One problem with the Gregorian calendar is that the years are not all the same length and this results in a wee bit of nonlinearity in the time scale. One can avoid this by using the Julian year as the unit of time.The figure below shows the formula used to determine the median time for the months and compares the angular frequency and function coefficients with the subscript G12 indicating the results using the Gregorian year and twelfths for the months and the subscript J indicating the results for the Julian year with decimal fractions. JD is a function that converts the Gregorian year, month, day and UT hour to the Julian Date which is used for astronomy.
The new time scale has a more noticeable effect on the coefficients for the functional form with the second harmonic and fitting the global monthly land temperature anomaly.
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