WMOD00474

• Title: The Evolution of Raindrop Spectra in Warm-Based Convective Storms as Observed and Numerically Modeled
• Date: 12/12/1978
• Weather Modification - Doc Type: Report

2310

JOURNAL OF THE ATMOSPHERIC SCIENCES

VOLUME 35

~ 10-2
..
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o

o
Z 10-3

10-1 49 47 45!:1-341

29
__ Model
== ass
o Time (min)

101
R (mm/hrl

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-2
<l:
Cl
lD
::!!:
<l:
...J

_ Model
=-= ass
o Time (min:

_T
T"_
I --_
-=~+----29
--- I
I
I
1

2 3xIOO 0
10 10

101.
R (mm/hr)

FIG. 7. Parametric cycles resulting from the model: (a) No marching with time; (b) A
marching with time. Regression lines of growth stage observations (dashed) and dissipa-
tion stage (long dash) are shown. Error bars indicate (Y= 1 limits for observations. Note
how model converges to Marshall-Palmer values during dissipation stage.

that collisional breakup is the dominant breakup pro-
cess when there is a high number concentration of
drops. The fact the Srivastava did not permit this
process in his model is a contributing factor to the non-
exponential spectral form which resulted. This has
been examined in more detail by Srivastava (1978),
and the results of this work \ show that spontaneous
breakup is not negligible if No"'" 3 X 10-3 cm-4 and
^"'" 10 cm-I. Production ratios, determined from
Srivastava's Figs. 1 and 2, substantiate this conclusion

2

'E
u

(0) ^ vs R (Single
Penetration)
C

,..---,
-<

311 1
1 ~2 3;12111 B
11 111 1 ))..3&583

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--
.....t-ttt.ttt.......

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A

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0.1 1.0
(c) NT vs R

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2. .11++
."

Cui +'1.-+:1

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3211 ....... 1
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22..... 11
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1 1. ..... 2:\ 22
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+; ~ z 12A

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,

.,

I
0,1 1.0 10 100
R (mm/hr)

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.,.
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~
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52
t9
o
--l -4

(b) No vs R (Single
Penetration)
,
'< l .l. C 1 263 B H
1 l5il lJJl7'+ ..+...tot
1 :1 1++++22
I ..t+++'t 136
11 1++++ t Z11
11..... +! 231
...... ;ji' 12
.. D1 1 Z~.1 ~~ A
l2 l 2

100

-5
0.1

1.0 10

(d) Points on the
Parametric Cycle

N
t

FIG. 8. Parametric cycles as evidenced from one aircraft penetra-
tion of a storm: (a) A, (b) No, (c) NT, (d) key points on the
parametric cycles with respect to schematic representation of rain-
fall rate isopleths. Arrow indicates typical aircraft flight path.
Regression curves in Figs. 8a-8c are indicated by plus signs.
Datum frequency indicated by numbers.

100

in that the spontaneous and collisional terms are
roughly equal in magnitude for the previously specified
parametric values.
A critical question arises as to how initial conditions
arise which are favorable to spontaneous breakup. The
observations presented here show that low concentra-
tions of drops < 2 mm diameter at cloud base occur
when an updraft is likely to be present. The most
straightforward explanation is that small drops are
unable to fall through the updraft. Furthermore, the
spectral form associated with updraft sorting is very
similar to that which results from the stochastic
coalescence and spontaneous breakup processes as given
by Srivastava (1971) and the model results presented
herein. The authors hypothesize that prior updraft
sorting of the drop spectrum lowers the total number
concentration to the point where spontaneous breakup
may be as or more important than the collisional
breakup process. Given that spontaneous breakup is
roughly proportional to total number concentration and
collisional breakup is proportional to concentration
squared, this argument is physically plausible. Con-
clusive demonstration of this sequence is not possible
from the observations alone due to limitations of sampl-
ing spectra within the storms. Interpretation of the
model results is ambiguous to the extent that the effects
of sedimentation cannot be readily separated from the
breakup processes.

6. Spatial variation of drop spectra

As evidenced by Fig. 3, some drop distributions are
not well described by the exponential parameters No
and t... Nevertheless, regressions were performed on all
individual (500 m path length) spectra for the purpose
of delineating power-law relationships between rainfall
rate R and exponential spectrum parameters. It may
be recalled that for MP distributions, No=0.08 cm-4