ce 401 climate change science and engineering solar input, mean energy budget, orbital variations,...

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