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Reproduce actual refraction measurements

• Astronomical refraction
  The refraction is determined for a light path from the eyes' position to the end of the Earth's atmosphere (in direction of a celestial object).
  
• Levelling refraction
  The refraction is determined for a light path that has a large part level with the Earth's geoid, aka towards/from a vast level surface below the eyes' position. Also known as dip.
  
• Terrestrial refraction
  The refraction is determined for a light path that goes from the eyes' position to a terrestrial object higher or lower than the eyes' position.

Astronomical (involving leveling/terrestrial) refraction

• Schaefer&Liller (1990)
  Date, time, locations, temperature, air pressure, RH, wind speed, wind direction and green flashes. Some data has been rectified/updated (Schaefer, pers. comm, 2006). The sea temperatures (a proxy to determine the temperature gradient) are derived through for instance this link. This will involve the sea as vast level surface: so levelling refraction is involved.
  
• Sampson (1994)
  Date, time, locations, temperature, temperature gradient, air pressure, RH, wind force, wind direction, cloud cover, cloud height and mirages/green flashes. This data is transcribed from Sampson's observation log book (Sampson, pers. comm. 2007) and MSc thesis (Sampson, 1994). This involves hills around Edmonton, Canada: so terrestrial (with perhaps some levelling) refraction is involved. The temperature gradient was taken from a balloon soundings at 0:00UT or 11.00 UTC (aka 16:00  or 04:00 MST), so not that close to Sunset/rise, considering the dynamics of the day.
  This is compared to HOSI_VR with the following date: Sampson's observer: date, time, location, temperature, pressure, calculated astronomical refraction; at weather station: temperature gradient; and using ARCHAEOCOSMO/Swiss Ephemeris: topocentric altitude of Sun.

Some conclusions around Schaefer&Liller's astronomical refraction

<to be worked on>

Some conclusions around Sampson's astronomical refraction

• Here is an overview of the astronomical refraction calculated by Sampson and by HOSI_VR:
  
  

• It looks that HOSI_VR calculates systematically a lower astronomical refraction than Sampson.
  
• The Temperature gradient looks to be quite larger on average +0.037K/m, this normally happens on clear nights but not that many times at Sun rise (which would be closer to D). So the question is: can the provided balloon sounding data be used for this Sun rise evaluation?
• If the temperature gradient was higher than around +0.12K/m, HOSI_VR is not able to calculate the refraction (brown crosses, in 3% of the events):
  
  The main reason is because the light ray radius is smaller than the Earth's and thus no visibility of the sky (but a Fata Morgana).
  

General observations on astronomical refraction

<to be worked on>

Levelling refraction

Terrestrial refraction

Sampson

As part of Sampson astronomical refraction measurements, he also performed theodolite survey of the horizon (Sampson, 1994, 2003).
The following issues can be found around his measurements:

• These measurements are at the middle of the afternoon on clear summer or autumn days and noted at observer: location, temperature, pressure, measured apparent altitude; and at weather station: temperature gradient.
  According to Sampson (2003, 1258): "The  horizon altitude measurements were made during the middle of the day when terrestrial refraction was assumed to be minimized as a result of boundary layer mixing (Bomford,1980)". Indeed these moments are expected to have the lowest temperature gradient (due to solar insolation), but this is a quiet different situation then at Sunset/rise. For the terrestrial refraction evaluation of the survey data only this fact is though not important.
  
• The temperature gradient was taken from a balloon soundings at 0:00UT (aka 16:00 MST), so that is close enough to middle of afternoon, considering the dynamics of the day.
• The survey data compared to calculated HOSI_VR with the following date: Sampson's observer: location, temperature, pressure, measured apparent altitude; at weather station: temperature gradient; and using HeyWhatsThat (which uses a constant temperature constant): distant height and distance.
• For many cases in the direction of Sunset (~85%) and several of Sunrise (~30%), the terrestrial path between the targets that have almost a zero apparent altitude that can't be determined. My present iterative terrestrial refraction function is not yet able to determine if levelling is also involved. As levelling is happening here, the terrestrial refraction function is being reworked (aka incorporating levelling refraction).
  In the meantime all Sun set observations were not included in the evaluation.
  

Some conclusions around Sampson's terrestrial refraction

Thom

• In some cases (~13%), Thom observed terrestrial targets (HI and Pl which are very close to the sea) which are below the Eye height. In that case the temperature gradient measured (an LABL environment) by Thom if of no use, as the light rays don't pass the atmosphere where the temperature gradient sensors are (which are at 0.75 and 7.5m near the Eye location). For example: an average December sea temperature around Arran Island of around 10C is used to determine the temperature gradient (aka MABL and not a LABL environment). Thom did not include these two targets in his evaluation, most likely because if this ABL difference.
  If this MABL is used, no solution is found using the ray tracing (reason yet unknown. If you have ideas, let me know), so for the present evaluation the LABL has been used.
  As mentioned on this archaeocosmology web site: people need to determine the temperature gradient not only at eye height, but they need to try to record the temperature profile along the ray path (RPTP).
• For some instances (~9%), Thom measured temperature gradients higher than +0.11K/m. In these cases one is not able to calculate the ray tracing integral (because the ray radius is smaller than the Earth's radius). It would be interesting to understand what Thom would have seen through his theodolite. If a Fata Morgana (aka superior mirage), then it would have been expected that Thom would have observed and noted such distortions!
  To include in the evaluation: the temperature gradient has been capped to +0.11K/m if it was higher.
  Mitigating circumstances could have been present, to make explain why Thom could observe the targets without distinguishable/note-worthy distortions:
  
1. his temperature gradient measurements and/or my evaluation of them, are wrong.
   In some cases the first could be true as the distant object was below eye height, see earlier bullet.
   
2. the atmosphere is not spherical symmetrical
   This sounds logical in a hilly environment which changes the meteorological  circumstances (such a down winds) and thus tampering with spherical symmetry,
   
3. Any other ideas (let me know)?
   
• For some cases (~4%), the terrestrial path between the targets that have almost a zero apparent altitude that can't be determined (-0.06deg; The Hill at 149m and AC at 340m, distance 62km). My present iterative terrestrial refraction function is not yet able to determine if levelling is also involved. As levelling is happening here, the terrestrial refraction function is being reworked (aka incorporating levelling refraction).
  In the meantime these observations were not included in the evaluation.
  
• There is one case (~1%, Pl) where Thom's temperature gradient is too low (+0.019K/m at Eye height) to determine a valid ray trace integral. If it is increased to +0.05K/m a result is gotten.
  This could be because the target is near the sea and below eye height, so using the measured temperature gradient at Eye height is no use. But this does not explain the result of ray tracing.
  To include in the evaluation: the temperature gradient has been set at +0.05K/m.
  Still strange that a +0.019K/m in principle does not work for this case. Any ideas, let me know?

Some conclusions and Thom's terrestrial refraction

General observations on terrestrial refraction

References

Acknowledgements

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