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

DECEMBER 1978

R. E. CARBONE AND LOREN D. NELSON

2307

over some portion of one rainshaft penetration. Path
lengths range from 2.5 to 6.0 km for each spectrum,
corresponding to minimum sample volumes between
1700 and 4100 .e in the 4.5 mm diameter size range.
Upper distributions result from averaging over rain-
shaft regions where rates exceed 10 mm h-1. Similarly,
the lower distributions are from regions where rates
are < 10 mm h-1. In the latter case data are used from.
noncontiguous regions and may represent an average
of two or more different spectral forms. For each mea-
sured distribution, the MP equivalent spectrum is also
plotted for the observed rainfall rate. The measured
rainfall rate R and reflectivity factor Z are shown for
each spectrum along with the MP equivalent values.2
While it may not be reasonable to expect drop-size
distributions similar to MP in the convective storm
situation, widespread familiarity with them permits
the authors to describe measured spectra in an easily
recognizable frame of reference.
Many of the sample spectra apparently do not
represent an equilibrium condition between the physical
mechanisms at work. This is evidenced by secondary
maxima of number density at large drop sizes-occa-
sionally exceeding 3 mm diameter. In general, the
spectra shown may be characterized as having a deficit
of small drops (< 2 mm) and an excess of large drops
(>3 mm) relative to MP equivalents. In terms of
exponential spectrum parameters this translates to
small ^ and low No values. Many spectra (even when
averaged over path lengths of several kilometers) were
not well approximated by the exponential form. Others
were approximately exponential but with flatter slopes
than MP. The relative excess of large drops shown in
Fig. 3 profoundly affects parameters inferred from
higher moments of the size distribution such as liquid
water content (3rd), rainfall rate ("-'3.6) and reflec-
tivity factor (6th). Clearly, reflectivity factor repre-
sents the largest departure from commonly accepted
parametric relationships associated with lower mOments
of the size distributions. Extreme cases (such as in-
dicated in Fig. 3d) reveal measured Z to be one order
of magnitude larger than the MP value for the measured
rainfall rate and, conversely, an implied MP rainfall
rate four times greater than that measured when this
relationship is employed. It should be stressed that the
examples shown are more extreme in spectral form
than" typical" spectra; however, they accurately con-
vey the sense of departure from MP spectra.

c. Radar/aircraft comparison

Given the extreme spectral forms shown in Fig. 3,
independent verification of large drop concentration is
essential. Fig. 4 shows flve cross sections of radar-
measured reflectivity factor and reflectivity factor which

2 Z = 200 Rl.', ^ = 41 R:'J.21, where R is in mm-" ^ in cm-I and
Z in mm' m-3.

50 I
~40

CD 30
E
.5 20

~ 5011
'--' 40
0::
o
t; 30
<l:
lL.

i ::11

~ 40
w
0::
30

20

( d)

j50
40
30

jl::
40
30
20

(e)

-4 -3 -2 -I 0 1 2 3
HORIZONTAL DISTANCE (km)

FIG.i. Reflectivity factor profiles on 14 August 1975 along air-
craft flight path. Solid curves were measured by 10 cm radar,
dashed curves calculated .from aircraft spectrometer measure.
ments of drop spectra. Note variable radar resolution in legend.
Negative abscissa values correspond to southwest flank in (a)-(c)
and west flank in (d)-(e).

has been calculated from the aircraft-measured size
distributions. Reflectivity factor Z is defined as the sixth
moment of the drop spectrum

Z= 1'" N(D)D6dD,

where Z has units of mm6m-3 and D is drop diameter
(mm). The excellent agreement between these measure-
ments for the sixth moment gives confidence that
large-drop concentrations (as measured by the air-
craft) are correct, since all significant contributions to
Z are from drops greater than 2 mm diameter.
The agreement between radar and aircraft measure-
ments compares favorably ~with associated statistical
uncertainty. Confidence limits (95%) of the radar
estimate3 are shown in Fig. 4 as well as the horizontal
radar resolution. Where the aircraft path is in the cross-
beam direction (such as Fig. 4e), the radar cannot
resolve fine-scale structure shown in the spectrometer
measurements. Uncertainty associated with spectrom-
eter values is highly variable on a point-by-point basis
and is generally greater than radar estimate uncertainty.
Near the periphery of rainshafts the presence or absence

3 Each radar value is estimated to represent 25 independent
samples. This is approximately correct if Doppler spectrum vari-
ance ? 1 m2 S-2.