WMOD00399

• Title: WMO Training Workshop on Weather Modification for Meteorologists - Lecture Notes
• Date: 12/1/1979
• Weather Modification - Doc Type: Report

- 48 -

Tp-K = const.

or

Cp
(~~) Rd

for dry air.

(1 )

2-
P1
where K = Rd/Cp (= 2/7 for air) and Rd the gas constant

The saturation ratio produced becomes approximately
( ) Cp/Rd
5 = .!:si = es1/P1 = es1 T2 .
rs2 es2/P2 es2 T1

(2)

If a Gardner counter is pressurized to 920 mm Hg at T1 = 293K the temperature drop upon ex-
pansion to the normal pressure of 760 mm Hg will be 15.6K and the maximum supersaturation
(5-1) will be 230%. According to theory developed in textbooks (see e.g. Wallace and Hobbs,
1977, p. 158; Twomey, 1977, p. 82; Pruppacher and Klett, 1978, p. 138) the equilibrium va-
pour pressure es(r) over the surface of a droplet with radius r depends upon its curvature
and is given by

"!t'

es(r) = es(oo) exp (2cr/rRvPLT 1

(3)

where es(oo) is the vapour pressure of a plane surface of water at temperature T and cr, PL'
Rv are surface tension and density of water at temperature T and gas constant for water va-
pour respectively. The net rate of growth of a droplet of radius r is propoDtional to the
difference e-es(r), where e denotes the actual ambient vapour pressure. Thus, drops with
radii such that e-es(r) < 0 tend to deD3ywhile those with radii such that e-'es(r) > 0 tend
to grow. The critical size rc is therefore the radius for which e-es(rc) = d or, according
to (3) e = es(oo) exp (2cr/rRvPLT1.Hence, the so-called Kelvin-equation reads::

2cr
r = R T 1 ,where 5 = e/es(oo) is the saturation ratio. (4)
vPL n S

With a critical saturation ratio Sc = 3.3 produced in our experiment, particles down to
rc ~ 10-7cm = 10g could be activated. This means that with the high supersa~urations, which
are obtained in expansion chambers, the total number concentrations of the atmospheric aero-
sol can be measured. Aerosol size distributions are usually described in terms of a distri-
bution function n(r) such that n(r)dlogr is the number of particles per unit volume of air
whose radii lie in the interval between rand r t dlogr. Alternately, the c~mulative distri-
bution N(r), expressing the number of particles per unit volume of air whose radii exceed
r is defined by N(r) = Joo n(r)dlogr. Accordingly, I
r

dN/dlogr = n(r) = Ar-a .

(5)

Fig. 1: The portable Aitken nucleus counter.