HIGH RADAR ECHOES FROM ALBERTA THUNDERSTORMS
by
Carman Dale Henry
A thesis submitted to the Faculty of
Graduate Studies and Researci in partial
fulfilmen t of the requireme nts for the
degree of Master of Science.
Departmen t of Meteorolo gy
McGill Universit y
Montreal
January 1964.
ACKNOWLEDGEMEN'I' S
The author wishes to express his appreciation
to Dr. R.H. Douglas, under whose direction this
study was carried out, for his constant encouragement and advice, to Drs. J.S. lfmrshall and
W. Hitschfeld, whose advice was most beneficial,
and to Mrs. M. Laidlaw and Mîss M. Candlish for
their assistance in computations and drawing of
graphs.
The author is indebted to the Director, Canadian
Meteorological Service, Department of Transport,
whose permission made this study possible.
TABLE OF CONTENTS
PREJ:t'ACE
LIS'I OF FIGURES
LIST OF 'l'ABLES
APPENDICES
I.
IN'l'RODUCTION
II. ACCUMULATION OF DATA
PAGE
1
4
1. Source of Data
4
2. Radar Operatio n
4
3. Echo Top Heights
6
4. Errors in the Echo Top
Height Neasurem ents
9
5. Other Relevan t Data
16
III. LOCATIONS OF HIGH ECHOES
18
1. Introduc tion
18
2. Analysis and Results
20
3. Topography
31
4. Discussi on
31
IV. ECHO TOPS NEAR THE 'l'ROPOPAUSE
34
1. Introdu ction
34
2. Tropopa use Heights
35
3. Relation of All Echoes to
the Tropopa use
37
4. Tropopa use Penetra tions
40
5. Discuss ion
45
TABLE OF CONTENTS (contin ued)
v.
TEMPERATURE AND
I'~'IOISTURE
CONDITIONS
PAGE
47
1. Introd uction and Analys is
47
2. Discus sion
48
VI. PARCEL 'l,HEORY CONSIDERATIONS
54
1. Introdu ction
2. Jlfaximum Sur·fac e Tempe ratures
and Dew Points
3. Positiv e and Negativ e Are as
and Energi es
54
54
56
4. Predic ted vs Actual Height s
5$
5. Vertic al Veloci ties
60
6. Discus sion
64
VII. Sill•IJlvlARY
66
BIBLIOGRAPHY
70
APPENDIX A
73
LIST OF FIGURES
PAGE
8
Fig. 1:
A typical echo top height vs time plot.
Fig. 2:
Distribution of the maximum heights of
the 112 echo tops of the sample.
Fig. 3:
Scatter diagram of maximum echo top
height vs range.
15
Fig. 4:
Geographical locations oi' the 112
high echoes.
21
Fig. 5:
Histogram of echo density in 10-mile
annular rings about the radar.
23
Fig. 6:
A circular histogram of echo frequencies
by octants in various directions from
the radar site.
25
Fig. 7:
Echo frequencies by sectors of the
project area.
29
Fig. 8:
Topographical map of the project area~
showing regions that had apparently
significantly high and low concentrations
of echoes.
32
Fig. 9:
Distribution of maximum echo top heights
relative to the tropopause.
39
Fig. 10: Distributions of the heights of all
echoes of the sample and the heights
of those that were penetrating the
tropopause.
39
Fig. 11: Echo top height vs time plot for one
echo that rose almost steadily to its
maximum height.
42
Fig. 12: Echo top height vs time plot for one
echo that lingered below the tropopause
for a considerable time before extending
on to maximum height.
42
Fig. 13: Histogram showing the number of cases in
the intervals of elapsed time from which
the echo top first came within 5000 ft of
the tropopa.use to the time that it went
higher than the tropopause.
43
LIST OF FIGURES (continued)
PAGE
Fig. 14: Median tephigram for 15 days with maximum
echo heights in the interval 20-30 k.ft.
49
Fig. 15: :Median tephigram for 15 days with maximum
echo heights 35 kf't ann higher.
50
Fig. 16: A schematic temperature sounding showing
the concept of positive and negative areas. 53
Fig. 17: Distribution of' parce1 theory positive
energies for the 31 days that had high
echoes.
Fig. 18:
57
Dis~ribution
of the ratios of negative
energies of the echoes to the positive
energies on their respective days.
57
Fig. 19: Distribution of echo heights relative to
the level of hydrostatic equilibrium.
59
Fig. 20: Distribution of echo heights relative to
the ultimate predicted height.
59
Fig. 21: Distribution of' maximum updraft velocities
calculated from equalized positive and
negative energies.
62
Fig. 22: Distribution of maximum updraft ve1ocities
ca1cu1ated from parcel theory positive
energies on the 31 days with high echoes.
62
LIST OF TABLES
2.
Table 1:
Il -test
on echo frequen cies by octants.
Table 2: t-test on echo frequen cies by sectors.
26
30
LIST OF jpPENDICES
APPENDIX A: WI-10 dei'initi on ot· the _tropopa use.
73
I. INTRODUCTION
The utilization of radar as a method of observing clouds
and cloud patterns h.:ls been most beneficial in the quest
for an understanding of cloud physical processes, because
radar is capable of "seeing" into the central parts of
precipitating clouds, and can reveal the distribution and
development of the precipitation patterns within them. One
of the first extensive programs that used radar as a cloud
physical research tool was the Thunderstorm Project (1949},
which was carried out in Florida and Ohio in 1946 and 1947.
Radar was used in this project to locate the levels of
formation of first radar clouds or first echoes, and to
study the vertical growth and horizontal and vertical extenta of thunderstorms. Since then, many researchers, several
of whom are mentioned throughout the text of this study,
have employed radar as a means of investigating various
aspects of cloud behaviour in almost all parts of North
America and many other parts of the world.
Battan (1959) has given a good account of the usefulness
of radar in meteorology, and indicates the contributions of
the many investigators to the studies of clouds. Sorne of
the applications of radar to meteorology have been the
measurements of precipitation rates, studies of growth,
horizontal and vertical extent, and duration of convective
clouds, studies of heights, locations, and movement of
2
thunderstorms, and projects involving the tracking and
study of hurricanes.
Among the many research projects that were made feasible
by using radar as the primary instrument of observation was
the Alberta Hail Research Project in Western Canada. This
project originated in 1957 in central Alberta, a notorious
hail country, and the emphasis of the research was on the
study of hail storms, the information being gathered from
surface reports of hail as well as radar echoes of the storms.
Throughout the summers of 1957 and subsequent years of this.
project, the radar echo patterns were continuously photographed during the operation of the radar, and these photographie records are now on file for research purposes. The
present study has made use of these photographie records,
being concerned, in particular, with the echoes of greatest
vertical extent that originated from presumably the most
severe storms.
The aim of this study is twofold. The first objective is
to investigate sorne of the characteristics of these high
storms and the days on which they occurred, and the second
is to investigate the applicability of parcel theory, with
the intention of presenting sorne information about the
processes involved in these storms.
The echoes used in this study were all 30,000 ft or higher
(above surface), and these were estimated to be about 10%
of all echoes detected by the radar during the period of
analysis. Throughout the text of this study, heights are
expressed in thousands of feet (kft) above the surface at
the radar site. (3000 ft above mean sea level) unless etherwise denoted.
Chapter II deals with the collection of data and a discussion of errors in radar measurements, while chapters III,
IV, and V reveal sorne of the characteristics of the highest
storms and the days on which they occurred. Chapter III
investigates the regional concentrations of the storms, chapter IV indicates the relationship of the highest echoes to
the tropopause, and chapter V compares median vertical profiles of temperature and moisture on days with the highest
echoes as opposed to days with considerably lower
maxim~
echo top heights. Chapter VI investigates the relationship
of the actual echo top heights to the heights predicted by
parcel theory, and presents values of vertical velocities
based on parcel theory principles.
+
II.
ACCUMULATION
OF
DATA
1. SOURCE OF DATA.
The data were collected from photographie records of
radar echoes received from Alberta thunderstorms during
the summer months of 1957, 1958, 1959, and 1962. These
records originated from the Decca weather radar operated
in conjunction with the Alberta Hail Research Project,
described in detail by Douglas and Hitschfeld (1959).
2. RADAR OPERATION.
The Decca radar, situated at Penhold, Alberta, in the
centre of the project area, operates at a wavelength of
3.2 cm, a peak power of 20 kilowatts, and provides onehalf power bearn widths of 3/4 degree in the vertical and
4 degrees in the horizontal, with an operational range up
to 100 miles.
During 1962, in the scanning programme of the radar, the
antenna rotated continuously at 20 revolutions per minute
and was elevated automatically by one-half degree every
two revolutions until it ·reached a maximum tilt of 20 degrees,·
at which time it was returned to zero elevation and started
another cycle. A time-exposure photograph of the PPI display was made on a frame of 35 mm film covering the two
successive antenna rotations at one particular elevation
(6 seconds), so that a complete photographie record of
one cycle consisted of 40 fra.mes corresponding to the 40
one-half degree antenna tilt steps. The complete scanning
cycle took about 4.3 minutes. Range and azimuth markers
appeared in each frame, and the result was then a record
of each detectable echo in four dimensions - two horizontal
directions, the vertical, and time.
During 1957, 1958, and 1959, the scanning and photographie
procedures were slightly different, and deta.ils of the operation during these three years are described by Douglas
and Hitschfeld (1959). The major differences were that the
photographing was done on 16 mm film and that the antenna
stepped up after each revolution instead of every two
revolutions as in 1962, so the scanning cycle wa.s half
that of 1962. However, one frame of the film was exposed
during two revolutions, and consequently two elevation
tilts, of the antenna, vvith the result that a complete
record of one cycle consisted of 20 frames, each frame
indicating approximately a one-degree slice through the
storm. This left a bit more uncertainty in the indicated
heights of echo tops for these three years than for 1962.
For this reason, the data were treated slightly different
than those of 1962, as is discussed further in section
II.4 below.
3. ECHO 'I'OP HEIGHTS.
The data most relevant to this investigation were the
heights of the echo tops, and in particular, the maximum
heights that the echo tops reached. These data were extracted by projecting the photographie records from the
1962 operations and recording the elevation angle, range,
and azimuth of each of the tops of those echoes which, at
any time, satisfied the requirement of being as high or
higher than 30 kft. The elevation and range values were
readily converted by trigonometrie means to give the heights
of the echo tops, with a correction being applied to account
for curvature of the earth's surface. The result was then
a record of the height of each echo top every 4.3 minutes,
the time resolution of the radar records. Height of echo
top vs time plots were then constructed for 66 high echoes
recovered from the 1962 records. Similar plots had already
been prepared for previous hail research projects on data
from 1957, 1958, and 1959, and another 46 height-time plots
of high echoes from these three years were added to the 66
collected from 1962, giving a total sample of 112 echoes
greater than or equal to 30 kft in height. These 112 echoes
occurred on 31 different days, with the number on any one
day varying from one to seventeen.
The original height-time plots showed slight irregularities
from point to point, so the points were smoothed by means
of a three-point overlapping mean method (Brooks and Car-
ruthers, 1953), the central point being doubly weighted
according to the formula
h~5 =(h,+2ha+h 3 )/4
, where h,, h,,
and ha are three consecutive points on the height-time
plots, and h 25 is now the smoothed value. All of the heighttime plots were smoothed in this manner. A typical heighttime plot is shown in Fig. 1, with both the unsmoothed and
smoothed curves displayed.
The maximum echo top heights were then easily recovered
from the smoothed height-time plots. Fig. 2 shows the
distribution with height of the sample of 112 maximum echo
top heights. The histogram shows that there is a definite
decline in the number of echoes that reached heights greater
than 35 kft, as compared to the number in the height interval
30-35 kft. Only 5 echoes had tops higher than 40 kft, with
the highest being 43.5 kft. This extreme height is considerably lower than maximum heights reported from other areas.
Donaldson (1958; 1959) in New England, Clark (1960) in
Texas, and Byers and Braham (1949) in Ohio all reported
maximum heights greater than 55 kft. This difference is
attributed mainly to the fact that the tropopause is lower
in Alberta than in the other regions. This relationship
between maximum echo top heights and the tropopause is
further discussed in chapter IV.
40
--
30
'' ''
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'' ''
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1-
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JULY 27, 1962
Fig. 1: A typical echo top height vs time plot. The
thin solid and heavy solid lines are the unsmoothed and
smoothed curves, respectively, and the dashed lines
indicate the uncertainty in the measured heights due to
the vertical bearn width. (All heights are above terrain).
30 1-
(/)
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u 20 r-
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0
a::
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==
z
10 1-
0
30
32
34
36
HEIGHT
38
ABOVE
1
1
1
1
40
42
44
46
SURFACE
( kft)
Fig. 2: Distribution of the maximum heights of the
112 echo tops of the sample.
4. ERRORS IN THE ECHO TOP MEASUREMENTS.
The most obvious source of error in the radar measurements
of echo top heights is that due to the vertical beam width.
The radiation is transmitted outward from the radar antenna
in a narrow beam of finite angular width, and there is an
uncertainty in the measured echo top height that is directly
proportional to this angular beam width. The conventional
definition of bearn width, for any particular radar, is the
angular separation of the points, on either side of the axis
of the main bearn, at which the power of radiation of the
bearn falls to one-half its maximum value at the main axis.
In the case of the Decca radar in Alberta, the vertical
bearn width is 3/4 degree.
The uncertainty arises because any part of the bearn may
be capable of returning power to the radar from the topmost
reflecting material of the storm. Even though the main axis
of the bearn may be above or below the top of the reflector,
radiation that was transmitted in the outer edges of the
bearn may be returned to the radar with enough power to be
detected, providing, of course, that the target is intercepting sorne part of the bearn. It is unlikely that radiation
would be returned in the above manner if the target were
intercepting the bearn outside the one-half power points,
bence the uncertainty is usually expressed in terms of the
one-half power bearn width. For the Decca radar, then, the
uncertainty may be as much as ± 3/8 degree. The uncertainty
lo
in the echo top height measurement is just the product of
the beam width and the rangel, and this amounts to ±1000
ft for every 29 miles range. This was the amount of uncertainty due to bearn width for the 1962 data, but for the 1957,
195$, and 1959 data, there was slightly more uncertainty in
the measurements, because, as mentioned in section II.2,
each frame of the photographie records for these three
years indicated approximately a one-degree vertical slice
of the storm rather than one precise elevation as in 1962.
The uncertainty for these echo top elevations was lt degree,
or the indicated elevation±5/$ degree. This amounted to
an error in echo top height measurement of ±1000 ft for
every 17 miles range.
More than $5% of the echoes of the sample were within the
20-60 mile range interval at the time of their maximum
heights, and the corresponding uncertainties in the height
measurements for these ranges were about ±500 ft to ±2000 ft
for the 1962 data, and about ±1000 to ±3500 ft for the
1957, 195$, and 1959 data. The maximum uncertainty for any
echo was about ±4000 ft. Fig. 1 shows the magnitude of this
uncertainty for a typical case.
Because the radar antenna was elevated in one-half degree
steps, there was a certain amount of overlap in the vertical
sections swept out by the beam in successive steps, and for
1 Since the elevation angles involved in the measurements
of the echo top heights in this study were never more
than 20 degrees, this rule holds with an accuracy better
than 4% for most echoes, and never more than 6% for
any echo.
Il
this reason the last detectable part of the storm would
probably have been detected by the lower part of the bearn.
This sU:ggests that the measured height may be too high by
as muchas one-half of the bearn width uncertainty, and
thus a correction should be made to the measured heights.
The smoothing procedure described above accounted for
sorne correction, lowering the maximum height in all cases,
but usually not as much as one-ha.lf o.f the bearn width
uncertainty. No further corrections were made, however,
.for reasons mentioned below.
The Decca radar operated in Alberta is a low power instrument (peak power about 20 kilowatts), and thus the radar
reflectivities that are necessary for detection are rather
high. At 20 miles range, the minimum detectable reflectivity
is about 5.5 x 10 2 rnrn.6/m3, and at 80 miles range, it is
about 8.8 x 103 rnm6 /m3. I.f the reflectivity does not drop
sharply to zero near cloud top, but decreases in an exponential
manner from a maximum near the centre of the storm.to the
cloud top (Donaldson, 1961), the radar may tend to underestimate the height of the cloud top. The radar will not be
able to detect the topmost part of the cloud if the re.flectivity of this portion is below the value of minimum detection of the radar. Only an estimate of the error from this
source can be given, because the reflectivity profiles in
Alberta thunderstorms are unknown, and may be quite different
than those given by Donaldson for New England storms, since
12
the former are continental and the latter are more tropical.
Also, the amount of error in individual cases is likely to
be highly variable, since the vertical profiles of reflectivity are probably different for various storms. However,
the profiles that Donaldson presented, in combination with
the minimum reflectivity requirements of the AlBerta radar,
give a first approximation to the magnitude of this error.
It v-m.s found that for a median profile of ha.ilstorms, the
underestimation due to the minimum reflectivity was comparable to the bearn width uncertainty, i.e. it was of the
order of a few thousand feet, but probably rarely more than
5000 ft.
Preliminary measurements were made on Alberta thunderstorms durine the summer months of 1963 to compare the
heights of the visible cloud tops (measured by optical
theodolite) and the radar echo tops, and the results (unpublished) indicated that, in all cases, the visible top
was higher than the radar top by several thousand feet.
However, further investigation of this problem is necessary
to determine the precise magnitude of the underestimation,
since only a few clouds were measured. Other investigators
also found that the visible top exceeded the radar top by
several thousand feet. Among them were Workman and Reynolds
(1949), Changnon and Bigler (1957), and Saunders and Ronne
( 1962).
Since this underestimation is probably of the same order
t.
ercerttrr ''ft'
.
r.
r:·.
13
of magnitude as the bearn width uncertainty, and tends to
offset any overestimations due to the bearn width uncertainty mentioned above, no correction was made to the
indicated heights, other than the amount that the smoothing
procedure reduced the initial rough data.
The problem of side lobes has been given considerable
attention recently, since the actual heights of the tops
of thunderstorms may be seriously overestimated when side
lobe power is appreciable. MOst of the radiation that is
transmitted outward from the antenna is focussed into a
narrow bearn (the major lobe), but also, sorne radiation is
transmitted outward into side lobes in directions at various angles from the axis of the major lobe. Battan (1959)
indicates that the shape of these lobes depends on the
shape and size of the antenna, the wavelength involved, and
the type of source used. Saunders and Ronne (1962) found,
that for the WSR-57 radar, the first side lobe occurs at
about 3 degrees from the axis of the major lobe and has a
power less than 1/100 that of the major lobe. The error in
the rneasurement of cloud top height would result when the
side lobes, which may be several thousand feet below the
indicated height at the centre of the major lobe, reach
into lower portions of the cloud (with higher reflectivities)
and return a power to the radar that is comparable to that
being returned from the major lobe. Donaldson and Tear (1963a)
and Aoyagi (1963) have considered theoretically the problem
14-
of side lobes, and both studies came to the conclusion
that the greatest error due to side lobes may be an overestimation by several thousand feet, and it increases with
range from the radar.
If side lobes are an appreciable problem of a radar, and
since the errors increase with range, one could expect to
find the highest measured echo heights at the farthest
ranges. Jordan (1962), in an analysis of radar errors,
found that the probability of echoes to great heights increased with range from the radar. An attempt was made to
determine if the same were true for the high echoes studied
in this project. Fig. 3 shows a scatter diagram of the
maximum height of each echo vs its range at the time of
maximum height. The diagram indicates that there is no
tendency to measure the highest echoes at the farthest
ranges, and there is thus no indication from this diagram
that side lobes are introducing any serious errors.
Donaldson (1963b) has indicated that the vertical bearn
width is also important in the magnitude of side lobe errors.
He gives a rule that, when the core of the thunderstorm is
intense, the errors due to side lobes become unmanageable
when the product of the ra.nge (in nautical miles) and the
antenna half-power bearn width (in degrees) approaches or
exceeds 100. This product is a maximum at the greatest
range, and in the case of the Alberta radar, has a maximum
value of 65, since the maximum operationa.l range of this
44
42
---
40
0
38
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1
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32
30
t
.. ...
..
.
. .. . •• .• ..
••
.. •.. .
.. ....•• . . . . . .
... . .
.•
•
•
20
•
•
.
30
40
RANGE
•
50
.• .
•
60
70
80
(miles)
Fig. 3: A scatter diagram of maximum echo top height vs range
from the radar at the time of maximum height, for the 112 echoes
of the sample.
'Oj
radar is about 100 statute miles (87 nmi) and the beam
width is 3/4 degree. More than 85% of the echoes of the
present study were within 60 statute miles (52 nmi) of the
radar, so this product would be less than 40 for the greater
part of the sample, well below the tolerance figure of 100.
Thus, on the basis of this rule, the Alberta radar should
be free of any serious overestimates of cloud top heights
due to side lobes.
Since both theoretical and observational evidence indicate
that side
lobe~
are not presenting any serious overestimat-
ions of the echo top heights for the echoes of this sample,
the greatest contributions to errors in the measurements
are apparently due to the beam width effect and the minimum
reflectivity effect, two sources of error that, to a certain
degree, tend to cancel one another. However, it is felt that
the latter dw probably the more important of the two in
many cases, on the basis of the preliminary visible top
vs radar top measurements, and there is probably an underestimation of many of the actual cloud top heights by as
rouch as 3000 to 4000 ft.
5. OTHER RELEVANT DATA.
Extensive use was made of data other than the echo top
heights, such as radiosonde soundings and daily maximum
temperatures. The daily radiosonde data - temperature and
moisture measurements from the surface to levels higher than
17
50 k~t - were available from the regular 0500 and 1700
(Mountain Standard Time) soundings at Edmonton, 100 miles
to the north of the radar site, for the four years relevant
to this study. In addition, special soundings were made at
Calgary, 80 miles south of the radar site, at 1700 MST
daily during the summer of 1962, and these were available
to augment the information from Edmonton. Also, sorne use
was made of soundings from Great Falls, Montana, about 200
miles south of the project area. These data were obtained
from monthly and daily reports of radiosonde data by the
Canadian Meteorological Branch and the U. S. Weather Bureau.
Sorne use was also made of daily maximum temperatures
(chapter VI) from several stations throughout the project
area for days on which the high echoes occurred. These data
were available for the four years from monthly tabulations
of meteorological data in Canada. The number of stations,
within the area, that reported maximum temperatures varied
from 12 in 1957 to 17 in 1962.
Data on the type of terrain in the project area (chapter
III) were obtained from topographical maps produced and
printed by the Surveys and Mapping Branch, Department of
Mines and Technical Surveys, 1959.
/~
III.
LOCATIONS OF HIGH ECHOES
1 .. INTRODUC'l'ION.
The locations of the highest echoes are of interest
in this project for the purpose of determining whether
any regions are favoured more. than others for the occurrence of the storms of greatest depth. Any regional favouritism of this type would be interesting from two viewpoints; these would be the areas affected most by probably
the most severe and damaging hailstorms, and secondly, of
more importance to this project, the physical implications
of any such favouritism, such as the relation of terrain
to these regions, could possibly be revealed.
Regarding the first of the above viewpoints, no separate
study was carried out to determine the severity of the 112
storms which made up the sample, but it was assumed that
most of them were severe on the basis of the high probabilities of hail that they would have. Donaldson (New England),
(1958} and Douglas and Hitschfeld (Alberta),(l959) found
that the probability of hail increased as the height of
the echo top increased, with a value of 70% probability
being given for Alberta echoes that reached 30 kft in
height, and larger probabilities of hail for higher echoes.
Also, Douglas (1961) found that there was very little large
hail (4 cm or more in diameter) associated with storms
whose echo top heights were less than 30 kft, with an
/f
increase in the large-bail probability as the echo top
reached to great er heights. Sin ce the echoes used in this
project were all 30 kft and higher, they would thus have
high probabilities of hail and large hail, and hence were
presumed to be the most severe storms. Any regional favouritism for their occurrence would then be of economie interest
on the basis of hail damage, since almost all the project
area is an agricultural region.
The effect of terrain on convective cloud development
in Arizona was revealed by Braham (1958). He found that
there was a large concentration of new echoes being formed
over terrain that was mountainous, 40% of the new echoes
\
being formed over terrain more than 5000 ft above sea level,
although this constituted only 14% of the land of his
project area. Although Braham's work was mainly with new
echoes, as opposed to the well developed ones of this study,
the indication was clear that terrain can play an important
part in cumulus cloud activity.
It is the aim of this chapter to determine whether there
are any regions favoured for the occurrence of high echoes,
and to indicate the type of terrain in any such regions.
2. ANALYSIS AND RESULTS.
The azimuth and range values of each of the 112 high
echoes were recorded during the analysis of the photographie records, so the precise location of each echo
was known at any time during its existence. Fig.
4 shows
the geographical locations of all echoes of the sample at
the time of their maximum heights. The diagram indicates
that almost all regions were affected by the high storms,
since there are echoes distributed over the whole project
area. However, there is sorne indication from this diagram
that there may be a greater concentration of echoes to the
northwest and to the southwest of the radar site. An objective analysis was then applied to determine whether
these regions were actually favoured.
In an objective ahalysis of this type, the radar characteristics that are range-dependent must be taken into account.
The radar equation (Wexler and Swingle, 1947), which is an
analytical expression giving the power returned to the radar
from a reflecting object, indicates that the power of the
radiation returned to the radar from a reflecting target
varies inversely as the square of the range of the target
from the radar. Thus a precipitating cloud with low reflectivities which could be detected at, say, 20 miles range,
may escape detection at èO miles range, since the power
returned to the radar from 80 miles would only be 1/16 of
that returned from the same reflector at 20 miles, and this
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•
O
0
O (
PENHOLD
0
000
1!>
)·
O0
~ADAR
SITE
0
~
o-90 _ . /
0
-
0
•
•
0
0
6.
00
~·o
••
0
00
•
o•
0
•o
/• o•
o-o
A
•
0
•
0
0
0
<f}
CALGARY
0
20
40
MILES
Fig. 4: The geographical locations of the 112 high echoes
at the time of their maximum heights. The circular rings are
the 20, 40, 60, and 80 mile range markers. Circles, dots,
and triangles indicate echoes whose maximum heights were 3034.5 kft, 35-39.5 kft, and 40 kft and higher, respectively.
may we11 be below the minimum operational detection power
of the radar. 'fhis would suggest that more echoes would
appear at closer ranges than at greater ranges, so that a
comparison of the numbers of echoes at 20 miles and at 80
miles from the radar would invariably indicate more storms
at the closer range, although there may well be as many
storms at the farther range. For this reason, it would be
incorrect to compare the numbers of echoes in regions at
different ranges.
Fig. 5 gives evidence of the above-mentioned radar range
deficiency, the histogram being constructed from the numbers
of echoes from the sample ( corrected for range, i.e. stated
as the
n~ber
per
squa~e
mile, or echo density) that were
detected in each 10-mile annular ring about the radar. The
absence of echoes within 18 miles of the radar is attributed
wholly to the 20-degree maximum tilt of the radar antenna,
i.e. the antenna could not elevate high enough to "see" the
top of a cloud higher than 30 kft at a range less than 18
miles. The value of echo density for the 10-20 mile range
interval in Fig. 5 is then probably not representative of
the true value. From 20-40 miles, the values of echo density
are almost the same, but from 40 miles to 80 miles range,
there is a decrease in the values that is almost inversely
cubic with ra.nge.
The first attempt at evaluating the significance of any
favoured regions was done on a directional basis, i.e. the
16
1
1
1
1
r<>
0
12
)(
-
\
\
N
\
\
E
\
...
Ql
o.
0
c:
\
8 f-
\
\
\
\
>-
\
1-
\
Cf)
z
w 4
1-
0
' ',
0
', ....
:I:
(.)
w
.... .....
....... ....
----
70
80
0
1
0
10
20
30
40
50
RANGE ( m1les)
60
Fig. 5: A histogram showing the echo density in
each 10-mile annular ring about the radar. The dashed
line indicates an inverse cubic relationship. The
value of 6.9 x 10-3 mi-2 in the range interval 1020 miles is probably not representative of the true
value. (For 112 echoes 30 kft and higher).
numbers of echoes that were located in various directions
from the radar site were compared. This type of analysis
should be independent of the above-mentioned radar range
deficiencies, since the same range values are involved in
all directions.
The method of analysis was to investigate the statistical
significance of the distribution of echo frequencies obtained by division of the project area into octants. The
azimuthal orientations of these octants were purposely
biased so that a particular region that had a high concentration of echoes vrould be completely contained within one
such octant. 'l'his was accompli shed, as far as possible, by
changing the orientations of the boundary lines in steps
and observing the number of echoes in each octant at each
step. The final orientation chosen was the one at which
there was the greatest echo frequency in any one octant,
and this had the octants displaced about 17 degrees of
azimuth in a clockwise direction from the north, south,
northwest, etc., directions. Fig. 6 shows a circular ·histogram of the echo frequencies by octants, and indicates that
the southwest octant had almost three times as many echoes
as the octant to the northeast (23 as opposed to 8).
To determine the statistical significance of the inequalities of the frequencies in the octants, a x~-test (described by Brooks and Carruthers, 1953) was applied to the
data. This is a statistical test that determines the
N
w
E
s
Fig. 6: A circular histogram showing the echo
frequencies by octants in the various directions
from the radar site. The circular rings indicate
frequency values of 5, 10, 15, etc.
significance of the deviations of observed values from
expected ones. The null hypothesis was made that there
was no real tendency for echoes to be concentrated in any
particular octant, so that one would expect the same number
of echoes to fall in each octant. In this case, the number
would be 112/8 =14. The ~~test was then used to determine
the validity of this hypothesis on the basis of the observed
distribution of Fig. 6. Results of the test are shown in
Table 1, in which f • =the expected frequency, f 0 =the
observed frequency, and d
=f
0 -
fe.
TABLE 1: ~').-test on echo freouencies by octants.
OCTANT
N
NE
E
SE
s
sw
w
NW
TO'l'ALS
lfo
9
8
14
14
11
23
14
19
112
lfe
14
14
14
14
14
14
14
1h
112
0
0
0.64
5.79
1.79
12.58
~1f. 1.79
2.57
0
c
The number of degrees of freedom is 7.
This gives a probability of on1y 0.08 that the nu11 hypothesis is correct, i.e. a distribution of the type of Fig. 6
would occur randomly only $ times in 100. The genera1ly
accepted significance leve1 is 0.05, so the significance
of the deviations of the ohserved values from the expected
values, on the basis of the above hypothesis, is uncertain.
However, with a probability level of 0.08, the chances are
;z.:7
more than 11 to 1 that the d,eviations are significant. Also,
almost one-half of the value of
Xis
1.
due to the deviation
in the southwest octant, so this value was tested
by means
of Student 1 s t-test (Brooks and Carruthers, 1953) to determine whether it was significantly higher than the other
7 values of echo frequency in the other 7 directions.
In this test, the null hypothesis was made that two
samples, the first having 7 observations of frequency from
the N, NE, E, SE, S, W, and
~w
octants, and the other
having 1 observation of frequency from the SW octant, were
drawn from the same population, and hence the mean values of
the samples would not be significantly different. The t-test
was then used to examine this hypothesis. The value of t is
given by the equation, t
=
M,- Ma
o-fYl,•+n
;
1
-n,n:a.
where M,and
M~are
t:r=
l:K~-+1:x!
l1,+n~_ -2
'
the mean values of samples 1 and 2, re-
spectively, n,and n:l.are the numbers of observations in the
respective samples, and x,and
x~are
the deviations of the
observations of the samples from their respective means. In
this case M,=23, n, = 1;
t
= 2.58.
There are (n,+n1
Mz=l2.71, nz.= 7;o- =3.73, and
-
2) =6 degrees of freedom. This
gives a probability level of only 0.04, i.e. only 4 times
in 100 would this high a value of t have occurred by chance,
or, there are only
4 chances in 100 that the two mean values
were drawn from the same population. This is slightly below
the generally accepted significance level of 0.05, so the
frequency of 23 in the SW direction is apparently significantly
higher than the values in the other directions. The values
in the other octants were similarly tested, but none gave
a probability level below 0.10, so the frequencies in each
of the other octants were not considered to be significantly
different than the rest.
It was desired to investigate the echo concentrations
on a regional basis in addition to the directional one,
so the project area was subdivided into
2L~
regions defined
by the oètants and also by the 20, 40, 60, and 80 mile
range rings. The regions within 20 miles of the radar were
neglected because the frequency values in these regions were
probably not representative of the true values. Fig. 7
shows the result of the subdivision, with the values of
echo frequency entered in each region. Frequency values
such as
8!
and
Ji
come about because any echo that was
located on a regional boundary was apportioned between the
two adjacent regions.
To overcome the above-mentioned radar range deficiency,
only the values of echo frequency in the 8 regions in the
same range interval were compared. The t-test was applied
to the 8 values in each of the two range intervals 20-40
and 40-60 miles in an effort to determine the significance
of the highest and lowest values, respectively, as compared
to the others in each interval of range. Table 2 gives the
results of the test. The values in the range 60-80 miles
were 'not compared because the total frequency in this range
interval was only 15.
N
w
s
0
20
40
MILES
Fig. 7: Subdivision of the project area into
regions or sectors defined by the 20, 40, 60,
and 80 mile range markers (the circular rings}
and the octants. The numbers indicate the echo
frequency in each sector.
3o
TABLE 2: t-test on echo frequencies by sectors.
RANGE: 20-40 miles
RANGE: 40-60 miles
Total frequency :53
Total frequency : 3 7!
Sector(s) frequency
tested
t
Pro b.
level
lmv vs
Ir est
11
1.99 0.10
{highest)
S and SE
IVs rest
(lowest)
Ji
2.35 0.06
t
Sector(s) frequency
tested
Prob.
level
SW vs
rest
(highest)
9!
2.65 0.04
NE vs
rest
0
(lowest)
2.54 0.05
Table 2 indicates that 4 regions apparently have significantly higher or lower concentrations than the other
regions. The frequency in the SW octant at 40-68 miles
appears to be significantly higher than the others, while
the frequencies at 20-40 miles in the S and SE octants, and
the one in the NE octant at 40-60 miles, apparently are
significantly lower than the others. The results of the
statistical tests are not cornpletely conclusive, but they
do indicate that the odds are more than 15 to 1, in each
of the 4 apparently significant cases above, that such
distributions would not occur by chance.
-31
3. TOPOGRAPHY.
Fig. 8 shows, on a topographical map, the regions that
apparently had significantly higher (denoted by "H") and
lower {denoted by "L•) echo concentrations than the other
regions. The type of terrain in these regions is not
outstandingly different than that of any other' regions,
but it should be pointed out here that the area of high
concentration to the southwest of the radar site is a
rolling, highland country in the foothills of the Rocky
Mountains, gradually sloping in elevation from about 4000
ft to 5000 ft above MSL toward mountain peaks of about
10,000 ft
(~~L)
to the west and southwest. The area of
low concentration to the northeast of the radar site
is characterized by small lakes and is generally a flat
country about 2500 ft above MSL, while the region to the
south and southeast of the radar site (an area of low echo
concentration) is again generally a flat area with an elevation of about 3000 ft (MSL).
4. DISCUSSION.
The results of the analysis indicate that the concentrations
of echoes in sorne regions are significantly different than
concentrations in other regions. On a directional basis,
it was found that the number of echoes to the southwest of the
radar was apparently significantly higher than the numbers
c::v
Fig. 8: A topographical map of the
Alberta Hail Research ?roject area.
The shaded regions marked 11 H11 and 11 1 11
are the regions of high and low echo
concentrations, respectively. The rings
are the 20, 40, 60, and 80 mile range
markers, and mountain peaks are denoted
by "x".
EDMONT ON
~
c:j> Cl
8~
û
~-
(j
~
l(
x
l(
l(
x
x
l(
x
x
l(
)( \
x
x
x
x
x
l(
;{]
x
x
'-.J
x
x
\
x
x
x
x
x
x
~<~.
~
'---""""
~·
.........
1>
A
x
CALGARY
~
lv
. tv
.33
in the other directions. Further subdivision of the project
area allowed an investigation of echo concentrations on a
smaller scale, and led to the conclusion that 3 regions,
already mentioned above, apparently had
signific~ntly
higher or lower concentrations than others. The objective
analysis was hampered by the radar's inability to detect
echoes at large distances as well as at close ranges, but
this was somewhat overcome by considering only values of
echo frequency in regions at the same range. The analysis
did not indicate, however, the significance of the differences
in the numbers of echoes in regions at different ranges·,
because it was impossible to determine how much of the
deviation between the echo frequencies of two such regions
was due to the radar range deficiency and how much was
due to real physical phenomena. However, the analysis did
indicate one region of significantly high echo concentration
to the southwest of the radar site in a high, rolling
country. The regions of low concentration were associated
with flat terrain, one region in particular having many
small lakes.
The physical effects that these types of terrain have on
the occurrence of high storms were not investigated, since
this was beyond the scope and intention of this project,
but a more detailed investigation of the terrain effects
on the development of convective cloud, possibly using all
echoes of all heights, might prove rewarding.
IV.
ECHO TOPS NEAR THE TROPOPAUSE
1. INTRODUCTION.
Ever since the heights of clouds have been measured by
radar methods, many authors have reported that convective
storms approach and "penetrate" through the tropopause.
Jordan (1962) gives a good summary of reports of extreme
cases of tropopause penetrations, indicating that sorne
measured echo top heights have
e~tended
more than 20 kft
above the tropopause. A cloud whose top reaches into the
stratosphere is of interest because the amount of penetration
into this stable layer can be used with sorne degree of
success to measure the intensity of the storm. For instance,
Vonnegut and Moore (1958) used the amount of negative
energy on an adiabatic chart (see Fig. 16) from the equilibrium level to the maximum height of the cloud top, to deduce
what the vertical velocities must have been at the equilibrium level. They deduced theoretically, from parcel theory,
that a parcel would need an updraft velocity of about 20 rn/sec
for every kilometer of penetration into an isothermal
stratosphere. Thus for a 20 kft penetration, this model
would require updrafts of the order of 120 m/sec, values
which were considered to be too high. Jordan points out
one reported extreme case of a 30 kft penetration, and the
updraft that this model would require would have been
about 180 rn/sec (350 knots), a fantastically high value.
Because these updrafts were considered to be unreasonably
high, much controversy arose about the validity of the
parcel method of obtaining energies associated with tropopause penetrations, in view of possible local variations
in tropopause height as pointed out by Kuettner {1958).
However, more recent knowledge of the magnitude of errors
due to side lobes, for some radars, has indicated that the
reported heights of echoes may be too high in many cases,
a fact which has added to the controversy about tropopause
penetrations.
In view of the fact that the echo top heights of the sample
used in this study are apparently free of serious overestimates
due to side lobes, it was of interest to investigate the
relationship of the highest Alberta storm heights to the
tropopause heights.
Th~s
section deals with the relationship of the heights
of all the echoes, 30 kft and greater, to the heights of
the tropopauses, the number of echoes
t~at
went higher than
the tropopause height, and the manner in which some of these
reached and exceeded the tropopause.
2. TROPOPAUSE HEIGHTS.
For all 31 days on which the 112 echoes of the sample
occurred, the regular 1700
Y~T
radiosonde soundings were
available at Edmonton, and the tropopause heights (by the
WMO definition -- see Appendix A) were found from these
soundings for all 31 days. Of the 31 days, 14 were drawn
from 1962, and complete 1700
I~T
soundings were available
at Calgary on 13 of these days, so the Calgary tropopause
heights were then found for all of these days. Calgary
and Edmonton are about
1eo
miles apart, on opposite sides
of the project area. Calgary's tropopause was, on the average,
about 1000 ft higher than Edmonton's, but not necessarily
higher on all days. Generally, the difference in their
heights was about 2000 to 3000 ft, with a maximum difference
on one day of 5000 ft. The tropopause height used in the
following analysis was the higher one of either station on
each of the days.
No soundings were available from Calgary for 1957, 195g,
and 1959, and since the 1962 data above indicated that the
tropopause height at
E~monton
may be too low to be rep-
resentative over the project area, the 1700 MST soundings
at Great Falls,
I~ntana,
200 miles to the south of the
project area, were used to gain sorne information about the
variation in tropopause height with location on the other
17 days on which the high echoes occurred. On 12 of these
days, the Great Falls tropopause was well defined and
within 4000 ft (usually higher) of the one reported by
Edmonton. For these days, the higher tropopause, again,
was used in the analysis. On the other 5 days, the Great
Falls tropopause was poorly defined and was about 10,000 ft
higher than Edmonton's. There was evidence of two tropopauses,
or a leafing effect, on these days, so that the higher
.37
Great Falls tropopa-use height was neglected, and the height
of the Edmonton tropopause plus 1000 ft (the mean difference
between Edmonton and Calgary for 1962) was used as the
representative tropopause height. For these 5 days, and the
one day in 1962 on which the sounding was incomplete at
Calgary, the tropopause heights were considered doubtful,
and the re1ationship of actua1 echo heights to tropopause
heights on these 6 days are subsequent1y denoted as doubtful.
On most days, the tropopause was we11-defined, i.e. the
discontinuity in the temperature lapse rate was very sharp,
but on severa1 days, it was not so well-defined. However,
in the uncertain cases, the WMO definition chooses a height
that is near the top of the inversion of lapse rate, and
since the higher of two measurements of tropopause heights
was used for a11 but 6 of the days, any corrections that
may be necessary to the tropopause heights used in this
analysis wou1d certainly not make them any higher.
A1most a11 the echoes of the sample reached their maximum
heights within three hours of the time of the soundings, so
the differences in the heights of the tropopause at the
time of tl:le occurrence of the echo and at the time of the
soundings shou1d be véry small.
3. RELATION OF ALL ECHO HEIGHTS TO THE TROPOPAUSE.
In order to determine the relationship between all maximum
echo heights and the tropopause, a histogram was prepared
38
from the values of echo top height relative to the tropopause
height, and is shown in Fig• 9. The positive values indicate
echoes whose measured tops were above the tropopause height,
while the negative values indicate echoes that were below.
The dashed portions, at the tops of the columns, indicate
additional ethoes on the 6 days on which the tropopause
height was considered doubtful.
This diagram shows that the tropopause is acting as a
"barrier" to the growth of the storms, since there is a
sharp decline in the number of echoes that reached or exceeded the tropopause. The decline in the echo frequency
on the left~hand side of the diagram is due to the fact
that only echoes as high or higher than 30 kft were used
to construct the histogram, and had echoes of all heights
been included, this decline would probably not have been
observed.
Since the tropopause is appàrently acting as a barrier
to the growth of the clouds, one would expect the maximum
echo heights to be lower in Alberta, where the tropopause
is usually about 35 kft, than in more southerly regions,
where the tropopause is usually about 10 kft higher. The
Alberta maximum heights were found to be lower, as was
previously mentioned in section II.3.
NUMBER
OF ECHOE S
r-,
-10
HEIGHT (kft)
1
1
-4
-2
RELATIVE
0
TO
TROPOPAUSE
Fig. 9: The distribution of maximum echo top heights
relative to the tropopause heights on their respective
days. The dashed portions of the frequency columns
indicate the numbers of cases that were doubtful because
the tropopause height was determined from only one station.
Negative values indicate echo heights below the tropopause,
and positive values indicate echo heights above. (112
echoes on 31 days).
30
rJ)
w
0
I
20
(..)
w
u...
0
Cl::
w
co
10
:::!:
:::>
z
0
30
32
34
HEIGHT
36
ABOVE
36
40
42
SURFACE
44
46
(kft)
Fig. 10: Distributions of the heights of the 112 echoes
of the sample (outer histogram) and the heights of the 19
that were penetrating the tropopause according to the·
criteria outlined in the text (shaded histogram). Four·
doubtful cases are included in the latter histogram.
4. TROPOPAUSE PENETRATIONS.
To constitute a tropopause penetration, the indicated
echo height and its uncertainty due to bearn width had to
be as high or higher than the tropopause height as determined
by the above analysis. According to this definition, there
were 15·echoes on 9 days whose heights clearly exceeded that
of the tropopause. Four other echoes, on three of the days
on which the tropopause height was considered doubtful, were
apparently higher than the tropopause, so that, of the
original· 112 echoes of the sample, 19 (with 4 doubtful) were
apparently penetrating the tropopause. The greatest amount
of penetration of any echo was 8000 ft. Fig. 10 shows the
number of echoes of the original sample that penetrated the
tropopause, the outer histogram being the distribution with
height of all echoes, and the shaded histogram, superposed,
indicates those that were apparent tropopause penetrations.
The four doubtful cases are included in the distribution.
No consideration was made for local variations in the
tropopause height, which might be caused by the storm
itself (Kuettner, 1958), since an analysis of this type is
impossible without soundings in the near vicinity of the
storm.
Of the 19 echoes that apparently penetrated the tropopause,
8 were recorded from first echo, and the manner in which
these echo tops approached and exceeded the tropopause height
41
proves interesting. Three of these 8 echo tops had the
tendency to rise at alrnost a constant rate, after first
radar detection, and to extend considerably higher than
the tropopause height, while the ether 5 appeared to rise
to heights just below the tropopause, and rernain there for
a considerable time before finally extending on into the
lower stratosphere. Figures 11 and 12 show echo top·height
vs time plots for two of these cases, Fig. 11 indicating
one that rose almost steadily to its maximum height, and
Fig. ·12 indicating one that lingered for sorne time below
the tropopause before penetration. The distinction between
the two types is apparent from Fig. 13. The abscissa of the
histograrn indicates the time from which the echo top first
came within 5000 ft of the tropopause to the time that it
went higher than the tropopause, and in 3 of the .cases,
this time was 10 minutes or less, while in the 5 cases
that lingered below the tropopause, this time varied from
30 to 80 minutes.
The difference between the two types of ascent of the
echo tops may be attributable to the environment around
the clouds. Each of the 3 cases that rose rapidly above the
tropopause height was a very strong echo in the midst of
much weaker echo, or in the midst of a large mass of less
intense echo. In all three cases, the echo was part of a
line of echoes. These cases were individual cells that
grew in a cloud environment, an environment that was
50
40
1::t:
(!)
w20
::t:
10
AUGUST
2, 1962
o~--~~--~-----L----~----~----~----._1900
2000
1930
TIME
(MST)
Fig. 11: Echo top height vs time plot for one echo that
rose almost steadily to its maximum height. Dashed lines
indicate the bearn width uncertainty.
50
40
.,.;.
~
30
..... ......
.,.., .,..
1::t:
'
(!)
w 20
'
' ' ' ' ' ' ' ... ...
''
::t:
10
JUNE
'
''
19, 1962
0~--~~--~-----L----~----~----~----._--~~--~----~----~----~
0000
2300
2330
0030
TIME
(MST)
Fig. 12: -Echo top height vs time plot for an echo that
lingered below the tropopause for a considerable time
before extending on to penetrate into the lower
stratosphere. Dashed lines indicate the bearn width
uncertainty.
43
3
8 CASES
en
IJJ
0
~2 IJJ
u..
0
0::
-
IJJ
al
::E
::>
z
0
0
40
20
TIME
60
80
(minutes)
Fig. 13: A histogram showing the number of
cases in the intervals of elapsed time from
which the echo top first came within 5000 ft
of the tropopause height to the time that it
went higher than the tropopause, for the 8
echoes that were considered.
apparently very moist,. since there was sorne weak echo
around the cells. On the ether hand, the 5 cases which
took longer to penetrate the tropopause were all isolated
from any other storms. In 4 of the cases, no other echoes
were detected within 20 miles, and the fifth might have
been considered part of a line of echoes, but it was at
the extreme south end of the line, and relatively isolatéd
from other storms on the line. It would seem that these 5
storms developed in an environment quite different than
that of the ether 3 cases, one that was probably much less
humid.
There is sorne evidence here of the importance of environmental conditions in the development of convective clouds.
The three echoes that rose rapidly to their maximum heights
\
did so in an environment that was cloud saturated, one in
)
'
which the entrainment of surrounding air would not have
as much of an inhibiting effect on the growth of the cell
1
as would dry air • The other five developed in an environment that was apparently much drier, since these echoes
were isolated. It appeared that these storms, over a period
of time 30-80 minutes, were "conditioning" their immediate
surroundings so that the parcel or column of air that
finally penetrated above the tropopause was able to do so
by rising through a well-modified environment.
1
Several authors who have shawn the effects of
entrainment on a parcel of air are mentioned in
Chapter VI.
5. DISCUSSION.
In this section, the relationship of the maximum heights
of the echoes, that were as high or higher than 30 kft, to
the height of the tropopause was considered. It was found
that a number of the highest echoes ~rere reaching heights
greater than the tropopause height as determined from two
nearby radiosonde soundings. In no case, however, was the
echo height more than $000 ft above. the tropopause.
Of the echoes that were apparently penetrating the tropopause,
there appeared to be two distinct types of growth to maximum
height, the first being a fairly steady rate of growth
from first echo to maximum height, and the second being a
more prolonged process, sometimes going on for more than
an hour before the top extended on to the maximum height.
The former cases took place in an environment that was
apparently very favourable for their development, the echoes
lying within lines of weaker echoes, while the latter cases
were developing in an environment that was apparently much
drier, since these were all isolated cases. The two different
regimes of development give sorne indication of the importance
of the
environm~ntal
conditions in the growth of convective
clouds, hinting at the effects of entrainment of the·surrounding air.
When all the echo top heights of the sample were compared
to the tropopause heights, it was found that the tropopause
was acting as a barrier to the growth of the highest clouds,
since there is a definite decline in the number of echoes
that approached or exceeded the tropopause height. This
barrier effect was attributed as a reason for the maximum
vertical extent of echoes in Alberta being lower than those
in more southerly latitudes where the tropopause is considerably higher.
47
V.
TElJ.lPERATURE
AND
IvlOISTURE
CONDITIONS
1. INTRODUCTION AND ANALYSIS.
An attempt was made to determine
wheth~r
there were any
differences in the vertical temperature and moisture profiles in the troposphere and lower statosphere on days
which had the highest echoes as opposed to days that had
maximum echo heights considerably lower. In the analysis,
15 days with echoes 35 kft and higher were compared to 15
days that had ma.ximum echo top heights of 20-30 kft. The
former were chosen from the 31 days on which the 112 echoes
of the sample occurred, and the latter were chosen from
da ys inde pendent of the sampl.e, but were days on which there
were no doubts of the maximum echo top heights. The 1700 MST
radiosonde soundings at Edmonton were used in the analysis,
and the median temperatures and median moisture.mixing
ratios were determined at each 50 mb level from the surface
(approximately 950 mb in Alberta) up to 100 mb (approximately
65 kft) for each day of the two groups. A composite sounding
was then constructed, for each of the two groups, using the
median values at each level. The median tropopause was found
in both cases by the point that represented the median pressure level and the median temperature of the 15 values of
each, and the median temperature at the surface was based
· on the maximum temperatures at Edmonton for the 15 days of
each group.
-------'-------.......;.;-~'----~---~--------~---~~ ...... ---··~··-
.....
-
Figures 14 and 15 show the results of the analysis. The
median temperature and moisture curves are shown for each
case, and also shown are measures of scatter or variability,
namely the upper and lower 20-percentiles of each sample.
2. DISCUSSION.
The median soundings of Figs. 14 and 15 are similar in
many respects. There is no significant difference in the
moisture content curves, since there is a large overlap of
1
the indicated percentile ranges for the curves • However,
the median values for the days with lower echoes indicate
slightly drier conditions aloft than the days with the
high echoes, but the median surface dew points are almost
the same. The temperatures and heights of the tropopauses
are almost identical, but there are sorne differences in
the temperature structures. The median sounding for the
days with low echoes shows greater stability in the upper
levels, i.e. from about 700 mb to the tropopause. The
most significant difference in the soundings, however, is
in the low levels, The zero degree Celsius level is higher
by about 2-3 kft, and the temperatures around the 700 mb
level are warmer, on the days with high echoes. The differences
1 MDisture conditions, such as precipitable water
vapor content, moisture layer thickness, mean
moisture mixing ratios, and mean relative humidities
were considered in detail, and no significance was
apparent.
49
200
300
500
700
900
1000
Fig. 14: A median sounding constructed from the median
values of temperature and moisture mixing ratio at each
50 mb level for 15 days on which maximum echo top heights
were in the height interval 20-30 kft. The heavy solid
line on the right is the median temperature sounding, and
the dashed lines indicate the upper and lower 20-percentile
temperatures of the sample. The heavy solid line on the
left is the median mixing ratio, or dew point temperature,
sounding, and the thin solid lines indicate the upper and
lower 20-percentile moisture values of the sample.
so
/
/
/.
/
/
/
/
/
/
/
200
300
500
700
900
1000
-20
c
20
c
Fig. 15: A median sounding for 15 days with maximum
echo top heights 35 kft or higher. The so1id and dashed
1ines are the same as indicated in Fig. 14.
are significant in that there is no overlap of the percentile ranges, i.e. the upper 20-percentile temperature
for the days with low echoes is less than the lower 20percentile value for the days with high echoes. There is
more positive area (see Fig. 16), for an unmixed parcel
lifted from tbe surface, on days with high echoes than on
days with low echoes, and the expected heights for clouds,
on the basis of parcel theory2 , are thus higher on the days
with high echoes, the predicted values of height being
about 26 kft and 32 kft for the low echo days and the high
echo days respectively. Although there is no great merit
in using
par~el
theory on the median soundings, since they
do not represent individual cases, the height predictions
from them indicate that an investigation of the ·applicability of parcel theory is in order. This is also indicated
by the fact that the main differences in the soundings are
in the low levels, the levels in which the temperature and
moisture profiles are most critical for parcel theory
considerations. This investigation is described in Chapter
VI.
The results of the analysis thus show that there are
significant differences in the low level temperature profiles in the troposphere between days that have the highest
echoes and days that have considerably lower echo tops. This
2 Described in most elementary physical meteorology
textbooks.
seems to emphasize the importance of the low level thermodynamic properties, and also, since the high level temperature and moisture structures were not appreciably different,
it seems to indicate the unimportance of the high level
structures in the development of towering convective clouds.
For this reason, the parcel theory calculations of section
VI were all carried out with a parcel originating at the
surface.
~--~········---~-
----
-20
c
oc
20C
Fig. 16: A schematic temperature sounding. ( heavy
solid line) on a tephigram, displaying the concept
of positive and negative areas/energies. The dashed
line 1-2-3-4 representa a pseudo-adiabat for a rising
parcel of air. 'l' indicates the starting level of the
parcel, '2' is the lifting condensation level, '3' is
the level of hydrostatic eouilibrium, and '4' is the
ultimate height that the parcel may reach. The shaded
area A indicates the positive area, and is a measure
oi' the maximum kinetic energy that the parc el acquires.
The shaded area B is the negative area, and by pure parcel
theory, should be eoual to the positive area.
VI.
PARCEL THEORY CONSIDERATIONS
1. INTRODUCTION.
In this section, the heights of the 112 highest echo tops
are compared to the values predicted by parcel theory. In
addition, measures of the "negative" energies associated
with the storms are compared to the "positive" energies
available from parcel theory, and an attempt is made at
evaluating updraft velocities.
For an interpretation of certain terms used in this section,
such as "level of hydrostatic equilibrium" and "ultimate
height", the reader is referred to Fig. 16.
2. MAXIMUM SURFACE TEMPERATURES AND DEW POINTS.
Since the results of parcel 'theory height and vertical
velocity computations are usually highly sensitive to the
values of temperature and dew point temperature at the
starting level (in this study, the surfaèe), special care
was taken in the selection of these temperatures. For any
given day, a median maximum temperature was chosen from
maximum temperatures reported by several stations within
the project area, This·was applied, together with the
Edmonton surface dew point tempera'bure, to the 1700 MST
Edmonton sounding aloft, which was assumed to be representative over the project area 1 , to give a measure of the
1
The 1962 so~dings from Calgary indicated that this
assumption was quite valid, since they were generally very
similar to the Edmonton soundings.
maximum positive area {or energy) available to a parcel
for that day.
The number of stations that reported daily maximum temperatures varied from 12 in 1957 to 17 in 1962, and on any one
day, there was usually a difference of S to 10 degrees F,
or about 5 degrees C, between the lowest and the highest
reported values. !he median of these temperatures was taken
to be the most representative temperature to use for the
calculations, and it was generally about 1 or 2 degrees C
higher than the maximum temperature at Edmonton, the site
of the sounding.
The surface dew point temperature was slightly more uncertain than the maximum temperature for any day, because
only a few of the stations reported dew points. The surface
dew point temperature at Edmonton at the time of the
sounding was taken to be representative of the air mass
over the project area, and was used for the computations.
If the parcel positive energy is large, a variation of 3
or 4 degrees C in the dew point temperature does not appreciably affect the height or updraft values corresponding
to this positive energy, because the latter are relatively
insensitive to small changes in a large amount of positive
energy. However, when the positive energy is small, a
small change in the dew point temperature is most important.
As indicated below, the positive energies were large on
most of the days under consideration in this study, so that
56
the values of height and updraft deduced from these energies
were not critically sensitive to the values of dew point
temperature chosen.
3. POSITIVE AND NEGATIVE AREAS AND ENERGIES.
For each of the 31 days on which the high echoes occurred,
the positive area (or energy per unit mass), for·a parcel
of air, was measured on a tephigram, the initial surface
conditions being determined by the above-mentioned method.
Fig. 17 shows, in histogram form, the distribution of these
energies for the 31 days. An auxiliary scale of maximum
potential updraft velocities corresponding to the energies
gives a more meaningful interpretation of the physical
implications of the energy values. The highest value of
positive energy was 2300 joules per kilogram of air (corresponding to 68 m/sec updraft), and the lowest was 150 j/kg
(17 m/sec}. Only two days hàd energies less than 400 j/kg,
and most days had values in excess of 1000 j/kg.
Parcel theory thus indicates that convective cloud activity
was possible on all 31 days, and highly probable on most
of them.
The negative energy associated with each of the actual
echoes was also measured. This was defined by the area that
was bounded by the maximum echo top height, the parcel
adiabat, and the environmental temperature sounding. An
index was devised as the ratio of this negative energy to
5'7
10
(/)
r-
8 i-
>-
4:
0
u..
6
r
4
r
0
0::
w
ID
::E
::::>
z
2
0~---L----L---~~--~--~L----L--~
0
400
800
POSITIVE
1200
40
49
28
MAX. POTE NTI AL
0
1600
ÉNERGY
2000
2400
2600
{joules/kg)
57
UPDRAFT
63
69
(rn/sec}
72
Fig. 17: Distribution of the parcel·theory positive
energies for the 31 days with èchoes 30 kft and higher.
Auxiliary scale is vertical velocity corresponding to
the energies.
50
NUMBER
OF CASES
30
20
10
-0 2
0
0·2
0·4 0·6
0·8
1·0
1·2
NEGATIVE
ENERGY
POSITIVE ENERGY
1-4
5·0
5·2
Fig. lS: Distribution of the ratios of negative energies
{between LHE and echo top), for the 112 high echoes, to the
positive energies for their respective days. Negative
values indicate echo tops that were below the LHE and
positive values indicate those that were above. An index
of 1.0 means that the echo top height was the same as
the ultimate height.
the positive energy available for the day on which the
storm occurred. An index of zero means that the maximum
echo top height coincided with the height of the level of
hydrostatic equilibrium (LHE), while an index of 1.0 indicates
that the ultimate parcel height was reached, i.e. the negative
energy equalled the positive energy. A negative index means
that the echo top was below the LHE. A value of the index
was thus obtained for each of the 112 echoes, and Fig. 18
shows the distribution of these values. There is a maximum
frequency at the LHE, and a secondary maximum at the ultimate
1
height. Of the 112 echoes, 80 reached or exceeded the LHE,
and only 51 were higher than the ultimate height. Thus, more
than 2/3 of the highest echo heights were between or at the
LHE and the ultirnate height. Only one echo had an unreasonably high negative energy (5.3 times as much negative as
positive energy).
4. PREDICTED VS ACTUAL HEIGHTS.
The actual echo top heights were also compared to the
predicted LHE and ultirnate heights on each of the days, and
Figs. 19 and 20 show the distributions of the echo heights
relative to the LHE and ultirnate heights, respectively.
Again, a maximum frequency appears at the LHE, with most
1 In the histograms, any value which fell on a class
boundary was divided between the two adjacent classes,
thusthe numbers in the text do not necessarily agree
exactly with the values indicated in the diagrams.
NUMBER
OF ECHOES
-6
ECHO
HEIGHT
-4
-2
RELATIVE
0
TO
2
4
12
10
8
6
LEVEL OF
14
16
( k ft)
EQUILIBRIUM
HYDROSTATI C
Fig. 19: Distribution or the 112 echo heights relative
to the height of the LHE on their respective days. Negative
values indicate echo tops that were lower than the LHE
and positive values indicate echoes that were higher. The
shaded part or the histogram indicates those 5 echoes
whose tops were higher than the ultimate height.
30
NUMBER
OF ECHOES
20
1---=r 10
-16
-14
ECHO
-12
-10
HEIGHT
-6
RELATIVE
-4
TO
-2
0
ULTIMATE
2
HEIGHT
4
6
8
{kft)
Fig. 20: Distribution of the 112 echo heights relative
to the ultimate height on their respective days. Negative
and positive values indicate echoes whose tops were below
and above the ultimate heights, respectively. The shaded
part or the histogram indicates those echoes whose tops
· failed to reach the LHE.
bO
the echo heights above this level. None exceeded the
o~
ultimate height by more than 7000
more than 1000
~t
~t,
and only two were
above this level. The mean ratio
o~
actual echo top heights to ultimate predicted heights
was 0.83, meaning that, on the average, the actual heights
were attaining 83%
o~
the parcel theory predicted height.
5. VERTICAL VELOCITIES.
An attempt was made to evaluate maximum vertical velocities
associated with the high storms
o~
this study. The results
the above analysis regarding heights and energies showed
o~
that in nearly all cases, parcel theory was overpredicting
slightly the actua1 heights (Figs. 19 and 20), and the
positive energy that was available was usually considerably
greater than the negative energy measured between the LHE
and the echo top (Fig. 18). This hints at two possibilities.
T.he
~irst
is that the surface temperature used
~or
the
parcel theory measurement was too high, the result being
an overestimation
o~
the positive energy and the predicted
height. The second is that entrainment
o~
the surrounding
air tends to reduce the actual heights from the unentrained
1
values •
I~
the
~irst o~
these is true, i.e. that pure parce1 theory
1 Among the authors who have shown the effects o~
entrainment with coo1er and drier air are Stommel (1947),
Austin (1948), Houghton and Cramer (1951), Ha1tiner (1959),
and Mason and Emig {1961).
is applicable to the situation, then updraft velocities
can be readily obtained directly from a tephigram by·
choosing the proper pseudo-moist adiabat that equalizes
the positive and negative energies between the cloud base
and the echo top heights. It should be pointed out here
that the surface conditions of temperature and dew point,
that were necessary to give an adiabat that equalized the
energies, were reasonable in all but two cases. These two
cases were the highest echoes of the sample, and both were
above the maximum predicted ultimate height.
Fig. 21 shows the distribution of the vertical velocities
calculated from the
resul~ant
equalized areas or energies.
As a comparison, Fig. 22 shows the distribution of the
potential updrafts corresponding to the positive energies
given by the maximum temperatures on the 31 days. The
latter diagram indicates that the potential updraft velocities for sorne days could have been as high as 70 rn/sec,
with a median value slightly above 40 rn/sec. This distribution
is skewed towards higher values. The distribution of Fig. 21
indicates, as expected, that most of the updrafts have been
reduced, since the distribution is skewed towards lower
values. The median for this sample is just below 40 rn/sec,
and most of the values are between 30 and 50 rn/sec. It is
felt, however, that the neglect of entrainment in the
evaluation of the vertical velocities is serious, and thus
the values presented in Fig. 21 are probably only a first
6.z
50
en 40L&.l
en
<l:
u
lL'
30
0
a::
20
ro
L&.l
::2
:::>
z
10
0
0
10
20
30
MAXIMUM
40
50
60
70
( m/sec)
UPDRAFT
Fig. 21: Distribution of the maximum updraft velocities
calculated from the eaualized positive and negative
energies between the lifting condensation level and the
echo top height. (112 cases).
10
r-
8
r-
en
L&.l
en
<l:
u
lL
6
0
a::
ro
4
L&.l
::2
:::>
z
2
1
0
0
10
20
MAXIMUM
30
40
UPDRAFT
50
60
70
( m/sec)
Fig. 22: Distribution of the maximum updraft velocities
corresponding to the positive energies derived from the
maximum tempera.t.ures on the 31 days.
63
approximation to the true values involved. However, since
most of the sample heights agree quite well with those
predicted by parcel theory, the implication is that the
real processes involved are not deviating a great deal
from parcel theory processes, and thus the vertical velocities presented in Fig. 21 are probably, at the least,
giving the proper order of magnitude of the true values.
The values of 30-50 m/sec are not unreasonable from the
standpoint of the fall speeds of large hailstones that
these updrafts would support. Macklin and Ludlam (1961)
have computed fall speeds for various sizes of hailstones,
and indicate that an updraft of 35 m/sec would support
a hailstone of about 2 inches diameter. Hailstones of this
size have been observed in Alberta. The Thunderstorm Project
(1949) indicated aircraft measurements of vertical velocities as high as about 30 m/sec, and these were measured
in storms that were probably not as vigorous as the storms
studied in this investigation, so that the values presented
here seem to be quite reasonable.
When entrainment of the surrounding air is considered,
the problem of evaluating updraft velocities is not a simple
one. The rate of entrainment, which was found to be inversely proportional to the radius of the element of rising
air (Squires and Turner, 1962), must, first of all, be
known. Secondly, the amount of the loss of excess temperature,
and bence buoyancy, due to the mixing process, must be known.
These have the net effect of reducing the updraft values
predicted by parcel theory. Because these parameters were
unknown, no simple way of obtaining updrafts, taking into
account entrainment, was possible.
6. DISCUSSION.
The analysis of this section has indicated that the
maximum heights of the highest Alberta echo tops are almost
always overpredicted by parcel theory, but on the whole,
do not deviate greatly from the parcel theory heights,
since, on the average, the echo heights attained $3% of
the ultimate parcel theory height. The fact that there is
fairly good agreement seems to imply that the inhibiting
affects of entrainment must have been small, and that the
final parcel or column of air that was responsible for the
carrying aloft of the precipitation particles that returned
the highest radar echo, may have originated at the ground
and risen through a "well-protectedtt environment in the
core of a large thunderstorm.
As a result of this, updraft velocities were calculated
on the basis of parcel theory principles, and the resultant
values of 30 to 50 m/sec were not considered to be unrealistic for severe storms.
No implication is made that all echoes of all heights are
attaining the parcel theory predicted heights, since the
sample includes only the highest echoes,
~nd
this
represe~ts
only about 10% of all echoes. The suggestion is, that in
the largest of storms, as studied here, the element of
convection (parcel or column of air) is able to rise
through an environment in which mixing with the element
does not seriously deviate the processes from the pseudoadiabatic processes of pure parcel theory.
VII.
SUMMARY
The purpose of this study has been to investigate sorne
aspects of the behaviour of the highest and most severe
Alberta thunderstorms, and also to investigate, by means
of parcel theory, sorne of the physical cloud processes
associated with them. The vertical extents and locations
of these high storms were extracted from the photographie
records of echo patterns displayed by the Decca weather
radar operated in conjunction with the Alberta Hail Research
Project. Information was obtained for 112 storms that had
maximum echo heights 30 kft and higher, and these storms
occurred on 31 different days during the summers of 1957,
195S, 1959, and 1962. MOst of the echoes of the sample
had maximum heights below 35 kft, with only 5 being 40 kft
or higher. The highest recorded echo top was 43.5 kft.
The first investigation of the behaviour of these high
storms had to do with their geographical locations, and
was performed to determine whether any regions were favoured
more than ethers for the occurrence of the storms. It was
found that the echo concentrations in 3 regions were significantly higher or lower than in other regions to which
they could be compared. An area to the southwest of the
radar site, a highland, rolling country in the foothills
of the Rocky Mountains, was found to have a high concentration of these echoes. Two other areas, one to the north-
east and the other to the southeast of the radar site,
were found to have relatively low concentrations of high
storms. Both these areas were quite flat, the former
occupied by several lakes.
The second investigation involved a comparison of the
actual echo top heights to the tropopause heights. It was
found that the tropopause appeared to be acting as a barrier
to the vertical growth of the highest storms, and this was
attributed as a reason for the Alberta maximum heights
being considerably lower than maximum heights measured in
more southerly latitudes where the tropopause is higher.
Of the 112 echoes, 15 were found to be extending higher
than the tropopause height as determined from two radio. sonde soundings on opposite sides of the project area. Four
other cases could possibly be added, although the tropopause
heights were rather uncertain on the days on which these
4 storms occurred •.
The manner in which some of the echo tops approached and
"penetrated" the tropopause proved interesting. Eight of
the 15 above-mentioned echoes were recorded from the time
of first echo, or the time of first radar detection, and 5
of these, all isolated from other echoes, appeared to linger
just below the tropopause for a considerable time before
finally extending on into the lower stratosphere. The other
3 echoes, however, rose almost steadily from the time of
first echo to the time of their maximum heights (which
were above the tropopause in all 3 cases). These 3 echoes
were parts of lines of echoes, and were intense cells in
the midst of rouch weaker echo. This suggests the importance
of the environmental conditions in the development of
convective storms. The 5· isolated storms appeared to have
been "conditioning" their own environment so that finally
an element of air could rise through a well-protected
environment and extend on above the tropopause, while the
other 3 storms appeared to have developed in an already
favourable environment and extended upwards at nearly a
constant rate.
The thermodynamic properties of the atmosphere were
considered for the days on which the highest echoes occurred,
and were compared to those on days that had considerably
lower maximum echo top heights. This was facilitated by
constructing composite vertical profiles of temperature
and moisture for the 15 days of each class. It was found
that the temperatures were significantly higher in the low
levels (below 700 mb) for days with the highest echoes,
and that no significant differences were apparent in the
moisture conditions or in the high-level temperature
structures. This seems to emphasize the importance of the
low-level thermodynamic conditions as far as convective
cloud activity is concerned.
Finally, the maximum echo top heights were compared to
parcel theory predicted heights, and it was found that
there was good agreement between them, since, on the average,
69
the maximum heights attained 83% of the ultimate predicted
heights. Only 5 of tne 112 highest echoes were above the
ultimate predicted heights, and most echoes were slightly
above the level of hydrostatic eauilibrium. An approximate
evaluation of updraft velocities followed, and the resultant
values of 30 to 50 m/sec were not considered to be unreasonable for severe storms. Thus it appeared that the
element of convection that was responsible for the hiehest
radar echo may have originated at the surface, and risen
through a well-protected environment in which the inhibiting effects of entrainment were small, and the processes may be approximated by the parcel theory processes.
------------~----~---~-~---~----·~ .......
----····-·----------
:;1o
BIBLIOGRAPHY
Aoyagi, J., 1963:
The quantitative estimation for the
heights of radar echo tops.
Proceedings of the •renth Weather Radar
Conference, pp 123-131.
Austin, J.M., 1948: A note on cumulus growth in a nonsaturated environment.
J. Met., 2, pp 103-107.
Battan, L.J., 1959:
Radar Meteorology.
University of Chicago Press, Chicago 37,
161 PP•
Braham, R.R., 1958:
Clli~ulus cloud precipitation as revealed
by radar - Arizona 1955.
J. I•1et. , 12., pp 75-83.
Brooks, C.E.P., and N. Carruthers, 1053: Handbook of Statistical Methods in Meteorology.
Her Majesty's Stationery Office, London,
412 PP•
Byers, H.R., and R.R. Braham, 1949: The Thunderstorm.
U.S. Department of Commerce, Washington,
287 pp.
Changnon, S.A., and S.G. Bigler, 1957: On the observation
of convective clouds and the radarprecipitation echoes within them.
Bull. Am. Met. Soc.,~, No. 5, pp 279-282.
Clark, R.A., 1960: A study of convective precipitation as
revealed by radar observations, Texas
1958-1959.
J. Met., 17, pp 415-425.
Donaldson, R.J.,Jr., 1958: Analysis of severe convective
storrns observed by radar.
J. Met., 12., pp 44-50.
----------' A.C. Chmela, and C.R. Shackford, 1959: Behaviour
patterns of New England hailstorms.
Geophysical Monograph, No. 5, pp 354-368.
_____ , 1961:
Radar reflectivity profiles in thunderstorms.
J. !JJ:et., là, pp 292-305.
71
_ _ _ _ _ ,and R.T. Tear, 1963a: Distortion in reflectivity
patterns by antenna side lobes.
Proceedings of the Tenth Weather Radar
Conference, pp 108-115.
_________ , 1963b:
Radar as a severe thunderstorm sensor.
Paper presented to the XIII General
Assembly-IUGG-Berkeley, California,
Aug~, 1963.
Douglas, R.H., and W. Hitschfeld, 1959: Patterns of hailstorms
in Alberta.
Quart. J. R. Het. Soc., 85, No. 364,
pp 105-119.
_______ , .L961:
Radar observations of Alberta hailstorms.
Nubila, 4, No. 2, pp 52-58.
Haltiner, G.J., 1959: On the theory of convective currents.
Tellus, 11, pp 4-15.
Houghton, H.G., and H.E. Cramer, 1951: A theory of entrainment
in convective currents.
J. Met., 8, pp 95-102.
Jordan, C.L., 1962: On the maximum vertical extent of
convective clouds.
Scientific Report to the U.S. Navy Weather
Research Facility, Dec., 1962, 18 pp.
Kuettner, J.P., 1958: Discussion-- Recent Advances in
Atmospheric Electricity.
Pergamon Press, New York, pp 410-411.
Macklin, W.C., and F.H. Lud1am, 1961: The fallspeeds of
hailstones.
Quart. J. R. Met. Soc., 87, No. 371,
pp 72-81.
Mason, B.J., and R. Emig, 1961: Calculations of the ascent
of a saturated buoyant parcel with mixing.
Quart. J. R. Met. Soc., 87, No. 372,
pp 212-222.
Monthly Bulletin (Canadian Radiosonde Data),
Department of Transport, Met. Branch,
Toronto.
MDnthly Record of Meteorological Observations in Canada,
Department of Transport, Met. Branch,
Toronto.
Northern Hemispheric Data Tabulations, Daily Bulletin,
U.S. Department of Commerce, Weather
Bureau, Washington.
Saunders, P.M., and F.C. Ronne, 1962: A comparison of the
height of cumulus clouds and the height
of the radar echoes received from them.
J. App1ied Met., 1, pp 296-302.
Squires, P., and J.S. Turner, 1962: An entraining jet model
for cumulonimbus updrafts.
Tellus, 1&, pp 422-434.
Stommel, H., 1947:
Entrainment of air into a cumulus cloud.
J. Met., 4, pp 91-94.
Vonnegut, B., and C.B. Moore, 1958: Giant Electrical Storms.
Recent Advances in Atmospheric Electricity,
Pergamon Press, New York, pp 399-411.
Wexler, R., ·and D.M. Swingle, 1947: Radar storm detection.
Bull. Am. Met. Soc., 28, No. 4, pp 159-167.
Workman, E.J., and S.E. Reynolds, 1949: Electrica1 activity
as re1ated to thunderstorm cell growth.
Bull. Am. Met. Soc., lQ, No. 4, ppl42-l44.
World Meteorological Organization, 1957, Commission for
Aero1ogy, Firial Report, Second Session,
Paris, 1957. WMO, No~ 65, Geneva, pp 56-59.
73
APPENDIX
A.
~40
DEFINITION OF THE TROPOPAUSE
The definition of the tropopause that was adopted by
the World Meteorological Organization (1957), is as
follows:
"the first tropopause is defined as the 1owest 1eve1
at which the lapse rate decreases to 2 degrees Celsius
per kilometer or 1ess, provided also the average 1apse
rate between this 1evel and all higher 1evels within
2 kilometers does not exceed 2°C/km."
"If, above the first tropopause, the average lapse
rate between any level and all higher levels within
1 kilometer exceeds j°C/km, then a second tropopause
is defined by the same cri te ria as the ±'irst tropopause.
This tropopause may be either within or above the
1 kilometer layer."