Simulating Milankovitch Cycles Derek Fox Client: Prof. Hollocher - geology dept. Advisor: Prof. Hemmendinger

What’s with the name? Named after the Serbian mathematician Milutin Milankovitch who first computed the cycles Lived from

Milankovitch Cycles – What are They? Consist of three astronomical cycles of the earth: 1.Eccentricity of Earth’s orbit 2.Axial tilt of the earth (Obliquity) 3.Precession of the equinoxes

Eccentricity Eccentricity is the amount of which an orbit is elliptical rather than circular Earth’s eccentricity is currently very slight Varies between.01 and.07 eccentricity Changes over a period of a period of approximately 100,000 years

Obliquity – Change in Axial Tilt Current axis is 23.5° Varies between 22.1° and 24.5° Changes over a period of 40,000 years Greater tilt = more severe seasons Lesser Tilt = milder seasons Looks like a small variation but can have a great effect on seasons

Precession of Equinoxes The Earth slowly wobbles as it spins on axis (like a top before it falls) Changes over a period of 23,000 years

Milankovitch Cycles – How Does it Affect Climate? They determine the amount of solar insolation that reaches the latitudes of the Earth at a given time of year Insolation = Solar radiation that strikes the Earth (W/m^2) The cycles have been correlated to the advance and retreat of glaciers during ice ages

Scientific Verification of Milankovitch Cylces Verified in 1976 study after examination deep-sea sediment cores Able to extract the record of temperature change going back 450,000 years Ice ages had occurred when the Earth was going through different stages of orbital variation.

Program Requirements Implement Milankovitch mathematics to visually simulate how solar insolation varies as the three cycles change –Have graphs that show the insolation change for specific latitudes over time –Have a model of the earth showing the insolation change at all latitudes Make it usable by Geology students in intro classes

Program Design Use Java- swing for the graphical user interface –Java is compatible across multiple platforms –Swing provides convenient graphics Get the applet onto the web for easy access

Graphical Interface User Inputs Latitude Duration Month Step Size Inclination Eccentricity Precession

Coloring the Earth The earth on the previous slide is really a many-sided polygon instead of an oval. Why? Easier to color by breaking the polygon into smaller, 4- sided polygons. I used 180 smaller polygons each corresponding to a degree of latitude. Example using a decagon If the polygons are small enough, the result is a smooth color transition

Class Diagram Milankovitch- the main applet class which builds the GUI and GetPoints- calculates the points on the Polygon. Polys- Breaks down the polygon into the smaller polygons for coloring Polygon1- Extension of the Java Polygon class to hold insolation and color values for each polygon Values- works with the Milankovitch equations to determine the insolation.

Using Threads Problem: Initially, when I tried to animate the graphing and color changes, Java would only update the display after the simulation was complete, only showing the final state Putting the custom painted swing objects in a separate thread solved this. Also fixed the problem where the simulation couldn’t be stopped once it had started.

Coloring Issues It was somewhat difficult to get smooth color transition from low insolation amounts to high insolation amounts. I used a java applet that let me specify the hue, saturation and brightness and it gave me the proper R,G,B value. The color range I chose Low insolationHigh insolation

The Mathematics Equations were derived by Andre Berger in the 1970s Three different Equations are used –One for the latitudes where there is a sunrise and sunset –Another for when there is no sunset (Arctic summer) –A third for when there is no sunrise (Arctic winter) I didn’t realize this until I saw that my program didn’t work for latitudes in the Arctic/Antarctic circle.

Conclusion I accomplished what I set out to do and incorporated the features requested. The program should be useable by students learning about Milankovitch cycles in Geology. Currently on the web at: