dependent sunrise and sunset: effects and implications of the varying times of occurrence for local ionospheric processes and modelling. In: Advances in Space Research 60  (2017), issue 8, pp. 1797-1806.
Witvliet, Ben and Erik van Maanen: Impact of a Solar X-Flare on NVIS Propagation Daytime characteristic wave refraction and nighttime scattering. In: IEEE Antennas and Propagation Magazine (2016), pp. 1-10.

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Major content related changes: November 29, 2021