Bob,
Some information below on the effects of above-freezing and below-freezing temperatures on various VLF losses, including (a) ground-wave losses, (b) near-field ground effects losses and (c) skywave (waveguide) ground effects losses.
A short preface:
The discussion below is for a VLF system with a vertical transmit antenna.
In a VLF system with a vertical transmit antenna, high surface conductivity under the antenna and in the near and far fields is desirable. (1)
In a VLF system with a horizontal antenna, low surface conductivity under the antenna is desired, and high surface conductivity is desired elsewhere in the near field, and in the far field. (1)
This makes Antarctica a great place for VLF QRP: ice under the antenna; salt water elsewhere (whence the 42 km long dipole at Siple Station: https://s3.amazonaws.com/Antarctica/AJUS/AJUSvXVIIIn5/AJUSvXVIIIn5p270.pdf http://nova.stanford.edu/~vlf/Antarctica/Siple/ )
Temperature coefficients of conductivity:
As temperature drops, non-frozen soil conductivity (mhos, siemens) decreases by roughly 1.9% per degree C. (2)
As temperature drops below freezing, soil VLF conductivity decreases rapidly; the rate of change is highly dependent on soil type, but a 2:1 change per 10 degrees C at 10 kHz (for below-freezing temperatures) is a reasonable example for some soils. (3)
Near field and ground wave losses:
As conductivity decreases (i.e. with decreasing temperature), VLF near-field and ground wave losses increase non-linearly (4)
At 30kHz, ground wave amplitude is low at 5000 km (4)
At 30kHz, ground-wave loss in non-frozen soil of poor conductivity (10^-4 mhos/m) might be 20dB greater (20dB more loss) than in non-frozen soil of fairly good conductivity (10^-2 mhos/m) (4)
At 30kHz, ground-wave loss in frozen soil would be very high (4)
All of the above might suggest a very low amplitude ground wave at TA distances in mid-winter (ground wave including direct, ground-reflected, Norton surface and trapped surface waves)
In that case the long-path part of the problem reduces to skywave losses (skywave ionospheric losses and skywave ground-effects losses):
Skywave loss (waveguide loss in this case) due to ground effects is nominally:
d_alpha_gnd = [.046 * sqrt(f)] * 1/{h * sqrt(s) * sqrt[1 – (fc/f)^2]} (in units of dB per 1000 km) (5)
where f = 29,500 (Hz), fc ~ 2100 (Hz) (day) or 1700 (Hz) (night), h ~ 70 (kilometers), .0001 < s < .01 [s for sigma (conductivity), in mhos per meter; range of values from .01 for very good (highly conductive) soil to .0001 for frozen earth; values below .0001 occur in arctic regions, but such regions tend to have snow and ice above the soil. A different formula is used for snow and ice losses at frequencies below 1 MHz]
The formula above may be sufficient for analysis of cold-weather propagation losses over distances of 5 Mm or more. Besides propagation losses, there are near-field and antenna-system losses.
Near-field and antenna-system losses:
VLF near-field and antenna-system losses associated with ground effects, increase as temperature (and therefore conductivity) decline. The increase in near-field and antenna-system losses can be between sqrt (s) and s^1.5, but the nominal value of these losses is hard to determine analytically for an electrically-short antenna. The calculation for ice/snow cover for your antenna system may be easier to determine analytically; if you’re interested I’ll send a notional formula.
If your VLF signal reports do not change appreciably after a snowfall or an ice storm, that information can be used to help generate a temperature model of your ground-effects-related near-field and antenna-system losses, in which case you might have a good starting point for a whole-system model for all temperatures. Noting what happens to signal reports after a freeze, after a snowfall and after an ice-storm can help to nail down the most difficult part of the system model for a VLF system with an electrically short antenna (antenna-system losses and near-field losses).
In summary:
A) VLF near-field and antenna-system losses associated with ground effects, increase as temperature declines. Noting what happens to signal reports after a freeze, after a snowfall and after an ice-storm can help to establish a good model for these. Such a model will be useful at all temperatures, and very helpful in the optimization of an electrically-short VLF antenna.
B) The formula above for d_alpha_gnd (relative ground-effects losses incurred by the skywave in the waveguide) gives values from about 2 dB per megameter to 6 dB per megameter at 29.5 kHz for soil conditions ranging from fairly good to frozen. This formula is useful by itself for assessing the difference in far-field path loss at various temperatures. Total path loss includes other terms that add to and subtract from* d_alpha_gnd, but those terms are not necessary for assessing changes in ground-effects-related skywave path losses (in the waveguide) over temperature.
C) Ideally, you would add (A) to (B) to obtain the sum of the predominant contributors to loss variation over temperature.
* terms such as the convergence factor, and reinforcements at discontinuities, subtract from path loss
(1) Biggs, AGARD, 1970
(2) a general approximation; Corwin 2005, Ma 2010
(3) Moore 1992
(4) Watt 3.2
(5) Watt 3.4.33
73, Jim AA5BW
Paul;
It is not only the ground but the air temp has great influence and maybe much more than the shallow depths of the ground freezing-Bob
> Date: Sat, 8 Mar 2014 17:06:09 +0000
> From: [email protected]
> To: [email protected]
> Subject: Re: LF: Daytime 29.499 kHz
>
>
> Bob wrote:
>
> > Wonder what effects soil conductivity changes has on the
> > propagation at these VLF freqs??
>
> I have no information. You would expect ground resistance
> to rise, but would that make noticeable difference to
> propagation if it is only a freezing of a shallow surface
> layer?
>
> I had to go to a narrower bandwidth to produce phase and
> amplitude plots for last night's test
>
> http://abelian.org/vlf/tmp/29499_140308a.gif
>
> Signal is down by some 5dB compared with some recent
> tests.
>
> Nothing detected this afternoon.
>
> Propagation seems normal, noise floor normal.
>
> Maybe the cold and frozen ground is affecting the tx
> efficiency, some lower Q of the loading coil - antenna -
> ground loop, or a reduction of effective height.
>
> Will be interesting to see what happens after the thaw.
>
> --
> Paul Nicholson
> --
>
