General Systems Theory Concepts in Atmospheric Flows - Rain Formation in Warm Clouds: General Systems Theory - page 17

Table 1.1 Primary eddy growth
Growth step number

±σ k Probability (%)

Model predicted Statistical normal

2 0.9000 0.8864 18.1555 18.4060

3 0.8000 0.7237 24.8304 21.1855

4 0.7000 0.6268 29.9254 24.1964

5 0.6000 0.5606 33.9904 27.4253

6 0.5000 0.5118 37.3412 30.8538

7 0.4000 0.4738 40.1720 34.4578

8 0.3000 0.4432 42.6093 38.2089

9 0.2000 0.4179 44.7397 42.0740

10 0.1000 0.3964 46.6250 46.0172

11 0 0.3780 48.3104 50.0000

tical normal probability density distribution corresponding to the normalized devia-
tion σ values are also given in Table 1.1 .
The model predicted probability density distribution P along with the corre-
sponding statistical normal distribution with probability values plotted on linear
and logarithmic scales, respectively, on the left- and right-hand sides are shown in
Fig. 1.8 . The model predicted probability distribution P for fractal space-time fluc-
tuations is very close to the statistical normal distribution for normalized deviation
σ values less than 2 as seen on the left-hand side of Fig. 1.8 . The model predicts
progressively higher values of probability P for values of σ greater than 2 as seen
on a logarithmic plot on the right-hand side of Fig. 1.8 .

1.6.4 Atmospheric Wind Spectrum and Suspended Particulate

Size Spectrum

The steady-state flux d N of CCN at level z in the normalized vertical velocity per-
turbation (d W ) z is given as follows:

(1.21)

d NNWz = ( d ) .

The logarithmic wind profile relationship for W at Eq. (1.4) gives

NNz w
k

(1.22) *

d = d (ln . z

Substituting for k from Eq. (1.2)

NNz w

(1.23)

* 2

d =

w Wz z Wz

d (ln) = d (ln . z

*