The Dynamics of the Initiation
of an Oklahoma Squall Line
by
FRANK PARKER COLBY, JR.
B.S., University of Michigan
(May, 1976)
Submitted in Partial Fulfillment
of the Requirements of the
Degree of
Master of Science
at the
Massachusetts Institute of Technology
(February, 1979)
Signature of Author.
...
February,
-.
Department of keteoology,
.
9
1979
Certified by...................................................
Thesis Supervisor
Accepted by...
....
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Department Committee
The Dynamics of the Initiation
of an Oklahoma Squall Line
by
FRANK PARKER COLBY, JR.
Submitted to the Department of Meteorology
on January 19, 1979 in partial fulfillment of the
requirements for the Degree of Master of Science.
ABSTRACT
The June 8-9, 1966 case from the National Severe Storms
Laboratory was used to study the initiation and organization
of deep convection into a squall line.
This case was outstanding
for this study due to its large amount of pre-convection radiosonde data.
Strong surface convergence was present at least one
to one and a half hours prior to the appearance of echoes on the
Norman, Oklahoma radar.
This convergence was examined in light
of the theory of inertial instability as developed by Emanuel(1978).
The results indicated that this theory could not explain the
initiation of the mesoscale circulation of which the convergence
was a part.
Subsequently, mesoscalc analysis was used in conjunction with
the calculation of cloud work functions (Arakawa and Schubert,
1974) to develop an understanding of the beginnings of deep convection.
It is concluded that a combination of thermodynamic
susceptibility to convection (manifested by the behavior of the
cloud work functions) coincident with strong frontal surface convergence initiated the deep convection.
ACKNOWLEDGEMENTS
I must give primary recognition to Professor F. Sanders,
who has helped me along numerous times, and who has allowed
me to proceed at my own speed.
I also thank the other members
of the MIT Konvection Club, especially John Gyakum for listening
to me organize my ideas and suggesting new ones.
Name and Title of Thesis Supervisor:
Frederick Sanders
Professor of Meteorology
TAELE OF CONTENTS
Page #
Abstract
2
Acknowledgements
3
Table of Contents
4
List of Tables
5
List of Figures
6
Introduction
8
The Data
11
The Synoptic Situation
12
The Mesoscale Situation
13
Evaluation of Inertial Instability
17
Mesoscale Analysis--Cloud Work Functions
20
Summary
28
Appendix
29
Tables
31-33
Figures
34-81
Pibliography
82
LIST OF TABLES
Table #
Description
Page #
1
Corrections made to RH of radiosondes
31
2
Virtual temperature differences across front
32
3
Comparison of CWF in detail for HYE 1530 and HYB
33
1530 moist
LIST OF FIGURES
Figure #
0
Description
Page #
1
Map of NSSL network for 1966
34
2
Synoptic analysis for.June 7, 1966, 1200Z, surface
35
3
500 mb analysis for June 7, 1966, 1200Z
36
4
Synoptic analysis for June 8, 1966, 1200Z, surface
37
5
500 mb analysis for June 8, 1966, 1200Z
38
6
Synoptic analysis for June 9, 1966, 1200Z, surface
39
7
Mesoscale analysis for June 8, 1966, 0800 CST
40
8
Mesoscale analysis for June 8, 1966, 1100 CST
41
9
Mesoscale analysis for June 8, 1966, 1400 CST
42
10
Mesoscale analysis for June 8, 1966, 1500 CST
43
11
Mesoscale analysis for June 8, 1966, 1600 CST
44
12
Mesoscale analysis for June 8, 1966, 1700 CST
45
13
Mesoscale analysis for June 8, 1966, 1800 CST
46
14
Mesoscale analysis for June 8, 1966, 1900 CST
47
15
Sounding for LTS 0548
48
16A
CWFs for SPS 1100
49
16B
Sounding for SPS 1100
50
17A
CWFs for SPS 1400
51
17B
Sounding for SPS 1400
52
18A
CWFs for SPS 1530
53
18B
Sounding for SPS 1530
54
19A
CWFs for CHK 1048
55
19B
Sounding for CHK 1048
56
20A
20B
CWFs for CHK 1400
57
Sounding for CHK 1400
58
20B
LIST OF FIGURES (cont.)
S Figure #
21A
CWFs for CHK 1536
59
21E
Sounding for CHK 1536
60
CWFs for WAT 1105
61
22B
Sounding for WAT 1105
62
23A
CWFs for COR 1400
63
Sounding for COR 1400
64
24A
CWFs for WAT 1526
65
24B
Sounding for WAT 1526
66
S 25
Sounding for WAT 1257
67
26
Sounding for HYB 1400
68
27
Sounding for HYB 1400 + 1
S 22A
S 23B
hours of lifting
69
CWFs for HYB 1530
70
28B
Sounding for HYB 1530 and HYB 1530 moist
71
280C
CWFs for HYB 1530 moist
72
Cloud tops for HYB 1530 and HYB 1530 moist
73
29A
CWFs for LTS 1527
74
29B
Sounding for LTS 1527
75
Schematic of mesoscale circulation of a squall line
76
31A
Stability analysis for 1100, 1400 CST
77
31B
Stability analysis for 1530, 1700 CST
78
32
Sketch of frontal circulation
79
33
Time evolution of CWFs
80
34
Results of divergence calculation at 1500 CST
81
S 28A
S 28D
S 30
0
Page #
Description
INTRODUCTION
Deep cumulus convection represents the growth of a cloud by
a buoyant updraft.
The buoyancy is a function of a density differ-
ence, manifested as a virtual temperature difference, between the
updraft air and the environment air.
Given the proper temperature
structure and an initial perturbation, a convective cloud can
grow to great heights.
Generally speaking, one needs a warm moist
layer of air near the surface, plus a mechanism to start the activity, in order to get deep convection.
Many mechanisms are
possible to provide the initial perturbation.
Orography can pro-
vide a forced ascent, simply by having the flow be upslope.
Dif-
ferential heating can create a mesoscale circulation (sea breeze
type) which includes rising warm air.
Low level frontal circu-
lation involves a direct thermal circulation which also incorporates rising warm air.
Gravity waves have been suggested as
mechanisms for setting off convection (Tepper, 1950).
Schaeffer
(1975) showed that mcdelling the diffusion of heat and moisture
across a dry line could produce convection too.
On June 8-9, 1966, a number of cumulus cells formed in the
National Severe Storms Laboratory(NSSL) radiosonde network.
After
a short while, the cells were deep enough and had become.organized
into a continuous enough line for the system to be considered a
squall line.
Upon examination of this case, some of the above
mechanisms for initiation can be ruled out.
The orography is not
strong enough in this area to affect the atmosphere by upslope flow.
Indeed, the flow also appears to be mostly parallel to what topography there is.
The moisture gradient in the area is smaller
by an order of magnitude than that used by Schaeffer (1975).
The
differential heating will be dealt with shortly in connection with
a theory suggested by Ogura and Chen(1977).
This particular case history from NSSL has been studied by
several investigators, including Eisen(1972), Fankhauser(1974),
Lewis et al.(1976), and Ogura and Chen(1977).
Eisen(1972) used
an objective analysis scheme to derive temperature, humidity,
pressure, wind, vorticity, mass convergence and moisture convergence fields.
He also made time sections of the vertical structure.
He was mainly interested in determining the effect the squall line
had on the larger scale environment.
lie did note that the squall
line had developed in response to a cold front and moved away
from it after it formed.
He also noted that the echoes formed near
an area of maximum moisture convergence, though not directly on
the maximum.
Fankhauser(1974) presented a partly objective, partly subjective technique for deriving a reliable height field using the
NSSL data.
He demonstra.ted this using the June 8-9, 1966 case,
but looked mostly at later stages (1700 CST and later) after the
convection had become organized into a squall line.
Ogura and Chen(1977) used an objective analysis technique to
derive various fields of interest.
They noted and discussed the
fact that significant surface convergence preceeded the initial
echoes, but were unable to conclude what was the cause of that
10
convergence.
They concluded that the vertical motion associated
with the convergence lifted the top of the mixed layer to saturation, and that this air then was buoyant enough to lead to deep
convection.
They offered four hypotheses for the convergence:
a) inland sea breeze, b) vertical transport of westerly momentum
c) Ekman pumping and d) synoptic scale convergence.
The inland
sea breeze is the result of differential surface heating creating
a direct thermal circulation just as in a 'real' sea breeze.
This
would be seen as a 'sea breeze' front along with its associated
surface wind convergence, or if the timing were perfect, as a
reinforcement of the existing cold front.
The former should have
been visible within 4-6 hours after the onset of the heating (Anthes,
1978).
As will be seen later, we don't see any convergence that
is not associated with the cold front, so the first option is not
operating.
The second possibility is really indistinguishable from
saying that diabatic heating is frontogenetical.
Hence, the inland
sea breeze does not explain the situation.
The vertical transport mechanism and the Ekman pumping are
both dismissed by Ogura and Chen.
The transport theory would imply
an increase in westerly momentum on the dry side of the convergence
line/front.
Ogura and Chen(1977) found this was contradicted by
the data.* The Ekman pumping theory predicts fairly large values
of vorticity at the top of the mixed layer, which again were not
found.
Ogura and Chen concluded that more work on the other
theories of initiation was needed.
We pursued one other theory, that presented by Emanuel(1978)
in which he suggested that inertial instability could predict the
formation of a mesoscale circulation similar to a frontal circulation.
We also did a mesoscale analysis of the state of Oklahoma
and a detailed study of the vertical temperature structure, together
with its susceptibility to convection.
The details will be pre-
sented in the rest of this paper.
THE DATA
NSSL is located in western Oklahoma, and in 1966 included a
radiosonde network and a surface recording network (see figure 1).
The radiosondes were taken on June 8, 1966, at 1100 CST, 1400 CST,
and every 11 hours thereafter until 2300 CST.
Two stations also
reported at 0600 CST and one station made a sounding at 0030 CST
on June 9, 1966.
The soundings were plotted at all of the signi-
ficant levels (about every 300 meters).
For 1100, 1400, and 1530
CST the soundings were smoothed by eye to 50 millibar levels (925 mb,
875 mb, 825 mb, etc.).
From 1700 CST on, the data was averaged
by a computer program written by Brian Reinhold, producing data
at the same levels as the eye-smoothing.
was compared using each technique.
Data from two soundings
It was judged that the two
were the same within a reasonable error (+ .50 C. in potential
temperature, t .5 g/kg in mixing ratio, and ± .5 m/sec in wind).
The winds were rendered into u and v components and also into a
natural coordinate system oriented to give components normal and
parallel to the line of convection.
The relative humidities were
corrected for their low bias as suggested by Teweles (1970).
table 1 for details.
See
The standard radiosonde was redesigned be-
12
tween 1970 and 1974 to correct this problem.
As seen on figure 1, the surface system was not extended as
far to the northwest as the radiosonde network.
As a result,
although the front and associated convergence penetrated the radiosonde network, the surface network was undisturbed until 1800 CST,
two hours after initiation of deep convection.
Consequently the data
did not play a direct role in the understanding of the initiation
of the convection.
The data consisted of copies of time records
from the various instruments showing wind, temperature, relative
humidity and rainfall.
A series of maps showing these variables
was drawn beginning at 1800 CST, but the series was used mainly
to deriveamean orientation for the line of convection and so
determined the natural coordinate system described previously.
THE SYNOPTIC SITUATION
Although others have discussed the synoptics, the situation
is recounted briefly here to orient the reader who has not seen
the previous work.
At 1200 Z (0600 CST), June 7, 1966, a developing low pressure center can be seen over station 72363 in Oklahoma, and a
surface front can be identified just west of station 72267 in
Texas on the surface map, figure 2. The low apparently developed
in response to the short wave trough discernible on figure 3 over
Nevada.
By 1200 Z, June 8, 1966, one can see in figure 4 that the
low has deepened and developed a stronger circulation.
The sur-
face front on figure 2 now shows fairly marked convergence across
13
it.
The 500 mb trough, as seen on figure 5,
of the low center.
By June 9,
is now almost on top
1200 Z, figure 6 shows the sur-
face low has filled, although the circulation has strengthened,
and it has moved rapidly east-northeast leaving a long cold front
trailing west through Oklahoma,
Note that the front has become
nearly stationary in Texas.
THE MESOSCALE SITUATION
A mesoscale analysis was made using the hourly station data
from the stations in Oklahoma and one in Texas.
The series for
times from 0800 CST to 1900 CST is shown in figures 7 through 14.
Where needed, reference is made to Eisen's(1972) analysis which
includes a somewhat larger area.
The wind field behaved similarly to what could be seen on the
synoptic scale.
Initially, winds were mainly from the south.
As
the front moved into the area northerly components could be seen
northwest of the front and an area of surface convergence could be
seen centered about the front.
This convergence line/front pro-
ceeded southeastward and at 1800 CST could be shown to be the same
wind shift which was subsequently tracked through the NSSL surface network.
Note, however, that between 1500 and 1600 CST the
front stagnated near Altus (LTS), and actually retreated northward in the area south of LTS.
became noticeably more complex.
After this time, the situation
The squall line appeared to have
moved away from the front,which is frequently observed.
However,
the NSSL surface network analysis (not shown) indicated that a
sharp wind shift moved ahead of the line of deep convection
14
itself as judged by the rainfall amounts.
Was this the gust front?
A gust front is air which has been carried downwards from higher
levels in a cloud through evaporative cooling, and has spread out
in a pool beneath the cloud.
Hence this air is cooler(not buoyant)
and more moist (through the cooling agent, evaporation) than the
air around it.
Given time enough, this pool can cut off the supply
of warm moist air which was the fuel for the buoyant updraft, thus
ending the growth of the cell.
However, this wind shift in the
surface network propagated as much as 30-40 km ahead of the rain
shield, which appeared to be quite a large distance.
In addition,
the largest temperature change appeared to lag the wind shift,
implying a complexity of structure.
This area will not be addressed
in this paper, but should be examined in the future.'
The cloud history was taken from the ceiling reports and perEarly in the
iodic synoptic reports made by the hourly stations.
day, many stations reported a high thin overcast.
Between 0600
and 1100 CST, many stations reported a lower stratus layer (or
alto-stratus) which broke up in the next couple of hours.
stations then reported broken stratus or scattered cumulus.
1400 CST, the reported clouds were few and scattered.
Some
By
At 1500
CST, stations began reporting cumulus and towering cumulus,
especially in the vicinity of the convergence line/front.
By
1600 CST, the reports all pointed to the line of cells which formed
along the convergence line.
The surface temperatures showed an interesting and important
behavior.
During the morning, general surface heating occurred
15
in most of Oklahoma, with the strongest occurring in a narrow tongue
as shown in figures 8 and 9.
This heating produced by 1500 CST a
tongue of 1000 F. air reaching from Altus (LTS) to near Watonga (WAT)
as seen on figure 10.
This strong heating at the surface had the
effect of destabilizing the boundary layer.
Note here that the
1400 CST map (figure 9), 6 hours at least after the onset of heating,
shows only convergence of the surface wind due to the cold front.
Hence, as previously mentioned, the inland sea breeze effect does
not show up in the data.
The radar history was taken from a 35 mm film taken of the
PPI display at Norman, Oklahoma.
The echoes were traced at
fifteen minute intervals starting as soon as they appeared shortly
before 1600 CST.
From various cloud models and a few observations,
this implies that significant cumulus clouds did not exist prior
to 1530 CST at the earliest (Silverman and Glass, 1973), or at
least those which finally produced precipitation sized particles
were absent.
Note, however, that various stations reported seeing
cumulus and towering cumulus at 1500 CST.
Apparently many non-
echo producing cumulus were forming by this time, implying that
conditions were becoming less stable.
From figure 10, it is clear
that the stations were viewing clouds mostly along the convergence
line/front where the echoes later appeared.
The lessened stability
was concentrated mostly in the convergence zone.
Through the many soundings, we discovered much about the presquall line environment in the vertical.
In the morning, all of
16
the soundings exhibited a mixed boundary layer structure with
potential temperature and mixing ratio approximately constant with
height.
It is even possible to see the conditions which were re-
sponsible for the low level stratus cloud in the morning.
The
early morning unsmoothed soundings showed high relative humidity at
the 910 mb level which was nearly the level of the reported ceiling
for the stratus deck.
(Figure 15 shows one of the early soundings).
Evidently the early morning heating created an adiabatic (probably
super-adiabatic) boundary layer (shallow and near the surface) and
turbulence saturated the top of this layer.
As the boundary layer
warming continued the temperature of the mixed layer rose as well,
thereby implying a higher saturation mixing ratio.
mixing ratios themselves remained constant.
However, the
Hence the air became
unsaturated, and the clouds dispersed.
The morning heating previously referred to was not limited to
the surface but extended in some cases at a lesser degree with
increasing height, to 700 mb.
Apparently this heating was from
diffusion and eddy transport from the surface layer.
One effect
of this was a growth in the height of the mixed layer with time
especially in the northwestern and central stations in the radiosonde network.
The other effect was that the small stable layer
visible in all the soundings at the top of the mixed layer was de-
stabilized until by 1530 CST a situation developed such as figure
21B, which shows only a conditional instability at the top of the
mixed layer, rather than the absolutely stable layer visible at
1100 CST (figure 19).
17
While the boundary layer was heating, the layer just above the
boundary layer cooled by about 10 C. up to about 600 to 500 mb.
So,
the entire atmosphere was destabilized, the sounding pivoting at
the top of the boundary layer.
The moisture was not very consistent.
Indeed, in the northwest, the surface front moved into the network
by 1400, so that part dried out at that time.
EVALUATION OF INERTIAL INSTABILITY
We considered as a possible explanation of the surface convergence the theory of inertial instability as recently presented
by Emanuel(1978).
In this paper, Emanuel derived stability char-
acteristics for perturbations in a rotating Boussinesq fluid.
A
zonal current with horizontal and vertical shear is assumed for
the equilibrium state, and thermal wind balance is assumed too.
The fluid is stratified vertically as well.
One result is that for
values of the Richardson number (Ri a N 2 /uz2) small enough, a convective circulation sets in oriented in a line parallel with the
vertical shear, just as is seen in a typical squall line. (See
figure 30.)
We then used this result in a modified way to examine
the stability of the atmosphere in the NSSL case of June 8-9, 1966.
If solutions to the linearized perturbation equations are
assumed to take the form exp( t), then ifT= a real number orI >0,
growth of the perturbation will occur.
statics) expressed as
/f= 1/Ri -
Vl/f
can be (assuming hydro-
/f, for a fluid with Prandtl
number (d C, dynamic viscosity/thermometric viscosity)= 1, and
d=
f - u .
(Emanuel, 1978 and Raymond, 1977).
This can be
18
related to q, the potential vorticity as follows:
d
v + if)
(7x
Take
V
Take
=
u
(zonal current) where u = u z (z )+ u (y)
U
=
uz~- - u A
v X=
7
* (.3'+
+ (f-uy)
q =/-uz
Fuze +
-
=U Z
&LA
i
(*)
+
Z v
be
2d
* VlnG
or
= N2/g
The assumed thermal wind balance implies as follows:
geostrophic wind
V = (g/f)k X Vz
if
u =
then
)
(
hydrostatics implies y
'
-(g/f)l
=
u = -(g/f)&
)p
p
or
Sol
S(g/f)
(1/.Sg)p
=(1/f)1
1$
a
p/S =RT
= (1f~ggR
R
bT
fp (- Z) )
uz
R
= b,
d
=
using hydrostatics again
uz
=
and using
z
=
fp
= - (1/
g)
p
an ideal gas is assumed, so
so)
-
Z:
p
S/p = (1/(RT))
fRT
potential temperature
(ideal gas again)
p
G)
f
P
T( 1000)
p
or 1/ =(FiT)/p
- Klnp
so InO= lnT + Kln1Ooo00
or (
(
)
)pp
(- )p
so, u z
)p
(
=
and (*)
( )z
Assuming 5
.
+z
(
)
-g (a.
+'-
u
implies q
= -fuz
g
implying
qg
fand since Ri d
then
-q
(-)
2
fN
2
-uz
ir2
2
is small implies
2
+
g
+
2
N2 / uz
=
1/Ri
-
= /f
If
/
-L
Hence, by evaluating the sign of q, we can evaluate the sign of T .
This was done by a graphical procedure.
The nine radiosonde sta-
tions were oriented in roughly three parallel lines, which themselves
were oriented roughly parallel to the mean orientation of the line
of convection.
(see figure 1).
The smoothed soundings were then
averaged along each line, producing a mean cross section for the
network, normal to the line of convection.
Components of the wind
parallel and normal to the line had been computed already.
was plotted in cross sections for each time.
The data
q was then measured
graphically along constant theta surfaces as detailed in the appendix.
The results are shown in figures 31A,B.
Notice that even at 1530 CST, just before the outbreak of
convection as seen on radar that only a very small part of the net-
20
work indicates an inertial instability.
This can hardly be con-
strued as a synoptic scale instability as required by Emanuel's
introduction,
"It
is the premise of this paper that the intensity
and persistence of organized convection are determined by the susceptibility of the synoptic scale temperature, moisture and wind
fields to mesoscale circulations..."
(Emanuel, 1978).
Indeed,
all that can really be postulated on the basis of this analysis is
that strong vertical shear was present in the vicinity of the place
where convection ensued.
It should also be noted that this cor-
responds to the top of a mixed boundary layer, where one would
expect strong shear.
This is not to say that the mechanism of
inertial instability was inoperative, but merely that its intensity
was too low to be considered as an important part of the initiation
of the convection.
MESOSCALE ANALYSIS--CLOUD WORK FUNCTIONS
If we suppose that the synoptic scale front is responsible
for the convergence, then we need to make sure that the details are
consistent with that structure.
Notice that the virtual temperature
was not the same across the front as seen on the figures 7 - 11 and
also table 2.
Southeast of the front, the air was warmer and wetter
than that northwest of the front, which implied a density difference
across the front.
Given a frontal discontinuity, plus horizontal
deformation, one expects to find a direct thermal circulation
across the front, as manifested by convergence (Hoskins and
Bretherton, 1972).
That too was present here.
This frontal cir-
21
culation is characterized by a zone of stronger horizontal temperature gradient and stronger vertical shear (locally stronger than
the surrounding area).
This is
(See figure 32 for sketch).
exactly what the analysis of the previous section showed especially
near 1530 CST.
Remembering finally that diabatic heating of the
warm air is frontogenetical, we can easily see that the frontal
circulation was enhanced by 1500 CST after the morning heating.
It appears then, that frontal circulation is sufficient to explain
the surface convergence.
In an attempt to analize the susceptibility to convection of
the soundings in an objective manner, cloud work functions (CWF)
were calculated for representative soundings at each time.
Arakawa
and Schubert(1977) (hereafter denoted AS) developed the CWF as: it
was used in our analysis.
Briefly, AS used a one dimensional en-
training cloud model which included variable rainout via a rain conversion coefficient (=CO) with units of 1/meters.
Entrainment was
also explicitly rendered by specifying fractional mass entrainment
1 dm
, with similar units.
Consequently, plots of CWF versus CO
m Z-Z
are shown as a family of curves, one for each A. The range of lambdas bracketed accepted values (Johnson et al., 1977).
Little is
really known about CO, so the values were taken directly from AS.
The CWF is really an integral between cloud base and cloud top of the
difference in virtual dry static energy (modified by water loading) of
the cloud and the environment.
The cloud top was determined as the
level where the CWF was maximum and positive.
So, when contributions
became negative (negatively buoyant) the cloud was assumed to end.
22
A computer program was written by John Gyakum which took data at the
levels where our smoothed sounding data existed.
The program then
interpolated hydrostatically between levels, and wrote out the contribution to CWF at each level for each combination of lambda and
CO.
The cloud base was determined by computing the lifting conden-
sation level (LCL) of a layer near the surface (900mb) which was an
average of the two lowest levels in our smoothed soundings.
The
mixing ratio was then adjusted to produce condensation at a 25 mb
level--a practical method allowing simplicity of programming.
The
mixing ratio was always adjusted upwards, if at all, a maximum of
1 g/kg.
This value was judged to be a reasonable estimation of
the magnitude of variation in mixing ratio under these conditions.
One comparison was made between using two different values for the
mixing ratio at cloud base leaving the rest of thesounding unchanged.
The sounding used was HYErid 1530.
sounding will be explained below).
was used.
figure 28A.
(The origin of this
Initially, a value of 11.5 g/kg
This implied an LCL of 700 mb.
The CWFs are shown in
The second run used 13.8 g/kg for the mixing ratio,
and this was just enough to lower the LCL to 725 mb.
shown in figure 28C.
Two changes occurred.
The CWFs are
One was that the moist
sounding produced cloud tops slightly higher, as seen in figure 28D.
The second was that the values were quite a lot larger in magnitude,
by as much as a factor of two.
Upon examination of the contributions
to CWF (see table 3), it is clear that the difference was not due
to the lower cloud base alone.
The contribution by the extra layer
was slight conpared with the magnitude of the total difference, and
23
the "moist" values were greater at every level.
must have been due to the moisture content.
however.
Hence, the change
One thing did not change,
The behavior of the CWFs was the same--less variability
with lambda and CO than for other soundings.
We have allowed a
variability in the other soundings of less that 1 g/kg, less than
half the change used in this example.
So, there is some uncer-
tainity in the values of the CWFs, but the general behavior of the
CWFs should remain unaffected.
Lambda, as discussed by Johnson et al. (1977) and others can
be regarded as a size parameter
=
constant/cloud radius.
So,
different lambdas can imply simply different sized clouds.
One
of the main differences between soundings was the effect of lambda
and CO on CWF.
For soundings very near the echo producing area,
lambda and Co had a much smaller impact on CWF (see figure 21A).
Evidently, for some soundings, clouds of any size could grow, whereas
other soundings needed very large clouds, (small lambda) (see
This is not to say that small clouds did not appear,
figure 18A).
or that large clouds grew more easily than small ones.
All this
means is that deep convection could only occur for large clouds,
but deep convection need not have occurred at all.
The requirement
stated in the introduction still held, namely that both the environment must be conducive, and there must exist a lifting mechanism to start things off.
Small scale turbulence and small inho-
mogeneities in moisture and temperature could and did produce many
small cumulus.
very deep.
However, these small scale clouds did not grow
What is being said here, then, is that for those
24
soundings which could grow only large clouds, it meant that larger
scale perturbations were required to produce deep convection.
For
those soundings which were not sensitivP to lambda, small inhomogeneities could lead to deep convection.
The second major difference between soundings was more obvious.
Many soundings indicated that the air was negatively buoyant for
some distance above cloud base.
To suppose clouds to grow under
such conditions implied strong vertical motion forcing the air to
rise through the stable layer.
So, the behavior of the CWFs indi-
cated something about the stability above cloud base and sensitivity
to cloud size.
(This second point can be seen best on the soundings,
figures 16B through 25P).
Before going on, it should be noted that as Warner(1970) pointed
out, assuming a constant lambda implies that there is no such thing
as an undilute tower growing inside a cumnulonimbus cloud.
Indeed,
the one-dimensionality itself prevents this, as long as lambda j 0.
However by choosing a range of lambdas, it seems that statistically,
the model is reproducing reality in some average sense.
And, even
if that vague assumption is not true, it is at least true that the
CWF represents a measure of susceptibility to convection, whether
or not the model accurately depicts reality.
Due to time limitations, all of the soundings could not be run
through the CWF program.
So, one sounding was chosen for each of
the three lines described above and shown in figure 1 at each time
prior to 2000 CST.
The stations were chosen to represent a cross-
section through the echo area but consideration was also given to
25
time continuity, trying as much as possible to keep the same station
at each time.
Looking at the results in time series, it can be seen that
as the heating destabilized the atmosphere, the negative buoyancy
decreased and the variability in CWF became less as well, as long
as the moisture level cooperated.
WAT 1526 showed a remarkable
temperature profile--very unstable--but could not grow large sized
clouds (see figures 24A,B).
CHK 1536, however, exhibited a stable
layer, but had a low CWF variability and high CWF values once the
negative buoyancy was overcome (figures 21A,B).
time sequence appears in figure 33.
Another view of the
Although only one choice of
CO and lambda is given, the indications are rather dramatic.
SPS
and CHK showed the rises mainly due to destabilization due to surface heating and 700-500 mb cooling, and also to some extent due
to an increase in moisture (* to 1 g/kg) near the top of the mixed
boundary layer.
For CHK from 1100 to 1400 CST moisture above the
boundary layer increased greatly.
This mitigated the effect of
destabilization, yielding CWF of not greatly higher value.
However
the moisture increase in the environment lessened the effect of entrainment as seen in comparing figures 19A and 20A.
From 1400 to
1530 CST the boundary layer moisture increased, which worked to
increase CWF values just as destabilization did.
WAT from 1100 to 1530 CST showed destabilization, but marked
moisture iedistribution.
Its boundary layer became much dryer
and the air from above the boundary layer to 550 mb showed increased moisture by as much as 2 times.
Hence, the moisture did
26
not cooperate and the behavior is as seen in figure 33.
The echoes which appeared at 1600 CST were located almost
midway between WAT and CHK (see figure 11), and were almost on
the axis of high temperature.
£n an attempt to make a guess at
what a sounding between CHK and WAT would have been like, a hypothetical HYBrid was constructed.
The temperature was set at 1000F.
at the ground, and presumed adiabatic up to 700 mb (average of WAT
and CHK).
The sounding above that was the average of WAT and CHK,
though WAT and CHK were quite similar above 700 mb.
The moisture
was taken as an average between the two, though presumably the
convergence line/front represented a discontinuity in moisture and
the cells formed on the moist side implying that the moisture in HYB
might have been too low.
figure 28B.
The sounding for HYB 1530 is shown in
To lend some credence to the existence of HYB, LTS 1527
is plotted next (figure 29B).
the front at 1530 CST.
LTS is located very nearly on top of
The two soundings were remarkably similar,
and both yielded CWFs quite similar (figures 28A,29A), though LTS's
were lower in value (remember the caution about the numbers).
Also
noteworthy is that both LTS and HYB exhibited no negative buoyancy.
However, no echoes appeared in the vicinity of LTS until after 1700
CST.
What was the difference if it was not the sounding?
A look at the 1500 CST surface analysis (figure 10) indicates
a region of strong surface convergence, nicely defined by six wind
reports.
We calculated the divergence in the box defined by the
six stations, and found its value to be -4.3 x 10- 4 sec Assuming a value of -4.0 x 10-
1
at 965 mb (ground), a linear
27
increase in divergence with pressure, going to zero at 800 mb, aiid
using continuity in pressure coordinates, we obtained the omega profile shown in figure 34.
Using
=
calculated time from 900 mb to 700 mb.
which implies
=
we
The time involved was on
the order of 2 hours, which indicated only that this magnitude of
convergence was sufficient to change the environment on a short
time scale.
CST.
An earlier HYB sounding is shown in figure 26 for 1400
This was constructed by averaging boundary layer top, boundary
layer potential temperature (one temperature for the whole layer,
assumed constant in the whole layer), and averaging potential temperature above the boundary layer for WAT 1357 (figure 25) and
CHK 1400 (figure 20B).
The moisture was assumed to be that of
CHK 1400, as the surface front had already passed WAT by 1400 (see
figure 9),
and WAT had dried out significantly in the boundary layer.
If we apply lift for 1
hours according to the divergence calculation
shown above, we have a sounding like figure 27 in the boundary layer.
Clearly, this ignores the fact that the convergence was not acting
on HYB at that magnitude for that length of time.
Also heating of
about 10 C., as seen at CHK, would change the sounding too, destabilizing it but raising the LCL.
However, it is apparent that
convergence of the magnitude shown could indeed have saturated the
air in the vicinity of HYB.
So, in the HYBrid sounding we have the most unstable boundary
layer coupled with sufficient moisture to produce significant CWFs
for all lambdas and Cos.
LTS 1527 does something similar, but what
LTS doesn't have is the surface convergence.
Although our analysis
28
does not show data south of LTS, Eisen's (1972) did.
He showed
that while there was strong convergence where we found it, the
divergence near LTS was on the order of 10
- 5
sec -
1
.
Therefore,
it appears that the convection started only when both the convergence and associated vertical motion and the proper thermodynamic
environment coincided.
SUMMARY
Our findings indicate that the line of convection was initiated
by frontally produced (and diabatically enhanced) convergence and
the diabatically destabilized boundary layer structure as demonstrated by the behavior of the CWF.
Of secondary importance was
the increase of moisture in the upper parts of the boundary layer.
The convection was organized into a squall line because its initiation was due to linear elements.
There is still much to under-
stand about the subsequent history of this squall line, especially
its behavior as it passed through the NSSL surface network.
Much
also remains to assessing the value of the cloud work function as
a measure of the susceptibility of the environment to convection.
We have, at least, shed some light on the initiation and organization of convection in this case.
29
APPENDIX
The method used for deriving the sign of q, and therefore
-
is as follows:
Assume a situation for a stable atmosphere as shown below
t%
so we have contributions from each term, and each contribution
can be written as the projection of the component along lk&
also make the approximation that the magnitude of
VG
=
. We
_
from the diagram, each is expressed as follows:
-ut
Notice from the diagram, the compnnent of the shear of U (zonal
wind, with horizontal and vertical shear) along a constant theta
surface in the +y direction is:
U-
LOLoSQ+
we
4_0 S 0 = -f
s~=
-
-1"'
ff
j
-
So
The diagrams are drawn for a constant two m/sec interval in u.
Hence, by measuring the distance between contours of u along a
constant theta line, we can measure the shear.
When measuring distance, we use the fact that the vertical
scale is much exaggerated.
For neutral stability,
and, indeed N2 breaks down.
0
implying
-
0, the assumptions made break down,
q/N 2
->
Co
.
So, the whole problem
Therefore, the diagrams should not be considered
below the 313 isotherm, as the soundings provide considerable
evidence that the boundary layer was neutrally stable in the
radi osonde network.
31
Table 1
Corrections made to the relative humidity as set forth by Teweles
(1970).
The day correction was used for 1100, 1400, 1530, 1700,
and 1830 CST, and the night correction was used for 2000 CST.
day factor
night factor
1000-701
1.18
1.06
700-501
1.28
1.09
500-250
1.61
1.20
pressure (mb)
RH(true) = RH(measured) x factor
32
Table 2
Virtual Temperature Difference Across the Front
taken from figures 7 through 14
Time
SE of the front
NW of the front
0800
GUY
296.0
1100
GAG
302.5
-
305.6
308.5
.
1400
1500
GAG
CSM
VAN
CSM1
309.5
310.1 -
GAG
-- -
..
300.2
LCSM
304.9
306.7
VAN
HOB
308.9
312.4
SLTS
311.7
END
HOB
311.3
-VAN
>
312.5
higher
elevation
33
Table 3
Contributions to CWF
HYBrid 1530 LCL mb
base = 700 mb
A = 10% per km
p(mb) above base
Co = 1 x 10 - 3
per
meter
HYBrid 1530 LCL*
moist
base = 725 mb
16.9
24.0
31.2
37.0
50.3
78.7
90.2
80.0
72.8
82.7
88.2
101
106
125
128
128
101
37.3
negative
R
Total
1380
25
50
75
10oo0
125
150
175
200
225
250
275
300
325
350
375
400
425
450
475
500
17
46.5
55.9
61.7
77.4
115
132
123
120
136
148
169
184
214
232
245
233
188
70.2
O CDS
O-Sutface Station (recording)
-Ro1winsonde Station
--- Boundary of ARS Rgingooe
Network(173 Recorders)
SInstrtmented Tower
FIGURE 1
This map shows the NSSL network as
it existed in 1966 for this case. Taken
from Farnes, et.al. (1971).
t
29
60
44'
0
4
1,
061
O
2
/
27
222
-'
FIGURE 2
o
6
374;.-
0"
~
2bi
-'
0
760Z2Z'
i
synoptic analysis for June 7, 1966, 1200 Z ~~:V-4(0600CST).
Solid lines are isobars at 4 nb intervals.
Each station has plotted pressure, wind speed and direc..
tlon, temperature and dew point, sky cover, currenit
Winds are in knots,
wather canrd 3 hour pressure cnange.
- \J
temperatures In OC. Plotting model follows US stanqard
(abbriev.) form.
Dashed lines show fronts. The approxA,
Irrate location of the NSLarea is shiown by a box with
clots at thie corners.
'
Surface
2.3
42-
A~
-
.&
/j402
0
o,
0
0
.
75
9
,
594
/00
5
_
V3
9
'o
280
is
3
also
9
4O5
'0
1g
0
_o
1
360
72
plotte5
in
L.0,0
5•3 o
60
0
o 330
7%
5
O
O
FI UPE
3
3
20.07
~
0ie,
o
, 460
and speed, are in
Solid
*2$5;e27
mb analysis for June
7, 1966 1200Z.
472
lines
are
constant height
each 1-decareters.
2.2
-/
lines,
~
'
51.
415
for
Wind direction numbers
254
,75j.
440
2
4--
Iw
.
30
.~~5
mb anlsLfo
_.1o
'
"
0.
Ov
nis.
I
'500
~
....I
_/55
b662
show
ad
Te pe0t r
also '.37p3ted30-.
are shown near barbs,
530
0
FIOU
500
~ ue7
~ ~~ 16 ~
ar costn hePh
ins
Soi
_5_ _
0.
7Z
3
)
74
5
1 0,"L
JO
-
, L
i
.Temperature
0
;j
--
.''"'
(
46
O
570
")
" '
-(6s
334 f
374
O
'
'*55
,- " 1
.-
0 *
-21
0
73
741
578,
278503
2
"33
6
578
87
0
O
0--
70
U
90
1
~
~
696
60
6
777%. 7
%
0
"ci
~
.
2
7-'
I')~
1&'.
2.
FITRE 1
Same as figure 2,
June 8, 1966.
except for
ICA
/
S9L
1'I
96
;6 0
60Q
97
59 4
619 /t
)1
J4,I,
O
O
-
3
OO 7
0
7
O*
O
57
0
"*
261O
85
for
40
7:10
8
1966.4
180
910
1
4
-
Je
la
.7
6
4
0
-,,,
J
8., 1
416
8, 1
O
16.1 5o
2
76
06t
,O
0
O5
- t 2
4
6576
0
56
.2
*D
43
74
"
O
567
_43
6z f
24
..
0
O
o349 348 330
o
.- 00.5 B
2
O
)
0
0
•
570
CO
7
Je
2
-
772J
0
\
74
572
R70
16
-
74
ro
"/5
4b
O
O
653
I
O
O
O
0
0
3'
5- 315-d
1-----2
.
-O.
,.
I___
7,.i
,o
.
265
O
C
C
264
t73C
S2
-
-
260
.i
.46
2t
,3
4 tsv
FIGUFE 6
Same as figure 2, except 0
for June 9, 1966.
.
,4232
-V--
V (i0
5 j
f
-
UY
*
37
I
I
FIGURE 7
Mesoscale analysis of Oklahoma at 0800 CST. Each station has plotted
wind speed (knots) and direction, temperature and dew point (OF.), sky
cover, current weather, anid high, middle and low cloud types where
available, following standard US form.
Temperature is analyzed
for each 201I' . and ;url'racte w'.' chift./cold J'oroit
s dhhefd.
'I
°, i
"
t2
.
4uv
trs
ri
cl
.'
S
-
...
of
'
i
1
s
sL
,
.3
-
4
Ko
!
13
tOl
FIGURE 8
Same as for figure 7, except for 1100 CST,
•. .:,..
Cloud typez from
comments are plotted to the right of station. Large
numbers with plus (+) sign indicate 3 hour temperature chnange.
IqO5
-GeST161"")"
0
0
0--
-- 37
iI-
i
I
CIL
FIGURE 9
Same as figure 8, except for 1400 CST.
I
(5Do
cST
•
J
8
au
1.O
.
3'
35
3s
FIGURE 10
Same as figure 9, except for 1500 CST. Where cumulus were
sirghted, the direction is plotted by arrows. Temperature changes
are for 1 hour. Off hour observations are designated by time (1530).
r
\?-
44Wv
qq
°
WP
1(
OQO
I
~s
>nan site.
4'.35
i
/0/1
ooc3
rzt"
)
34
3I~
i
's
v Jo
W
41A
l
e'^
%.0
FIGURE 1
Saea
rereen
FIGURE 11
I
iue10
radrehe
,,--man
site
xetfr100CT
s ena
seik
omaOlhm
Same as figure 10, except for 1600 CST.
Asterisks
represent radar echoes as seen at Norman, Oklahoma
70
0
s5r
3Jo
S
e , IA&G
,0~4
-
*-
--
'A
4,
qb
0
M\JS
-.
L.
.
I
I
FICURE 12
Same as figure 11 except for 1700 CST.
Arrows not drawn anymore.
*
oo
es
e sTV@J
t.
0
04
84
*,
0.
1'
eq? j
;to6 11
3q
,4%
1
ii
I
,~t- -
FIGURE 13
V
Same as figure 12,
except for 1800 CST.
10o
O
(
I
I
i
~-~L~tp
p
I
i
o
1
q
MUS
.35
r
i
96
:I
" '"
r
FIGURE 14
Same as figure 13, except for 1900 CST.
Isothernms around STI were not resolvable.
*
~4,
-Ijo
A!'
t are
ar re
v
i 0:M
,
..
ar J "o'
Q.2b3
the
I
Idi
'I 3)IX
i4'
.L1
pte.ed'hz
t rc In .M
rrr~r a lwei
lccI
7
tNre. Th
.w\ututtt
\I
(4 )
1
1.;IA
r
rr r
su
\UI(
ery-
Ir(
tn. 4
grtee
t
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overrvrnejd r.tct res
t-4rll
(s)
wIw for r
J
A
k
curistant %4%rat(9 4.
on', n.pret
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flrat.,
V
.'EIf
o
areI nes
ater
0
.er
cO ents, n grim, o vafeef ar r-.r i 4r- r
air, re'.feed or tfurdA.onat t4 . :ated
!or ratwes ard preti'es.
U.y
3 40
3$
24
\
WD W s 0'V.,;
1G
T"e 13laer two
pJ rnJr #10
.*
ie en4,
that f r
t'r.,
. tWu
J.n th) * Clouw0 C ,
4
\I \
'"esc'
to fli
S, aoce
t
p
:
are com-
ll tempe 3saturten
I quid
aler,
is
16
2v
'\
16
\'
N!
H
PIGURE 15
Sounding for LTS 0548. Temperature is solid line with dots, dew
point is dashed line with .
3-1
II
\
V~~~
\
'\
~
I
\
$'74
~
3\
o
oo20o
\
ii
o
~
~"\1
-C
it
1
7
U-- 0
;0
,.
"
.•
•
--:-'
~~~~
.,-.
.. ,. /
'+
-.. I,,",-
/
,
,
".
X, :.;
a.
.
-,.
I
-
...
;I-'
....
I
-
- "
1---
-. i..
'
"'
... ........
.............
.
..
..
~.. ,
,- ,,2
.....
:
:-FIGURE
-i.
.
,,,,,.
-1--~
-:40
" .!
..
" ,---
-
.
.
.
-
:
: : .- ; .
•,.
..
.
16A
.-
FI
I GUREI~
.
. .
:
,
-
1-6AI
.
CWFs, on ! log scale versus CO for
SPS 1100 sounding for various values
~o010*)w ith WAT 1105.r..
:
!
..
:
.....
,....."-M
- :..,Y
: ':..... ...
"
of lambda. Values
for both cloud top
,..
:i ' '
/tand
325 mb ar plotted for comparison
with WAT 1105.
.
.
.
.
i.
....
1,
4",...
.I
!' i '
(i
+i
i +I
,i,
'*
.
,r
.......
.
,- ...
..
.
i....
l'ue
•
UR
,
,
i
,+ .... . . . . .
i
:
VA
'
. ..
" ':
i
,PS
..
. .
.
.
!
. .
.
..
,
.
,/
j, ....
" .: -
I
. .:
•
.
.
*to',,
..
.
!
l
,
:
'
o
,...
,
o'
, ,
c
le
v
,Wsr
u
l
:t,
..
of
la
b
a
,,,t soundfna
b:'"
cl
u
p
O
O
-
0
-"
O
1
-*i
I
-&7
-,
Ni
A
0
Je emr erah.res in C.
I1) Alnr~nns
in Erwwnaredry
I.nes
ats,
I e.. Ire% cf
-. iart poten:ittempr
ertre. .D et are droaw for tveryto .g:;s
Ita.
asolute.
a
21
cures are pseudo4(4)8r ktn, nverprited
'
Ti
112
slraq.,t
13)Sloping,
CIN:
-
"N;j
0*
*
SO
O
~I
adiahats.
7,
potent at
are equ'vjert
fgures th,.rcar,
Stmperaurte
( A.).
curves are hlts of
.:i 45) Unbroken,overprinted
g:vng water vl 'r
raLto,
ra'"Om, erg
Sconstant .ata
_V
:i
contents, in grams ofwater vaporper llogrm oi
dry at:,
reqr.,red
forsaturation
at the indicated
~tu-m--+ 0
rNVK77kL
t
i I tt--tt~I
~~-rt
iH-t*
-L~
8
t:
-
h~\C'\Yds
N1I
-
~S-Y--ILLLII[LLU--YL;~-U~.)-~)-~eih~tC--
?"L
~~-~i-
Swill"lp
>1
N I
it
1kKL
-;4j
e r in IIc
ble
FIGURE 16B
Sounding for SPS 1100. All
soundigs follow format in figure
15. Large * indicates cloud base
S conditions used in CWP program and
.
'
X'
00
w th "ospect
to a Iat surace
of Il'.ud water.
81
s
13
Stmperaiures and prrsturts.
twj sets of cures are con.
t&l T, ITttter
N Fuled under the rna
ptao !hat re':I te perajn thosebrtow O'C.,satar,ioni
inclu
lures,
S will appear in all applicable
At,
N
S soundings.
%4\ C
N-KI
if . I
I N~I>I'Ni
IW
A
IA
-to=
-
3-
J\
71
Ac
'
I
4
- 5
-
-
4+N
~-
4
K
-NON
3
4
o_
I
S?0
k
c7\1
N
0.
V
'
X1
1
h
wA
-:,O 0-
abl
S0Q
f
-20-
-
T I , ,f ,r I TTI
lII,
-100
ll
I -II
, , , , I
00(f.)
Il-10, Il
',-
lr
100
200
--- o- (C.)
i
300
%-
I
I
4o0
II I
IV
I
500
I
°
"l"20"
IIIIII1
600
11
T
1 1
100
1
20' "Y
I
1 11 111 I 1 1 1 1I1.
I I I 1o
800
0
4
,
1000 (M,)
0
A
. ........
•
.
-
,
T-)
-- _-. 't- - ..........
.
--
0
.VVV
0
.S
..
...
.....
...
- i ..--- ....
- i. .
i-
_----i--S;-
St
_i.i
325 mb values
.....
r-ot-
1400.
pl...ot ed.
-'A-
..
..
I .
•1
...
•".,~~
-, ~. ~ ~. ~-..
'-.
..
'
..
+ -~
"
*
•' ----
-'
,
~
~
~
---
'
+~
-;
. !-.+
. ..
:
,,
,"--~-": ...... ,.-t-
'
,!
r-
..:...
. ..
-..
....
I
i- ...-1 . . .;
i
.
1o'
i---t
'
: _i
"
~ + f-r- ..
" ='
..
i .- •
:- ",-
.i
.
..+1 . • I -. . - .- -
'.....
-
..
.
_-
.
.
.
i
~~~.
l-i
..
.t
.
. .
:-.
.
,
. r' .... ' . .
__.. Ii
,
:--i
;
... .
..
.
.
..
.i
. .
I
5
'
'/
'
.
.
fk'
,---i..
.
+
.
........
....
o.
i+
.
++;.
+d.
.
..
' - -:,"
,,
"
1
i
*
.
- .....
51
,.
I,
*
.
-1
i--.-t
.
,
t--
;.
/
--
.
t
,
-
++
7
! iit.-.i
...
,
.
+
"..
i'
;.i
.
.-- ,
. t
i
.
I
,,
-. i
,-
. . .
'
.
i
.
'
'..
I
n o
.
.
r- .
"I
...
.
. ..
I
.
,-
... t _- . . . ..
i-.I.-
. . ..
II.f
1
--
i,/
'ptf
_. .
...
. . .
. ..
.. 1 .. . 7.
.......
+. . _..
.... I .
:-4
... i-
.
,
,
-
.+
_
. + +_
.-
-" .
-Cli .. ... ....... ..... .. .-. .
!
,
.e
,
i - .
.....
. +k
---,-----
I
....
.. . . ....t,...... .. .
- -: - r----..
.
.
•,+.....i
i
,
-+
" -;
.
:....
'
+ 1..
i
41
+
. . .. .. ... .. ..
i~ i_ _i-F i
;
,
-. I.
I-
"7
3 .......
2+
.
(V,
-
il.
-,
.
...
..
15,_
.-..
+i
-. _~~~
: '.
.
I
-;
' ~--
...P
t 5:/
i.:
"-'~~~
! 7!--i
I ;' ; ; !
• :_ i_ +!.. ....... . ....+--!
...
.....
i-;----- i -, . . .i--.
.
. .
L--
+ : -. -*"
;
.
.
*--
i
......-- . ....I
... i,
.
+i ,
I
i
-.
4
..
. . ..
.
.
..
il
.
.
.---
,--i .
;
...
•
..
i;-"
_
..
).
:C,
:_-
"
-. -. I.- I -... . r+.
t
11 10
?
, , .. .
....
-.
-:i
I
i
i
,
:
',i~
I
*
Al %-,
,s aire
**.o
p r
t%.r
,n C.
(
Ordnates are t~I 0.281 po*ersot te
prvrurer n mthsars.
13) Slupog, straigr.t lrnesko brown are Jry
adahat i. e. Inmeof costantpoten.tal
te"rerature.
Terse are drawn for every two depreet
aholut-.
(4 t Bruken,ovrrprntf-d
are pseudol
ad-ahats.Fgu'les
lhrert,areequvalent
puotnt
al
22
atu've
t,.mperatures l A.t.
20
(5) Unbhrocen.ovrprmnt cirresare rees
of
constant saturat-on
,nong
rat,.g.ving
watervapor
contents. o grains of watervapor reIligram of
dry air, requredfor w.euraflon at the ,njicated
temperatures
and pressures.
16) The latter
two ses of curves are com.
puterunJr t'e assumptorthIlforalltempera.
tures,ncludmg tho.ebelow OCC., satirahona1
1
with *0peCtto a flatst.,
ace o Iquidwater.
19
18
5"
1
FIGURE 17B
Sounding for
SPS 1400.
4-
w
Qc
(II
zx
7oo
K
o
-e3-4
-30
tItiWr iT
-30c
tl
-0*
'
l:1 1
l
-200
l i
tttl ji
-100
l
|1
,
-10
fl
il
0. (F.)
ll
I
l
tI
e
IO
i
I
I ijti
2(01
0" (C.)
'l"j|T ,' '
l' 1
300
ItAiRATUROE
rrr
I
400
10*
I
,I
500
20*
%
,I
i
i
III,
600
,I
~
30
III
70
O
I I II
I
800
T
1I1
9
.
40*(C.
. ,-.,
I
, I
1
t00oO
(F.)
0-
*(
*
*
I t---;
: -t- t- ,-: i-
...: -I... ...
. . .:...: I,
'
r.i
I ]
;i
'
!--f
;-7 -~._. ...L..
-C,---.L_.
.
_ i.....
--
_..
.
i
_'
i
_
'
i
t
.
..
-"--- i
t
r
!
.i..
-
. .
-.. .
.
s. I ..
-" ;.
i.
.
..
. .. .
.
.
'.: /
;
I
+..
-
.,',-
'.
+.
•.
+.' ..
..
i-
-t
.
--
r
. .
..
',
+
. . ... .. i + :+.. ..
'.
1
..f
!
i
-.1
I.
'
-
t
......
,
-
..
:
-
.
-- .--
'
,--',
.,
:
'i.
"
_i
. ...-
'-
-1
-
.j ... ...- -. . ....
-. .
i---. t-H--H
-.---- -.
..
...
_..._
..-i .
. ~ ..
. '-. -
. ..
.
i.
'''
..j, ...
.
..
. . .
i.
. . . ..
-
i,
.i , J
'
,-II
. .. .
-
.
....
._
. ,
t -.
.
: ..
,
t
,.,~
i
t
.. -+.
_:'
.
.
..._.
... :-_.-~ .t
.
l ......
_'.
.!
. ,
. .. .
--_
_
, , ' • ,
: t: :
'
+.I _i
. t.
..
I
.. ..
t
....
1,
L I + +
,
i
.i
.
.
--- ------ '-,
...
.
I
.i.+
. . ._1--_;__
+
+ -t- -i+
i
'
.
,
,.
,
. . . i... . . . . . '--
,
..
|,
,
,
..-.l.. . ... , ..!... - +
r--6
_!
-
....
.. .. - . . . .... .......
"... ..i ......... -... .. . . .. .
i
.~. ,
t
i
-
,
.... ...i
i... ..
. .
i .
-: .. I . .i -, +-- +--l -,
.-- •
;.. . . .
.
,
4
.
I
...
+'/+
.. .~ - ) , ..
- .- ,........
:-.
I
~
-.. ..
:
tt
• ..
. ;'~~
i- -;-! •.
'-
! --. --f~
•
. --
Same asforf'igure
1A except
SPS 1530.
I
... ... .. . ~._
.!
-
,
.. ... .
.i.-i~
,
.
...... . . . .
;
I
I +'
,
i
'
.1- -'~
, , ,
+
i
: ]-- i
---
'
-
.+
; I
I
+
..-*+
_i ;_i
. ......
'. ;
I.
0
i
I
.- '
--
,
i - .I-
- : . I.. ,
,
i~
i
I
;-
,
+: ' _,i
''
.I
.
t
-.
~~~~.
-. "r
.
.
.
I:.
...... .'. . ., . .,-- .i .-, ' .' .
'
:-
i
,
-----1-
--
,,
£
i
9)
I U. I ___.
+ 8
FIGURE 18A
'j
. . !..
,,
- + -'t. . .-
... . - - -; , +
. . .. . .
. '....
i"
,
. .. :-
.--
.
. ..
,'
, ,
. .1-i ... I
,
.
.. :
.
,.
-? !-t-.
_. _ ~...... = _ +.. ... . . _ _
I. ib,
.
_.-
'
1
i i
JJ
)
_i-__
j ! , ! {
I1I
• J
.t. .
j.
I' --
-~i~-
. . ..
_~....,
.. _!_+.
.. .
:.
: . ,! . i . : ..: . -- -
.
. + i ;
:
.....
0.-
.I |
|
, --•
9)
.....
<
,.,i<4
"I
9
'
,-I
I
'
. ... .i. i.
t"I
-
I
I
!..
+j
Ie.i.
-'
t
I ,.
,
I
+
I
.. .. ...+. .i.... +.
Ica:rsis
:|
...
'
"
,
'
v
__
S
-
U
-..
..
S(I AI~,~l
.lre
teIempermturesin C.
I21 Ordinates iretie 0.288 pow*rsof the
pe ssures I mrilhars.
t
Slop,rq, strgh :lee in rown are dry
adIahaJt-I..ies Of constant poteIn.,al temperalure. These are drawn
every ,*o de :rees
alsoliute.
(4) Broken,ovrprintd curves are PeeAdod1aahti,.
Figorest'.rrecn are eqlillent
potienta
temperatures (' A.).
(5) Unbrkien, oserpreted urves.re lines
of
constonltsaturationreeg ratio. einnm water vapor
contents, in gramsof water vapor per ilogramof
dry 3r, relqred foorsuratnf at the ndcaled
timperatures .nd presulrel.
(6) The latter
Iwo setsof curves are compute under the assumptonthat fr alltempers.
lures, includnlg
those below 0 C., sat.ral'or
is
with spert to a Ilit
surlace of I quid water,
I3)
22
421
to
20
t9
18
17
FIGURE 18B
Sounding for
SPS 1530
,5
14
600
4-
13
K:K
.
700
3;.;
1 ,r o-t- :
r
Q
:
-7 :7
i'
[i
l l
I I I [ I T
-
I1111
1
I
01(.)
111
I1
1 I f
e
10
1
V
lll
l
T
l
Tl
l l
I
v
20"
I
.l "
1
1
T r
400
ruetfutUl[
i l l
it
'
r
a
(pe
.
n
..
.20" .
40 (c.)
3-
*
*•
0
.
S
••
FIGURE 19A
Same as figure 1 6 A
except for CHK 1048.
...
.
S----
I
.
p
. .. .
.
. .
.
'
..
. .
,
. .
'
,-,
.'.,-,
-
<"-
r3z
.7-
:
.
-
.
.
.
'
-I-.P
~~;i~~I
i
, 4C -
".....-.
.
.- ,"
)-%
-
..
1.
.. --
301,
-,
to
40)
6
T. T.'
K '>vc
22t
Fue
\4.
ir
'ra
2
%
2.0..
L.
____________________.4o
V
Ktnerl
1ry(f
ThTh are
TI
44
i'f'i
\n
4
T A.~
~~'Nfe
t" h~
1
JK\
F3 ivl
e Ao
So
ro
'
600~
~
4bN2
~
TI
\W
i'-'0
tO
p n # i ,00
IGR 9
h40v
Ns
nd n
rmi1*seI
61le
N
QN~
ii
Ip ts
'ed
Sat ItX~ z\i are bi't+
Water,
\C
S-O\rk1'.F
7
16t ., 1*
I-T--r----7~i
blI01mowpintL-N Ar
Sordin
_fl
7i.
_k
fo
SI
117
\
.. '
t>I
-
N2
tot
00070
Ni
co
02
LL~~~i
3-
N
F
{'.
~
U(.
r T T Y r rrtr
I rj~
't' 'r r rT,-IWO1 T T T T T T T - r ' T r T -rrr
-
MY'
-Inv
IN,~'
t
(
-7C
0~f1~
I,,1
"N.~K>
*
0
0
U
2 A0
.
I
.. . ..... __
....... .... .
-.....
•|
+
.
+..
.
.
i.
.
+-
.
'""
".
.'
.
'
li
.
.
f
•
---
.
. ..
-
,
:-•
-L.!-.
.
,
_
I
--
-
,
,
.
I
'
-, ..
,---...
.
-
-
...
' ^-.
.
--
.~1
. , o i ,...
. .
.
. .
. .
.
'
: i~
~
'
i;i
'
'
*
+ ~ i.
Ii
t
!
"'
..
- . -.+.
.
:
:
..
..... ..
7
: ,
. ., :' . - -
7"
~ ;
'
- i
i
........
i
. .
:
•
+
:
,~
. .
1.
_.
.
.
.
.
' i
,
I
,
., . . :-;...
i. . . i. : . ..
t o. ,.
+
.
'
....
FBI
..
.i ...
.,
.
., .
i
- -C - '----.
. . v -' '
." _.....
.... ....
;
..
.
.
.... ....... : -+~-
J
,
...
,
-g/
... ."
: !-"i
.
.' " ,
.
: -'
.
104.1
..
'I
.
except
for1 _ CHK
I
:f
I
.
~......
-.
,
- '
'
-+ -: ,--
,
,
4
!..+:
+,~~I
....
..
"'"
,--;
..
...
/~-+
.. .
,i
,
.
.
_+
'... /
..
:~ +
-
" "
:. . .......
•
;
..
. / t - ;--r
.
/-
:
.
.i,~.
wll,.
.
1.
.
-
!..-
1
I
f
...
-
17
.
;i
: - -.-, ...
;
',
+
,'i
..
O.
as f
.......
..-.........,
.
. I.i . . .. ..-. .
S
,
'
I
.
.
.
.
..
,-
+... ,
t.
1
'
,-
..
..
!r - ,
I
'
•
'
I
+
'
"i
g"
.. . .
.
.
. ..
.
. .
.
. . ..
. . ... . %
.-
-
I
T
,
r~a
.S
,are
preajes mathwars, te 1.2
N3)S'opw.g, str.i:t t.s
31.e.u
t
e
C,
8 p,,we,%of *1,
a
ad.,.h
t re.
V 11kLo;,jte.
L
Sdry
A
20
air. reqed
fo, saturation at the Ind-cated
and pressures.
2
1P
t
repeeaturee ( A.'.
(L) Unreroke , 0oer.rmted cwrves are !,eo of
cunstanl saturaston ,r-xfvnratio. giving
wate Vp)r
contents, in Krams of water vapor per ,,gram of
4temperatures
rr
22
jem
. e., Ines of constAnt 'potent4,
er.
Thtre are drawn for everytwo deprees
t41, Broken, -verprinted ctrves are pseudio.
ad,ah.ats. rigjros v Preer- (e eqo,valen! poternt-&I
~t
'~j\\
&%
7
O
m Erown Ire ay
e
The lau
tr6
two sets of
curves
that for 'all tcrmpDra. 500
underthe assumnpt.on
fl500e,.l
ures, iriciu,3ng tnoie b elow O-C , station
with "o-spect to i flit Srfae of I'j d water.
4
19
are com.
'
SFIGURE 20B
16
Sounding f or
CHK 1400
15
14
0
600
41
l
-
C.)
I
\r~~~~~~l
r'?l1t*3-1-tirTrT''t
-4,)
(VF)
1
taJ
-31)
IIIl'
-30
•
\\. --
-0
-0
\
IpiJTltittillfl
-20"
t4
°
-10
illiaift
0,(r
)
~iT
A
,
f~h~ttteluiIadujil
0
100
Z o
(c.)
Iit
300
It Ot( ATUt
40"
3
\~~'Nr
f~
ITT't
°
5o
tii
1
6'o"
10"
II~ll
:+$.
ljliI
80
900
4C.1
0
-
i
1000 (f.)
0
*
*
I
O
I
'
,
0
0
'
'TTT
~
.,
,,.
.
I,
.. .............. . - . . .
"
'
:'
;
4--
I
:
'
; .-... te
.
I
.
,
. . . . I. .
.:
-- ;
( ",
:
'
"i,
:
. .. ..,. .... 4?.
.
.-
i
. -!.
.
.Ii..
.
...
..
....
.. ..
. .,L ]: i
.
_: _-I., . ii ,+ ,1 : . f ;
''
.. 4_ ,1--].. .
',-i-- :'
_
-.
t"
'.
;I~
"
...: .. -
..... .. . -1 . .
.......
t ... L
...
.
-
.-
.--
.'
:
,._.;..
I .
.
,-I , __.
..
i
1
'
- .- ...
.
...
.. ....
i
j
!- . I ,..
;..
. ..
'
;
I ;
...i
,,.,
,
. ..'+ +
..z
-
.
.
-..
.
1-
.
1!...11..
,~~,;+I
.
:
-i
.
.
.
....
-......
1.
i,
(--
. --
I
.
,
...., i--...
-
.. ... . .
.
.
-
'
...
'
... -:
,, ...
- - .
... .
..
i._ .
i
"i -:
i
~
-
f..
.,
_.
-"; .-,i ',
t
--
.
,
t -l Ic
++~..
'
_
.
.-
-- . -
,
,
- •,-
, -
'.
+ .......
. . .o
.. .. ,
.
t
i
i
,
,
_
._. :
-
!
+i..
.
..
!I
+JLi.
+"
'
....
.
...
.,.-.
r".
. .
.. ,
'
i-.
. . ..
i
I+- . -i+ _i...
i
,
-
.
+
'+
, " - :'-i
.
:.-
. .
.
. +'
..
'
S f
,
,
..
i
t
-i?
1536
. . .
.
.
6 / - .,'
, -+-- _. +. : . .
i. .- _- -, I-
'.'
+~
..
~
-:,,_,,
t. :
i
-
,
4.
..
;
.
. . ... . . - - ... 'E. -, -
. .
Si+
. .. .
Lu
excep L for C K
Nowr
:
.
...
.? -.. --- . ..
1
:
. .. .- +
.
i
,'
I .. . ;.
I,'
-i... ,;-. .. .
as figure 17A
''I
,
r--.
i
...... _ ,. ..
!
i-
p
.
21A
-FIGURE
.
ISame
,.
V I, I1
--
.
0
-'1
-;
.
*
O.
! I , ' ,. . J -j I I: i
! I
[ ,
! ,
I...........
.
O
-
,----
,
.0.
l
....
i
..
_l _
1" -
"J',
."-i
i;.
,
*
@.
i!:
Ab,$.,, ,r, *mperttres
In ' C
t?) OJrdnates atr the C.289 powers of the
pe t*sar
4 mlitlharl.
S:opm.g,straght Ines in rown are dry'
daJa.. ir e.
I,. Ier of consta.t noitnlal *eirerao
1lr?. These are driwvo for every *A', det t*
3)
-21
abolute.
(4 Brouen, Av.rprmte cutes at,' -tedo
ad alat.
I res t,er cr are equ.iale n? ;pc!.a!
It mperituret t A. I.
(5) Unbroken, oerprn!ted curv s are hnes of
constlant saOiraton minmg ratio, givni wale, vapor
cutont,
io grams of water vapor per kl gram of
dr:y a,, reqWred for sa'uraton at the ,ndicated
and pressures.
t,'mperfaures
(6) The latter two sets of curve. are com.
pute. unler the l'uoirption that 'or all tempera.tres, includn.: thos- below 0 C , satiralio it
with '-spe.t to a flat surface of
,ater.
wI'qjd
20
6-
19
0
FICGURE 21B
Sounding for
CHK 1536
S18
14
- 13
t12t
0- (c.)
r1TT
'
t
40 (.)
T
I
-30
-20
I
-- 00
IT
I
II
I
O0(r.)
I
I I I II
0t
I I I l iI
I I
20"
IIII1
I
ItII I
30
T[IPLRAtURE
10
I Ii
40o
1r
1"1 i Ir
11Ii
IlilnII l I
50"
'
lI I j lV
60"
20'
.1
,
l
Ilit
It
"
40*(C.)
rf i
lr
IIItI I IIlt
i'
80
I
Ir
l
o
900
rT
I j ItI
If
I
1000 (r.)
FIGURE 22A
Same. as figure 16A
except fox WAT 1105, and
.
"+
3,
.
:
.
.
:
......
3t-
"
I
.
.
:,
I-
I"I
.I...
..
..
,
".
.
...
I .
-
..
i
+
,
,
S : 5#,,
,
....
.
-- ;
, ,
.
.
;"'.
...
.
.
.
.
.
'
,
.
.
''
to
.
%
..
.
-
.
...
"
-
+
;.
.
I.
."..
...
i
..
:
.
I+
,
.
.
.
-
i
...'
..
,
......
S
,-
r
,-
+
•..
+..
, -I
r'
,a
\
t
"
"..........
'. ,, ...............
.
'
X1
I~q
-
above 325 mb.
.
.
.
.
.
r
without dEata
.
o
I
30
.
..
,
I
.
." ...
:
I
,
.
......
.
I
"
: , "]
.
,., ..
'
<
..
...
+
.
C
"
-30'
is0
-?0,
--i
O
0'
w
12;O
.
e tpr r.2nd
'ee pors
of
press,rr $ ' ...1 an .
13) Sh .lo,, stragt Ines in tro-n
jeJ r
a4,htts, .. e , 1nes of contart p,!entci tenfretat.re.
Thee are dr.w, for ever! to
~er.
(4) 8oken, overprimted
ctiei aret pStti'O.
dadhls. FTgurrs
a.-'reequiaeint ptenj al
tempmrature: ( A.'.
(5) UnhroLen. orrpont.d crst .e "rat )f
cunstant satur-ao m
,n g ratio. g1v ng wattlr vaprt
cont"nti., n grami of ater vipr ;er kloyrnm of
d:v air, requ red f,,r .aturat,o at t,a irdcaled
and presvures.
(6) The latter to, sets of
are com.
pute under the ssurnMon that for allt tempera.
lures, ncluding thioe elow 0 C. sa jratilo is
wit" '"sp ct to a 'lt strfae of I q .d watr.
21
are
tr.nperalures
curves
500
-I
FIGURE 22E
Sounding for
20
5-
WAT 1105.
600
4-
1*
700 3-
-6to
-8
3
O0(C,0
-to
(C)
-4t
(1.)
40 (.)
'j
-30'
- 30
--30
'
'-20
-20"
"J,
-- to
.*;o
230
".,'
o
2n
(.
30' 01
o-c
300
i-r TT rT1
,,,as
I I1 11ttI
I-
nll
I I IIII
I
I l II I II I Ii
r
i
s
404(c.)
IV.I
rTT
i'/
*
9..
0
-
*
o1
.
:,
---.-
.....
eU
.
I
e
t
(Do
E
-
.
HL'
D
'
,*I
o
..
....-
.-.. ..
i!
I
"
-
...
:_i ,
-
1__I__-' i
.-
44L
-- .. --.. ,
-----.
...
'
-
... .... .-
,41.---------.-----ItIlI
- -:-.-..
-
*
-
I
. ..
+
,
!
-,
F-]
,
. ...
",
-
,,
.
- -
-..
-
-
..,i
l
-
- -
.
.)
-
.
...
I:
-.
-
. ...........-..
"
'
-'
-7,.
_.--.
l
.
-
.......
.......
4 . .....
'
Il
___,
'
I--
I'
, •
..- _
I
tI
-- .--
-
:
.
.
.
-
;
)
-
--
..
..
.
-
.
.
-
.
I
_
I
'"i
'--
...
.
-
.
.
-
Ii
i$
"
..
I)
.
.
-
--. .
...
.
-
. . .. ... "
--
- ....--...
-
. i•
.
-
. .
..
:'
. .6
..
_- ..:
.-,
i-
,
4
i
.. .
:
3
. ...
. . -.
,
..
i
...
t
----.......... "--
° '
.
,1
•
:
i
.
1
i
.
"-....
I
.. ..
1
.. _L
I
..1:
...
:.
•..
+
..
,
;
-'
.
....--.
"
.. . . .. . . .. . ....
1,
.
. -
.
....
,
i--.
-
•
4-- "
;
-
..
.
'- . .
4
I
,
..
I
-
s
urt
1 A,
%a%
Are! 'n,vel.t
n
(
O(
jatrs ai- tle fL2F4 pnworm of :hc
pre%,jre
t q mlhlars,.
13) Slcp,g, straight 'Ines 6rown are dry
ad3aht,i.e.,Inesvf co anto
potent al ternmerature. There are drawn for every two drgrees
ahbolute
(4) Broken. overprinted crves artpseudo.
I.
22
In
adtasAts r aicrr h-e
temperatures I 'A. 1.
L
(5) Unb:oken, overprinted curves are net of
c.nstant saturation mang rat-o, xvr.g water vapor
contents, n gram of watervapor per kelloram of
Lry air,rerqwred !o satura,ton at the ndcated
temperaurelandpressures.
(6 P The latter two ows of curvesare com
puletJ underthe ta.urption that for all tremenraturms,
includng those'
oelow 0C., satr.Ation
's
with
spStct
to a flat sfr,,eof I.quid
wnter.
*t
FICURE 23B
Sounding for
COR 1400.,
600
4-
700
3-
800
2-
,0
ta, '1
7O
2.
L
(F.)
-30'
-200
-100
400
TrMPRlATURE
500
600
20
6-
-r-rr-r-rr-r-r-r-r-r
-40
21
rea equ'aen pute'l al
~
-'i- ;.-
F
'
,$-,
'1
-
-
" ; ' ,
+
'
:
I
.
.
r.-
.
i
,
t- -- - .
" ,I 1
-'I.
.......
t,
.
+.
! ~i
"'~ +--l--
I
'.
'I '
t
.
.
.,
''
I
'1 i 4 .- +i
-.. 4
:.
...
.
..
.
i
-,
L
.:
4 ,1
.....
.
.
.
.
.
.
.' .
:-
--
'.-
.
..
. . . . .,
,,
..
.
"
+
..| -,."
'
-
.:
?-:--
-
-.. -
.
,
.
.
-
+..
,
.
.
t
,
I
'
I!
'
"
'
J
+
I
i
'
"
.
.5 ..
,
t
-.-
+..:.. ... . 'I. -'-7
+ I
.1'
-
--~i
~ t
"'
i
- ,L,
-i
,
.
-
I
..+ !
-I
I
/-_.
tI
.:
.
......
..
.
.
iA
::
.
.
!-
.---
A,
+
--
-i-,,-.-'
,
Ii
- I
-
I
1
...-
....
"!
jR
[
-.
I
SI
. ..
;
'
,
.
7
t1
+ -
t , i '--.. ,..... ~~~~5
. ...
-
'
,
'
. . . 4 . .;
..
.
. .
L._~J !
---" .... •....
1
i
.. i !
...
,
. . .+...
..
,
I
.. .
... .
.i"--!;
r I -i
-
. . .
.
i -
+
i-i
:
++
i+ ./ t!:~~~ .M.
..
-
I..
-
...
.i.... ..r . . . . :i
i -
'
. . .I
'
' ......
,
l
'
t ............
'
"I,
.
.
"
'
. . ..
-
I
..
L
'-
I
!
+
i
'
L 4 .. 4 : - ... .
L4i.+
.
. . i
I
l
"
i ;
1526. 17A
WATfig&ure
for as
exceptSame
, ,
' ':
I-
......
-
r
;
,......
.,
-
;
FIGURE 24A
-.
---
I '
i1
, ;,
;
!--
t i- ....
II..
I '-
i-
.I ,
i
j
.
.
.
.-- .
-r.
.-
'...+-
i
L,'
.
i
-i , I
:
.- --- .... - - .
I
--
.
,.. .
--
,
-
_t ,
, ,, t, , , +,-
.
.
•,
,
.
Z 'z)
v
ai
. . .
.
'
'
..
:
a .,
. ..
I
-'.
..
. .
"
I i.-
.
-+-~..........
-------
V.
e~.'
, '
-
[ ..
,--. . i .,1ll
..
.
.
.
.
,'
,
.
....... ....
,O
I 0. -.
Prh
VI0
Asr rie
powl
a
of tl.
13) S!opng. str.s lin
t es ;n
i rown are dry
ada'!,, !.. . ,et of constr, poter,all nreralure. Thes* are drawn for every two d
ahsolute.
(4) Broren, overprinted
curves are pseudoad al,,ts.
F gures flerer-n
are equ:valent potrenral
trmp-raluei (' A. .
(1, Unlboken, overprnted
tures are nel
of
constant saturation1
msang ratio. g,v:ng
water vapor
contents,,n grams ofwater vapor Ier kiagram of
dry aer, requ red fo' sacurat on at theandcated
tfmperaures and pressures.
16) The latter
two sets of cuves are rom.
putedunder tre assu ptl.os that for all ternperatures,
ancluding
thnse be'pw
O-C., lsalration as
with sepert to a flat ,sralce of Lqu.aid
wa er.
egree
S2
20
-19
18
\ 111|111 11 i.l I
IT
FIGURE 24B
Sounding for
WAT 1526
-55
14
-
600
4-
-
OD
0
P
-5312 w
W
cr
700 3-
4
-4
3
-0
-10,
-20'
-- 40 !C }
-"
rI lTT
I
- 0 f
1i7
T
i f'
lTT r fI
4
(. -3
0
)
v
-200
-10C
I1
l
0 (F.)
IT
1
I0
200
40*(C.)
20"
%
I I
1III 1 1 I 1 1
I
1 l
1 I
I
I 11
I
30"
i
I ,I
400
i
, I' ' ' ' I ' ''
500
i '
I
to,
'
I
I
700
I
l
l
il
o
80
i
l
l ,
I
900
IMURAIURE
IMel**
,
I
,
I
100 (V.)
0
30'
w
I, CIt
-*--*----4'--.
--
-- 20'
WCeThse
~tOt
t rsq4 t,, e
l'o j
'lta
akio!ut .
44 Brukt-n c:.-trpriritd curves are plej'joAdjIa.s. Forr'tre
.: Ar ej't.
pte %*
I4~i
\\
3
I
ereMd cjrves are I flt$ 1
e r i,,e
c; fu'1:O..
at tbr:
'
e
14ptessu-p,
f 11)The
tjttfr t. a wit
'rioite
ntrJ
aoJ ?.r
le
of cOlin~ jr.,. rum.
,hp 1. all It. ?~ra*
Sounding for
WAT 1357
514
3r
1~
0
-20
., is )
l
.lij
(1
1.
)
2 V)
%11-
3u*
.h-v
:1IAV
Pf'.h~s
fl
3%
Ar
'n
A
orP 4, 111.11
?J~
rI
It
T -ese VPs dIAWf for tely .sro J 'jceet
qol'Iff.
14 Breok-ft, Oveptnld cjerves a,t rseu,4.
lure.
tejflOPraturs~(
A A,
151 Uni,,hcr, owpne.ed curv', te les of
conilant .ztjrmA'on misng
gvn( w~ apor
Co""MISt 1"
Ul Wm~
fel3ePO* Per kljgrami of
J:Y -f.r.t 4rd
to' 141.ra,.n it t~g fnclicte'j
I-t'a.ues
an~dP'rs'jes.
t 1 1 he la-ter two tels 0' cLCCe34ef cornl.
W~led6nler th~e jtuenpt.nnthat for I,ll r'peea.
lures, tnrdrg 1110,'
r.a'C %at..ra'an
#tYll 'e'sPedto10- fl-t $-'-~C of I ;:,.d wlt
~d
f or
-z0.
40
(f ).
- 20"
-10'
~10'
411
( ). 20'10
"
*r
~r-rT~
TTr-TTTTTrflrl
rr r
~~
1.:
0
20
. . ..
-zo
-.
trll
1e
N
\.A
lt 0."44 Pr' I of ifte11
N
I
J-Kht
j
1
i
I -. ,
ltN''F
X
>I--i
'F
tare. Th,. Ore
e
drar.w for p
'I)
'j
Ilp
"4
rn~
14 4-1
~
l~~~~'~~~*;~r
N ~ ~ I
}
;NFFVj
~
\
F
>
4
\, t~
i
F
,7-
,
,
*41e
1
1
fl
\
b-i\
~Ir'nrrtr
c
V
f
-
f-
"
r
'
L'
l I:
r-'
ut
re
at t'
201
dre
19
oaof cur!,., are ocm,.
orrarrr Fee~or a:lrr of
rAt:1, fr .r all cempr a' r
rlgt"Ole '010W0' C.,
1 to
o
9\
\
a i1t :lp $6(14 cllof
'
i
qj.d
r:
FIGURE 27
'
w
i\I
Sounding fr
or
HYB 1400 after f Ij
hours of lifting.
-Ti
si
A'
i-I\:
"N,
I\
'LL
AiJ
\II
J
f\
Fl
A
\rc-
I;-
~
~
j
_
\I
I
'IVFF4'
ii\1-11.
Nj
;
\
\
\I
Ai
\N
O'N
4N;
'4
r
I
I
4
4-r
KI
\I
\:
':AV,
I
r
Ht
~rud,
IS~1
\\V
X1,
Theeaiter t~
rn graro,
cIorst~rf
un 5ot~id
:uIou'ept
20e.
-
20
:x
cmt
adhrea,
r vr(Lre!to, sarfratrc
L.j
~
; fB..r,,
cjre r~rorsj
e r. ud.). '
.,''~
Aoverprinted
orf
o re 's r
LFrorrr
.res
e rre
e af..I
t e r otre
CO~tlit Sald"Al :)m
iN'
rert
two d-getes
N
1
19
-
1
70
1V
a
K
ii
34
3
i;Jim
I
.Tt
'r-r
TT-
L
40r
0
-
'L
: C.)
it
-70,,
r
F
ri
irT7r7r
TrrT- -ITT
J%
rTI-r-
,451)118
\I
i
-4A
-T
i-r\
tk
\i"
ro()02'r.
I I
F
, I i T
r
30
11-TT-
i~L~LF
-f
-4)C)
r*30
r'-n-~
rtrTr1rrrnr~
rrr
'r
~
Fi~
0
r,1-rr-
-Fr
U
T Jf~r--riT
Tr~r-r--
rnrrr
0F.'F40(.
1----rr-p-rr
1
1
iF
0
*
*
,
0
,
I
~_____~C_
___ _
__ __
.......
.. . ......
,
'"
FIGURE 28A
Same as figure 17A
except for HYB 1530
I
I~)) '
41A
I :
''''
44-t
cl.c"Ac
~_
~~_~,C~.,~HIILII~-U~CI~
Z ~
ILIICn~
I
~--c------c---
L~CLIVMCI
r*I~
~-U
rY~UI
~CIII~llll
-----~u.l~.
-u
__.._,~..._- ~-L1 * 1 ----1 ---lrr-----.,~---;I
.....
.
-*-
q
*
*
"-I
..
-
-*.
(I
'cv'
'''
1I+-
f t
I
-t
4,
CWP Aiuoc
4
+
a
y
c
tr(o
20
19
-q,
Sounding for HYB 1530
HYB 1530 and HYB 1530 moist
(moist dew point has open c Ircle
t4
0
JC
co 0
NI
2I
M,
700
39
-8
.(
800
2-
-4
900
I-
N0
,
0
-) .
4-I T
40
(f.)
30
3'
"
rlIi- 20
201,
t
-
-20
II
I I
- 100
.(F-. )
1
0
10^
' t i
i
0
2
I
I
riI
0 ,
30
400
4o"
60
601
T
'
70"
I r I
--
7r0 IIT Ir I I
,O o
7T'
900
{ t rT7
o001
(U.)
FIGURE 28C
-
Same as figure 17A
except for HYB 1530 moist.
qlI CWr shkonf a
4t
1-t
St+
I
,
.
bus
FIGURE 28D
Plot of cloud tops as defined in text
for two lambdas, as a function of CO, for
the HYB 1530 and HYB 1530 moist soundings.
-(-.. - -- rf-;-X
GIUD
"5., X- -
-
-
' " -"-
..
-
--
--
3-
R '\= zo 4X0 P 0V C*
4mi
qo1 t
100
+o
"-
0
2.0
-' ---
----
-------
-------- ----- 'L-.
~ ".'I~----
1-----------,
430
--
~--"'.'I'UI-'.
-I"~~-~-' ---
LC
*-
Moi 1.
0
r
I I
-
F
I~
FIGURE 29A
Same as figure 17A
except for LTS 1527
All t
---- - -- ~
tsl-
____
- ...-,--.. , o:" . . ....
i.
AurCL4
I
----
-------
-- ----------- ------ ---r---- -- ii- --~nsm~a zra
-t
4. 0
cd(X(t'
---
..........
--,.
--..
. A01 15 /,a&/,b
v.
-- -
3
30
biovy
- fro cOubb sc
Miin
A. 1.
!'r.
~
\
0v~~~~~'~
06
*O-<
f
N~
N0
3
*
Q4
_\
~~
.
\Iir
1
I
hf
~
conttSt urationix nit rito.
X vong waer papor
contents, in graini of *Ite! vqyoe
perkit p~arm
Of
. reqL.,tdfI(,. a-Ural",e S! the~ mOratid
-4
-
i
4
~
2~Puted
ifluIJ;II thouo I11-w 0i C, jAj(jtjhrjI,
V
t
,
II
4
~
~
4K
i f>F
~
n in
o
IG UJR E 2 9 B
Soudin
1 'F
f or
1527
~
T7
,\
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undo, heatsumplon tat for 21, CrMpfres 500
12tutes.
1
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V
2
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.,
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1
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7
co1
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V
i~
\
LA
t
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-T'~-
170
F'
lf\
NL'\K
~~~~
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J
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-4
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~
~
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N
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t
r
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20
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IT
~
~
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ti
,0,
.
I
4
ipf0
3'K~
_
1_1___________1___
__
__
__
~t-
-.
--
~ou-
FIGURE 30
Schematic of mesoscale circulation associated with a squall line.
Taken from Emanuel (1978). Streamlines are solid curves with arrows.
Rain is shaded, the density of which
Cloud outline is scalloped.
indicates heaviness of rain.
-----
J--
77
SFIGURE
31A
Stability analysis for 1100, 1400 CST.
Areas of qT7> 0 are shaded in black.
Boundary layer analys.is meaningless (see Appendix).
k
-
.....
I-
r
oili
I
-
,
:33V
- .
-4K-
o~,,, -~
/"
d_,,,
:
-,
-/T
---
144---
@ ~ ~ .....
k,. s ~ -S
1~ 34
:25
o
. .. ...
.
o
'tj
"
3,43
1'
-34-)t-6
0
K
~
....
3gr
I
a.T
'------
-*-
_.
"- ---
_
i
...
_.
- -
--...-....-•:3z
--
/sS-lyo1
-A
$-
-
_
.--
..
.
t
'°- US. -
-g
'. . ,
,o
..- --.. \ . ."...
~---doo
...
77.
"t
--
,L
,
C
.. .
...--.
...
,
1"9.....5
-
_UIY
. .
--~
"L
3.
L
____
-
---
.
t'=-;%....
__)"Io
343;
t4W
.
'.
I
4.)
----
Y, - ,ts
, ,- I+TO
.. -"..
~
LE
_
-
. 33.
. . ..
2 1---
~
:13.
0' 5,
t r
.....
_~~~
..&,
Ft ,.,
,
-----
*3j:
-3t~iZt
--.
__
I S-3
I13.
3z"
........................
.
*r.
-,4
\\
...
, ,j
* lr, Ib•
Z-
~x..-,
- ~
.. ~ s- ~---
"N
@----I-----
4--
-.
.
.
-
78
FIGURE 31B
Same as figure 31A, except for 1530,
1700 CST.
-- - . .,_. . - - _ +-__
-
. .
. .
33---I-S
-
-3IbLI.----.
-
.
--
e01
/ .1.
:
~-
-
-.
0--
324V
..
•. _------.-
.3 .
;
'3--.
IL
.. ',, -it
- -
'
-
"---
---
.
--
',----
-.
-*
---
. ..
........
---.. ....
3u,
5.
3L~ -
\~
.
--
6
.3
, ..----/;.
. .....
3' .4....
~,---
-
76,:
-13213irl7
r~
!o
-.
.I=-
__
--
-,----
'I~
'
-
" --
-
.... f. . ............
-,2:
-~
z
se
>
Ommmaw
WMMOR
ago=*
9
&1
_II
~ln
l~1
T
___I__
__
ZbrrC
FIGURE 32
Sketch of frontal circulation in 3-D. Arrows
show direction of flow. Hollow arrow shows sense of
vertical shear associated with the horizontal temperature gradient.
FIGURE 33
Time evolution of CWFs for
one choice of lambda and CO. Plotted
on a log scale versus time.
A= to /, pet to
CO. - x l, 'S
I"
-t
/t,0
*~~
TigA
tJ~o
0,
(csr)
~1WA
0 0h4.S CofI,*Do
0
ISIIXLC W 71wc- "% hot ("VicII)
~-_---_-__ _~- -C- --- ~-C-
-
_L~-----------LII
-
81
FIGURE 34
Results of divergence calDeculation done at 1500 CST.
tails are in text.
IW -
r
I
-1.3
90
- 1.0
-to
-30
Vt)
b,
82
BIBI IOGRAPHY
"The height of the planetary boundary
Anthes, R.A., 1978:
layer and the production of circulation in a sea
breeze model", J.A.S., v. 35, pp 1231-1239.
Arakawa, A., and W.H.Schubert, 1974: "Interaction of a cumulus cloud ensemble with the large-scale environment" ,
Part I, J.A.S., v. 31, pp 674-701.
Barnes, S.L.,J.H.Henderson, and R.J.Ketchum, 1971: Rawinsonde
Observation and Processing Techniques at the National
Severe Storms Laboratory, NOAA technical Memorandum,
ERL NSSL-53.
Eisen, P.A., 1972: "A mesoscale study of the Oklahoma squall
line of 8 and 9 June 1966", M.3. Thesis, Dept. of Meteorology, Pennsylvania State University, 88,bp.
Emanuel, K., 1978: "Inertial stability and mesoscale convective systems", Ph.D. thesis, Dept. of Meteorology,
M.I.T., 207pp.
Fankhauser, J.C., 1974: "The derivation of consistent fields
of wind and geopotential height from mesoscale rawinsonde data", J.A.M., v. 13, pp 637-646.
Hoskins, B.J., and F.P. Bretherton, 1972: "Atmospheric frontogenesis models: mathematical formulation and solution",
J.A.S., v. 29, pp 11-37.
Johnson, et al., 1977: "In site measurement of moist adiabatic
ascent in developing cumulus congestus in northeastern
Colorado by coordinated instrumented aircraft", Preprnts
of the 10th conference_QanSevere Local Storms, Omaha,
pp. 120-125.
Lewis, J.M.,S.C. Bloom and J.D. Gray, 1976: "Organization of
a prefrontal squall line by mesoscale processes", _Preo
of the 6th Conferenoe_ n_etherr_e_c
Albany, pp 213-220.
in
nts
nd Analys_,
Ogura, Y. and Y.-L. Chon: "A life history of an intense mesoscale convective storm in Oklahoma", J.A.S., v 34, pp 14581476.
Raymond, O.J., 1977: "Instability of the low level jet and
severe storm formation", Preprints.of_the 10th Conference
on Severe_Loal Sorms, Omaha, pp. 515-520.
83
Schaeffer, J.T., 1975: "Nonlinear, biconstituent diffusion;
a possible trigger of convection", J.A.S., v.32, pp.
2278-2284.
Silverman, B.A. and M. Glass: "A numerical simulation of warm
cumulus coouds: part I, parameterization vs non-parameterization of micro physics", J.A.S., v. 30, p1620.
Tepper, M. 12 0: "A proposed mechanism of squall lines: the
pressv-' jump line," Journal of Meteorology, v. 7,
pp 21-2-.
Teweles, S. 1970: "A spurious diurnal variation in radiosonde humidity records", Bulletin of the A.M.S., v. 51,
pp 836-840.