Spencer ... here's a response
On 9/18/2011 2:32 PM, David Patte wrote:
Actually, this should have been addressed to Spencer, not me.
On 2011-09-18 13:01, Robert Kellogg wrote:
David,
The majority of refraction occurs in the earth's troposphere, being a
function of pressure, temperature, and humidity. The radio
communication horizon is 4/3 larger than our optical horizon because
of the way these parameters interact with photons.
It is interesting that the NOAA sun position calculator *does* take
into account atmospheric refraction both for azimuth and more
dominantly, for elevation. Cernic's "Sun" calculator (available on
Sabanski's site: http://www.mysundial.ca/tsp/sun.html) is also based
on NOAA's algorithms and also includes sun refraction.
Assuming that the atmosphere is more humid (hurricanes?) then the
sun's elevation will appear to be slightly more elevated in the sky.
This in turn will very slightly alter azimuth. But the major effect
is changing elevation.
What's the maximum refraction effect? At sea level with the setting
sun on the horizon, the atmospheric refraction bending seems to
"lift" the sun. So to see the last grazing limb of the sun over the
level horizon (sunset or sunrise), the *center* of the sun is still
0.833 degrees below horizon.
Although we can calculate these effects, most sundial purists choose
the hour lines to be drawn geometrically, according to the equation:
tan(dial hour line) = sin(latitude) x tan(hour angle of sun)
So, what are you exactly observing? And unfortunately, I don't think
you can attribute it to pollution, climate warming or depletion of
the ozone layer. There probably is a seconds of arc change in
elevation due to weather changes in temperature, pressure, and humidity.
By the way, the radio wave refraction is computed as follows:
Let N=(n-1) x 10^6 where n = atmospheric refraction ~1.0003...
The Hopfield model for refraction is
N = 77.6 x (P/T) - 5.6 x (e/T) + 3.75 x 10^5 x (e/T^2)
where
P = atm pressure in millibars
T = atm temperature in Kelvin
e = water vapor pressure in millibars.
Typical
P = 1000 mb
T = 300 K
e = 20 mb
Giving
N = 341 or n = 1.000341 atmospheric refraction at the surface of
the earth.
The bending of light or radio waves can be described by the radius of
curvature of the ray. This means that we need to know the change of
the index of refraction with height above the earth. This is where
we need to worry about the first 10km of the earth's atmosphere. In
general the equation is:
R = 1/(dn/dz)
where R = radius of curvature and z = height above the earth and
dn/dz = the change of refraction with change of height.
Regards
Robert L. Kellogg
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