Dan,
Now I have finished my calculations.
The first table below shows the latitude that gives the minimum total
error evaluated over the whole the year, where error is assessed as the
square of the difference between true day length and day length given in
your calendar (in other words, I'm using a Least Squares fitting
method). There are three rows of results, for each possible definition
of sunset. There are two columns of results, for the two ways that day
length can be obtained from the calendar - sunset minus sunrise; stated
day length.
The second table shows the same combinations of options. The latitude is
again chosen for the smallest error, but for this table the result is
assessed using the smallest individual error for any day of the year
(that is, the minimum absolute value of 365 daily values).
I did my calculations using the "Solver" goal-seeking add-on for Excel.
For the first table it used non-linear regression. For the second table
it used an evolutionary algorithm.
I haven't looked at the reliability of the sunrise and sunset times
(except to use the difference to get day length).
My overall conclusions: you're right - it's not possible to extract the
latitude from the data (the result varies significantly depending on the
evaluation method and assumptions used); as well, the calendar isn't
very reliable (whichever way I did the calculation, I found that that
day length errors of a least 1.2 hours occurred at some point in the
year, compared to the true values [not considering twilight as day time]).
Steve
Best Latitude: By Minimizing the Sum of Squares of Daily Errors
Estimated Latitude Using Stated Sunset minus Stated Sunrise Using
Stated Day Length
Sun sets when centre is on the true horizon 0.00 47.045 44.888
Sun sets as upper cusp dips below horizon -0.26 46.958 44.794
Sun sets as upper cusp dips, with allowance for refraction -0.83
46.708 44.532
Best Latitude: By Making the Worst Error As Small As Possible
Estimated Latitude Using Stated Sunset minus Stated Sunrise Using
Stated Day Length
Sun sets when centre is on the true horizon 0.00 45.320 47.043
Sun sets as upper cusp dips below horizon -0.26 45.327 47.050
Sun sets as upper cusp dips, with allowance for refraction -0.83
45.336 46.468
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