60=E RN BErI8MRIC 14MDIONAL CICULATION
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tiVRIN'O EME ICY
JOSEPH Uvzs vwerc
RdEs
Catholique do LOUtMd
Licencle en Sciences* UnlweeIt
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$U~Es?1tLD IN PARTAL J JLFILLW--W
OF TiU, IMQIRENUS FM TZ
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INUIITUTE
NAMAE$AWS
July 2002'
Signature of Author . t
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of Meteorology, Jtily 20, 192
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Chaiman, DepaWtmental Ccittee on Graduate Studente
mthrnf.ula neric MeridinalM Caemlat ion
by
Joseph Louis Victor FPrere
Submitted to the Department of Meteorology on
July 20, 1962 in partial fultillment of the
requirement for the Degree of Master of cience
ABSTRACT
Tabulations of daily observational values of the wind were made
for eight leels (860e o00 800. 400, 800, 200, 100 and 50 ab) frm
142 stations for the sitamonthe period from April to September 1958.
tndividual station and levels the seridional componente of
For ea
the daily values of the wind were coeputed, together with their mean
value and their standard deviation. Maps of theme mean value and
standard deviations were analysed to obtain grid point values for the
nuerical approKimations of their sonal means.
The values obtained for the man neridional wind as a ftention of
latitude and height show a three cellular pattern for the seridlonal
circulation. A strvag direct cell is found In the equatorial region,
a strong indirect cell occurs in the middle latitudes while in high
direct cirolation.
latitudes there Is agaln
Thesis Supervisors Victor P. Starr
Profesor of Meteorology
Title
il
ACKWIEDGWE1N
The author Is indebted to Proftesm
Victor P. Star for his
advice and eneruaeat throughout the course of this study,
The author is also grateful to Mr. G. O Patrickt
8.oM,
for his
assistance and tor the large amount of data he has tabulated.
Acknowledgement is made to Mrs. Barbara Goodwina and the eneputlng
staff of the M1I.T. Planetary Circulation Project for pertoratg the
calcultions upon which this woris
work is based
the drafting of the maps and to
thesis.
to Miss
Isabel
ole for
,Mrs
Jane McNabb for typing the
iv,
TABMZ0 O OMMMi1
11
3
DIGCA
III11CBIDOK
WIND GT4IIiCO
IM
INDIVIMJAL
ci' IN NEaioiinw0"
IV
i'm HS311uiuc DIWTIIC
WIN) WiE'fics
V
IIST1C8 AS A IUNCICW Ci'
MBRIDCKAL WIM
AND I=I
~LU
VI
DI8D18810W C'
ViI
MS MEULTS
CCUIt
6
12
19
Vill
suOf#IOus Fm IWTR E120
IX
APPENDIX
21
X
DID6LIOI3AMB
27
TAWULM'D WA
28
PSRIDIOKAL CROS NCtIOCK
RJLES
I.
INTROXCTION
Sme attempts to determine thhe mean
eridlional wind as a function
of latitude and height have been made in the Northern Hmaaphere by
Starr and White (1954)(], Buch (1084) (2) and Tacker (1980) [3). Such
an attempt was never made in the Sothern Heamisphere because of a lack
of sufficiently reprsentative observational data.
This situation was
changed thanks to the extensive amount of observations made during
the International Geophysical Tear (19
).
The object of the present
work isoto extend to the Southern Hemisphere the analysis previously
done in the Northern Hemisphere.
The analysis covers the entire Southern Hestaphere for the six
months period trm April to September 198.
The calculations involved
tabulations of daily valas of winds and computations of their merdional components for all the statione
throughout the Southern Heaisphere
and the Northern Heamspherlc Stations in the vicinity of the equator.
The basic material was obtained prinipally froma
the World Metewoological
Organisation and also trom the IGT Meteorological Data on tMicocards
supplied by the National Academy of Sciences and National Research Council,
Washington, D. C.
The tabulated material was used to cmpute the mean meridional wind
2.
with its standard deviation for the six months period (April-Septesber)
Such coptations were made at each of th
1988.
at the presusre levels 8680
700. 600. 400,.
bmikpherie distributions of these quantitie
lines drwn on oirm
polar
142 stations considered.
00. 200. 100 and 80 ab. The
are represented by iso-
aps.
From these maps one can easily evaluate sonally averaged values
of
the meridional wind with the standard deviations by Integration along
the latitude circles.
However, the Isoliae configrations are by necessity aoerotain
over lage regions of the hemisphere because of lack of suffieent data
Such sparsity of data in certain regions would undebtedly
coverage.
reduce the objectivity of the present study.
important because the tma
present study
period to restricted to six months.
But the
ay serve as an Indication of what can be obtained from the
direct observed wiad data available*
amputations of the mean meridional
strophl
Statistical errors awe also
It
sbould be noticed here that the
i1rculation cannot be based on geo-
swinds obtained trm the observed or extrapolated presesre and
temperature distribution in the atmaophre; because the Sonal averages
of the meridional component of the geostrophie wind is then always aro.
In
uoch a case the planetary oellle+ circulation is automatically
ellinated.
II.
DANA
Table I contains a list of 142 stations tfro
used in this staudy
which wind data were
Of these statins 22 are actually not Southern
BemOqpherie stations but are situated slightly north of the Equator.
They wete used in order to allow for a better analysis in the equatorial
ergionl thus pesmittlg the identifiottion of lateation with the
Northern
etamiOpbe.
All wind reports used were observed in the period extending from
the first of April 1988 until the thirtieth of September of the mae
This corespoads to the winter season in this bealsphoewe
year.
The tame of observation
except in the
at that time
12002,
ases wher
s geneally 00002 for all the
tations
the observations wee missing or ietufticlent
other observations were then used instmad, geneslmly at
A few Africalon stations had only the 08002 report while
the stations in South AMerica reported at 1800.
swae of
The mean values and
standard devistions oalculated for the individual stations mar
Supposed
to be representative of the wind conditlons throughout the winter.
This
required, however, that the selection of data involved in the calulations
be a randm.
sample i.ee
pletely aeoldental.
that the method of selcting the data
s cami
Data based on observations at regular time intervals
4,
are not exactly r ndea samplese but for a large number of observations
they may be considered as such, unless the period of observation (one
day) ooaneides with a period in the tluctuations of the wind.
For
tunately the daily variations of the ~tropopherio motions eae In general
Sextwaely mall exmept close to the ground.
Data were empiled tr=o
radowadin
and pilot-balloon observations.
Data aompiled tfm pilot belloon observatlons are genems lly subject
to bias for two major reasons:
a)
In cloudy weather the sounding balloon disappears into the
clouds and may be lost already at a low elevation.
circulation on
ppe-aIr
lear days Is in general substantially difterent fro
that on cloudy days, and hence the realts
observations, aW be
b)
The saeemn
obtained ftra pilot balloon
sghly erroneous (Mintz and Dean, 1952) (4].
Daring strofg wind conditions through a deep layer the balloon
soon dlsappears in the distance.
vations available fo
x
The data compiled from the wind obsew
the higher levels are therefore libely to be
selective in favor of light wind conditions in the tropoaphee.
Strong windse
an also seriously atfect the
epiesentativenees
of
radlo-wind data aItho0gh probably to a lesser extent than for pilotballoon observations.
The data available for the higher levels must
therefore be suspected of being highly selective it
a large fraction of
the 183 possible wind reports is massiaw .
Of the 142 stations ased in this study, 96 we radio*wind
Most of them have fairly emplete set
tations.,
of data, except for the stra-
toaphere where the ammber of reports deteriorated,
Unfortunately, these
relatively good stations are very mnequally distributed over the hemisphere.
A dense network is found over Australia and New Zealand, the
Antarctic Continents and the west coast of South America,
A reliable
analysis say be expected over these regions, although the degree of
reliability in likely to decrease upward in the atmosphere.
Fairly
reliable analysis are expected also over Africa, Madagascarp and the
equatorial region In the Northern
Ocean.
ieFsphere except the North Pacific
In the South Pacific Oceans no data are available for a large
region (0 o - 600 S, 900 - 1400 W) wbhle in other oceanic regions there
are a few Island reportiag stations.
III.
IERIDIONAL WIND SrB
IICS FOB INDIVIDUAL S~tJIONr
The horisontal wind vector ema
meridional and
onral components.
omponent of the wind by
be resolved at any point into
Let Us deslgnate the south-Borth
v.
As mentioned in the introduction, the basei
tabulations of daily values v 1 of the
material conslsted of
aeridional wind component for
each Individual station and for eght standard pseesure levels in the
free ataosphere (the 850. 700, 500, 400, 800, 20. 100 and 80 mb levels).
The six months mean value of v for an individual station may be
estimated byt
V
=
N
where N is the nmber of observations throughout the six sonthe period.
A bar over the different statstical variables will here always denote
averaged values with respect to time.
The standard deviation d (v) of
v may be esttimated by
SviV)
N-1
7.
The standard deviation is
convenient measure of the variations
of the individual values about their mean.
Buch (1954) [2] made a closer Investigation of the distribution
of v throbWhout a year in a single cae, namely, for the 347 wind reports
available for the 800 ab surface at Aldergrove. England.
It was found
that v was noaally distributed about its mean value to a high degree
of approlimation.
Whenever this is the ease, the distributions are
oepletely deteamined by mean values and standard deviations.
Assminag random amspling, the statistical unoertainty in the deter
minations of msan valtes may be estmasted from their standard errors,
which for a ample of large siae N mWabe estimated by
a (v) / j
It was found in this work that for fairly complete sets of data (N k 144),
the standard error of the mean values of v never exceeds 1a/sac at the
880 and 700 mb levelg it reaches or eoceeds 1.
am/sec only in lim1ted
regions of the upper troposphere.
Of course, for maller values of N, the standard error ts much
larger.
In some
ass where N was malls, even at low levels, all the ob-
servations were concentrated in two or three months in themseas
sampling might have been biased.
the
IV.
TM EMISERIC DISflIBUTION
lWRIDIOW
C TI
WIND WCIrICs
The values of v and d (v) for eaeh individual station and for the
eight levels in the atmophere wee plotted on bhmispherio maps.
The analysis of the asps was based on these values.
of observations, frs
Also the ntuber
which each statistical quantity was evaluated, was
taken into account, because it allowe a direct estimate of the reliability of each individual quantity.
The naps were analysed over the entire hemisphere.
lack of data in the region (Oo - 606o8
900 -
Because of the
140ow) the configuration of
the isolines are these only a more or less plausible gueass
On the maps
presented herein, the isolines are dremn in dashed-dotted lines in that
egilon.
In the analysis of the neridional component of the wind
presents a oingularity.
the pole
Theoretieel considerstiens permit us to make the
analysis in the polar region.
They ae derived in the appendix.
The hemiepheroi diltribution of the mean soutbhto-novth component
v of the wind are hfown in Plates 1 - 8.
intervals.
-1
Isolinos are drawn at 1 a see
The hemispheric distributions of the standard deviation 0 (v)
are shown In Plates 9 - 16
are abown in Platea 9 - 18.
Isolines aee drawn at I s sec
Isolinea are dawn at 1 a see
interval1
intervals.
94
V.
NERIDIONAL WIND
f4TIrfICS AS A FUNCTION 0F L&ITUIE AND REIGH
Zonally averaged values of v ad C~v) were evaluated frem the maps
by using a systse
of gridpolnts tor every 50 of latitude and 100 of
longitude.
The monal average of v and 0 (v) are estimated by
Iv]
0)a a
36
Since te e
36
aps in any case cannot be expected to detewaine the
monally averaged values with any great accuracy, it
seems frtless
to
apply a more elaborate idtegration process for deteining these mean
values.
Let us mention that brackets will here alwaqs denote sonally averaged
values.
The sonal standard deviation
values of
(,
o
(v) of v was also competed.
[o (v)] sad C(v) ae preented in Tables II,
The standard errr of [;] is eqpal or less than 0.36
The
IV and V.
/see except
in limited regions of the upper atmophere, especially in high latitudes.
The mesan mas
we should have
flow across a latitude circle being vanishingly small
10.
(assumed in this analysi
where po is the pressure at the Outfae
to be
1000 ab).
The vertically averaged values of [C] is given by
f
*
ANNU
and they should in actuality be very
They were computed
(
dp
small
aseesuming that the meridional wind was barotrople
in the layer 80 to 1000 ab.
This was a good assnmption since the data
indicated that the winds were generally blowing in approximately the same
direction and were of the ame order of magnitude at 8850 and 1000 ab.
The sae asumptions were made in the layer 50 ab to the top of the
atmosphere.
The values of
{1)
were then detemined as weighted means between
the values representing the Individual pressure levels.
The weighting fattors applied were 225, 1", 150. 1000100, 100,
75 and 78 for the 850, 700, 500, 400, 3W0. 200. 100 and 50 ab pressure
levels, respectively.
The results are ahowa at the bottom of Table II.
expected they are not all.
As might be
Ihis indicates that unfortunately the methods
used here do not allow any precise deteraination of the strength of the
sean meridional cells.
11,
In order to tp to eliminate this error, partially at least,
(v} was subtracted from the values of I at each level, so that
p
wbe rJ'
o
S
The values of
( '
(Jimm
B
are presented in Table Il1.
Merldional orose sections shoiag conditions averaged over all
longitudes were construted from the values presented in Tables III and
IV (Figures I and 2).
In Fle
1 te
th
isolines are drawn at 40 a
see
intervals.
Posi-
tive values are tour south winds, lhile negative values are for north
winds.
Above the 80 mb level and below the 850 ab level the ioolines are
drawn in dased lines.
They are vertical in these layers asooording to
our barotropic assumptions.
-1
intervals.
In Figure 2 the isolines are drawn at 2 a seo
12.
VI,
DISCUSSION OF TE RESULTS
Let us first exomine the
shown on Plate 1.
ric v maps,
Between Oo and 20o 68,
a strong center north of Madagas
Theehes
850 mb level is
is generally equatorward with
(10 a/see). This must represent the
equatorward component of the trade wind.,
In thse latitudes there are, however, some centers of poleward winds,
the strongest of whiah beina
on the South American continents around
1800 W in the Pacific Ocean and over Java.
Between 200 8 and 400 5 the wind blows southward over the continents
and northwards over the oceans.
At the ground level these centers of
north and south wind would according to the trend at the upper levels,
probably be displaced slightly towards the east.
This should correspond
with the interrupton over the continents of the continuous belt of high
pressures between 200 8 and 40o 8*
At ?00 ab (Plate 2), the isolines pattern Is very similar to that
of the 880 ab level.
The main differences are a weakenlg of the souther-
lies at low latitudes and a displacement towards the west of the centers
of north and south winds in the 200 8 to 400o
belt.
At the 800 ab level (Plate 3) the belt of seutherlies has disappeared
at low latitudes, the merldional components of the wind being very asall
13.
in that region. In the intermediate region the centers of north and
south winds are again pushed towards the wests by cmparison with the
700 mb level.
South of 850 8 the winds are generally southward
except
over the Antarctic continent whose circulation we ahall discuss later.
At 400 mb (Plate 4) a belt of northerlies appears between Oo and
200 S. the winds being northward only over Africa and South America in
these latitudes.
Between 200 8 and
50o S there Is a belt of southerlies.
Farther to the south there is again a belt of northerlies.
Nowever. this
belt is not centered at the pole but is displaced towards Australia.
At 300 mb (Plate 5) we have eveywhere an Intensification of the
circulation described at 400 ab
except that the center of southerlies
has disappeared over Arica at low latitudes.
At 200 mb (Plate 6) we have the same pattern but the eIrclation is
here at a maxaus
strong northerlies (maxima 418 a/seo) from 00 to 200 So
strong southerlies (maxia
east part of South America.
7-10 a/gee) frm 200 8 to 600 8 end over the
The high latitude northerly belt is however
weakened at this level.
At 100 ab (Plate 7) the circulation is the ease again, but is such
weaker than at 200 ab excoept for the high latitude northerlies which are
stronger.
The 50 ab analysis (Plate 8) is not very reliable becase of the lack
14.
of sufftolent data, the general ciroulation seems however to be the
same as at the lower levels, but is
Let as no. ezamlnr
noeh weaker.
the ciroalation over the Antartilo continent.
At the Pole in the upper troposphe s
tfe
mean vector wind is very strong (fies 6 to 3
is approuJatsely onustant
The mean wind has then
t each level0
00 ab up to 900 ab. the
/seo)
i.e., tfre
and its
direction
800 1 touead
1000 Eo
in the po1m leglon, a northward comronent along
the 1000 E mariditan sad a southward oesponent on the other side of the
pole.
At all these levels, the polo is also in the region of slnmum
standard deviationg this suggests a relative
wind in that reglonR
Acoording to the lf
great stability of the
General Report Series
Number 4 [e]. there Is a persistent depoession over the Rose Bea. This
should be the reason fo
the strong mean wind at the Pole in the tro-
posphere (TO0 ab presurme level is below the ground level at the Pole,
so that we have no wind data below 800 rb).
In the stratosphre
howevere the mean voetor wind blows in the
opposite direction and is quite strlea
standard deviation is still
at 50 ab (3.08 a I
not too large (?.8 a sml).
)
and the
This mean wind
is assoolated, aooerding to the Rt Report [(J with a vortex whose center
is located In the vioinity of 840 5 and 30o So
The analysis made by Such [2] toe the winter soths
of the year 190
18.
over the northern hemisphere at the 880. 700. 800o 300. 200 and 100 ab
levels
hos that the oirculation pattern is much more complex in that
hemslphere, with many scattered
enters of northerlies and soatherlies.
So does also the analysise ade b the marahast (1982) [e0 at the 100, 50
and 30 ab levels tfor the three saonthe period October to December 1987i
in the northern hamisphbse.
The scnally aweeged values of v are shown in Table II with the
vertical wighted
oesges at the botto .
value of 1.87 at 400 8.
This Indicates that thelr
Althoeh the oerwer
in our reslts.
These averages bhae a eaximum
each level, we oonsiderod the vertical
are actualy probably ditterent at
averages to be in the nature of
mean errors and applied them as acorotions.
Table III and in Figuw
are unavoidable errors
The results ae
absown in
38
Figure 1 shows at lee latitudesp strong southerlies at lee levels
(1 a see
at 860mb) and northerlies alot
(2 a se
indicates the exostence of a streaf direct oir mlation.
at 200 ab); this
The southorn
limit of the southerlies is 2So 8 at 880 Ab, and the limlt of the northerlies is 200 at 200 abo
hemsphere.
mowever, this cell is not limited to the southern
Inatead, the meridional sinds are at a maximma in the vicinity
of the equator.
According to the reslts obtained by Booh [2](Jigure 3)
and Tuoker [8) (tgasre 4) tor the gamer season in the northen hemisphere,
16.
the southerltes extend to 200 N at 850 mb and the northerlies at 200 ab
perhaps to 12o N.
(auoh studied both msmer and winter seasons over
the entire northera hbeisphese durina
the year 1980.
Tooker studied
also both smmer and winter seasons but only over the 15o N - TON
1600 W - 0 * 400 E
legion and for a two-ear period from Otober 1949
to September 1981.)
The sametrical lo
latitude circulation during the winter season
of the northera hemiphebre would have a northern 11iit at about 190N
according to udch and at about 250o N according to Tuoker (270 N at
850 ab, 24o N at 200 ab) (Figures
and 6).
The Intensity of the olre
eulation is sensibly the se.
Returning to Figure
riddle latitudes.
With winds bloving equatorward at high levels, and
poleward at lou levels.
B to 190o
indirect
1, we en observe an iadirect circulation in
The upper southerlies region extends t ar
and the lover northerlies region from
irculationa
540
8 to 240 8.
bas, according to our results, the
as the low-latitude direct circulation (maximas 1.95 a se
1.1 R see
-1
at 850 ab).
600
This
aseo intensity
"l
at 200 rb,
The indirect circulation of the Riddle latitudes
was generally not expected to be so strong.
cussed, the results eight still
Hoower, as previously die-
oontain some important statistical errors,
and our methods most likely do not allow any precise detemination of the
17.
strength of the mean meridional cellso except for order of aeagnitude.
According to Buch and Tucker, the indirect circulation is not so strong
in the Northern Hemisphere.
Buch reported a
aximum value of 1.36 a
-1
at 200 ab and 0.6 at 850 ab$ while the cell extended free
see
N to 54oN aloft and ftram 1
170
N to 460 N at 880 ab.
Tucker reported velocities loes than 0.7 m/see for both northerlies
(25o N
850 N) aloft and Iouterlies (270 N -
50o
N) at 800 Ob.
Another direct oirculation talMs place at high latitudes.
not extend above 230 ab.
-2
*1
see .
It does
The maimum winds are ot the order of 0.8 a
Duch and Tubier obtained emparsble results, with, however,
intensities of the order of 0.8 a se
Let us nma
are, in groes
.
esmne the 0 (v) maps (Plates 9 - 1)., The isolines
concentrie around the pole with a belt of maximum values
in middle latitudes In the tropophee.
In the upper troposphe e, this
maximue belt is situated approximately between the south wind belt in
msiddle latitudes and the north wind belt in the high latitudes.
precisely, the centers of sexiuma
(v) occur Just to the south of the
centers of masimum intensity of the middle latitude southerlies.
lower troposphere the emalmu
More
belt is found around 40o - 60
In the
latitude.
These maiema of stadard deviation corsepond to the perturbations duoe
to the polar fronts.
Nigher values ae found in the upper troposphere
18.
whibh huWIests that they may be due to the displacement o
the RosAby
waves.
In the stratophere, the belt of mana,slants towards the pole.
The y (v) maps drawn by
ueah and MIrakml possent the sme pattern
Nmisaprse.
In the Northera
Figure 2 presents a meridionl oarose
deviations,
().
The maximum values occur at 800
region and at 200 ab ear the equator.
is at 800 ab and 00o8.
in the Northern
Southern
b in the polar
The largest value (18 a sec
)
Buh (Figae ?) obtalued a cmprarble pattern
misphere with however values about I at seeo
at latitudes lower than
that latitude.
otion of the standard
O60
8
and about I a
eeo
-1
larger
naller sathward of
This aigests that the meridional oirculation In the
ei sephee Io a little sore stable at low and middle latitudes
and less stable at high latitudese
19,
VII.
COPCIUSION
The IGY obs rmtionl data peasitted us to stady, for the first
in the Bouthern
time, the meridional circulatio
eailphere.
The
analysis was made for the period extending from April 1st 1988 to
leptember 30th 1988.
It was found that our methods did not allow a
precise determination of the meridional cIrculation, but pemitted us
to dete3miae at least the order of magnltude of the intensity of the
eirculation.
The results Abowed that like In the Northermn
oulation in the Southern Hemisphe
emisphere
the ci-
presents a three cellular pattern,
i.e., a direct cell at low latitudese an Indirect cell at middle
latitudes and again a direct cell at high latitudes.
The circulation in the indirect cell was found to be slightly
more intense tha in the correspoandin
indireet cell in the Northern
Beisphese.
The analysis of the standard deviation 0 (v)
ndicated that the
meridional oirculation, was smre stable in the Southern Heaisphere than
in the Northera Btmisphere at middle and low latitulesl while at high
latitudes this situation Is reversed.
j
20.
ll
VIII.
FURTIER WRK
BrWTIONS IO
It would be of interest to ooaplete the analysis of the f0W data,
for southern misphare by exteading this study to the ammer season
end the yearly seas circlation.
This work is presently undertsaen at
Institute of Tedoa#legy
Insahmaustts
the
the direotioe
of Professr V. P. Starr
study of the gemesl eiralatioe ni
a more precise
by Mr. G. 0. Patrvik, under
as a part of a more extensive
the .outhems HieteSpee.
However.
detemination of the seridional circulation would necessl-
tate fairly good observational data, extended over many years
in order
to reduoe the statistical errors and also to obtain estimates of the
seasonal and yearly oirtwlations for several years instead of the values
for one particular year.
This would require the maintesne
10G,
of the stations Initiated for
plus extending the coverage of euthern Hemisphere observations
by establidhin
astations on sma
ew
of the isolated islands and by
developing a system of weather ships similar to that in the Northern
esmisphere.
21,
IX.
APPENDIX
In this work we have resolved the horisontal wind in meridional
and zonal cemponents in order to study the nerldional ciroulation.
However, both the north pole and the south pole constitute singularitlee
where the meridional and sonal components of the horizontal wind are not
uniquely defined.
Barnes (192)
I] has studied the configuration of the isolines
eridional and sonal components of the wind over a sall neighbor-
of the
hood centered at a pole
Let us apply his study to a mall neighbowbood centered at the
south pole.
It we take this neighboehood
mall enough, then the hor-
aontal wind velooity may be considered as constant.
If one assmes also that the neighborhood is amll enogh so that
the spherioal surface may be considered flat, the horizontal wind velocity
in the neighborhood of the south pole ean be defined in the following
manner.
First redefine the longitudes so that 0o west longitude becomes
(S60 - 0o) east loegitude.
Then the horisontal wind is uniquely defined
by the non-negative quantity C. the wind speed, and 0
*
the meridian
from which the wind is blowing towards the south pole.
Let us now consider the map of the v coaponent of the wind in this
22.
neighborhood.
This component is given by v u -C cos (a - g)
at any
point, except the pole, along a meridian 9.
It in this neasighborhood, we approach the pole along the meridians
(c + 900) and (0
" 900)0 we find the value of v to be aero
No matter
bow close we come to the pole along these lines, v will be aero.
In the same sanner, v is maximm
and equal to C along the meridian
9 + 180o and tainum and equal to -C along the meridian 9.
A map *all be said to be a Mttern 1 nma
can be expressed
it
by -C cos ( - 9 ) for a > 0 (whee ~ is the distance from the pole),
in the neighborhood of the pole.
The asp of the
*
onal
C
cos ((- o90o)
omponent a is given by -C sin (-
,
aJ .o
it is also a pattern 1 msp.
)
Thus the
a asp is Just the v ap rotated about the pole 90O to the west.
This
means that the aero isopleths for a and v IMould be at right eagles to
each other in the neighborhood of the pole.
In the following discussion we
all be concerned only with the
neighbohood of the pole and not with the value at the pole itselt.
Ae
stated before a pattera 1 map is represented
by -C cos ( -
e
f
) for
athematically
> 0 where C and 9o are constants but is undefined
for s a 0, bhere a is the distance trom the pole.
We now wiAh to show that the maep v and v9*
v
-
v and consequently
23.
a and u' m u - u am pattern 1 sp.
of the o
The sun of two saps is defined as the
of the values
Adding two pattern 1 maps we obtain, for
at the individual poinate
s>0
.CCt
os ( -
t)
+
C'cos ( -
-[C, (oes d oo* Al + sinsi
-[oo8s
(C
0s
M
na
1
,3)]
=
) + ca(eose
cos a2 + sna 0 sin
a2 )]
+ Ca cos g) + sin (CI sain 0 + C8 stn g2 )]
If we now let
CS coG OB
a
C sin s
a C, sin bl+
C,
+ C2 a"*6a
o" 0,
c sinm
then we have
+
oC
0 aao
~{C*
sin 0 sin
8
]
or
.ca
cos(
-
)
for e > 0
Thus pattern 1 is ooservod under addition.
The negation operation is defined by multiplying all point values
of the map by minus one.
giving -C cos ((
- 180 o ) -
This Is equivalent to replacing
o)
for e
> 0.
by (1800 +
Thus pattern 1 is conserved
)
24.
under negation.
It diould be noted that the orientation is not unique
unless C is always taken as non-nsgative.
Subtraction of map A trm sp 8 is per emed by the subtration of
the point values of A from the point values of 8.
This is equlvalent
to the additio of map B and the negative of ap A, so pattern I is
conserved under the operation of subtraction.
the point seas.
A saen map is obtained by taki
map of a finite
Sines
Bease the man
maber of pattern 1 saps is also a pattern I asp.
v' a v -
e v' is a pattern map.
Tor our analysis we had wind
eports frm the Amundein-Sott
station, situated exactly at the soath pole.
pute the man wind vector at the pole.
map at the nelghbaJhood of the pole
This peramitted us to com-
It was then easy, to dram the v
knowing C and
,
assumed constant,
in this anighboshood.
In the ame manner and with the sne assemptions and conventions,
we made a study of the coaiguration of the 0 (v)
and
0 (a)
isolines
over a mall nelghbbohood centered at the south pole.
The standard deviation 0 (v) is estimated by
()
/ N-I
Maps of a Cv) will have positive values everywhere in the aesghborhood
25.
£ > 0.
It has been adown that the v' sap has the pattern -C coe (j enc
the value at in
The map of
point of the asp v '
16 C coos (C -
wOuld have the value
(v')
C' cos(
-
)
/2
C + 3/2
jCa cow 2(0 -
Now
A) + Cga coo 8( - 0s)
C, cos 2(0 -
h
2 sinta
C1 (oos 2 cos
2
ca2 (eos
aWA + sin 20 tna a 2 )
a co
sina
+ C88
coo *
coo 2 (Cla
a (C,0a
+ sin
in 2J1
)
coo 2e )
+ Cs2 sin
s)
If we elL
ca 2 cos 2k
a C,' cos
C8 2 sin 20
a
C1 a sion
a 20
+ C 2 cos
2
, + Cs
sin 2a2
we have
+ C8 a sin V sin 296
ca8 coo 20 coo a2
or
Cg2 coo 2
(m-
)
Mo)
o)
).
26.
C Cos 2 d
bence 1/2
1/2 K2 co
)
anm be written
2( - ON)
This tero is always inferior or equal to 2/2 L CR
X a along the
eridians 0. and (Ol + 1800o)
(OX + 900) ad
)s
W
ca + EP- > 0
in conolwsion, In a mall neilhb
e > 0, a (v) is maxim
minimum along the meridians
that the
a
to -42 along the mseridans
and (0 + 800)O
(OX - 600)
Along theseridians (O + 900) a
for
Is equal to
*90),
Along the meridians 0
L
And it
hood centered at the pole, but
along the meridlsans
(
E
490
)
ad (
O ) and
and C( + 180
900)
It
osn easily be
(a) map is just the 0 (v) map rotated about the pole 900 1to
the west.
For
our analysis, the standard deviation of two componeant
of the
wind at the pole, namely in the 00 and 900 E directions were computed.
Taking acont
of the consderations bhere above about the pattorn of the
0 (v) map near the pole
analysis of that region.
it was then possible to make a fa-rly good
27.
X. BIBLIOMRAPB
1
[2]
Buoh (1954)t Md.I.T,
Res. Pap., Cmbride, MPAs., No. 35,
GeopMy.
BtWr and White (19804)
Dept. Mt.o, Gen.
rclation ProJect
Final
Rep., Part 2, No. AT 19(122)1688.
[3]
Tclers
(190) Quarterly Journal of the Royal UMteorlogieal
Sootety, Vol.
5, No. 361.
Geop~s. Rea. Pap, Crbridge,
[4]
Mtnts and Dean (1982)s
[5]
Alt, Astapenko,Iopart (199)s:
eas. , No. 17.
IM! General Report Series
No. 4,
Waohiston, Do C.
[6]
Iarahml (192)s
MIT Dept. Mlt., General Ciraulation Project,
Report No. 6, Part I,
[7]
Barnes (192)
No. *(801l) 2241 and AI9(0o4)-5228.
Phb.D. Tbhesi,
MIT, Dept. Met.
28.
Table 1.,
Lit
atations
(Stations are listed according to 340 index
the letter W Indicates
numbers. Under B
Sandicates Radio Winds.
Pibsal;
ad
ttia
e
stad
Lftlade
23
49-.71
43-369
43t486
Trivmdra
Minicoy
Colambo
0B 29 N
08 18 N
06 64 N
76 t 2
73 00 E
5982
R
W
R
484694
61-832
Stagapeo
Conakry
01 18 N
09 3 N
103 58 E
13 37 W
R
R
6e31
Sl. Tme
00 238
06 43 E
01-9 7
61-474
Diego GOavea
07 14 5
10 3s 8
72 26 E
56 48 E
W
28
41 6
26 8
18 a
0 N
0 8
18
48 8
08 N
SON
19 6
38 8
5 S33 E
88 27 E
67 40 E
57 30 E
S8 44 E
32 32 E
36 49 E
30 12
18 17 E
30 13 E
15 18 E
27 32 E
W
W
R
W
W
R
R
W
R
W
R
R
08 48 E
18 342
R
42 3
20 E
56 1
12 E
18e
32 E
R
R
R
R
R
R
1e-988
681-988
61-993
61-495
638430
83-708
63-741
63-94
64-005
684-076
64-210
64-300
Agalega
st. Btnadon
Rodrlgts
Pample Moumss
acos
Addli Ababa
Entebbe
Nairobi
DSPerm4 laa
Coqulahatville
Bunai
Leopoldwille
ElIabethrille
64-601
64-860
Port-Gentil
Bans
00 42 8
04 22 N
64-910
201
65-878
86-160
867-00
67-086
Dosala
Lagos
Abidjan
Loanda
Diego-gnsws
Tananiarre
04
06
05
068
12
18
67-197
Ft. Dauphin
25 02 8
46 48 E
867-41
07-198
67-587
87-63S
Mlgpme
N'lle asterdim
25 O
3750
13 e
14 28
8
8
32 34 E
TI? 4 E
W
R
8
33 45 E
R
8
28 21 E
R
Lilonlgu
Bromn Hill
16
19
20
20
09e
00
01
06
00
01
04
11
01
35
18
0
IT
4
N
N
N
8
8
8
00
03
03
13
49
47
29.
fiLattu
EIdIe
IIM
LonIltatdS
4
07-774
Sallsbeuj (Obervatory)
17 50 8
31 01 E
R
8-100
8-032
68-262
406
66-442
68-588
66-816
68-906
688-994
78-806
81-405
82-400
82-798
83-781
84-129
84-377
84-390
84-452
84-6831
84-691
85-406
85-442
86-487
65-543
8-879
88-801
87-187
87-344
87-576
87-598
87-715
87-748
87-774
87-860
87-938
88-890
88-952
88-968
fBawkopend
MaUn
Pretoria
leander Bay28
Bloestontein
Drlban
Capetown
Gough Island
Rio Gallegos
Albrook
Cayenne
ernando Noronha
Monteiro
See Paulo
aquil
O
Iquitos
Talara
Chiciavo
Lita
Piso
Arica
Antofagasta
Valleima
Quinter
Los Cerrillos
Puerto Montt
M.A. Resistencia
Meteo Aero Corbuba
LEefa
Punta Indlo
Neuqen
Base Aerea Command Epoa
Maquinehao
Coaodoro Rivesdvia
Ushula
Port Stanley
Arentin. Island
Orcadas
22 41 8
19 5o 8
25 46 8
8
29
8
07
29
29 80 8
33 88 8
40 08 8
46 81 8
08 a8 N
04 50 N
03 50 8
07 53 S
2 s33
02 10
03 45
04 34 8
06 47 8
12 04 8
13 45 6
18 22 8
23 28 S
28 36 8
32 47 8
33 30
41 27 8
27 28 8
31 19 6
84 80 8
35 22 6
8 ST 6
38 44 8
41 15 8
45 47 8
84 48 8
51 42 6
65 15 8
60 44
14 31 E
23 26 L
28 14 E
E
26 11 E
31 02 E
18 36 .
09 58 W
37 52 E
79 34 W
52 22 W
32 28 W
37 07 W
46 38 W
79 52 W
73 11 W
81 15 W
79 50 W
77 02 W
76 14 W
70 21 W
70 26 W
70 47 W
71 32 W
70T42 W
72 50 W
58 59 W
64 13 W
32 W
57 27 W
68 09 W
62 10 W
68 44 W
67 30 W
68 19 W
57 52 W
64 16 W
44 44 W
R
R
R
R
W
R
R
w
R
R
R
R
R
R
I
W
W
R
W
W
R
w
R
W
R
R
R
R
W
R
W
w
R
W
R
R
R
30.
Inex
Stat 1a re
latitat
LIItiIde
I
89-001
89-009
89-022
89-043
89-125
Base
Nor
mundseen-Soott Station
alley SW
Ellsworth Station
Bywd Station
TO70 20 s
90 00 8
02 00 W
7681 9
77 43 8
80 00 8
'268 S W
41 07 W
120 00 W
R
R
R
R
R
89-162
89-522
Little america V
Base Belge
78 14 8
71 00 8
161 55 W
23 00 E
R
R
89-592
89-601
89-606
89-811
89-864
89-871
91-334
01-348
91-366
91-376
91-408
91-413
91-680
91-517
91-489
91-700
91-830
91-843
91-938
91-958
93-112
93-291
93-401
93-434
93-780
93-844
94-027
94-035
94-120
94-203
94-234
94-287
Mirz
Oazis
Bootok
Wilkes ZG0 Station
Williams Facility
Adare Station
Truk
Ponape
wavJalein
Majuro
Koror
Yap
Nandi
Honiara
Chrlstmas Island
Canton Island
AItuataki
Rarotonga
Tahiti
Repa
Whemnupal
GOsborne
Ghbesa
Wellington
Birewood
Inverauill
Laee
Port Moreab
Darwin
Broome
Daly Waters
Cairns
8
6
78
66
T77
72
07
068
08
07
07
09
17
09
02
02
18
21
17
27
36
3S
40
41
41
46
06
09
12
17
16
18
s66 8
168
6
15 8
0
28 8
28 N
8 N
43 N
05 N
20 N
29 N
48 8
25 8
00 N
49 s
52 8
12 8
82 8
90 8
47 8
40 8
12 8
17 8
29 8
28 8
43 8
26 S
26 8
S7 8
16 8
55 8
93
100
107
110
166
170
151
188
167
171
134
138
177
159
157
171
159
150
149
144
174
177
175
174
172
168
147
147
130
122
133
145
00 E
44 E
E
35 E
36 E
58 E
51 E
1S E
44 E
23 E
29 E
08 E
27 E
58 E
23 W
43 W
46 W
46 W
35 W
31 W
38 E
59 E
23 E
46 E
32 E
19 E
00 E
13 I
52 E
13 E
23 E
46 E
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
W
W
R
W
R
W
R
R
R
R
R
R
R
R
W
W
31.
LgI
18sta0.on
Latitude
kame
Lo.Itih
Z
94-294
Townsville
19 15 8
146 46 E
R
94-299
Willis Island
16 18 8
149 59 E
W
94-800
94-312
94-326
94-338
94-374
94-403
94-461
94-510
94-810
94-637
94-693
94-776
94-791
94-821
94-865
94-907
94-910
94-926
94-968
94-974
94-986
94-995
94-996
95-502
96-413
96-933
97-602
97-580
97-690
97-980
Carnarvon
Port Dedland
Alice Spring
Cloncury
Rockhampton
'Geraldton
Giles
Cherleville
Guildford
Kalgoorlie
Mlldura
Williawtown
Cofts Harbour
Mt. Gambier
e lbourne
rast Sale
Wogga
Canberra
Western Junction
obaert
MOason
Lord lowel Island
Norfolk Island
Dtmont d'Urville
Kuching
Surabaja
Jefaan
Biak
Seatani Hollandia
erauke
24
20
23
20
23
28
25
26
31
30
34
32
30
37
37
38
S5
S5
43
42
67
31
29
66
01
07
00
01
02
08
113 39 L
118 7 E
133 83 E
140 s0 E
180 29 E
114 42 E
128 18 E
146 17 E
115 57 1
121 27 E
142 10 E
151 50 E
153 08 E
140 46 E
144 48 E
147 08 E
147 28 E
149 12 E
147 13 E
147 28 L
62 83 E
189 04 E
167 86 E
140 01 E
110 20 E
112 43 E
131 07 E
136 00 E
140 29 E
140 23 E
W
R
R
R
W
W
R
R
R
W
W
R
W
W
R
W
W
W
W
R
R
R
R
R
W
R
W
W
W
W
53 8
23 S
48 8
40 8
23 S
48 8
02 8
25 8
56 8
46 8
12 8
49 8
18 8
49 8
52 8
06 8
08 8
18 £
33 8
O 86
36 S
31 8
03 8
40 8
29 N
13 8
658
108
30 8
28 8
32,
Table
80
50
100
200
300
400
500
700
850
mean
-0.389
-0.058
-0.478
-0.661
-0.528
0.106
0.744
-0.40
o0.256
,*0.796
0.594
-0.683
0.142
0.706
0.140 -0.128 -0.159
35"
30
'1v m..c
65%
70"
-0.403 -0.650 -%.656
0.228
0.436
=0.036
0.064
-0.136
-0.358
0.997
l.
25"
20CY
60
,
0.611 -0.403
-0.489
"0.225
.-0680
-0.283
'-0.494
0.486
0.828
-0.389
0.267
-0.183
-.033
-0.244
0.500
0.811
-0.001
0,179
50
55
45
40
0.586
0.511
1.742
1.067
1.036
0.561
0.292
0.172
1.186
1.236
2.919
1.944
1.556
1.058
0.603
0.103
1.272
2.036
3.331
2.386
1.289
0.756
0.250
0.358 0.641
1.111
1.368
0.061
0.050
0.969
0.425
0.442
0.153
0.267
0.428
15"
50
100
200
300
400
500
700
850
0.908 0.742
2.167 1.581
2.986 2.550
1.961 1.608
1.406 1.097
1.0106 0.456
0.450 0.503
0.475 0.472
0.469
0.867
1.850
1.164
0.533
0.242
0.317
0.556
0.172
0.139
.656
0.339
0.014
0.111
0.419
0.647
-0.028
-0.272
-0.486
0.347
-0.203
mean
1.202 0.962
0.672
0.360
5f
-0.136
-0.481
-1.4l28
0
a0.231
*0.114
0.478 0.372
0.786 1.083
0.236
-0.578
-1.975
-0.906
-0.114
-0.097
0.450
0.967
-0.281
,0.611
-2.214
-.0.919
0.067
-0.044
0.392
0.703
0.130
-0.079
-0.153
-0.739
-0.0131
0.006
1.664
S3.
Table III.
80"
75'-
70r
50
10r
20
30
400
-0.543 -0.522 -0.497
-0.368 -.0.261 0.241
0.296 0.070 .0.o97
-. 176 -0.350
*0.597
-. 0n76 -0.533 -0.435
500
-0.276
700
850
-0.498
0.857
35'
50
100
200
300
400
500
700
850
0.400
t0.524
30"
250
0.022
0.872
0.301
0.865
65N
fv)' a/see
60(
0.610
-0.488
-0.224
0.649
0.282
-0.582
0.528
0.088
0.362
*0.212
-.0.494
-0.423
0.487
0.828
20
-30.294 0.235 -0.203 0.188
.965 0.604 0.195 ,0.221
1.784 1.573 1.178 0.296
0.759 0.931
0.492 *0.021
0.204 0.120 -C.139 -0.346
-0.196 -0.521 -0.430 -0.249
-n.752 -0.474 -0.355
0.059
0.727 -0.505 -0.116
0.287
551
50r
-0.297 0.055
-0.308 -0.130
0.611 1.101
0.067 0.426
0.084 0.395
0.205
-0C.080
0.321 -0.091 -03.349
0.632 0.069 -0.469
15"
'-0.158
.0.402
-0.616
-0.477
-0.333
-.0.161
0.348
0.656
10"
-0.142
-0.487
-1.434
0.745
0.237
-0.120
0.366
1.077
45
0.075 -0.096
0.125
1.808 1.963
0.833 1.018
0.445 0.296
-. 053 -0.079
0.508 -i.612
-.1.008 -1.118
5'
-0.157
-0.499
-1.896
-0.827
-0.035
.0.018
0.529
1.046
40"
-0.138
0.458
w2.061
.0.766
0.220
.109
0.545
0.856
s3.
Table IV,
80"
50
100
200
300
40n
500
700
850
65"
60"
55"
50
7.56 7.46 7.39 7.26
6.31 7.00 7.56 8.07
8.87. 9.58 10.37 11.28
11.95 12.67 13.18 13.99
10.71 11.31 11.92 12.96
10.64
9.43 9.79 10.9
7.81 7.88 7.81 7.86
6.21
6.88 6.53 6.14
6.92
8.42
11.99
15.03
13.59
11.20
8.05
6.63
6.52
6.10
350
50
100
200
300
400
500
700
850
75m
300
70"
[o()j */sec
250
4.61 4.11 3.82
7.66 7.28 6.92
13.09 12.57 11.81
13.66 12.46 11.11
11.08 9.78 8.60
9.49 8,09 7.00
7.21 6.43 5.56
6.13
5.58 4.80
45"
40"
5.67
8.51
12.49 12.78 13.04
15.83 16.10 15.62
13.88 13.76 13.12
11.50 11.54 11.24
8.26
8.14
6.88. 7.03 7.03
5.12
8.09
13.22
14.70
12.21
10.62
7.88
6.65
8.73
150
10
3.73
6.46
10.30
9.82
3.69
5.97
8.97
8.23
6.13
4.82
3.81
5.29
4.24
3.41
3.73
5.58
7.79
6.87
5.27
4,45
3.77
3.20
200
7.50
6.29
8.76
50
00
3.81
5.23
6.80
5.76
4.34
3.81
3.35
3.84
4.88
6.13
4.78
3.77
3.50
3.25
3.01
2.89
35,
50
100
200
300
400
500
7ro
850
50
100
200
300
400
500
700
850
Table V.
0S (v)
/see
50" - 45'
80"
75"
70
65
60'
55-
3,62
3.25
2.64
2.60
2.49
2.25
1.56
1.89
3.50
3.15
2.77
2.47
2.35
1.97
1.46
2.01
3.03
2.61
2.09
2.05
1.75
1.45
1.18
1.71
2.62
2.57
2.05
1.97
1.70
1.56
1.87
1.70
2.21
2.46
2.05
1.91
1,76
1.66
2.25
1.77
1.70
2.04
1.92
1.77
1.60
1.54
2.35
1.73
1.33
1.54
1.73
1.66
1.41
1.46
2.21
1.65
1.51
1.60
2.09
1.79
1.43
1.44
1.90
1.57
35"
30r
25"
20^
150
10
5'
On
0.78
1.81
2.03
1.94
1.49
1.30
2.05
1.47
0.93
1.66
2.54
1.95
1.38
1.64
1.66
1.68
0.93
1.63
2.67
1.80
1.42
1.44
1.68
1.60
0.75
1.44
2.48
1.83
1.62
1.39
1.40
1.446
0.58
1.13
0.45
0.31
0.73
1.57
1.37
1.04
0.24
0.72
1.31
1.31
O.87
0.65
0.63
1.14
1.96
0.97
1.45
2.08
1.57
1.50
1.20
1.24
1.68
0.93
1.75
1.40
1.29
0,90
1.26
2.28
40n
1.46
2.26
2.37
2.03
1.36
1.34
1.73
1.51
70
Fig. I.
60
VJ decimeter
50
sec "
40
Apr - Sept
30
1958
70
Fig. 2. jj-(V]
60
m/sec
50
Apr-
40
Sept
20
1958
10
I_1PD-s~~--llil----XiY~ii*~~~IIII1.1IDI^-11
111~-s_~
0
30
0
0
700
-44
850
70
60
50
40
20
30
I
Lotitude (ON)
Fig.3.
EV]
dm sec - '
Buch
Summer N.H.
ossumed decreose to zero of p= o
z200
oo-
1-0
S4000
0
cQ.
\
-.25..
/0
25
Latitude (!N)
Fig. 4. EV.
m/sec
Tucker
Summer N.H.
XI
300 -
500-
0
S-4
700 -9
850
70
60
50
30
40
Latitude
Fig. 5. EVJ
dm
sec-
20
10
(O N)
l
Buch Winter N.H.
assumed decrease to zero at p= 0
200 .25
600
S8
25
0
I800-
70
60
50
40
30
20
10
Latitude (ON)
Fig.6. C V
m/sec Tucker Winter N.H.
~~CIIUTX--_-IIII~
700-
8
70
4
60
Fig,7.C,LO"V)
50
30
40
Latitude (oN)
m/sec Buch
20
Winter
IC
N.H.
--
o~
6.
_oo
2e
-IN
o
4
1391.
+P
Sm/se$
6-
Apr -Sept 1958
850 mb
~-
crno~-r
.W3
.Po
o
433ft
o
433"
o
433"
o
433?1
ess,
0
N
.022
o
e
*
B
\
I....
ao
3
.45
.3
743\
.,
oo
II
3
o
o
NO
S
6oo
Isp
.4mse
~lo;---~
M41o
r-
L
i_-- i-
"+
Set15
2o
200o
o
0
.33"
0
433n
OL
.a."
020,,
0
44
1 \
I.N
so
\..
IOWIN
-00
mJi
lk,,
o
\
'Apr
-Sept 1958
b.
1
soo~
me
B
-
Apo.-Sp
o
o.
0
o
433"
oL
0
-3m
0
.M
0&
o
we
de
at.
\0
OM
5
** m
5
JI
n
'
..
\1K
4
sr
og
o
65
44
.t--~
+
sOmm
.4
00
6
oi
"
10
oe
1
,.7
54
*L
,.oAp
195
Apr-Sept
4
-ep.
10 m
+
sYo
I
'
I
3.
10
t
113
o9
00m
ko
95
0
.33"
4&