WMOD00290 ‎(3)‎

• Title: Automated Objective Analysis and Prediction of Mesoscale Convective Systems
• Prepared By: David A. Matthews, Leon Osborne
• Date: 6/6/1983
• Weather Modification - Doc Type: Report

. T~e analysis ~ystem provides a two-step
lteratlOn, where the first estimate of gridded
values for some parameter f is given by

~, N
L.. Wn f n (x,y)1 L: W
1 1 n
where the weight function Wn is
Wn = exp (-dn2/4c) (2)

fO(i,j) =

(1 )

. The wei g~t funct i on constant cis chosen
~o flt a partlc~lar grid scale and phenomena of
lnterest. The dlstance from a grid point (i j)
to the location of the observed data fn(x yj is
d~noted by d~ and N is the number of ob;erva-
tlons that lnfluence a computed grid point
value. The second correction pass uses a
reduc~d value of the weight function, so that
the flnal low pass grid point values are given
by

N N
f(i,j) = fo (i,j) + ~ W' D I ; W' (3)
1 n n 1 n,

where the modified weight function W'n is

W'n = exp (-dn2/4gc), O<g<l

(4)

Dn is the difference between the observed
data value and its first estimate value at the
same point. A simple biquadratic interpolation
between the values of fo(i,j) at the four
nearest grid points is used to estimate fo(x,y).
Barne~ has shown that the final response is a
functlon of wavelength A, is

R = Ro (1 + Rg-1-Rg)
00'

(5)

where

Ro = exp (- TT 24cl A 2)

(6)

The same pro~edure is followed using a
second low pass f1lter to determi ne the band
pass field, which is the difference between the
~wo low pass analyses. The band pass analysis
1 s performed us i ng wei ght function constants
such that. t~e fi lter response (BR) is peaked
at a speclflc wavelength of interest shown in
Fi g. 2. The band pass fi e 1 d defi nes the meso-
~cale features which occur at the wavelength of
lnterest. The total field is then computed as
the sum of the macroscale (first low pass) field
and the mesoscale (band pass) field. This
analysis system is fast, economical and enables
the met~orologist to specify a res'ponse on the
appropnate scale of the mesoscale triggering
phenomena.

The response curves for the fi lters used
in the following examples are shown in Fig. 2.
The low pass responses R1 and R2, used to define
the mesoscale band pass BR response, are shown.
Note the peak at Amax of 200 km. The total
fi e 1 d response (TR) is the sum of the BR and
R2 response curves.

l' ..

RESPONSE rUNeT IONS

! ,.

, -----
! ----
if.......
ff
/
I;
1/
j
J

'-

---

--.

----

---

...

CI- 1C1Xl.
iii- .40
C2- 70u0.
'2~ .40
It,,- 1.:SS

\
\

lIeO.,
.. - RI
... R2
"- BT
"- TR

"

.,

"

.,

0.0
,

Figure 2:

Band pass analysis response functions
for the low pass (R1), high pass
(R2), mesoscale band pass (BT), and
total field response (TR) analyses.

3. NUMERICAL CLOUD MODEL

.Analyses of the effect of lifting on con-
vectlve thermodynamics that control cloud growth
are simul ated using the MESOCU cloud model
dev~l?ped by Kre.itzberg and Perkey (1976) and
modlfled to provlde an analysis of the convec-
tive potent~al (Matthews and Silverman, 1980).
The convect lYe potent i a 1 index (CP I) is defi ned
from a 3 h model simulation of cloud-environment
inte,:,action as the total depth of all clouds
pr~d1ct~d by the model during that simulation.
ThlS arlthmetic sum of the depths of all clouds
formed by the model is taken as a measure of the
thermodynamic potential for convective cloud
growth of each sounding. The CPI is a simple
measure of the relative potential for convective
cloud growth wh~ch.may be realized when synoptic
or mesoscale l1ft1ng creates potential buoyant
energy.

. The MESOCU model used in thi s study is
sll!lple, fast, and one-dimensional, capable of
belng used operationally in weather modification
projects and forecasting. It simulates several
basic proce~ses a.ssoci.ate~ with the development
of clouds, lncludlng llftlng, subsidence induced
~y convective development, mixing of the cloud
l~t~ the environme~t, entrainment, surface eddy
mlxlng, solar heatlng and subcloud evaporation.

.The model is initialized by a vertical
prof1le of temperature and moisture interpolated
to 250 m grid levels from significant level data
observed in a rawinsonde. In these simulations
a convective base is determined from the initial
sounding, and an impulse of 2 mls is applied to
a p.arce.l at t~i~ level. The initial parcel
radlus 1S speclfled as 2 km. Previous sensi-
tivity studies by Matthews and Henz (1975)
showed that 2 mls initial parcel vertical motion
resulted in observed cloud-base heights in most
cases, and that a 2-km initial parcel radius
generally resulted in model prediction of
c ~oud-top hei ghts s imi 1 ar to those observed by
alrcraft or radar echo tops in the vicinity of
soundings.

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