What is climate? Temperature, precipitation. Good/bad climate. Factors affecting climate: latitude, altitude, continental, maritime, orography,

Components of a climate system

Solarsphere

1)  Stellar life cycle

a)  Hertzprung Russell diagram, main sequence star, gravitational collapse. VG1

b)  Stellar furnace, nuclear fusion. Luminosity (Energy radiated/s), L = 4 π r2 σT4, H → He (Hans Bethe, 1939) → stellar density increases. As a new balance is struck between radiation pressure and the increasing gravitational pressure, the temperature of the sun increases, so also does L.

c)  Thus M increasing → T increases → L increases → L(t) = L(to)/[1 + 0.4(1-t/to)] → L(0) = L(to)/1.4 = 0.7 * L(to), to = current age of sun = 4.6 Ga.

2)  Blackbody radiation - 3.2

a)  Radiation – Maxwell’s equations in free space lead to wave equation, del2 E – 1/c2 ∂2E/∂t2 = 0

b)  → E&M radiation is a wave → f(υ, λ, and wave number = 2π/λ)

c)  Planck’s law (1900) for BB radiation, B(υ,T)=2hυ3/c2 [1/(ehυ/kT-1)] (power/m2 s), or B(λ,T) = -8πhc/λ5 1/[ehc/(λkT) -1]. Derivation requires assuming E=hυ → light is quantized. Beginning of quantum mechanics

d)  Stefan Boltzmann law ∫0∞ (B(υ,T) ) dυ = σ T4, σ = 2 π4 k4 / (15 c2 h3) = 5.67 e-8 W / (m2 K4)

e)  Wien’s displacement law – λmax = hc/(kT 4.965) = 2901(µm K) /T

f)  Sun as a blackbody. To understand the radiation from sun need size and T. How to measure T?

3)  Radiative equilibrium – 1.3, 1.4, 3.3

a)  Luminosity ≡ energy radiated/s, L = 4πr2 σT4

b)  Energy balance for a planet with radius rp, distance from sun, r, and albedo, α.

c)  4πrp2 σTp4 = 4πrs2 σTs4 • πrp2/(4πrsp2) • (1-α) = σTs4 (rs/rsp)2 • πrp2 • (1-α)

d)  Solar characteristics. Measures of solar output. Sunspots. – VG2-4

e)  Solar constant, Lo= σTs4 (rs/rsp)2 and so σTp4 = Lo • (1-α)/4, or

f)  Tp = √(rs/2r) • Ts • (1-α)1/4

g)  Tp significantly cooler than Ts, and λmaxp > λmaxs

h)  Questions:

  1. Temperature of sun, earth, mars, venus now, and 3.5 Ga ago

4)  Orbital mechanics - 7.3, 7.5, 7.6. (Croll, Milankovitch) – Ice ages first proposed Aggassiz (Swiss) in 1840, to wide disdain. But the evidence was too great. 1846 to Harvard and started Cornell, NAS and AAAS. Implications for biology and the reasons behind ice ages left to others. James Croll, poor Scot, many professions, 1859 finally caretaker Anderson college, 1861 first scientific paper appears. 1864 finally settled on carrying out the calculations to see if astronomical variations could change the temp enuf to cause ice ages. End of 1800s after much success fell into disfavor – the alternating hemispheric glaciation could not be found in the evidence. Further work had to wait to the 1900s, Milutin Milankovitch searching for a problem to be tackled mathematically came upon Croll’s theories and decided to redo the calculations and theories more carefully. 1913 first paper published. Still widely discussed, but questions persist.

a)  Obliquity (tilt) – 41 ka, Earth varies from 22.1-24.5º. Today 23.4º.

  1. importance of the moon (pH 1.3) in stabilizing obliquity. Moon formed 4.5 Ga. Theories proposed, fission, capture, co-formation (can’t explain lead deficit on moon). Thus most likely is impact with the moon. Moon gravitationally locked to earth.
  2. Solar constant as a function of latitude, φ, = Lo cos(φ)/π, for tilt=0 → φ=sza
  3. Cos(sza) = cos(φ) cos(δ) cos(h) + sin(φ) sin(δ), h=hour angle (0 at noon), δ = latitude where sza=0 (sun overhead) aka solar declination. δ ranges from ± the obliquity. To obtain solar constant over a diurnal period need Lo f(φ,δ) = 1/(2π) ∫-htht cos(sza) dh = 1/π[cos(φ) cos(δ) sin(ht) + sin(φ) sin(δ) ht]. ht = terminator. Fig. 7.6
  4. Compare tilt of Earth and Mars. Fig 7.16

b)  Precession - 26 ka – precession angle = 0, when NH summer occurs at periastron≡distance of closest approach. Current precession ≈ 180º → Earth at rp in NH winter.

c)  Eccentricity – 100 ka, perihelion, perisatron =a(1-e), aphelion (apastron≡furthest distance=a(1+e)), e(Earth,Mars) = (0.017, 0.093).

  1. In polar coordinates, r = a(1-e2) / (1+e • cos(κ)), a=(rp + rap)/2, κ≡angle between star and planet. κ=0 at periastron.
  2. Distance seasons, synchronous between hemispheres.
  3. Then for Io = solar output, Lo(r) = Io/(4 π r2), then Lo(rap)/ Lo(rp) = (rp/rap)2 = (1-e)2/(1+e)2 = 6.6% for Earth, 31% Mars. For Earth this is a difference of ≈ 90 W/m2
  4. Keppler’s equal area law → planet moves slower at rap than at rp
  5. Mean solar insolation however varies little from a circular orbit by < 1% for e =0.1 > e for earth and Mars. → eccentricity has to be coupled with obliquity seasons to have an impact. Fig. 7.12
  1. Of these 100 ka shows up most in the climate record, yet precession “should” have the bigger impact. Picture clouded by thermal inertia from oceans. The answer as to the importance of the Milankovitch cycles not firmly resolved for Earth. Clearer pictures may be available for Mars, but our climate records on Mars are extremely limited.

Pierrehumbert, R. T., Principles of Planetary Climate, 2011, 3.2, 1.3-1.4, 3.3, 7.3, 7.5, 7.6

Liu, N. S. K., An Introduction to Atmospheric Radiation, 2nd Edition, 2002

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Lecture notes, Terry Deshler, University of Wyoming Page 3 9/11/2013