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!