THE EFFECT OF AN UNBIASED GRID IN DETERMINING THE KINETIC
9NERM &MANCX OF TfMNORTH
____g_&N MXjSpH g
by
B.S.,
HAROLD CYRIL WALKER
Pennsylvania State University
(1963)
SUBMITTED IN PARTIAL FULFILLMENT
OF THE REQUIREMENT FOR THE
DEGREE OF MASTER OF
SCIENCE
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
August 18, 1969
Signature of Author
Department of Ateorology, 18 August 1969
Certified by
Thesis Supervisor
Accepted by
Chaip n,
NSN
fepartmental
Committee on
Graduate Students
- - ___L_
V...w
Z-- - " -
-
- - _' I
- -
A '
Harold Cyril Walker
Submitted to the Department of Meteorology on 18 August
1969 in partial fulfillment of the requirement for the
degree of Master of Science
ABSTRACT
For the past several years computational studies of such
topics as the northern hemisphere kinetic energy balance and related subjects have been performed by the Planetary Circulation
Project of the Massachusetts Institute of Technology. Numerous
integrals required were recently evaluated directly from a fiveyear period of observations using a network of nearly 800 stations.
The stations, however, were concentrated primarily over temperate
latitude continents, and the data from maritime and tropical areas
The question then arises whether the
were compartively sparse.
The problem undertaken in this thesis
results are representative.
uniformly spaced stations and to
more
of
subset
was to select a
balance. This was accomplished
energy
kinetic
recompute the zonal
presented.
and the results are
Thesis Supervisor: Victor P. Starr
Title: Professor of Meteorology
TABLE OF CONTENTS
I
INTRODUCTION
II
ANALYTIC CONSIDERATIONS
III
METHOD OF ANALYSIS
IV
DEVELOPING AN UNBIASED GRID
V
ANALYSIS
VI
EVALUATION
Eddy Terms
Coriolis Terms
Other Considerations
Summary of Conclusions
TABLES 2 -
17
BIBL IOGRAPHY
ACKNOWLEDGEMENTS
-~
-1
%.
-
-.
AI
4.
LIST OF FIGURES
1.
2.
3.
4.
5.
6.
7.
Complete set of stations used in the June 1968
computations
Reduced set of stations of unbiased network used
in March 1969 computations
Vertical meridional cross sections of wind components and stream function
Vertical meridional cross sections of momentum
transport and angular velocity
Vertical meridional cross sections of the generation of zonal kinetic energy
Vertical meridional profiles of the quantities in
Figs. 3-5
Illustration of the problems involved in computing
18
19
23
25
27
29
35
[IT]
LIST OF TABLES
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
Generation of zonal kinetic energy in the atmosphere
Station list and percentage of observations
60-month vertically averaged wind components
60-month vertically averaged profiles of momentum transport
60-month vertically averaged generation of kinetic energy
Spring vertically averaged wind components
Spring vertically averaged profiles of momentum transport
Spring vertically averaged generation of kinetic energy
Summer vertically averaged wind components
Summer vertically averaged profiles of momentum transport
Summer vertically averaged generation of kinetic energy
Fall vertically averaged wind components
Fall vertically averaged profiles of momentum transport
Fall vertically averaged generation of kinetic energy
Winter vertically averaged wind components
Winter vertically averaged profiles of momentum transport
Winter vertically averaged generation of kinetic energy
8
41
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
I.
INTRODUCTION
For more than 200 years the theory of the general circulation of the atmosphere has been undergoing continuous modification
as inadequate hypotheses give way to improvements based on observational fact.
As late as the mid-1930's efforts by Hadley (1735),
Ferrel (1856,1859) and others had resulted in what appeared to be
an acceptable three-cell, atmospheric general circulation scheme to
account for the mid-latitude mean westerlies and low-latitude mean
easterlies.
The different wind regimes were thought to be caused
essentially by the balance between Coriolis forces and friction
acting on zonally averaged flow.
However, Jeffreys (1926) suggested
that eddy actions might be able to account satisfactorily for the
required poleward transport of angular momentum.
A transport was
required since the rotation of the earth against the mean easterlies
in the tropics would impart a torque on the atmosphere, and, conversely, westerlies would impart a torque on the earth at higher
latitudes.
Clearly, a poleward transport mechanism for angular
momentum must exist to account for the balance.
Unsatisfactory explanations in terms of mixing length theory
were unable to cope with the requirement that momentum be trar-sferred from~ regions of low angular velocity (tropics) to regions
of higher angular velocity.
Further, traditional eddy viscosity,
if acting alone, would require the atmosphere to revolve eventually
in solid rotation.
Some combination of transport by the mean meri-
dional circulation and turbulent mixing was the mechanism originally
thought to be important.
In time researchers came to believe that
some modified mechanism must be present.
In 1948 V. P. Starr, following Jeffreys, proposed that tilting
troughs and elliptical closed circulations could account for the
required momentum transfer needed to maintain the westerlies against
friction.
A NE-SW tilting trough would transfer positive momentum
poleward across latitude circles in the northern hemisphere.
The
transport could be determined by calculating the covariances of the
wind components multiplied by appropriate terms to account for the
density of the air and the shape of the rotating earth.
The stbject
is so well known by now that no further explanations are in order here.
Subsequent momentum transport computations by Widger (1949),
Mintz (1951) and Starr and White (1954a) produced convincing evidence
that the required transport was in fact accomplished mainly by the
eddies (tilting troughs and ridges, etc.).
Transport by the mean
meridional circulation was found to be small.
Later calculations
using more data were designed to better evaluate the magnitude of
the transport by transient eddies, standing eddies, and the mean
meridional circulation.
The Planetary Circulation Project at M.I.T.
collected five years of daily upper air observations from May 1, 1958
to April 30, 1963 for 704 stations in the northern hemisphere, and
the calculations were repeated.
In these computations the zon&l
kinetic energy balance was also evaluated.
The results were both encouraging and perplexing.
Contributions
to the kinetic energy of the mean zonal easterlies and westerlies by
the eddies were significant as had been shown a few years earlier.
7.
The Coriolis force acting on the mean meridional circulation was
found to be applying a brake on the atmosphere, but to such a
large extent that
very little kinetic energy would be left over
for dissipation by frictipn.
Efforts over the next year were devoted to an evaluation and
improvement of the objective analysis techniques used, but the
most significant change resulted when the calculations were repeated
in June 1968 after about 95 stations were added in the tropics,
Values obtained from this larger list of 799 stations are shown
in TABLE 1 opposite the row labeled June 1968.
The data listed
after the row labeled March 1969 will be explained later.
The 1968
results were more acceptable than previous computations in that the
contribution from the mean meridional circulation term was somewhat less negative; however, the trouble that existed in the previous analyses was still evident.
putations were still unacceptable.
Magnitudes in the seasonal comIn spite of the improvements
with the addition of the tropical stations, the Coriolis term (mean
meridional circulation term) still remained too large.
The change
after the addition of the tropical stations suggests that results
could be further enhanced by a better network of stations.
Even
with the added data from the tropics, the vast majority of stations is still located over the most densily populated land areas
of Europe and North America, and comparatively few stations exist
over oceans, especially tropical oceans.
the Coriolis term is
The question arises whether
sensitive to a land-ocean bias in the stations
TABLE 1:
Generation of Kinetic Energy in the Atmosphere
-1
20
ergs sec , the numbers in the following
Expressed in units of 10
table represent the values obtained for the generation of kinqtic
energy in the northern hemisphere for the periods indicated by the
prooesseo described in the left-hand column. The firat not of
values represent those calculated in June 1968 from the full list
of 799 stations. The second entry represents the values obtained
in March 1969 from the reduced set of 206 stations. The difference
between the two calculations is the third set of numbers.
5 Years
60 months
Spring
15 months
Summer
15 months
Fall
15 months
Winter
15 months
Transient Eddies
6.9739
6.8452
5.5754
5.4923
5.101
4.739
6.9200
7.2024
4.8967
5.6653
-0.1287
-0.0831
-0.362
+0.2824
+0.7686
0.3678
0.2515
0.4553
0.4044
1.855
1.377
2.1121
1.6820
1.2801
-0.1683
-0.1163
-0.0509
-0.478
-0.4301
-1.4484
June 68
Mar 69
Difference
Standing Eddies'
June 68
Mar 69
Difference
Mean Meridional Circulation
Jun 68
Mar 69
Difference
~
-5.251
-3.653
-12.4950
-10.6103
-6.921
-2.048
3.3490
2.7529
+1.598
+1.8847
+4.873
-0.5961
-4.439
-3.961 _
+0.478
9.
used in the computations.
What would be the result if a net-
work of stations were chosen so that the land-ocean bias were
reduced as much as possible?
This question was investigated in
some detail, and the results will be discussed after some analytic
considerations are presented.
10.
II.
ANALYTIC CONSIDERATIONS
The following is essentially that development presented by
Starr (1968) and is included here for completeness.
A quantity may be defined as comprising an average value and
a departure from that average value.
In our problem involving com-
ponents of the wind field the portion of the wind that blows from
the west,&L., can be defined as
?
--
(1)
where the brackets represent the longitudinal average along a latitude circle,
at
and 14*
(2)
represents the departure.
Here
represents longitude.
The quantity,t4( , may also be described in terms of its time mean,
where the bar represents the time mean and the prime represent3 the
departure from its mean value.
An analogous treatment, of course,
applies to the southerly wind component, V .
positive toward the north, and
The latter will 'e
"- will be positive toward the east.
To compute the poleward transport of some atmospheric quantity,
-.
* '% Ar
W, ,
11.
we need to consider the product of that quantity and the poleward
component of the wind,
V
would then be
sions (1)
V .
and (2)
where
,
is
the density.
are substituted for M4. and V
where such quantities as
Here
The transport of momentum per unit volume
U'
,
If
the expan-
we have
are discarded because they are zero.
. will be assumed sufficiently constant at a constant
pressure surface along a latitude circle to be removed outside the
brackets.
The first right-hand term represents the effect of the mean
The second term is a time and longitudinally
meridional circulation.
averaged product of temporal deviations and represents the effect
due to transient eddies.
The last term is the equivalent represen-
tation for standing eddies.
Time averaging has been performed before
space averaging.
Considering now the transport of absolute angular momentum,
across a latitude surface, we may write
V(5)
M
may be resolved into the part due to the rotation of the earth,
1,.
,
and a part due to
M
LA.
Thus
e-
(5).
(, I (
12.
where J2.=
R COS
the distance to the axis of rotation;
is
is the latitude.
is the mean radius of the earth, and
RI
Sub-
stituting into .(5) we have
a vcLX I
+~~
/0f
vc x/P
./1
(7)
The first integral represents the mass transport across a latitude
The second term
surface and must be zero in the long-term average.
represents the transport of relative angular momentum.
The torque applied by
Pu4 l
in (7) acting across a unit
area of a vertical surface of constant latitude is
or -a 7714 4
s (2
.
Z77^-
4/ V
Then the net torque in the zonal direcand unit depth is
tion upon an annular volume of width
- zrr
-
_. puVR'eos')
')
(8)
After eliminating boundary terms, the generation of kinetic energy
in a polar cap can be written, with the help of (4), as (see Starr
1968)
Vj6OS~_(
t
)(9
(10)
(11)
13.
or the system may be written in pressure coordinates.
The Coriolis
effect has been included in (11) and that integral could have been
written in a form symmetric with (9) and (10).
See Starr and Gaut
(1969).
It can be seen from (9) and (10) that kinetic energy can be
produced only when momentum is transported against the gradient of
angular velocity.
The Coriolis effect in (11) will result in a
loss of kinetic energy whenever
related.
and
C-j
are negatively cor-
Equations (9) and (10) may also be described as the con-
version of eddy kinetic energy to zonal kinetic energy through eddy
(Reynolds) stresses.
Fourier analysis by Saltzman and Teweles (1964) shows that
hemispheric wave numbers 1 through 15 all furnish kinetic energy to
the mean zonal flow by this negative viscous effect.
Dissipation
occurs through molecular stresses and by retardation by (11).
An analogous treatment of the vertical velocity would result
in another set of integrals as would inclusion of boundary considerations.
The vertical velocity is, however, small and difficult to
determine, and the transport between the hemispheresacross the equator must also vanish in the long-term average.
integrals, then, would seem to be (9),
The significant
(10) and (11).
They were evaluated for the northern hemisphere by Travelers
Research Center (T.R.C.), Hartford, Connecticut, through use of finite
difference techniques and objective analysis methods.
automatic computation
Programs for
were written by T.R.C. under contract with
14.
M.I.T. and computations were performed on the UNIVAC 1108 of the
U.S.
*
Geophysical Fluid Dynamics Laboratory at Princeton.
Environmental Science Service Administration's.
15.
III.
METHOD OF ANALYSIS
The five years of data originally used in
these analyses
consisted of daily upper-air observations from all available
stations in the northern hemisphere and extended as far as 20
degrees into the southern hemisphere.
The data were obtained
on tape from the U.S. Weather Bureau's National Records Center
as Asheville, South Carolina.
Programs were developed so that
observations that exceeded normal expectations in various ways
were discarded, hopefully eliminating most erroneous observations.
By 1968, 799 stations had been checked for usable information.
At this point the time averages of Lt and V were computed
From these values
for each station at each of 20 pressure levels.
the covariances of temporal deviations, A'v'
, were developed and
these were averaged in both time and analyzed in space to produce
Similarly, the standing eddy term
computed.
[*
q],
was
From these and other quantities cross-sections were
analyzed and printed out by the computer.
The cross-sections
were copied in drafted form so they could be reproduced.
In the objective analysis, values were determined for each
10 degrees of latitude and longitude, except near the poles where
five-degree blocks were used.
From these fields values were in-
terpolated at two-degree intervals.
and
fields.
LEC
In all, the quantities [a]
were determined from these latter
16.
Available data was read in at 50-mb intervals.
Since most sur-
face pressures are above 1000 mb, climatological values were used
at that level when actual data were missing.
Further, when a value
was not available at the next higher 50-mb interval, the lower
value was used as a first guess for the upper value.
Also, time
averages for a particular station level were not computed from the
data at a given point unless at least 30 percent of the total
possible number of observations at that point were available.
This 30-percent cutoff was used to preclude calculating unrepresentative averages.
As we shall see shortly, the transient eddy term is the most
significant contributor to the generation of zonal kinetic energy,
and it is this term that cannot be evaluated from a mean map without
individual instantaneous observations.
In the objective analysis
this would not seem to present a serious problem except in certain
large areas of missing data.
This, then, is a brief account of the methods used in the June
1968 computations which will be compared with the results obtained
by this writer using an unbiased network of stations instead of the
total 799 stations.
Except for using fewer stations no changes were
made in the method of analysis so that the effect of a land-ocean
bias could be studied properly.
17.
IV.
DEVELOPING AN UNBIASED GRID
It was felt that by selecting a set of stations which were
uniformly spaced and equally distributed between land and ocean
areas any land-ocean bias could be reduced.
It was realized at
the onset that a perfectly unbiased grid could not be developed
because of the available station distribution, but if the integral
(11) because less negative, we would feel that a land-ocean bias
in the original network did exist and that it had been partially
corrected.
In order to develop an unbiased network it was first necessary to reduce the number of stations over continents (there was
of course no way to add stations over the oceans).
It then became
essential to select only the best stations from which data were
available.
The latter requirement involved checking the total number of
observations recorded by each station at each of 10 pressure
levels.
"Good" stationsbecame those that had at least 30 percent
of all available observations at all pressure levels from 850 mb
to 100 mb, inclusive.
"Mediocre" stations were those that had at
least 10 percent at any pressure level.
These latter stations
were scanned for whatever usable information they contained when
it became necessary to use them for lack of other data.
Stations
with less than 10 percent were discarded.
The vast majority of missing observations occurred at 1000 mb,
70 mb and 50 mb.
But discounting these levels, 396 stations
18.
Fig. 1.
-
Dots represent locations of stations at 400 mb
which had at least 30 percent of the total possible observations available. They approximate
the distribution of stations used for all levels
in the June 1968 computations. The outer latitude
circle
represents
the
equator.
The
addi-
tional stations in the southern hemisphere were
used to improve the tropical analysis.
19.
/~~~~
Fig. 2.
@
This subset of 206 stations represents a network
which has a minimum land-ocean bias. Those stations which have at least 30 percent data from
850 mb - 100 mb, inclusive, are represented by
circles. Some stations with less than 30 percent
of the data at all levels were added to improve
the tropical analyses. These stations are represented by triangles.
20.
remained that had 30 percent at each level from 850 mb to 100 mb,
inclusive.
This set became the basis from which the unbiased
grid was attempted.
Because some crowding still existed, 182 of these stations
were eliminated.
Tropical areas were deficient and 62 of the 10-
percent stations were added to balance out the lower latitudes.
Roughly half of the original 799 were deficient in some serious way.
The final network is shown in Fig. 2, which should be compared
with Fig. 1.
Th.e latter figure represents the distribution of sta-
tions at 400 mb which had 30 percent of the total possible observations available.
The 400-mb set is reasonably representative of all
levels except 1000 mb, 70 mb and 50 mb.
The 30-percent cutoff used
per level in the June 1968 calculations would have resulted in a
map similar to this.
Looking at Fig. 2 one notices that some bias still exists and
that there are virtually no data available in the eastern Pacific
and very little south of 30 degrees north latitude in the Atlantic.
Not apparent is the fact that practically no data were available
from below 850 mb or from above 100 mb from the U.S.S.R.
(This de-
ficiency is currently being corrected, but the data from these levels
are not included in the present computations.)
During the calculations a 10-percent cutoff was applied at
each station at each level as the data were used.
A 30-percent cutoff
could not be applied without eliminating absolutely essential, if
mediocre, data from the tropics.
The cutoff had virtually no effect
21.
on northern latitude stations since most of those stations had
densities far greater than 30 percent.
The remaining sections of this paper will be devoted to a discussion and comparison of the results obtained by this writer using
the so-called unbiased grid with the computations made in June 1968
using the complete station list.
TABLE 2 contains all of the information from which the unbiased grid was developed.
22.
V.
ANALYSIS
The numbers presented in TABLE 1 represent the integrated
values of expressions (9),
(10) and (11) in ergs sec
generation of zonal kinetic energy in the atmosphere.
1 for the
In the 60-
month column the biggest change between the June 1968 and the March
1969 computations occurred in the mean meridional circulation term.
It became less negative, as was hoped.
noted in the standing eddy term.
generation by transient eddies.
A small change was also
The most stable term was the
Roughly half of the zonal kinetic
energy generated or transformed from transient and standing eddies
is dissipated by the Coriolis effect on the mean meridional circulation acting as a brake on the atmosphere.
Of the 7.1..ergs seca1
generated, 3.7 are dissipated by this effect, leaving 3.4 units for
dissipation by friction.
The percentages involved here agree with
the required results obtained by Gilman (1965), who derived meridional circulations of the southern hemisphere from indirect methods.
Seasonal values in TABLE 1 were also calculated, and the
largest difference is again seen in the mean meridional circulation
term.
The spring values for the mean term are still much too large
negative, and it would appear that the atmosphere would cease to
function (see Starr, 1953) if these values represented the true
conditions in the atmosphere.
Summer values seem much more realistic.
In the June 1968 computations for this season, practically no energy
was left over for dissipation by friction, while in the March 1969
computations, the Coriolis effect dissipated only about one-third
23.
IU
MB
200
J
2
6
-
~
2--
5000
--
200-
-25
-
-
0
--
I3O
02
600-25
-
'
-5
O
0
-
'-O,
- -
-s
---------4
S 5
C
o
0I
0
0
-00
20
0
201\
~o
o
25
'
-So-10
-25
0
,
5
.
0
I~5
80
0
0
5C/
0
0
\_1
\'25
-SO-'40
0
-
0
400
26'-
200
10 0-
-25
--
-2
25
60
0
~-*
-~~\
2-25- - ,S
0
-o25
C --
~
20~'
SC
-25
26
2000
600-
-z.
-
- --------
1000
25
5
5
0
5
-5-10-
0
8
~
40
-- M
I
1
25--~ 60
-
-00
4
80
0
0
8
LAT TUDE
Fig. 3.
These panels represent vertical meridional cross sections through the atmosphere for the quantities
indicated. Column I was computed from the March 1969
unbiased network and is to be compared with column II,
which was computed from the complete network of stations
represented in Fig. 1. The upper panel represents the
mean zonal wind and is in m sec a; the center panel
represents the mean meridional wind and is in cm sec ;
the streamlines for the mean meridional velocities and
the mean vertical velocities are depicted in the lower
panel. Vertical velocities were obtained from continuity
considerations of [3v]. Units for the stream function
g sec .
(see Eqns. [12] and (13]) are 2 x 1
24.
of the total amount generated.
The same type of problem seen in
spring occurred in fall, except it appears that too much kinetic
energy is generated.
Here the Coriolis term contributed to the
total zonal kinetic energy instead of depleting it.
The winter
season was the only period where the standing eddy term showed a
marked change in contrast to the Coriolis term which changed very
little.
In all computations the transient eddy term changed least
of all.
Because of non-linear effects the sum of the seasonal terms
i s not equal to the values computed for the 60-month period.
A
possible explanation for the behavior of the terms seen here will
be presented after the comparison between the two sets of computations has been completed.
In the vertical meridional cross sections through the atmosphere which follow, column I represents the results obtained from
the unbiased network of 206 stations.
These values are to be com-
pared with the results obtained in June 1968 from the complete network of 799 stations presented in column 2.
Cross sections and
profiles are presented for the 60-month period only.
The top panel in Fig. 3 represents the mean zonal wind,
in m sec~1.
Plus values represent winds from the west.
sections are virtually identical.
mean meridional wind,
differences are noted.
[O
,
[U3
Both cross
The center panel represents the
positive toward the north.
Here some
The negative area in the middle latitudes
has been reduced, and the positive area further north has been increased.
Units are cm sec~1.
Values near the poles are suspect due
25.
[U' Vl Cos 2 S6
MB
200
600
1000
[U V*] COs
#
200
06-
---
600
-19I
-
-
1000
200
600
1000
0
20
40
60
80
0
20
40
60
80
LATITUDE
Fig., 4.
These vertical meridional cross sections through the
atmosphere represent the northward transport of angular
momentum by transient eddies (top panel) and by the
The mean angular velocity
standing eddies (center).
of the air motions about the polar axis are shown in
Units of the momentum transport are
bottom panel.
Units of
m2 sec 2 and are to be multiplied by 2TWR.
angular velocity are m sec~l to be divided by the
earth's radius, R, to obtain the relative angular
velocity. Column I was computed from the reduced set
of stations and is to be compared with column II, which
was computed from the complete network of stations.
26.
to lack of data north of 800 and are inconsequential because of the
comparatively small volume of the polar cap north of 800.
The stream function at the bottom of Fig. 3 shows some significant similarities and differences.
The driven cell in middle
latitudes is smaller in both size and magnitude.
The tropical cell
is slightly larger in size, but only slightly different in magnitude.
The direct polar cell is larger.
The vertical motions implied in
the cross sections were derived from continuity considerations of
the mean meridional wind component.
The picture was obtained by
fitting a stream function to the distribution of
The analytic form of the stream function is
VO
in center panel.
defined by
+j7 Iy(12)
066
2.77) dS
and
77"-2
where CA> is
<
.Units
(13)
do95~~
are 2 x 1011 g sec -
The top two panels in Fig. 4 represent the northward transport
of angular momentum evaluated across each two degrees of latitude.
The values given are of
L4 7C 05$5;
due to transient eddies.
Vf
showing the transport
The values in the center panel are of
showing the effect of standing eddies. Both
-2
2
The
*
, the units being m sec
are to be multiplied by 2 7~
COSIO
transient eddy term shown in the top panel is significantly larger
27.
MB
,
M B
cos2#0
M[TV,]
,
Z-([I]/Cos$
600
1
-
0.
6002d9
00
1000
(Z2
%.
-
.
0
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-9-0.2
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a3
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*
-
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600
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0.
.
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[U]cos
[i
__L
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I I.A I
son
I
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.
sin
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IU1CS$
2
600
--5
00.
'6.j
-00 1 0,,
100025,
00
~
-
0
0
600-
0
20
40
60
80
~
09
0
-
-.
-.
20
0
0
--
0
.
40
60
80
LATITUDE
Fig. 5. Generation of zonal kinetic energy by transient eddies
(top), by transient eddies (center), and by the mean
meridional circulation (bottom) is represented by thesei
vertical meridional cross sections through the atmosphere.
The top two panels represent the integrand of expressions
(9) and (10), respectively, and the .values, in m sec 8 ,
are to be multiplied by 2TR. The units of the bottom
panel are m2 sec" 2 , representing the integrand of expression (11). These values are to be multiplied by 47rAR /g.
Hemispheric integrals of the quantities are presented in
TABLE 1. Values in column I were computed from the unbiased network of stations while column II values were
computed from the complete list of stations.
28.
than the standing eddy terms shown in
the center panel.
The main
change in the computations of momentum transports by the transient
eddies is the high latitude smoothing in the 1969 analysis.
The
strong counter-gradient flux of momentum at lower latitudes from
regions of low angular velocity into the mean jet stream through
negative viscous effects is essentially unchanged.
The mean angular velocity of the air motions about the polar
axis is shown in the bottom panel of Fig. 4.
This panel was obtained
from the top panel of Fig. 3. The values given are ofU6lI1
m sec
in
1, and are to be divided by the mean radius of the earth,
to obtain the relative angular velocity.
..
Because the term becomes
indeterminant near the pole, very high values in this region develop
in the computations and were arbitrarily eliminated from the cross
sections.
Except for some such residual difference in the analyses,
very little change is noticed between the two computations.
Fig. 5. represents the production of zonal kinetic energy due
to conversions by transient eddies (top panel), standing eddies (center
panel), and the mean meridional circulation (bottom panel).
The top
two panels represent the distribution of the integrands of expressions (9) and (10) and are to be multiplied by
3
-3
are m sec .
2 771c .
The units
The bottom panel represents the distribution of the
integrand of (11)
and is
to be multiplied by
£ 7TR./.
No
.
significant difference exists between the two computations in the
top two panels.
The decrease in the values of the integral (11)
represented by the bottom panel is not immediately apparent.
The
T
29.
M/S
EC
40
20
12
6
0
-6
0
-20
M3/SEC
3
-
K.E.
GEN ERATION
M3/
--
-
12
6
0
.- 6
-12
-
--
-
SEC3
12
6
0
-6
-12
0
Fig. 6.
20
40
60
80
0
20
LATITUDE
40
60
80
These profiles represent vertical averages of the quantities presented in the preceding cross sections. In
the top two profiles the first quantity in the heading
is represented by the heavy line, the second quantity
by the dashed line, and the third quantity by the thin
In the bottom panel the production of zonal
line.
kinetic energy by transient eddies is represented by the
heavy line; the production by standing eddies is represented by the dashed line, and the production by the
mean meridional circulation is shown by the thin line.
[v] is in cm sec~1. Functions of [I only are in m sec~
2
2
while product terms of u and v are in m sec . Values
in column I were computed from the reduced network of
stations while the values in column II were evaluated
from the complete network of stations.
30.
positive area near 600 is larger, and even though the maximum value
of the middle latitude negative region is greater, the location has
shifted sufficiently so that the vertical average is less.
Fig. 6 represents the vertical averages of the quantities
just described in the cross sections.
heavy line in
the top panel,
is
Here
[a3
essentially the same in
except for some smoothing at higher latitudes.
holds for
£7 's
-5 $
is
.
both analyses,
The same observation
representing the angular momentum per
unit mass of the atmosphere.
m sec
, shown by the
Units for both these quantities are
[
The quantity of most interest in this discussion
shown by the thin line in
Since there is
the top panel and is
plotted in
cm sec
-1
no net mass transport of dry air across latitude cir-
cles in the atmosphere, this term should be essentially zero in the
long-term average.
South of about 400 the magnitude of the term was
decreased by the unbiased network.
North of 400 some "noise" was
introduced and the term is more positive.
300 and 400,
The extreme value between
In the
however, has been reduced by about one third.
energy calculations the vertical averages of [P] weresubtracted
from values at each level before the computations were made.
The
resulting vertical average would then be zero as would be expected
physically.
The center panel of Fig. 6 shows the vertically averaged
momentum transport across any particular latitude circle and the
angular velocity of the air motions about the polar axis.
transport per unit mass by the transient eddies is
Momentum
represented by
-I!
.
31.
_V
COS4 9
and is shown by the dark line.
transport is represented by
thin line.
L7z
1
The angular velocity is
of the latter are in m sec
-l
CosaJ6
The standing eddy
and is shown by the
shown by the dashed line,
Units
2
-2
while the other terms are in m 2ee .
The differences between columns I and II are slight.
Both columns,
however, vividly illustrate the transport of angular momentum against
the gradient of angular velocity.
The bottom panel of Fig. 6 is the vertically averaged distribution of the integrands of expressions (9),
(10) and (11).
The
heavy line represents the generation of zonal kinetic energy by
transient eddies; the dashed lines represent generation by standing
eddies, and the thin line represents generation by the mean meridional
The values of the integrand of expression (11) have
circulation.
been converted to the same scale as expressions (9)
reduction of I
and (10).
The
near 480N seen in Fig. 3 shows up here as a smaller
negative value in the Coriolis term.
The positive area to the north
is also larger.
The first conclusion from examining the cross sections and
profiles is that the reduction of stations produced very little
effect on the mean zonal wind or eddy terms.
are noted, however, in
[V
Significant differences
and in terms computed from it.
Throughout the discussion reference to the Coriolis term, the
mean term, or the mean meridional circulation terms all refer to
expression (11).
32.
VI.
EVALUATION
Two main questions now need to be considered:
How reliable are
the results obtained from these and previous evaluations, and why
has the Coriolis term been so negative?
Eddy Terms
It
(1964)
has been suggested by Lorenz (1967)
and by Priestly and Troup
that computations of momentum transport by transient eddies
are seriously affected by missing data.
Every station used in the
analysis had some missing observations, especially at higher pressure levels where strong winds exist, and presumably computations
would be biased toward lighter winds.
Some of this bias may have
been reduced by the objective analysis which used values at lower
levels as a first guess for missing data at higher levels.
When
the weather balloon was lost near the surface a light wind bias would
be propagated upward, and when the balloon reached jet levels before
being blown away, excessively high wind values would be propagated
into the region of lower winds above the jets.
Use of the unbiased
network cannot really answer this question of light winds since the
stations removed to form the network may have been biased in exactly
the same way as the stations which remained, but the fact that the
results computed from the reduced network of stations were virtually
unchanged is encouraging.
The question concerning the adequacy of the existing network of
stations in the northern hemisphere can be answered somewhat more
emphatically.
Ideally, one would want observations every few degrees
33.
but of course, this is impossible, and since no important changes
were noted when only one-fourth of the available stations were used
suggests that the same results would be obtained if more stations
were somehow added and that the atmosphere had been sampled
adequately,
at least for processes involving transient and standing eddies.
Further,.it was felt that since expressions (9) and (10) for
the eddy generation of zonal kinetic energy involve a triple product
of the wind speed components, reducing the total number of stations
would eliminate some extreme values and would result in a smoothing
that produced smaller values of the expressions.
Some smoothing did
occur, as seen in the profiles of Fig. 6, but the overall values
of the integrals was not reduced significantly, in contrast to the
value of the Coriolis term, which did change.
Coriolis Term
One possible explanation for the behavior of the Coriolis term
is that
[IV
represents a small difference between large quantities
and is therefore too sensitive to handle.
If this were entirely
true, then different computations of
and terms computed from
V
it should oscillate about some mean value and no pattern in the
results should exist.
term did result
Some oscillation in
(
and in the Coriolis
from the reduced network of stations, but the pat-
tern one would expect from an atmosphere with a tropical Hadley cell,
indirect Ferrel cell, and direct polar cell existed in both computations.
Profiles of
NO
in Fig. 6 should be zero since they
represent the long-term vertical and longitudinal mean condition
34.
and since there can be little or no net mass transport of dry air
across a latitude circle.
The consistency of the non-zero value
and the fact that they became less negative by use of the unbiased
network suggests the need for a physical, rather than a purely
numerical, explanation.
It was for this reason that the following
exercise was performed.
The experiment was not designed to dupli-
cate the objective analysis, but the same data were used.
In the experiment the value of
was computed as more and
more stations were added along a latitude circle.
The area chosen
to study was the latitude belt extending from 50 to 60*N because of
the comparatively high density of stations there.
The latitude
belt was then divided into 10-degree blocks from which stations were
selected.
Cumulative averages were developed and the values obtained
every time four more stations had been included were plotted on Fig. 7.
Stations were added symmetrically so that if a station was available
every time a 10-degree block was sampled a completely unbiased network would exist.
The abscissa in Fig. 7 represents the total number
of stations sampled.
The small triangles along the abscissa repre-
sent each cycle around the globe in an attempt to select a station
every 10 degrees of longitude.
The first triangle is plotted at 34,
indicating that two 10-degree blocks had no stations.
The ratio of
the number of stations found to the number missing formed what was
called the bias, which is also plotted.
The second triangle was
plotted at 61, indicating that a total of 11 stations were missing
after two cycles around the globe.
A 10-degree block with only one
35.
SIAS
SIAS
4
-
(U
s
-(
.
.
4a
)
-0
0.6
4
SA
(2)
[0] [
3
00.6
IS
-0.4
AS,
0
OFSTATIONS SAMPLEO
Fig. 7.
..
0.11
o 0
0
0
o
o00
o00
NUM9t1 Of
t
o
to 0
o
STATIONS SAMPLEO
0o
Two graphs which represent the results of an
experiment designed to illustrate the problems
Stations were added
involved in using [v.
symmetrically, four at a time, to form longitudinal averages in the latitude belt extending
from 50-60 0 N. Each small triangle at base of
graph represents one complete cycle around the
world in an attempt to add one station every
100 of longitude. The bias is the ratio of
the number of stations used to the number of
stations missing. [v) and the product term
becomes more negative as the bias increases.
36.
station would produce a missing station on every cycle after the
first one.
Results obtained at 700 mb are plotted in the left-hand portion of Fig. 7 next to the values obtained for 300 mb.
and
BothE§3
1 against the left-hand scale.
are plotted in m sec
Their
product is also plotted on the same scale although the units of
the latter are taken negative.
Negative values of the product were
plotted to facilitAte comparison on the same graph.
In both graphs values of [2
and lK1 appear to vary by
about the same magnitude, but the percentage of variation for
is much larger because of its- smallness.
doubles from 0.25 m sec
[0
At 700 mb, for example,
1 to slightly greater than 0.50 m sec
It is interesting to note that the most positive values of
occur when the bias is also the smallest.
_'3
At this point one could
assume that almost all geographical bias, or asymmetry in station
location, had been eliminated.
the absolute value of
[O
The product term, -j9[vI
In each instance up to six cycles
increased each time the biased increased.
,
also varied in the same way.
the effect was more pronounced, and
Es]
At 300 mb
and the product term even
changed sign at the point of minimum bias.
The profiles represent cumulative averages so that the addition
of fewer and fewer stations per cycle produced a decreasing effect.
The dependence of
on the symmetry is amplified further
by the values obtained on each pass before they were averaged with
preceding data.
These values of 1
from the stations selected
37.
on pass 2 only, for example, are much larger.
These values are
plotted next to the circle representing the pass number.
The implication of this simple exercise seems to be that
stations should be chosen symmetrically around the globe if
is to be measured accurately.
The decreasing values of N
nV
here
represent the strong bias toward Europe where the station density
was the highest.
One could surmise, then, that at these pressure
levels winds tend to blow more from the north at this latitude in
Europe than they do in the Pacific where fewer stations were located.
Of course, an accurate representation of a quasi-sinosoidal weather
pattern can only be obtained if measurements are taken from both
sides of the troughs and ridges.
As mentioned earlier, this exercise was not intended to duplicate the objective analysis used in evaluating expressions (9),
and (11), but merely to illustrate the problems involved in
(10)
handling
In the objective analysis adjacent stations and values from
lower pressure levels were used to estimate values when data were
sparse.
The objective analysis could not, however, create data in
large areas where none was available.
Hand analysis in these areas
of missing data, notably the eastern Pacific and Atlantic oceans,
produced no better results than the objective analysis; see Starr
(1969).
then
If either of these regions had persistent south winds,
would be too large negative since the positive values
in the region of missing data could not be included in the longitudinal average.
38.
This bias was precisely the problem under investigation in
this thesis.
Data from the oceans could not be increased but the
bias from the-continents was decreased and MV
became larger
algebraically.
The large seasonal variations of
at least in part, to the same effect.
[Vj
may also be attributed,
In the Pacific, for example,
if mean southerly winds existed in the region east of about 1550,
then
and the Coriolis term would be too large negative.
If,
on the other hand, seasonal shifts in weather patterns produced
[Sj
persistent north winds in this region of no stations, then
and terms computed from it would be much too large positive.
This
type of reasoning is not restricted to the Pacific; it applies to
any portion of the earth where the network of stations is too sparse
.for the objective analysis to handle adequately.
It seems from charts
of average cloudiness taken from satellite pictures that a special
physical condition of some magnitude exists in the eastern Pacific.
See, for example, Sadler (1968).
Further, data being gathered by
the University of Wisconsin suggests that the region is occupied by
clouds of all types (low, middle and high) which seems to indicate
some sort of dynamics other than air-sea interaction.
Synoptic
experience (Sanders, 1969) suggests that numerous cirrus streaks
are present, indicating a possible southwest-to-northeast jet stream
or wind flow.
Further investigation of this area, possibly from an
investigation of airline Doppler wind reports, is in order.
The conclusion then, from the preceding discussion of
;
and
39.
the Coriolis term, is that the negative values are due to a
biased sampling of the sinosoidal wind patterns of the atmosphere.
This suggestion is emphasized by the fact that the unbiased
net-
work produced more reasonable values for the Coriolis term for
the 60-month average than were obtained using all available data
in the northern hemisphere.
Other Considerations
WhilLe it is felt that asymmetry in any available network of
stations is the main reason for the inaccurate values obtained
for
[OJ,
other considerations must be discussed.
ment of equations (9),
(10) and (11) boundary integrals were omitted
as were vertical motion terms.
a significant effect.
In the develop-
Either or both of these may produce
Reliable vertical motions are difficult
to obtain, and it may be some time before such effects as diabatic
heating, for example, can be included in the formulations of vertical motions.
Inclusion of boundary integrals is more feasible,
and they will be evaluated in the near future by the Planetary
Circulation Project.
The fact that
LEI
See Starr and Gaut (1969).
was not zero in the vertical averages seen
in Fig. 7 may also be due to errors in upper wind measurements-and
it may not be possible to produce values of
better.
which are much
Ideally, one should calculate confidence limits for
and the Coriolis term in order to determine if the changes seen
by using the unbiased network are significant.
Unfortunately, such
calculations for the amount of data used here exceed the economic
40.
limits of present computer facilities.
Momentum transport calculations for the tropics by Kidson
(1968) varied between odd and even years, possibly due to the wellknown biennial oscillation. 'Data in this study comprised a five-year
average and one might suspect that a bias is indicated.
Further, work
by Newell et al (1969) suggests a biennial variation in the strength of
the Hadley circulation.
But the five-year sample used suggests a some-
what equal sampling of the different effects noticed on odd and even years.
Summary of Conclusions
In
spite of the questions still unanswered, it
would seem that
this study has shown that processes involving transient and standing
eddies have been evaluated as well as they could be evaluated even
with a greater number of stations in
hemisphere.
sparse data areas of the northern
This conclusion is supported by the fact that no important
changes were noted in the values obtained when the existing network
of stations was reduced by three-fourths.
In order to measure the mean zonal wind a symmetric network of
stations is probably needed.
The large seasonal variation in the
Coriolis term may be due to seasonal shifts in weather patterns which
move in and out of regions of the earth where observations are not
available.
-
41.
The following table represents a summary
of stations used in the computations.
EXPLANATION OF TABLE 2:
The columns are identified as follows:
1.
Sequence (dictionary) number
2.
W.M.O. block and station number
3.
Latitude
4.
Longitude
5.
1000-mb level
6.
850-mb
level
7.
700-mb
level
8
500-mb
level
9.
400-mb
level
10.
300-mb
level
11.
200-mb
level
12.
100-mb
level
13.
70-mb
level
14.
50-mb
level
15.
Overall rating
16.
"x" means used in
subset
During the five-year period a total of 1800 observations (once
daily) were possible.
If a station recorded at least 540 observa-
tions (30 percent) the figure "3" appears in columns 5-14, which
represent various standard pressure levels.
If a station did not
rate a grade of "3", but had at least 180 observations (10 percent),
the figure "1" appears in
the appropriate column.
Levels with less
42.
than 10 percent were given a figure "O".
A similar procedure was used in column 15 to summarize the
results of the preceding columns.
at each level from
rating of "3".
If the station had 30 percent
850 to 100 mb, inclusive, it receivod an overall
If it had no usable data (i.e., less than 10 percent),
it received an overall rating of "0" in column 15.
An "x" in column
16 means the station was used in the unbiased grid developed by
this writer.
The rating system is summarized below:
(d
= percentage of
observations).
Ratings for Columns 5-14
3
1
0
d
>
10% < d
<
d
<
30%
30%
10%
Overall Rating, Column 15
3
1
0
d > 30% for all levels, 850-100 mb, inclusive
30% at any level
10% < d
d < 10% at all levels
<
In all there was a total of
799
689
396
206
60
stations, of which
had usable data;
had 30 percent for each level from 850 to 100 mb, inclusive;
stations were used in subset, of which
were 10-percent stations, located primarily in the tropics.
43.
TABLE 2:
1
Station List and Percentage of Observations
2
3
01001
01005
01020
01028
01030
01152
01241
01324
01415
02062
71.01
78.04
80.05
74.52
69.70
67.27
63.70
60.20
58.88
63.18
8.28
-13.38
-18.30
-19.02
-19.02
-14.37
02077
02084
02836
02963
02935
02005
03026
03170
03171
03322
59.35
57.72
67.37
60.82
-17.95
03496
03774
03808
03917
03920
03953
04018
04202
04220
04270
52.68
51.08
50.22
54.65
54.48
51.93
04310
04320
04340
04300
06011
05180
06181
06260
06447
06610
81.60
76.77
70.42
65.62
62.05
55.38
55.77
52.10
50.80
46.82
62.24
60.13
58.22
56.43
56.38
53.47
63.95
76.52
68.70
61.18
4
-9.62
-11.08
-5.63
-14.62
-11.78
-26.65
-23.48
-25.67
1.17
6.33
2.87
2.88
2.92
-1.68
.22
5.32
6.22
6.10
10.25
22.62
68.84
52.87
45.42
16.67
18.77
21.97
37.65
6.76
-12.67
-12.53
-5.18
-4.35
-6.95
5
6
7
8
9
101112131415 16
3
0
0
3
0
3
3
3
3
0
3
0
0
3
0O
3
3
3
3
0
44.
1
2
3
40
41
42
43
44
45
46
47
48
49
07110
07145
07170
07180
07354
07510
07645
08001
08159
08221
48.45
48.77
48.07
48.70
46.85
44.85
43.87
43.38
41.68
40.47
50
51
52
53
54
55
56
57
58
59
08302
08495
08509
08521
08536
08594
10035
10184
10202
10338
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
4
5
6
7
8
9
10 11 12 13 14 15
4.42
-2.02
-5.03
-6.22
-1.72
.70
-4.40
8.37
1.07
3.57
3
1
0
0
1
3
3
1
0
0
3
3
1
1
3
3
3
1
3
3
3
3
1
1
3
3
3
1
3
3
3
3
1
1
3
3
3
1
3
3
3
3
1
1
3
3
3
1
3
3
3
3
1
1
3
3
3
1
3
3
3
3
1
1
3
3
3
1
3
1
3
3
1
1
3
3
3
0
3
0
1
1
0
0
1
1
1
0
3
0
1
1
i
0
3
1
1
0
3
0
3
3
1
1
3
3
3
1
3
1
39.62
36.15
38.75
32.63
38.77
16.73
54.53
54.10
53.37
52.47
-2.70
5.35
27.09
16.90
9.15
22.95
-9.55
-13.38
-7.22
-9.70
1
1
3
0
3
0
3
1
3
3
3 3
3 3
3 3
0 0
3 3
0 0
3 3
3 3
3 3
3 '3
1
3
3
0
3
0
3
3
3
3
1
3
3
0
0
0
3
3
3
3
1
3
3
0
3
0
3
1
3
3
1
3
3
0
3
0
3
1
3
3
0
3
3
0
3
0
3
0
3
3
0
1
1
0
0
0
1
0
0
0
0
1
3
0
0
0
3
0
3
3
1
3
3
0
1
0
3
1
3
3
10393
10454
10486
10513
10610
10739
10866
11035
11518
11934
52.22
51.85
51.12
50.87
49.95
48.83
48.13
48.25
50.10
49.07
-14.12
-10.77
-13.68
-7.13
-6.57
-9.20
-11.70
-16.37
-14.28
-20.25
1
0
0
1
0
0
0
0
0
0
3
1
3
1
1
3
3
3
3
3
3
0
3
1
1
3
3
3
3
3
3
0
3
1
1
3
3
3
3
3
3
0
3
1
1
3
3
3
3
3
3
0
3
1
1
3
3
3
3
3
3
0
1
1
1
3
3
3
3
3
1
0
1
1
1
3
3
3
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
3
3
3
0
0
1
J.
1
1
1
3
3
3
3
3
12330
12374
12425
12577
12843
13130
13276
13334
15120
15420
52.42
52.42
51.13
50.28
47.43
45.82
44.78
43.52
46.77
44.50
-16.85
-26.97
-16.98
-21.43
-19.18
-16.03
-20.53
-16.43
-23.60
-26.08
1
3
3
0
3
3
0
3
0
1
3
3
3
0
3
3
3
3
3
3
3
3
3
0
3
3
3
3
3
3
3
3
3
0
3
3
3
3
3
3
3
3
3
0
3
3
3
3
3
3
3
3
3
0
3
3
3
3
3
3
0
3
1
0
3
3
3
3
3
3
0
1
1
0
3
3
3
3
3
3
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
3
3
3
3
3
3
16
x
x
x
x
x
45.
1
2
3
4
80
81
82
83
84
85
86
87
88
89
15614
16044
16080
16239
16242
16320
16420
16560
16596
16622
42.82
46.03
45.47
41.80
41.80
40.65
-23.38
-13.18
-9.28
90
91
92
93
94
95
96
97'
98
99
16716
17030
17062
17130
17220
17280
17606
20046
20047
20069
37.90
41.28
40.97
39.95
38.40
37.92
35.15
80.62
79.50
-23.73
-36.33
-29.80
-32.88
-27.17
-40.20
-33.28
-58.05
-52.80
-76.98
100
101
102
103
104
105
106
107
108
109
21007
20274
20292
20353
20667
20674
20744
20891
21358
21432
78.07
77.50
77.72
76.95
73.33
73.50
72.38
71.98
76.15
76.00
-14.22
-82.23
-104.28
-68.58
-70.04
-80.23
-52.73
-102.47
-152.84
-137.90
110
111
112
113
114
115
116
117
118
119
21504
21647
21824
21946
21965
21982
22113
22165
22217
22522
74.65
73.18
71.58
70.62
70.63
70.97
68.97
68.65
67.13
64.98
-112.83
-143.23
-128.92
-147.88
-162.40
178.53
38.20
39.25
35.83
40.52
80.45
-12.60
-12.23
-17.95
-15.55
-9.05
-14.45
-22.97
-33.05
-43.30
-32.43
-34.78
5
6
7
8
9
10 11 12 13 14 15
16
46.
1
2
3
4
64.58
61.72
61.80
69.77
69.40
68.47
67.65
-40.50
-30.72
120
22550
121
3 22
123
124
125
126
127
128
129
22802
22P20
23022
23074
23146
23205
23274
130
131
132
133
134
135
136
137
67.47
-34.27
-61.68
-86.17
-73.60
-53.02
-86.57
-66.53
-57.10
23330
66.53
23418
65.12
23472
23552
23804
23884
23921
65.78
64.92
61.67
61.63
60.68
60.97
60.43
-87.95
68.50
67.55
66.77
-112.43
-133.38
-123.40
23933
23955
24125
138
139
24266
140
141
142
143
24507
24621
24688
24759
24790
24793
24817
24908
24944
24959
64.17
24343
5
-77.82
-50.85
-90.23
-60.43
-69.07
-77.87
-100.07
0
63.77 -121.62
63.27- -143.15
62.02 -129.72
0
0
0
61.80
-148.80
0
62.70
-149.10
0
61.27
-108.02
0
60.33
-102.27
0
60.40
-120.42
0
62.08
-129.75
0
25042
25123
25173
25399
69.75
68.80
-167.67
-161.28
0
0
68.92
66.17
-179.48
-169.83
0
0
154
155
156
157
158
25428
65.08
-160.62
0
25551
25563
25594
25677
64.68
64.78
-170.42
-177.57
0
1
159
25703
64.43
63.03
62.93
-173.23
-175.42
-152.43
3
0
0
144
145
146
147
148
149
150
151
152
153
6
7
8
9
10 11 12 13 14 15
47.
1
2
3
160
161
162
163
164
165
166
167
168
169
25822
25913
25954
26038
26063
26258
26298
26406
26422
26477.
61.82
59.58
60.35
59.42
59.97
57.83
57.90
56.55
56.97
56.38
170
171
172
173
174
175
176
177
178
179
26628
26629
26702
26781
26850
27037
27196
27553
27595
27612
180
181
182
183
184
185
186
187
188
189
4
5
6
7
8
9
101112131415
-159.52
-150.78
-166.00
-24.80
-30.30
-28.35
-34.05
-21.03
-24.07
-30.60
0
0
0
0
0
0
0
0
0
0
3
3
3
3
3
3
3
1
3
3
3
3
3
3
3
3
3
1
3
3
3
3
3
3
3
3
3
1
3
3
3
3
3
3
3
3
3
1
3
3
3
3
3
3
3
3
3
1
3
3
3
3
3
3
3
3
1
1
3
3
3
3
3
3
3
3
1
1
3
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
3
3
3
3
3
1
1
3
3
54.92
54.88
54.70
54.75
53.87
59.28
58.65
56.22
55.78
55.75
-23.93
-23.88
-20.62
-32.07
-27.53
-39.87
-49.62
-43.82
-49.18
-37.57
0
0
0
0
0
0
0
0
0
0
0
3
3
3
3
3
3
3
3
3
0
3
3
3
3
3
3
3
3
3
0
3
3
3
3
3
3
3
3
3
0
3
3
3
3
3
3
3
3
3
0
3
3
3
3
3
3
3
3
3
0
3
3
3
3
3
3
3
3
3
0
3
3
3
3
3
3
3
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
3
3
3
3
3
3
3
27707
27731
27949
27962
28225
28275
28440
28698
28722
28900
54.11
54.62
52.73
53.13
58.02
58.15
56.80
54.93
54.75
53.25
-35.33
-39.72
-41.47
-45.02
-56.30
-68.18
-60.63
-73.40
-56.00
-50.45
0
0
0
0
0
0
0
0
0
0
3
1
3
3
1
3
3
3
3
3
1
1
3
1
1
3
3
3
3
3
1
1
3
1
1
3
3
3
3
3
1
1
3
1
1
3
3
3
3
3
1
1
3
1
1
3
3
3
3
3
1
1
3
1
1
3
3
3
3
3
1
0
3
1
1
3
3
3
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
1
1
3
3
3
1
3
190
191
192
193
28952
29231
29282
29574
53.22
58.30
58.42
56.00
-63.62
-82.90
-97.40
-92.88
0
0
0
0
3
3
3
3
3
3
3
3
3
1
3
3
3
1
3
3
3
1
3
3
3
1
1
3
3
1
1
3
0
0
0
0
0
0
0
0
3
1
1
3
194
195
196
197
198
199
29612
29634
29637
29698
29865
30054
-55.37
55.03
54.97
54.88
53.75
59.45
-78.40
-82.90
-82.95
-99.03
-91.40
-112.58
0
0
0
0
0
0
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
1
3
3
3
3
3
1
3
3
3
3
3
1
3
3
3
3
3
1
3
1
3
0
0
0
0
0
0
0
0
0
0
0
0
3
3
1
3
1
3
16
x
48.
1
2
3
200
201
202
203
204
205
206
207
208
209
30230
30521
30554
30635
30636
30673
30692
30710
30719
30758
57.77
54.80
54.62
53.43
53.62
53.73
54.00
52.27
52.27
52.05
210
211
212
213
214
215
216
217
218
219
30935
30965
31004
31088
31168
31300
31329
31369
31510
31538
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
4
5
6
7
8
9
10 11 12 13 14 15
-108.12
-105.17
-113.13
-108.98
-109.63
-119.78
-123.97
-164.35
-104.32
-113.48
0
0
0
0
0
0.
0
0
0
0
3
3
3
3
1
3
3
3
1
3
3
3
3
3
1
3
3
3
1
3
3
3
3
3
0
3
3
3
1
3
3
3
3
3
0
3
3
3
0
3
3
3
3
3
0
3
3
3
1
3
3
3
3
3
0
3
3
3
1
3
3
3
3
3
0
3
1
3
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
3
3
1
3
1
3
1
3
50.37
50.38
58.62
59.37
56.45
53.75
53.07
53.15
50.27
50.07
-108.75
-116.52
-125.37
-143.20
-138.15
-127.23
-132.93
-140.70
-127.50
-132.13
0
0
0
0
0
0
0
0
0
0
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
1
3
3
1
3
3
3
3
3
3
1
3
3
1
3
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
3
1
3
3
1
1
3
3
31561
31707
31735
31770
31873
31909
31960
32061
32099
32150
50.68
47.73
48.52
48.97
45.87
45.03
43.12
50.90
43.88
46.92
-137.40
-130.97
-135.17
-140.28
-133.73
-136.67
-131.90
-142.17
-144.63
-142.73
0
0
0
0
0
0
0
0
0
0
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
3
3
3
3
3
3
3
3
32165
32186
32195
32217
32387
32540
32618
33008
33036
33317
44.02
46.20
46.85
50.00
56.32
52.97
55.20
52.12
52.03
50.17
-145.82
-150.50
-151.87
-155.38
-160.83
-158.75
-165.98
-23.68
-29.18
-27.05
0 3
0 3
0 1
0 -3
0 3
0 3
0 3
0 3
0 3
0 3
3
3
0
3
3
3
3
3
3
3
3
3
0
3
3
3
3
3
3
3
3
3
0
3
3
3
3
3
3
3
3
3
0
3
3
3
3
3
3
3
3
1
0
3
3
3
3
3
3
3
3
1
0
3
3
3
3
3
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
3
3
3
3
3
3
3
16
x
x
x
x
x
x
49.
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16
240
241
242
243
244
245
246
247
248
249
33345
33393
33631
33658
33791
33815
33837
33838
33946
34009
50.40
49.82
48.68
48.27
47.93
47.02
43.48
46.43
45.02
51.75
-30.45
-23.95'
-22.27
-25.97
-33.33
-28.87
-30.63
-30.77
-33.98
-36.20
0
0
0
0
0
0
0
0
0
0
3
3
3
3
3
3
0
3
3
3- 3
3 3
3 3
3 3
3 3
3 3
3 3
0 0
3 3
3 3
3
3
3
3
3
3
3
0
3
3
3
3
3
3
1
3
3
0
3
3
3
3
3
3
1
3
3
0
3
3
3
1
3
1
1
1
3
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
3
1
1
1
3
0
3
3
250
251
252
253
254
255
256
257
258
259
34122
34139
34172
34247
34300
34560
34731
34858
34880
35108
51.70
51.05
51.57
50.42
49.93
48.68
47.25
45.92
46.27
51.25
-39.17
-40.70
-46.03
-41.05
-36.28
-44.35
-39.82
-43.35
-48.03
-51.40
0
0
0
0
0
0
0
0
0
0
3
1
3
1
3
3
3
3
3
3
3
1
3
1
3
3
3
3
3
3
3
0
3
1
3
3
~3
.3
3
3
1
0
3
1
3
3
3
3
3
1
0
3
1
3
3
3
3
3
3
1
0
3
1
3
:3
3
3
3
3
1
0
3
1
3
3
3
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
1
3
3
3
3
1
1.
260
261
262
263
264
265
266
267
268
269
35121
35229
35361
35671
35394
35700
35746
35796
36003
36096
51.75
50.28
50.13
47.80
49.80
47.12
46.78
46.90
52.28
51.67
-55.10
-57.15
-65.23
-67.72
-73.13
-51.92
-61.67
-75.00
-76.95
-94.38
0
0
0
0
0
0
0
0
0
0
3
3
0
1
3
3
3
3
3
3
3
3
0
1
3
3
3
3
3
3
3
3
0
1
3
3
3
3
3
3
3
3
0
1
3
3
3
3
3
3
3
3
0
1
3
3
3
3
3
3
3
3
0
1
3
1
3
3
3
3
3
3
0
1
3
1
3
3
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
1
1
1
3
3
3
3
270
271
272
273
274
275
276
277
278
279
36177
36859
36870
36880
37018
37054
37260
37549
37789
37860
50.35
44.17
43.23
43.48
~44.10
44.22
42.87
41.68
40.13
41.00
-80.25
-80.07
-76.93
-77.03
-39.07
-43.10
-41.13
-44.95
-44.47
-49.00
0
0
0
0
0
0
0
0
0
0
3
3
3
0
3
3
3
3
3
3
3
3
3
0
3
3
3
3
3
3
3
3
3
0
3
3
3
3
3
3
3
3
3
0
3
3
3
3
3
3
3
3
3
0
3
3
3
3
3
3
3
3
3
0
3
3
1
3
3
3
3
3
3
0
1
3
1
1
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
3
3
0
1
3
1
1
3
3
3
:3
k
x
x
x
x
U
50.
1
2
3
4
280
281
282
283
284
285
286
287
288
289
37985
38061
38062
38353
38392
38413
38457
38507
38613
38687
38.73
44.85
44.77
42.83
41.83
41.73
'41.27
40.03
40.92
39.08
290
291
292
293
294
295
296
297
298
299
38750
38836
38880
38954
38989
40007
40181
40427
40597
40648
5
6
7
8
9
10 11 12 13 14 15 16
-48.33
-65.50
-65.53
-74.58
-59.98
-64.62
-69.27
-52.98
-72.95
-63.60
3
1
3
3
3
3
3
3
3
3
3
1
3
3
3
3
3
3
3
3
37.47
38.58
37.97
37.50
36.07
36.18
31.93
26.27
12.83
33.37
-53.97
-68.78
-58.33
-71.50
-62.72
-37.21
-34.83
-50.62
-45.02
-43.57
3
3
3
1
0
0
0
3
3
0
3
3
3
1
0
0
0
3
3
0
300
40650
301 .1',41530
302
41640
303
41660
304
41780
305
41920
306
42071
307
42182
308
42339
309
42361
33.33
34.03
31.45
30.25
24.90
23.77
31.63
28.58
26.30
26.23
-44.40
-71.58
-74.43
-66.88
-67.13
-90.38
-74.88
-77.20
-73.03
-78.25
0
0
0
0
0
0
0
1
0
0.
0
0
0
0
0
0
0
1
0
0
310
311
312
313
314
315
316
317
318
319
26.08
26.18
25.45
23.07
22.82
21.10
20.90
19.12
17.72
13.00
-91.72
-91.75
-81.73
-72.63
-88.45
-79.05
1
0
0
0
0
l
0
1
0
l
0
0
0
0
0
1
0
1
0
1
42410
42411
42475
42647
42809,
42867
42909
43003
43149
43279
-70.37
-72.85
-83.23
-80.18
-
51.
10 11 12 13 14 15 16
6
7
8
9
-77.58
-92.72
-76.95
-106.93
-110.13
-104.40
-114.17
-121.52
-121.22
-119.57
0
0
0 0
1
1
0 3
0 3
0 -1
3 3
3 3
1
1
0
0
0
0
1
3
3
1
3
3
1
0
0
0
0
3
3
1
3
1
1
0
0
0
0
3
3
1
3
1
1
0
0
0
0
3
3
1
3
1
1
0
0
0
0
3
3
0
3
0
1
0
0
0
0
1
1
0
3
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
3
1
1
0
22.47
39.03
37.10
36.33
33.17
45.42
43.05
43.33
40.68
39.72
-120.43
-125.82
-127.04
-127.28
-126.20
-141.68
-141.33
-145.58
-141.38
-140.10
1
0
3
0
3
3
3
3
0
3
1
3
3
0
3
3
3
3
0
3
1
3
3
0
3
3
3
3
0
3
1
3
3
0
3
3
3
3
0
3
1
3
3
0
3
3
3
3
0
3
1
3
3
0
3
3
3
3
b
3
1
1
3
0
3
3
3
3
0
3
1
0
3
0
3
3
:3
3
0
3
0
0
1
0
1
3
3
0
0
3
1
0
3
0
3
3
3
0
0
3
1
1
3
0
3
3
3
3
0
3
38.27
-140/.90
3
3
3
3
3
3
3
3
3
3
3
3
3
3
1
3
3
3
3
3
3
3
3
3
1
2
3
4
320
321
322
323
324
325
326
327
328
329
43295
43333
43371
44292
44354
44373
45004
46692
46697
46734
12.97
12.67
8.48
47.90
44.89
43.60
22.32
25.03
25.05
23.52
330
331
332
333
334
335
336
337
338
339
46747
47058
47122
47132
47187
47401
47412
47420
47580
47582
340
47590
5
341
47600
37.38
-136.90
3
3
3
3
3
342
47646
36.05
-140.13
3
3
3
3
3
343
47678
33.12
-139.78
1
3
3
3
3
3
3
3
0
0
344
345
47744
47768
35.43
34.68
-133.35
-133.92
3
0
3
0
3
0
3
0
3
0
3
0
3
0
3
0
3
0
3
0
3
0
346
47778
33.45
-135.72
3
3
3
3
3
3
3
3
3
3
3
347
348
47807
47827
33.57
31.63
-130.35
-130.60
3
0
3
3
3
3
3
3
3
3
3
3
3
3
3
3
0
3
0
3
3
3
349
47909
28.38
-129.55
0
3
3
3
3
3
3
3
0
0
3
350
351
352
353
354
355
356
357
47931
47963
48327
48455
48568
48694
48819
48855
26.35
30.48
18.78
13.73
- -7.18
1.35
21.05
16.05
-127.75
-140.30
-98.98
-100.50
-100.62
-103.92
-105.87
-108.18
3
3
0
3
1
0
0
1
10.82
49.22
-106.67
-119.75
3
0
3
3
1
3
1
3
0
1
3
3
3
1
3
1
3
0
1
1
3
3
1
3
1
3
0
1
3
3
3
1
3
1
3
0
1
3
3
3
0
3
1
3
0
1
3
1
0
0
0
0
3
0
1
1
3
3
1
3
1
3
0
1
48900
50527
3
3
1
3
3
3
0
1
3
0
0
0
1
0
3
0
1
358
359
3
3
1
3
3
3
0
1
3
1
1
3
3
3
3
3
3
1
0
0
1
x
x
x
x
x
x
x
x
x
x
x
52.
5
6
7
8
9
10 11 12 13 14 15 16
-125.22
-122.05
-130.33
-126.63
0
0
0
0
3
3
3
3
3
3
3
3
3
3
1
3
3
3
1
3
3
1
1
3
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
47.88
-88.10
0
3
3
3
1
1
1
0
0
0
1
46.75
45.78
45.23
43.92
43.92
-82.00
-84.87
-90.53
-81.28
-81.28
0
0
0
0
0
3
3
0
0
3
1
3
3
0
3
1
1
3
0
3
1
1
3
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
51463
51623
51644
51656
43.77
41.17
41.75
41.50
-87.61
-80.22
-83.07
-86.15
0
0
0
0
3
1
3
3
3
1
3
3
3
1
3
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
374
375
376
51769
51777
51828
39.40
39.07
37.12
-76.05
-S8.05
-79.92
0
0
0
3
3
3
3
3
3
3
3
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
377
51895
37.85
-91.65
0
0
3
3
1
1
0
0
0
0
1
-93.45
0
3
3
3
3
1
1
1
0
0
1
3
3
1
1
1
0
0
1
1
2
3
360
361
362
363
50557
50838
50873
50953
49.17
46.22
46.82
45.75
364
51076
365
366
367
368
369
51133
51243
51288
51430
51431
370
371
372
373
378
52203
42.83
4
379
52267
42.25
-101.22
0
3
3
380
381
52313
52323
41.78
41.60
-95.11
-95.45
0
0
0
0
0.
3
0
3
0
3
0
1
0
1
0
1
0
0
0
0
0
1.
382
52391
41.70
-104.03
0
3
3
1
1
1
0
0
0
0
1
383
52418
40.13
-- 94.78
0
3
3
3
3
1
1
1
0
0
1
384
52533
39.83
-98.25
0
3
3
3
3
1
1
1
0
0
1
385
386
52602
52633
38.90
38.90
-92.80
-98.22
0
.0
0
0
3
0
3
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
387
388
389
52652
52681
52818
38.43
38.73
36.20
-100.58
-103.10
-94.38
0
0
0
3
3
0
3
3
3
3
3
3
1
3
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
1
390
391
392
52836
52866
52889
36.33
36.58
36.05
-98.04
-101.92
-103.95
0
0
0
0
0
3
0
3
3
3
3
3
3
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
393
53068
44.22
-111.53
0
3
3
3
3
1
1
0
0
0
1
394
53276
42.62
-112.83
0
0
0
0
0
0
0
0
0
0
0
395
396
397
398
399
53420
53463
53513
53546
53614
40.97
40.82
39.97
39.28
38.42
-107.17
-111.68
-106.75
-109.75
-106.27
0
0
0
0
0
1
3
3
3
3
1
3
3
3
3
0
3
3
3
3
0
3
3
3
3
0
3
1
3
3
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
x
x
53.
2
3
10 11 12 13 14 15 16
4
5
6
7
8
9
3
3
i1
3
3
3
3
3
3
0
3
1
1
3
3
3
3
3
1
0
3
1
1
3
3
3
3
1
1
0
1
0
1
1
3
3
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
37.92
36.60
35.42
43.85
43.69
43.87
42.27
42.90
-41.15
41.15
-112.52
-109.54
-106.63
-116.07
-122.25
-125.33
-118.90
-129.52
-121.12
-122.75
0
0
0
0
0
0
0
0
0
0
3
3
406
407
408
409
53772
53845
53915
54102
54135
54161
54218
54292
54337
54339
3
3
3
3
3
3
1
3
3
3
3
3
3
3
3
3
1
410
411
412
413
414
415
416
417
418
419
54342
54374
54497
54511
54534
54662
54714
54823
54843
54857
41.78
41.72
40.07
39.93
39.67
38.90
37.48
36.70
36.70
36.07
-123.40
-126.85
-124.12
-116.33
-118.12
-121.63
-116.38
-117.07
-119.12
-120.32
0
0
0
0
0
0
0
0
0
0
3
3
0
3
0
0
1
3
0
0
3
3
0
3
0
0
1
3
0
0
3
1
0
3
0
0
1
3
0
0
3
1
0
3
0
0
1
3
0
0
3
1
0
3
0
0
1
3
0
0
1
1
0
3
0
0
1
1
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
1
1
0
0
420
421
55299
55591
32.00
29.72
-92.12
-91.04
0
0
0
0
0
0
3
3
3
3
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1'
1
1
400
401
402
403
404
405
422
423
424
56029'
56080
56096
33.10
34.72
33.38
-96.75
-103.67
-104.68
0
0,
0
0
0
3
0
3
3
1
1
3
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
425
426
427
428
429
56137
56146
56172
56294
56492
31.17
31.60
31.85
30.68
28.82
-97.27
-99.98
-102.68
-104.07
-104.54
0
0
0
0
0
0
0
0
3
3
0
0
1
3
1
3
3
0
3
1
3
1
0
3
1
1
1
0
3
0
1
1
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
1
3
1
430
431
432'
56533
56571
56691
27.67
27.88
26.81
-98.38
-102.30
-104.25
0
0
0
0
0
0
1
3
1
0
1
L
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
433
56739
25.12
-98.48
0
0
3
1
1
0
0
0
0
0
1
~25.04
-102.73
0
0
3
3
3
3
1
1
0
0
1
0
0
0
0
0
0
3
3
3
3
1
'3
1
3
3
1
1
0
3
3
1
1
0
1
3
1
0
0
1
3
1
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
1
1.
1
1
1
1
434
56778
435
436
437
438
56779
56964
56989
57036
25.10
22.55
22.45
34.25
-102.85
-101.04
-103.90
-108.92
439
57083
34.72
-113.72
0
Q
x
x
x
x
54.
1
2
3
440
441
442
443
444
445
446
447
448
449
57127
57245
57328
54747
57461
57494
57515
57516
57679
57745
33.09
450
451
452
453
454
455
456
457
458
459
4
5
6
7
8
9
10 1112 131415 16
31.27
30.27
30.70
30.42
29.50
~ 29.48
28.25
27.45
-107.17
-109.35
-107.47
-109.37
-111.07
-114.28
-106.55
-106.33
-112.85
-109.63
0
0
0
0
0
0
0
0
0
0
3
3
3
3
3
3
1
3
3
3
3
1
1
1
3
3
1
1
3
3
1
1
1
1
3
3
0
1
3
1
1
0
0
1
3
3
0
0
1
1
0
0
0
1
1
3
0
0
1
1
0
0
0
0
1
3
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
57816
57957
57972
57993
58027
58150
58203
58238
58321
58367
26.57
25.25
25.75
25.83
34.25
33.75
32.92
32.07
31.88
31.20
-106.70
-110.10
-112.98
-114.83
-117.25
-120.50
-115.83
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69.88
83.93
66.10
79.56
61.78
61.78
63.10
61.52
61.35
3
1
3
3
3
3
3
3
3
3
x
660
661
662
663
78988
80001
80224
91066
91115
91131
91165
91217
91218
91245
12.22
12.80
68.98
81.67
74.08
177.32
-141.33
-153.97
159.35
-144.84
-144.92
-166.65
3
3
0
3
3
3
3
3
0
3
x
91250
91275
91285
91334
91348
91366
91376
91408
91413
91700
12.33
17.33
19.73
7.45
-162.33
169.52
155.07
-151.83
-158.22
-167.73
-171.40
-134.48
-138.13
171.72
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
l
0
0
3
3
l
0
0
3
3
l
0
0
3
3
l
0
0
3
3
l
0
0
3
3
1
0
0
3
3
l
0
0
3
3
1
0
0
3
645
646
647
648
664
665
666
667
668
669
670
671
672'
673
674
675
676
677
678
679
17.40
18.45
8.97
17.11
17.12
18.04
16.27
10.68
4.60
28.22
24.78
24.28
21.87
14.96
14.97
19.28
- 6.97
8.72
7.10
7.35
9.52
-2.27
x
x
3
3
3
x
x
x
x
x
x
x
x
x
x
x
x
x
60.
4
6
7
8
9
10 11 12 13 14 15 16
-120.57
-123.90
16.00
20.00
20.00
-.33.00
151.00
-115.60
49.00
-135.00
0 3
0 0
3 3
1 3
1 3
1 3
0 1
0 0
0 1
0 0
3
0
3
0
3 3
3 3
3 3
l
1
0 0
l
1
0 0
3
0
3
3
3
3
1
0
1
0
3
0
3
3
3
3
1
0
1
0
-160.90
-115.00
-152.80
-2.00
110.33
114.60
51.00
35.50
41.00
48.00
0
0
0
3
0
1
3
3
3
3
1 1
1 1
0 0
3 3
1 1
3 3
3 3
3 3
3 3
3 3
34.00
40.00
-. 68
25.08
24.90
23.77
28.58
26.30
145.00
140.00
-164.00
172.00
-73.17
-61.82
-67.13-90.38
-77.20
-73.03
3 3
3 3
3 3
0 0
0 3
0 0
3 3
1 1
3 3
3 3
3
3
3
0
3
00
31
1
3
3
3
3
3
0
3
0
1
3
3.
3
3
25.45
22.82
21.10
19.12
17.72
13.00
12.67
8.48
6.90
22.32
-81.74
-88.45
-79.05
-72.85
-83.23
-80.18
-92.72
-76.95
-79.87
-114.17
1
3
1
3
3
3
3
3
0
0
3
3
3
3
3
3
3
3
0
0
3
3
3
3
3.
3
3
3
0
0
3
3
3
3
3
3
3
3
0
0
1
2
3
680
681
682
683
684
685
686
687
688
689
93327
98645
99041
99052
99061
99063
99176
99183
99185
99223
15.17
10.33
45.00
52.50
59.00
62.00
83.10
86.50
86.60
29.00
690
691
692
693
694
695
696
697
698
699
99276
99285
99286
99360
02B
79.30
85.00
82.70
66.00
31.59
32.66
56.50
03C
52.80
04D
05E
44.00
25.00
700
701
702
703
704
705
706
707
708
709
17P
24N
25V
26R
41350
41756
41780
41917
42182
42339
50.00
710
711
712
713
714
715
716
717
718
719,
42475
42809
42867
43003
43149
43279
43333
43371
43466
45004
30.00
5
1
1
0
3
1
3
3
3
3
3
3
3
3
3
3
3
3
3
0
0
3 3 3
0 0.0
3 1 0
3 3 1
3 3 1
3 3 1
1 1 0
0 0 0
1 1 0
0 0 0
3
0
1
3
3
3
1
0
1
0
1 1
0 0
0 0
3 3
1 1
3 3
3 3
3 3
3 3
3 3
1
0
0
3
l
3
3
3
3
3
1x
3 3
3 3
3 3
0 0
3 3
0 0
l1
3
3
3 3
3 3
3 3
0 0
3 3
0 0
0 0
0 0
3 3
1 0
3
3
3
0
3
0
lx
lx
3
1
3
3
3
3
3
3
3
3
0
0
1
3
3
3
3
3
3
3
0
0
1x
1x
3 x
1x
lx
1x
1x
lx
0
0
1
0
0
3
1
3
3
3
3
3
0
1
3
1
1
1
0
1
0
0
0
0
0
.1
0
1
1
1
1
1
0
3
1
3
3
3
3
3
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
61.
5
6
7
8
9
-119.57
-120.43
-127.75
-96.17
-96.17
-100.62
-103.92
-103.82
-105.85
8.03
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
25.23
11.62
0
1
1
1
-9.72
-7.23
-20.30
9.00
-1.30
-6.87
.05
-4.32
-11.60
14.42
-72.43
-57.50
-38.73
-36.75
-39.20
-18.27
-15.32
-27.53
3
0
0
0
0
1
1
0
0
3
0
1
0
0
3
1
1
0
3
0
1
1
3
3
1
1
0
3
0
1
1
3
3
1
1
0
-4.83
-. 70
4.38
9.15
-11.90
-8.75
-18.57
-18.38
3
3
0
0
3
3
0
1
3
3
0
1
64700
12.13
-15.03
0
0
745
746
747
748
749
64870
64910
65201
65578
66160
7.28
4.02
6.58
5.25
-8.85
-13.32
9.72
-3.33
3.93
-13.23
0
3
0
0
3
750
751
752
753
754
755
756
757
758
759
66422
67001
67009
67085
67197
67241
67475
67587
67663
67774
-15.37
-11.70
-12.28
-18.90
-25.03
-15.02
-10.20
-13.98
-14.47
-17.83
-12.15
-43.23
-49.30
-47.53
-46.97
-40.67
-31.10
-33.75
-28.45
-31.02
0
0
3
0
3
1
0
0
0
0
1
2
3
720
721
722
723
724
725
726
727
728
729
46734
46747
47931
43097
48455
48568
48694
48802
48819
61290
23.52
22.47
26.35
16.77
16.77
7.18
1.35
22.35
21.01
12.62
730
61401
731
732
733
734
735
736
737
738
739
61900
61967
61995
63450
63741
63894
64005
64210
64360
740
741
742
743
64400
64501
64650
64750
744
4
10 11 12 13 14 15 16
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
x
1
1
1
1
x
3
0
1
0
3
3
1
1
0
3
0
1
0
3
3
1
1
0
3
0
1
0
3
1
1
1
0
3
0
1
1
1
1
1
1
0
x
3
3
0
1
3
3
0
1
3
3
0
1
3
3
0
1
x
x
0
0
0
0
0
3
3
0
0
3
3
3
0
0
3
3
3
0
0
3
3
3
0
0
3
3
3
0
0
3
3
3
0
0
3
0
0
3
3
3
0
0
0
1
1
0
0
3
3
3
0
0
0
1
1
0
0
3
3
3
0
0
0
1
1
0
0
3
3
3
0
0
0
1
1
0
0
3
3
1
0
0
0
1
1
0
0
3
3
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
3
0
1
0
3
3
1
1
0
3
3
0
1
3
3
0
1
0
0
3
3
0
0
3
3
3
0
0
3
0
0
3
3
3
1
0
0
1
1
0
0
3
3
3
1
0
0
1
1
C
0
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
62.
1
2
760
761
762
763
764
765
766
767
768
769
78089
80401
81405
82400
82898
83781
84129
84631
91131
91334
770
771
772
773
774
775
776
777
778
779
3
4
5
6
7
8
9
10 11 12 13 14 15 16
24.07
10.25
4.83
-3.83
-8.02
-23.55
-2.17
-12.10
24.28
7.45
74.53
67.60
52.37
32.42
34.85
46.63
79.87
77.02
-153.97
-151.83
0
0
3
3
3
0
3
1
0
3
0
0
3
3
3
1
3
3
0
3
0
0
3
3
3
1
3
3
0
3
0
0
3
3
3
1
3
3
0
3
0
0
3
3
3
1
3
3
0
3
0
0
3
3
3
1
3
3
0
3
0
0
3
3
3
1
3
3
0
0
3
0
0
0
0
3
3
3
1
1
3
0
1
91348
91376
91408
91489
91517
91643
91680
91843
91938
94027
6.97
7.10
7.35
2.00
-9.42
-8.52
-17.75
-21.20
-17.53
-6.72
-158.22
-171.40
-134.48
157.40
-159.97
-179.20
-177.45
159.77
149.58
-147.00
3
3
3
0
3
0
0
0
3
1
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
0
0
0
3
3
3
3
3
3
3
0
0
0
1
3
3
3
3
3
3
1 :-x
1 x
1 x
1 x
3 x
3 x
3 x
3 x
3 x
3 x
780
781
782
783
784
785
786
787
788
789
94120
94294
94299
94312
94335
96745
96933
96996
98836
08521
-12.43
-19.25
-16.30
-20.38
-20.67
-6.18
-7.22
-12.08
6.90
32.63
-130.87
-146.77
-149.98
-118.62
-140.50
-106.38
-112.72
-96.88
-122.07
16.90
3
0
3
1
0
0
0
3
0
0
3
3
3
3
3
0
0
3
0
0
3
3
3
3
3
0
0
3
0
0
3
3
1
3
3
0
0
3
0
0
3
3
1
3
3
0
0
3
0
0
3
3
l
3
3
0
0
3
0
0
3
3
1
3
3
0
0
3
0
0
3
3
1
3
3
0
0
3
0
0
3
3
1
3
3
0
0
3
0
0
790
791
792
793
794
795
796
797
798
08594
60571
60625
60680
59211
59287
59317
59431
59559
16.73
31.63
26.97
22.76
-23.42
23.17
23.35
22.85
22.00
22.95
2.25
-1.08
-5.51
-106.54
-113.33
-116.67
-108.32
-120.75
0
0
0
0
0
0
0
0
0-
0
3
3
3
0
0
0
0
0
0
3
3
3
0
0
0
0
0
0
3
3
3
0
0
0
0
0
0
3
3
3
0
0
0
0
0
0
3
3
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
l
1
1
0
0
0
0
0
0
0
3
3
3
1
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
63.
TABLE 3:
60-Month Vertically Averaged Wind Components
[7
Lat (ON)
m sec
March 69
June 68
90
2.42
88
86
84
82
80
78
76
74
72
70
68
62
60
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
2.43
2.45
2.48
2.56
2.65
2.84
32
30
28
26
3.05
3.27
3.61
3.88
4.23
4.59
4.94
5.45
5.85
6.34
6.85
7.41
8.21
8.78
9.34
9.95
10.50
10.80
11.00
11.00
10.80
10.40
9.80
9.01
8.03
22
20
18
16
6.91
5.60
4.19
2.71
1.17
-1.92
14
-1.37
12
10
8
6
-2.24
24
4
2
0
-2.85
-3.28
-3.40
-3.23
-2.91
-2.66
m sec 1
March 69
June 68
1.54
1.52
1.53
-0.56
-0.17
-0.52
1.69
-0.40
-0.16
-0.14
2.02
2.31
-0.15
-0.11
-0.02
2.70
-0.04
-0.07
-0.09
-0.08
-0.07
-0.04
0.01
0.04
0.05
0.06
0.05
0.03
0.01
-0.03
-0.06
-0.04
-0.01
-0.03
3.09
3.40
3.78
4.01
4.18
4.36
4.60
5.00
5.39
6.60
6.63
7.27
8.15
8.77
9.38
10.00
10.50
-0.56
-0.06
-0002
0.02
0.07
0.12
0.12
0.10
0.08
,0.05
0.02
0.03
0.07
0.05
-V-0.08
-0.20
-0.18
10.90
-0.12
10.10
11.10
10.90
10.50
9.83
8.97
7.92
6.75
5.43
4.03
2.58
-0.13
1.04
-0.32
1.52
-2.43
-3.08
-3.56
-3.71
-3.54
-3.20
-2.94
-0.14
-0.13
-0.11
-0.09
-0.08
-0.08
-0.07
-0.07
-0.07
-0.07
-0.06
-0.05
-0.02
0
0.02
0.04
0.06
0.08
0.08
0.08
-0.18
-0.17
-0.28
-0.23
-0.15
-0.14
-0.16
-0.13
-0.09
-0.08
-0.10
-0.11
-0.12
-0.13
-0.13
-0.12
-0.10
-0.09
-0.06
-0.04
-0.03
-0.01
0.02
0.04
.0.05
0.05
64.
TABLE 4:
Lat (IN)
60-Month Vertically Averaged Momentum Transport
By Transient Eddies
2
m sec
Mar 69
90
88
86
4
82
80
78
76
74
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
0
0
0
0
-0.02
-0.06
-0.10
-0.17
-0.26
-0.39
-0.52
-0.62
-0.71
-0.80
-0.82
-0.81
-0.67
-0.44
-0.12
0.46
1.01
1.77
2.74
3.72
4.68
5.53
6.31
7.05
7.73
8.39
8.89
9.03
8.92
8.57
8.07
7.52
6.82
6.06
5.24
4.50
3.85
3.16
2.58
2.08
1.57
1.25
2
Jun 68
0
0
0
0
-0.02
-0.06
-0.10
-0.16
-0.23
-0.34
-0.42
-0.44
-0.43
-0.51
-0.65
-0.74
-0.71
-0.61
-0.36
0.21
0.78
1.63
2.73
3.85
4.93
5.89
6.79
7.77
8.66
9.27
9.56
9.33
8.84
8.25
7.60
6.97
6.24
5.52
4.79
4.16
3.61
3.00
2.42
1.94
1.42
1.09
By Standing Eddies
m2 sec-2
Mar 69
0
0
0
0
0
0
-0.02
-0.05
-0.09
-0.16
-0.22
-0.28
-0.34
-0.36
-0.31
-0.26
-0.19
-0.07
0.10
0.35
0.47
0.41
0.42
0.46
0.44
0.40
0.41
0.47
0.58
0.74
0.89
0.92
0.85
0.61
0.31
0.05
-0.21
-0.41
-0.48
-0.47
-0.49
-0.52
-0.50
-0.40
-0.38
-0.38
Jun 68
0
0
0
0
0
-0.01
-0.02
-0.04
-0.07
-0.13
-0.20
-0.30
-0.42
-0.49
-0.52
-0.52
-0.40
-0.21
0.38
0.38
0.53
0.43
0.42
0.54
0.60
0.64
0.72
0.94
1.16
1.24
1.21
1.10
0.90
0.64
0.36
0.12
-0.13
-0.32
-0.38
-0.38
-0.42
-0.49
-0.48
-0.39
-0.36
-0.37
65.
TABLE 5:
60-Month Vertically Averaged Generation of Kinetic
Energy.
Lat (ON)
90
88
86
84
82
80
73
76
74
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
36:
32
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
By Transient
Eddies m3 sec- 3
Mar 69
Jun 68
0
-0.28
-0.01
0
-0.14
-0.01
-0.02
-0.01
-0.06
-0.08
-0.09
-0.12
-0.13
-0.14
-0.02
-0.02
-0.01
-0.03
-0.05
-0.09
-0.14
-0.17
-0.07
-0.03
0.07
0.11
0.08
0.11
0.09
0.01
-0.24
-0.23
-0.32
-0.62
-0.89
-0.82
-0.41
-0.67
-0.97
-0.81
-0.40
0.33
0.30
1.40
1.28
2.65
2.65
4.15
5.67
7.01
8.05
8.81
9.08
.8.69
8.25
7.27
5.95
4.26
2.81
1.93
1.10
4.75
6.86
8.29
8.97
9.05
8.81
8.17
7.60
6.59
5.43
3.98
2.72
1.93
1.14
0.39
-0.44
-0.17
-0.14
By Standing
Eddies m3 sec~3
Mar 69
0
0.08
Jun 68
By Mean Meridional
Circulation m 2 sec~ 2
Mar 69 Jun 68
0
0
0
-0.03
0
0
0
0.02
0
0
0
0.01
0.04
0.01
0.06
0.03
0.05
0.01
0.01
0.01
0.01
-0.01
0.0
0.0
0.0
0.0
0.0
-0.03
0.0
0.08
-0.01
-0.03
-0.08
-0.10
0.09
0.06
-0.16
-0.04
-0.04
-0.04
-0.02
0.11
0.10
0.18
0.08
0.09
0.10
-0.13
-0.02
-0.10
0.23
0.10
-0.07
0.0
0.13
0.24
0.21
0.14
-0.15
0.02
-0.03
0.24
0.09
0.03
0.02
0.02
0.08
0.21
0.07
0.01
0.0
0.11
0.04
0.18
0.11
0.05
-0.08
-0.05
-0.13
-0.04
-0.19
-0.10
-0.08
-0.07
-0.02
-0.16
-0.13
-0.12
-0.09
0.03
-0.03
-0.12
-0.22
-0.08
-0.15
-0.24
-0.36
-0.42
-0.63
0.03
-0.02
0.06
0.09
0.16
0.29
0.48
0.70
0.86
0.91
0.74
0.43
0.14
-0.14
-0.31
-0.31
0.04
0.13
0.31
0.63
0.91
1.05
1.07
0.96
0.74
0.44
0.18
-0.08
-0.26
-0.27
-0.62
-0.61
-0.54
-0.58
-0.89
-0.82
-0.63
-0.59
-0.64
-0.58
-0.56
-0.43
-0.47
-0.30
-0.13
-0.02
0.06
-0.26
-0.12
-0.01
0.05
0.10
0.10
0.14
0.12
0.16
0.12
0.15
0.12
0.14
0.09
0.11
-0.23
-0.21
-0.18
-0.12
-0.16
-0.12
0.44
-0.05
-0.04
0.0
-0.13
-0.12
0.01
0.03
0.01
0.03
0.03
0.03
0.07
0.05
0.03
0.02
0.01
0.01
0.0
0.0
0.08
0.06
0.03
0.02
0.01
0.01
0.0
0.0
66.
TABLE 6:
Vertically Averaged Wind Components
15-Month Spring (AprilMay,June)
(u]
Lat (ON)
m sec
March 69
June 68
90
88
86
84
82
80
78
76
74
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
2.49
2.52
2.53
2.48
2.38
2.36
2.45
2.56
2.692.92
3.13
3.44
3.76
4.06
4.49
4.83
5.26
5.71
6.20
6.92
7.45
8.01
8.65
9.22
9.68
9.99
10.01
10.01
9.89
9.39
8.71
7.78
6.71
5.44
4.08
2.68
1.21
-0.09
-1.23
-2.09
-2.72
-3.19
-3.34
-3.18
-2.84
-2.58
0.80
0.08
0.82
0.99
1.34
1.64
2.00
2.36
2.63
2.97
3.19
3.40
3.61
3.78
4.04
4.33
4.85
5.40
5.98
6.80
7.40
8.04
8.73
9.28
9.70
10.0
10.2
10.1
9.91
9.36
8.61
7.64
6.53
5.24
3.88
2.49
1.06
-0.20
-1.33
-2.21
-2.86
-3.36
-3.55
-3.43
-3.13
-2.88
[v)
m seci
March 69
June 68
-0.68
-0.68
-0.66
-0.53
-0.28
-0.14
-0.11
-0.10
-0.08
-0.06
-0.04
0.01
0.05
0.05
0.01
-0.02
-0.07
-0.10
-0.08
-0.01
-0.02
-0.16
-0.28
-0.22
-0.12
-0.11
-0.13
-0.10
-0.06
-0.04
-0.04
-0.04
-0.05
-0.06
-0.07
-0.08
-0.10
-0.11
-0.10
-0.09
-0.07
-0.05
-0.03
0.01
0.03
0.04
0.05
0.04
0.03
0.04
0.07
0.07
0.06
0.05
0.06
0.07
0.06
0.01
-0.04
-0.07
-0.10
-0.12
-0.13
-0.13
-0.12
-0.10
-0.13
-0.27
-0.38
-0.28
-0.15
-0.16
-0.19
-0.16
-0.11
-0.10
-0.11
-0.11
-0.12
-0.12
-0.13
-0.13
-0.12
-0.11
-0.09
-0.07
-0.05
-0.03
-0.02
0.03
0.04
0.05
67.
TABLE 7:
Lat (ON)
9)0
88
86
84
82
80
78
76
74
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
26
24
22
20
18
16
14
12
10
86
4
2
0
Vertically Averaged Momentum Transport
. 15-Month Spring (AprilMay, June)
By Transient Eddies
m2 sec-2
March 69
June 68
a
0
0
0.01
0.01
-0.02
-0.06
-0.09
-0.11
-0.17
-0.26
-0.35
-0.45
-0.54
-0.63
-0.68
-0.67
-0.55
-0.36
-0.09
0.38
0.81
.1.38
2.12
2.95
3.85
4.81
5.79
6.75
7.58
8.19
8.56
8.63
8.44
7.93
0
-0.01
-0.03
-0.05
-0.08
-0.09
-0.10
7.23
6.48
5.57
4.66
3.81
3.12
2.57
2.04
1.64
1.35
1.01
0.79
-0.15
-0.25
-0.35
-0.44
-0.54
-0.66
-0.80
-0.89
-0.85
-0.72
-0.44
0.16
0.71
1.44
2.36
3.27
4.21
5.23
6.27
7.32
8.18
8.67
8.83
8.62
8.16
7.47
6.66
5.87
5.01
4.23
3.49
2.90
2.45
1.99
1.59.
1.30
0.96
0.72
By Standing Eddies
m2sec 2
March 69
June 68
0
0
0
0
0.01
0.02
0.01
-0.02
-0.04
-0.09
-0.14
-0.21
-0.29
-0.35
-0.38
-0.40
-0.40
-0.36
-0.26
-0.12
-0.08
-0.14
-0.09
-0.01
-0.03
-0.07
-0.04
0.06
0.23
0.43
0.61
0.65
0.61
0.48
0.32
0.23
0.19
0.14
0.09
0.11
0.09
0.05
0.02
0.10
0.06
-0.01
0
0
0
0
0
-0.01
-0.02
-0.05
-0.07
-0.11
-0.16
-0.27
-0.40
-0.51
-0.60
-0.65
-0.61
-0.53
-0.40
-0.19
-0.12
-0.26
-0.28
-0.17
-0.10
-0.04
0.13
0.42
0.69
0.77
0.76
0.72
0.65
0.52
0.39
0.28
0.20
0.14
0.17
0.26
0.27
0.23
0.18
0.23
0.15
0.07
68.
TABLE 8:
Lat (ON)
too
88
86
84
82
so
78
76
74
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
Vertically Averaged Generation of Kinetic Energy
15-Month Spring (April ,May ,June)
By Transient
Eddies m3 sec-3
Mar 69 Jun 68
0
1.05
0.07
-0.02
-0.13
-0.14
-0.09
-0.08
-0.07
-0.07
-0.06
-0.01
-0.01
0.04
0.05
0.02
0.05
0.03
-0.01
-0.16
-0.22
-0.45
-0.70
-0.76
-0.62
-0.24
0.49
1.60
3.23
4.89
6.24
7.23
7.82
7.87
7.27
6.65
5.62
4.48
3.10
2.02
1.39
0.81
0.33
0.02
-0.08
-0.08
By Standing
Eddies m 3 sec~3
Mar 69 Jun 68
0
0
-0.81
-0.05
-0.01
0.01
0.01
0.02
0
-0.01
-0.03
-0.07
-0.08
-0.10
-0.10
-0.06
0.09
0.23
0.22
0.18
-0.10
-0.26
-0.54
-0.82
-0.81
-0.74
-0.48
0.28
1.58
3.69
5.77
7.14
7.89
8.09
7.76
6.86
6.00
4.95
4.11
2.97
1.99
1.39
0.81
0.38
0.11
-0.01
-0.03
-0.04
0
0.01
0.02
0.02
0.01
-0.01
-0.01
-0.02
-0.02
0
0
0.02
0.04
0.04
0.06
0.06
0.09
0.06
0.06
0.12
0.13
0.11
0.12
0.10
0.05
0.03
0.06
0.20
0.39
0.52
0.59
0.54
0.40
0.31
0.28
0.25
0.16
0.11
0.08
0.03
0
-0.02
-0.02
-0.01
0
0.01
0
0
0
0
0
0
0
-0.01
-0.03
-0.05
-0.07
-0.06
-0.01
0.09
0.17
0.15
0.17
0.09
0.07
0.15
0.16
0.11
0.10
0.90
0.07
0.12
0.29
0.45
0.55
0.60
0.61
0.62
0.38
0.27
0.18
0.12
0.10
0.11
0.10
0.05
0
-0.02
-0.02
-0.01
By Mean Meridional
2
Circulation ni
sec- 2
Mar 69 Jun 68
-.
-0.03
-0.07
-0.07
-0.04
-0.02
-0.01
0
0.01
0.03
0.05
0.07
0.09
0.08
0.04
0
-0.08
-0.17
-0.21
-0.24
-0.30
-0.49
-0.69
-0.64
-0.55
-0.65
-0.80
-0.80
-0.72
-0.56
-0.41
-0.31
-0.24
-0.19
-0.14
-0.08
-0.03
-0.02
0.01
0.01
0
0
0
0
0
0
0
0
0
0
0
0.01
0.02
0.03
0.04
0.06
0.06
0.02
-0.03
-0.07
-0.10
-0.12
-0.17
-0.22
-0.28
-0.40
-0.54
-0.78
-1.02
-0.93
-0.76
-0.80
-0.87
-0.72
-0.52
-0.37
-0.27
-0.23
-0.20
-0.16
-0.11
-0.06
-0.02
0
0.01
0.02
0.01
0.01
0.01
0.01
0
0
69.
TABLE 9:
Vertically Averaged Wind Components
15-Month Summer (July,August,September)
Lat (ON)
m sect
March 69
90
88
86
84
82
80
78
76
74
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
1.63
1.65
1.68
1.75
1.90
2.05
2.28
2.52
2.72
2.99
3.21
3.50
3.82
4.22
4.85
5.40
6.11
6.83
7.48
8.31
8.82
9.15
9.38
9.35
9.01
8.31
7.29
5.91
4.37
2.70
1.08
-0.40
-1.70
-2.70
-3.51
-4.08
-4.54
-4.85
-5.06
-5.19
-5.24
-5.23
-5.12
-4.83
-4.42
-4113
June 68
1.20
1.20
1.22
1.37
1.67
1.94
2.29
2.64
2.87
3.12
3.28
3.40
3.53
3.81
4.33
4.84
5.61
6.41
7.16
8.13
8.75
9.21
9.57
9.56
9.19
8.44
7.36
5.91
4.33
2.63
1.03
-0.38
-1.59
-2.51
-3.26
-3.85
-4.35
-4.73
-5.03
-5.23
-5.35
-5.38
-5.28
-5.00
-4.59
-4.30
m secX
March 69
June 68
-0.15
-0.15
-0.14
-0.04
0.13
0.18
0.07
-0.06
-0.07
-0.01
0.02
0.03
0.03
0.04
0.06
0.06
o''0 5
0.03
0.04
0.04
0.02
-0.06
-0.12
-0.08
-0.01
0
0.01
0.04
0.07
0.05
0.03
0.02
0.02
0.04
0.05
0.05
0.04
0.04
0.03
0.03
0.02
-0.06
-0.07
-0.08
-0.09
-0.11
-0.14
-0.19
-0.23
-0.15
0.04
0.13
0.15
0.15
0.12
0.07
0.04
0.02
0
-0.02
-0.06
-0.10
-0.20
-0.27
-0.22
-0.13
-0.09
-0.06
-0.03
-0.01
-0.01
-0.01
-0.01
0
0.03
0.05
0.04
0.04
0.06
0.08
.0.07
0.07
0.07
0.08
0.10
0.12
0.11
0.09
0.11
0.02
0.04
0.07
70.
TABLE 10:
By Transient Eddies
m2 sec-2
March 69
June 68
Lat (ON)
0
0
-0.02
-0.04
-0.06
-0.10
-0.13
-0.17
-0.22
-0.25
-0.30
-0.34
-0.38
-0.36
-0.22
-0.06
-. 20
0.55
0.98
1.66
2.32
3.20
4.19
4.91
5.36
5.54
5.51
5.35
5.10
4.76
4.38
4.00
3.62
3.31
90
88
86
84
82
80
78
76
74
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
Vertically Averaged Momentum Transport
15-Month Summer (July,August,September)
~
0
0
0
-0.01
-0.02
-0.04
-0.05
-0.07
-0.09
-0.14
-0.19
-0.24
-0.30
-0.36
-0.40
-0.40
-0.29
-0.10
0.31
1.11
1.89
2.95
4.17
5.07
5.65
5.83
5.74
5.48
5.11
4.63
4.10
3.57
3.06
2.66
By Standing Eddies
m 2 sec 2
March 69
June 68
0
0
0
0
-0.03
-0.01
-0.01
-0.02
-0.02
-0.02
-0.03
-0.03
-0.04
-0.03
-0.02
-0.02
0.02
0.08
0.14
0.23
0.28
0.25
0.23
0.23
0.25
0.31
0.43
0.77
1.22
1.56
1.76
1.81
1.72
1.48
0
0
0
0
0
0
0
0
0
-0.01
-0.03
-0.06
-0.09
-0.10
-0.09
-0.06
-0.03
0.01
0.09
0.22
0.28
0.16
0.06
-0'.04
-0.08
0.06
0.31
0.65
1.03
1.32
1.48
1.54
1.50
1.36
3.01
2.33
1.22
1.24
2.73
2.41
2.07
1.73
1.45
1.23
1.01
0.85
0.72
0.53
0.40
2.09
1.87
1.67
1.40
1.14
0.95
0.76
0.60
0.45
0.30
0.20
1.00
0.77
0.57
0.43
0.33
0.20
0.10
0.13
0.31
0.31
0.23
1.23
1.17
1.09
1.06
1.00
0.82
0.60
0.48
0.50
0.40
0.27
71.
TABLE 11:
Lat (N 0 )
Vertically Averaged Generation of Kinetic Energy
15-Month Summer (July,August,September)
By Transient
3
Eddies m sec-3
Mar 69
Jun 68
R
88
86
84
82
80
78
76
74
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
-1.77
-0.13
-0.09
-0.06
-0.05
-0.04
-0.06
-0.07
-0.07
-0.07
-0.04
0
0.09
0.06
0
-0.12
-0.24
-0.47
-0.07
-0.36
-0.14
0.44
1.77
3.60
5.46
7.04
7.85
7.69
6.95
5.71
4.44
3.23
2.27
_1.53
1.04
0.77
0.61
0.42
0.28
0.21
0.12
-0.05
-0.31
-0.37
-0
. 3 1
-0.44
-0.03
-0.02
-0.01
-0.01
0
-0.01
-0.02
-0.04
By Standing
Eddies m sec-3
Mar 69
Jun 68
p
q
-0.07
0
0
-0.01
-0.01
-0.05
0
0
0
-0.01
0
0
0
-0.01
-0.02
-0.03
-0.02
0.01
0.02
0.03
0.02
0
-0.03
-0.06
-0.02
0.05
0.05
-0.01
-0.01
-0.01
-0.01
-0.07
-0.09
-0.07
0.23
0.91
0.16
0.18
0.06
-0.18
-0.01
-0.64
-0.02
0.01
0.04
0.05
0.07
0.08
0.18
0.48
1.17
2.01
2.52
2.58
2.37
1.93
-0.60
-0.66
-0.06
1.65
3.91
6.03
7.59
8.19
7.74
6.68
5.14
3.69
2.49
-0.01
0
0.01
0.01
0.01
0
-0.01
-0.02
1.64
1.10
0.78
0.60
0.52
0.36
1.40
0.24
0.24
0.19
0.10
-0.03
-0.22
-0.28
0.19
0.06
-0.17
-0.39
-0.35
-0.23
-0.25
0.93
0.62
0.46
0.38
0.31
-0.11
-0.04
0.33
0.98
1.71
2.13
2.12
1.89
1.51
1.09
0.75
0.56
0.41
0.25
0.17
0.12
0.07
-0.03
-0.18
-0.31
-0.25
-0.14
By Mean Meridional
Circulation m2 sec-2
Mar 69
Jun 68'
-0.01
-0.02
0
0
-0.02
0
0
-0.02
0.03
-0.02
0.02
0
-0.01
0
0.01
0.02
-0.04
-0.05
-0.04
-0.01
0.02
0.03
0.03
0.03
0.03
-0.01
0.02
-0.09
0
-0.04
-0.10
-0.18
-0.29
-0.38
-0.48
-0.53
-0.38
-0.19
-0.11
-0.66
0.01
0.09
0.12
0.12
0.10
0.08
0.05
0.03
0.02
0.03
0.03
0.04
0.04
0.06
0.07
0.07
0.05
0.02
0
-0.15
-0.20
-0.26
-0.35
-0.51
-0.67
-0.92
-1.13
-0.95
-0.63
-0.41
-0.23
-0.05
0.07
0.10
0.12
0.11
0.12
0.11
0.10
0.10
0.12
0.13
0.13
0.12
0.13
0.12
0.10
0.07
0.03
0
T
72.
TABLE 12:
Vertically Averaged Wind Components
15-Month Fall (OctoberNovemberDecember)
(H
Lat (ON)
m sec 1
March 69
June 68
2.35
2.31
2.32
2.54
2.99
3.25
3.36
3.45
3.61
3.90
2.41
2.39
2.38
2.47
2.68
2.87
3.16
3.47
3.73
4.10
4.20
4.34
4.72
5.27
5.85
6.67
7.29
7.97
8.66
9.35
10.3
10.9
11.4.
11.8
12.2
12.5
12.6
12.6
12.4
12.0
11.3
10.5
9.52
8.33
6.83
5.18
3.50
1.78
0.31
-0.91
-1.77
-2.34
-2.69
-2.71
-2.46
-2.10
-1.83
4.56
4.80
5.21
5.92
6.58
7.50
8.45
9.29
10.4
10.0
11.5
12.0
12.3
12.6
12.7
12.7
12.5
12.2
11.5
10.7
9.52
8.22
6.69
5.05
3.39
1.68
0.22
-0.10
-1.87
-2.44
-2.80
-2.82
-2.56
-2.19
-1.92
m sec 1
March 69
June 68
-1.30
-1.31
-1.28
-1.06
-0.62
-0.38
-0.32
-0.29
-0.22
-0.10
-0.02
0.02
0.05
0.08
0.12
0.13
0.10
0.08
0.09
, 0.11
0.10
0.01
-0.08
-0.08
-0.06
-0.07
-0.10
-0.10
-0.10
-0.27
-0.25
-0.23
-0.20
-0.13
-0.08
-0.08
-0.08
-0.04
0.04
0.09
0.11
0.14
0.13
0.10
0.06
-0.02
-0.09
-0.07
-0.02
-0.01
-0.13
-0.23
-0.20
-0.14
-0.13
-0.13
-0.09
-0.05
-0.07
-0.05
-0.07
-0.05
-0.08
-0.04
-0.05
-0.10
-0.12
-0.07
-0.13
-0.06
-0.05
-0.03
0.01
0.05
0.08
0.10
0.12
0.13
0.12
0.10
-0.11
-0.08
-0.07
-0.04
0
0.02
0.04
0.07
0.09
0.08
0.07
-0.08
73.
TABLE 13:
Lat (ON)
90
88
86
84
82
80
78
76
74
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
26
24
22
20
18
16
14
12
10
8
-6
4
2
0
Vertically Averaged Momentum Transport
15-Month Fall (October,November,December)
By Transient Eddies
m 2sec~2
March 69
June 68
0
0
0.01
0.01
-0.02
-0.06
-0.11
-0.17
-0.24
-0.34
-0.44
-0.52
-0.61
-0.76
-0.96
-1.10
-1.12
-1.06
-0.86
-0.35
2.03
1.15
2.42
3.66
4.82
5.71
6.46
7.24
7.92
8.39
8.66
8.73
8.61
8.24
7.74
7.22
6.54
5.70
4.82
4.02
2.23
2.42
1.86
1.43
1.02
0.78
0
0
-0.01
-0.03
-0.06
-0.10
-0.13
-0.16
-0.20
-0.25
-0.30
-0.35
-0.34
-0.56
-0.85
-1.07
-1.14
-1.15
-1.03
-0.65
-0.17
(0.78
2.07
3.31
4.49
5.55
6.52
7.50
8.32
8.81
8.97
8.68
8.17
7.57
6.92
6.30
5.58
4.81
4.10
3.50
2.87
2.20
1.69
1.29
0.90
0.64
By Standing Eddies
m2 sec 2
March 69
June 68
0
0
0
0
0
-0.01
-0.04
-0.09
-0.14
-0.22
-0.28
-0.34
-0.39
-0.34
-0.15
0.02
0.22
0.49
0.86
1.40
1.70
1.63
1.61
1.90
2.23
2.37
2.44
2.55
2.73
3.05
3.35
3.38
3.21
2.72
2.06
1.46
0.92
0.47
0.16
-0.02
-0.18
-0.38
-0.50
-0.54
-0.54
-0.52
0
0
0
0
0
-0.01
-0.02
-0.05
-0.10
-0.18
-0.28
-0.37
-0.46
-0.49
-0.41
-0.32
-0.11
0.24
0.76
1.52
1.90
1.81
1.80
2.26
2.73
2.82
2.92
3.49
4.09
4.28
4.17
3.82
3.32
2.73
2.06
1.47
0.91
0.39
0.02
-0.19
-0.35
-0.52
-0.59
-0.57
-0.54
-0.52
74.
TABLE 14:
Lat (ON)
90
88
86
84
82
80
78
76
74
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
Vertically Averaged Generation of Kinetic Energy
15-Month Fall (October, November, December)
By Transient
Eddies mased-3
Mar 69 Jun 68
0
1.16
0.06
-0.04
-0.08
-0.12
-0.16
-0.20
-0.21
-0/117
-0.07
0.08
0.15
0.34
0.46
0.39
0.40
0.34
0.31
.0.02
-0.16
-0.36
-0.56
-0.52
-0.20
0.40
1.20
2.31
3.94
5.55
6.85
8.02
9.28
10.0
9.63
9.04
7.73
5.94
4.01
2.48
1.53
0.72
0.17
-0.08
-0.11
-0.08
0
-2.59
-0.19
-0.04
-0.12
-0.12
-0.08
By Standing
Eddies m3 secd'*
Mar 69
0
-0.19
-0.01
0
0
-0.02
-0.06
-0.09
-0.08
-0.08
-0.10
-0.10
-0.12
-0.03
-0.11
-0.08
0.04
0.06
0.11
0.06
0.28
0.52
0.73
0.59
0.48
0.14
-0.14
-0.37
-0.49
-0.29
-0.07
0.26
0.84
1.89
4.06
6.36
8.04
-0.09
0*04
-0.01
-0.07
-0.15
0
-0.14
-0.01
-0.01
-0.01
-0.01
-0.01
-0.03
-0.03
-0.05
-0.10
-0.10
-0.05
0.10
0.15
0.15
0.05
-0.15
-0.40
-0.59
-0.32
-0.30
-0.46
-0.78
-0.46
-0.38
-0.33
-0.29
-0.34
-0.16
0.08
0.38
0.78
-0.15
-0.22
-0.39
0.20
0.75
1.36
2.00
2.06
2.76
3.24
3.99
4.25
4.10
3.61
2.74
1.96
1.19
0.54
0.15
-0.01
-0.05
-0.05
0
0.05
9.00
9.38
9.31
8.53
7.75
6.44
4.88
3.27
3.34
0.65
-0.06
-0.17
-0.18
-0.13
0.17
-0.49
-0.80
-0.04
0.04
0.06
-0.56
0*06
2.12
1.33
Jun 68
3.68
3.51
2.70
1.87
1.00
0.30
0.06
0.05
By Mean Meridional
Circulation m2 sed-2
Mar 69
0
0.01
0.03
0.03
0.03
0.03
0.05
0.08
0.11
0.15
0.18
0.23
0.27
0.28
0.24
0.21
0.17
0.12
0.04
-0.08
-0.18
-0.32
-0.45
-0.40
-0.30
-0.30
-0.32
-0.30
-0.24
-0.07
0.11
0.29
0.40
0.38
0.34
0.31
0.28
0.22
0.17
0.13
0.09
0.06
0.04
0.02
0.01
0
Jun 68
0
0
0.01
0.01
0.03
0.04
0.07
0.10
0.14
0.18
0.21
0.23
0.25
0.25
0.23
0.21
0.12
0.01
-0.09
-0620
-0.32
-0.57
-0.81
-0.73
-0.53
-0.42
-0.32
-0.10
0.13
0.29
0.41
0.49
0.53
0.51
0.47
0.44
0.39
0.30
0.21
0.16
0.10
0.06
0.04
0.02
0.01
0
.75..
TABLE 15:
Vertically Averaged Wind Components
15-Month Winter (January,FebruaryMarch)
[]V]
Lat (ON)
m sec 1
March 69
June 68
m secx1
March 69
June 68
90
S.51
2.30
-0.84
0.07
88
86
84
82
80
78
76
74
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
26
24
3.52
3.51
3.43
3.30
3.33
3.67
4.07
4.45
5.01
5.36
5.65
5.91
6.05
6.18
6.27
6.36
6.50
6.89
7.60
8.25
9.16
10.3
11.4
12.6
13.7
14.8
15.8
16.6
16.9
16.9
16.4
15.5
13.9
2.26
2.25
2.44
2.83
3.17
3.65
4.14
4.55
5.08
5.38
5.53
5.66
5.76
5.88
6.01
6.23
6.49
6.91
7.64
8.29
9.21
10.3
11.5
12.7
13.8
15.0
16.0
16.8
17.1
17.0
16.2
15.1
13.4
-0.81
-0.77
-0.64
-0.38
-0.22
-0.18
-0.16
-0.14
-0.10
-0.04
0.10
0.22
0.23
0.17
0.13
0.11
0.09
0.14
0.22
0.21
0.02
-0.17
-0.18
-0.13
-0.16
-0.21
-0.24
-0.25
-0.23
-0.20
-0.19
-0.20
-0.22
0.12
0.16
0.13
0.08
0.05
0.01
-0.03
-0.08
-0.14
-0.14
-0.05
0.04
0.05
0.02
0
0
0.01
0.06
0.16
0.15
-0.06
-0.25
-0.23
-0.16
-0.19
-0.24
-0.22
-0.18
-0.16
-0.15
-0.16
-0.18
-0.20
12.0
11.3
-0.24
-0.21
9.51
6.77
4.24
1.94
0.15
-1.22
-2.31
-2.81
-2.81
-2.59
-2.38
8.96
6.32
3.87
1.65
-0.08
-1.39
-2.41
-2.87
-2.83
-2.59
-2.37
-"0.22
-0.18
-0.16
-0.11
-0.06
-0.02
0.01
0.04
0.05
0.04
0.04
-0.19
-0.16
-0.15
-0.13
-0.11
-0.09
-0.07
-0.04
-0.02
-0.01
-0.01
22
20
18
16
14
12
10
8
6
4
2
0
-
-
--------
76.
TABLE 16:
Lat (ON)
90
88
86
84
82
80
78
76
74
72
70
68
66
64
62
60
58
56
54
52
50
48
46
'44
42
40
38
36
34
32
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
Vertically Averaged Momentum Transport
15-Month Winter (JanuaryFebruary,March)
By Transient Eddies
m 2 sec 2
March 69
June 68
By Standing Eddies
m2 sec"2
March 69
June 68
0
0
0.01
0.03
0.04
0.04
0.01
-0.05
-0.13
-0.25
-0.34
-0.37
-0.38
-0.40
-0.34
-0.22
0.09
0.40
0.90
1.44
1.90
2.39
3.00
0
0
0
0
0
0
-0.05
3.71
4.56
5.65
6.83
7.99
8.97
9.64
9.97
9.83
9.45
9.00
8.44
7.70
6.73
5.65
4.49
3.45
2.50
1.56
0.87
0.30
-0.18
-0.43
0
0.01
0.03
0.06
0.06
0.04
-0.01
-0.10
-0.18
-0.25
-0.26
-0.10
0.13
0.24
0.28
0.35
0.53
0.75
1.00
1.34
1.68
2.17
2.82
3.64
4.67
6.01
7.44
8.81
9.89
10.3
10.3
29.70
8.87
8.05
7.21
6.33
5.34
4.40
3.50
2.72
2.00
1.27
0.68
0.13
-0.32
-0.56
-0*15
-0.30
-0.58
-0.84
-1.07
-1.32
-1.51
-1.58
-1.64
-1.64
-1.55
-1.26
-0.66
-0.26
0.17
0.90
1.49
1.84
2.13
2.37
2.25
2.20
2.67
3.21
0
0
0
0
0
-0.01
-0.06
-0.13
-0.27
-0.52
-0.76
-0.98
-1.23
-1.49
-1.75
-1.92
-1.86
-1.67
-1.31
-0.64
-0.23
0.14
0.90
1.63
2.07
2.28
2.62
3.17
3.75
4.37
4.83
3.34
4.80
3.18
2.65
1.90
4.45
3.87
3.07
1.27
2.26
0.71
0.19
-0.27
1.45
0.74
0.22
-0.16
-0.50
-0.87
-1.04
-1.05
-0.60
-0.90
-1.23
-1.39
-1.41'
-1.29
-1.20
-0.96
-0.89
77.
TABLE 17:
Lat (ON)
90
88
86
84
82
80
78
76
74
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
26
2422
20
18
16
14
12
10
8
6
4
2
0
Vertically Averaged Generation of Kinetic Energy
15-Month Winter (January,February,March)
By Transient
Eddies m 3 sec 3
Mar 69 Jun 68
0
By Standing
Eddies m3 sec3
Mar 69 Jun 68
3.31
6.83
10.3
13.1
14.5
15.1
13.4
10.5
7.04
0
5.62
0.40
0.20
0.08
0.02
-0.01
-0.04
-0.06
-0.09
-0.15
-0.06
0.08
0.14
0.16
0.18
0.21
0.15
-0.11
-0.37
-0.07
-1.48
-2.28
-2.95
-3.93
-5.16
-6.30
-6.33
-3.47
0.84
5.22
8.69
11.0
12.5
12.5
12.1
10.2
7.87
5.32
4.20
3.25
2.38
0.91
0.09
-0.19
1.93
0.83
0.17
-0.05
-0.15
-0.03
-0.14
-0.08
-0.08
-0.03
1.24
0.09
0.10
0.08
0.03
-0.02
-0.07
-0.09
-0.10
-0.17
-0.13
-0.08
-0.03
0.02
0.06
0.18
0.19
-0.10
-0.46
-0.83
-1.63
-2.41
-3.10
-3.94
-4.84
-5.52
-5.28
-3.28
-0.26
0
-0.24
-0.01
0.01
0.03
0.01
-0.04
-0.11
-0.15
-0.24
-0.48
-0.58
-0.73
-0.84
-0.76
-0.69
-0.55
-0.20
0.23
0.18
0.08
-0.18
-0.86
-1.33
-1.58
-1.77
-1.86
-1.43
-0.76
-0.09
1.09
2.46
3.70
4.08
3.40
2.52
1.34
0.06
-0.83
-1.18
-1.33
-1.25
-0.83
-0.42
0
-0.41
-0.01
-0.01
-0.02
-0.02
-0.04
-0.08
-0.13
-0.23
-0.50
-0.66
-0.76
-0.84
-0.80
-0.60
-0.35
-0.06
0.29
0.21
0.09
-0.14
-0.84
-1.43
-1.83
-2.05
-2.32
-2.41
-1.42
0.30
2.60
4.71
6.15
6.61
5.84
4.65
2.96
1.31
0.20
-0.39
-0.67
-0.77
-0.54
-0.27
-0.08
-0.01
By Mean Meridional
Circulation m2 se-2
Mar 69 Jun 68
0
-0.01
-0.02
-0.03
-0.06
-0.09
-0.09
-0.08
-0.06
-0.03
0.02
0.16
0.32
0.36
0.32
0.29
0.20
0.11
0.06
0.02
-0.04
-0.26
-0.55
-0.66
-0.73
-0.09
-1.11
-1.23
-l.22
-0.91
-0.52
-0.17
0.12
0.28
0.41
0.53
0.60
0.56
0.46
0.36
0.25
0.16
0.09
0.04
0.01
0
0
0
-0.01
-0.01
-0.01
-0.02
0
0.02
0.03
0
0
0.09
0.19
0.21
0.18
0.16
0.12
0.07
0.05
0.03
-0.07
-0.44
-0.93
-1.09
-1.13
-1.31
-1.48
-1.44
-1.22
-0.80
-0.34
0.05
0.36
0.56
0.72
0.82
0.86
0.76
0.60
0.45
0.29
0.17
0.09
0.04
0.01
0
78.
BIBLIOGRAPHY
Crutcher, H. L., USWB, 1959: Upper wind statistics charts of the
northern hemisphere, NAVAER 50-lC-535, Vol. II.
Ferrel, W., 1856: An essay on the winds and the currents of the
ocean. Nashville J. Medicine and Surgery, II, 287-301.
Reprinted (1882) in popular essays on the movements of the
atmosphere. Prof. Pap. Signal Serv. No. 12, Washington, 7-19.
,
1859;
The motions of fluids and solids relative to
the earth's surface.
,
1889:
Math. Monthly, 1, 140 fp.
A popular treatise on the winds, New York, Wiley,
505 pp.
Gilman, P. A., 1963: Indirect measurements of the mean meridional
circulation in the southern hemisphere. Scientific Report
No. 3, Planetary Circulations Project, Massachusetts Institute of Technology, 49 pp.
Hadley, G., 1735: Concerning the cause of the general trade winds.
Phil. Trans., 29, 58-62.
Jeffreys, H., 1926: On the dynamics of geostrophic winds.
Roy. Meteor. Soc., 52, 85-104.
Q. J.
Kidson, J. W., 1968: The general circulation of the tropics.
Unpublished Sc.D. dissertation, Massachusetts Institute
of Technology, Chapter 5.
Kuo, H. L., 1951: A note on the kinetic energy balance of the
zonal wind systems. Tellus, 3, 205-207.
Kidson, J. W., D. G. Vincent, and R. E. Newell, 1969: Observational studies of the general circulation of the tropics.
Quart. J. R. Meteor. Soc., 95, 258-287.
Lorenz, E. N., 1952; Flow of angular momentum as a predictor
for the zonal westerlies. J. Meteor., 9, 152-157.
Available potential energy and the maintenance
, 1955:
of the general circulation. Tellus, 7, 157-167.
-
, 1967: The nature of the general circulation of the
atmosphere. W.M.O. 161 pp.
79.
Manabe, S., and J. Smagorinsky, 1967: Simulated climatology of
a general circulation model with a hydrological cycle.
M.W.R., 95, 155-169.
Mintz, Y., 1951: The geostrophic poleward flux of angular
momentum in the month of January 1949. Tellus, 3, 195-200.
Newell, R. E., J. W. Kidson and D. G. Vincent, 1969: Annual and
biennial modulations in the tropical Hadley cell circulation. Nature, 222, 76-78.
Priestly, C. H. B., and Troup, A. J., 1964: Strong winds in the
global transport of momentum. J. Atmos. Sci., 21, 459-460.
Sadler, J. C., 1968: Average cloudiness in the tropics from
satellite observations. International Indian Ocean Expedition. Meteorological Monographs No. 2, Honolulu. EastWest Center Press.
Personal conversations with author.
Sanders, F., 1969:
Saltzman, B., and S. Teweles, 1964: Further statistics on the
exchange of kinetic energy between harmonic components of
the atmospheric flow. Tellus, 16, 432-435.
Starr, V. P., 1948a: An essay on the general circulation of the
earth's atmosphere. J. Meteor., 5, 39-43.
, 1948b:
atmosphere.
,
On the production of kinetic energy in the
J. Meteor., 5, 193-196.
1949:
Transport of kinetic energy in the Atmosphere.
J. Meteor., 6, 160.
, 1951a:
Application of energy principles to the
general circulation.
, 1951b:
Compendium of Meteorology, A.M.S., 568-576.
The physical basis for the general circulation.
Compendium of Meteorology, A.M.S., 541-550.
,
1953:
Note concerning the nature of the large-scale
eddies in the atmosphere.
, 1956:
Tellus, 5, 494-498.
Modern developments in the study of the general
circulation of the atmosphere.
, 1958:
circulation?
J. Geophys. Res., 61, 334-340.
What constitutes our new outlook on the general
J. Meteor. Soc. of Japan, Ser. II, 36, 167-173.
Now
80.
, 1968: Physics of negative viscosity phenomena.
McGraw-Hill, 240 pp.
, 1969:
Progress Report 7491-354 from Traveler's
Research Corp., Hartford, Conn.
Starr, V. P., and N. E. Gaut, 1969: Symmetrical formulation of
the zonal kinetic energy equation. Tellus, 21, 185-192.
Starr, V. P., and R. M. White, 1951: A hemispherical study of the
atmospheric angular momentum balance. Q.J. Roy. Meteor. Soc.,
77, 215-225.
,
1952a:
processes.
,
Tellus,
1952b:
4,
___
_
,
Two years of momentum flux data for 310 N.
332-333.
, 1952c:
tropics.
Schemes for the study of hemispheric exchange
Q.J. Roy. Meteor. Soc., 78, 407-410.
Meridional flux of angular momentum in the
Tellus, 4, 118-125.
1954a:
Two years of momentum flux data for 13 0 N.
Tellus, 6', 180-181.
, 1954b:
lation.
Balance requirements of the general circu-
Geophys.
Res. Pap.
No.
35,
57 pp.
Vincent, D. G., 1968: Mean meridional circulation in the northern
hemisphere lower stratosphere during 1964 and 1965.
Q.J. Roy. Meteor. Soc., 94, 333-349.
Wallace, J. M., 1967: On the role of the mean meridional motions
in the biennial wind oscillation. Q.J. Roy. Meteor. Soc.,
93, 176-185.
White, R. M., 1951: On the energy balance of the atmosphere.
Trans. Amer. Geophys. Union, 32, 391-396,
White, R. M., and G. F. Nolan, 1960: A preliminary study of the
potential to kinetic energy conversion process in the
stratosphere. Tellus, 12, 145-148.
Widger, W. K., 1949: A study of the flow of angular momentum in
the atmosphere. J. Meteor., 6, 291-299.
Wiin-Nielson, A., 1968: On the annual variation and spectral
distribution of atmospheric energy. Tellus, 19, 540-559.
81.
ACKNOWL .EDGEMENTS
This writer should like to acknowledge the support rendered
to him by his thesis advisor, Professor Victor P. Starr, who not
only suggested the topic for investigation but also provided
continuing assistance and guidance until its completion.
And one can not ignore the value one obtains from discussing
ideas and problems with one's fellow students, namely, Major
George Chapman, Captain Thomas Dopplick, Captain Edward Blish,
Lieutenant Joseph Sims, all of the U.S. Air Force, and Mr.
Dayton Vincent of M.I.T.
My attendance at M.I.T. was sponsored by the U.S. Air Force
through the Air Force Institute of Technology.
Research was
supported by National Science Foundation Grant GA-1310X.
Drafting was accomplished by Miss Isabelle Kole, and typing
was done by Mrs. Jane McNabb.