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Chapter 2 基本原理 - atmos.pccu.edu.t · 2-3 2-1-3 輻射強度...
Transcript of Chapter 2 基本原理 - atmos.pccu.edu.t · 2-3 2-1-3 輻射強度...
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2-1
CChhaapptteerr 22
2-1 2-1-1
c ~= (2.1)
c 1~ == (2.2) (wave length) ; ~ (frequency)
(wave number) ; c (= 2.99793*108m sec-1) m 10-6 m () (micro-meter) ; nm10-9 m (nano-meter)
()10-10 m
UL ; IR
alpha beta gamma delta epsilon zeta eta theta kappa lambda mu /mju/ nu /nu/ or /nju/ xi /ksi/ rho sigma tau phi chi psi omega
Fig 2.1: The electromagnetic spectrum in
terms of wavelength in m , frequency in GHz, and wavenumber in cm
-1. [Liou02,
Figure1.1]
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2-2
2-1-2 solid angle
2r= (2.3)
=
= 24 r
= 4
Fig2.3 )sin)(( drdrd = (2.4) ddrdd sin2 == (2.5)
Fig 2.2: Definition of a solid angle , where denotes the area and r is the distance. [Liou02, Figure1.2]
Fig 2.3: Illustration of a differential
solid angle and its representation in
polar coordinates. Also shown for
demonstrative purposes is a pencil of
radiation through an element of area dAin directions confined to an element of
solid angle d . Other notations defined in the text. [Liou02, Figure1.3]
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2-3
2-1-3
(dA) d()(dt)
+d dtddAdIdE = cos (2.6)
dAdtdddEI
=
cos)( (2.7)
() Defining (F) (() )
= dIF cos (2.8)
=
dAdtddE
(2.5)
( ) =
ddIF2
0 0
2 sincos,
(2.9)
( ) ,I (isotropic radiation)
=
ddIF2
0 0
2 sincos
(2.10)
I = (2.11) Defining (F) (() )
=
0dFF (2.12)
Defining ()(f) (flux) ( = w )
= AFdAf (2.13)
Table 2.1 [Liou02, Table1.1]
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2-4
2-1-4 () (Scattering)
( ax 2= )
Rayleigh scattering () 1x (geometric optics)
Figure 2.5: Multiple scattering process
involving first(P), second(Q), and third (R) order scattering in the direction denote by d.[Liou02 ,Figure1.5]
Fig 2.4: Demonstrative angular patterns of
the scattered intensity from spherical
aerosols of three sizes illuminated by the
visible light of 0.5 m ,(a) 10-4 m , (b) 0.1 m , and (c) 1 m . The forward scattering pattern for the 1 m aerosol is extremely large and is scaled for
presentation purposes. [Liou02, Figure1.4]
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2-5
2-1-5 (extinction cross section) (extinction coefficient)
(m2)
0Ff = ( see (2.13) )
0F
f
n = (m-1)
n 2-2
(blackbody radiation):
()
(homogeneous)(unpolarized)(isotropic)
2.6
2-2-1 Plancks ()
nhE ~= (2.14)
)1(2
5
2
= Thce
hcB (2.15)
BPlancks ( I)
h Plancks = 6.626810-34 Jsec
Boltzmann = 1.3806810-23 Jdeg-1
~ n
depends on T() ()(2.15)
Figure 2.6: A blackbody radiation cavity to
illustrate that absorption is
complete.[Liou02,Figure1.6]
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2-6
Tm
310*897.2 =
2-2-2 Stefan-Boltzmann -
40 )()( bTdTBTB ==
(2.16)
3244 15/2 hckb =
(isotropic) (see (2.11))
( ) 4)( TTB == (2.17)
(Stefan-Boltamann ) = 5.67*10-8 Jm-2
(T)
2-2-3 Wiens -
0)( =
TB (2.18)
(2.19)
2-2-4 Kirchhoffs
(absorption)(emission) ( ) ( ) tyabsorptiviAemissivity = (2.20)
=
Fig 2.7: Blackbody
intensity (Planck
function) as a
function of
wavelength for a
number of emitting
temperatures.
[Liou02, Figure1.7]
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2-7
=
1== (2.21)
1
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2-8
(/ = = )
dsJkdI =
Combining (2.23), (2.24) and (2.25)
dsjdsIkdI += (2.26)
dsJkdsIk += (2.27)
JIdsk
dI+= (2.28)
NoteWhen radiation passes through a medium, the change of radiation is determined
by
I extinction of incident radiation, including absorption and scattering by
medium
J radiation sources in medium, including emission and multiple scattering
(2.28)
() ds (k)()
(ds)(I)
(J)
Fig 2.8: Depletion of the radiant intensity in traversing an extinction medium.[Liou02, Figure1.13]
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2-9
2-3-2 Beer-Bouguer-Lambert (Beers) Assuming I(0) at s = 0, I(s1) at s = s1
From (2.23)
dskI
dI
=
( )
( ) =
11
00
1 s
sI
I
dskdII
( )
( ) =11
0 0ln
s
I
IdskI s
( )( )
=
1
01 exp
0s
dskI
sI
( ) ( )
=
1
01exp0
s
dskIsI
(2.29)
If the medium is homogeneous, defining (path length)
=1
0
sdsu
uk
eIsI = )0()( 1
the change of the radiation exponentially depends on the path length of the
medium.
Defining (optical depth) ()
( ) 1
010,
s
dsks
(2.30)
(note ( ) dskssd =,1 )
( ) ( ) ( )0,1 10 s eIsI = (2.31)
( )
Note s ( 0) dskssd ),( 1 =
Defining (transmissivity)
( )( )0
I 1
Is
=
-
2-10
( )0,1se= (2.32)
For () ( )0,111 s eA
== (2.33)
For
1=++ RA (2.34)
R (reflectivity)
Note
2-3-3 Schwarzschild (2.38)
Considering (e.g.) Planck
( )( )TB J in(2.28) using(2.30) ( )( ) ( ) ( )( )sTBsIssdsdI
+= ,1
(2.35)
(2.35) ( )sse ,1
( ) ( ) ( ) ( ) ( )( ) ( )( ) ( ) ( )ssdesTBssdesIsdIe ssssss ,, 1,1,, 111 = ( ) ( ) ( )( ) ( ) ( )ssdesTBdesI ssss ,1,, 11 =
( ) ( ) ( ) ( ) ( )( ) ( ) ( )ssdesTBdesIsdIe ssssss ,1,,, 111 =+
( ) ( )( ) ( )( ) ( ) ( )ssdesTBsIed ssss ,1,, 11 = (2.36)
(2.36) from 0 to s1
( ) ( )( ) ( )( ) ( ) ( ) = 1 1 110 0 1,, ,
s s
ss
ss ssdesTBsIed
(2.37)
( ) ( ) ( )( ) ( ) ( ) =
11
11
0 1,
0
, ,s
ss
s
ss ssdesTBsIe
Fig 2.9: Configuration of the optical thickness defined in Eq. (1.4.15). [Liou02, Figure1.14]
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2-11
( ) ( ) ( ) ( )( ) ( ) ( ) =+1
11
0 1,0,
1 ,0s
ss
s
ssdesTBeIsI
( ) ( ) ( ) ( )( ) ( ) ( ) =1
11
0 1,0,
1 ,0s
ss
s
ssdesTBeIsI
(2.38)
(2.28) 2-3-4
point ( ) ,;z ()
(2.28) ( ) ( ) ( )zJzIdskzdI ,;,;,; +=
( ) ( ) ( )zJzIdzkzdI ,;,;
sec,;
+=
( ) ( ) ( )zJzIdzkzdI ,;,;,;cos += (2.39)
Defining (normal optical depth)
=
zzdk ( dzkd = )
( )0= z
z
(2.39) ( ) ( ) ( )JIddI ,;,;,; = (2.40)
cos=
Following section 2-3-3 (2.40) e
( )0> ( from to * )
Fig 2.10: Geometry for plane-parallel
atmospheres where and denote the zenith and azimuthal angles,
respectively, and s represents the
position vector. [Liou02, Figure1.15]
Fig 2.11:
Upward ( ) and downward ( ) intensities at a given level and at top ( 0= ) and bottom ( = ) levels in a finite,
plane-parallel atmosphere.
[Liou02, Figure1.16]
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2-12
( ) ( ) ( ) ( ) ( )
+= ** ,;,;,; *
deJeII
(2.41)
( )0> ( from 0 to ) ( ) ( ) ( ) ( )
+=
deJeII
0,;,;0,; (2.42)
(2.28) 1st term of r.h.s. (outside of to ) 2end term of r.h.s level of
(homogenous)
2-4
Fig 2.12(a) Blackbody radiation curves for temperature characteristic of the Suns surface
and upper levels on Earths atmosphere from which infrared radiation escape to space.(b)
Absorption of radiation at each wavelength if the beam passes through the entire atmosphere
from top to ground level or vice versa. (c) As in b, but for radiation passing from the top
of the atmosphere to 11 km or vice versa. After Trenberth (1992) and Goody and Yung (1989).
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2-13
2.4-1 () 2.4-2 ()
Fig 2.13: Solar irradiance curve for a 50 cm
-1spectral interval at the top of the atmosphere (see
Fig.2.9) and at the surface for a solar zenith angle of 60oin an atmosphere without aerosols or
clouds. Absorption and scattering regions are indicated. See also Table 3.3 for the absorption
of N2O, CH4, CO, and NO2. [Liou02, Figure3.9]
Fig 2.14: Theoretical Planck radiance curves for a number of the earths atmospheric
temperatures as a function of wavenumber and wavelength. Also shown is a thermal infrared
emission spectrum observed from the Nimbus 4 satellite based on an infrared interferometer
spectrometer. [Liou02, Figure4.1]