Bases Físicas do Aquecimento Global

Bases Físicas do
Aquecimento Global
Mariane Coutinho
Centro de Ciência do Sistema Terrestre
Instituto Nacional de Pesquisas Espaciais
Radiation Balance of the Earth
Source: ceres.larc.nasa.gov/ceres_brochure.php - J. Kiehl and K. Trenberth
Curso de Introdução a Mudanças Climáticas – Bases Físicas do Aquecimento Global Mariane Coutinho
The electromagnetic spectrum
Electromagnetic radiation described as an ensemble of
waves propagating at the speed of light
§
Energy that it carries partitioned into contributions from
different wavelength bands
§
1 nm = 10-9 m
1 m = 10-6 m

Wavelength bands carrying most of energy associated with:
solar radiation  shortwave ( < 4 m, concentrated in
visible 0.4 - 0.7 m
and near infrared 0.7 - 4 m)
terrestrial radiation  longwave ( > 4 m, infrared)
§
Curso de Introdução a Mudanças Climáticas – Bases Físicas do Aquecimento Global Mariane Coutinho
Effective Temperature of Earth
or Equivalent Blackbody* Temperature  Temperature detected from space
Balance between energy absorbed
and emitted by surface+atmosphere
§
1.5x108 km
Earth
Energy emitted
Stefan-Boltzman law: total energy radiated per unit
surface area per unit time (flux density or
irradiance) of a blackbody* is given by
Fe =  T4, where  = 5.67 x 10-8 W m-2 K-4
à
Energy emitted =  Te4 x (4  re2),
Te = effective temperature of Earth
ü
§
Energy absorbed
Solar constant (flux density) at Earth's distance: 1368
W m-2
ü
Albedo (reflectivity) of Earth ~ 0.3
à
Energy absorbed = (1 - 0.3) x 1368 x ( re2)
ü
Incident solar radiation intercepted
over the area  re2
re
 Energy balance:
 Te4 = (0.7 x 1368) / 4 = 239.4 W m-2

Outgoing (blackbody) terrestrial
radiation emitted over the area 4 re2
Te = 255 K = -18ºC
(cold!)
*A blackbody is an ideal body that absorbs all radiation
incident on it. It is also a perfect emitter.
Curso de Introdução a Mudanças Climáticas – Bases Físicas do Aquecimento Global Mariane Coutinho
Natural greenhouse effect of atmosphere on
temperature of Earth, Mars and Venus
Decrease in temperature (ºC) with distance from the sun (x 106 km):
Solid curve – planets with no reflection and no atmospheres
Open circles – reflection taken into account
Solid circles – actual temperatures at the surfaces
The length of each dashed line is a measure of the greenhouse effect
(from Philander, 1998)
Curso de Introdução a Mudanças Climáticas – Bases Físicas do Aquecimento Global Mariane Coutinho
The greenhouse effect
Some of this outgoing
infrared radiation
passes through the
atmosphere back to
space
Some solar
radiation is
reflected
Infrared radiation is
emitted from the surface
Some of this outgoing
infrared radiation is trapped
by the atmosphere and
warms it
Most solar
radiation is
absorbed by the
surface and
warms it
The greenhouse effect  Terrestrial radiation emitted
from the surface is absorbed and reemitted in its
upward passage through the atmosphere.
Curso de Introdução a Mudanças Climáticas – Bases Físicas do Aquecimento Global Mariane Coutinho
The greenhouse effect
Solar and terrestrial radiation
occupy different ranges of the
electromagnetic spectrum
(shortwave and longwave,
respectively)
Lei do Deslocamento de Wien: O valor do
comprimento de onda para o qual a
radiância emitida por um corpo negro é
máxima é
inversamente proporcional à sua
temperatura.
(and above)
(entire atm.)
Water vapor, carbon dioxide and
other gases whose molecules have
electric dipole moments absorb
more strongly in the longwave
part of the spectrum (terrestrial
radiation)
Curso de Introdução a Mudanças Climáticas – Bases Físicas do Aquecimento Global Mariane Coutinho
The greenhouse effect: simple model 
isothermal layers
Assume that the incoming shortwave radiation (after removing
the reflected component) is transmitted by the atmospheric
layers, and is all absorbed at the surface.
§
Assume that the surface emits as blackbody with Ts.
§
Assume the atmosphere absorbs all of this energy, and reemits
as a blackbody with Ta to space and back to surface.
§
Single isothermal
layer
i.
Solar radiation
F
Ta
Energy balance at the top-of-atmosphere:
F = (0.7 x 1368) / 4 = 239.4 W m-2 =  Ta4
(using the Stefan-Boltzman law for the atmosphere)
 Ta4
Energy balance at the surface:
F +  Ta4 = (239.4 x 2) W m-2 =  Ts4
(using the Stefan-Boltzman law for the surface)
Atmospheric layer
F
Ts
 Ta4
Solving the equations for Ta e
Ts:
 Ts4
temperature of surface 48 K higher than in absence of the
greenhouse effect
§
Ta = 255 K
temperature of atmosphere is 255 K as calculated for the planet
before
§
Curso de Introdução a Mudanças Climáticas – Bases Físicas do Aquecimento Global Mariane Coutinho
Ts = 303 K
The greenhouse effect: simple model 
isothermal layers
ii.
Two isothermal
layers
Solar radiation
F
F
Atmospheric layer
F
2F
Stefan-Boltzman law:
F
3F = (239.4 x 3) W m-2 =  Tg4 
Atmospheric layer
F
iii.
2F
335 K
3F
Ts =
 = 5.67 x 10-8 W m-2 K-4
N isothermal layers  Ts = [(N+1)F/]1/4 K
The above model assumes pure radiative balance and is greatly
simplified.
The global mean surface temperature of the Earth is ~288 K
(15ºC) as a consequence of the greenhouse effect.
We can make the simple model more realistic…
Curso de Introdução a Mudanças Climáticas – Bases Físicas do Aquecimento Global Mariane Coutinho
More realistic models
Consider other forms of energy apart from radiation: latent
and sensible heat fluxes.
§
Consider the dependence of absorption on the wavelength of
the radiation.
§
(and above)
(entire atm.)
The wavelength dependence is
quite pronounced, with well
defined absorption bands identified
with specific gaseous constituents
and also windows in which the
atmosphere is relatively
transparent.
Curso de Introdução a Mudanças Climáticas – Bases Físicas do Aquecimento Global Mariane Coutinho
Non-blackbodies
Unlike blackbodies, which absorb all
incident radiation, non-blackbodies
can also reflect and transmit
radiation.
§
The radiation laws derived for
blackbodies can be applied by
defining the emissivity ε(λ) as the
fraction of the blackbody irradiance
emitted at a given wavelength. The
emissivity varies between 0 and 1
and is a function of wavelength and
type of surface.
§
For non-blackbodies, the StefanBoltzman law is written as F =  ε
T4
where ε is an average emissivity
value.
§
Also useful are the absorptivity,
reflectivity and transmissivity,
Curso de Introdução a Mudanças Climáticas – Bases Físicas do Aquecimento Global
defined as the fractions of the
§
Mariane Coutinho
Modified single layer greenhouse model
Assume ε (long) < 1 for the atmosphere
Note: Kirchhoff’s law states that absorptivity equals emissivity, at all
wavelengths 
absorptivity of atmosphere for longwave (terrestrial) radiation = ε.
Solar radiation
F
Ta
Atmospheric layer
F
Ts
 εTa4
 εTa4
 (1-ε)Ts4
 εTs4
 Ts4
Energy balance at the top-of-atmosphere:
F =  εTa4 +  (1-ε)Ts4
Energy balance at the surface:
F +  εTa4 =  Ts4
For example, assuming ε (long) = 0.7 for the atmosphere we
obtain
Ta = 238.7 K (~-34ºC)
Ts = 283.9 K (~11ºC)
Curso de Introdução a Mudanças Climáticas – Bases Físicas do Aquecimento Global Mariane Coutinho
Exercício
Utilizando um modelo com uma única camada atmosférica
isotérmica análogo ao discutido, mostre a expressão mais
geral para Ts a seguir:
T
S
=
4
S 0 (1 − α )
2σ ( 2 − ε )
, assumindo:
S0: constante solar
α: albedo planetário
ε: emissividade de onda longa para a atmosfera
σ: constante de Stefan-Boltzman
Curso de Introdução a Mudanças Climáticas – Bases Físicas do Aquecimento Global Mariane Coutinho
Implicação
Considerando-se a expressão obtida para a temperatura de
equilíbrio global média da superfície nesse modelo simples:
S 0 (1 − α )
T
S
=
4
2σ ( 2 − ε )
vemos que há três termos no lado direito que podem variar
significativamente e alterar o clima:
www.windows2universe.org
1. S0: variações na constante solar,
parâmetros orbitais
2. α:
variações no albedo planetário
www.windows2universe.org
3. ε: variações da emissividade no infravermelho – aumento nas concentrações
de gases de efeito estufa devido a
atividades humanas ou outras causas
em diferentes escalas de tempo
Curso de Introdução a Mudanças Climáticas – Bases Físicas do Aquecimento Global Mariane Coutinho
Exercício para Avaliação
Mudanças no Balanço de Energia:
Seja Q a radiação líquida absorvida pelo sistema climático
medida no topo da atmosfera. Considerando-se médias
anuais globais temos Q=0 para um sistema em equilíbrio.
Para o modelo com uma única camada atmosférica
isotérmica mostre que Q é dado por:
S
ε
Q = 0 ( 1 − α ) − ε ′ σ TS4
ε ′ = 1−
4
2
onde
.
Obs.: Isso equivale a dizer que a Terra emite como um corpo
cinza para o espaço.
Curso de Introdução a Mudanças Climáticas – Bases Físicas do Aquecimento Global Mariane Coutinho
Greenhouse gases
 Gases which absorb in the longwave
region.
The energy of an infrared photon is
insufficient to cause electronic excitation
but can cause vibrational or rotational
excitation.
Molecular vibration
Vibrational energy is quantized and the
frequency of a vibration is the frequency
of the photon necessary to excite the
molecule to that vibrational energy level.
For example:
HCl  frequencies of vibration are integer multiples of 8.66 ×
1013 Hz.
 vibrates at 1 × (8.66 × 1013 Hz) and 2 × (8.66 × 1013
Hz) and so on.
 can only be excited between adjacent vibrational
energy levels.
Curso de Introdução a Mudanças Climáticas – Bases Físicas do Aquecimento Global Mariane Coutinho
 Wavelength is λ = c/ν = (2.998 × 108 m/s)/(8.66 ×
www.windows2universe.org
Molecular vibration
Fundamental vibrations
The number of possible types of vibrations is restricted by the
number of atoms (N) in a molecule:
3N–5 for a linear molecule (all the atoms arranged in a line)
3N–6 for a non-linear molecule.
For example, the number of vibrations for H2O is 3(3) – 6 = 3:
O
H
H
stretching
O
O
H
H
H
H
stretching
bending
Curso de Introdução a Mudanças Climáticas – Bases Físicas do Aquecimento Global Mariane Coutinho
Fundamental vibrations
For CO2, which is a linear molecule, there are 3(3) – 5 = 4
fundamental vibrations:
O
C
+
O
O
bending
in plane
O
C
stretching
C
+
O
bending out of plane
O
O
C
O
stretching
Curso de Introdução a Mudanças Climáticas – Bases Físicas do Aquecimento Global Mariane Coutinho
Vibrations and IR absorption
Molecule must have change in dipole moment due to vibration
or rotation to absorb infrared radiation. Thus, vibrations that
do not change the overall dipole of the molecule do not lead to
IR absorption.
CO2, for example. has three vibrations that change the overall
dipole of the molecule (called IR active):
O
C
O
symmetric stretching
O
C
bending
in plane
O
O
C
O
anti-symmetric stretching
+
-
+
O
C
O
IR
ACTIVE
bending out of plane
Curso de Introdução a Mudanças Climáticas – Bases Físicas do Aquecimento Global Mariane Coutinho
Atmospheric gases
Most abundant gases in the dry air close to the Earth’s surface:
Gas
% Volume
Nitrogen
N2
78.08
Oxygen
O2
20.95
Argon
Ar
0.93
Carbon Dioxide CO2
0.03
Each of the first two most abundant gases in the
atmosphere has only 3(2) – 5 =1 fundamental vibration
and it is symmetric:
N
N
symmetric stretching
O
O
symmetric stretching
 Neither O2 nor N2 absorbs infrared
Curso de Introdução a Mudanças Climáticas – Bases Físicas do Aquecimento Global Mariane Coutinho
Atmospheric gases
Third most abundant gas is Argon  atom, so does not vibrate
(no bonds)  No infrared absorption by Ar
Next: CO2 and water  both have non-symmetric vibrations
à
Both, CO2 and H2O absorb and emit infrared radiation in the
atmosphere
à
Greenhouse effect
There are trace gases in the atmosphere which are also important
for the greenhouse effect, for example, CH4, N2O, O3, etc.
More greenhouse gases in the atmosphere means more infrared
radiation is absorbed and Earth’s surface becomes warmer!
http://www.skepticalscience.com/graphics/SkepticsvRealists_500.gif
Curso de Introdução a Mudanças Climáticas – Bases Físicas do Aquecimento Global Mariane Coutinho