# [time-nuts] Rain, Water, etc

Tom Clark, K3IO (ex W3IWI) K3IO at verizon.net
Mon Mar 6 15:28:24 EST 2006

```   [1]time-nuts-request at febo.com wrote:

David and Tom opined:

Rain should have an effect on the timing of the signal, since the
propagation speed of radio waves through water is different from that
through air. It will also attenuate the signal, causing worse S/N
ratio which would cause the lower-elevation satellites to not be seen.

David,

Maybe we can figure this out. First, the refractive
index of water is about 1.3. So I think this means
the propagation speed of radio waves in water is
down to about 0.75 c, right?

Then, how much water are the GPS signals traveling
through? Let's assume the typical amount of rain in
a heavy storm is a couple of inches. All that water is
either puddles already on the ground, drops on their
way down, or moisture still in the clouds waiting to
come down.

The total amount of water in a cross section column
of the atmosphere that the GPS signals travel though
is thus a couple of inches total, max. Let's assume
a worst case -- 6 inches.

So, those GPS signals go through 20,000 km of
empty space and atmosphere containing a total of
6 inches of water; in which it slows down by 30%.
At a ns/foot, this comes to 25 ps per inch of water
content in the air; a total of 150 ps in my worst-case
example above.

My conclusion is that rain or snow, light or heavy,
has no effect, even at the ns level. Can someone who
really knows double check this back of the envelope
calculation?

Thanks,
/tvb

If it is in fact raining, rain will act as an absorber, decreasing the
SNR. If you don't believe this, take a small "hockey puck" GPS antenna
and drop it into a dish with an inch or 2 of water in it and watch the
signals go away. This is why GPS doesn't work for swimmers.
The real "wet" effect comes from water vapor in the atmosphere. The
index of refraction of water departs from unity by about 300 parts in
10e6. Plug this into the fact that the water vapor in in the bottom ~2
km of the atmosphere and you will see that the number works out to be
< 1 meter of path delay change in the zenith, and it will increase
towards the horizon as secant(zenith angle) [strictly speaking, this
is true only for a plane parallel atmosphere, but it gives an order of
magnitude idea].
Secant(60º)=2, so the number at 30º elevation is twice what it is in
the zenith [assuming that the weather is the same in both directions].
To show the range it can be, at -60° F (or C, it makes little
difference!) in the dead of winter in Fairbanks, I have seen under 1
mm of zenith path delay. Similarly, in the middle of the Alticama
desert at 13,000ft altitude, it can also be ~1mm (this is why so many
radio & optical telescopes are located in Chile).
The other extreme is in more tropical regions. In St Croix & Miami, I
have seen as much as 2M in the summer afternoon.
As an aside, geodetic quality, dual frequency GPS receivers at fixed
locations are used to measure precipitable water. The ionospheric
delays are measured using 2 frequency observations. The stations are
assumed to be fixed. Precision orbits are extracted from a global
network of GPS sites, and what's left is the water vapor contribution.
In "Tornado Alley" in the Oklahoma-Kansas area, a network of many
types of sensors (including GPS) are used for research attempting to
You can glean some more info on these GPS factoids at the IGS web
site: [2]http://igscb.jpl.nasa.gov/
While I am on such topics, we can't forget the ionosphere. While the
troposphere & water vapor are only in the bottom ~2 km of the
atmosphere, the ionosphere sits at ~300 km altitude. Ionospheric
effects vary with time-of-day, solar cycle, solar flux and location in
a complex manner. While the water vapor contributions at all radio
frequencies are equal, the ionospheric contributions scale as
1/frequency². While the water vapor zenith path delay is ~50cm-2M, it
just so happens that the typical ionospheric range over one day is
also typically 50cm-2M at S-band (2.3 GHz).  Noting that
(2.2/1.57)²=2.15, we would expect the "typical" zenith value to be in
the 1-4M range for GPS in the zenith. At a more oblique angle the
effect is larger so we can expect the GPS "signature" to be something
like 5-6M. And it turns out that it is not unusual to see daily timing
variations at the ±10 nsec level.
Back in 2002, in conjunction with an effort to calibrate the "DC"
timing offset of the Motorola GT+ timing receiver, Rick Hambly and I
happened to catch a ~50 nsec ionospheric excursion due to a solar
flare which then also produced a spectacular aurora. You can see the
"Critical Evaluation ..." paper at [3]http://gpstime.com/. In the
paper, you will see the interesting result that the ~50 nsec timing
"glitch" reproduced perfectly with receivers separated 22 km. And you
can see some pretty pictures (including a "movie") of the Aurora as
seen at 39º latitude in Maryland on my photo web site at
[4]http://www.pbase.com/tomcat/aurora.
73, Tom

References

1. mailto:time-nuts-request at febo.com
2. http://igscb.jpl.nasa.gov/
3. http://gpstime.com/
4. http://www.pbase.com/tomcat/aurora

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