the К-integral:
Kðt; m 0 Þ ¼
ð
2p
0
d’
ð 1
À1
Iðt; m; m 0 ; ’Þm
2 dm
(1.28)
The value [I(t,m 0 ) À K(t,m 0 )] defines the diffuse radiative flux to the horizontal
direction. After integrating the Eq. 1.25 over the viewing angle cosine m and with
taking into account above introduced definitions and Eq. 1.10 – the phase function
normalizing, and the definition of the mean cosine of the scattering angle (1.16) it is
possible to obtain the system of differential equations:
dHðt; m 0 Þ
dt
¼ À 1 À oðtÞ
½
Iðt; m 0 Þ þ oðtÞF 0 expðÀ
t
m 0
Þ
3
dKðt; m 0 Þ
dt
¼ À 3 À oðtÞx 1 ðtÞ
½
Hðt; m 0 Þ þ oðtÞF 0 expðÀ
t
m 0
Þ
(1.29)
This system will be used below for the derivation of asymptotic and Eddington
approaches.
18
1 Radiation in the Earth Atmosphere
Kðt; m 0 Þ ¼
ð
2p
0
d’
ð 1
À1
Iðt; m; m 0 ; ’Þm
2 dm
(1.28)
The value [I(t,m 0 ) À K(t,m 0 )] defines the diffuse radiative flux to the horizontal
direction. After integrating the Eq. 1.25 over the viewing angle cosine m and with
taking into account above introduced definitions and Eq. 1.10 – the phase function
normalizing, and the definition of the mean cosine of the scattering angle (1.16) it is
possible to obtain the system of differential equations:
dHðt; m 0 Þ
dt
¼ À 1 À oðtÞ
½
Iðt; m 0 Þ þ oðtÞF 0 expðÀ
t
m 0
Þ
3
dKðt; m 0 Þ
dt
¼ À 3 À oðtÞx 1 ðtÞ
½
Hðt; m 0 Þ þ oðtÞF 0 expðÀ
t
m 0
Þ
(1.29)
This system will be used below for the derivation of asymptotic and Eddington
approaches.
18
1 Radiation in the Earth Atmosphere