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Atmospheric Physics – a
short introduction (part II)
Helen Brindley
November 2012
© Imperial College London Page 1
What drives our climate system?
Outgoing Thermal
Radiation
Incoming Solar
Radiation
http://sohowww.nascom.nasa.gov/
TSUN ~ 5780 K
TEARTH ~ 255 K
Planck ‘Blackbody’
curves:
lI l
(n
orm
aliz
ed)
Visible
UV Near IR
Thermal
IR
WAVELENGTH (mm)
Solar/’Shortwave’ Terrestrial/’Longwave’
Spectral Implications
scaled by
rs2/rd
2
In steady state, global energy balance at the top of the atmosphere:
Incoming Solar Radiation = Outgoing Thermal Radiation
(wavelengths < 4 mm) (wavelengths > 4 mm)
• Incoming solar energy flux
So (the solar ‘constant’) or energy
flux from the sun
Intercepted by the Earth’s disc, area pRe2,
with average reflectivity or ‘albedo’ A
Incident solar energy flux = So(1-A)pRe2
• Outgoing thermal energy flux
Earth surface can be assumed to emit
as a ‘black-body’ (a perfect emitter)
Emission occurs from the entire surface area
Outgoing longwave energy flux = 4pRe2 s Ts
4
The role of radiative transfer – some (very) basics
Simple energy balance at TOA:
Slightly better – 1 layer, grey-body atmos with emissivity e,
transparent to solar radiation, surface a perfect blackbody
4
e
2
e
2
eo T R 4R )(1S spp
1/4
o
4σ
)(1ST
e
4
a
4
so T )(1T )(1
4
Ssees
4
a
4
s T 2T sese
4
s
4
ao T T )(1
4
Ssse
TOA
Atmosphere
Surface
1/4
os
)(2 2
)(1ST
es
Solve:
Invoke Kirchoff, e = 1-tr
The role of radiative transfer – some (very) basics
Simple energy balance at TOA:
Slightly better – 1 layer, grey-body atmos with emissivity e,
transparent to solar radiation, surface a perfect blackbody
4
e
2
e
2
eo T R 4R )(1S spp
1/4
o
4σ
)(1ST
e
4
a
4
so T )(1T )(1
4
Ssees
4
a
4
s T 2T sese
4
s
4
ao T T )(1
4
Ssse
TOA
Atmosphere
Surface
1/4
os
)(2 2
)(1ST
es
Solve:
Invoke Kirchoff, e = = 1-Tr
Absorption of radiation by matter: e/Tr
Below the ionisation threshold, If there are no available quantized energy levels
matching the quantum energy of the incident radiation, then the material will be
transparent to that radiation* (*in the absence of scattering)
Wavelength
Energy Photodissociation
+ Photoionization
E = hn = hc /l
Ultraviolet + Visible interactions
• Ozone in the upper atmosphere
(stratosphere) is both created and
destroyed by UV solar radiation via
dissociation of oxygen and of ozone
itself
UV-A: 320-400 nm
UV-B: 280-320 nm
UV-C: 100-280 nm
Photodissociation +
UV and visible photons below
the ionization energy are
absorbed to produce transitions
between electronic energy levels
Photoionization
Infrared (IR) interactions
Quantum energy of IR photons (~0.01-1 eV) matches the ranges of energies
separating quantum states of molecular vibrations
For a molecule to absorb IR radiation it must undergo a net change in dipole
moment as a result of vibrational or rotational motion
The total charge on a molecule is zero, but the nature of chemical
bonds is such that positive and negative charges do not
completely overlap in most molecules (e.g. H2O)
NB also see vibration-rotation effects...
Infrared radiation
vibrates
molecules
The electric dipole moment, p, for a pair of opposite charges of
magnitude q is the magnitude of the charge times the distance
between them, with direction towards the positive charge
Key atmospheric constituents
• Diatomic, homonuclear molecules
(e.g., N2, O2) have no permanent
electric dipole moment
• Oxygen (O2) has rotational
absorption bands at 60 and 118 GHz
due to a weak magnetic dipole
• Linear and spherical top molecules
have the fewest distinct modes of
rotation, and hence the simplest
absorption spectra
• Asymmetric top molecules have the
richest set of possible transitions, and
the most complex spectra
• Note lack of permanent electric
dipole moment in CO2 and CH4:
induced by vibration No
Permanent electric
dipole moment?
No
Clear-sky!
Atmospheric composition
N2
O2
CO2
1/l4
1-4 % at surface
Definitions of the radiation field
Page 12
(i) Irradiance or Radiant flux density or Radiant Flux per unit
area (sometimes just called flux!)
(ii) Radiance: Radiant flux/unit solid angle/unit area normal to
beam
So Irradiance ≡ Radiance integrated over
all solid angles
Upwelling irradiance:
d
d
L (,)
p
p
2
0
2
0
ddsin )cos,L(F
Special case of isotropic radiation:
F = pL
Interactions with the atmosphere
Radiance measured at a point in the atmosphere consists of
three components:
(i) Direct beam:
Beer-Lambert:
ken is the mass extinction coefficient*: sum of absorption and
scattering terms: ken = ka
n + ks
n
Ratio ksn/ke
n = wn, the single-scattering albedo
Integrate BL:
where tn is the optical depth, and total transmittance = exp(-tn)
ek dz secLdL nnn
Ln
dz
0
TOA
TOAeTOAD )exp(Ldz)k sec exp(LL nnnnn t
Spectroscopy, atmospheric
conditions, composition, optics…
Direction W’
Direction W
Requires the phase function, P(W,W’): the fraction of radiation
scattered by an individual particle from W’ into W
Generally P(W,W’) is normalised such that:
Scattered contribution to source term is then:
Interactions with the atmosphere
(ii) Emitted energy
(iii) Scattered radiation into incident direction
dz seck JdL a nnn
Source term: in
LTE Jn ≡ Bn(T)
WWWWp
nn
n
w
4
s 'ˆ)'ˆ,ˆ(P)'ˆ(L
4πJ d
1'ˆd)'ˆ,ˆ(P 4π
1
4
WWWp
And all together (again!)
Total radiance change a sum of direct, emitted & scattered
components – leads to the radiative transfer equation
'Ω̂)dΩ̂,Ω̂()P'Ω̂(Lπ4
(T))B-(1Ldsk
dLν
4π
ννe
ν
ν
nnn
ww
NB. Solar: thermal emission negligible
Thermal: scattering negligible
In the latter case, wn=0, kne = kn
a so, dskρdτ aνν Recall
ννν (T)]dτBL[dL n Schwarzchild’s Equation
(T)B)L(dτ
dν
τ
ν
τ
ν
νν ee
(s)τ
0
ν
)'τ(s)(τ
νν
(s)τ-
ν
ν
ννν 'dτ)]'[T(τB)0(L(s)L een
Incident radiance
transmitted to s
Radiance
emitted by
atmosphere and
transmitted to s
Surface term Integral emission
Tr3 = exp -t3
Tr2 = exp -t2
Tr1 = exp -t1
T2
T1
T3
Ts
Surface
term
Integral emission
dzz
zTrzTBTrLL sfc
0
, ),0(n
nnnn
Interpreting LW observations from space
If monochromatic,
Total Transmittance = Tr1 x Tr2 x Tr3
Page 17
In practice – a
warm, wet
atmosphere…
Total water vapour column = 4 g cm-2
Atmospheric ‘window’
From 500 mb
From surface
© Imperial College London Page 18
…and a cold, dry case
Total water vapour column = 0.4 g cm-2
From 500 mb
From surface
© Imperial College London Page 19
(z)
z
dTrn(z) / dz
Trn(z)
dzz
zTrzTBTrLL sfc
0
, ),0(n
nnnn
Weighting function
Indicates where radiation
is being emitted from in
the vertical
5 10 15
200
250
300 Wavenumber
Some ‘real’ weighting functions: SEVIRI
10.8 mm 6.2 mm
Clouds (and aerosol!)
Step back: spherical particles, scattering described by Mie theory, domain
governed by: size parameter: X = 2pr/l
Radius of particle
X > 1
NB. Non-spherical particles
– complicated!
e.g. large water droplets in visible - Geometric optics
© Imperial College London Page 22
Calculating key cloud/aerosol optical properties
Assumption of particle
shape + appropriate
scattering code
PROCESSING
Mass extinction coefficient, ke
Single-scattering albedo, wo
Scattering phase function
OUTPUTS
Size distribution
Chemical composition
(complex refractive index)
INPUTS
ke (
m2 g
-1)
Particle diameter (mm)
Peak extinction
e.g. Spheres: Mie theory
Spheroids: T-Matrix
Calculating key cloud/aerosol optical properties
Recall that phase function gives direction of scatter
Forward
scatter
Forward scattering in water clouds:
SW ~ 90 %, LW ~ 75 %
Single scattering albedo:
SW wn > 0.9, LW wn < 0.5
So why do clouds appear highly reflective and
cold from space?
Clouds (and aerosol) a collection of droplets: multiple scattering
SW
Redirection of beam via
multiple collisions
LW
50 % chance of abs at each collision:
~ black-body over cloud layer
NB: don’t forget underlying conditions!
The Global Energy Balance
© Imperial College London Page 25
The global annual mean Earth's energy budget for 1985-1989
in W m-2 (Kiehl and Trenberth, 1997)
Balance at
TOA
Balance in
atmosphere
Balance at
surface
The Global Energy Balance?
The global annual mean Earth's energy budget for the March
2000 to May 2004 period in W m-2 (Trenberth and Kiehl, 2008)
Incident Total Solar Irradiance measurements
Yikes!
Phew!
Kopp and Lean, 2011
Wielicki et al., 2002
Tropical (20°N-20°S) anomalies
relative to 1985-1989
Variability in tropical ERB
Unexplained semi-annual
oscillations in reflected SW
Tropical cloudiness?
Monthly mean averaging:
aliases diurnal cycle into time-
series because of orbital
sampling
Averaging period adjusted to
remove aliasing
Wong et al., 2006
Edition 3_Rev1
Decrease in satellite altitude over time: results in a
increase in measured outgoing fluxes with time
e.g. Eruption of Mount
Pinatubo, 1991: massive
amount of aerosol
injected into atmosphere
So (1 – A) / 4 = s e’TS4
SW LW
hydrological cycle,
circulation patterns,
cloud cover & type + … Large increase
in A (SW ),
smaller
reduction in e’
(LW ) due to
aerosol
albedo/ greenhouse forcing
Delay due to slow feedback processes: e.g. deep ocean warming
+ p1 + p2 + …
Climate system is incredibly complex!