Cumulus Cloud Model - Rain Formation in Warm Clouds: General Systems Theory - page 33

cloud. (ii) Regions of ascending currents are associated with higher liquid water
content (LWC), and negative cloud drop charges and the regions of descending cur-
rent are associated with lower LWC and positive cloud drop charges. (iii) Width of
the ascending and descending currents is about 100 m. The ascending and descend-
ing currents are hypothesized to be due to cloud-top-gravity oscillations (Selvam
et al. 1982a , 1982b ; 1983 ). The cloud-top-gravity oscillations are generated by the
intensification of turbulent eddies due to the buoyant production of energy by the
microscale fractional condensation (MFC) in turbulent eddies. (iv) Measured LWC
( q ) at the cloud-base levels is smaller than the adiabatic value ( q a ) with q / q a = 0.6.
The LWC increases with height from the base of the cloud and decreases towards
the cloud-top regions. (v) Cloud electrical activity is found to increase with the
cloud LWC. (vi) Cloud-drop spectra are unimodal near the cloud base and multi-
modal at higher levels. The variations in mean volume diameter (MVD) are similar
to those in the LWC. (vii) In-cloud temperatures are colder than the environment.
(viii) The lapse rates of the temperatures inside the cloud are less than the imme-
diate environment. Environmental lapse rates are equal to the saturated adiabatic
value. (ix) Increments in the LWC are associated with increments in the temperature
inside the cloud. The increments in temperature are associated with the increments
in temperature of the immediate environment at the same level or the level imme-
diately above. (x) Variances of in-cloud temperature and humidity are higher in the
regions where the values of LWC are higher (Selvam et al. 1982a , 1982b , 1982c ,
1982d ). The variances of temperature and humidity are larger in the clear-air envi-
ronment than in the cloud air (Selvam et al. 1982a , 1982b , 1982c , 1982d ).
The dynamical and physical characteristics of monsoon clouds described above
cannot be explained by simple entraining cloud models. A simple cumulus cloud
model, which can explain the observed cloud characteristics, has been developed
(Selvam et al. 1983 ). The relevant physical concept and theory relating to the dy-
namics of atmospheric planetary boundary layer (PBL), formation of warm cumulus
clouds and their modification through hygroscopic particle seeding are presented in
the following sections.
The mechanism of large eddy growth, discussed in Sect. 2.4, in the atmospheric
ABL can be applied to the formulation of the governing equations for cumulus
cloud growth. Based on the above theory, equations are derived for the in-cloud
vertical profiles of (i) ratio of actual cloud LWC ( q ) to the adiabatic LWC ( q a ), (ii)
vertical velocity, (iii) temperature excess, (iv) temperature lapse rate, (v) total LWC
( q t ), (vi) cloud growth time, (vii) cloud drop-size spectrum, and (viii) raindrop size
spectrum. The equations are derived starting from the MFC process at cloud-base
levels. This provides the basic energy input for the total cloud growth.

2.1.1 Vertical Profile of q/q a

The observations of cloud LWC, q , indicate that the ratio q / q a is less than 1 due
to dilution by vertical mixing. The fractional volume dilution rate f in the cloud
updraft can be computed (Selvam et al. 1983 ; Selvam et al. 1984a ; Selvam et al.