Download Temperature increases

Road map to EPS 5 Lectures 3 and 4: Atmosphere Heat, Energy, Radiation
Black Bodies, Planck Function,
Stefan Boltzmann Law
Solid bodies emit thermal
radiation at rates that
depend on temperature.
Hot bodies (sun) emit more
radiation at shorter
wavelengths than cold
bodies (earth).
Emission
rate=T4
Effective T, greenhouse effect
Planets radiate on average at the
Effective Temperature, to maintain
energy balance with sun and space,
Absorption of ir in the atmosphere
traps energy, radiating back to the
surface and causing it to warm up.
Teff = [Fs(1 - A)/(4)]¼
= 252.6 K
Tg = [n + 1]1/4Teff.
Feedback!
Atmospheric Radiation: The Earth receives energy from the sun (on
average 344 W/m2) and emits the same amount to space
The energy balance of planet earth
The temperature of the earth’s surface has been remarkably constant over
geologic time. Even the dramatic cooling during the ice age represented a
change of only 3 C in the global average surface temperature, occurring over
thousands of years. Seasonal changes in temperature, although large in a
particular place, correspond to very tiny changes in global mean temperature.
How is this remarkably steady condition maintained?
To maintain the long-term stability of earth’s temperature, the planet must
radiate to space a flux of energy sufficient to just balance the input from the
sun, i.e. the earth is, to good approximation, in radiative energy balance.
Scientists determined by direct experiment that the total energy flux from an
object, at all wavelengths, depended only on temperature, and they derived an
empirical equation called the Stefan-Boltzmann law to describe this
relationship:
TOTAL ENERGY FLUX =  T4
Here the total energy flux (units: W m-2) is shown to vary as the 4th power of
the absolute temperature, T (K), with a constant of proportionality  = 5.67  108 W m-2 K-4, the Stefan-Boltzmann constant. The Stefan-Boltzmann law was
obtained in the 19th century by observing the rate at which real objects lost
energy via radiation
Many decades passing Planck showed that this relationship could be derived
from his radiation law, which describes the complete spectrum of radiation from
a “perfect” (black, absorbs and emits with 100% efficiency at all wavelengths)
object.
If we could take a snapshot of a light wave as it traveled for 1 s, it would
be 3108 m long, and would look like the sine wave shown in the figure.
The distance between two successive crests on the wave is called the
wavelength (denoted  ). The frequency (denoted  ) is the number of
wave cycles (wavelengths) that pass a reference point per unit time, and
since our snapshot shows exactly the number of peaks that passed in
one second,  is also the number of peaks in the picture, i.e.  =c/ .
Alternatively, 1/ is the time it takes the wave to travel one wavelength at
speed c.
Electromagnetic radiation, although wave-like in nature, is composed of
packets of energy called photons. Thus light is both a wave and a particle. For
a given electromagnetic wave of wavelength  the energy associated with
each photon is given by
E = hc/ = h
where h is Planck's constant (h=6.626x10-34 J sec). This was one of Planck's
great discoveries; it implies that photons with shorter wavelengths are
more energetic than photons with longer wavelengths and light comes in
defined packets with a particular amount of energy in each one (given by
h ).
 max = b/T
(Wien's displacement law: peak of Planck function)
The Planck function gives the energy flux from an object divided up
according to wavelength (or frequency), for a given temperature—it is pictured
on the next slides.
Electromagnetic spectrum: Atmospheric Radiation
106
visible
"color temperature"
Albedo
The earth’s albedo (fraction of solar radiation *reflected* to space)
was first measured by observing earthshine on the moon, reflected
back to earth and visible just after the new moon. It is now
measured from spacecraft. About 33% of the solar energy incident
on the earth is reflected back to space, A=0.33.
Most of the reflection of solar radiation from earth is due to
clouds, with help from sea ice and glacial ice in Antarctica and
Greenland, plus snow and deserts (albedo 0.6—0.9).
The albedo of the earth’s surface is mostly much lower than 0.33,
about .07 for land with vegetation, 0.05-0.1 for the ocean.).
Thus the albedo, and the entire energy budget of earth, is
sensitive to cloudiness and ice cover, factors that change on
both weather and climate time scales (short and long times).
Earth's albedo for March, 2005 (CERES satellite)
ALBEDO
The term has its origins from a Latin word albus, meaning “white”. It is
quantified as the fraction of incident solar radiation of all wavelengths
reflected by a body or surface.
Diagram of the sun and earth,
and an imaginary sphere with
radius 1.5x1011m with the sun at
the center.
r=1.5 x 1011 m
O
sun
o
earth
The surface area of this sphere is
4r2.
We can compute, using the Stefan-Boltzmann Law, the total
amount of energy (L) radiated by the sun each second,
L = Ts4 4Rs2 = 3.9 x 1026 watts,
where 4Rs2 is the surface area of the sun (Rs=6.6  108m), Ts4
is the Stefan-Boltzmann law giving the energy flux per unit area,
and Ts is the temperature of the sun’s surface, 5800 K.
The same total amount of energy L must also cross the sphere of
radius r each second.
The solar flux (Watts m-2) at the earth, Fs, is defined as the
energy crossing a square meter of the sphere at earth's orbit each
second. It is given by
Fs = L/(4r2) = Ts4 (Rs2/r2) = 3.9x1026/( 4(1.5x1011)2 ) =
1379 W m-2
The solar flux Fs (also called the solar constant) is the radiant energy from the
sun that falls per second a 1 m2 surface oriented perpendicular to the sun’s rays,
at the top of the earth's atmosphere.
1379 / 4  344
The total solar energy striking by the earth per second can be calculated by
multiplying Fs by the shadow area (not the total surface area!) of the earth , i.e.
the area of solar beam intersected the earth.
SUN
The amount of energy striking the earth is given by the
[shadow area (black circle)  the solar flux] =Re2 Fs. (Re is the radius of the
earth).
The total energy flux striking the surface of the earth is therefore Fs Re2.
Energy INPUT to the earth from the sun
Not all solar radiation intercepted by the earth is absorbed. The
fraction of incident solar radiation reflected is defined as the
albedo, A, and the fraction absorbed is therefore (1-A).
The total energy input to earth (Joules per second) is thus
Eabs = FsRe2(1 - A).
INPUT
Energy OUTPUT from earth by thermal radiation
The total energy emitted per unit area is given by T4, and the
emitting area is the surface area of the earth, 4Re2.
The total energy emitted by the planet per second is therefore
Eemit = 4Re2 T4 .
OUTPUT
Energy balance requires that input=output, when averaged over a longenough period of time, i.e. on average Eemit = Eabs. Thus
4Re2T4 = FsRe2(1 - A) .
(This is the Energy Balance Equation). This equation can be solved for
the average temperature at which the earth must emit radiation to bring
the energy budget into balance, called the effective temperature Teff of
the planet:
Teff = [Fs(1 - A)/(4)]¼ = 252.6 K.
Effective Temperatures of the Planets
planet
solar flux
(W m-2)
orbit radius albedo Te
(1011 m)
(K)
Tg
(K)
Ground pressure
(bar)
Mercury
9200
0.6
0.058
442
442
~0
Venus
2600
1.1
0.77
227
750
90
Earth
1400
1.5
0.33
253
288
1
Mars
600
2.3
0.15
216
240
0.007
49
7.8
0.58
98
Jupiter
(no surface)
(no surface)
After Goody and Walker, "Atmospheres"
2001
Top of Atmosphere Flux Anomaly W m-2
Earth's Albedo can change with time, affecting the
energy budget and temperature of the planet.
Atmospheric absorption of infrared radiation
•The most abundant gases in the atmosphere, N2, O2,
and Ar, neither absorb nor emit terrestrial radiation.
(They also neither absorb nor emit most wavelengths of
solar radiation, except for ultraviolet light).
•The relatively rare molecules that can absorb long-wave
(terrestrial) infrared radiation are called greenhouse
gases. They can trap infrared radiation emitted by the
Earth much as the glass in a greenhouse traps heat.
•The most important greenhouse gases in the
atmosphere are H2O and CO2, and gases such as
methane (CH4) and chlorofluorocarbons are also
significant.
Greenhouse gases: Water, CO2, CH4
O=C=O
-
-
O
O
C
+2
CO2 with electromagnetic waves with
only dynamic ("transition") dipole
moment due to the changes in the
+and –as the molecule vibrates
(bending or "asymmetric stretch").
Water interacts with electromagnetic waves
with both a permanent dipole moment (left)
and dynamic ("transition") dipole moment
due to the changes in the +and –as the
molecule vibrates.
molecules radiate frequencies they can absorb: Kirchhoff's Law
•Due to the presence of gases that can absorb
infrared radiation, the atmosphere acts as a blanket,
allowing solar energy to reach the surface but
preventing the heat from escaping directly back to
space.
•The atmosphere is warmed by the absorbed
terrestrial radiation.
•Molecules that can absorb radiation of a particular
wavelength can also emit that radiation according to
Kirchhoff's radiation law. The Greenhouse gases in
the atmosphere will therefore radiate, both to space
and back towards the earth's surface. This backradiation warms the earth's surface.
The Greenhouse Effect: influence of atmospheric absorption
and emission of planetary (infrared) radiation
incoming solar radiation (Fs)
(visible, near infrared)
Te4
z=H
Te4
far infrared radiation
from the atmosphere
reflected
solar
(A)
T4g
terrestrial (far infrared)
radiation from the surface
The atmosphere and the ground radiate energy according to the Stefan-Boltzmann law.
Examine the energy balance of the layer at H (intended to be a scale height, or ~ 7km,
on earth) in this hypothetical planet. The total amount of energy radiated per square
meter per second is 2T14, (OUT) because the layer radiates equally both up and down.
But the amount received by the layer is Tg4, (IN) (heated only from below!). If the layer
has a balanced energy budget, these two fluxes must be equal (IN = OUT),
Tg4 = 2T14 .
{ T1 =>> Teff}
Thus the ground is warmer than the atmosphere by Tg = 21/4Teff. This happens
because the atmosphere is warmed only by absorbing radiation from the earth's
surface, i.e. from one side (below), but it radiates both up and down.
The atmosphere must have a lower temperature than the ground in order to
satisfy its energy balance.
This result for 1 layer in the atmosphere can be generalized to any number (n) of
layers,
Tg4 = [n + 1] T14
Tg = [n + 1]1/4Teff.
The atmosphere therefore gets colder as we go up due to the effects of absorption and
emission of radiation (terrestrial infrared radiation).
SOLAR RADIATION SPECTRUM:
blackbody at 5800 K
TERRESTRIAL RADIATION SPECTRUM FROM SPACE:
composite of blackbody radiation spectra for different T
Scene over
Niger valley,
N Africa
cf. clouds, aerosols
Climate forcing due to changes in concentrations of greenhouse gases,
atmospheric aerosols, and clouds, since 1850 (Hansen, 2001).
Class discussion
What about engineering the climate:
•add aerosols to the atmosphere?
•add iron to stimulate the ocean ?
•plant trees to take up CO2 and cool the surface?
ATMOSPHERIC CO2 INCREASE OVER PAST 1000 YEARS
FEEDBACKS
Consider how these factors may change, what may cause these changes, and
how the various changes may interact with each other. This brings us to the
concept of feedback:
property A increases →
property B changes →
+ positive feedback
(amplification)
causes property A to increase further
+ negative feedback
property A increases →
(damping)
property B changes →
causes property A to decrease
Positive feedback makes the climate system more sensitive to a change in
property A; negative feedback makes it less sensitive. The concept of feedback
depends on a formulation of direct vs. secondary effects, based on separation in
time or some other criterion.
FEEDBACKS INVOLVING ALBEDO (continued)
ice-albedo feedback – solar radiation
Temperature increases → polar ice recedes → Albedo decreases
→ Temperature increases
+
This is a very strong feedback when there is a lot of polar ice, for example, at the height
of the last ice age. It works both ways, helping the ice sheets to advance as the earth
cooled, by amplifying the cooling, and accelerating the retreat of the ice sheets as the
climate started to warm. There is rather little polar ice in glaciers today, so feedback on
land ice is not likely to play a major role in climate change. But sea ice coverage is
significant, and uptake of heat by the underlying ocean could have effects on both
temperature and rainfall. Sea ice will be discussed in detail later.
FEEDBACKS INVOLVING ABSORPTION OF IR (HEAT)
Examine some of the most important feedbacks in the Earth’s atmosphere.
water vapor feedback.
Temperature increases → atmosphere H2O increases (Clapeyron equation)
→ atmospheric absorption increases (n) → Temperature increases
+
This is the strongest feedback mechanism in the atmosphere. It is also the best
understood since it is based simply on the measured increase in water vapor pressure
increase with temperature (Clapeyron equation).
cloud feedback – terrestrial radiation
Temperature increases → atmosphere H2O increases (Clapeyron equation)
→ cloudiness increases (n) → Temperature increases
+
This is a very strong feedback that is not well understood because it is hard to know
whether or how much cloudiness would increase as temperature does—cloudiness
depends on upward air motion more than on T or H2O directly.
FEEDBACKS INVOLVING ALBEDO
cloud feedback – solar radiation
Temperature increases → atmosphere H2O increases (Clapeyron equation)
→ cloudiness increases (n) → Albedo increases
→ Temperature decreases
This is also very strong feedback that is not well understood because it is hard to know
whether or how much cloudiness would increase as temperature does, and because of
the trade-off (competition) between the effects of clouds on absorption of infrared
radiation versus reflection of solar radiation. Low-altitude clouds affect albedo more than
they affect ir radiation, and conversely for high clouds (discussed below).
vegetation feedback – solar radiation
Temperature increases → deserts expand → Albedo increases
→ Temperature decreases
This is a very complex feedback that will take a long time to be realized. Maybe
deserts won't expand, or plants will be greener because there is more CO2 ?
Longwave radiation as viewed from Low OLR in the tropics is due to: 1. Obscuring
the satellite sensor "ERBS" on
the surface by clouds; 2. Cold T at cloud tops
NOAA-9, April, 1985
3. Smoke from fires 4. Both 1 and 2 are correct.
No Data 100
150
200
Watts m-2
250
300
350
FUTURE TEMPERATURE PROJECTIONS
FROM CLIMATE MODELS (IPCC, 2001)
Atmospheric aerosols: Global cooling?
Aerosols are suspended particles in the air which are small enough
to resist gravitational sedimentation (i.e. they remain afloat despite
the force of gravity acting on them). Aerosols can be solid, liquid, or
a combination of both. They typically range in size from 0.1 to 1.0
micrometers. The main sources of aerosols are dust from the
surface, sea spray (liquid droplets and solid sea-salt particles),
volcanoes, forest fires, and anthropogenic combustion.
Direct effect: aerosols scatter sunlight, increasing albedo, cooling
the atmosphere.
Black carbon effect: if aerosols have black carbon (soot…)
inside, they can be heated by sunlight, warming the atmosphere.
Indirect effect: aerosols affect the formation of cloud droplets.
Increased aerosols may lead to smaller droplets, more cloudiness,
and higher albedo, cooling the earth by lowering Teff.
Aerosol Optical Depth after the eruption of Mt. Pinatubo
(SAGE-II Satellite data)
-0.4
-0.2
0
Climate Model
-0.6
Temperature Change (oC)
+0.2
Global Temperature
1991
1992
1993
1994
Mt. Pinatubo eruption
Effect of a major volcanic eruption on climate ( after Hansen et al., 1993).
Note: many feedbacks have not come into play.
http://www.atoptics.co.uk/atoptics/sunvolc.htm
Volcanic eruptions can inject millions of tonnes of dust and gaseous sulfur dioxide
into the stratosphere. The finer dust particles remain aloft for years and spread
around the world while the sulphur dioxide evolves to an aerosol of sulfur acids
that add to the particulates.
The dust and aerosol produce vivid sunset and twilight effects like the intense
yellow-red horizon and purple-pink glows of the photograph. The purple glow is
probably a combination of red-orange light transmitted through the lower
atmosphere and scattered blue light from still sunlit stratospheric dust.
AEROSOL OBSERVATIONS FROM SPACE
Biomass fire haze in central America (4/30/03)
Fire locations
in red
Modis.gsfc.nasa.gov
BLACK CARBON EMISSIONS
DIESEL
DOMESTIC
COAL BURNING
BIOMASS
BURNING
“…Kyoto also failed to address two major pollutants that have an impact on
warming: black soot and tropospheric ozone. Both are proven health
hazards. Reducing both would not only address climate change, but also
dramatically improve people's health.” (George W. Bush, June 11 2001 Rose
Garden speech)
EPA REGIONAL HAZE RULE: FEDERAL CLASS I AREAS
TO RETURN TO “NATURAL” VISIBILITY LEVELS BY 2064
clean day
moderately polluted day
Acadia National Park
http://www.hazecam.net/