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
> --
>
