Transcript Earth

CE 401
Climate Change Science and Engineering
solar input, mean energy budget, orbital
variations, radiative forcing
18-20 January 2011
a quick business item:
CE 401 is NOT a Tier III class. So anyone taking it to meet
the Tier III requirement
will not be given credit for this class as a Tier III
any questions from last time?
we did the entire science section
homework 3: due Thursday 1/27
• read Houghton Chapter 2
• do some computations (see website) 
(1) use the Stefan-Boltzmann law as described in class:
(a) if the solar output as measured at the top of the Earth’s atmosphere (1368 W m-2) were reduced
by 1 W m-2, then how much would the equilibrium temperature of the Earth be
changed (assuming no atmospheric gases)?
(b) if the amount of solar radiation reflected by clouds, aerosols, and atmospheric
gases were changed from the current 31% to 30%, then how much would the
equilibrium temperature of the Earth change [K]?
(2) use Houghton Fig 2.5 to estimate the change in Earth equilibrium temperature that would occur if
CO2 were completely removed from the atmosphere. Hint: the total energy radiated by the Earth
plus atmosphere should remain the same  the area under the radiation curve should not change.
(3) The solar flux S arriving at the top of the atmosphere varies by +/-3.3% as the Earth revolves
around the sun. By how many degrees should the effective temperature of the Earth vary each year
as a result?
Read chapter 2 of Houghton
due Tuesday, 1/25
HW 2 due on Thursday
what cause 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 dynamic
object
number of sunspots vs time
Sun varies in output on an 11 yr and 22 yr cycle, but also over longer
periods that are not understood
modeled solar irradiance at top of the atmosphere
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 pR2 (watts)
where R is the radius of the Earth (6370 km)
energy reflected back into space by Earth = S pR2 a
where a is the Earth’s average albedo (reflectivity) ~ 0.31 on average
energy absorbed by Earth system = SpR2 (1-a)
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 = s 4p R2 Te4 [the Stefan-Boltzmann law]
where
s = 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 pR2 (1-a) = s 4pR2 Te4
solving for Te using a = 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 pR2 /4pR2 = 1368/4 = 342 w m-2
since albedo a is 0.31, amount of incoming radiation reflected back to space
is:
[solar energy reflected/surface area of Earth] = S pR2 a / 4pR2 = 107 w m-2
absorbed energy:
[solar energy absorbed/surface area of Earth] = S pR2 (1-a) / 4pR2 = 235 w m-2
global energy balance – bold black numbers are W/m2
342-107=235
absorbed
no atmosphere  Te = 255K = -18°C
Earth radiates 235 w m-2 at this temperature and this radiation is in the
infrared 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 StefanBoltzmann, we compute the radiated energy is s Te4 = 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
Space: 107 + 165 + 30 + 40 = 342
OK
OK
Earth ~33°C (60°F) warmer than without GHG
measured thermal Earth radiation over the Mediterranean sea
H2O
O3
CO2
H2O
CH4
N2O
thermal radiation curves (T)
GHG absorbers are indicated with atmospheric transmission “windows”
what physical parameters affect the ability of an atmospheric gas to
be a greenhouse gas?
see
http://www.ciesin.columbia.edu/docs/003-074/003-074.html
for GH effect: science and policy
radiative forcing: IPCC
“Radiative forcing is a measure of the influence a factor has in altering the balance of
incoming and outgoing energy in the Earth-atmosphere system and is an index of the
importance of the factor as a potential climate change mechanism. In this report
radiative forcing values are for changes relative to preindustrial conditions defined
at 1750 and are expressed in watts per square meter (W/m2)”
factors that influence the radiative equilibrium of the Earth system
average solar input: 342 w/m2
global warming potential (GWP) of a gas GWPg:
a weighting factor to compare the GHG efficiency of a gas relative to CO2
GWPg =

Fg x Rg(t) dt /

FCO2 x RCO2 dt
where
Fg = radiative forcing efficiency of the gas in question [w m-2 kg-1]

FCO2 = radiative
forcing efficiency
 of CO2 [w m-2 kg-1]
Rg = fraction of the 1 kg of gas remaining in the atmosphere at time t
RCO2 = fraction of the 1 kg of CO2 remaining in the atmosphere at time t
radiative forcing efficiency is usually an exponential decay function, or ~ constant
with time, depending on the gas. For CO2 the decay is rapid the first few
decades as the biosphere absorbs the carbon, then it decays at a much
slower rate corresponding to the slow CO2 uptake of the oceans
Choice of time horizon for GWP depends on what a policy maker is interested in
e.g. CH4 GWP is 62 for 20 yr horizon, 23 for 100 yr, and 7 for 500 yr
• astronomical forces drive global climate change
• seasons are driven by astronomical causes, as is the 24 h da/night cycle
Earth orbital changes that vary the solar input and cause the ice ages: the
Milankovich cycles – these cycles change the solar input to the Earth system
eccentricity changes
varies from nearly circular
to high eccentricity 0.058
with mean 0.028.
Caused by perturbations
from the other planets
shape of earth’s orbit changes during a cycle of about 100,000 years
axial tilt (obliquity) – increased obliquity  increased seasonal amplitude change
axis of rotation changes from about 21.5° to 24.5° --> seasonal variations over a period of
41,000 years. Tilt is the most significant cause of seasonal temp change. Modulates the
seasons, does not change climate overall
axial precession – trend in direction of axis of rotation in inertial space – gyroscopic motion
the earth’s rotation axis precesses (wobbles) with a period of about
26,000 years
due to tidal forces exerted by sun and moon on solid Earth since Earth is not spherical
affects climate extremes
problems with the Milankovitch theories:
• 100,000 yr problem: eccentricity variations should have a smaller impact that the other
mechanisms, but this is the strongest climate signal in the data record
• 400,000 yr problem: eccentricity variations also show a 400,000 yr cycle but that cycle is only
visible in climate records > 1My ago
• observations of climate changes show behavior much more intense than calculated
• the 23,000 yr cycle dominates, the opposite of what is observed
• so the explanation is not 100% - there are still issues with the explanation
deg change
obliquity=axial tilt
long of perihelion
precession index
calc. insolation to TOA
Benthic and Vostok
ice cores