A Paleoclimate Model of Ice-Albedo Feedback Forced by Variations in Earth's Orbit

For millions of years, glaciers have been a permanent feature on Earth’s surface. The climate has cycled through relatively warm periods, such as we are experiencing now with glaciers confined mostly to Antarctica and Greenland, to relatively cold periods with vast ice sheets extending over the continents. The Sun provides the energy powering the Earth’s weather and climate. The incoming solar radiation, or insolation, varies over several time scales. Changes in Earth’s orbit and rotation axis, called Milankovitch cycles, cause variations in the insolation at time scales comparable to the glacial cycles. These cycles contain three components: (1) the eccentricity of the Earth’s elliptical orbit around the Sun, (2) the tilt, or obliquity, of the Earth’s axis of rotation, and (3) the precession of the Earth’s rotation axis. These components will be discussed in detail below. Many studies, dating back to the mid nineteenth century, have shown that the Milankovitch cycles affect the Earth’s climate [7]. In a seminal paper, Hays, Imbrie, and Shackleton [2] firmly established that the Milankovitch cycles contribute substantially to the glacial cycles. Since the incoming radiation is a fairly complicated function of both time and space, it is often convenient to reduce it to a single quantity. A quantity traditionally used is the daily average insolation at a particular latitude on a particular day, typically at 65◦ north on the summer solstice [7, 11], a quantity we will denote by Q65. This quantity changes slightly from year to ∗School of Mathematics, University of Minnesota †Department of Ecology, Evolution and Behaviour, University of Minnesota