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Alex in blue (or whatever you have set for preferences, bill in green, same
deal.)

> That's what I am inclined to believe too.
> There was strong glare of the sea under the Sun.
> Having no horizon filter, I could misjudge what the real
> horizon was. Two observations using the shoreline seem
> to confirm this. But still, taking the shoreline
> instead of the horizon, I would expect an OVERSHOT rather than
> and UNDERSHOT.

There may be case based on irradiation(?).  Normally bright sun, darker sky,
darker water.  Hopefully it cancels out.  But you have no horizon shades, so
bright sun, bright water, darker sky is possible.  It might be very
interesting to try some upper-limb observations and compare them with lower
limb observations under the same conditions as you initial observations to
see if that makes a difference.  Also try some polarizing sun glasses to
reduce the glare off the water.

What shoreline/waterline?  Water sloshing about with less amplitude a
hundred meters away than a few miles away in unsheltered waters? Lets take a
case where your Ho (without dip adjustment) matches your Hc because wave
height on the horizon was the same distance above mean water level (calm
shoreline) as your height of eye; so dip is 0 in reality. If you subtracted
dip (in this case) based only on your height of eye above the mean water
level, your Ho would be less than your Hc.  A problem here is I don't know
whether you are subtracting Ho from Hc or vice versa.  Based on the
intercept convention, I am assuming you are getting a negative difference
(plot intercept away) so subtracting Hc from Ho. Put simply, If I understand
correctly, your Ho is consistently smaller than your Hc.

Imagine this:

First on the sea.  6' swells.  How do you measure on a small craft?  Wait
until the craft is at the top of a wave so you are at the same "level" as
the horizon.

But what if you are stuck on the shore, at mean water level?  You need to
account for wave height. I recall the post of member in a small craft in 60
foot swells.  The body actually set below the wave crest when he was in the
trough.  In this case he was below the mean water level so positive dip!

I am hardly learned enough to speak to terrestrial refraction anomalies.
Read through the Frank's beach shots from Indiana thread.  If the calculated
distance was too close, the observed angle was too large for the T15
equation; if the calculated distance was too far the angle observed was too
small. (If I recall Frank's and my calculations placed him too close. (In
all fairness, Frank was initially playing with the difference of building
heights, not equal distance from his position.)

Any calculations based on Bowditch T15 put Frank to close vs., GPS and
chart, so the angle he read from the horizon to top of the building was too
large (about 3' if I recall).  If Frank's measurements were on, something
else was wrong:

1.  The refraction index(s) used in the T15 calculations
    are off nominal values

2.  There was anomalous dip

Based on Frank's data he believes there was a thermal inversion that raised
the apparent height of the buildings relative to the horizon. (If I
understood correctly.)  As George pointed out, this could be a problem for
you as well.

I have failed to get a handle on this to my satisfaction, and I had asked
the list to play with new constants derived from the web-site Frank had
pointed out, as well as his constants. No feedback.  Hopefully George's
reference will shed some light.
>
 >> The upshot was that Frank was using the height of Chicago Buildings (and
>> there differences) to calculate distance. His calculations did not match
>> actual measurements.
>> Possible reasons included the refraction index(s) used
>> in Bowditch formulas and hefty anomalous dip (thermal inversions).
>
> He probably measured their height above the lake level.
> While actually they are not standing on the lake level,
> and I don't see how one can measure the actual height of
> the building from the ground level from a distance.

See Bowditch, Table 15 (in my on-line version).  Base below horizon.  Height
above water level of the top already known--established by building height
plus topo map of base height, minus lake water level above sea level. I did
factor this in. Then I used the the T15 formula (with their constants for
terrestrial refraction) to establish distance from the objects.  My problem
(and others) being it doesn't work all that accurately, and the Bowditch
constants do not seem to conform to those suggested by Frank or the web site
he pointed out in correspondence long ago.
>
>> "I've just received an offprint of a new article by Andrew T Young, of
>> the Astronomy Department, San Diego State University, "Understanding
>> Astronomical Refraction", which has recently appeared in the journal
>> "The Observatory"(Vol. 126, no. 1191, pp. 82-115, 2006 April.)"
>
> Have you seen the paper? Is it available on the web?

I have not.  I intend to follow up on George's lead.  Hopefully I will
receive hard copy.  At very least, with enough requests from the list
he/they will eventually make the paper available online.

Let me know if you try upper-limb vs. lower-limb observations, and how it
works out.

Bill

   

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