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

102

R. E. CARBONE AND LOREN D. NELSON

2311

DECEMBER 1978

(0) Four Parametric Cycle
----~Growth
'E --Dissipation
o
.~ C
<t _"::~~--=.~--.......
Cl --~... 18
~ 101---....---- ~~)
S ,.,-/IA
",.."""." // 0
,
AG/

3XIOO 0
10

101
R (mm/hr)

102

10-4
100

c ,,"----/-::-~ 8
". ~-R...
".',_... ....,..'X". I
__~7 ". \. I
....._......:::.,.,.. ""II" ,Of!'
--_/" "."" ,,/ ,
"" I AD
/' '---Growth
./ AG / --Dissipation

101 102

R (mm/hr)

FIG. 9. Parametric cycles for two-growth-stage and two-dissipation-stage storms.
Lines represent computer smoothed median point frequency curves from ,original
scatter diagrams. Growth-stage clouds show very low No and ^ values at pomts A G.

and

A=41R--{).2\

where A is in cm-1 and R in mm h-1. Results from
logarithmic regressions performed. on measurements
presented herein were both unexpected and disappoint-
ing witli respect to the original objectives in that-. the
data did not fit similar relationships. Figs. 8a and 8b
show examples of exponential spectrum parameters
obtained from regressions as a function of rainfall rate.
Data are indicated by numbers which are the number of
data points within each character bin determined by the
computer output resolution (0.1 decade). The resulting
regression equation is shown by" +" symbols. The data
are from one echo penetration. It is clear from Figs. 8a
and 8b that linear regressions of log IoN 0 and IOgloA
with log loR are not appropriate for these nonlinear data.
Similarly, Fig. 8c shows a regression for total number
concentration NT.
More important than the lack of a simple power-law
relationship between spectrum parameters and rainfall
rate is the fact that most of the scatter diagrams reveal
nonlinear (but deterministic) patterns for each variable
as revealed in Figs. 8a-8c. These patterns indicate fairly
continuous relationships between spectrum parameters
and rainfall rate. From a time"sequential tabular listing
of the data, it was determined that the patterns of A,
No and NT represented spatial variations as the air-
craft flew through the precipitation region. As illu-
strated in Fig. 8d, point A represents the southwestern
edge of the precipitation region; point B, the high-
rainrate core of the precipitation; arid points C and D
the northeastern portions of the rainshaft all of which
were revealed from the time-sequential tabular listings
of spectrum parameters. Due to large gradients of rain-
fall rate on the southwest boundary, point A usually
occurs at higher rainfall rates than point D because of
.. minimum aircraft sampling volume (distance) con-
siderations. It can be seen that the southwest edge of
the precipitation region is characterized by low No, ^
and NT values which are indicative of relatively large-

,''1

drop weighted spectra wit? a deficit of small drops.
Values of all three parameters increase toward the core
of the rainshaft. In this particular example between
the core and the northeast edge, ^ continues to increase,
No remains essentially constant and NT decreases. In
all cases parameter values are larger (for equivalent
rainfall rate) on the northeast flank than the southwest
flank. At the northeast periphery all parameters sharply
decrease in value possibly due in part to evaporative
effects. The systematic behavior of exponential spec-
trum parameters as indicated by spatial variability
through rainshafts may be referred to as a "para-
metric cycle" of drop-size distribution characteristics.
It must be emphasized that the data shown are the
result of a single aircraft penetration into a rainshaft
with a relatively uncomplicated profile of rainfall rate.
Diagrams similar to Fig. 8 were compiled for data
previously described in Section 4 which were simul-
taneously examined by radar and aircraft. The para-
metric cycles of each are shown in Fig. 9, where each
line was formed from median point frequency values of
each parameter in each storm. Each curve represe?ts
data from five penetrations totaling ",30 min samplmg
time. Rainfall rates < 1 mm h-1 were not included due
to inadequate sample volume. Computer graphics h~ve
objectively smoothed the lines by means of a splme
fit. Since the four storms were originally selected for
analyzing temporal changes in drop spectrum param-
eters, the growth stage storms are indicated by dashed
lines and dissipation stage data by the long dash-dot
pattern. Figs. 9a and 9b are qualitatively similar to
Fig. 8. The parametric cycle is evident with differenc~s
in detail among the four storms. Temporal changes m
spectrum parameters are evident in Figs. 9 in that both
growth-stage rainshafts have much lower values of No
and A on the southwest flank of the precipitation
regions. This result is consistent with averaged distribu-
tions shown in Fig. 5 in that growth-stage spectra
exhibit a very low numher density of small drops.
When updrafts were observed, they occurred on the

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