Astronomical Control of Solar Radiation Chapter 7 Astronomical Control of Solar Radiation By: Jessica Juday, Lyudmila Koba, Luke Mros, Grant Prehn and Vincent Xu

Earth’s Tilted Axis of Rotation and the Seasons Earth spins on its axis Makes 1 complete revolution every 24hrs Earth’s axis is tilted at 23.5° Earth’s tilt referred to as it’s “obliquity”

Earths Rotation Around the Sun 1 revolution around the Sun = 365 days Earth’s tilt combined with solar orbit gives us seasons Seasons accumulate at Solstices Summer Solstice - longest day Winter Solstice - shortest day Northern Hemisphere: Summer Solstice Jun 21st Winter Solstice Dec 21st Southern Hemisphere: Summer Solstice Dec 21st Winter Solstice Jun 21st (reverse from that of the north)

Earths Tilt and it’s Direction Are Constant Throughout Orbit Reason why we have regular seasons Earths tilt defines the Arctic Circles at 66.5° During Winter Solstice, no direct sunlight reaches poleward of this latitude

At Winter Solstice, no direct sunlight reaches past this point

Equinoxes Equinoxes occur midway between solstices. Direction of Earth’s tilt not pointing towards/away from the sun. Days/Nights become equal in length

Earths Eccentric Orbit Earths orbit is “Elliptical” Orbital eccentricity is due to gravitational pull on Earth from other planets Earth’s distance from the Sun varies due to position in elliptical orbit Close pass: “Perihelion” Distant pass: “Aphelion”

Close pass: “Perihelion” Distant pass: “Aphelion” 146 million km Jan 3rd Distant pass: “Aphelion” 152 million km Jul 4th 7 days longer between equinoxes 3% variation in distance Slight changes in radiation received Small effect on seasons

Long-Term Changes in Earth’s Orbit Orbit varies due to gravitational attractions between Earth and other Celestial bodies Causes variation in Earth’s angle of tilt, eccentricity of orbit and positions of solstices/equinoxes in the orbit These variations are Cyclical…

Cycles and Modulation… Changes like Earth’s orbit and amount of radiation received occur in cycles. We express these cycles as “Wavelengths”

Period Frequency Amplitude A wavelength expressed in units of time # of cycles that occur in 1 Earth year Amplitude Measure of deviation from long-term average

Modulation Amplitude of peaks and valleys change in a cyclic way Modulation of a cycle is not in itself a cycle!

Extremes of Tilt If the Earth had a circular orbit with no tilt to the axis, we would have no seasons for there would be no change in solar radiation. No Tilt

Extremes of Tilt Alternately, if Earth’s axis had a tilt of 90 degrees, the poles would alternate between day-long darkness, and day-long direct overhead sunshine. Equator 90 degree tilt

Decreasing Tilts Decreased axis tilt diminishes the difference in seasons and brings it closer to that of the example below.

Effects on Polar Regions Increased tilt of the axis results in more solar radiation at the summer season poles, and less to the winter season poles.

a and b = ½ the lengths of major and minor The Shape of an Ellipse This can be described by reference to the major (longer) and minor (shorter) axis. The degree of departure from a circular orbit can be described by this equation. E = Eccentricity a and b = ½ the lengths of major and minor

The eccentricity of an ellipse is related to half of the lengths of it’s longer and shorter axes

Changes in Earth’s Orbit Through Time The earth’s orbit used to be more elliptical or “eccentric” than it is today. There is orbital variation at periods of 413,000 years, and 100,000 years.

Eccentricity Cycles The longer cycle of 413,000 is not as noticeable because it appears in between the 100,000 year cycles between large and small peaks. Larger amplitudes appear at 200,000 yrs, 600,000 yrs, and 1,000,000 yrs. A third cycle happens at 2.1 million years, but it is weak in amplitude.

Precession What is it? -The motion of the axis of a spinning body, such as the wobble of a spinning top,when an external force acting on the axis.

Earths Three Forms of Precession Precession of the Axis Precession of the Ellipse Precession of the Solstices and the Equinoxes

1. Precession of the Earths Axis -One rotation every 25,000 years -Caused by the gravitational pull on the earth's equatorial bulge

-Causes the Celestial northern star to vary -Bright star at the bottom is the star Vega

Axial Precession Cycle

2. Precession of the Ellipse - The ellipse of the earth’s orbit also has a precession -Rate of precession is even slower than that of the axial precession ~22,000 years http://www.youtube.com/watch?v=82p-DYgGFjI&list=PL1Iewcbx3MoVFpQmNOgSy1cu8LeNZUegN

3. Precession of the Equinoxes - The point where the equinoxes and solstices occur has a precession of it’s own. Why is it important? -the point at which the solstices and equinoxes occur determines the intensity of the seasons What is it caused by? -the combination of the precession of the axis and the ellipse.

One full rotation take between 19-23 Thousand years What does it look like? One full rotation take between 19-23 Thousand years

Insolation Changes by Month and Season Long-term changes in tilt Long-term changes in precession

June and December insolation variations Precession at low and middle latitudes effects of tilt evident only at higher latitudes

Phasing of insolation maxima and minima Difference between North Pole and South Pole

Insolation Changes by Caloric Seasons Family of monthly precession curves Caloric insolation seasons

Caloric season insolation anomalies

Complication from overlapping cycles Searching for Orbital-scale Changes in Climatic Records

Time Series Analysis Power Spectrum Time Series Analysis A method used to analyze climate record data, in hopes to extract rhythmic cycles. References patterns against a time component. Spectral Analysis Referencing sine waves with climate data to measure their correlation. A strong correlation indicates a strong cycle. Power Spectrum the result of a spectrum analysis Used to show data. prone to interference from equipment and climate irregularities. Filtering A method of honing in on a specific set of data to better analyze it without referencing other data.

Effects of Undersampling Climate Records Time series analysis requires multiple cycle sightings to be accurate (>4). Aliasing False trends found by way of undersampling. Combated with frequent readings and large sample sizes. False trends tend to only measure part of natural cycles. This causes skewed results.

Tectonic-Scale Changes in Earth’s Orbit Earth’s characteristics are not set in stone and are prone to change over time. Coral studies from 440 million years ago. 11% more tidal cycles per year. Earth spun 11% more on its rotational axis. Not everything in earth is a cycle we can see.