The apparent altitude of Sun is affected by the atmospheric refraction which makes the objects appear higher above horizon than they would if there should be no atmosphere. The amount of refraction depends on the local atmospheric temperature and air pressure, thus an exact value of refraction cannot be predicted.
A study was made to compare the values
as calculated on my Excel spreadsheet and the sunrise and sunset data published
by Ursa, the Finnish Astronomical Society. The average of the daylength deviations
for the latitude of 60 degrees can be adjusted to zero thru increasing the
refraction angle from the original 34 minutes to 38.8 minutes. With this
set the deviations are in the worst case +-86 seconds as shown on the graph
below.
The most positive
deviations (the calculated daylength is longer than the right one) are found
to appear at the aphelion on July 4th while the distance of Earth to Sun
is at maximum. However, the deviation is rapidly going down to the negative
side (the calculated daylength is shorter than the right one).
A similar study on the deviations at
the latitude 65 degrees has shown essentially higher deviations for some
short periods. However, on the most days of the year is a satisfactory accuracy
shown.
In this case,
the refraction angle was adjusted again to 35.8 minutes to give a zero average
of the daylength deviations. The latitude 65 ° is rather near to the Arctic
circle at 66.5 ° which will explain the greater deviations. It may be seen
that the extreme deviations on the latitude 65 ° are found on different dates
than on the latitude 60°. The most positive deviation is appearing on June
6th already, about four weeks before day of aphelion. In contrary to the
deviations on latitude 60°, the most negative deviation is found just during
the aphelion.
The last update on 17th February, 2005