A 3D Earth orbit model; visualization and analysis of Milankovitch cycles and insolation

An astronomically precise and accurate Earth orbit graphical model, Earth orbit v2.0, is presented. The model offers 3D visualizations of Earth's orbital geometry, Milankovitch parameters and the ensuing insolation forcings. Prevalent paleoclimatic theories invoke Milankovitch cycles as a major forcing mechanism capable of shifting Earth's climate regimes on time scales of tens to hundreds of thousands of years. Variability of eccentricity (ellipticity of orbit), precession (longitude of perihelion) and obliquity (Earth's axial tilt) changes parameters such as amplitude of seasonal insolation, timing of seasons with respect to perihelion, and total annual insolation. Hays et al. (1976) demonstrated a strong link between Milankovitch cycles and paleoclimatological records, which has been confirmed and expanded many times since (e.g. Berger et al., 1994; Berger et al., 2010). The complex interplay of several orbital parameters on various time scales makes assessment and visualization of Earth's orbit and spatio-temporal insolation variability challenging. It is difficult to appreciate the pivotal importance of Kepler's laws of planetary motion in controlling the effects of Milankovitch cycles on insolation patterns on various spatio-temporal scales. These factors also make Milankovitch theory difficult to teach effectively. The model allows substantial user control in a robust, yet intuitive and user-friendly graphical user interface (GUI) developed in Matlab. We present the user with a choice between Berger et al. (1978) and Laskar et al. (2004) astronomical solutions for eccentricity, obliquity and precession. Berger solutions span from -1 Myr to +1 Myr, while Laskar provides solutions from -101 Myr to +21 Myr since J2000. Users can also choose a "demo" mode which allows the three Milankovitch parameters to be varied independently of each other, so the user can isolate the effects of each on orbital geometry and insolation. For example, extreme eccentricity can be chosen, which is useful for illustrating Kepler's laws, and precession can be varied to illustrate its effect on the timing of the seasons. Earth's orbit is plotted in 3D with the chosen real (past, present or future) or demo Milankovitch parameters. Earth is placed in its orbit using Kepler's Laws and the calendar can be started on either vernal equinox (March 20) or perihelion (Jan. 3). The Sun, perihelion, and the equinoxes and solstices are displayed in a plot that can be zoomed, panned and rotated in three dimensions. The model can also output time-series plots at varying scales from Berger and Laskar's solutions. Coupled with the orbit plotting and time-series functionality, global insolation is computed as a function of latitude and day of year, using the chosen Milankovitch parameters. 3D surface plots of insolation and insolation anomalies (compared to J2000) are then produced. Insolation computations use the model's own orbital geometry with no additional a-priori input other than the Milankovitch parameter solutions. Insolation computations are successfully validated against Laskar et al. (2004). Envisioned future developments include more options for insolation plots on user-chosen spatio-temporal scales and overlaying various paleoclimatological proxy data.