CE 401 Climate Change Science and Engineering
-
Upload
damian-lott -
Category
Documents
-
view
27 -
download
1
description
Transcript of CE 401 Climate Change Science and Engineering
CE 401Climate Change Science and Engineering
solar input, mean energy budget, orbital variations, radiative forcing
17-19 January 2012
any questions from last time?
we did the entire science section of 401 in a flash
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
what causes natural variations in the climate system
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)
the solar energy input to the Earth system
1000 nm = 1 µm
solar and earth spectra
1000 nm = 1 µm
1000 nm = 1 µm
why would solar energy output vary?
the sun is a dynamicobject
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
satellite measurements of solar brightness
0.1% variation
individual instruments vary in calibration – so bring them to a normalization, usually 1368 w/m2
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-)
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
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
global energy balance – bold numbers are W/m2
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
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
Earth ~33°C (60°F) warmer than without GHG
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
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