WMOD00554

• Title: Seeding Summertime Convective Clouds to Increase Black Hills Rainfall
• Weather Modification - Doc Type: Report

radar, visibility below cloud base, and
a need to develop a statistical base by
sampling clouds rather uniformly
distributed along the size range from
cumulus congestus to moderate
thundershowers.

Numerous studies have shown that
small convective clouds greatly
outnumber large ones. For example,
Dennis and Fernald (1963) found that the
radii of radar echoes from showers in
many parts of the world follow an
exponential distribution. Miller et al.
(1975) fitted exponential distributions
to the diameters of echoes in the North
Dakota pilot Project radar data from
1972 to determine the parameter a in

N = No exp(-aD)

(3)

where N is the number of shower echoes
with diameters between D and (D+dD), No
is a constant reflecting the number of
showers in the space-time domain
studied, and the parameter a
characterizes the size distribution.
They found a for the entire data set to
be about 0.35 km1, in good agreement
with Dennis and Fernald (1963). As the
height of a convective cloud tends to
approximate its diameter (e.g., Miller
et al., 1975), o/e assume that the
exponential relationship with a similar
value for a holds for CDP.

Equation (3) was derived from
hourly snapshot views. As there is a
positive correlation between echo size
and echo lifetime, a large shower has a
greater chance of showing up in such a
census than does a smaller one. Miller
et a1. (1975) studied a supplementary
sample of 479 echoes, from which echoes
that were obviously multi-cellular were
excluded; they found a roughly linear
relationship between echo diameter and
echo lifetime (I' = 0.65). Therefore, in
order to make table 1 reflect more
closely the size distribution of all
echoes that form, exist, and dissipate,
as opposed to the size distribution
observed at a given moment, we have
modified (3) as follows:

N' = No D-1 exp(-aD)

(4)

There is a further complication in that
the snapshot views must catch some
undefined fraction of the echoes in
their growing or dissipating stages,
thereby leading to underestimates of
their maximum size. No satisfactory
method of adjustment for this second-
order complication has been devised.
Therefore no allowance is made for it in
the calculations that follow. It is
considered a minor factor compared to

I ~

the other um:ertainties in the analysis.
All results should be interpreted as
indicating only general trends, rather
than as exac1: calculations of the
possible rainfall increases.

Column 2 of table 1, which shows
the relative frequency of clouds of
different sizes, was obtainE!d by
applying (4) with the paramE!ter a set at
0.35 km1 and normalizing so that the
total number of clouds consi.dered came
out to 100. This is a trunc:ated
distribution. Ignoring clouds with CDP
exceeding 12.5 km is of litt:le
consequence as far as number of clouds
is concerned, although such clouds may
be significant in terms of t.otal
rainfall. On the other hand, there are
many clouds with CDP less than 2 km.
Dennis and Fernald (1963) quoted work by
earlier authors showing that the
exponential distribution they observed
for radar echoes from isolated showers
extends down-scale to the visual
dimensions of small cumulus clouds.
However, we can ignore such clouds in
the present case because they do not
produce any precipitation whether seeded
or unseeded.

The numbers in column 4 of table 1
arl::! the products of the corresponding
numbers in columns 2 and 3. They show
the relative contributions of clouds of
different sizes to the total natural
convective rainfall over the Black
Hills, and peak for CDP around 10 km.
As the bases of summertime convective
clouds near the Black Hills are, on
average, very close to 3 km above sea
level, the 10 km value corresponds to
large storms with cloud tops about 13 km
above sea level. This number agrees
with the common perception that much
Black Hills slimmer rain falls from large
thunderstorms.

The entri.es in column 6 of table 1
for all values of CDP up to 10 km were
obtained by multiplying the
corresponding numbers in columns 2 and
5, and represent the expected rainfall
from silver iodide seeded showers
according to (2) and (4). On the
assumption that seeding would not be
done on clouds more than 10 km deep or,
if it were done, would have no effect,
the entries of column 4 for such clouds
are repeated in column 6.,

A comparison of columns 4 and 6
ignores the possibility of increases in
CDP but suggests, nevertheless, that
silver iodide seeding can increase the
total rainfall from isolated summertime
convective clouds by a factor of roughly
1.7. It is instructive to consider

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