where *c*l is the fractional low cloud amount, *c*eff and *c*eff are the effective middle and high

cloud cover amounts based on the principle of random overlap, and χ (*i*,*m*,*h *) is the cloud

irradiance factor for low, middle, and high clouds, respectively. *c*eff and *c*eff are given as

(3.6)

where *c*m (*c*h) are the fractional middle (high) cloud cover amounts. Hodges et al. (1983)

originally defined χ (*i*,*m*,*h*) as

χ (*i*,*m*,*h *) = 80 - 5*Z*(*l *,*m*,*h *)

(3.7)

where *Z*(*l *,*m*,*h *) is either the low, middle, or high cloud base altitude in kilometers. Equation

(3.7) has been modified based on the Geophysics Laboratory model atmospheres (tropics,

given as

χ (*i*,*m*,*h*) = 94 - 5.8*Z*(*l *,*m*,*h*) .

(3.8)

The cloud base altitude, if not available from observations, has been parameterized in

terms of season and latitude following the approach by Stowe et al. (1980) and London

(1957) and data from the *Global Distribution of Total Cloud Cover and Cloud Type*

equation is given as

(3.9)

coefficients given in Table 3.1.0.

latitude, and cloud type.

Winter (Dec, Jan, and Feb)

Cloud Type

Latitude

a

b

c

d

low

>=25

1050

600

1.5

25

low

<25

1050

600

5.0

25

middle

>=25

4100

2000

1.7

25

middle

<25

4100

300

4

25

high

all

7000

1500

3

30

Non-Winter (Mar, Apr, May, Jun, Jul, Aug, Sep, Oct, and Nov)

Cloud Type

Latitude

a

b

c

d

low

>=25

1150

600

1.5

25

low

<25

1150

450

5.0

25

middle

>=25

4400

1200

3.0

25

middle

<25

4400

300

4

25

high

all

7000

1500

3

30

The total downwelling radiation is given as

(3.10)

16