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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!
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