06.fr COS

1
3. Transfer equation (放射伝達方程式)
Extraterrestrial irradiance
Solar insolation
Transfer of radiation
2
Upwelling radiance
L-
F0
TOA
Emission
Atmosphere
()
Scattering volume
Airmass
Absorption
Attenuated direct
() flux
Lg
-
E(T)
Downwelling radiance
F
L+
Water/Ice body
Earth’s surface
Soil/Plant canopy
Radiation budget () of the atmosphere
3
(102)
(175)
(26)
198
(385)
(345)
BSRN (A. Ohmura)
IPCC-AR4 (2007)
The radiation transfer equation
4
Optical thickness: d= -edz
Single scattering albedo: = s/e
Scattering angle: dL() = edxL() + sdx P(, )L( )d + adxB(T )
Extinction
4
Scattering J
Emission
Source
dx
L-edxL
d
L
adxL
5
Radiative transfer equation for a plane parallel atmosphere
Optical thickness: d= -edz
Single scattering albedo: = s/e
Scattering angle: d= dz/μ
2
dL( , μ, )
μ
= L( , μ, ) + d μ d P( μ, μ , )L( , μ , ) + (1 )B(T )
d
1
0
1
μ = cos
z
(e) = (sin cos , sin sin , cos )
L
cos = = cos cos + sin sin cos( )
= μμ + 1 μ 2 1 μ 2 cos( )
y
x
6
4. Transfer of Thermal Radiation
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Transfer of thermal radiation
=0 for > 4 m in cases other than cloudy atmosphere
TOA radiance and black body radiances at various temperature(Goody and Yung,
1989 )
±μ
dL ± ( , μ, )
= L ± ( , μ, ) + B(T )
d
L (0) = [ s B(Ts ) + (1 s )F ( s ) / ]e
+
s / μ
s
+ B(T (t))et / μ dt / μ
0
s
L+ (0) = B(T (t))e( s t )/ μ dt / μ
0
L
0
B(T)
dt
sB(Ts)
s
8
Remote sensing of temperature
Weighting function
s
s
0
0
=k
Lpath B(T (t))et / μ dt / μ = B(T )W (P)dP
dP
dt = a(T )dz = a(T )
g
M n M P
PV = nRT , = air = air
V
RT
N
CN air
CN air P
CN A P
a=k =k
=k
=k
V
V
nRT
RT
a
CN A P RT
dt =
dP = k
dP = PdP
g
RT M air Pg
=
k̂ CN A
CN A
k̂
, if k = k̂P
P M air gP
M air g
p
t = PdP 0
P2
, if = const
2
W (P) = e P /2 P
CN A
CNA
kˆ
MairgP
M airg
= 1,
2, 3, 5, 10
P
2
Pmax = 1 / , Wmax = e
1/2
W
Tiros Operational Vertical Sounder/HIRS Remote sensing of temperature profile
Use of infrared radiance spctrum
9
10
High resolution spctrum
Gas absorption line and band
E = E e + Ev + E r + Et
Water vapor: 0.7, 0.8, 0.9, 1.1, 1.4, 1.9, 2.7, 6.3, rotation
CO2　：2.0, 2.7, 4.3, 15
O3 ：UV, 0.76, 9.6, 14
p T0 n
L ( p, T ) = L ( p 0, T 0 ) p ( )
0 T
f (0)
f (0)/2
0 +
11
12
Polar clouds over snow
(3.7m)-
(10m)
Cirrus
(10m)-
(11m)
Yamanouchi et al. (JMSJ1987)
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14
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5. Radiative Transfer in Optically Thin
Atmospheres
Solar radiation transfer(B=0) in the Clear sky atmosphere
(Optically thin atmosphere)- Direct radiation
2
dL( , μ, )
μ
= L( , μ, ) + d μ d P( μ, μ , )L( , μ , )
d
1
0
1
L = L(0) ( 0 ) + L(1) ( 1 ) + L(2) ( 2 ) + ...
Non scattering, single scattering, multiple scattering
dL(0) ( , μ, )
μ
= L(0) ( , μ, )
d
L(0) ( , ) = F0 e / μ0 ( 0 ) ( 0 )
L0 ( , ) = F0 ( 0 ) ( 0 )
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Solar radiation transfer in the Clear sky atmosphere (Optically
thin atmosphere)- Single scattering radiation
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L(0) ( , , ) = e / μ F0 ( 0 ) ( 0 )
dL(1) ( , , )
μ
= L(1) ( , , ) + d μ d P( μ, μ , )L(0) ( , , )
d
1
1
1
1
= L(1) ( , , ) + P( μ, μ0 , 0 )e / μ0 F0
μ
dL( , μ, )
= L( , μ, ) + J( , μ, )
d
L( , μ, ) = L( 0 , μ, )e
+
Z
F0
0
( 0 )/ μ
t
1
J(t, μ, )e( t )/ μ dt
μ 0
P()
F
t+dt
L(, )
Solar radiation transfer in the Clear sky atmosphere (Optically
thin atmosphere)- Single scattering radiation
L( , μ, ) = L( 0 , μ, )e
( 0 )/ μ
1
+ J(t, μ, )e( t )/ μ dt
μ 0
J( , μ, ) = P( μ, μ0 , 0 )e / μ0 F0
e / μ0 e / μ
L1 ( , + μ, ) = F0 P(+ μ, μ0 , 0 )
1 μ / μ0
L1 (0, μ, ) = L( 0 , μ, )e
( 0 )/ μ
1 e (1/ μ +1/ μ0 )
+ F0 P( μ, μ0 , 0 )
1 + μ / μ0
<< 1
2nd term 1
F0 P(± μ, μ0 , 0 )
μ
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Thin atmospheres
Molecules and aerosols in the shortwave region
2 wavelength problem (color ratio)
μ > 0, L P()F0
μ
μ < 0, L P()F0 + Lg , =
P() + Ag
μ
μ μ0
2 2 2 P2 () 2
= ( 2 ) 1 1 1P1 () 1
1
Reciprocity principle
F0
Lg
P()
F Comparison of Aerosol optical thickness (AOT)
from MIROC-GCM and two satellites (GLI
and MODIS) (Nakajima and Schulz, 2009).
April 2003
L(, )
MIROC+SPRINTARS
ADEOS-II/GLI (Fukuda)
TERRA/MODIS (NASA/GSFC)
AOT
20
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9) Atmospheric correction and Land PAR
Only Rayleigh
correction
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After the 380nm
correction
•By using GLI 380nm channel, we can estimate aerosol scattering.
Courtesy: H.Murakami (JAXA)
Global monitoring and simulation of aerosols
Model underestimation of AOT
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Nakajima and Schulz (FIAS2008)
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ADEOS-II/GLI products
April 2003 (Spring) San Francisco 250m ocean
GLI 250m RGB:
22/21/202003.5.
26
Snow grain size
Snow surface tempearture
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Angular scattering cross section
)4!/(&'1,$00#(01/(!21(-,9:L(μ, μ0, -0)
(/$"10-* /(// #( ,"$:;F0 " 11$/(,&.' 0$%2,"1(-,9:P()
P( + )F0
μ
P( + ) = sdzP( + ) = Csca NdzP( + )
L
, =
P( + ) = drn(r) r 2Qsca ( , , m)
0
n(r)
P( + ), Qsca ( , m)
dV
4 r 4
v(ln r) =
n(r)
d ln r
3
2 r
,3$/0(-,./-!*$+-%0(5$#(01/(!21(-,
8679:
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Dubovik et al. (2002)
Early 80s situation
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Heavy
Manual
Difficult data analysis
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SKYNET
Sky radiometers
IMD in New Delhi, March, 2006, Kazuma AOKI
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Angular integrations of the phase function
Legendre polynomial expansion
Asymmetry factor
g: 0 (isotropic), 0.6-0.7 (aerosols), and 0.8-0.85 (clouds)
Forward and backward scattering fractions
Up and down scatter fractions
1 1
P(cos) =
(2n + 1)gn Pn (cos) (1 + 3g cos)
4 n = 0
4
cos ± = ± μμ0 + (1 μ )(1 μ ) cos( 0 )
2
2
0
F0
2
1
0
d cos dP(cos) = 1
1
0
1
2
1
0
b
d cos d cosP(cos) = g
1
2
± ( μ0 ) = d μ dP(cos ± ) =
0
0
1
2
0
0
f = d cos dP(cos) =
b = 1 f
f
1
3
(1 ± gμ0 )
2
2
P()
1
3
(1 + g)
2
2
g > 0.7 f > 1, b < 0!
Flux transmissivity and reflectivity
+
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Unidirectional flux transmissivity: t(μ0)
Unidirectional flux reflectance: r(μ0)
Spherical reflectance: <r>
μ = cos , μ0 = cos 0
m = 1 / μ , m0 = 1 / μ 0
(m + m0 ) << 1
L e m0 ( μ μ0 ) ( 0 )F0 + mP(+ μ, μ0 , 0 )F0
1
t( μ0 ) =
μ0 F0
=e
m0
2
1
0
0
d d μμ L(μ, μ , )
0
2
1
0
0
0
+ m0 d d μ P() = e m0 + m0 + ( μ0 ) = 1 m0 [1 + ( μ0 )]
r( μ0 ) = m0 ( μ0 )
1
2
0
0
± ( μ0 ) = d μ dP(cos ± ) =
1
3
(1 ± gμ0 )
2
2
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Radiative energy budget
3
1
(1 + gμ0 )]
2
2
3
1
r( μ0 ) = m0 (1 gμ0 )
2
2
3
3
1
1
t + r = 1 m0 [1 (1 + gμ0 )] + m0 (1 gμ0 )
2
2
2
2
= 1 m0 (1 )
t( μ0 ) = 1 m0 [1 t +r+a =1
32
Spherical albedo (Planetary albedo)
1
2
1
2
1
2
0
0
0
0
0
0
r = d μ0 d0 r( μ0 )μ0 F0 / d μ0 d0 μ0 F0 = d μ0 d0 ( μ0 ) / 1
= d μ0 (1 0
3
3
1
1
gμ0 ) = 2 (1 g) = r( )
2
4
2
2
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Atmosphere-Earth’s surface problem
Principle
of reciprocity
L = mP( μ, μ0 , 0 )F0 +
1 t ( μ )A(1 rA)1 t + ( μ0 )μ0 F0
L
= mm0 P( ) + t( μ )A(1 + rA)t( μ0 )
μ0 F0
1
t( μ0 ) = 1 tˆ( μ0 ) , r = r̂( )
2
3
3
1
1
tˆ( μ0 ) m0 [1 (1 + gμ0 )], r̂( μ0 ) m0 (1 gμ0 )
2
2
2
2
1
mm0 P( ) + A [tˆ( μ ) + tˆ( μ0 ) r̂( )A]A
2
=
34
Reflected radiation from a thin atmospheres (Detailed) Neutral reflectance: deriving d
= mm0 P( ) [tˆ( μ ) + tˆ( μ0 ) r̂A]A = 0
d
A << 1
mm P(cos )
An = 0 t ( μ ) + t ( μ0 )
35
Equation for the planetary albedo
Averaged
radiation field for the planet
S
(global average)
4
S
= (daytime average)
2
QSW =
a 2 S
36
Earth’s reflectance in the clear sky condition
Flux reflectance
Planetary albedo
mm0 P( ) + t( μ )t( μ0 )Ag
rAL ( μ0 ) Fref
μ0 F0
1
2
0
0
= d μμ d[mm0 P( ) +
1
t( μ )t( μ0 )Ag ]
1
rAL ( μ0 ) = r( μ0 ) + t( )t( μ0 )Ag
2
dS = 2 rE sin 0 rE d 0 = 2 rE2 d μ0
dSr
AL
rP =
2
( μ0 )μ0 F0
rE2 F0
1
1
= 2 d μ0 r( μ0 )μ0 = rAL ( )
2
0
rE
Latitude
37
Shortwave radiative forcing of aerosols
1
t( μ0 ) = 1 tˆ( μ0 ) , r = r̂( )
2
3
3
1
1
tˆ( μ0 ) m0 [1 (1 + gμ0 )], r̂( μ0 ) m0 (1 gμ0 )
2
2
2
2
1
mm0 P( ) + A [tˆ( μ ) + tˆ( μ0 ) r̂( )A]A
2
1
A 0.07 rP = r̂( μ0 ) + A 2tˆ( μ0 )A , μ0 =
& %
2
"$#'!'
rP {r̂( μ0 ) 2tˆ( μ0 )A}
= 1 tˆ( μ0 ) = r̂( μ0 )
g
gamtau
n
Tu
A
ARF
rP r̂( μ0 )(1 2A)
Charlson et al. (1992)
FS = (1 n)rp rE2 / 4 rE2
= 2(1 n)tu 2 (1 A)2 ( μ0 ) Q
F
Q = 0 , = 0.04, FS = 1.3W / m 2
4
0.60
0.28
0.04
0.60
0.76
0.15
-1.26
38
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References
Charlson, R. J., S. E. Schwartz, J. M. Hales, R. D. Cess, J. A. Coakley, Jr., J. E. Hansen,
and D. J. Hofmann, 1992: Climate forcing by anthropogenic aerosols. Science, 255,
423-430.
Dubovik, O., et al., 2002: Variability of absorption and optical properties of key aerosol
types observed in worldwide locations. J. Atmos. Sci., 59, 590-608.
Takemura, T., T. Nozawa, S. Emori, T.Y. Nakajima, and T. Nakajima, 2005: Simulation
of climate response to aerosol direct and indirect effects with aerosol transport-radiation
model. J. Geophys. Res., doi:10.1029/2004JD005029.
Tanaka, M., T. Takamura and T. Nakajima, 1983: Refractive index and size distribution
of aerosols as estimated from light scattering measurements. J. Climate Appl. Meteor.,
22, 1253-1261.