Orbital Parameters
Preserving info from NASA GISS in the hope it serves others as well as it has served (and saved) me. This is going to be a messy copy/paste but the gist of things ought to be preserved. Note these values are what are used for arguments to ECHAM5 (and possibly ECHAM6). ORBPAR.FOR can be compiled via gfortran (tested with gcc version 6.3.1 20161221 (Red Hat 6.3.1-1) (GCC)).ModelE AR5 Simulations: Past Climate Change and Future Climate Predictions
Determination of the Earth's Orbital Parameters
The Earth's orbital parameters are:
Eccentricity of the Earth's elliptical orbit about the Sun
Obliquity = dihedral angle between Earth's equatorial plane and Earth's orbital plane
Longitude of Perihelion = spatial angle from moving vernal equinox to perihelion with Sun as angle vertex
Orbital parameters used in climate models are based on the work of Andre L. Berger. We cite two references to his work:
Berger, A.L. 1978: Long-term variations of daily insolation and Quaternary climatic changes. Journal of the Atmospheric Sciences, 35, 2362-2367, doi:10.1175/1520-0469(1978)035<2362:LTVODI>2.0.CO;2.
Berger, A.L.,1978: A Simple Algorithm to Compute Long-Term Variations of Daily or Monthly Insolation. Institut d'Astronomie et de Geophysique, Universite Catholique de Louvain, Louvain-la-Neuve, No. 18.
Berger's orbital parameters are considered to be valid for approximately 1 million years.
More recent calculations and other methods of calculating the Earth's orbital parameters are discussed in:
Berger, A.L., and M.F. Loutre, 1992: Astronomical solutions for paleoclimate studies over the last 3 million years. Earth and Planetary Science Letters, 111, 369-382, doi:10.1016/0012-821X(92)90190-7
Discussion by Allison and McEwen that concentrated on Mars' insolation is also relevant for insolation on Earth. The reference is:
Allison, M., and M. McEwen, 2000: A post-Pathfinder evaluation of aerocentric solar coordinates with improved timing recipes for Mars seasonal/diurnal climate studies. Planetary and Space Science, 48, 215-235, doi:10.1016/S0032-0633(99)00092-6.
The following Fortran programs are used to calculate the orbital parameters of the Earth:
ORBPAR.SUB Calculates the three orbital parameters as a function of year. The values are based on Andre Berger's 1978 solution.
ORBPAR.FOR For a range of Years, display a table of the Earth's orbital parameters.