# [time-nuts] Atmospheric effects in Geodesy

Wed Aug 3 00:52:17 EDT 2005

```Poul-Henning Kamp asked:

Could you explain one little detail for me ?  What is the mechanism
that makes air pressure affect antenna height ?  Is it simply the
weight of the air on the ground ?  Or is it because it affects
the speed of light in the atmosphere ?

The radio waves from outside (this applies to both VLBI and GPS) must
travel thru the atmosphere to reach the antenna. The index of
refraction for the "dry" (i.e. Oxygen + Nitrogen) is about 3 parts in
10e4 larger than one (i.e. for vacuum). At low altitudes, this means
that the "dry" troposphere adds about 2 meters to the zenith path
delay (ZPD), and this correction is constant with frequency. A
barometer is merely a scale that weighs the atmosphere, and 1 mbar
change corresponds to about 2mm change in ZPD.
But neither VLBI nor GPS observes very much directly overhead, so a
correction needs to be applied; if the earth were flat (i.e. ignoring
curvature), the correction away from the zenith would then need to be
ZPD * secant (Zenith Angle). This means that at ~30 degrees elevation,
the ~2M ZPD would become ~4M. When you factor in curvature and the
vertical structure of the atmosphere, the numbers are slightly
different but you get the idea.
In addition to the ~2M ZPD that can be calibrated pretty well with a
barometer, water vapor in the earth's atmosphere adds a variable
ranging from 0 to about 50 cm ZPD. I have seen zero in Fairbanks in
the dead of winter at -40 (makes no difference C or F -- it's cold!).
I have seen as much as 50-60 cm in Miami and the Virgin Islands. Here
in the Washington DC area today, I'd guess it's about 40 cm.
In fact, with both GPS and VLBI, you can use the barometric
calibration of the "dry" part along with precise radio observations
and turn the problem around to measure the integrated water vapor
content. In the USA in Oklahoma and Kansas, where severe summer storms
is used (along with radars) to provide warnings of severe storms.
In addition to the tropospheric components that are constant with
frequency, the earth's ionosphere also perturbs the path delay. At
S-band (~2.3 GHz, right where 802.11b/g operate), the ZPD is typically
~2M. It scales as 1/f**2, so at GPS (L1=1575 MHz) the ZPD is more like
4M. GPS uses two frequencies (L1=1575, L2=1226) to calibrate this
bias. In VLBI we have typically used 2.3 GHz & 8.5 GHz, with the
longer "lever arm" being one reason for VLBI's exquisite measurement
precision! Another manifestation of the ionosphere of possible
interest to time-nuts is that single frequency GPS timing receivers
exhibit about 20 nsec of daily noise. This shows up especially well in
Figure 7 of the [1]M12+ timing receiver paper on gpstime.com. This
plot is interesting because it also show a ~50 nsec timing "glitch"
due to an [2]ionospheric storm that later caused an aurora visible
here in MD.
One last factoid to throw into this discussion. The "wet" bias arises
primarily in the first 1-2 km of altitude, the "dry" atmosphere is
more like 5-10 km in depth, while the dominant ionospheric effects
arise at 200-400 km altitude. Since the earth isn't flat, this makes
the zenith scaling laws different for the 3 atmospheric biases. That
fact alone has accounted for a half-dozen PhD thesis!
Back to Poul-Hennings question, there is actually another small
effect. The earth is an elastic sphere. The crust is ~20 km thick and
"floats" on mush below. Atmosphere pressure changes actually do have a
small local effect raising and lowering the antenna at the 1 cm level.
This is small compared with the changes in altitude caused by the
tidal response of the earth to the gravitation of the sun & moon. You
don't normally notice the ~20 cm height changes because everything
near you is moving at the same time unless you have a very precise
accelerometer or you make observations with networks like VLBI and GPS
that span the whole earth.
Now, I'm certain that is much more than you wanted as an answer to a
simple question!
73, Tom

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