Dynamical Climatology

Gerrit Lohmann23. May 2005

• Milankovitch Theory of Ice Ages

Statistical Interpretation „upscaling“

Practical units

Anomalien und Spektren

Milankovitch Cycles

timeLea et al. 2000

Eccentricity

Precession of the axis of the earthYear:

Example for Milankovitch forcing

winter summer

insolation anomaly

The Eemian climate (the last interglacial, 124 000 years)

Jan–Feb-Mar-Apr-May-Jun-Jul-Aug-Sep-Oct-Nov-Dec

During the equinoxes, the axis of the Earth is not tilted toward or away from the sun and the circle of illumination cuts through the poles. This situation does not suggest that the 23.5° tilt of the Earth no longer exists.

During the summer solstice the Earth's North Pole is tilted 23.5° towards the sun relative to the circle of illumination. This phenomenon keeps all places above a latitude of 66.5° N in 24 hours of sunlight, while locations below a latitude of 66.5° S are in darkness. The North Pole is tilted 23.5° away from the sun relative to the circle of illumination during the winter solstice. On this date, all places above a latitude of 66.5° N are now in darkness, while locations below a latitude of 66.5° S receive 24 hours of daylight.

Hypotheses to explain the Ice Ages by insolation variations historically

• have drawn upon the independent work of astronomers. Formulas that allow the changing orbital shape and the axial precession of the planets to be calculated were originally published by planet Neptune discoverer (in 1846) Urbain Le Verrier (1843-1855).

• Beginning in 1864, James Croll used these formulas to graph the changes of Earth's orbital eccentricity for the past 3 million years. He found that cycles of high eccentricity follow upon each other for hundreds of thousands of years and then cycles of low eccentricity become the pattern as is the case today and calculably was so for the last 10,000 years. The present eccentricity is about 1%. The highest eccentricity for a time during the ice ages was 6%.

• But Croll realized the importance of calculating when during the year the heat arrived. When the winter season and Earth farthest from the sun coincide during an epoch of high orbital eccentricity, winter will be prolonged. A greater snow accumulation there will prolong its winter by increasing that hemisphere's albedo (reflectivity). This amplifying effect, James Croll claimed, triggered the growth of icesheets. At times of low eccentricity, such as exist today, winters are evidently not long and cold (snowy) enough to prolong or induce an ice age.

• Croll's hypothesis takes into account the precessional cycle of the equinoxes and variations in the shape of Earth's orbit. It predicts ice age triggered in the hemisphere that is near midwinter at apogee. At the same time, an icesheet will not exist in other hemisphere. This latter provided for a possible test. It has be shown that ice ages occur simultaneously in the two hemispheres.

Insolation theory developed by Milutin Milankovitch in the 1940s

finds by predicting the observed periodicity (but not the magnitude of the temperature variations).

• tilt of Earth's axis is a key player in what may trigger an ice age. If Earth's axis had no tilt, then the poles would always be in a winter (ice age) condition. The obliquity (tilt) of Earth's axis, that is 23° today, precesses with a maximum of 25° and minimum of 22°. In 1938, Milankovitch published graphs which showed radiation curves that he had calculated for summer-time insolation. These show, at 15° and 45° North latitude, the effect of the 22,000-year precession cycle (studied by Croll) is strongly apparent. The same effect does not show at 75° North latitude. There the 41,000-year tilt precession insolation (obliquity) cycle that could cause an ice age simultaneously in both hemispheres is dominant.

• Milankovitch had used for his astronomical calculations the mathematical solution for the behavior of the planets published by Ludwig Pilgrim, in 1904. The climatologist Wladimir Köppern collaborated in the 1920s and gave him a method for calculating the radiation at any given latitude and season.

Portrait of Milutin Milankovitch by Paja Jovanovic, 1943, courtesy of Vasko Milankovitch

Key elements of James Croll's Astronomical Theory Ice Ages  

1. Earth's climate was influenced by changes in its orbit around the sun    

2. Croll focused on changes in precession and eccentricity.     

3. He was aware of changes in the Earth's tilt but had no means of  quantifying it.    

4. He hypothesized that ice sheets would grow during severe winters resulting from the interacting effects of precession and eccentricity.    

5. To explain how very small changes in eccentricity could influence climate  he formulated the concept of a "climatic feedback", specifically the Ice-Albedo Feedback.

Key elements of Milankovitch's Astronomical Theory Ice Ages   

1. Quantified variations in the Earth's obliquity, precession and eccentricity.    

2. Determined the seasonal and latitudinal distribution of solar radiation (insolation) on Earth.   

3.  Argued that obliquity, followed by precession forcing, should dominate the  climate response, with less influence due to eccentricity.   

4. Argued that summer insolation at mid-latitudes rather than winter insolation was the critical forcing for ice sheet growth. 

Despite these considerable advances, Milankovitch's theory was not widely accepted in his day. It's major limitation was the lack of a well dated, continuous climate curve to test the hypothesis.

The modern rebirth of the Milankovitch Hypothesis

required several advances 

1. Continuous sedimentary sequences    

2. A reliable means of extracting continuous climate information from these  sediments    

3. Improved dating methods (chronology)    

4. Quantitative analysis methods

Frequencies

65 degrees north latitude from the present to 1 million years ago.

Spectral analysis: examine the frequency distribution of these oscillations over the last 6 million years. With this method one can see how the strength of the orbital frequencies varies over time.

0.024 = 41 ky

0.052 = 19 ky0.043 = 23 ky

Phase• The phase difference between

two paleoclimatic time series is used to interpret processes that link Milankovitch-cycle-driven insolation changes with Earth's climate (Imbrie et al., 1993).

• top figure: two time series have different amplitudes but are exactly in phase (Phase=0).

• middle diagram: two time series are exactly out of phase (Phase=180).

• Bottom: the general case where one time series leads or lags a second time series. The magnitude of the lead or lag is the phase angle and can be positive or negative.

Deglaciation

Earth Orbital Parameters:Obliquity

•

 • Obliquity refers to the tilt of the Earth's axis. Over time, the

angle of Earth's tilt varies between 22.2 and 24.5 degrees (currently the tilt is 23.5 and decreasing). These variations, discovered by French astronomer Urbain Leverrier in the 1840s, are caused by the gravitational pull of large planets, including Jupiter. Earth's obliquity varies cyclically with a period of 41,000 years.

• What is the effect of variations in obliquity? Changes in obliquity amplify or suppress the seasons. A larger tilt means that the summer hemisphere will receive more solar radiation, while the winter hemisphere will receive less.  

Eccentricity

• 100,000 year eccentricity of the orbit (ellipse) cycle which is actually the rough average of 95,000 and 123,000 year orbit cycles, and there are subsidiary oscillations at periods ranging from 50,000 to 1.9 million years due mostly to the gravitation perturbations due to Venus.

Earth Orbital Parameters:Precession

The cause of the precession is the equatorial bulge of the Earth, caused by the centrifugal force of the Earth's rotation. That rotation changes the Earth from a perfect sphere to a slightly flattened one, thicker across the equator. The attraction of the Moon and Sun on the bulge is then the "nudge" which makes the Earth precess.

Planets

 FORTRAN code based upon the Laskar solution is at  http://xml.gsfc.nasa.gov/archive/catalogs/6/6063/index_long.html

FUNKTIONSTHEORIE UND PHYSIK 1. EINLEITUNG: PHYSIKALISCHE MOTIVATION

The Keppler Equations

FUNKTIONSTHEORIE UND PHYSIK 1. EINLEITUNG: PHYSIKALISCHE MOTIVATION

FUNKTIONSTHEORIE UND PHYSIK 1. EINLEITUNG: PHYSIKALISCHE MOTIVATION

FUNKTIONSTHEORIE UND PHYSIK 1. EINLEITUNG: PHYSIKALISCHE MOTIVATION

FUNKTIONSTHEORIE UND PHYSIK 1. EINLEITUNG: PHYSIKALISCHE MOTIVATION

FUNKTIONSTHEORIE UND PHYSIK 1. EINLEITUNG: PHYSIKALISCHE MOTIVATION

upsc

http://www.inference.phy.cam.ac.uk/teaching/dynamics/tex/precession.pdf

Effect on climate

Rough locations of the Intertropical Convergence Zone (ITCZ), the Congo Air Boundary (CAB), and the southen margin of the Sahara Desert for the present-day, and for the monsoonal maximum.

Upscaling

Interpretation of Proxy Data

Proxy Data

• Aunnual, seasonal, etc.

• 18-O, etc.

Statistic

Covariance (cross, auto)

x (t) x ) ( y (t + ) – y )) e.g. coral e.g. meteorol. data

Correlation (cross, auto)

xy =

measures the tendency of x (t) and y (t) to covary

normalized

Spectrum (cross, auto)

(spectral density)

e-2i

measures variance

8

8

Practical units

• Analysis of spatio-temopral pattern

• Upscaling system

• Open mozilla

• kiste.plamod.uni-bremen.de

• Time series (choose one, calculate one)

• Write a report (2-4 pages)

Wanderung des Himmelspols

The Keppler Equations

1) FORTRAN code based upon the Laskar solution is at  • http://xml.gsfc.nasa.gov/archive/catalogs/6/6063/

index_long.html• Calculate insolation at 65N, 30N, summer, winter

2) Explain why periods of glacial advance in the higher latitudes tend

to occur with warmer winters and cooler summers.

3) Are ice ages in the Northern Hemipshere more likely when:• a. the tilt of the earth is at a maximum or a minimum?• b. the sun is closest to the earth during summer in the Northern

Hemisphere, or during winter?• Explain your reasoning for both (a) and (b).

Practicals:

Practicals cont.• http://apollo.lsc.vsc.edu/classes/met130/notes/chapter18/precession.html

• http://apollo.lsc.vsc.edu/classes/met130/notes/chapter18/tilt.html