\"ST. OF TECfyt
IE3R 27 1 7
I8RARIE
POTENTIAL VORTICITY CONSERVATION IN UPPER
TROPOSPHERIC FRONTU
by
LANCE F. BUSART
Mmasachusetts Institute of Technology
S.B.,
(1904)
SUBMIMTD IN PARTIAL FULFILLMENT
OF Th REUIREMNTS FOR THE
D~R;e;
OF
MASTER OF OCINCE
at the
MASSACHUSETI
INSTITUTE OF TSCHNOLOGY
July 1900
Sgnature of Author
.....
...
,
,
..
.- ,-. - - .
Department of Meteorology, 18 July 19668
Certitfed by.
r'c-rr
.'
Thesis 8uperviaor
e Ut.
Accepted by . . .
. . . . .
..
.
.
.
.
. .
. . .
.
.. ..... *
. .
0
Chairman, Departmental Comittee on (raduate
Students
.
1i,
POTTIAL VORTICITY CONEIRVATION IN UPPER
TRUPOSPHRIC FRONTS
by
LMNCE F. iBEART
Submitted to the Department of Meteorology on 18 July 1966
in partial fulfillment of the requirements for the degree
of Master of Science
ABBSTRT
An intensifying upper tropospheric front is exaained over the
period 19 kecember 1983 at 1200 GMT to 20 December 1963 at 0000 GMC
with particular regard to le validity of the conservation of the
Ertel potential vqrticity along trajectories ending in the baroclinic
same. The adiabatic assumption is justified by the extreme dryness
of the frontal sone. A total energy equation is used as an aid in
the traeoctory construction.
With only one exoeptian potential vorticity either increased or
conserved folloeing the trajeotories over the twelve hour period.
ies terminated in the central and western portions of
These traj~g
the eastern and probably most intense portion was over
troataas
the
the Atlantc Ocen an 20 December 1963 at 0000 GWe'. The potential
vorticity inoreases were due to a large positive relative vorticity
change on the northern periphery of the trontal ane and a marked
stability increase on the southern periphery of the frontal sone.
Diabatic effects oould not explain the observed Increases In potenvertictty, Rather turbulent processes in the tatmosphere see
tal
i portant. In particular, esosecale motions say be exerting an inFinally, an observation linking
fluence on the synopto featurse
the intensification of upper
with
developments
possible surface
presented.
is
zanes
tropospheric baroclinio
w
Theasis
Title;
upervisor:
Frederick Sanders
Associate Professor
ACKWLED aIMI 1
Special thanks must go th several people whose aid made this
My thanks go to Mrs.
thesis possible.
Jane McNabb for typing
the paper and to liss lsabelle Kole for drafting the more dit-
ficult accompanying figures and instructing me in the use of
drafting equipment.
Thanks go to fellow students, Mike Wallace and Ken Campana,
for occasional fruitful disusseions.
and Bob Ulchak
The help of Bill Somers
ith the more tedious aspects of the paper must
not go unrecorded.
Of course, special thanks go to Professor Frederick Sanders
without whose invaluable help and inspiration this thesis wuld
not have been possible.
TABLE OF CONTT
I
11
INTRODUCTION
A.
Bistorial Background
1
B.
C.
Recent Developments
Goals of this Study
2
4
TERLOTICAL BACKGROUND
A.
B.
C.
D.
E.
5
Adiabatic Assumption
NMntgomery 8tream Function
Total Snergy Equation
Potastial Voritty
Factors ihoh Influence Potential Vorticity
5
5
6
8
14
III 8YNOPTIC SITUATION 19-30 December 183
17
IV
19
W0CATION OCF mB FONT
A.
B.
C.
Collection of Pertinent Data
Display of Front on Potential Temperature
Surfaces
Cross Sections of Potential Taeperature and
19
20
22
Isotache
V
DISCUSSION OF R~SUTS
A.
8.
C.
Do
E.
VI
' Fields
8stlsoaction of the Total Energy Equation
Conservaton of Potential Vortiolty
Moisture analysis
Factor Efftecting Non Conservation of
Potential Vorticty
Trajectories and the
24
24
28
27
32
33
CONCLUSIONS
A.
B.
C.
D.
g.
Role of Turbulent Processes
Reliability of Entire Analysis
Problem of Clear Air Turbulence
Stratospheric Origin of TraJeotories
Surface-Upper Tropospheric Interactlon
38
38
40
41
41
42
APPENDICES
43
FIGURES 3 - 33
47
BIBLIOGRAPEY
78
INTRODUCTION
1.
A.
Bieorcal Bacgroud
What to a front?
The question is not asked to be facetious but
to indicate the often widespread differences of opinion about them
among meteorologists today.
BJerknes (0919)
of air
Surf&ace fronts wre first
school just after the first
postulated by
world war to mark boundaries
Since then they have
asses with different characteristics.
brought both Joy and disillustoament to synoptic neteorologists searching
for an Infallible tool to forecast the weather.
to the contrary some meteorologists still
Yet, despite evidence
Ansist that the observed
weather changes can be explained by frontal movements.
one often observes ftroat
kven today,
moved about on surface maps like opposing
armtes in all the war games played in the various world capitals.
With the advent of good upper air coverage fronts have been found
in the middle and upper troposphere.
with the name
"front".
However,
zones of varying intensity.
For better or worse we are stuck
uhbt one means here are baroclinle
These baroclinl
zones are charactertized
by strong vertical wind shears through various stable layerse
Other
features of these barocltnIc aones include an often large mixing ratio
decrease in the vertical and high potential vorticity values.
These
baroclinic zones or fronts are not rare phenomena In the atmosphere
but are almst independent of the more fatiliar
(1954)
and many others have showi.
usually first
surface front as Sanders
These upper level frontal zones
appear on the western sides of troughs and then intensity
they descend around to the southeast side of the trough where they
are strongest at 500 and 600 Sb.
B,
Recent DevelonUant
Reed and sanders (1983) and Sanders (1954) have found that these
at the
baroolinic sones are characterised by the largest subsidence
warn edge of the frontal boundary.
This resulted in an intensification
of the horisontal temperature gradient.
Reed (1965)
in a case study
thin
found that the intense portion of the frontal zone consisted of a
wedge of stratospheric air
ftieh had descended down to 700 and 800 ub.
the
He considered that the frontal boundaries were a folded portion of
The ciroulation within the frontal sone was
original tropopause.
thermally indirect.
Reed (1956)
further noted that "surfaoe cyclo-
upper
genesis accompanied or slightly preceded the strengthening of the
level frent."
Inspection of Reed's figures disclosed that the front
woe associated with the first
upstream 500 ab vortiotty maxtium from
the one assooiated with the strong surface cyclone.
More will be said
about this feature later
the Brtel oooservation of potential vortioty theorem following
an air parcel along an isentropic surface has proved to be an invaluable
aid for studying upper tropospherio fronts.
quantity will result if
or if
a vertical
Non conservation of this
tradient of diabatic heating exists
a component of the curl of the friction force exists normal to
an isentropic surface.
Staley (1960)
has evaluated these two efftets.
8is results show potential vortity inoreases in the lower stratosphere
3*
and upper troposphere on the cold side of the front.
tial
vorticity changes occur within the frontal zone and around the
entire periphery of the positive area.
tial
Negative poten-
Staley finds that the poten-
vortic ty changes are everywhere due to the vertical gradient of
diabetic heating rather than the curl of the frictional force.
Additional support for the stratospherio origin of the high potentiat vortioity air within a frontal some cane from Reed and Danielson
(1989).
Dantelsen in a detailed study in 1960 showed that the original
radiosonde traces contained many
in
time.
which tended to persist
lainas
"st~ble
In addition, ientropic trajectories established a stratospheric
source for many of these stable laminae.
cept of a folded tropospause.
This tended to support the con-
Further support came in
1961 when Danielsen
used a total energy relation as an aid into the construction lentropio
trajeotorles.
Campeas (1965)
of lsentropia
investigated an intense frontal soe through the use
trajectories tnvolving satisfaction of the total energy
Like Reed, he found
equation and potential vortiotty oonservation
descent everywhere and evidence for an indirect thermal c
trculation.
In addition, potential vortlolty Values increased along the higher
ieentropes through most of the trontal some
haich Campana attributed to
diabetic effects rather than frictional torques.
This
s In contrast
to the potential vortieity docreases vlthin the frontal aome found
by Staley in 1940.
C.
Gas
this
%ofStudy
Many avenues for further study lie opesw.
pheric stratospheric mass transport
Among them are tropos-
hbich has been studied by Danielsem,
8taley and others and the problem of clear air turbulence for example.
The main goal of this thesis will be to investigate the question of
potential vortiity
conservation during the formation of a strong upper
tropospheric baroolinie
none.
This issue is
Iaportant becoase,
for
example, it potential vorticity increases with time in the frontal
asom
than the oxplanation of the folded tropopauso with stratospherc
air may not be entirely persussive.
that If non conservation is
In addition, it
would be hoped
significant then some measure of diabatic
or frictional effects might be attainable.
In any event, it
that this case study will add a further contribution t
is
hoped
the record.
REBIZCA L BACKGROND
*
II,
A.
Adabatic AsamntOfl
Let us now consider sO
Most of the particulars have been elaborated
ground for this study.
by Campana (1986)
of the fundametal theoretical back*
and will not be conssdered here.
suine poper tra-
jectories are so critical to this study we will first examinae
the necessary constraints in this area
ase of
First of all, we will assume
that the first law of thermodynamcs for adiabatic flow may be written
as:
(1)
This states that potential teperature is
an air parcel.
Of critical
conserved if one follows
mlportance bhre is the adiabatic assumption.
Any upward motion with subsequent condensation would ruts our efoforts
before we could start.
Fortunately, the intensification of upper tro-
pospheric fronts is generally assoiated with subsidence in relatively
cloud free regions.
Furthermore, the process takes place above the
lower turbulent boundary layer and surface oadensation effects.
8.
Montesry Stream FuSation
Since we will be working on surfaces of constant potential tempera-
ture the Montgomery strem func1ion,
,
determining the geostrophic motion field.
will prove invaluable for
The Nontgomery stream function
io defined as
=
where Cp
)
pT
-
(2)
=
1s the specifio heat of air at constant proemse,
anid --e are the temperature and height
aceleration of gravity, T
of the specific isentropio
the
~
urtfae.
Danlse
(19O1) notes that it a
reliable estimate ef the geostx hiC wind is to be made than
must be measured to four significant figures.
Xhis would inovave
measuring Te to within 1 0.1 C which is not possible with present
radioeonde equipent.
Danielse
suggesooted as an alternate approach
rT
the use of Potsson's equation vwhch relates
sure on an Ieantropic surface.
to "p
,
the pres-
The latter leads directly to
e
-Q
.
In this manner the error in the computed - up to the middle troposphere will be no worse than the error of the computed height of a
constant pressure surface.
C.
Total
erIar EaRuat4~
In order to study potential vorticity changes duri t
the iute st-
fication of the firat ieentropio trajectortee will be needed.
Initially,
In constructinag trajectories the best one can do isto to nake use of the
ambiguous kinematic relation
Here
3
Is the total distance traversed by the parcel,
j
is an
velocity for the first
average geostropht
\
half time perod,
an average geostrophic velooity for the second half time priod
- L the total time prieor.
and
The essential
oughness of (3) led Danielsoe
(1961)
to develop a
This
total energy equation as an aid In traJectory construction.
Involves a deviation fram the geootropbhi
devations will occur when the *-
, G
the total drVati
space
s
Under our assumption of adiba
sero.
vector.
(8)
y be writte
* of
motion the last ter
Now,
in
as
in (4)
is
riotionless notion on an
The vector equation for horisoutal
isentropic surface
where
tic
time
field changes over a gives
period such that the parcel to acelerated or decelerated.
-
Such
path for a parcel.
ay be expressed as:
t o the unit vertical
iso the Coriolis parameter and
Following Denielsen (191) take the dot product of
and add ft tM (4).
The resulting equation is
length of the trajectory to yield:
I...
4C~(0
'r
with
integrated over the
where the subscripts
'-
and x refer to conditions at the final and
In this equation +
initial times respectively.
potential and internal energies while
-
is a sum of the
is a neasure of the
2
kinetic energy of the air parcel.
The right hand side of (8) can be approximated by a still
specified tine interval in
points of the trajectory.
to be
at the Initial, middle ad final
%
Graphical subtracton of the analysed
fields will do the trick in this case.
Danielsen' s total energy equationa
Thus a practical tform of
8:
'4 't(
-
the value at the aid point of the
rters to to
where the subscript
trajectory and N refers to a
*
change over a fixed time period.
Descent maut take place along the trajectories for otherwise (7)
would have to Include a term
the release of latent heat.
nust be taken for parcels
of the jet because
nvolving the
In addition, as Danielsea
O)
due to
notes, oare
thih originate on the anticyclonlc side
ore than one ponut may satisfy (3) and (7) * This
arises because the gradient of
).
Icreasei
and
I
are negatively correlated.
Potetial Vrtinitt
The crux of the trajeotory analysis will depend upon the concept
of conservation of potential vorticity.
A theorem for this ms first
9.
established by Ertel In 1942.
Rather than stating the theorem &
proof based partly on physical reasouag will be inoluded
fluid is assumed invisid and a scalar quantity
such that
in ftiL
e
is a oanstant.
is postulated
A curve C
,
Consider a surtaee on
encloses an area
P
as absho
1
he oirculation,
P
, around this closed curve Is defined by:
r
whore
The
is a ftunoton of presure, -p , and density %
This scalar quantity will sattty (1).
aloQe.
which
1
1
.
Z
I
C
the veloIty vectr.
(8)
Now we may write
Based In part on M.I.T. 18.01 course notes of Proteseor Joseph
Pedlosky.
10 a
k
3cEa~
C\
Here
kL
(1o)
to the relative vrticity and
LO= o
(C)
awa---"AY
n
Is
tho unit
normal.
Let us now examine relvints thoorea.
"k "n
Uj
Noting (8)
we mra
write
(ll)
S.
ihere the subsorilt in roters to the inertial frame and the other
symbols have their usual meanings in that co)se
(12)
P,,
~ UIoK
(-~iXlrita4
-
CO
*%r
Th1us,
P%(N =
% - 61 -4
~2-;h
.vk\
(14)
(18)
Thus, ignoring friction,
11.
(17)
aQ-4-w"S"3V
Noting (10)
w .awe lod to a statement of Kelvin's theorems
Consider now a
which lies copletely in
and moves with the fluid.
We bmov that along
are constant.
and
must lie in
x
T
osly
Since-,,
surface.
a
a constant
a constant I
ufaace
both
-x 9
Thus,
and (18) may be written as
where
surfaces as shon
whIah is
. Consider now toa closely spaced constant
n
ig.
.
The smas
constant follownlag the
enclosed by the cylinder
otion is
given by
132
F\. a
wn
(21)
q"
But )
AS
or
'bL
6$M
",
(as)
Thus,
(23)
Substituting into (20) we hbVe
,,n
.-'
-
(24)
VA
esi
whero
u
.,
are parallel to
and 4
C1
.
aince
m
anda
e
are constat we have
(25)
\-.~"
13.
of finaally,
Taking the cpeaent of absolute vorticity in the direction of the e
gradient and making use of the hydrostatic approcintios with
my finally write
<
Lwe
murfac
ito the relative vortiaty oan an istropio
Here
and
iblch is on the
and we ignore the difference between Z
~8-1
ictionless and adbatio assumptions
see . It the
order of 10
are not made than a formal derivation (Campama 196)
yields the
folloving results.
where
1
,
direction of
is the component of the aurl of the friction force in the
q
G
and the first term oa the right takes Into
account that the vertical variation of heating it
the largest contri-
button to diabatic effetcts
It
we consider (27)
for the amenat we see that
the stability of an air parcel in up and doen motion.
always negative.
Z
represents
This term to
After some thought and exprimentation It
was decided
14.
to evaluate this term by a centered finite difference appromsation
with a
interval of eight degrees Relvin such that
1
-
(2)
G.
________
interval of tfour degrees Kelvin but it
4
Compana (1968) used a
was felt that the eight degree interval was less sensitive to uncertainties of analysis aend was still
acteristis of the front.
a good measure of the gross char-
The relative vorticity,
3 ,
o
an
isentropio surface is computed in the folloang manner.
vhere
.~-
is the wind speed and
r4
Is the radius of ourvature
A similar finite difference technaiqe involving
of the streamlines.
a horlonatal increment of 12D nautical miles is used to evaluate the
shear term,
"
*
term is evaluated as
line and
The units involved here are sec
here
Ah- "
is thelnd
s
e
.
The ourvature
is parallel to the stream-
direction In radians.
With 130 nautical
miles as the distance increment this term is again evaluated by fitnite
difference techniques.
E.
Factors
abch Infingcg
Since the upper level
PoteaLtM l
Vorticity
inad directions in data available on telotype
18.
have been rounded off to 10 dogrees errors are quite likely in 7e The saving grace here is that wind directions in the area of interest
Because of the steeper slope of
are pretty such unifornm
faces compared to isobaric srface the relative vorticity
8
sur-
assoned
on the former is often antioylsio and the latter cyolocto for the
same area at the same time.
~
forms In the troposphere
e
but
a constant
owsmhow sben a front
iereases, the stability
tnareases
Thus there must be a divergence of air on
decreases
9
Danielsen (1984)
to de
surse ace for
ase.
Note that them
changes are compatible with the conservatien of potential vortioty.
The results of this study and many others generally established
that the stability term ms the most important in doeterminng the
ito defined as:
vhere
also of
Simply on this basis we would expeot to find
toepherit
orders of magnitude.
non conservation of
shere
I-
P
air to ezced
values ton tropopheric air by one or mrs
Let us now aine
'
.
values in stra-
hat
effects oa
lead to the
We have ftrom (28)
is the stress vector.
Now, dtaley (190) has made some
1e.
He
rough estImates of both terms an the right hand aide of (28).
found that the vertical variation of heating tor
10
mas approiately
-14 dog oa ga-1 while the normal cponent of the curl of the tricto
tional force to the isentropic surface vws approiuately 10
dies
.~g
-1 .
1
0
It should be emphasised as Staley notes that these esti-
mates may be off by several orders of magnitude.
friction in the free atmosphere, radiational proo
The effects of
ases, eddy bhat
conduction and latent beat release are so poorly known as to make
any estimates quite speculative.
sary to make s,
Yet later on ve
hall find it
additional comots about these eoffats.
noces-
Let us
now turn to a consideration of the synoptic events for the case of
December 1983.
17.
IIl.
SEXIPTIC SITUATION:
This particular
19aO
DECIIMB
1903
it had one of the strangest
uase Vas chosen becaus
000 ab temperature gradients in Professor Sanders' surve
season.
of the 19034
The 000 ab maps for this parlod revealed the eaistence of a
sharp temperature gradient trm the Great Lakes easturd throug
New
The front as at its sharpest
Igland on 20 December 1903 at 0000 GUT.
on 2a December at 0000 GUT in comparison to relatively veak frontal
boundaries twelve hours earlier and later.
At 0000 Gl
on 19 December 1903 the 00
b map revealed a large ridge
anchored over the Rocky mountains and a deepening trough oentered over
Virgisna.
A secondary vorticity maximum
Superior.
The surface ap at this tle
s centered just north of Lake
showed a wekeming 980 ab storm
centered near Syracuse and a deepening 1000 ab secondary foring
of Nantucket.
southeast
An east-west dry cold frot was located Just north of
Minnesota in connection with the upper air vorticity manimm there.
19 December 1200 GMT the deepenaa
By
secondary storm mus don to 974 ab
and as located 400 miles east of Boston.
See tg
3.
The good cold
advection Into the trough aloft foretold of the deepening off the meat
coast as can be seen from tig. 4.
By this time the 00 mb Vrtex was
almost pia beel shaped with the next upstream vorticity maim
centered near
aulte
ant Marie.
The sharpea
waus associated with this latter vorticity maxitm.
upper levl
treat
Reference to the
synoptic details at the time of fig. 3 reveals the omplete absence
18.
of precipitation with the surface cold tront except for minor activity
along the lee shores of the Great Lakes.
On the twemtieth at 0000 OGX our nov sharp upper level tront is
assoiated with a barely distiaguishable cold tront at the surface
(see fig. 5) and a moderate vorticity
Yet despite
awmu at 500 ab.
these iannouous ftesares the teperature gradient has irsed
nearly 20C in almost 240 nautical miles (inoe
ASB
n tig. 0).
to
Mean-
while our surface atorm has deepened to an almost fantastie 950 Ob
centered over northeastern Nova Scotia.
The 500 ab tmue
h in this
region is diffittot to discern because of the abseme of data, not
surpristig in view of the hurricane force w
onds.Thus, at first
glance the connection between the surfaoe storm and the upper level
trot
seems minmal.
The partial low level oloudiness beenth the
front seems to refleot daytime heating by the ieo free and relatively
warn Great Lakes of the bitter cold air mass rather than any extensive
moisture
ssooated with the upper level tfrnto
19.
IV.
LOCATION OF TIM FIWANT
A. Colletion of Piertient Data
In order to locate the froat the pOrtinent radiosonde data for
the 19 December 0000 Grf through
o December 1200 QT me punched
on oards to be run by the MIT meteorology department Isentropto proThe amber of individual radiosoade statioas to run for each
grem.
teo
period was determined on the basis of the area of significant
vertical wind shear.
A shear of twenty knots in 2000 teet ma
b* vertical
arbitrarily considered to be significant.
shear
es
usually associated with a signifcant change in the vertiaol lapse
rate and a rapid decrease in minag ratio through the trontal aone.
A fairly substantial rinag of stations around the oritieal wind shear
area was then chosen in order to assure data of enough horisontal
extOnt for the trajectory analysis.
The oomputer progra
evaluated the pertlnent data at each statin
9
surfaces at 4K intervals ranging in general tron a67°E to
327OK.
All the essential imorMation was to be found botween these
for
surfaces.
For each station on every
the pressure in ab, mininS
e
ratio in g/kg, relative humidity, wind
direction to the nearest itoLe degree,
a2 secr
surfaoe the progrncputed
and the total energy in
I2
se
ind speed in m se
.
1 ,
in
Errors may result beomse
ignificant temperature points on the sounding are left to the discretion of the radiosonde opirator and teletype
ind data are rounded
20.
off to the nearest ten degrees,
In particular, the height of the
intersection of the measured lapse rate with a given e
level may be
Rowevor, we note that we are dealing with a strong
in slight error.
feature idose spawsal and temporal variations occur over a large area
errors will be relatively isignificant.
such that minor little
Of
more concern will be the analysis problem in southern Canada due to
the sparcity of data.
B., DisAlar of hrot on Potential Teaoeratura Surfaces
the first
order of busIs as is to display the
ront on costant
Since the tront is most likely located betwoem
pressure surtaces.
300 and 700 ab bounds on the necessary
G
levels were determined
from the highest and lowest potential temperatures at these pressure
levels respeotivoly.
vertical on each
8
In order to visualime vhat is happening in the
level the pressure and the difference in pressure
between this surface and the one 4
Now, on each 6
higher
is plotted at each statics.
level the pressure is analysed in 50 mb inorements
along with the help of the ditfference field of the lower level obtained
by graphical s.btratio.
is obtained it
Once a map of the pressure on a
is very easy to get a picture of the eS
specific pressure level.
good as possible we ,ake
surface
ield at a
In order to insure that the analysis to as
use Of the relation.
21.
is
to evaluated on an Isentropc surface while
Here
evaluated an an isobarto srtfae.
The right hand side of (33) can be
written in finite difterence tors as:
AG
mined froa the plotted sounding.
the analysis is correct.
if
deter-
is arbitrarily set equal to tour degrees Kelvin and ts
Squation (34) should be satisfied
Thus, Infermation that we have in the
vertical is used to more accurately locate the ftront In the horsontal.
Using the actual temperature gradient in locating the front
ould only
enable us to see a more or less unitorm change in temperature between
stations voreas by employing the isentropic analysis the stability
values at the various stations have been used to obtain a better idea
of the frontal intensity and Its horisontal location.
Compare figs.
3 and 8.
Figures 7 through 9 show the front at 400,
tively on the 19 December 1903 at 1200 GFT.
00 and 00
b rpec-
The frontal ase is
weakly defined at all three levels vith a muamm gradient of about
8OK in 40 nautical ariles.
uch parallel to the flow.
The orientation of the grontal sone is pretty
The situation 13 hours later ea
0000 GW for levels 400 through 700 ub
13.
0 December
s shoan by figs. 10 through
We do not see the marked strengthenig of the front that Campana
observed in his case.
Yet overall the frotal sone sharpened up someMat.
22.
0
The strongest gradient on 20 Deceasbr at 0000 GOT Is 12 K over 60
nautical males at 500 ab.
Unfortunately, we are only looking at the
upwi.rd and a portion of the middle part frontal ane.
The easteraost
part of the front extends out over the Atlantic south of Loag Island.
The data hints that the frontal sone may be even stronger here but
the actual analysis is uncertain because the
ntucket radiosonde
observation me not available on 20 Deceaber at 0000 GMT.
C.
Cross 8etione of Potentis
Two cross setions of the
TWaneraturn
e
surfaces and the isotachs were
structd on 20 Pecember at 0000 GOr.
the extent of the crose sections.
Istasha
and
It
on-
Lines AD and CD in fig. 14 show
was felt that the data was accurate
enough to draw direct cross sections normal to the flow instead of restoring to the necessity of a cross section based
tioas only.
analysis.
The thermal wind equation was us e
on radiosonde loca-
as a cheek on the
Figure 15 cowrespNnds to line CD and is an attempt to depiot
the conditions in the vicinity of the entrance to the tfrot.
The familiar
packing of the asentropes Vithin the front some and the steepeisng ot
the tsentropes in the region of *aximu
evident.
vertcal wind sheA
The shift of the front to higher (
altitude is noticeable also,
r is quite
values with increasing
The jet is looated above the region of
strongest horisotal temperature gradient in the vicianty of 800 ab.
Furthermore, the strong cyclonic shear north of the Jet coupled with
the epected stability indicate a rapid insrease in potential vorticity
23.
values.
Figure 16 oorrespouds to line AB in fig. 14#
not placed any oloser to the coast beo.we
close to the ocean.
There is very little
m
of the data uncertainty
differece In the isentrope
packing and isotach pattern between the two cro
indicates the relattVel
Line AB
sections.
This
steady state situation at least over the
western half of the front at that time.
34.
DISCUMSION OF R8SULT8
V.
A.
Tta1ectories and the 'y 112ed
The task of construotting trajeotoriee was by far the most time
tedious.
oonsumMing an
In order to improve the accuracy of the truat
Jectories a11 end points on 20 December 0000 UWf were choseo
Unt rtAately, all observa-
regularly reporting radiosonde stations.
tions at Nantucket and tm upper
this time period.
The winds and
ids
at Flitt were unavailable for
vlues at these Stw
stations were
determined IIeotrophtlly with the aid of the surroundin
A
analyses.
small coeasoton factor based on the analysis wue applied because the
winds were generally subgeostrophi
The
and 283K.
in the area of interest.
G surfaces chosen for the traJectory analysis were 20,
291
These surfaces beat represented the top, middle and lower
rom figts. 18 and 16.
part of the frontal sane as can be seen
In general,
the frontal zome stretched from the Great Lakes to New England at the
higher elevations and strtohed southward throuh Illinois to Virgnia
at lower elevations.
the
his area plus periphery boundary values dictated
hoile of stations for the end points of the trajeotortes.
very careful analysts of the
draing the '
field was made at each (
isoplethe most attention
as paid to the
Next, a
level.
In
ad field.
The generally uniform wind direction leat confidence to this decisiona
Values of
W
were dran for every 600
a
sec*
.
A geostrophic velocity
based on contour Intervals for this inrement is included in Appendix I.
26.
The values of
selected for the contouurrs were identical to the
ones Compana used for consistenoy,
on the
E
At several statioas, expecially
a 2990 K urtface it was impossible to draw for the sind field
value at the ese time.
and satisfy the
In these situatios the
contours weore drawn so as to satisfy the wind field.
since graphical subtraction of the '
hand side of (7),
At the saw time
fields was used to get the right
the computed energy values on the left hand side were
modified by the apprpriate
M
field change in order to be consistent.
The time period involved in all computations was twelve hours.
Similarly,
and lootach fields were constructed for eah level.
-the appropriate isogo
ws used to get geostropho winad
e(
isopletho
The spacing of the Q
values as an aid to drawing iootach contours between the reportiag
radiosondo stations.
The isegon analysis ws constructed over the
field on a light table.
fvery ettort was made to sort out the systematic
errors.
The first trajectories were constructed to satisfy (3) and witbout
The procedure involved here ms to trace a
reference to (7) or (27).
path backwards parallel to the
pertod.
*
isoplethe for the last siz hour
This point was transferred to the
analysis twelve beire
tepleths for
earlier and the trajeotory continued parallel to the *
the first six hour period.
The results are sbown In figse
17 through 19.
No attempt was made to smooth the trajectorles.
The smoothness and
teadiness of the wind field over the twelve
hour period is evident from most of the trajectorloes
The trajectories
terminating at Great Lakes stations are open to doubt indicating large
local changes of wind velocity,
This is in the more intense area of
the front and hinte that trajectory corrections
ay have to be made
in this area.
B.
Satslaction of the Ttal
neraEY Loution
Trajectories at the expected points of interest were then constructed so as to satisfy the energy equation (7).
22 show these trajectories.
The supersoript 4
indicates that the trajectory stisfies
(7).
Figures 20 through
after each letter
For refoereme the end
point of the trajectories which satisfy (3) have been labeled with the
appropriate letter.
Note that the trajectories in figs. 30 - 22 also
satisfy (3) based on average geostrophic winds over their length. Thee*
figures also reveal that the air on the southern periphery of the frontal
oane was accelerating in view of the less oyelonically curved trajectories.
On the
4
2910K and
) =299,K surfaces trajeotories ending at
stations 637, 646 and 747 which satisfy (3) and (7)differ considerably
from the trajectories which only satisfy (3).
Station 637 to at the
extreme entrance to the frontal saoe while stations 845 and 747 are
located more or less in a region of weak
;
gradient (see Itg. 11)
These three trajeotories at each level initiated in the light
of a cold vorticity masuirs at 500 ab so it
tnd area
is not surprising that they
are mach more anticyclonio as they undergo acoeleoratic.
27.
C.
Conservation of Potential
ortioMty
Obviously, the next step was to calculate
subject to (29)
and (30)
P
values using (27)
Figures 23 through 25 show the P values
at the final potats of the
tively,
P
In addition, on the
'
a 283, 291 and 2r K surfaoes respeca 20 E surfatce (tig. 2)
valweo of
were calculated over New Sgl and and Nev York State at a number
of points between ralnonde stations.
This
as done, as will be
explained later, because of the suspected low ?
Siallarly, figures 26 through 28 show ~
value at station 48.
values at the initial points
of the trajectories on 19 December at 1300 GOl.
The mupersoripts again
refer to the trajectories which satisfy both (3) and (7).
In all cases
P
.
values are given in units of
21 sad 28
am/soc 3 x 10
K/ib
In figs.
values were calm4ated at extrs points to give a better
resolution of the field in the victinty of the poteantal vorticity
maxima,
subscript.
These extra points are labeled by an X wth & aumerical
Trajectories are again constracted but this time so as to
satisfy (27) subject to (29) and (30) while hopefully satiefyian
Those trajeotoroies are shon by figs. 29 through 31.
v
refoer
(3)
The superscrpt
to the fact that they conserve petential vortieity.
Again.
for reference the inltial points of the trajectoriee wih satiety (3)
along and (3) and (7) together are ncoluded.
Unfortunately, no tra-
jeotory satisfying (3) and (27) aould be drawn for ACK (100) because
the absence of data made it itpossible to
aloulate the fsml ' value there.
£axminstion of figs. 20 through 31 clearly show that several of the
28.
et al cannot even appra~dately
trajeotorles which satisfy (27)
Overall, there seems to be
satiety the displacement relation, (3).
In
a potential vortioity increase over the twelve-hour period.
particular, attention should be paid to the areas with
values
P
in excess of 16 units since this represents a lower bound an air
Now, let us exaine what hap-
that ay be of stratospherico origin.
surfaces before ay attempt at an aeplana-
pens on each of the 8
through IV.
Note appendieoo
tcMn of the behavior is made.
and
as well as the faotors
initial and final values of
The
are presented for each type of tragjetory for the sore
(o '+)
twelve hour pressure change
vertical velocity.
level.
G
interesting stations at each
Also presented is the
bich is a rough measure of the average
If there is adiabatic descent everywhere saong
the trajectory than the aiag
onserved followinag
ratio should be
the parcel.
First, let us exsdue the 6)a
trajectories 1,
L.N
versus
20).
cannot oatstfy (3).
O
and
,
surface (ts.
2983
Clearly,
While
satisfies (3) the ditterene between the initial location of L
L.
sakes these trajeotorles questionable.
oor
to satisfy (3) by pulling it back to
I.
Now, It
than it would be
necessary to postulate a potential vortitity doorease.
stability decrease along with a
decrease.
Siuilarly, it
K ,
then tig. 31 indicates that ?
7~
ac nd
ere
A slight
decrease accouats for the P
0
aust inLrease.
are to satsty (8)
Here the mechnsm
ses to be a near doubling of the stability values over the twelve
hour period without a commrsurate decrease in
4
In fact,
.
decreases only slightly along K4 and Increases someMhat along
when these trajectories are corrected so as to satisty (3).
and h
Any attempt to reduce the diftorence between
decrease through a large '7
,
, 3
that
satisfy (3) and conserve
take place it
(I
I
, O
,
K
?
,
and S
6R
1
P
?
ust
v11 take
However, this latter
change asy be due to an inadequate isotach analysis.
On the 20
station 468 As just north of an isotach maximau
while station 405 is Just south of this maxdmm.
gradient as strong as it
With the l otach
is the relatively large distance between
the two stations is si gnfiant.
oulsted from the
decrease.
) are to be dran so
and S
,
is redram so as to satisfy (8).
December at 0000 G
P
oannot
Growth ei
at the same tiae.
Ot.
by re-
is inmediately clear
as to satisty (3). Sltalarly, a slight decrease in
place it
.
decrease and a slight "re
surface (tig. 30) it
= 291I
On the
and
L
1 result in a
will
locating the nitial point nearer to
From the geostrophic dnds oal-
field analysis it
seems quite reasoable that
a stronger wind maximum than analysed lies boteen
405.
O
This would cause the shear term in
so as to raise the final -
"4
tatatos 486 and
to inorease enough
value at station 486 thereby brinsain
about conservation of this quantity.
A point to be noted is
that
the horisontal incresent of 120 nautical miles used in evaluating
derivatives by finite diffttreace methods may not be accurate for the
30.
haose true positions
data resolution in the vicinity of lootach ma3dea
are somewhat dubious.
The
Increases for trajeotories ending at stations 320,
r
637, 045 and 747 ( t,
) tos prdominately due to a large
O,
At the same
stability increase as can be seen from appendix II.
time, however, there are also varying small ireases in
.
On
the wholo these four traJectories end in the western part of the
frontal some and tend to be located on the southern periphory of
the mone between 500 and 600 ab.
For the trajectory ending at 734 ()
groth results from a large increase in
the
increase in stability.
anda small
for the trajectory ending at 518 C I)
Sjlarly
growth results more from a
the "
3e
7
Increase than a stability
liowever, the difference Io not as proniouned as for tra-
increase.
jectory R
These latter two trajectories terdante on the northern
.
periphery of the frontal afte between 400 end 600 ab.
299K surface we agaia note that trajeotories
On the
O
*
A
relation.
se
4anda
incapable ofmatisfying the displaemet
Of these four trajeotories only
satisfy (3) would show a
the same trajectory on the
spurious.
On the
0 Dcembe
decrease.
a 291
Tv corrected so as to
Again, as in the case of
rface the result seem
* 299K' station
at 0000 GM on the
-1
analysis supports an argument for a o6 to 70 a seo
just south of station 456.
,
a
amwmm
This difference would be enough to
i
enable one to draw an.
there is no doubt that if
saetiey (3) than a
and
0
However,
bich satisfies (3) as well.
,
0
~
and
? increase muat result.
are drawn so as to
~)
In the case of the
trajectories there seem to be a large and almost unreasonable
versus WN
growth.
The difference is that
4
show the P
,)
and
W
growth
increase with only a very slight pool-
as the result of a
the result of a 7
P
Yet, in both cases there is clear out
and N
tive change in 74
O
0 versus
horisontal difference between the Initial polnts of
0
d
and
bhile
growth as
show the
inor changes in
increase with only
2
.
)
It the trajectories which satisfy (7) and (3) are accepted ( N,
then we again have the suggestion of
periphery of the frontal
growth found when
increase.
V~
the 2011
On the other hand the definite
is drawn so as to satisfy (3) is mostly
the result of a large and posltive 3~
are nil with 1"
growth on the southern
stability
aome due to a marked Oncrease
with only a very slight
?
1
increase.
in very good agreement with N
surface there to the suggestion for ?
Otabtlity changes
•
Thus, as on
growth on the
*
northern boundary of the frontal sone, due to an increase in 7
It should be empBhiised that these changes are along an iseatropic
surface and not along a horiaontal- surface.
are the many trajectorees which were drauw
Not shown in the figures
so as to conserve
and satiety the energy equation at the same time.
for the same trajectories in figs.
P
It was impossible
29 through 31 to satisfy the
32.
displacement relation (3)
to postulate
P
To satisfy (3)
as well.
It
ws necessary
growth.
D. .Mistue An at
The next step is
entire analyses.
to stand back and take a good look at the
after smse thought it
First of all,
became clear
that the mixing ratio data was generally unreliable, due to the
the very dry air within the
large number of notorboating values in
frontal sone.
ful results.
In a few cases, however,
For example, on the
are not important here.
= 2830K surface a amixing
despite
,
ratio increase occurs along
slight to moderate descent.
e
we were able to obtain use-
Motorboating and saturation problems
On the
=
surface it
2
3911
seems diffiand
cult not to postulate an increase despite descent along the t4
trajectories.
A slight increase may also take place almag the
trajectories.
Similarly, on the
L
2 9OK surface there may be
a slight increase with descent along the
L
trajectoriees.
Wide-
spread motorboating sin the other cases makes compareons impossible.
Thus,
we have a good exsample of an area of neglect in
The conservative nature of the maxing ratio is
turs under conditions of adiabatio
descent.
just this last year the standard radiosonde
meteorology.
a very valuable fea-
Unfortunately, until
nstruments had a low
relative humidity bias and were incapable of measuring humiesditi
belo*w
40 C.,
This bias has been eltminated by new carbon elements
5
33.
on the radliosades in use for the last year.
A recent article by
Masterson et al (1986) indicates that water vapor
seasurements by
balloon-borne trost-polat bygraoeters have provided very accurate
relative humidity measuremnts to the upper troposphere and lower
stratosphere.
In fact, sa mist layer with mmimm relative humidities
eibo to 80%bas been discovered below the tepiol tropopne but
above the out off of the conventional Weather Buren radobnades.
Mixitg ratios of less than 0.000 ga kg
1
have been measured accurately
It is very i portant that accurate humidity measurements like these
become routinely avalrable.
ihis would led a great deal aore eon-
fidence to trajectory analysis and wmld probably be useful to
diffusio
and turbulent mixing studies,
A. Fatrsn ttfo ntin
Non-Conservation of Poetial Yorticitr
th a definite arease I potential
There is very little doubt tht
vort
it
ty occurred with one exception throughbout the froental sae as
intensitfed over a twelve hour period.
The
amet etrigent require-
ent an the trajectories is the conservation ot P beeause
and :
muat be sero for this to hold ~r
lyk
oers
must be zero for the energy equation to be satisfied.
thintak of the an-o-oservatite
of
i.
and friction
Now. we can
: as the result of three etteets
One, the normal component of the curl of the triotion foree, T
e
to the imentrp~a
adabatc.
The
ts not conserved in this case.
Two,
surface is not sero but the flow S
trajectories are correct but ?
,
the flow is adiabatic on a given imentropto surface but diabetic
In this case, even though the
motions exist on adjacent surfaces.
isentrepti
trajectory is valid, diabetic
faces yield ?
changes.
oations on adjacent sur-
Three, the flow is not adiabatic so that
W1il not be conmerved.
the trajectories are wrong and P
In addi-
tion, stability changes are going to be effeted mostly by diabetic
motions whereas relative vorticity changes will be influenced
mainly by frictional effttects.
The surprising feature of this oase is the generally positive
, along the traectorles
changes In the relative vortio ty, T
obere ?
Increases.
As the front
ntensities and the ieentropes
are squeeed together we would expeot
oonserve
7,0
to deoreas tin order to
,. This only seems to happen in the middle of the
frontal sone viewed from above.
oreases go along vAth slight 7.
To the south large stability ininareases Vile to the north mitor
stability changes go along with large "
increases.
anitial
laoee the
poiats of the trajeotories were located between radiosone stations
it
a100 GfT
was necessary to make a asp of the stability on 19 Deoember
in order to calculate V
values.
any of the initial points were
located just north of the U. 8. border in the data sparse region of
southern Canada.
on
Now, errors in stability can have significant etfects
calclations.
With this error source in mind the necessary
soundings for the 19 Decober 1200 ~ir were scrutinied to see it the
stability field could be remapped so as to increase the stability
north of the Great Lakes.
This sould lead to higher inittal
?
values
35.
and reduce the P
growth.
The data did not justify doing this,
however.
Another question to consider is the poosible role of diabattoc
Values of
effects.
of
P
n.
were calculated for various changes
(31)
up to 20 units under the assumption that friotion was un-
important.
per day
This corresponded to a cooling rate of 0.RO
per 100 meters and was well within
Doeller's (1951) cooling rates
above cloud tops of 2 to SoC per day per thousand fest.
Cloudiness
beneath the Intensifying upper front over the twelve hour period
us
sparse with one excaptIon.
On the 19 Deooeber 1200 OG elloudiness
and some light snow flurry activity over Michigan and the eastern
Great Lakes sreas w as
Green Bay.
s ooiated with a weak low just northeast of
Cloud bases were in the viciatty of 2000
type was generally stratooumlus.
teet.
The cloud
Twelve hours later the weak surface
system had all but disappeared leaving some lee shore cloudiness and
snow flurries in the eastern Great Lakes region.
It
mset be roembered
that at that time of the year the Great Lakes were relatively wore
and 1eo
free.
Bence, they were able to supply moisture to the lower
levels of the overlyinag bitter cold air mas.
This shows up in tfi.
32 and 33 *ich are plots of the relative humidities on the 45
surface.
23oM
Note the 40% relative humidity at 037 In fig. 32 and the
49% value at 528 In fig. 33.
The stratocumlus clouds at best are probably a couple of thousand
feet,.thick and extend up to around the 850 ab level.
This is well
36.
below the 500 to 600 ab position of the ~
283 OK surface over
the Great Lakes for the twelve hour period.
tops for r dtional
nimal.
coolali
and the associated stability changes seem
Now, Btaley (19M6)
ratio through a baroclinio
sho
tat
the distributtion of mixing
eom in the upper troposphero
marked offeoot en the radiatiomal
tainod or sPrfthed
nomehat
ooing rate.
The Averorea
lo
lsia-
dluilarly, the inverslan tends
1akeed
if this conditis is not net.
that thi
as have a
ter Mixing ratos vhch decrease
rapidly upward from the inversion base.
to be
Thus, the influence of cloud
We will now try to show
latter coanditon my have played a role in our cas-e
ammina
tion of the Buffalo (528) sounding for 20 December at 0000 GWt reveals
a fairly moist layer tp to
about O0f at
6
~8.
2
= 297-K with a relative humidity of
The mixinb ratio falls off only ever so
slightly upward through the inversion and wind shear layer.
DeOenbe at 1200 MZWAt stations (S3?)
hint of the relatively
the
(837)
:
83K
ost
surface.
On 19
and (734) there is a slight
layer etending up to and slightly Beyond
Unortunately an incomplete sounding st
and teperatures in the region of
nterestt at (734) colder than
-40-QC make it
bpossible
to be oertain of the humidity struture.
This area includes
large part of the reglon through which traec.rtores
I and L pau an the
4
that the I
=283oL surface.
decrease algto
Thus one can ony speculate
I and possible decrease along L on this
surface is due to a slight destablisatios.
seem unimportant in this study.
decrease in stability along
, I,
Otherwise, diabatio otffets
Refrece to Appendix II shows the
L
and
L
to be the chiet
37o
for the
reaso
and (27)
deocrease*
Mote that while
satisties (3)
\_.
and
the large horizontal difference between L
\
(iSg.
29) arouses sueplclon in the trajectory.
The positive relative vorticity
hanges stood out the met on
the northern fringe of the frontal zone.
to markedly Increase the stability of the
southern boundary while still
there.
Overall, the behavior was
reontal sane along the
Increasing the relative vortietty
As the froot intensifies and the stability increases we would
expect the relative vortitty to decrease it
?
is conserved.
Ths
dose not happen and we have sees that diabatic efftets do not offer
muach of a clue to the mas-onemrvation of "
.
Our
ase would be
strengthened It data were available for the wastern Atlantic ooean.
All evidence points to the strongest portion of the frontal some being
otStarhore o
20 shows that the area of maxiau
hour period aon the lower G
6
Coparison of figures 23 end
0 December at 0000 GfT.
= 21 and 2
sirarfaes
P
surface.
values increased over the twelve
A slilar
oqmparson on the
s not possible because the maimam
region is somembere southeast of Nantucket 0a.
W
December at 0000 GME.
r arease would be
Thus, one can only speoulate that a suallar area
found on these surfases.
38°
VI.
COiCLUSIONS
Thus, we are forced to the conclusion that fricetimal effects
through the catch all
our case.
term (32) played a significant role to
F
This has not been previously found to be true for these
upper tropospherio baroolinle sones.
The potential vorticity either
Increased or was conserved with one exception within the frontal
Staley's (1960) claim for a
P
decrease on the cold boundary of
an upper tropospheric front was noire substantiated.
tien, his assertion of P
is not valid in this case.
is knoen
So very little
one.
growth due
In addi-
bhietfy to diabatie effects
In a way the results are quite disappointing.
about turbulent processes in the free atmos-
phere that very few quantitative statements can be made.
It may be
quite likely that mesoscale atmospheric sotions are rmportant enough to
etffect synoptic scale features in this case.
It turbulent processes are indeed playing a role here than we are
left with three possibilities, all somesbat unappeallng.
bulence be it
nseosale or synptic sale
One,
tur-
to somehow strenengthening
the Jet gradient over the twelve hour period.
This can take place
either it the Jet Intensities or the gradient across the Jet axis
Increases.
however.
The data only bhats at either of these posibilities,
It seems unlikely the friction thought of to its
sense can accomplish the above.
dissipative
Two, turulent processes somehow act
to form and strengthen temperature inversions within the layer of
39.
This is
strong vertical wind shear.
atmspheric amotions may be Important.
an area in
which mesoscale
For example,
mesoscale motions
may be responsible for the bringing together of stable laminae of the
Viewed on a synoptic scale this would
type found by Danielsen (19g0,
have the effect of creating a temperature inversion or a notieable
discontinuity in the lapse rate whore one did not exist before.
Of
course, the same result could be accomplished by synoptic scale vertical motions but that does not rule out the former possibility.
We know from observation that the various patterns in the atmosphere all have a certain degree of orgasItatio,
clouds, for example, tend to be arranged in
Individual cumulus
rows and the many small
cumuli of late morning are often a few larger clouds by late afternoon.
The downdraft from a thunderstorm oan result in a psuedo cold
front several times the diameter of the individual cell.
A cluster
of sterms say yield a psuedo cold front tens of atles long.
This front
then possesses many of the observed features of a true synoptic scale
that
;soscoale effects can operate so as to
front.
The point here is
proece
a system visible on the synoptic scale.
motions may be operating in
barocliate
eones,
By analoy, mesoscale
a similar manner in upper tropospheric
although on a scale of tens of ables to a synoptic
seale of hundreds of miles.
The very dryness of these baroclinte
mones should not hinder the analogy since, for example, numerical
models have been able to generate synoptic scale systems like squall
lines from meoscale effects without incorporating the release of
latent heat.
See Sasaki (1902),
for example.
The latter, vbile
40.
important, has yet to be shown to be both & necessary and eufficient
condition for squall line development
B.
Rge lability Of Sntre Anlysts
The third possibility is the most mnappealing of a11.
Namely,
that the analysis contains enough errors to render the results
neatangless.
It
is hoped that this did not happen here.
£very offort
was made to make the analysis consistent through numerous cross checks.
In addition, the palustaking trajeotory analysis gave the author a
good idea of the sensitivity of the variou
factors.
Djuri
(191)
has shown that the greatest source of error to trajectory analysis is
the sparlty of radiosonde data coupled with roundottf errors in wind
direction and inaccuracies in the wind speed as the result of the length
of the sampling period.
After
Danielsen has also studie
these latter etfects.
orkting with the data the author agrees with the c nclusions.
Undoubtedly, the trajectorite
still
contain sme errors but it
that they are the best possible with the given data.
to felt
In paticular,
the spareity of data in southern Canada lends uncertainty to the
teld analysis there because of the marked eyoloaic ourvature of the
isopleths.
there.
Thus, tootaobh ai espetally i0ogs analysas Is uncertain
The only significant oqtributions of the arvature term of
the relative vortiolty to
nounced
the 'A-
curvature.
evaluation occurs in regions of pro-
Bowever, a little
experimentation In changing
field to get somehat different trajectories failed to alter
ny of the results.
At
C, . ProbM e
of Clr
Air Turbu1noe
Perhaps the results of this study will tipart aosentum to the
easmsoale
developing studies of turbulent processes and in parttoular
The problen of clear air turbuleae (CAT)
motions.
here also.
Is likely
nvolved
vidence has been offered that occurrences of CAT have
In turn,
ben assoiated with upper tropospheric baroctWe sounes.
the whole probleo is connected with the dynamics of the jet stream.
Also, topographic features at the surface aMy play a role.
be that the Great Plains on the dorstrea
side of the cimatological
ailthese
of
steh
North American ridge is a favorable location for the
intense baroolinia
saoes.
It may
tne cannot help but wnader if
soe oamn-
neetion exists between these aones and the dynamics of stratospheric
earing phenomena with particular regard to CAT.
(1981)
Charney and Draain
among others have shows that the western North AmericWn mountain
barrier and the associated eliaatological 800 ab ridge are able to act
as a souree for a perturbation
roee below to trigger baroolaic insta-
bility in the polar night vortex.
This is by no sameans to suggest that
upper tropospheric froets are related to stratospheric vaaig
but that a coomn factor may exist.
p
m
na
For emnple, substantial vertical
motions are involved In both cases.
.
8tr9atosnheri
Oriatn of TrPalajceria
A further thought is ~ndicated at this poant.
It has been shows
by Reed, Danielsen and others for the cases that they have studied that
air contained in the baroolia c extrusion is really of stratospheric
42a
origin.
This forms the basis for the folded tropopause argument.
The results of this study do not dispute this claim but they offer
another possibility.
Stratospheric air may still
emne but the
the frontal
'
be present within
growth over the twelve hour period may
indicate that such air does not reach as close to the surface as
otherwise thought.
The whole point here Is that the folded topopause
with air of stratospherto origin way not provide the entir explanation of high potential varticity values within the frontal
ner Trm mmek
1aurtsfMce
t.
none.
Interacmon
One observation In conclusion that may be of interest: followaS
The formation and intensification of the upper tropospherico baroolinio
enoe was associated with the nest upstream 800 ab vortIcty maxima
ftr
one associated vith a very intense surface cyclone.
phenomenon
oan be noted trom Campana' s (19
A quiek check
) case.
offered similar evidence for Staley's case In 190 and
1960.
The asse
eood's case in
Finally, a further chock through all of Professor Sanders' oases
for the 1988-4 winter season established that the above ware not isolated
observations.
The more intense fronts at 500 ab were often assootated
with the vortiocty maxis m in the aids of the trough.
The deepening
surface storm was associated with the immediate downstreamn 00 nb
vortioty maximm or at least are areas of positive votiotty advection.
This suggests that some form of surface-tropospheric interaction may be
associated wvth the upper level baroclinio aones.
In any event the
presence of a doep 600 ab trough seems to be a necessary condition for
the formation of thoese baroclinic mones.
interest to warrant further study.
The oblervations are of enough
43.
The follov ng table presents the values of a distance incre. for various latitudes.
aont, 2
of
W
It
is used itf the oatours
are analyzod at Intervals of 800 a2se*2.
The number
(and fraction) of contour Intervals contained in 2
plied by 10 to give the joostrophic velocity in a see
LtgAMe (degrees)
10
tol
-1y
eL. (dgrees of latttde)
25
8.8
30
7.4
.*8
35
65
BS
40
5.8
45
8.2
50
4.8
55
4.5
60
4.2
SS
is multi-
3.9
44.
e
203oK
=
45b
26.3
I
.133
18.8
23.'7
L
2.01
.133
-
2* 3
.102
23.3
.174
-17
go
"77
1.00
1.90
.113
21.1
1.82
13
-
.094
30.0
K
.125
"48
m
-18
a
.119
+6
15.7
27.8
L
L
.143
.099
1.98
+03
1w
2.03
-14
23.7
L
"48
.083
27.7
12.9
tJ
.172
.083
12.8
1.84
.143
22.32
10.2
0
9.
-
1o
"85
-180
0
do
418
148
1.45
1.40
.070
.100
Subscripts >
1.04
1.0
*
-117
-
*
S
.072
1.0
and
a ~a~b
-82
4m
and fisal values respoctively
refer to the ltttal
"
in units of QK umb
4~rP
n units of 10"
*
~-1
soo
potential vortioity in units
of 10 "4 °5/Nb
=/smm3
pressure chauge in rb, sinus sign indicates descent
45.
1
30.9
I
31.5
-
I
S2,6.
34
26*
"
18.2
0.6
K-
14.2
w3
1
17.6
N
-
o
6.
26.0
.170
.14
.162
-
1.9
-
-
.167
-
-
-
305.
*168
-
.196
d
.17
27.8
.124
.195
-
.222
.+
1.623
1.8
-
1.62
-
-3S
1.49
1.SS
-102
.128
-
.76
-
-41
-
.12
-
-
-
91
28A4
.090
.170
1.03
1.70
-142
-
.107
-
16,e
-
-106
-
.180
-
-
-
-07
25.4
,00
.162
06
-
0v
-
-
136
-
R
10.6
R(
8.9
-*
-
-
20.8
10.3
7 2
-
-31
-
-
S
-21
-17
11.6
7.6
1.72
-
0I
S
1.8
-
1.08
1.37
-
116
1.21
079
-
118
.114
-
.084
.076
.098
.064
-
.000
-
-
1.9
-193
-
-25
-
-105
1*83
-
-
-1
-
-13
1.04
1.06
-102
1.14
m
-77
-
-92
o
4,.
AR4endJLx
-1
a
IV
299K
51.5
32.4
41.6
as
*1L
-235
2.49
.43
2.12
-30
4J
m
+17
.151
1.7
26e.5
N4
29.7
1.89
*20911
*0
.leo
21.8
3.07
los
-143
-160
.1307
V
18.3
.128
24.9
19.7
1.40
1.99
2.09
1.0
04
a
.178
24.8
22.2
ob,
o
.
m
.162
*ale
g.78
40
Im
-177
.48
1.42
1.40
.190
IM
-94
-9
0
906
C '00
0
867
0
O0
826
848
X)
- ---
- ---
-
,
f-,
0
722
O
476
0456
FIG.
SURFACE
19
DEC
3
ISOBARS
1963
1200 GMT
S
32
37
3 27
24
--1111
1 - IXI
se
867
I
522
0
848
-4n
-40
s6
S510
768
534
764
0 4
540
722
546
655
0
662
76
552-35
20
564
4
FIG 4
500 MB
19
DEC
3
1963
1200GMT
340
3
O
906
764
O
655
32
0
476
554
4
429
0456
0
445
FIG. 5
SURFACE
20 DEC.
ISOBARS
0
1963
0000GMT
327
0
340
-30
o
867
0
662
;06
/
/
'/
558 o
506....
o
469
FIG.
6
500 MB
20
DEC
1963
OOOOGMT
51 0
O
906
299
295
0
879
307
867
0
848
0
600
0
662
576
311
o
469
315
0456
0
445
FIG.
POTENTIAL
-
7
TEMPERATURE
400 MB
19
DEC
1963
303
307
311
--3
1200GMT
o
340
II
_
_
0
906
287
867
0
826
848
287
836
O
0
775
768
747
764
734
722
0
655
5
576
307
%
662
645
606
0
637
0
0
476
469
O
a518
283
0
506
0
562
0
52
554
0
311
352
486
O0
291
520
0
0456
429
04O
445
0
295
FIG. 8
POTENTIAL TEMPERATURE
0
500 MB
19 DEC
1963
1200 GMT
287
o
340
o
-299
303
7
____I_
O
906
0
879
848
299
836
O
0
600
722
303
0
0
662
576
506
0
469
0456
287
FIG. 9
POTENTIAL
TEMPERATURE
295
500 MB
19
DEC
1963
1200GMT
303
I_
I
303
299
295
\o
867
o
307
0
600
0
0
655
662
0456
FIG.
POTENTIAL
315
10
T E MPERATURE
0.
400MB
20 DEC
1963
327
OOOOGMT
0
340
O
906
0
879
295
867
0o
o
299
826
848
291
03
287
283
0
662
576
287
0
-
299
303
307
469
0456
0
445
FIG.
POTENTIAL
311
II
TEMPERATURE
500MB
20 DEC 1963
307
OOO0GMT
o
327
0
340
311
311
O
906
O
879
291
o
867
0
848
295
0
600
0
662
0
576
279
0
554
- 287
291
19 5
0456
FIG. 12
POTENTIAL
303
TEMPERATURE
600 MB
20
DEC 1963
OOOOGMT
o
340
L
O
906
0
879
O
O
826
287
- -. 29
27
o
600
0
662
:-.
0
506
562
0
469
271
0456
275
.279
283
287
291
o
445
FIG. 13
POTENTIAL
TEMPERATURE
295
700 MB
20
DEC
1963
OOOOGMT
271
~L
---C--L---~I -I
_
906
906
913
907
o
879
816
O
867
o
o
848
826
ell
836
815
0
775
768
0
76 4
0A
655
0
0
576
662
0
476
0
600
0
722
734
06
0645562
469
486
O
532
0
445
FIG.
405
425
14
308
EXTENT OF CROSS
o
SECTIONS
327
D
o
317
B
340
304
1
59.
P(MB)
300-
40
315
30
20
55 /
600
/
65
\
,o
287
/
/
20
-267 1
15
0010
8501
)
,
,1
BUF
528
PIT
520
FIG.
1600-
800-
ISENTROPES (OK)
36.5ON
/
\
/
227
82.2ow
00
/
-
ISOTAGHS (M SEC
15
303
30299
S
/
//
S/
\ \
/
20 DECEMBER
1963
0000 GMT.
45.OON
75.40 W
60.
35.00 N
77.2o0 W
RIC
DCA
JUST EAST
FIG. 16
20
403
HAR
JUST EAST
DECEMBER
1963
BGM
515
0000 GMT
MSS
622
~__
o
879
816
O
867
O
O
826
848
P
S
--
0
775
O
I
"-
768
/
-i
\
I
-747K
7
\
\\
655I
*0\
520
\
1
\
6456
F
%3
7H
0
476
2
562
0
600
722
L
E
o.
'b
734
\\
F
662
662
712
Q
I
S\
764
576
-
I
G-
T
815
81
/a36
0
518
528
7
%
N
3
6
-.
469
486
\
0456
WHICH
19 - 20
.520
C
D
"429
445
FIG. 17
ISENTROPIC
532
\
-
A
TRAJECTORIES
SATISFY
DEC
EQ (3)
1963
S= 283 oK
,.
S304
3o
40
:40
327
317
-0
.o*
O
906
Op
867
0
0
848
K
R
-//
836,
G
\
\
-
-I
T
\
O
\E
'
\\\
764
\\
\
0
600
0
O
662
576
-0
0
0
469
506
10
562
554
IN
045
N.
ml
N\
0456
N
-1
445\
N
FIG. 18
N
425
N
NN
ISENTROPIC
WHICH
TRAJECTORIES
SATISFY
19 -20 DEC
9
EQ (3)
1963
= 291 °K
327
k486
520
a~l~
_ __
O
906
O
879
O
867
I
848
-
N
I
\\
,
E
I/
O
764
/
/
/L
\
M
N
1\
\
*
0
722
722
600
0
0
576
662
\\
-o
0
506
1%
562
0
469
%%
N
D\
N
1
520
0456
I
FIG.
4 29
445
19
S
4 25
TRAJECTORIES
ISENTROPIC
WHICH SATISFY EQ (3)
19-20
DEC
1963
3270
3?7
35.7
0 = 299 'K
____I_~_
___I
0
906
0
879
0
867
0
848
/
0
Ke
747
0
764
L
0
0
576
Ne
--
/
655
662
Fe
Ee
64
Be
0
562
0
476
O
554
532
0456
425
425
FIG. 20
ISENTROPIC
WHICH
TRAJECTORIES
SATISFY
19 - 20
DEC
-0420
S429
EQNS (3),(7)
1963
P = 283 OK
0
340
II
I
I
I
oo
906
907
0
879
816
se
867
o
Oe
/
Re
/848
826
Ne
N*
//
5
II
815
" -sit836
Ke
K-.
"
0Q
768
775
Ge
I
Ee\ \
Le
74
\
I
I
74 \
\
\
712
\
AC
655
662
0
600
722
\
576
606
645
,,.
528
637
0
0
562
0
469
476
554
486
486
0
O
532
520
0456
429
445
21
FIG.
ISENTROPIC
WHICH
TRAJECTORIES
SATISFY
19 - 20 DEC
9
425
308
EQNS (3),(7)
1963
2910 K
0
0
397
317
304
30
-O
506
0
879
d9*,
Neo
!
f
t"i
O
867
0
'l l
I
Ke
848
*I
Ee\
le
\
Le
I
836
~s/
I
0
764
34
\t
0
655
0
662
0
576
-0o
506
0
562
O
476
520
0456
O
445
FIG. 22
ISENTROPIC
TRAJECTORIES
SATISFY
WHICH
19 -20
#
DEC
EQNS (3),(7)
1963
= 299 *K
0
340
429
O
906
0
879
0
867
0
848
O
826
747
0
O
662
576
0
562
O
469
-o0
0
506
554
0456
O
445
FIG.
POTENTIAL
8
23
VORTICITY
283
K
0
340
20 DEC 1963
OOOOGMT
0
879
O
867
848
--
-Pr
O
600
0
O
662
576
0
506
0
554
0456
FIG.
POTENTIAL
24
VORTICITY
0
S=291 OK
20 DEC 1963
OOOOGMT
327
o
340
I I
O
906
0
879
0
867
0
848
O
775
%-10
\
O
764
0
600
0
O
662
576
0
562
O
476
-0
506
O
554
0456
FIG. 25
POTENTIAL
VORTICITY
8 = 299 OK
20 DEC
1963
OOOOGMT
0
340
_
~
0
906
91390
907
o0
879
816
O
867
0
0
848
826
815
15
0
768
775
all
836
---
2o"o 0
0
747
?3
0
0
722
600
S25
0
576
662
606
O
518
0
0
0
476
0
562
469
506
4
O
486
532
0
0456
429
O45
POTENTIAL
045
4
425
5
26
FIG.
520
VORTICITY
283
19 DEC 1963
308
OK
1200GMT
0-.
o
340
0
0
327
317
304
o0
I
.
O
906
0
879
0
826
0
775
5
o
600
0
O
662
576
0
506
562
0
476
0456
FIG.
POTENTIAL
27
VORTICITY
o
S= 291 OK
19 DEC
1963
1200GMT
327
0
340
O
906
0
879
0
867
O
826
z
~
0
775
30
35
O
600
0
0
576
0
476
662
0
0
554
469
0
0
429
FIG.
VORTICITY
POTENTIAL
8
19 DEC
28
0
=299 OK
1963
1200GMT
327
0
340
520
O
906
0
879
0
867
O
O
826
848
0
747
0
K
764
Lv
0
722
734
O
655
0
0
662
576
\
0
0
506
562
0
469
05
532
0456
0
445
FIG. 29
19-20 DEC
-o520
5 20
429
425
425
ISENTROPIC TRAJECTORIES
WHICH SATISFY
\
EQ (27)
1963
0 = 283 OK
0
340
O
879
0
867
0
. S
INV
LV
848
a
I
0
775
0
768
I
S
E ,
1
\ 747
\\
\
KvV
--
o
600
0
655
662
O
476
0
0
562
O
506
469
520
0456
429
445
FIG. 30
ISENTROPIC
TRAJECTORIES
EQ (27)
WHICH SATISFY
19 - 20
1963
DEC
= 291
0
K
0
340
O
906
Sv
-O
/
0
848
S
Ev \
I
I
\
'
0
,N
/
/
/
I
l
/
I
1
-
L
*
I
I
Rv
\
0
764
\
o
O
O
%
655
662
576
\6
6
0
554
O
476
0
429
0456
FIG. 31
ISENTROPIC
WHICH
TRAJECTORIES
SATISFY
EQ (27)
19 - 20 DEC 1963
S= 299 oK
340
" 520
O
906
0
775
0
576
0
662
0
562
0
476
20
0456
FIG.
% RELATIVE
32
HUMIDITY
8 = 283 OK
19 DEC 1963
1200GMT
0
0
429
520
I~P~IIOPPIIIIIII
O
906
0
879
\-20
I,
\
7o
764
0
662
0
562
O
476
0456
445
FIG.
% RELATIVE
HUMIDITY
0 = 283
20 DEC
1963
425
33
60
K
OOOOGMT
340
00
O
fll
78.
BIBLICRAPHY
Bjorknes, J., 1919:
1, mo. 2.
On the dtructure of Moving Cyclones,
Get.aL
au.,
Campana, K., 196: lPreamto
etical Proceses i the Upper Troposphere
(uapubl. B.M. Thesi), Cmb., Mol.T, 64 pp.
Charney, J., and P. Draiat, 1961s Propagatiou of Planetary Sale Dieturbnoes from the Lower nto the Upper Atmphere, jOU.
83-109.
Geh. Al., *6,
Deaielsen, N., 198;9
The Lasiar ltru
ture of the Atmosphere and its
Relation to the Concept of a Trpopause, ArMh tKrJ t.
MDILk
hA
*Adbi.k,
A 11, 3, 293-32.
S.. 191: Trajectories: Iuobrio, Iseatrop
of Xt.*, 18, 407-456.
Iur.
and Actual,
1041 Project Springfield Report, Defense Atomia
-.
Support Agency. 06 pp.
Djurto, D.,
1901:
On the Acauray of Air Trajectories Computattions,
mrunaml 0e st.,
16, 897-603.
Masterson, Jo, et al, 1966 8strato4MesopherLo Mesurem"nts of Density,
Temperature, and other Meteorological Variables in the Central
Tropieal Pacifio, Journal of Aq . Net.,
, 182188
Mller, f., 1961
Lng-Wave Radiaton,
Mae..) 34-8.
ComendlM
of Iet, (A.M.0S.-soton,
Reed, R., 1958; A Study of a Characteristlo Type of Upper-Level FrontoeVtM.p, 12, 22S-237.
gemnesis JMagr
Reed. I.
and N. Dahnilsea, 1986:
M
pause. Mb.rarJt
Reed,
l.
Fronts in the Vicinity of the Tropo-
eosh
wad ik ., A 11, 1, 1-17.
An Investigaton of the Development of
t., and F. Sanders, 193s:
a Mid-Tropospherio Frontal Zome nd its Assotc ted Vorticity
Field, jOunl o&NE
J
t., 10, 36-349.
Sanders, F.*, 1984: An Iuvestigation et Atsepherlo Frontal Zones
(unpubl. S**o.
Dissertation), Camb.,
I.T., 132 pp.
taley, Do., 1960: Evaluation of Potential Vartlty .....
Debris trom
Stratosphere to Troposphere, Jral
of lt.,
17, 891-622.
79.
Staley. D., 1905: Radiativo Cooling to the VicinItY of Inversions and
,19, 282-301.
ANe.
r.
JoIu. Ro.
the Tropopause, Art.
Staley, D., and Iuhb, P., 1961 s Mesurementa of Radtative Cooling
Through Two Intense sarocliao Zones in the Middle Troposphere,
Jmou.
o
15,
st.18
0-210.
sasOtl, Y., 103: ISttets of Coadensatiou, Evaporation and Raintall on
A Nuaerril Laperalmet,
Diaturbeesa:a
Development of NesOo le
Proc. Int. . n
Na
~m. Wa
Pred., 47-000.