放射過程によって調節された二酸化炭素氷雲による古火星大気の温室効果

The greenhouse effect of radiatively adjusted CO 2 ice cloud in aMartian paleoatmosphere MITSUDA Chihiro Division of Earth and Planetary Sciences,Graduate School of Science, Hokkaido University2007 12

i, , , , , . 38 . ., . , . , , ., , . ., . , , , . , 75 % 2 , (10 5 – 10 7 kg −1 ) 3 – 20 µm . , 100 , (1 ) , .

ii, , 20 – 30 K., , 10 4 kg −1 , ., , ., . ., , , . , , ., , ,. , .38 2 , . . , , . , . 100 – 300 , . , ., ,Habitable Zone . 10 38 , 2.9 AU .

iii. F, G, K, M , , .

v 1 11.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3.1 . . . . . . . . . . . . . . . . . . 21.3.2 . . . . . . . . . . . . . . 21.3.3 . . . . . . . . 31.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 112.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3 193.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.2 . . . . . . . . . . . . . . . . . . . 223.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.5.1 . . . . . . . . . . . . 323.5.2 . . . . . . . . . . . . . . . . . . . . . . . . . 343.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.7 . . . . . . . . . . . . . . . . . . . . . . . 393.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.8.1 . . . . . . . . . . . . . . . . . . . . . . . . . 413.8.2 . . . . . . . . . . . . . . . . . . . . 45

vi3.8.3 Habitable Zone . . . . . . . . . . . . . . . . . . . . . 51 4 57 59 A 61A.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61A.2 . . . . . . . . . . . . . . . . . . . . . 62 B 65B.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65B.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66B.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66B.4 CO 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67B.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 C 69C.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69C.2 . . . . . . . . . . . . . . . . . . . . . . . . . . 71C.2.1 . . . . . . . . . . . . . . . . . . . 74C.2.2 . . . . . . . . . . . . . . . . . . . 75C.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78C.3.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78C.3.2 CO 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 790–300 cm −1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 791150–1850 cm −1 . . . . . . . . . . . . . . . . . . . . . . . . . . 80C.3.3 H 2 O . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81C.3.4 . . . . . . . . . . . . . . . . . . . . . . . . . . 82C.3.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83C.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87C.4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87C.4.2 Eddington . . . . . . . . . . . . . . . . . . . . . . . . . . . 88C.4.3 δ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 D k 93D.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

viiD.1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93D.1.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 . . . . . . . . . . . . . . . . . . . . . . . . . . 94 . . . . . . . . . . . . . . . . . . . . . . . . . . 95 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96D.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96D.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98D.3.1 . . . . . . . . . . . . . . . . . . . . . . . . . 98D.3.2 . . . . . . . . . . . . . . . . . . . . . . . . . . 100D.3.3 . . . . . . . . . . . . . . . . . . . . . . . . . 101 E 105E.1 . . . . . . . . . . . . . . . . . . . . . . 105E.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106E.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 111 1.1 . Viking Orbiter . 160 km. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.2 (, Gouth 1981) , (). , 0.216 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.3 . . . . . . . . . . . . . . . . . . . . . . . 81.4 . Colaprateand Toon (2003), Fig 9 . . . . . . . . . . . . . . . . . . . . . . 92.1 . . . . . . . . . . . . . . . . . . . . . . 122.2 2 , . 1 k . , (), (), () . 13

viii 2.3 . () .) (Komabayashi, 1970). -100 ◦ C ( 1 ) . ) .http://www.exo.net/˜pauld/Mars/4snowflakes/martiansnowflakes.html. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.1 () () () . . . 2 , 10 7 kg −1 . (a) 0 , (b) 10 3 , (c) 10 4 , (d) 10 5 , (e) 10 6 , (f)10 7 , (g) 10 8 , (h) 10 9 . . . . . . . . . . . . . . . . . . . 203.2 (a) () () . (b) () () . , . 2 , 10 7 kg −1 . . 213.3 . . (a) , (b) , (c) , (d) . (a) . . . . . . . . 253.4 () () . . . . . . . . . . . . . . . . . . . . . . . 263.5 . . , 10 3 kg −1 (), 10 4 kg −1 (), 10 5 kg −1 (), 10 6 kg −1 (),10 7 kg −1 (), 10 8 kg −1 () . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.6 (a) () () . (b) () () . , (a) 10 3 kg −1 , (b) 10 4 kg −1 , (c) 10 5 kg −1 , (d) 10 6 kg −1 , (e)10 7 kg −1 , (f) 10 8 kg −1 , (g) 10 9 kg −1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

ix3.7 . . (a) , , , . . (b) , (c) . . . . . . . . . 293.8 . . , 0.5 (), 1 (), 2 (), 3 (), 5 (), 10 () .. . . . . . . . . . . . . . . . 303.9 . , 10 3 kg −1 (), 10 4 kg −1 (), 10 5 kg −1 (),10 6 kg −1 (), 10 7 kg −1 (), 10 8 kg −1 () . , . . . . . . . . . . . . 313.10 . , 0.5 (), 1 (), 2 (), 3 (),5 (), 10 () . . . . . . . . . . . . . . . 333.11 . , 10 3 kg −1 (), 10 4 kg −1 (), 10 5 kg −1 (), 10 6kg −1 (), 10 7 kg −1 (), 10 8 kg −1 () . . . . . . . . . . . . . . . . . . . . 363.12 . .. . . . . . . . . . . . . . . . . . 383.13 . , 10 −5 kg −1 (), 10 −6 kg −1 (), 10 −7 kg −1 (), 10 −8 kg −1() . , , Pollack et al. 1989 , Kasting 1991 () . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

x 3.14 . , 2.0 (5.37 × 10 5 kg m −2 ) . , . (a) , , , . (b) , (c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.15 3.14 . , 2 . . . . . . . . . . . 433.16 . . . . . . . . . . . . . . . . . . . 433.17 . . . . . . . . . . . . . . . . . . . 443.18 . (110 W m −2 ) . ,: 7200 K (F0 ), : 6000 K (G0 ), : 5780 K (Sun), : 5300K (K0 ) : 3900 K (M0 ) . . . . . . . . . . . . . . . . . 463.19 (). . . . . . . . . . . . . . . . . . . 473.20 . , . . . . . . . . . . . . . . . . . . . . . . . 483.21 . . (a) , , , . (b) , (c) . . . . . . . . . . . . . . . . . . . . . . . . . . 493.22 . , : 10 5 kg −1 , : 10 6 kg −1 , :10 7 kg −1 , : 10 8 kg −1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

xi3.23 . 10 6kg −1 , 10 . .(a) , , . (b) , (c) . . . . . . . . . . . . . . . . . . . . . . . 523.24 . , 10 5 kg −1 10 6 kg −1 10 7 kg −1 . 10 , . . . . . . . . . . . . . . . . . . . . . . 533.25 . , 10 5 kg −1 , 10 6 kg −1 , 10 7 kg −1 , 10 8 kg −1 . , () , () . 10 , 5.37 × 10 3 K . , (a) 1.29 m s −2 (b) 3.72 m s −2(c) 9.80 m s −2 (d) 17.4 m s −2 . . . . . . . . . . . . . . . . . . 543.26 . , 10 5 kg −1 , 10 6 kg −1 , 10 7 kg −1 . , () , (). (a) M0 (b) K0 (c) G0 (d) F0 . 10 , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55C.1 . , j . . . . . . . . . . . . . . 72C.2 CO 2 ice . Warren (1986). . . . . . . . 84C.3 H 2 O . , . Hale and Querry (1973), Warren (1984) . . . . . . . . . . . . . 85C.4 CO 2 (:, :, : ). Mie . (: 1 µm, : 5 µm, : 10 µm). . . . . . . . . . . . . . . . 86D.1 ) . ) () (). . . . . . 97

xii D.2 HITRAN 2004 (Rothman et al. 2005). 99E.1 . . . . . . . . . 106E.2 . , . . . 107E.3 . . . 10 . . . . . . . . . . . . . . . . . . . . . 108E.4 CO 2 . . . . . . . . . . . . . . . . . . . . . . . . 109

1 1 1.1 . , . , , .-, . .1.2 4 , . 43 % , 216 K 40 K . , 1/200 , 218 K ( Houghton 2002). , , 273 K ,

2 1 .1.3 1.3.1 , 38 , , . , ( 1.1) , km , . , (Jakoskyand Phillips 2001). , , (Golombek and Bridges 2000). , ( 1997).1.3.2 , . , 75 % (Newman and Rood 1977, Gough 1981). , 198 K 20 K , , 75 K ( 1.2).. Pollack et al. (1987) , , 5 , , ., , , ,

1.3 3 (Kasting 1991)., , . Squyres and Kasting (1994) , . (Kasting 1991) , , , . , (Pollack et al. 1987, Sagan and Mullen1972, Kasting 1997a), ,. Sagan and Chyba (1997) , , , , (Kasting 1997a).1.3.3 , (Kasting 1997b). , , (Pollack et al. 1987). Kasting (1991) , , . , , (Forget and Pierrehumbert 1997, 1.3). () ., 7–20 µm (Pierrehumbet and Erlick 1998). 5 µm , , 20 µm , , . , , , , (Mischna et al. 2000, Yokohata et al. 2002).

4 1 , . Colapreteand Toon (2003) , 1 , . , , , , . , . , , .1.4 , . , . , , , . , () () , . , , ., , . , , , ., , . , , ., , , . , ,

1.5 5.1.5 2 , 1 , . 3 , , . , , . , , , . 4 .

6 1 1.1. Viking Orbiter . 160 km.

1.5 7Effective temperature (K)220210200190(Gough 1981)Solar LuminosityEffective temperature1.00.90.80.74 3 2 1 0Time (Gyr ago)Solar luminosity(present:1) 1.2 (, Gouth 1981) , (). , 0.216 .

8 1 solar radiationinfrared radiation 1.3.

1.5 9Pressure (bar)0.00010.0010.010.1C O 2 saturat ewithout CO 2 condensation(Pollacek et al. 1987)with CO 2 condensation(Kasting 1991)* but neglect cloud optical propertieswith Optimal cloud(Forget and Pierrehumbert 1997)12At 75% present solar flux, CO 2 -H 2 O atmosphere10140 180 220 260 300Temperature (K) 1.4. Colaprate andToon (2003), Fig 9 .

11 2 2.1 , .. . , , , . , , . , , . , , . , . . ( 2.1). , , 1 . , , , . , , . .

12 2 , . Toon et al. (1989) . , , (Coakley and Chylek 1975, Toon etal. 1989). δ-Eddington (Joseph et al. 1976) ., k . 8 (10 −6 – 10 ), 6 (100 – 350 K) , , . 50 cm −1 1 , 5 k HITRAN2004, HITEMP (Rothman et al. 2005) . initial vertical profile(temperature and cloud mass mixing ratio)radiative heating/coolingCO 2 condenses/evaporatesconvective adjustmentconvergence conditionNoYesequilibrium profile 2.1

2.1 13, 25 cm −1 , 300–600 cm −1 ν 2 wing , 500 cm −1 . , Gruszka and Borysow (1997) (, 0–300 cm −1 ), Kasting et al. (1984a) (, 1150–1800 cm −1 ), Roberts et al. (1976) (, 350–1250 cm −1 ) ., 2.1 ( Liou 1992). (Warren 1986) ( Bohren and Hoffman 1998). , . ( 2.3), . , . , , . 1e+081e+0610000Optical Depth10010.010.00011e-061e-081e-100 500 1000 1500 2000 2500 3000wavenumber [cm -1 ] 2.2 2 , . 1 k . , (), (), () .

14 2 , . , , . , , . , CO 2 · 5.75 H 2 O , , ., , .dT ∗ wetdz= dT sat,CO 2(z)dpdpdz(2.1) z , T ∗ wet , T sat,CO 2, p . , (, Houghton 2002). , ,.dT ∗ drydz= − g [1 + L ] [H 2 Op sat,H2 OM H2 O1 + L H 2 OM H2 OC p pRTpRT] −1M H2 OL H2 O(2.2)M CO2 C p T 2.3 . ( ) . ) (Komabayashi, 1970). -100 ◦ C ( 1 ) . ) . http://www.exo.net/˜pauld/Mars/4snowflakes/martiansnowflakes.html .

2.2 15 L i , p sat,i , M i i , , , , g, R, C p, , . Antoine ,log p sat,CO2BmmHg = A −C + (T − 273.15)A = 27.48, B = 3103.39, C = −0.16(2.3) Wagner log p sat,CO 2= Ax + Bx1.5 + Cx 4 + Dx 6p c 1 − x(2.4)x = 1 − T T c, P c = 73.8 , T c = 304.1 K,A = −6.927.48, B = 1.197, C = −3.126, D = −2.994. (p sat,H2 O(T ) = 2.341 × 10 11 exp − 5399 )T(p sat,H2 O(T ) = 3.438 × 10 12 exp − 6132 )TPa (at T > 273.15 K) (2.5)Pa (at T < 273.15 K) (2.6) ( 1986), , 0.1 µm 1 % (E.1 ), .2.2 , 25 . . , , . 50 –10 4 , , 10 −8 K s −1 . 2.1 2.2 . 38 , 0.75 . , , . , 2 (Kasting 1991) . , (Mischna et al. 2000) . ,

16 2 10 7 kg −1 . , .

2.2 17 2.1 - σ 5.67 × 10 −8 J m −2 N A 6.02 × 10 23 mol −1 k 1.38 × 10 −23 J K −1 c 2.997 ×10 8 m s −1 h 6.626 ×10 −34 J s −1 R 8.31 J K −1 C p 860.0 J K −1 kg −1CO 2 M CO2 44.0 ×10 −3 kg mol −1CO 2 η 8.0×10 −6 Pa s 170 K, CO 2 α 1.62 ×10 −24 m −3 Marchetti and Simili (2006)CO 2 L CO2 5.73×10 5 J kg −1CO 2 ρ ice 1.565 ×10 3 kg m −3 CO 2 C ice 1.7 ×10 3 J kg −1H 2 O M H2 O 18.0 ×10 −3 kg mol −1H 2 O L H2 O 2.834×10 6 J kg −1 at T < 273 K2.495×10 6 J kg −1 at T > 273 K 2.2 () () P s 2.0 0.1 – 10.0 ( kg −1 ) N CCN 10 7 10 3 – 10 9 (m s −1 ) g 3.72 1.29 – 17.4 () (W m 2 ) 1.11 × 10 2 1.11 × 10 2 – 1.6 × 10 1 () (K) T ⊙ 5.379 × 10 3 3900 – 7200 A s 0.2 ( ◦ ) θ 60

19 3 3.1 , , , 3.1 . ( 5.37× 10 3 K, 1.11 × 10 2 W m −2 , 3.72 m s −2 , 2 10 7 kg −1 ) , 10 3 . , Kasting 1991 . , , , . ., . ,. ( 3.1b, 3.2). , , .. , . 10 4 , . , , 10 5 ( 10 ) ( 3.1d)., .

20 3 (a)(b)0.001CO 2 saturateTime: 0 [sec]0.001CO 2 saturateTime: 10 3 [sec]0.010.01Pressure [bar]0.1Pressure [bar]0.11.01.02.0140 180 220 260Temperature[K]0 2 4 6 -0.2 0 0.2Parcitle size [µm] Heating rate [K day -1 ]2.0140 180 220 260Temperature[K]0 2 4 6 -0.2 0 0.2Parcitle size [µm] Heating rate [K day -1 ](c)(d)0.001CO 2 saturateTime: 10 4 [sec]0.001CO 2 saturateTime: 10 5 [sec]0.010.01Pressure [bar]0.1Pressure [bar]0.11.01.02.0140 180 220 260Temperature[K]0 2 4 6 -0.2 0 0.2Parcitle size [µm] Heating rate [K day -1 ]2.0140 180 220 260Temperature[K]0 2 4 6 -0.2 0 0.2Parcitle size [µm] Heating rate [K day -1 ](e)(f)0.001CO 2 saturateTime: 10 6 [sec]0.001CO 2 saturateTime: 10 7 [sec]0.010.01Pressure [bar]0.1Pressure [bar]0.11.01.02.0140 180 220 260Temperature[K]0 2 4 6 -0.2 0 0.2Parcitle size [µm] Heating rate [K day -1 ]2.0140 180 220 260Temperature[K]0 2 4 6 -0.2 0 0.2Parcitle size [µm] Heating rate [K day -1 ](g)(h)0.001CO 2 saturateTime: 10 8 [sec]0.001CO 2 saturateTime: 10 9 [sec]0.010.01Pressure [bar]0.1Pressure [bar]0.11.01.02.0140 180 220 260Temperature[K]0 2 4 6 -0.2 0 0.2Parcitle size [µm] Heating rate [K day -1 ]2.0140 180 220 260Temperature[K]0 2 4 6 -0.2 0 0.2Parcitle size [µm] Heating rate [K day -1 ] 3.1 () () () . . . 2 , 10 7 kg −1 . (a) 0 , (b) 10 3, (c) 10 4 , (d) 10 5 , (e) 10 6 , (f) 10 7 , (g) 10 8 , (h) 10 9 .

3.1 21Surface Temperature [K]Radiative cooling rate [K s -1 ]260(a)250CO 2icepath240230Surface Temperature2200.1(a)Troposphere0Cloud layer-0.110 3 10 4 10 5 10 6 10 7 10 8 10 9time [s]0.100.050.00CO 2Icepath [kg m -2 ] 3.2 (a) () () . (b) () () . , . 2 , 10 7 kg −1 . . 10 7 ( 100 ) . , . , . . , . 18 – 50 km 3 µm, 0.05 ( 20 µm) , 251 K . 26 K.. . .

22 3 3.2 , , .F ↓ S (1 − A) + F ↓ IR − F ↑ IR − Q conv = 0 (3.1) F , ↑ , ↓ , , S , IR , . A , Q conv ., .∫ ∞Q conv = − C p ρ dT ∫ Ps0 dt dz = − dTC p0 dt. T s dPg(3.2)σT 4 s = F ↓ S (1 − A) + F ↓ IR − Q conv (3.3). , 2 . 1 F ↓ S (1 − A) + F ↓ IR. . 1 , Q conv ., 6 W m −2 . , , , . 23 W m −2 . 4 ., , , . . , 22 K . 26 K .

3.2 23, , ., . ,.

24 3 3.3 3.3 . 3.1 2 . , 270 K , ., , 10 3 kg −1 10 8 kg −1 , 200 µm 2 µm . 10 5 kg −1 ., , , . , , , . 10 5 kg −1 . 15 µm , . -, 9, 12 25 µm ( 3.4). , . , ., , . , , 10 8 kg −1 .. , 1 µm , ( 3.6 g)., , ,

3.3 25.Surface Temperature [K]Particle size[µm]Icepath[kg m -2 ]300280260240220200100101110 -3(a)(b)(c)10 3 10 4 10 5 10 6 10 7 10 8 10 9Number concentration of Cloud Condensation Nuclei [kg -1 ] 3.3 . . (a) , (b) , (c) , (d) . (a) .

26 3 upward infrared radiation flux [W m -2 (cm -1 ) -1 ]0.250.20.150.10.050top of atmpspheresurface0 500 1000 1500 2000wavenumber [cm -1 ] 3.4 () () . .

3.3 2710 1CO2 saturate10 2Pressure [Pa]10 310 410 5 120 160 200 240 280Temperature[K]1 10 100Particle size [µm] 3.5 . . , 10 3kg −1 (), 10 4 kg −1 (), 10 5 kg −1 (), 10 6 kg −1 (), 10 7 kg −1 (), 10 8 kg −1 (). .

28 3 (a)(b)280 10 3280 10 3Surface Temperature [K]26024022010 210 110 0Particle size [mm]Surface Temperature [K]26024022010 210 110 0Particle size [mm]Radiative cooling rate [K s -1 ]20010 -10.50-0.510 3 10 4 10 5 10 6 10 7 10 8 10 9time [s]Radiative cooling rate [K s -1 ]20010 -10.50-0.510 3 10 4 10 5 10 6 10 7 10 8 10 9time [s](c)(d)280 10 3280 10 3Surface Temperature [K]26024022010 210 110 0Particle size [mm]Surface Temperature [K]26024022010 210 110 0Particle size [mm]Radiative cooling rate [K s -1 ]20010 -10.50-0.510 3 10 4 10 5 10 6 10 7 10 8 10 9time [s]Radiative cooling rate [K s -1 ]20010 -10.50-0.510 3 10 4 10 5 10 6 10 7 10 8 10 9time [s](e)(f)280 10 3280 10 3Surface Temperature [K]26024022010 210 110 0Particle size [mm]Surface Temperature [K]26024022010 210 110 0Particle size [mm]Radiative cooling rate [K s -1 ]20010 -10.50-0.510 3 10 4 10 5 10 6 10 7 10 8 10 9time [s]Radiative cooling rate [K s -1 ]20010 -10.50-0.510 3 10 4 10 5 10 6 10 7 10 8 10 9time [s](g)280 10 3Surface Temperature [K]26024022010 210 110 0Particle size [mm]Radiative cooling rate [K s -1 ]20010 -10.50-0.510 3 10 4 10 5 10 6 10 7 10 8 10 9time [s] 3.6 (a) () () . (b) () () . , (a) 10 3kg −1 , (b) 10 4 kg −1 , (c) 10 5 kg −1 , (d) 10 6 kg −1 , (e) 10 7 kg −1 , (f) 10 8 kg −1 , (g)10 9 kg −1 . .

3.4 293.4 ( 3.7 ). . , 10 315 K . , K . , , .. , , , 320Surface Temp. [K]Icepath [kg/m 2 ]Cloud Particle size [µm]300280260240220200107.552.500.10.010.0011 10Surface Pressure [bar] 3.7 . . (a) , , , . . (b) , (c) .

30 3 10 1CO2 saturate10 2Pressure [Pa]10 310 410 510 6 120 160 200 240 280 320Temperature[K]1 10Particle size [µm] 3.8. . , 0.5 (), 1 (), 2 (), 3 (), 5 (), 10 () . .. , . . , ( 3.8 ). 3.9. , , .. , . , , . , () .

3.4 313020100∆ Surface Temp. [K]-10-20-30-40-50-60-70CCN : 10 3 [kg -1 ]CCN : 10 4 [kg -1 ]CCN : 10 5 [kg -1 ]CCN : 10 6 [kg -1 ]CCN : 10 7 [kg -1 ]CCN : 10 8 [kg -1 ]1 10Surfate Pressure [bar] 3.9 . , 10 3 kg −1 (), 10 4 kg −1 (), 10 5 kg −1 (), 10 6 kg −1 (), 10 7kg −1 (), 10 8 kg −1 () . , .

32 3 3.5 , . , , .3.5.1 , . , ., . n g , n ∗ g(T ) . ∆n = n g − n ∗ g(T ) , .∆ṅ = −4πrcn 2 c v T ∆n (3.4), r c , n c , v T . , τ cond τ cond = ∆n∆ṅ = ( 4πr 2 cv T n c) −1(3.5). ,r c = 5.0 × 10 −6 m (3.6)n c = 10 −5 m −3 ( 10 6 kg −1 , 0.1 kg m −3 ) (3.7)v T = 3.1 × 10 2 m s −1 ( 170 K ) (3.8)( ) −1 () −1 ( ) −1/2 ( ) −2τ cond ∼ 10 2 NCCNρTrc10 6 kg −1 0.1 kg m −3 (3.9)170 K 5.0 µm. . . ,

3.5 331000Ps = 0.5 [bar]Ps = 1.0 [bar]Ps = 2.0 [bar]Ps = 3.0 [bar]Ps = 5.0 [bar]Ps = 10.0 [bar]Condensation Tims [s]10010110 3 10 4 10 5 10 6 10 7 10 8 10 9Number concentration of Condensation Nuclei [kg -1 ] 3.10 . , 0.5 (), 1 (), 2 (), 3 (), 5 (),10 () . . ∼ r 2 cn c L (L:) , . r 2 c n c , .τ conv . L, g ′ . ˙ T . , 12 g′ τ 2 conv = L (3.10)g ′ = ∆ρρ g = T ˙ τ convT12T˙τ convTg (3.11)gτ 2 conv = L (3.12)

34 3 [ ] 1/32Lτ conv =( T ˙(3.13)/T )g. , ,L = 2 × 10 4 m (3.14)T ˙ = 2 × 10 −6 K s −1 (3.15)T = 170 K (3.16)g = 3.72 m s −2 (3.17)τ conv ≃ 10 4 (3.18). , , .. .3.5.2 , , , ., , N 2 . . (A.1 ).N 2 ≡ g ( )∂ρρ ∗ ∂z − ∂ρ∗∂z≃ g ( dTT dz − dT ∗ ) (g dq∗+icedz 1 + q ice dz− dq )icedz(3.19)(3.20), g , T , ρ , z , q ice (/) , ∗ ,

3.5 35, . , (N 2 g dq∗≃ice− dq )ice1 + q ice dz dzdq ∗ icedz (A.2 ).= 1L CO2[(C p + q ice C ice ) dT ∗dz + g ](3.21) 3.11 . () . 0.1 – 0.01 . , 1.9 × 10 −5 s −2 .. , 10 −5 kg/kg , . , .{ [()N 2 g CpC ice dT∗=1 + q ice1 + q ice L CO2 C p dz + g ]C p[ ( gCp dT∗≃dz + g )]C pL CO2− dq }icedz(3.22)(3.23)

36 3 10 110 2Pressure [Pa]10 310 4010 5 5e-05 0.0001 0.00015Stability [s -2 ] 3.11 . , 10 3 kg −1 (), 10 4 kg −1 (), 10 5 kg −1 (), 10 6 kg −1 (), 10 7kg −1 (), 10 8 kg −1 () . .

3.6 373.6 . , ., τ loss .τ loss =Lv(¯r) L , v , ¯r (3.24)¯r =∫ ∞0∫ ∞0n c (z)r(z) dzn c (z) dz(3.25). , n c .v(r) = 9 2ρ ice gη r2 (3.26). , ρ ice , η . L ¯r 3.12 . , 10 4 10 7 . 1 10 , .. , 2 . −1/2 , . , ., , . 3.2 10 4 – 10 5 .

38 3 10 5 kg −1 . , 10 4 kg −1 , ., 10 7 – 10 8 . , ., 10 7 kg −1 , . 10 8kg −1 . , 10 5 kg −1 , , .10 8 10 3 10 4 10 5 10 6 10 7 10 8 10 9Precipitation Time [s]10 710 610 510 410 3Ps = 0.5 [bar]Ps = 1.0 [bar]Ps = 2.0 [bar]Ps = 3.0 [bar]Ps = 5.0 [bar]Ps = 10.0 [bar]Number concentration of Condensation Nuclei [kg -1 ] 3.12. . .

3.7 393.7 , 38 . , ( 3.13). 273 K , 3 -. , 5 (Pollack et al. 1989) .MarsEarth340Surface Temperature [K]320300280260240220CCN : 10 5 [kg -1 ]CCN : 10 6 [kg -1 ]CCN : 10 7 [kg -1 ]CCN : 10nocond8 [kg -1 ]nocloudNumber concentration ofcloud condensation nuclei: 10 5 kg -110 6 kg -1 10 7 kg -1200cloud-free10 8 kg -11800.001 0.01 0.1 1 10Surface Pressure [Pa] 3.13. , 10 −5 kg −1 (), 10 −6 kg −1 (), 10 −7 kg −1 (), 10 −8 kg −1 () . , , Pollack et al. 1989 , Kasting 1991 () . . .

40 3 , 10 5 – 10 7 kg −1 ., . . , , . 100 –300 , . 10 4 kg −1 . , ., . , . , , ., , , . . 1991 , 100 (Hayashida and Horikata 2001). , .. 38 . , , . (Carslaw et al. 2002) . .

3.8 413.8 2007 , 200 . , (Idaand Lin 2004), . , , ., , (), , . , .3.8.1 3.14 . . , . , . 2 , . , . , , .. 2 ( 3.16). , , ( 3.17 ), . , . , , . ,

42 3 .Icepath [kg/m 2 ] Surface Temp. [K]Particle size [µm]32030028026024022010 110 00.10.010.0010 5 10 15 20Gravity [m/s 2 ] 3.14 ., 2.0 (5.37 × 10 5 kgm −2 ) . , . (a) , , , . (b) ,(c) .

3.8 43Icepath [kg/m 2 ] Surface Temp. [K]Particle size [µm]3203002802602402201010.10.010.0010 5 10 15 20Gravity [m/s 2 ] 3.15 3.14 . , 2 .10 105 10 15 20Precipitation Time [s]10 910 810 710 610 510 410 310 2gravity [m s -2 ]CCN: 10 3 [kg -1 ]CCN: 10 4 [kg -1 ]CCN: 10 5 [kg -1 ]CCN: 10 6 [kg -1 ]CCN: 10 7 [kg -1 ]CCN: 10 8 [kg -1 ] 3.16. . .

44 3 Altitude [km]1206017.3gravity = 1.29 [ms -2 ]0100 140 180 220 260Temperature [K] 3.17

3.8 453.8.2 . , ,. , . 3.18 . . , 25000 cm −1 , M0 , F0 , 0.5 ( 3.19). 2 , . , ( 3.20). . , . , . , M0 G0 40 K . , ., , 10 K ( 3.21). 3.1 (1=)F0 7200 K 1.4 R ⊙ 4.72G0 6000 K 1.0 R ⊙ 1.16 5780 K 1.0 R ⊙ 1.00K0 5300 K 0.8 R ⊙ 4.52 ×10 −1M0 3900 K 0.6 R ⊙ 7.46 ×10 −2

46 3 Incident Flux [W m -2 (cm -1 ) -1 ]0.010.0080.0060.0040.002Present SunM0K0G0F000 10000 20000 30000 40000 50000Wavenumber [cm -1 ] 3.18. (110 W m −2 ) . , : 7200 K (F0), : 6000 K (G0 ), : 5780 K (Sun), : 5300 K (K0 ) : 3900 K (M0) .. , , ( 3.21a). . , , , ., 20 K , ( 3.22). 10 5 – 10 7 kg −1 , 5000 – 6000 K . , 10 8 kg −1 , . , .

3.8 4710.8Planetary Albedo0.60.40.203500 4000 4500 5000 5500 6000 6500 7000 7500Temperature of Star [K] 3.19 (). . .

48 3 Surface Temperature [K]260250240230220210200190180cloud-free (without cond.)cloud-free (with cond.)effective temperature1703500 4000 4500 5000 5500 6000 6500 7000 7500Temperature of Star [K] 3.20 . , .. .

3.8 49Icepath [kg/m 2 ] Surface Temp. [K]Particle size [µm]30028026024022020010 110 00.10.010.0013500 4000 4500 5000 5500 6000 6500 7000 7500Temperature of Star [K] 3.21 . . (a) , , , . (b) , (c) .

50 3 Surface Temperature [K]320300280260240220no-coolingCCN: 10 5 [kg -1 ]CCN: 10 6 [kg -1 ]CCN: 10 7 [kg -1 ]CCN: 10 8 [kg -1 ]2003500 4000 4500 5000 5500 6000 6500 7000 7500Temperature of Star [K] 3.22 . , : 10 5 kg −1 , : 10 6 kg −1 , : 10 7 kg −1 , : 10 8kg −1 . . .

3.8 513.8.3 Habitable Zone 3.23 . , 38 , . 10 10 5 kg −1 . ., . , 40 W m −2 , 30 W m −2 . , ., 3.24 . , 10 5kg −1 , . , , , . , , , .38 10 -, 273 K 30 – 40 W m −2 , Habitable Zone , 1.3AU (Kasting et al. 1993) 2.9 AU . , ( 3.25). , 2.5 AU , , , . , ,Habitable Zone 2.4 – 2.9 AU ., M0 – F0 ( 3.26), HabitableZone .

52 3 Surface Temp. [K]Icepath [kg/m 2 ]Particle size [µm]34032030028026024022010 110 010 110 010 -110 -2120 100 80 60 40 20Incident Solar Flux [W m -2 ] 3.23 . 10 6 kg −1 , 10 . . (a) ,, . (b) , (c) .

3.8 53Orbital Radius [AU]3401.52.02.53.03.5320Surface Temp. [K]30028026024022012010080604020Incident Solar Flux [W m -2 ] 3.24 . , 10 5 kg −1 10 6 kg −1 10 7 kg −1 . 10 , . .

54 3 (a)(b)3401.5Orbital Radius [AU]2.02.53.0 3.53401.5Orbital Radius [AU]2.02.53.0 3.5320320Surface Temp. [K]300280260Surface Temp. [K]300280260240240220120100 80 60Incident Solar Flux [W m -2 ]4020220120100 80 60Incident Solar Flux [W m -2 ]4020(c)(d)3401.5Orbital Radius [AU]2.02.53.0 3.53401.5Orbital Radius [AU]2.02.53.0 3.5320320Surface Temp. [K]300280260Surface Temp. [K]300280260240240220120100 80 60Incident Solar Flux [W m -2 ]4020220120100 80 60Incident Solar Flux [W m -2 ]4020 3.25 . , 10 5 kg −1 , 10 6 kg −1 , 10 7 kg −1 , 10 8 kg −1. , () , () . 10 , 5.37 × 10 3 K . , (a) 1.29 m s −2 (b)3.72 m s −2 (c) 9.80 m s −2 (d) 17.4 m s −2 .

3.8 55(a)(b)3400.5Orbital Radius [AU]0.60.70.81.0 0.91.13401.2Orbital Radius [AU]1.52.02.5320320Surface Temp. [K]300280260Surface Temp. [K]300280260240240220120100 80 60Incident Solar Flux [W m -2 ]4020220120100 80 60Incident Solar Flux [W m -2 ]4020(c)(d)3402.0Orbital Radius [AU]2.53.03.5 4.03404.0Orbital Radius [AU]5.06.07.0 8.0320320Surface Temp. [K]300280260Surface Temp. [K]300280260240240220120100 80 60Incident Solar Flux [W m -2 ]4020220120100 80 60Incident Solar Flux [W m -2 ]4020 3.26 . , 10 5 kg −1 , 10 6 kg −1 , 10 7 kg −1 . , () , () . (a)M0 (b) K0 (c) G0 (d) F0 . 10 , .

57 4 , . , , , , , .. , , . , , .. 10 5 – 10 7 kg −1 , , . 10 4 kg −1 , , . , , , . 10 8 kg −1 ., . , ,

58 4 . . . 38 , 3 -. (Pollacket al. 1989) . . , , , . , , . ., , Habitable Zone . 10 , , 38 2.9 AU . 1.3 AU . ,, , , . , 3.0 AU , , , ., , , . , , . , , . , M F G . () , . , , .

59, . , . ., ., , . , , , . , , , , , . OB . . , ,, , , , . ., SX-6 . .

61 AA.1 , .• ()p ∗ = p(A.1)• ρ ∗ | z=z0 = ρ| z=z0 , q ∗ ice| z=z0 = q ice | z=z0 (A.2)• , . δz . d 2 δzdt 2 = (ρ − ρ∗ )gρ ∗(A.3). ρ , ρ g ρ c . ∗ . , g . ρ, ρ ∗ , ,(ρ − ρ ∗ )gρ ∗ ≃ g ρ ∗ {(ρ| z=zo + dρdz δz )−(ρ ∗ | z=zo + dρ∗dz δz )}

62 A = g ( ) dρρ ∗ dz − dρ∗ δzdz(A.4). δz = A sin(Nt + C) N 2 = g ( dρ∗ρ dz − dρ )dz(A.5). , N 2 > 0 , δz = A sin(Nt + C) , , N 2 < 0 , . q ice = ρ c /ρ g ,dρ cdz = q dρ gicedz + ρ dq icegdz(A.6),N 2 = g ( dρ∗gρ ∗ dz − dρ gdz + dρ∗ cdz − ρ cz=gρ ∗ g(1 + q ice )){(1 + qice) ∗ dρ∗ gdz − (1 + q ice) dρ gdz + dq ρ∗ ice∗gdz}dq ice− ρ gdz(A.7). ,N 2 gT ∗ {=(1 + q ∗(1 + q ice )ice) d ( ) 1dz T ∗ − (1 + q ice ) d ( ) 1dz TgT ∗={−(1 + q ∗(1 + q ice )ice) dT ∗dz+ (1 + q ice) dTdz + 1 dqice∗T ∗ − 1 dz T= g ( dTT ∗ dz − dT ∗ ) (g dq∗+ice− dq )icedz 1 + q ice dz dz+ 1 dqice∗T ∗ dzdq icedz− 1 T}}q icez(A.8). T q ice .A.2 , 1 kg q ice kg , . , dQ = C v dT + q ice C ice dT − p dρ gρ 2 g+ L CO2 (− dq ice ) (A.9)= 0 (A.10)

A.2 63. , C v , C ice , L CO2. −p dρ gρ 2 g+ dpρ gp = ρ gRTM CO2= R dTM CO2(A.11)(A.12)= (C p − C v ) dT (A.13),C p dT + q ice C ice dT − dpρ g− L CO2 dq ice = 0(A.14). , C p . ,C p dT + q ice C ice dT + g dz − L CO2 dq ice = 0. , dqice∗ = 1 [(C p + q ice C ice ) dT ∗ ]dz L CO2 dz + g(A.15)(A.16).

65 BB.1 N , . . P n−1/2 , T n , q ice,n . 1/2 (P = 0) , N + 1/2 (P = P s , P s ) . P 3/2 = 1.0 [Pa] , , ,( )Pn+1/2log∝ (1 + a) −1P n−1/2. , a = 0.1 . ,(B.1)P n = P n−1/2 + P n+1/22(B.2).,T 1/2 = T 1T n+1/2 = T n log(P n+1/2 /P n ) + T n+1 log(P n+1 /P n+1/2 )log(P n+1 /P n )n = 1, 2, · · · , N − 1(B.3)(B.4)T N+1/2 = T N

66 B . , ∆T n = T n+1/2 − T n−1/2∆T n−1/2 = T n − T n−1(B.5)(B.6). .B.2 Toon et al. (1989) , ( C ). , , , . Q rad K s −1 Q rad,n =g ∑[Fnet∆P n Cn+(ν) − F net1p2n−(ν)]∆ν (B.7)12. , F net (ν) ν (W m −2 (cm −1 ) −1 ),P , C p .B.3 .T t+∆tn = T t n + Q t rad,n × ∆t (B.8) Q rad K s −1 Q t rad,n = (F t net,n+ 1 2− F t net,n−) × g × 1 12 ∆p n C p(B.9), F net , p , C p .

B.4 CO 2 67B.4 CO 2 CO 2 , CO 2 . . CO 2 , ..ˆT < T sat,CO2 (p)(B.10), ˆT , T sat,CO2 CO 2 .T = T sat,CO2 (p) (B.11), .Q cond = −( ˆT − T sat,CO2 (p)) × C p(B.12), q ice , .q ice =q ice ˆ + Q condL CO2(B.13), L CO2 CO 2 ., .r =( ) 1qice33N CCN 4ρ ice π(B.14), N CCN kg −1 , ρ ice CO 2 ice .B.5 , ,, .

68 B .ˆT n−1 < T ˆ n − ∆ ˆT n−1/2∗= ˆ T n + log(pnM CO2 g × d ˆT ∗∣dzp n−1) R ˆTn− 12∣n−12(B.15), . , , .C p T n∆p n−1/2g+ C p T n−1∆p n−3/2g= C p ˆTn∆p n−1/2g+ C p ˆTn−1∆p n−3/2g(B.16), .( )∆T n−1/2 = ∆ ˆT n−1/2 ∗ = log pn R ˆTn− 12p n−1 M CO2 g × d ˆT ∗∣dz∣n−12(B.17), .T n =Tˆn ∆p n−1/2 + T ˆ n−1 ∆p n−3/2 + ∆ ˆT n−1/2 ∗ ∆p n−3/2T n−1 = T n − ∆ ˆT ∗ n−1/2∆p n−1/2 + ∆p n−3/2(B.18)(B.19), , . , n n − k ,if ˆTn−k < T n−k+1 − ∆ ˆT n−k+1/2∗∑ k ˆT i=0 n+i ∆p n−1/2−i + ∑ ki=1T n =∆ ˆT n−i+1/2 ∗ ∆p n−i−1/2∑ ki=0 ∆p n−i−1/2(B.20)j∑T n−j = T n − ∆ ˆT n−i+1/2 ∗ (j = 1, 2, · · · k) (B.21)i=1., 5 .

69 CC.1 µ ∂I ν(τ ν , µ, φ) = I ν (τ ν , µ, φ) − S ν (τ ν , µ, φ)∂τ ν− ω 0ν4π∫ 2π ∫ 10−1P ν (µ, µ ′ , φ, φ ′ )I ν (τ ν , µ ′ , φ ′ ) dµ ′ dφ ′(C.1). , I , τ , µ , φ , ω 0, P , ν . , , . S νe (τ ν , µ, φ) = (1 − ω 0 )B ν (T ),(C.2)S νs (τ ν , µ, φ) = ω 0ν4 F svP ν (µ, −µ 0 , φ, φ 0 ) exp(−τ ν /µ 0 ) (C.3). , B , T , πF sν , µ 0 , φ 0 .(C.1) ,µ ∂I ν(τ ν , µ) = I ν (τ ν , µ) − S ν (τ ν , µ) − ω 0ν∂τ ν 2∫ 1−1P ν (µ, µ ′ )I ν (τ ν , µ ′ ) dµ ′(C.4)

70 C . ,I ν (τ ν , µ) =∫ 2π0P (µ, µ ′ ) = 12πI ν (τ ν , µ, φ) dφ∫ 2π0P ν (µ, µ ′ , φ, φ ′ ) dφ(C.5)(C.6), .S ν (τ ν , µ) =,∫ 2π0S ν (τ ν , µ, φ) dφS νe (τ ν , µ) = 2π(1 − ω ν )B ν (T )(C.7)(C.8)S νs (τ ν , µ) = ω 0ν2 πF svP ν (µ, −µ 0 ) exp(−τ ν /µ 0 ) (C.9)∂F ν± ∫ 1∫ 1= ± I ν (τ ν , ±µ) dµ ∓ S ν (τ ν , ±µ) dµ∂τ ν 00∓ ω 0ν2∫ 1 ∫ 10−1P ν (±µ, µ ′ )I ν (τ ν , µ ′ ) dµ ′ dµ(C.10). ,F ± ν =∫ 10µI ν (τ ν , ±µ) dµ (C.11).(C.10) I P (µ, µ ′ ) , , . , ν .∂F +∂τ (τ) = γ 1F + (τ) − γ 2 F − (τ) − S + (τ)∂F −∂τ (τ) = γ 2F + (τ) − γ 1 F − (τ) + S − (τ)(C.12)(C.13) S ± (τ) , S + s (τ) = γ 3 πF s ω 0 exp(−τ/µ 0 ),S − s (τ) = (1 − γ 3 )πF s ω 0 exp(−τ/µ 0 )(C.14)(C.15)

C.2 71. ,S + (τ) = 2π(1 − ω 0 )B(T )S − (τ) = S + (τ)(C.16)(C.17). γ 1 , γ 2 , γ 3 2 , .C.2 , k . , Toon et al. (1989) . , , .F netn+(ν) = ∑ 12j[F ↑ n+ 1 2 ,j(ν) − F ↓ n+ 1 2 ,j(ν)]∆g j (C.18), . δ-Eddington . , (δ-) , . , Toon et al. (1989) . . , . F n + (τ), Fn − (τ) . + , − , . n . τ ( C.1 ). .∂F + n∂τ (τ) = γ 1nF n + (τ) − γ 2n Fn − (τ) − S n + (τ)∂Fn−∂τ (τ) = γ 2nF n + (τ) − γ 1n Fn − (τ) + Sn − (τ)(C.19)(C.20), n τ F n + (τ) = Y 1n {exp[−λ n (τ n − τ)] + Γ n exp(−λ n τ)}+Y 2n {exp[−λ(τ n − τ)] − Γ n exp(−λ n τ)} + C n + (τ) (C.21)Fn − (τ) = Y 1n {Γ n exp[−λ n (τ n − τ)] + exp(−λ n τ)}

72 C Top of Atmospherelayer 1layer 2τ 1τ c3τ cnτ cN+1F n+(0)τ = 0layer nτ nF n+(τ)τ = τF n+(τ n)layer NSurfaceττ = τ n C.1. , j .+Y 2n {Γ n exp[−λ n (τ n − τ)] − exp(−λ n τ)} + C − n (τ) (C.22). , τ n n , τ cn n , n−1∑τ cn =l=1τ l(C.23). Γ n , λ n .Γ n = γ 1n − λ nγ 2nλ n = (γ1n 2 − γ2n) 2 1/2(C.24)(C.25) γ 1n , γ 2n , , C.1 (, C.4.1, C. 4.2 ). C n . , Y 1n , Y 2n , F n ± (τ). C.12 γ 1 , γ 2 , γ 3 . γ 1 γ 2 γ 3Eddington 1 4 [7 − ω 0(4 + 3g)] − 1 4 [1 − ω 0(4 − 3g)]14 (2 − 3gµ 0) 2 − ω 0 (1 + g) ω 0 (1 − g)

C.2 73, F + N (τ N ) = R sfc F − N (τ N) + S sfcF + n (τ n ) = F + n+1 (0)F − n (τ n ) = F − n+1 (0)(C.26)(C.27)(C.28). , R sfc , S sfc . ,A l Y l−1 + B l Y l + D l Y l+1 = E lY l ={Y 1n , l = 2n − 1Y 2n , l = 2n(C.29)(C.30). .if l = 1,A l = 0,B l = e 1,1 ,D l = −e 2,1 ,E l = −C1 − (0),if l = 2n, (n = 1, 2, · · · , N − 1)A l = e 2,n+1 e 1,n − e 3,n e 4,n+1 ,B l = e 2,n e 2,n+1 − e 4,n e 4,n+1 ,D l = e 1,n+1 e 4,n+1 − e 2,n+1 e 3,n+1 ,E l = (C n+1 + (0) − C+ n (τ n ))e 2,n+1 − (Cn+1 − (0) − C− n (τ n ))e 4.n+1 ,if l = 2n − 1, (n = 2, 3, · · · , N)A l = e 2,n−1 e 3,n−1 − e 4,n−1 e 1,n−1 ,B l = e 1,n−1 e 1,n − e 3,n−1 e 3.n ,D l = e 3.n−1 e 4.n − e 1,n−1 e 2,n ,E l = e 3,n−1 (C n + (0) − C n−1 + (τ n−1)) + e 1,n−1 (Cn−1 − (τ n−1) − Cn − (0),if l = 2N,A l = e 1,n − R sfc e 3,n ,B l = e 2,n − R sfc e 4.n ,D l = 0,E l = S sfc − C n + (τ n ) + R sfc Cn − (τ n ),e 1n = 1 + Γ n exp(−λ n τ n )

74 C e 2n = 1 − Γ n exp(−λ n τ n )e 3n = Γ n + exp(−λ n τ n )e 4n = Γ n − exp(−λ n τ n ). , Y l .{A l X l , l ≠ 2NAS l =A l /B l , l = 2N{(E l − D l DS l+1 )X l , l ≠ 2NDS l =E l /B l ,l = 2NX l = (B l − D l AS l+1 ) −1{DS l , l = 1Y l =DS l − AS l Y l−1 , l ≠ 1(C.31)(C.32)(C.33)(C.34) Y l (C.21), (C.22) , F ± n (τ) .C.2.1, δ -Eddington ., δ , (C.4.3 ).τ ′ n = (1 − ω 0n g 2 n)τ nω 0n ′ = (1 − g2 n)ω 0n(1 − gnω 2 0n )g n ′ g n=(1 + g n )(C.35)(C.36)(C.37) D.1 γ 1n , γ 2n . , ,C n + (τ) = ω 0nπF s exp[−(τ cn + τ)/µ 0 ][(γ 1n − 1/µ 0 )γ 3n + γ 4n γ 2n ]λ 2 n − 1/µ 2 0Cn − (τ) = ω 0nπF s exp[−(τ cn + τ)/µ 0 ][(γ 1n + 1/µ 0 )γ 4n + γ 2n γ 3n ]λ 2 n − 1/µ 2 0γ 4n = 1 − γ 3n. (C.38)(C.39)(C.40)R sfc = 0.2(C.41)

C.2 75S sfc = πµ 0 exp(−τ cN+1 /µ 0 )F sF − 1 (0) = 0(C.42)(C.43). F + , F − (F − n,dir (τ) = µ 0πF s exp − τ )cn + τµ 0(C.44)., ,.F ↑ 1/2 = F + 1 (0)F ↓ 1/2 = µ 0πF s(C.45)(C.46)F ↑ n+1/2 = F n + (τ n ) (n = 1, · · · , N) (C.47)(F ↓ n+1/2 = F n − (τ n ) + µ 0 πF s exp − τ )cn+1(n = 1, · · · , N) (C.48)µ 0C.2.2, δ-., . τ ,C + n (τ) = 2πµ 1[B 0n + B 1n(τ +C − n (τ) = 2πµ 1[B 0n + B 1n(τ −)]1γ 1n + γ 2n)]1γ 1n + γ 2n(C.49)(C.50)µ 1 = 1 2B 0n = B(T n−1/2 )B 1n = B(T n+1/2) − B 0nτ n(C.51)(C.52)(C.53). .R sfc = 0(C.54)

76 C S sfc = πB(T sfc )F − 1 (0) = µ 0πF s(C.55)(C.56), T sfc ., , . .µ ∂I∂τ (τ, µ) = I(τ, µ) − S(τ, µ) − ω ∫ 10P (µ, µ ′ )I ′ (τ) dµ ′2 −1(C.57), I ′ , {I ′ 2F + (τ), µ > 0(τ) =2F − (C.58)(τ), µ < 0. , , ,.F + n (τ) = Y 1n {exp[−λ n (τ n − τ)] + Γ n exp(−λ n τ)}+Y 2n {exp[−λ(τ n − τ)] − Γ n exp(−λ n τ)} (C.59)F − n (τ) = Y 1n {Γ n exp[−λ n (τ n − τ)] + exp(−λ n τ)}+Y 2n {Γ n exp[−λ n (τ n − τ)] − exp(−λ n τ)} (C.60), S t (τ) = S(τ, µ) + ω 02∫ 1−1P (µ, µ ′ )I ′ (τ, µ ′ ) dµ ′(C.61). , , S t + = G exp[λ(τ − τ n )] + H exp(−λτ) + α 1 + α 2 τ (C.62)St − = J exp[λ(τ − τ n )] + K exp(−λτ) + σ 1 + σ 2 τ (C.63). ,( ) 1G n = (Y 1n + Y 2n ) − λ nµ 1H n = (Y 1n − Y 2n )Γ n(λ n + 1 µ 1)(C.64)(C.65)

C.2 77(J n = (Y 1n + Y 2n )Γ n λ n + 1 )µ 1( ) 1K n = (Y 1n − Y 2n ) − λ nµ 1()}1α 1n = 2π{B 0n + B 1n − µ 1γ 1n + γ 2nα 2n = 2πB 1n()}1σ 1n = 2π{B 0n − B 1n − µ 1γ 1n + γ 2nσ 2n = 2πB 1n. , , .(I n−1 + (τ n−1, µ) = I n + (τ n , µ) exp − τ )nµ(C.66)(C.67)(C.68)(C.69)(C.70)(C.71)G n+(λ n µ − 1) {exp(−τ nµ) − exp(−τ n λ n )}+ H [(n1 − exp{−τ n λ n + 1 )}](λ n µ + 1)µ(+α 1n{1 − exp − τ )}nµ(+α 2n{(µ − (τ n + µ) exp − τ )}nµ(In − (τ n , µ) = In−1 − (τ n−1, µ) exp − τ )nµ[(J n+− exp{−τ n λ n + 1 )}](λ n µ + 1)µ+ K { (nexp − τ )}n− exp(−τ n λ n )(λ n µ − 1) µ(+σ 1n{1 − exp − τ )}nµ(+σ 2n{µ exp − τ ) }n+ τ n − µµ(C.72)(C.73), ,I1 − (0, µ) = πF sI + N (τ N , µ) = 2πB(T sfc )(C.74)(C.75)., 4 ,

78 C .F ↑ 1−1/2 =F ↓ 1−1/2 =F ↑ n+1/2 =F ↓ n+1/2 =4∑I n + (0, µ l )µ l ∆µ l(C.76)l4∑In − (0, −µ l )µ l ∆µ ll(C.77)4∑I n + (τ n , µ l )µ l ∆µ l (n = 1, · · · , N) (C.78)l4∑In − (τ n , −µ l )µ l ∆µ l (n = 1, · · · , N) (C.79)lC.3 , τ n , ω 0n , g n . , CO 2 H 2 O , CO 2 , , , τ n,j = τ L,j + τ c,CO2 + τ c,H2 O + τ P I,CO2 + τ R + τ iceω 0n,j = τ Rω R + τ ice ω iceτ n,jg n = τ Rω R g R + τ ice ω ice g iceτ R ω R + τ ice ω ice(C.80)(C.81)(C.82). , , L , C, P I , R , ice ..C.3.1CO 2 H 2 O k . 50 cm −1 1 , 5 ., CO 2 H 2 O , ,

C.3 79.τ L,j = (σ j1,CO2 n CO2 + σ j2,H2 On H2 O)∆z, j = 5(j1 − 1) + (j2 − 1)(C.83) 6 (100 – 350 K, 50 K ), 8 (10 6 –0.1 Pa, 1 ) , .σ(T n , P ) = σ(T 1 , P ) + {σ(T 2 , P ) − σ(T 1 , P )} T n − T 1T 2 − T[{ } 1]σ(T, P2 ) log(Pn /P 1 )σ(T, P n ) = exp log{σ(T, P 1 )} + logσ(T, P 1 ) log(P 2 /P 1 )(C.84)(C.85)C.3.2CO 2 CO 2 , 0-300 1 1150 – 1850 cm −1 . 0–300 cm −1 Gruszka and Borysow (1997), 1150 – 1850 cm −1 Kasting et al. (1984a) .0–300 cm −1, τ P I,CO2 = σ P I,CO2 n CO2 ∆z (C.86). .σ P I,CO2 = (α(ω, T ) × 10 2 )( nn L) 2n (C.87)α(ω, T ) = SP M 0 ν 2 I N (ω)M 0 = 3ckπ 2 T γ 1(T )( ) 2SP c = 2π2 1 13ck n2 L2πc T(C.88)(C.89)(C.90),I N (ω) = [1 − f(ω)]I L BC(ω) + f(ω)I H BC(C.91)

80 C .I BC (ω) =τ 2(1 + τ 2 1 ω2 ) 1/2 exp(τ 2/τ 1 )K 1[τ2τ 1(1 + τ 2 1 ω 2 ) 1/2 ]γ 1 (T ) = 1.059 × 10 −40 exp(−10.486 log(T ) + 0.7321(log(T )) 2 )τ L 1 (T ) = 1.587 × 10 0 exp(−9.3443 log(T ) + 0.6944(log(T )) 2 )τ L 2 (T ) = 1.286 × 10 −25 exp(9.4210 log(T ) − 0.7856(log(T )) 2 )τ H 1 (T ) = 3.313 × 10 −22 exp(7.2857 log(T ) − 0.6733(log(T )) 2 )τ H 2 (T ) = 1.961 × 10 −4 exp(−6.8346 log(T ) + 0.5517(log(T )) 2 )(C.92)(C.93)(C.94)(C.95)(C.96)(C.97), , SP c 1.296917d+55 , . , γ 1 , τ 1 . σ m 2 /moleculeα cm-amagat −1ω sec −1γ 1 0th cm 5 secτ secI N , I BC , sec −1T Kn m −3n L 1 , 0 ◦ C 2.687E+25 m −31150–1850 cm −1.( ) ( ) tiτ P I,CO2 = (C i × 10 2 PE T)WP 0 T 0P E = (1.0 + 0.3f(CO 2 ))PW = 1 ∆Pρ 0 g(C.98)(C.99)(C.100).

C.3 81 τ C i cm-amagat −1t i -1.7T KT 0 300 KP PaP 0 1.013E+5 PaP E PaW CO 2 (1 , 0 ◦ C ) atm-mρ 0 1 , 0 ◦ C CO 2 1.96 kg m −3f kg kg −1g m s −2C.3.3H 2 O 8 µm 12 µm H 2 O , Robert et al. (1976) . , Kasting etal. (1984b) .τ c,H2 O = σ c,H2 On H2 O∆zσ c,H2 O = C 0 (ν, T )[P H2 O + γ(P − P H2 O)]/1.013E + 5[C 0 (ν, T ) = C 0 (ν) exp T 0 ( 1 T − 1 ]296 )C 0 (ν) = a + b exp(−βν)(C.101)(C.102)(C.103)(C.104) σ c,H2O m 2 /moleculeC 0P PaP H2 O H 2 O Pam 2 atm −1 /molecule

82 C γ H 2 O 0.0008T KT 0 1800 Ka 1.25E-26 m 2 atm −1 /moleculeb 1.67E-23 m 2 atm −1 /moleculeβ 7.87E-3 cm −1C.3.4, Liou (2002) .σ R = α2 128π 5(ν × 10 2 ) 4 (C.105)3, , ,ω 0,R = 1g R = 0(C.106)(C.107).. , Marchetti and Simili 2006 CO 2 . σ R m 2 /moleculeν cm −1α CO 2 1.6279E-24 m 3

C.3 83C.3.5, . ,ω 0,ice = σ ice,scaσ ice,sca = 2πk 2σ ice = 2πk 2σ ice∑∞n=1∑ ∞n=1(C.108)(2n + 1)(|a n | 2 + |b n | 2 ) (C.109)(2n + 1)Re{a n + b n } (C.110). , ,g ice =[ πr2 4 ∑σ ice,ext x 2 nn(n + 2)n + 1Re{a na ∗ n+1 + b n b ∗ n+1} + ∑ n]2n + 1)n(n + 1) Re{a nb ∗ n}(C.111) (, Bohren and Hoffman 1998, 4 ). a n , b n a n = mψ n(mx)ψ n(x) ′ − ψ n (x)ψ n(mx)′mξ n (mx)ξ n(x) ′ − ξ n (x)ξ n(mx)′b n = ψ n(mx)ψ n(x) ′ − mψ n (x)ψ n(mx)′ξ n (mx)ξ n(x) ′ − mξ n (x)ξ n(mx)′(C.112)(C.113). , ψ, ξ Riccati-Bessel ψ l (x) = xj l (x), ξ l (x) = xh (1)l(x) (C.114), j n , h (1)n Bessel , Hankel .( ) n 1j n (x) = (−x) n d sin xx dx x( ) n 1h (1)n (x) = (−x) n d exp(ix)x dx ix(C.115)(C.116). , x , m , x = 2πN airr, m = N iceλN air(C.117). , N air , N ice , r , λ .

84 C , , , ., C.2, C.3 , , C.4 .wavelength (µm)100041001010.10.01CO 2 redractive index (REAL)3.532.521.510.50CO 2 redractive index (IMAGINALY)10 110 010 -110 -210 -310 -410 -510 -610 -710 100 1000 10000 100000 1e+06wavenumber (cm -1 ) C.2 CO 2 ice . Warren (1986).

C.3 85wavelength (µm)10002.21001010.10.01H 2 O redractive index (REAL)21.81.61.41.210.810 0 10 100 1000 10000 100000 1e+06H 2 O redractive index (IMAGINALY)10 -110 -210 -310 -410 -510 -610 -710 -810 -910 -10wavenumber (cm -1 ) C.3H 2 O . , . Haleand Querry (1973), Warren (1984) .

86 C wavelength (µm)Extinction efficiencysinghel scattering albedo1004.543.532.521.510.5010.80.60.40.2011010.2ansymetry factor0.80.60.40.20100 1000 10000wavenumber (cm -1 ) C.4 CO 2 (:, :, : ). Mie . (: 1µm, : 5 µm, : 10 µm).

C.4 87C.4 C.4.1, 2 .• µ < 0, µ > 0 (Coakley and Chylek, 1975;Meador and Weaver, 1980)• P (Θ) (Θ ) , Θ < 90 ◦ , Θ > 90 ◦ (Toon et al. 1989), (C.11) .F ± = 1 I(τ, ±µ)2 (C.118), , ∫g = cos ΘP (Θ) dΩ4π4π(C.119),P (Θ) ={1 + g, Θ > 90 ◦1 − g, Θ < 90 ◦ (C.120).(C.118), (C.120) , − ω 02∫ 1 ∫ 10= −ω 0[∫ 10−1∫ 0−1P (µ, µ ′ )I(τ, µ ′ ) dµ ′ dµP (µ, µ ′ )F − (τ) dµ ′ dµ +∫ 1 ∫ 100]P (µ, µ ′ )F + (τ) dµ ′ dµ= −ω 0[(1 − g)F − (τ) + (1 + g)F + (τ) ] (C.121), ,+ ω 02∫ 1 ∫ 10 −1P (−µ, µ ′ )I(τ, µ ′ ) dµ ′ dµ

88 C = ω 0[(1 + g)F − (τ) + (1 − g)F + (τ) ] (C.122). (C.118), (C.121), (C.122) (C.12), (C.13) ,γ 1 = 2 − ω 0 (1 + g)γ 2 = ω 0 (1 − g)(C.123)(C.124).C.4.2Eddington Eddington , .• . , • . , I(τ, µ) = I 0 (τ) + µI 1 (τ)(C.125). (C.125) (C.11) ,F ± (τ) =∫ 10µ(I 0 (τ) ± µI 1 (τ)) dµ = 1 2 I 0(τ) ± 1 3 I 1(τ), ,I 0 (τ) = F + (τ) + F − (τ)I 1 (τ) = 3 2 [F + (τ) − F − (τ)](C.126)(C.127)(C.128), .I(τ ± µ)+ = 1 2 [(2 ± 3)F + (τ) + (2 ∓ 3)F − (τ)](C.129), ,∫ 1{F ± (τ) = [F + (τ) + F − (τ)] ± 3µ }2 [F + (τ) − F − (τ)] dµ.0= 1 4 [(4 ± 3)F + (τ) + (4 ∓ 3)F − (τ)] (C.130)

C.4 89 l P l P (µ, µ ′ ) =1∑(2l + 1)g l P l (µ)P l (µ ′ ) (C.131)l=0 (e.g. Chandrasekhar 1960). g l = 1 2∫ 1−1P l (µ)P (µ, 1) dµ(C.132), P 0 (µ) = 1, P 1 (µ) = µ ,g 0 = 1 2g 1 = 1 2∫ 1−1∫ 1−1P (µ, 1) dµ = 1(C.133)µP (µ, 1) dµ = g (C.134). (C.133), (C.134) (C.131) , ,P (µ, µ ′ ) = 1 + 3gµµ ′(C.135)., (C.129) (C.135) . − ω 02= − ω 02= − ω 02∫ 1 ∫ 10 −1∫ 1 ∫ 10∫ 10−1P (µ, µ ′ )I(τ, µ ′ ) dµ ′ dµ}{[F + (τ) + F − (τ)] + 3µ′2 [F + (τ) − F − (τ)] (1 + 3gµµ ′ ) dµ ′ dµ{2[F + (τ) + F − (τ)] } + { (3gµ)[F + (τ) − F − (τ)] } dµ= − ω 04 [(4 + 3g)F + (τ) + (4 − 3g)F − (τ)] (C.136). ,ω 02∫ 1 ∫ 10−1P (−µ, µ ′ )I(τ, µ ′ ) dµ ′ dµ = ω 04 [(4 − 3g)F + (τ) + (4 + 3g)F − (τ)] (C.137)., (C.130), (C.136), (C.136) (C.12), (C.13) ,γ 1 = 1 4 [7 − ω 0(4 + 3g)](C.138)

90 C γ 2 = − 1 4 [1 − ω 0(4 − 3g)]γ 3 = 1 4 (2 − 3gµ 0)(C.139)(C.140).C.4.3δ , , Eddington 0 , . , δ , P ′ , P δ (Joseph 1976).P ′ (µ, µ ′ ) = 2fδ(µ − µ ′ ) + (1 − f)P (µ, µ ′ )(C.141), , g ′ .g = 1 2,∫ 1−1µ ′ P ′ (µ, µ ′ ) dµ ′ = f + (1 − f)g ′ (C.142)g ′ = g − f1 − f(C.143). , f P ′ f∫1 1P 2 (µ)P ′ (µ)2 −1(C.144). P . P , Henyey-Greenstein P HG (µ) =∞∑(2l + 1)g l P l (µ) (C.145)l=0. ,f = g 2g ′ =g1 + g(C.146)(C.147).

C.4 91, (C.4) .µ ∂I∂τ(τ, µ) − I(τ, µ) + S(τ, µ)= − ω 02∫ 1−1[2fδ(µ − µ ′ ) + (1 − f)P (µ, µ ′ )]I(τ, µ ′ ) dµ ′= −ω 0 fI(τ, µ) − ω 0(1 − f)2∫ 1−1P (µ, µ ′ )I(τ, µ ′ ) dµ ′(C.148), .τ ′ ν = (1 − ω 0 g 2 )τ ν ,(C.149)ω ′ 0 = (1 − g2 )ω 0n(1 − g 2 ω 0 ) , (C.150)

93 Dk D.1 ν σ , .σ(ν) = ∑ iσ i (ν)(D.1), i i . i ν S f ,σ i (ν) = S i (T )f(ν − ν 0,i )(D.2). , T , ν 0 .D.1.1, (Rothman et al. 1998).S i (T ) = S i (T ref ) exp(−hcE j,i/kT ) Q(T ref ) [1 − exp(−hcν 0,i /kT )]exp(−hcE j,i /kT ref ) Q(T ) [1 − exp(−hcν 0,i /kT ref )](D.3)

94 D k , T ref , h , c , E j , k , Q . S i (T ref ), E j .Q(T ) ≡ ∑ j(g j exp − ε )jkT(D.4). , g , ε j . , , HITRAN TIPSglh . TIPSglh , 25 K 4 , Q(T ref )/Q(T ) .D.1.2, .(1) (natural broadeing),(2) (pressure broadening or collision broadening)(3) (doppler broadening)(1) (2) , (3) , . (1) , .. .f L (ν − ν 0 ) =α L (p, T )π[(ν − ν 0 ) 2 + {α L (p, T )} 2 ](D.5)

D.1 95, ν 0 , α L α L (p, T ) = α L (p ref , T ref )p ( ) TLTref(D.6)p ref T. , p ref , T L . α L (p ref , T ref ), T L ., .[ ( ) ] 21ν −f D (ν − ν 0 ) =α D (T )π exp ν0−(D.7)1/2 α D (T )α D (T ) = ν ( ) 1/20 2RT(D.8)c M r M r ., .f V (ν − ν 0 ) =,=∫ ∞0∫ ∞0f L (ν ′ − ν 0 )f D (ν − ν ′ ) dν ′α L (p, T )π[(ν ′ − ν 0 ) 2 + {α L (p, T )} 2 ]= 1α D√ πV oigt(x, y)(D.9)[ ( ) ]1ν − ν′ 2α D (T )π exp −(D.10) dν ′1/2 α D (T )(D.11)V oigt(x, y) = y π∫ ∞−∞1y 2 + (x − t) 2 exp(−t2 ) dtx = ν − ν 0α D (T ) , y = α L(p, T )α D (T ) , t = ν − ν′α D (T )(D.12)(D.13). Kuntz 1997 Ruyten 2004 .

96 D k , . , χ , wing (cut off), .f ′ (ν − ν 0 ) = f(ν − ν 0 )χ(ν − ν 0 )CUT (ν − ν 0 )(D.14), , (2004) LBLTRM , 25 cm −1 wing .χ(ν − ν 0 ) = 1(D.15)CUT (ν − ν 0 ) = 1 (|ν − ν 0 | ≤ 25cm −1 ) (D.16)= 0 (|ν − ν 0 | > 25cm −1 ) (D.17)D.2 line-by-line , 1/4 , . k . k line-by-line , . , .line-by-line , σ(ν) . k (ν min –ν max ) , σ g (g) . , g . T ¯ ¯ T ==∫1νmaxν max − ν min∫ 10exp(−σ g (g)nl) dgν minexp(−σ(ν)nl) dν (D.18)(D.19). , n , l .

D.2 97-20-20Absorption crosssection log σ(ν) [m 2 ]-22-24-26Absorption crosssection log σ g(g) [m 2 ]-22-24-26σ 1σ 2σ 3σ 4σ 5-28650 660 670 680 690 700Wavenumber ν [cm -1 ]-280 0.2 0.4 0.6 0.8 1Cumulative Probablity g D.1) . ) () ()., ¯ T ≃ ∑ iexp(−σ gi ρl)∆g i(D.20)., , . 0.1 ,200 K , 5 . , .( 1∑) [ {σg (1)σ g ∆g i = exp logσi=1g (0)( 2∑) [ {σg (1)σ g ∆g i = exp logσi=1g (0)) [ {σg (1)∆g i = exp logσ g (0)σ g( 3∑i=1}]0.15 + log{σ g (0)}}]0.30 + log{σ g (0)}}]0.45 + log{σ g (0)}(D.21)(D.22)(D.23)

98 D k σ g( 4∑i=1) [∆g i = exp log{ }]σg (1)0.60 + log{σ g (0)}σ g (0)(D.24)σ g( 5∑i=1∆g i)= σ g (1) (D.25), σ gi ∫ P i1 ∆g iP i−11∆g iexp(−σ g (g)nl) dg = exp(−σ i nl)∆g i (D.26)[σ i = − 1 ∫nl log 1P i∆g iP i−11 ∆g i1∆g iexp{−σ g (g)nl} dg](D.27). , σ i , nl . ,σ g nl 10 −5 – 1 nl ., , σ i (T, P ) .D.3 D.3.1, , . HITRAN (HIgh resolution TRANsmission molecular absorption database), GEISA(Gestion et Etude des Informations Spectroscopiques Atmospheriques; Managementand Study of Atmospheric Spectroscopic Information) . HITRAN (the Air Force Geophysics Lab; AFGL) 1960 . , HITRAN2004 . HITRAN2004 39 , 173 (Rothman etal. 2005). HITRAN HITEMP(High-Temperature molecular spectroscopic database) , , 4 320 .

D.3 99GEISA , 1970 (Center National de laRechrche Scientifique;CNRS) . 2003 41 , 166 (Jacquinet-Houssonet al. 2005). HITRAN , , (Hussoun et al. 1992)., , CO 2, HITRAN2004 HITEMP.HITRAN Database 296 K , ν η (HITRAN E j ) ν ηη ′. Q(T ) HITRAN 2004 TIPS 2003 (Global data/TIPS 2003/TIPS 2003.for) . D.2 HITRAN 2004 (Rothman et al. 2005).

100 D k D.3.2, . (1) (), (2) () () , A [(molecules −1 )], B [(molecule s −1 J −1 )] . A , B , , ., η η ′ . S ηη ′ [cm −1 /(molecule cm −2 )] S ηη ′ = hcν ηη ′1N (n ηB ηη ′ − n η ′B η′ η)(D.28)g η B ηη ′ = g ′ ηB η′ η (D.29),.S ηη ′ = hcν ηη ′n ηN(1 − g )ηn η ′B ηη ′g η ′n η(D.30), n T P n = n ηQ(T ) ≡ ∑ i(g η expN =g i exp− hcν ηkTQ(T )(− hcν ikT))(D.31)(D.32). Q(T ) , . ,( )g η n exp − hcν η ′ (η′kT= ( ) = exp − hcν )ηη ′(D.33)g η ′n η kTexp− hcν ηkT

D.3 101,.S ηη ′ = hcν ηη ′(g η expQ(T )− hcν ηkT)( (1 − exp − hcν ))ηη ′B ηη ′kT(D.34)D.3.3 (Kuntz 1997, Ruyten 2004) .|x| + y > 15 V oigt(x, y) = a 1 + b 1 x 2a 2 + b 2 x 2 + x 4a 1 = 0.2820948y + 0.5641896y 3b 1 = 0.5641896ya 2 = 0.5 + y 2 + y 4b 2 = −1.0 + 2.0y 25.5 < |x| + y < 15 V oigt(x, y) = a 3 + b 3 x 2 + c 3 x 4 + d 3 x 6a 4 + b 4 x 2 + c 4 x 4 + d 4 x 6 + x 8a 3 = 1.05786y + 4.65456y 3 + 3.10304y 5 + 0.56419y 7b 3 = 2.962y + 0.56419y 3 + 1.69257y 5c 3 = 1.69257y 3 − 2.53885yd 3 = 0.56419ya 4 = 0.5625 + 4.5y 2 + 10.5y 4 + 6.0y 6 + y 8b 4 = −4.5 + 9.0y 2 + 6.0y 4 + 4.0y 6c 4 = 10.5 − 6.0y 2 + 6.0y 4d 4 = −6.0 + 4.0y 2|x| + y < 5.5 y > 0.195|x| − 0.176 a 5 + b 5 x 2 + c 5 x 4 + d 5 x 6 + e 5 x 8V oigt(x, y) =a 6 + b 6 x 2 + c 6 x 6 + d 6 x 8 + e 6 x 8 + x 10a 5 = 272.102 + 973.778y + 1629.76y 2 + 1678.33y 3 + 1174.8y 4+581.746y 5 + 204.510y 6 + 49.5213y 7 + 7.55895y 8 + 0.564224y 9

102 D k b 5 = −60.5644 − 2.34403y + 220.843y 2 + 336.364y 3 + 247.198y 4+100.705y 5 + 22.6778y 6 + 2.25689y 7c 5 = 4.58029 + 18.546y + 42.5683y 2 + 52.8454y 3 + 22.6798y 4+3.38534y 5d 5 = −0.128922 + 1.66203y + 7.56186y 2 + 2.25689y 3e 5 = 0.000971457 + 0.564224ya 6 = 272.102 + 1280.83y + 2802.87y 2 + 3764.97y 3 + 3447.63y 4+2256.98y 5 + 1074.41y 6 + 369.199y 7 + 88.2674y 8 + 13.3988y 9 + y 10b 6 = 211.678 + 902.306y + 1758.34y 2 + 2037.31y 3 + 1549.68y 4+793.427y 5 + 266.299y 6 + 53.5952y 7 + 5.0y 8c 6 = 78.866 + 308.186y + 497.302y 2 + 479.258y 3 + 269.292y 4+80.3928y 5 + 10.0y 6d 6 = 22.0353 + 55.0293y + 92.7568y 2 + 53.5952y 3 + 10.0y 4e 6 = 1.49645 + 13.3988y + 5.0y 2|x| + y < 5.5 y > 0.195|x| − 0.176 V oigt(x, y) = exp(y 2 − x 2 )cos(2xy)−(a 7 + b 7 x 2 + c 7 x 4 + d 7 x 6 + e 7 x 8 + f 7 x 10 + g 7 x 12 + h 7 x 14+o 7 x 16 + p 7 x 18 + q 7 x 20 + r 7 x 22 + s 7 x 24 + t 7 x 26 )/(a 8 + b 8 x 2 + c 8 x 4 + d 8 x 6 + e 8 x 8 + f 8 x 10 + g 8 x 12 + h 8 x 14+o 8 x 16 + p 8 x 18 + q 8 x 20 + r 8 x 22 + s 8 x 24 + t 8 x 26 + x 28 )a 7 = 1.16028e9y − 9.86604e8y 3 + 4.56662e8y 5 − 1.53575e8y 7+4.08168e7y 9 − 9.69463e6y 11 + 1.6841e6y 13 − 320772.0y 15+40649.2y 17 − 5860.68y 19 + 571.687y 21 − 72.9359y 23+2.35944y 25 − 0.56419y 27b 7 = −5.60505e8y − 9.85386e8y 3 + 8.06985e8y 5 − 2.91876e8y 7+8.64829e7y 9 − 7.72359e6y 11 + 3.59915e6y 13 − 234417.0y 15+45251.3y 17 − 2269.19y 19 − 234.143y 21 + 23.0312y 23−7.33447y 25c 7 = −6.51523e8y + 2.47157e8y 3 + 2.94262e8y 5 − 2.04467e8y 7+2.29302e7y 9 − 2.3818e7y 11 + 576054.0y 13 + 98079.1y 15−25338.3y 17 + 1097.77y 19+97.6203y 21 − 44.0068y 23d 7 = −2.63894e8y + 2.70167e8y 3 − 9.96224e7y 5 − 4.15013e7y 7+3.83112e7y 9 + 2.2404e6y 11 − 303569.0y 13 − 66431.2y 15+8381.97y 17 + 228.563y 19 − 161.358y 21e 7 = −6.31771e7y + 1.40677e8y 3 + 5.56965e6y 5 + 2.46201e7y 7

D.3 103+468142.0y 9 − 1.003e6y 11 − 66212.1y 13 + 23507.6y 15+296.38y 17 − 403.396y 19f 7 = −1.69846e7y + 4.07382e6y 3 − 3.32896e7y 5 − 1.93114e6y 7−934717.0y 9 + 8820.94y 11 + 37544.8y 13 + 125.591y 15−726.113y 17g 7 = −1.23165e6y + 7.52883e6y 3 − 900010.0y 5 − 186682.0y 7 + 79902.5y 9+37371.9y 11 − 260.198y 13 − 968.15y 15h 7 = −610622.0y + 86407.6y 3 + 153468.0y 5 + 72520.9y 7 + 23137.1y 9−571.645y 11 − 968.15y 13o 7 = −23586.5y + 49883.8y 3 + 26538.5y 5 + 8073.15y 7 − 575.164y 9−726.113y 11p 7 = −8009.1y + 2198.86y 3 + 953.655y 5 − 352.467y 7 − 403.396y 9q 7 = −622.056y − 271.202y 3 − 134.792y 5 − 161.358y 7r 7 = −77.0535y − 29.7896y 3 − 44.0068y 5s 7 = −2.92264y − 7.33447y 3t 7 = −0.56419ya 8 = 1.02827e9 − 1.5599e9y 2 + 1.17022e9y 4 − 5.79099e8y 6 + 2.11107e8y 8−6.11148e7y 10 + 1.44647e7y 12 − 2.85721e6y 14 + 483737.0y 16 − 70946.1y 18+9504.65y 20 − 955.194y 22 + 126.532y 24 − 3.68288y 26 + 1.0y 28b 8 = 1.5599e9 − 2.28855e9y 2 + 1.66421e9y 4 − 7.53828e8y 6 + 2.89676e8y 8−7.01358e7y 10 + 1.39465e7y 12 − 2.84954e6y 14 + 498334.0y 16 − 55600.0y 18+3058.26y 20 + 533.254y 22 − 40.5117y 24 + 14.0y 26c 8 = 1.17022e9 − 1.66421e9y 2 + 1.06002e9y 4 − 6.60078e8y 6 + 6.33496e7y 8−4.60396e7y 10 + 1.4841e7y 12 − 1.06352e6y 14 − 217801.0y 16 + 48153.3y 18−1500.17y 20 − 198.876y 22 + 91.0y 24d 8 = 5.79099e8 − 7.53828e8y 2 + 6.60078e8y 4 + 5.40367e7y 6 + 1.99846e8y 8−6.87656e6y 10 − 6.89002e6y 12 + 280428.0y 14 + 161461.0y 16 − 16493.7y 18−567.164y 20 + 364.0y 22e 8 = 2.11107e8 − 2.89676e8y 2 + 6.33496e7y 4 − 1.99846e8y 6 − 5.01017e7y 8−5.25722e6y 10 + 1.9547e6y 12 + 240373.0y 14 − 55582.0y 16 − 1012.79y 18+1001.0y 20f 8 = 6.11148e7 − 7.01358e7y 2 + 4.60396e7y 4 − 6.87656e6y 6 + 5.25722e6y 8+3.04316e6y 10 + 123052.0y 12 − 106663.0y 14 − 1093.82y 16 + 2002.0y 18g 8 = 1.44647e7 − 1.39465e7y 2 + 1.4841e7y 4 + 6.89002e6y 6 + 1.9547e6y 8−123052.0y 10 − 131337.0y 12 − 486.14y 14 + 3003.0y 16h 8 = 2.85721e6 − 2.84954e6y 2 + 1.06352e6y 4 + 280428.0y 6 − 240373.0y 8−106663.0y 10 + 486.14y 12 + 3432.0y 14

104 D k o 8 = 483737.0 − 498334.0y 2 − 217801.0y 4 − 161461.0y 6 − 55582.0y 8+1093.82y 10 + 3003.0y 12p 8 = 70946.1 − 55600.0y 2 − 48153.3y 4 − 16493.7y 6 + 1012.79y 8+2002.0y 10q 8 = 9504.65 − 3058.26y 2 − 1500.17y 4 + 567.164y 6 + 1001.0y 8r 8 = 955.194 + 533.254y 2 + 198.876y 4 + 364.0y 6s 8 = 126.532 + 40.5117y 2 + 91.0y 4t 8 = 3.68288 + 14.0y 2

105 EE.1 P ′ sat , P sat ( 1980).(P sat ′ = P sat exp − 2γv )rkT(E.1), γ , v 1 , r , k , T . 1 , ρ ice 1 m , .v =mρ ice(E.2) E.1 γ 1.055 ×10 −2 N m −1ρ ice CO 2 1.565 ×10 3 kg m −3m CO 2 7.31 ×10 −26 kgk 1.38 ×10 −23 N m K −1T 170.0 K

106 E 1.005(P sat ’ / P sat )1.002510.1 1 10 100 1000Particle Size (µm) E.1. .E.2 , .Re() = vrρ airη< 10 , r v 6πηrv (). , ..0 = 6πηrv − 4πρ icer 3g3(E.3)v(r) = 2 ρ ice g9 η r2 (E.4), . 1atm 100 micron Re < 10 .Re = vrρ airη= 2 9ρ air ρ ice gr 3η(E.5)

E.2 107, , r l .Stokes Velosity [m/s]10001001010.10.010.0010.00011e-051e-061e-071e-07 1e-06 1e-05 0.0001 0.001particle size [m]MarsEarth E.2. , . E.2 ρ ice- CO 2 1.565 ×10 3 kg m −3- H 2 O 1.0 ×10 3 kg m −3η Pa s

108 E 10000100Reynolds Number10.010.00011e-061e-08ρ a = 1.0 [kg/m 3 ]ρ1e-10a = 0.1 [kg/m 3 ]ρ a = 0.01 [kg/m 3 ]ρ1e-12a = 0.001 [kg/m 3 ]1e-07 1e-06 1e-05 0.0001 0.001particle size [m] E.3 . . . 10 .

E.3 109E.3 , []. 10 Pa– .( ) ( ) 3/2 T0 + C Tη = η 0 (E.6)T + C T 0viscosity [Pa s]2.4e-052.2e-052e-051.8e-051.6e-051.4e-051.2e-051e-058e-066e-064e-06100 150 200 250 300 350 400temperature [K]CO 2air E.4CO 2 E.3 η Pa sη 0- CO 2 gas 1.47×10 −5 Pa s - 1.82×10 −5 Pa s T KT 0 293.0 KC - CO 2 gas 240.0- air 117.0

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