( ) ( ) 2002.11
1 1 1.1 (Blackbody Radiation).............................. 1 1.2 (Stefan-Boltzmann s Law)................ 1 1.3 (Wien s Displacement Law)....................... 2 1.4 (Kirchhoff s Law)........................... 3 1.5 ( Radiative Equilibrium Temperature ).................. 4 1.6..................... 5 2 7 2.1 ( Sun )......................................... 7 2.1.1...................................... 7 2.1.2.............................. 7 2.2 (Solar radiation).................................. 8 2.2.1...................... 8 2.2.2 (Solar constant).............................. 10 3 11 3.1............................................ 11 3.1.1............................ 11 3.2 (Terrestrial Radiation)............................... 13 3.2.1 (Greenhouse effect)............................ 13 3.2.2................................ 14 3.2.3.......................... 16 A 19 B (1) (2) 25 I
1 1.1 (Blackbody Radiation) (black body) ( ) 500K ν ( λ ) T Planck Planck Planck B ν (T ) B ν dν = 2hν 3 c 2 {exp( hν (1) kt ) 1}dν B λ dλ = h =6.626 10 34 [Js] k =1.3806 10 23 [J/K] c =2.998 10 8 [m/s] T [K] ν λ ( ν = c λ ) 2hc 2 λ 5 {exp( hc (2) λkt ) 1}dλ 1.2 (Stefan-Boltzmann s Law) T Stefan-Boltzmann Planck B λ (T ) B(T ) = = 0 0 = 2k4 T 4 h 3 c 2 B λ (T )dλ 2hc 2 λ 5 {exp( hc 0 λkt x 3 e x 1 dx ) 1}dλ ( x = hc λkt ) 1
= 2k4 T 4 x 3 h 3 c 2 0 e x (1 e x ) dx = 2k4 T 4 h 3 c 2 x 3 (e x + e 2x + + e nx )dx 0 = 2k4 T 4 h 3 c 2 6 1 n 4 n=1 = 2k4 T 4 h 3 c 2 π 4 15 = 2k4 π 4 15h 3 c 2 T 4 = bt 4 πb(t )=πbt 4 = σt 4 (3) 1 Boltzmann σ = 2π5 k 4 15c 2 h 3 =5.6698 10 8 [W/m 2 K 4 ] σ Stefan- 1.3 (Wien s Displacement Law) W.Wien Wien Planck B λ (T ) λ 2hc 2 ( 5+ hc λ 6 {exp( hc λkt ) 1} λkt λ = λ max 1 5+ x me xm e xm 1 db λ (T ) =0 dλ ) =0 exp( hc λkt ) exp( hc λkt ) 1 = 0 hc λ maxkt = x m 0 x s e x 1 dx = n=1 0 x s dx = s! e nx n=1 1 = s! ζ(s +1) ns+1 (s =1, 2, 3, ) ζ s ζ(s) ζ(2) = π2 π4, ζ(3) = 1.202, ζ(4) = 6 90 2
e xm = 5 5 x m x m = 4.9651 Wien x m = hc λ max kt =4.9561 λ max =2.89 10 3 /T [m] = 2897/T [µm] (4) 1.4 (Kirchhoff s Law) ( j ν ) ( k ν ) B ν (T ) j ν = k ν B ν (T ) (5) ν ε ν = α ν (6) ε ν B ν (T )=α ν B ν (T ) (7) ε ν = α ν =1 (8) ε ν = α ν < 1 (9) Kirchhoff Kirchhoff 40 km Kirchhoff ( local thermodynamic equilibrium : LTE ) 3
1.5 ( Radiative Equilibrium Temperature ) (Radiative equilibrium temperature ; T e ) S (2.2.2 ) (S) (A) 0.30 S (1 A) πr 2 e = 4 πr 2 e σt 4 e (10) r e : T e : σ : 5.67 10 8 [Wm 2 K 4 ] πr 2 e ( ) T e T e = 4 S (1 A) 4 σ = 255 [K] (11) 288 K 3.2.1 1: 4
1.6 2: 6000 K 255 K 2(a) 6000 K 255 K (1.2 ) (1.3 ) 0.4 µm (ultraviolet ; UV) 0.4 0.7 µm (visible) 0.7 100 µm (infrared ; IR) 100 µm 0.7 3 µm (near-infrared) 3 6 µm (midinfrared) 6 15 µm (far-infrared) 15 µm (ultra far-infrared) 0.2 4 µm 0.5µm 4 100 µm 15 µm 4 6 µm (Short wave ; SW) (Long wave ; LW) 2(b) (c) 11 km 0.3µm UV 11 km O 2 O 3 2 H 2 O CO 2 H 2 O CO 2 8 12µm O 3 2 O 2 O 3 (photo dissociation) ( )(photo ionisation) 5
(d) O 3 CH 4 N 2 O H 2 O CO 2 H 2 O 6
2 2.1 ( Sun ) 1.5 10 8 km 3 6.96 10 5 km 1.99 10 35 g 5 10 6 K 5800 K 150 g cm 3 10 7 gcm 3 90% (H) 75% (He) 25% (Fe) (Si) (Ne) (C) (4H He ) 2.1.1 (photosphere) 500 km 4200 6200 K (sunspot) 2000 K (faculae) 11 8000 160000 km 4500 5000 K (choromosphere) (10 6 K) (corona) 2.1.2 3 (absorption line) (Fraunhoferline) ( ) 69 (Fe) 388nm (Na 589.6nm Mg) 518.4nm (H) 656.3nm ( ) 3 1 (Astronomical Unit ; AU) 7
3: : http://www.cc.nao.ac.jp/oao/pub/telescope/sun/sun.htm 2.2 (Solar radiation) 6000 K 6000 K ( 0.4 0.7 µm) 46 % ( 0.7 µm 100 µm) 46 % ( 0.4 µm) 7% 4 4 6000 K 2.2.1 (1) (absorption) ( 0.4 µm ) O 2 O 3 0.3µm ( 0.4 0.7 µm ) N 2 O 2 ( 0.7 µm ) 4 H 2 O CO 2 O 3 ( ) (scattering) 4 8
4: [nm] [Wm 2 nm 1 ] 6000 K (Rayleigh Scattering) (Mie Scattering) 1 1.3 9
2.2.2 (Solar constant) L =3.9 10 26 W (solar luminosity) S 1 (AU) 1.495985 10 8 km = R R S S = L 4πR 2 = 1386.7 106 [W km 2 ] = 1386.7 [W m 2 ] (12) S = 1386Wm 2 (Solar Constant) C.G.Abbot 1970 11 0.1 % 10
3 3.1 46 O 2 CO 2,H 2 O,N 2 (78 %) (20 %) 2% A CO 2 O 2 15 C A 3.1.1 (E t ) (E r ) (E v ) (E e ) (Translational Energy) (photon) ( ) (collision/pressure broadening ) (Lorents width) (Lorentz profile/shape) (Doppler broadening) 11
(Doppler profile/shape) (Void profile/shape) (Rotational Energy) OH 0-1000GHz 3 (Vibrational Energy) 300K (Electronic Energy) ( 2 ) 1. (H 2 O) (asymmetric top) - 6.3µm (8 12µm) 2. (CO 2 ) - 15µm 3. (O 3 ) 12
- 9.6µm 14µm UV-A(320-400 nm), UV-B (280-320 nm), UV-C (200-280 nm) UV-C UV-B UV-A 4. (CH 4 ) 7.6µm 6.5µm 5.2µm 3.3µm 7.6µm 1 20 5. (N 2 O) N-N-O 17µm 7.8µm 4.5µm 7.8µm 7.6µm 1 200 ( ( ) ) 2 Rayleigh Mie ( 2.2.1 (2) ) Mie Rayleigh ( ) 3.2 (Terrestrial Radiation) 3.2.1 (Greenhouse effect) 288 K 1.5 255 K 13
ε ν 0.61 61 % 39 % (H 2 O) (CO 2 ) (CH 4 ) (greenhouse effect) CO 2 90 atm 3.2.2 ( 5) 5: ( ε =1.0) I αi (1 α)i σt 4 g ( T g ) σt 4 ( T ) 14
(1 α)i + σt 4 σt 4 g = 0 (13) αi 2σT 4 + σt 4 g = 0 (14) (13) (14) T = 4 I σ, T g = 4 (1 + (1 α))i σ I α T g = 4 I/σ ( 6) 6: T 1, T 2,T 3 σt2 4 2σT 1 4 = 0 (15) σt1 4 + σt3 4 2σT2 4 = 0 (16) σt2 4 + σtg 4 2σT3 4 = 0 (17) I + σt3 4 σt g 4 = 0 (18) 15
,, I T 1 = 4 σ, T 2 = 2 Iσ 4 T 3 = 3 Iσ 4 T g = 4 4 I σ n T g = 4 n +1(I/σ) 1/4 n 3.2.3 7: (Goody,1964) τ<1, =1, 4 τ 6.5 Kkm 1 7 6.5 Kkm 1 ( 7 ) 16
8: ( Manabe and Strickler, 1964) (L+S) ( ) H 2 O(L+S), CO 2 (L+S), H 2 O+CO 2 (L+S) 8 H 2 O,CO 2 H 2 O+CO 2 7(Goody 1964) O 3 10 km 9 H 2 O H 2 O+CO 2 8 6.5K km 1 O 3 17
9: ( Manabe and Strickler, 1964) H 2 O,H 2 O+CO 2,H 2 O+CO 2 +O 3 18
A (%) N 2 78.09 O 2 20.94 Ar 0.93 CO 2 0.035 Ne 1.8 10 3 CH 4 1.7 10 4 He 5.24 10 4 Kr 1.14 10 4 H 2 5.0 10 5 N 2 O 3.1 10 5 CO 0.4 1.0 10 5 Xe 8.0 10 6 O 3 1.0 10 10 6 H 2 S 0.5 50 10 9 NH 3 0.1 10 10 8 SO 2 2.0 10 10 8 NO 2 0.1 100 10 8 H 2 O 0.1 2.0 ( ) 78 % ( ) 19
NO x 46 27 20 3.1 50 (15µm) (2.7, 4.3µm) ( 10) 20 20
10: 1958 1992 25 km 60 N 90 % 10 % CO 2 H 2 O 3 ( ) 21
(Aerosol) 10 3 10 2 µm 10 7 m ( ) 10 7 10 6 m 10 6 m 11 11: (Mie Rayleigh ) 12 ( ) ( ) ( ) 13 22
12: (CH 4 ) (rainout) 1991 SO 2 14 23
13: ( &, 1980) 14: 24
B (1) 15 16 15: ( 1) 16: ( 2) Kiehl and Trenberth, 1996 15 100 % 0.3 30 % 25
0.6 60 % 16 342W m 2 ( 1364W m 2 ) 15 49 % 26
(2) [ ] (CO 2 ) ( ) ( ) (= σt 4 T ) [ ] (CO 2 ) ( ) CO 2 27
1. 1999 1982 MACS 28