## 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 |
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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.

Produce a table of the Earth's orbital parameters for selected years -999999 and 999999 A.D. (Limited to 1001 values.)

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. |
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ORBPAR.FOR | For a range of Years, display a table of the Earth's orbital parameters. |

#### Contact

Please address questions about these AR5 webpages to Dr. Gary Russell.