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2

1. Atmospheric Radiation

3

Radiation ()






Radiation: electromagnetic wave
Light, photon, visible light, infrared light, solar radiation,
Maxwell equation
Velocity, wavelength, frequency (/time), wavenumber (/distance) : = c/, E= hElectric permitivity, magnetic permiability
Poynting vector
P = E  H*

=kE = E0 ei( tkx )

EEEC1k1
μc=iEE 2
2E = cEμP=k  = 2   dt  kdx = constdx= kc
dt

HH

HHkC3
EC2

HE
H=i  H =  E
tAmpere’s law (1820s)   E =  μ HtAmpere’s law

Faraday’s law (1831)

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Radiance
Radiance (, W/m2/str/m): L

dE = L (e)d  dtdSd
Plane parallel lighte

L(μ,  ) = F0 ( μ  μ 0 ) (  0 )dW

Isotropic light

L(μ,  ) = LPdS
dS: Receiver area
d: Solid view angle

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Flux, irradiance () Plane flux, hemispherical flux, irradiance1200

F =  d μ  d L( μ,  )μ Plane parallel radiation field

F = μ 0 F0
 Isotropic fieldF = LZenith

(, )L(e) Wavelength integration,broadband fluxes

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Reflectance and transmittance Flux reflectivity(), reflectance, albedo

Frr=Fin Transmissivity (), absorptivity ()FtFat=, a=FinFin
 Radiant energy conservation law

r+t+a = 1FrFin

FaFt

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Coordinates

Zn Polar coordinatese = (sin  cos  , sin  sin  , cos  )d = sin  d d = d d μdS

μ = cos

YP Nadir () and zenith () Upward (welling) and downward(welling) Nadir system
μ < 0: upwardμ > 0 : downward

Y



Z8

Blackbody radiation 1
Quantum photon theory by M. Plank’s in 1902

ce = 0, h , 2h , 3h ,...
 Boltzman’s law
p = exp()k BT
 Definition of temperature

=TT

Mean energy is same for each degree of freedom(Equi-partition law of energy)<  >=h nh exp(nh / k T ) = h exp(h ) = exp(nh / k T ) 1 exp(h ) exp(h )  1
BB



1
kBT

Number of quantum sates of photon inside a box L^32 2 n=, (n = 0, ± 1, ± 2,...)
L4 k 2 dk
V 24 V 2g( ) ==kdk=
 d(2 / L)3 2 2c3k=

=2 polarization states: 2g()

kz
kykx

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Blackbody radiation 2
Radiant energy density with two polarization states Plank Function for Blackbody radiation
 Radiant energy density (W/m3)u (T )d = 2 <  > g( )

d 8
h
= 3
 2 d
Vc exp(h / k BT )  1

u dV =  dLd dt =  d
4

4

L4
dV =LdVcc2h 3
L = B (T) = 2c [exp(h / kB T )  1]

L(x+dx)dds

Plunk functionuds
L(x)dds

dx=cdt10

Blackbody radiation 3
 Blackbody radiationL = B (T ) =2h2c [exp(h / k BT )  1]
3

wavelength: frequency: = 2/wavenumber: = c/, ’= 1/ (cm)

d c
2hc 2
B (T ) = B (T )= 2 B (T ) = 5d  [exp(hc / kB T )  1]
 Wien’s displacement law
 Stefan-Boltzman’s law

 max T = 2900 ( μmK)

F =   B d = T 4
02 5 k B4
82 4
==5.67
10W/mK15h3 c 2

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Emission () of the radiation
Local Thermodynamic Equillibrium (LTE) state z<50km
 Kinetic temperature T = Internal state temperature Ti
 Electronic - Vibration - Rotation - Translation
n( )  exp(Boltzman’s lawKirchihoff’s law; absorptivity)k BT

E(T ) = aB(T)Emissivity ()E(T) = B(T) = a
 

Solar and terrestrial radiation
Satellite bands12
Solar radiation
Shortwave radiation()
Terrestrial radiation()
Longwave radiation()Thermal radiation

Microwave

UV

Visible window

IR window

Goody and Yung (1989)

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14


 6000K

 15

Color of the environment

Invariance principle of radiance

16 Emitted radiation and recieved radiance Point source problem

d0

0

RL0d

L(0)

dS
dS0

L0 dS0 d0 = LdSd
dS = R 2 d0 , dS0 = R 2 ddS
L = L0 , F = Ld = L0 20
R17

Solar constant () Radiative flux at the sun surface: F (W/m2)
 Radiative flux at the earth's orbit: S (W/m2)
 Radius of the solar disk: rF (W/m2)

 Angular radius () of the solar disk: rdisk
 Distance between earth and sun: Rps

Es4 r 2 F22
4
S===r
F=r

T
disc
discsun4 Rps2
4 Rps2TS In case of Rps= mean orbit: S is called Solar constantrdisk=D/2=16’
Ts=5790K, S=1370W/m2r

rdisk
Rps

Variation of the solar output

NASA (EO 2004)

18    

19
U= 70S= 1.5

Lean et al. (2000)

Lean et al. (2002)

Sun spot variation

W/m220U= 100
S= ? W/m2
Solar activity periods
11, 22 year cycles < 2 W/m2
Large UV variation
55, 80 year cycles% !#
(/+02  34
,'1)2  35
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21



Statue of Prof. Boltzman

1948



   

Prof. Helmuth Horvath

22

Newton’s 2nd law

Boltzman’s law

dv
m=Fdt)n( )  exp(k BT

Statue of Prof. Boltzman
23

Prof. Helmuth Horvath24

25Ludwig Boltzmann (1844-1906)

Ernst Mach (1838-1916)

Christian Doppler (1803-1853)

Erwin Schrödinger (1887-1961)
Nobel prize
Johann Josef Loschmidt (1821-1895)

26

John William Strutt Lord Rayleigh

1842-1919, Essex, England
Trinity College, Cambridge
Prof. Stokes
Maxwell’s 1865 paper
Rayleigh's theory of scattering, published in 1871, was the first correct
explanation of why the sky is blue. In the same year he married Evelyn
Balfour, the sister of Arthur James Balfour who was to be a leading
member of the Conservative Party for 50 years and Prime Minister ofBritain 30 years later. Rayleigh had been a student at Cambridge withArthur James Balfour and through him had met Evelyn. Shortly after
their marriage Rayleigh had an attack of rheumatic fever which nearlybrought his scientific activities to a premature end. He was advised totravel to Egypt and indeed he did just this with his wife. They sailed down
the Nile during the last months of 1872 and early 1873, returning toEngland in the spring of 1873.

27

Acceraration of gravity
9.80665 m/sec2
Speed of light
2.9979e8 m/sec
Boltzman constant
1.3807e-23 J/K
Plank constant
6.6261e-34 Jsec
Avogadro number
6.0221e23 /mol
Volume of ideal gas at 0｡C and 1 atom
2.241e4 cm3/mol
Absolute temperature
273.15 K (0C)
Gas constant
8.314 J /deg/mole
Stephan-Boltzman constant
5.670e-8 W /m2 K4
Molecular weight of dry air
28.964 g/mol
Latent heat of vaporization at 273K
2.500E6 J/Kg
1 bar 10^6 dyne/cm2 = 10^5 N/m2 = 10^5 Pa
Earth's radius
6370 km
Mean solar angular diameter
31.99 minutes of arc
Air= 0.78083 (N2)+0.20947 (O2)+ 0.00934 (Ar)+0.00033 (CO2) by volume ratio
Globe= 0.708 (Ocean)+ 0.292 (Land) by area ratio
Molecular weight of air
29 g/mole

Textbooks and reviews

$1982(!'%!&   "
Chandrasekhar, S., 1960: Radiative transfer. Dover, 393pp.
Goody, R. M., and Y. L. Yung, 1989: Atmospheric radiation, Theoretical Basis.
Second Edition, Oxford Univ. Press, 519pp, ISBN 0-19-505134-3.
Houghton, J., 1977, 2001 (3rd): The Physics of Atmospheres, Cambridge
University Press.
IPCC, 1990: Climate Change, The IPCC Scientific Assessment. Eds. J. T.
Houghton, G. J. Jenkins, and J. J. Ephraums, Cambridge Univeristy Press, 364 pp.
IPCC, 1996: Climate Change 1995, The Science of Climate Change, Eds. J. T.
Houghton, L. G. Meira Filho, B. A. Callander, N. Harris, A. Kattenberg, and K.
Maskell, Cambridge Univ. Press.
IPCC, 2001: Climate Change 2001: The Scientific Basis. Houghton, J.H., Y. Ding,
D.J. Griggs, M. Noguer, P.J. Linden, X. Dai, K. Maskell and C.A. Johnson (eds.),
Cambridge University Press, Cambridge, UK, 881pp. Junge, C. E., C. W. Chagnon,and J. E. Manson, 1961: Stratospheric aerosols. J. Meteor., 18, 81-108.
IPCC, 2007
Liou, K.-N., 1980, 2002 (2nd)An introduction to atmospheric radiation. AcademicPress.
柴田 清孝!&#!& 
Van de Hulst, H. C., 1957: Light scattering by small particles. Dover, 470pp.

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