Astronomical Control of Solar Radiation Variations in Earth’s orbit occur at cycles ranging from ~20,000 to ~400,000 years and they cause cyclic variations in the amount of solar radiation received at the top of the atmosphere and by season. Astronomical Control of Solar Radiation • Axial tilt • Equinox • Solstice • Orbital Eccentricity • Perihelion • Aphelion • Precession of axial tilt • Precession of the equinoxes • Changes in insolation • Learning Objectives • Slow cyclic variations in Earth’s orbit and axial tilt due to gravitational interactions between Earth, Moon, and Sun cause slow changes in Earth-Sun distance and aspect which affects insolation. • The cyclic variations in insolation cause Earth’s temperature to vary in sync with the cycles. • The cycles have periods of 23,000, 41,000 100,000, and 413,000 years. At present Earth’s rotational axis tilts at 23.5 ° throughout its orbit Tilt of the axis causes Earth’s seasons as the north and south poles become closer and farther away during the planet’s orbit about the sun. Wednesday, September 22, 2021, at 2:20 P.M. CDT NASA photograph of sun with Earth inset for scale A solar eruption gracefully rose up from the sun on December 31, 2012, twisting and turning. Magnetic forces drove the flow of plasma, but without sufficient force to overcome the sun’s gravity much of the plasma fell back into the sun. Extremes of tilt If Earth’s orbit were circular and the axis had no tilt, solar radiation would not change and there would be no seasons (A). For 90° tilt, the poles would alternate between day-long darkness and day-long overhead sun. The Tilt of Earth’s axis cycles slowly between 22.2° and 24.5° with a period of 41,000 years. Both the period and amplitude are fairly regular, but the amplitude does vary by several tenths of a degree between cycles. This implies that succeeding cycles could have warmer or lesser insolation at the polar latitudes. Changes in tilt amplify or suppress the seasons, particularly at the poles. Precession of the tilt • Like a spinning top, Earth’s rotational axis not only tilts it also wobbles. • The wobble is called axial precession and is a slow turning of Earth’s axial rotation through a circular path. • https://www.youtube.com/watch?v=Mekf0oycidk The orbit is not a circle, but an ellipse. An ellipse has two foci. In Earth’s case, one focus is in the sun and the other is empty. The deviation from a circle is called eccentricity and is represented as 𝑎2 − 𝑏2 𝜀= 𝑎 The points at which the planet is farthest or closest to the sun are not at the solstices. Perihelion closest point Aphelion farthest point 1.496e8 km The eccentricity of Earth’s orbit varies over time with two different periods. One is 413,000 years and the other is 100,000 years. ε of 0.0365 derives from a = 1.497 x 108 km and b = 1.496 x 108 km (1.496 hundred million km). The difference is 100,000 km. For ε =0.06, the difference is 275,000 km. Eccentricity has varied over time between 0.005 and 0.0607. The current value of ε is 0.0167 so the orbit is nearly circular. 1.497e8 km 1.4972 − 1.4962 𝜀= 1.497 In addition to precession of the rotational axis, the ellipse also precesses so that the perihelion and aphelion shift slowly with a combined period of 23,000 years. Precession of the equinoxes and the ellipse combine for a 23,000 year cycle. If you ever considered a situation that would confound a calendar maker, this is it. Changes in eccentricity magnify or suppress contrasts in Earth-Sun distance around the 23,000-year precession cycle. The effect is variation of insolation, i.e. solar radiation intensity on earth. The combined effects of eccentricity and precession appear as cycles of 23,000 y, 100,000 y, and 413,000 y. Insolation at a particular latitude varies due to the tilt cycle of 41,000 years and due to the eccentricity cycle of 100,000 years. The precession cycles are dominant at low and middle latitudes. The tilt cycles are dominant at high latitudes. The maximum change is about 30 W m-2. Average insolation today is 1,364 W m-2 and the maximum variation in seasonal insolation is 2.2%. insolation Tilt causes in-phase changes for polar regions of both hemispheres in their respective summer and winter seasons Precession causes out-of-phase changes between hemispheres for their summer and winter seasons Precession causes the seasons to shift so that the summer caloric season changes on a 2000-year cycle. Caloric seasons? a) Lose 1 pound per week b) Gain 1 pound per week c) Atkins diet d) Keto diet e) My Fitness Pal f) None of the above Caloric insolation season? Summer: Insolation during 182 days exceeds insolation during the other 182 days of the year. Model of caloric insolation anomalies An anomaly is a measure of deviation from the normal or expected value. Large insolation anomalies at high latitudes are due to the tilt cycle. Anomalies at lower latitudes are more influenced by the precession cycles. Can we detect the cycles in the climatic records? • Combining the cycles makes them nearly impossible to detect visually. • We use several methods to separate the combined cycles. • Time series analysis – • Analyzing climate records vs. time to detect cycles. A power spectrum with three cycles Spectral analysis Essentially sliding sine waves with different periods over the power spectrum Filtering The time scale is logarithmic. The power scale is linear Always gather as much data as possible! Ruddiman’s guidelines: 1) The cycle must be repeated at least four times in the original record. 2) At least two points per cycle are needed. Example of aliasing by under sampling. Three scientists sampling the same 23 ky cycle but at different starting points. One at the high peak, one at the low peak, and one at the crossover point. They get three different results. Comparison of orbital cycles as control of insolation with oxygen isotope data as a proxy for ocean temperatures. Complex differences combine precession, tectonics, and uplift and weathering. This is not simple! Tectonic signals in precession and tilt. Due to tidal interactions between the Moon and Earth’s oceans as Earth spins, the Moon is slowly spiraling away at a rate of 3.82 cm per year. This causes Earth’s rotation to slow. We can project back into the past and see that the Moon was much closer to Earth and the rotation was much faster 1.5 Ga the length of an Earth day was 18 hours. We see this in fossil corals with seasonal growth patterns showing 400 days per year. Astronomical Control of Solar Radiation • Axial tilt • Equinox • Solstice • Orbital Eccentricity • Perihelion • Aphelion • Precession of axial tilt • Precession of the equinoxes • Changes in insolation • Learning Objectives • Slow cyclic variations in Earth’s orbit and axial tilt due to gravitational interactions between Earth, Moon, and Sun cause slow changes in Earth-Sun distance and aspect which affects insolation. • The cyclic variations in insolation cause Earth’s temperature to vary in sync with the cycles. • The cycles have periods of 23,000, 41,000 100,000, and 413,000 years. • Tilt cycles (41,000 y) affect insolation at the poles. • Precession cycles (23,000 & 100,000 y) affect overall insolation.

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