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CE 401Climate Change Science and Engineering
solar input, mean energy budget, orbital variations, radiative forcing
17-19 January 2012
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any questions from last time?
we did the entire science section of 401 in a flash
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homework 3 [Stefan-Boltzmann] on website: due Tuesday 24 January 2012• read MacKay Chapter 2• do some computations
HW 2 [Mauna Loa data] due on Thursday, 19 January = next class period
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what causes natural variations in the climate system
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natural variations in Earth energy balance are caused by (at least):
• changes in the radiation balance of the Earth-Sun system• intrinsic changes in solar flux
• long term - must be modeled using sunspot numbers• solar cycle - only two cycles measured + 0.05%
• changes in Earth orbital parameters - Milankovitch cycles• periods of 20k - 100k years• explain all the major ice ages – dramatic changes in temperature
• changing aerosol concentrations (e.g. volcanic activity)
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the solar energy input to the Earth system
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1000 nm = 1 µm
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solar and earth spectra
1000 nm = 1 µm
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1000 nm = 1 µm
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why would solar energy output vary?
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the sun is a dynamicobject
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Sun radiation varies in output on an 11 yr and 22 yr cycle, but also over longerperiods that are not understood
number of sunspots vs time
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satellite measurements of solar brightness
0.1% variation
individual instruments vary in calibration – so bring them to a normalization, usually 1368 w/m2
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Stefan-Boltzmann law:
Let S = rate at which the Sun produces energy as measured at the Earth’s orbital distance = solar constant = 1368 w m-2
then
rate at which solar energy strikes the Earth = S R2 (watts)
where R is the radius of the Earth (6370 km)
energy reflected back into space by Earth = S R2
where is the Earth’s average albedo (reflectivity) ~ 0.31 on average
energy absorbed by Earth system = SR2 (1-)
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the Earth cannot get rid of energy by conduction or convection to space, so must radiate its energy to space thermally
energy radiated to space is = 4R2 Te4 [the Stefan-Boltzmann law]
where
= Stefan-Boltzmann constant = 5.67 x 10-8 [w m-2 K-4]
Earth in equilibrium (temp not changing with time), rate of absorption = rate of emission
S R2 (1-) = 4R2 Te4
solving for Te using = 0.31 gives
Te = 255K = -18°C
this is the equilibrium temperature of the Earth in the absence of the atmosphere and it is much lower than observed
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distributed over the entire surface of the Earth, average incoming solar radiation is:
[incoming solar/surface area of Earth] = S R2 /4R2 = 1368/4 = 342 w m-2
since albedo is 0.31, amount of incoming radiation reflected back to spaceis:
[solar energy reflected/surface area of Earth] = S R2 / 4R2 = 107 w m-2
absorbed energy:
[solar energy absorbed/surface area of Earth] = S R2 (1-) / 4R2 = 235 w m-2
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global energy balance – bold numbers are W/m2
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no atmosphere Te = 255K = -18°C
Earth radiates 235 w m-2 at this temperature and this radiation is in theinfrared spectral region where many atmosphere gases absorb radiation
Thus, energy balance is NOT achieved at -18°C, and the Earth temp must increase to get rid of the energy and achieve a balanced equilibrium
Measured average Earth temperature is 288K = +15°C. Using Stefan-Boltzmann, we compute the radiated energy is Te
4 = 390 w m-2
of the 390 w m-2 , only 40 passes directly through (gases do not absorb ALL radiation) 350 w m-2 is absorbed by atmospheric gases, and 324 w m-2 is radiated back to the surface
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checks on our numbers: rate of gain = rate of loss
at Earth surface: 168 + 324 + 30 = 78 + 24 + 30 + 390 OK
Atmosphere: 67 + 78 + 24 + 350 + 40 = 165 + 30 + 324 + 40 OK
Space: 107 + 165 + 30 + 40 = 342 OK
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Earth ~33°C (60°F) warmer than without GHG
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what physical parameters affect the ability of an atmospheric gas tobe a greenhouse gas?
see
http://www.ciesin.columbia.edu/docs/003-074/003-074.html
for GH effect: science and policy
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energy radiated to space is = 4R2 Te4 [the Stefan-Boltzmann law]
where = Stefan-Boltzmann constant = 5.67 x 10-8 [w m-2 K-4]
342 w m-2 is the average energy input to the Earth system
235 w m-2 is the average radiated energy from the Earth system, all radiated in the infrared part of the spectrum