General Systems Theory Concepts in Atmospheric Flows - Rain Formation in Warm Clouds: General Systems Theory - page 18

σ σ

Fig. 1.8 Model predicted probability distribution P along with the corresponding statistical nor-
mal distribution with probability values plotted on linear and logarithmic scales, respectively, on
the left- and right -hand side graphs

The length scale z is related to the suspended particulate radius r a (Eq. 1.14). There-
fore,

3
2

r
r

a
as

ln z = ln . (1.24)

r
r

a
as , i.e., r an represents the suspended par-
ticulate mean volume radius r a in terms of its mean volume radius r as at the surface
(or reference level). Therefore,

Defining a normalized radius r an equal to

= 3
2

ln z ln r , (1.25)

an

= 3
2

(1.26)

d ln z d ln r .

an

Substituting for dln z in Eq. (1.23)