Oceanographic effects of the Bermuda-Azores anticyclone.

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OCEANOGRAPHIC EFFECTS OF
THE BERMUDA -AZORES ANTICYCLONE

*****

9 William Stevens

OCEANOGRAPHIC EFFECTS OF
THE BERMUDA-AZORES ANTICYCLONE

by

William Stevens

r/

Lieutenant, United States Navy

Submitted in partial fulfillment of
the requirements for the degree of

MASTER OF SCIENCE
IN
METEOROLOGY

United States Naval Postgraduate School
Monterey, California

1961

AK )c s

Library

U. S. Naval Postgraduate School

Monterey, California

OCEANOGRAPHIC EFFECTS OF
THE BERMUDA-AZORES ANTICYCLONE
by
William Stevens
This work is accepted as fulfilling
the thesis requirements for the degree of
MASTER OF SCIENCE
IN
METEOROLOGY
from the
United States Naval Postgraduate School

ABSTRACT

The monthly values of a function which measures the Ekman drift
across a portion of the Gulf Stream near the Florida-South Carolina
coast are computed. The function depends upon geostrophic winds which
are obtained from monthly mean surface weather maps .

The values are compared with the secular variation of the areal ice
extent in the Barents Sea , the annual variation of sea level along the
Florida-South Carolina coast, and the annual variation of Gulf-Stream
surface velocity in the same area»

Results indicate that the variation of these winds off the south-east
coast of the United States is an important factor in the determination of
ice extent in the Barents Sea, that these winds have a minor influence on
the annual variation of local sea level, and that they are highly correlated
with the annual variation of local Gulf-Stream velocities .

The investigation was carried out at the U.S. Naval Postgraduate
School, Monterey, California, during the period March 1961 to May 1961
in partial fulfillment of the requirements for the degree of Master of
Science in Meteorology.

Grateful acknowledgement is made for the advice and assistance
rendered by Associate Professor Jacob Bo Wickham in the preparation of
this paper o

11

TABLE OF CONTENTS

Title Page

1
2
4

4. Results, Conclusions, and Illustrations 8

5= Bibliography 17

6. Appendix I, Data 18

Section

1.

Introduction

2.

Theory

3.

Method

111

LIST OF ILLUSTRATIONS

Plate Page

1. Curve of integration 10

2 . Vector wind diagram 1 1

3. Secular variation of F compared with the secular 12
variation of the areal extent of ice in the Barents

Sea

4„ Annual variation of sea-level anomalies due to 13

non-advective heat transfer and mean annual
variation of sea level (1945-1955). Florida-South
Carolina area

5. Mean annual sea level variation corrected for non- 14
advective heat transfer (1945-1955). Florida-
South Carolina area

6. Mean annual variation of sea level anomalies due 15
to advection compared with the mean annual

variation of F (1945-1955). Florida-South
Carolina area

7. Mean annual variation of F (smoothed) compared 16
with the mean annual variation of Gulf-Stream
velocities „ Florida-South Carolina area

IV

TABLE OF SYMBOLS

IM) = mass transport

T = coriolis parameter

IP = unit vector normal to curve

IF = vector wind stress

p = integrated Ekman drift

Cci = drag coefficient

l«x = air density

UU = surface wind speed

^o = surface wind velocity

LA = surface wind speed uncorrected for friction

L4<i = geostrophic wind speed

Q = angle between surface and geostrophic winds

o( = angle between geostrophic wind and curve of integration

"H = subscript used to indicate component normal to curve
of integration

£ = subscript used to indicate component parallel to curve
of integration

(X = geostrophic wind ratio

1. Introduction,

Iselin [_ 13 has suggested that during periods of increasing Gulf-
Stream flow less heat may be available downstream in the Gulf-Stream
system. This is based on the hypothesis that increased flow of the
Stream occurs simultaneously with a contraction of the warm surface
waters into the Sargasso Sea area.

Elliott C.2J attempts to relate changes in the areal extent of ice in
the Barents Sea to fluctuations in the Florida Current deduced from varia-
tions in sea level along the Florida-South Carolina coasts His hypothesis
is that low sea level along the coast indicates an increase in the speed of
the adjacent current system, which, in turn, is indicative of the decrease
in heat flowo Eventually the Barents Sea, downstream in the Gulf-Stream
system, is deprived of heat.

This paper originally was planned to investigate a hypothesis similar
to Elliott's from a slightly different point of view. A function representing
the normal component of Ekman drift currents is computed from the field of
atmospheric pressure across a line roughly paralleling the mean Gulf-
Stream position from Florida to about 40 N latitude,, Data are presented
comparing the value of the computed drift function with a measure of the
heat budget of the Barents Sea.

During this investigation, results were compared with the annual sea
level variation in the area, suggested by Patullo et al \~33 , and with
Fuglister's work [4] on Gulf-Stream velocity variations in the area,

2. Theory.

Stommel [_ 5 j has shown that the intensity of the Gulf Stream is
related to the curl of the wind integrated over the entire North Atlantic
Ocean; this implies that convergence of warm water (Ekman drift) in-
creases into the Bermuda-Azores area as the intensity of the Stream
increases. If there is a secular variation in the curl of the wind, then
one can expect a comparable secular variation in the heat available to
be transported downstream by the Gulf Stream; roughly, the downstream
heat transport would be inversely proportional to the Gulf-Stream inten-
sity. To partially test such a model, the secular variation in Ekman drift
across a portion of the Gulf Stream is compared with the secular variation
in the areal extent of ice in the Barents Sea, which reflects the down-
stream heat transport of the Gulf Stream with a time lag.

Patullo \_3^ observes that, in subtropical latitudes, sea level varia-
tions are principally steric; the steric departures are mostly thermal, and
they usually agree with recorded departures of sea level. Therefore, a
curve much like the recorded annual sea-level oscillation should be ob-
tained by calculation of monthly values of the heat budget in a given
locality and the corresponding changes in density and sea-level . These
thermally induced density changes (and sea-level oscillations) represent
the net effect of radiation, evaporation, sensible heat transfer, and ad-
vection. If it is assumed that advective changes are primarily caused
by the Ekman drift of warm surface waters, then the influence of this
drift can be shown by removing the non-advective thermal effects from

2

actual sea-level oscillation curves .

Since the Ekman transport is a function of surface winds \__ see
equations (1) and (4)J , purely local fluctuations of surface velocities
of the Stream can be compared with local variations in the Ekman trans-
port across the selected curve of integration to verify the relation of
Iselin [_l ~\ .

The primary tool in the proposed investigations results from Ekman 's
classic study of wind-drift currents [_6^ • According to this theory, the
net mass transport is given by

H =— $ MT. (1)

Integrating the normal component of this mass transport along a curve
yields

F - ^H'in <U . " (2)

Substituting (1) into (2) results in

F -- -S"Kk*"0>in<JsJ (3)

which is the rate at which the integrated Ekman flow crosses the curve
of integration outward from the Bermuda-Azores gyre {Y >0) 0

3„ Method.

In order to evaluate (3) in terms of some measurable quantity for
which data exist, i.e., the surface pressure field, certain simplifying
assumptions had to be made.

Standard texts define the wind stress by the formula

Changes in Ccl and ^ in (4) were assumed to have little effect on
gross variations of the integrated stress function , and Ccl and W
were assigned constant values.

The following identities are illustrated in plate 2%
U - U i • (5)

a ^

U0-- u U '- <x U^ (6)

U»^^U^! ca. U^ s«^ O ^oO^ (7)

UoS = aUs a °- u^cos (e + a )3 (8)

U^s = U^ cos^, (9)

1 1 - a ^ (10)

In (6) through (8) , the geostrophic wind ratio, (\ was taken to be a
constant value less than one. The angle between the geostrophic wind
and the surface wind, Q , was taken to be a constant, eleven degrees
[_ 7] o By expanding (7) and (8) and inserting (9) and (10) into these ex-
pansions, it is possible to eliminate o^ , the widely-varying angle be-
tween the isobars and the curve of integration.

Plate 2 shows that
Uo; [Uo^tU'i] ^ (11)

The finite difference approximations for the normal and parallel
components of geostrophic wind, relative to the line of integration,

U^s = - <^-f & N (12)

and

() -_ -i- A? (13)

are used, as well as (4) through (10) , in the manner described; thus,
(3) becomes

where W c ,

Originally, it was planned to determine the Ekman drift across a
line paralleling the mean Gulf-Stream position around the west and north
sides of the Bermuda-Azores anticyclonic area. Preliminary computations
of the drift across the line proposed above indicated that the most signifi-
cant fluctuation took place in the western segment of the Gulf Stream from
Florida to about 40 N latitude; as a result, the determination of Ekman
drift was restricted to this segment (plate 1) . A grid was constructed
along the line of integration (plate 1) . Only the terms inside the integral
sign of (14) were computed. Hence the P values, to which later refer-
ence is made, are in reality the evaluation of a function T7 , which is
proportional to Ekman drift. The computed values of F for each month

were recorded, deduced from monthly-mean surface weather maps of
1945 through September 1955. The net F across that part of the grid
labeled S2 (plate 1) was almost always smaller than that across the part
SI by at least two orders of magnitude. As a result, only the values of
F across SI were graphed in arbitrary units.

Data are not available to determine the variation in ice coverage in
precise quantitative terms. However, a subjective description of this
variation is possible, based on information in [_8^ • A heavy ice year
may be defined as one where the limit of the ice exceeds the limits of
the average of years 1919-1943,, and a light ice year where the ice lies
within these limits; then certain gross comparisons to the secular varia-
tion in F can be made (plate 3) .

The average heat transfer due to evaporation, radiation, and sensible
heat exchange in the area west of SI was computed for each month (see
Appendix I) . These values were used to estimate local density and result-
ing sea-level changes (plate 4) . To estimate advective thermal effects
on sea level the values estimated above were subtracted from the observed
annual sea-level variation (plates 4 and 5) . Since the annual variation of
sea level remaining after the removal of these changes (see Theory) repre-
sents the cumulative effect of heat advection in the area, the first deriva-
tive of this cumulative curve was obtained to determine the monthly ad-
vective anomalies. This curve was compared to the mean annual fluctua-
tion of F (plate 6) .

The mean annual variation of r determined in this paper represents a

6

small sample (1945-1955) . In order to compare this variation to local
velocity oscillations computed on the basis of observations taken over
many years [4 ~] , it was necessary to minimize effects of random varia-
tion in the shorter record. This was done by smoothing the annual varia-
tion of r in the manner

These smoothed monthly values were then compared with the local velocity
oscillations of the Gulf Stream (plate 7) .

4. Results, Conclusions, and Illustrations.

Plate 3 shows that 1949 through 1952 were "heavy" ice years , while
1953 through 1956 were "light", as defined earlier o There is large nega-
tive correlation between the net annual values of the function F and the
ice year intensity, with a four-year lag„ Going further, it would be con-
cluded that 195 7 was a "heavy" year and 1958 a "light" year. Unfortunate-
ly, information was not available to determine if, in fact, this were so.
The results do suggest a significant influence of the wind field off the
south-east coast of the United States on the Barents Sea climate. Since
the sample is small, a continuation of the study is recommended to further
test this indicated relation.

Plate 6-compares the annual variation of sea level anomalies due to
advection with the annual variation of \- in the investigated area „ During
the summer and winter stable periods the curves appear to be generally in
phase. Near the time of the equinoxes the curves are definitely out of
phase. It would appear that during the stable periods Ekman drift is a
factor of some importance to sea level oscillation. During the equinox
periods, which are times of great change in the sea-air relationships,
Ekman drift appears to have little significance. Some other advective
factor(s) , perhaps due to the Gulf Stream itself, apparently become domi-
nant during these unstable periods .

Finally, plate 7 compares mean annual fluctuations in the velocity of
the Gulf Stream with the smoothed variation of F in the same geographi-
cal area. The variations are in accordance with Iselin's suggestion [l]

8

(see Introduction) , since negative values of r do indicate movement of
warm surface waters into the Sargasso-Sea area with the corresponding
increase in Gulf-Stream velocity. Specifically 0 plate 7 indicates that the
annual variation of local winds is a significant factor influencing the
annual variation of Gulf-Stream surface velocity in the same area .

Wertheim ^9"] compared consecutive monthly values of mass trans-
port of the Florida Current with wind curl over the North Atlantic for a
period of 16 months with little correlation . It may be that if Wertheim
had available longer samples of these quantities, allowing determination
of mean annual variations, a significant relationship would be shown as
in the present study. There is evidence that short term Florida-Current
transport between Key West and Havana is influenced by factors other than
wind stress \j> , pp. 142-1433 • Thus, only for long-term averages does
one expect to find the close correspondence shown in plate 7.

PLATE 1. Curve of integration
10

PLATE 2. Vector wind diagram

11

Years for Ice Extent
51 52 53 54 55 56

T

58

Heavy

48 49 50 51
Years for F

■p
C

(D

-p
x
w

<u
o

M

Light

Ice Extent
Unverified Ice Extent

PLATE 3. Secular variation of P compared with the secular
variation of the areal extent of ice in the Barents Sea

12

F

M

M

J

A

0 N D

Sea Level

Density Changes

PLATE 4. Annual variation of sea- level anomalies due to
non-advective heat transfer and mean annual variation
of sea level (1945-1955). Florida-South Carolina area

13

28 -

24

20 —

16 -

g 12

0)
CD

s

•H
-P

C

Q)
O

8

o —

-4 -

-8 -

PLATE 5. Mean annual sea level variation corrected
for non-advective heat transfer ( 1945-1955 )
Florida-South Carolina area.

14

20

16 -

12 —

: 8

»4«out «4» in —

•H 4 —

S
o

>

CO

0

-4

-8

-12 —

0.4

- 0.3

0.2
0.1

0

fe

- -0.1

-0.2

-0.3
-0.4

Sea Level Anomalies

F

PLATE 6. Mean annual variation of sea level anomalies
due to advection compared with the mean annual
variation of F (1945-1955)
Florida-South Carolina area

15

0,2

0.1

— 0

-p
o
o

s

w

— -0.1

-0.2

--0.3

M

A M

0 N

D

Velocity

F( smooth)

PLATE 7. Mean annual variation of F( smooth) compared with
the mean annual variation of Gulf-Stream velocities
Florida-South Carolina area

16

BIBLIOGRAPHY

1. Iselin, C. O' D. , Preliminary Report on Long-period Variations
in the Transport of the Gulf-Stream System, Papo Phys. Ocean,
and Met , Vol. 8 , 40 pp„ , 1940.

2. Elliott, F. E. , Some Factors Affecting the Extent of Ice in the
Barents Sea Area, Arctic, Vol . 9, pp. 249-259, 1956.

3. Patullo, J. G., Wo Munk, R„ Revelle, E, Strong, The Seasonal
Oscillation in Sea Level, J. Mar. Res., Vol. 14, pp„ 88-155, 1955

4. Fuglister, F. C. , Annual Variations in Current Speeds in the Gulf
Stream System, J. Mar. Res„f Vol. 10, pp. 119-127, 1951.

5. Stommel, H. , The Gulf Stream, a Physical and Dynamical
Description, Univ. Calif. Press (Los Angeles) , 1958.

6. Sverdrup, Ho U., M. W. Johnson, R. H. Fleming, The Oceans,
Prentice Hall, Inc. (New York) pp. 492-500, 1942.

7. Jeffrey, H. , On the Relation Between Wind and Distribution of
Pressure, Proc. Roy. Soc. (London) A. Vol. 96, p. 233, 1919,

8o Danske Meteorologiske Institut, Isforholdene i de Arktiste Have
(The State of the Ice in the Arctic Seas) , Copenhagen, 1945-1956 „

9. Wertheim, G. K. , Studies of the Electric Potential Between Key
West, Florida, and Havana, Cuba, Trans Amer. Geop. Union,
Vol. 35, pp. 872-882, 1954.

10. Sverdrup, H. U., M. W. Johnson, R. H. Fleming, The Oceans,
Prentice Hall, Inc. (New York) p. 103, 1942.

11. Ibid. , p. 111.

12. U. S. Navy, Marine Climatic Atlas of the World, North Atlantic
Ocean, Vol. I, CNO, 1955.

13. Houghton, H. G. , On the Annual Heat Balance of the Northern
Hemisphere, J. Met., Vol. 11, pp. 1-9, 1954.

14. Jacobs, W. C. , The Energy Exchange Between Sea and Atmosphere
and Some of its Consequences, Bui. Scripps Inst. Ocean. , Vol. 6,
pp„ 27-122.

17

APPENDIX I
DATA

Sea-level records for the period 1945 through September 1955 were
obtained from United States Commerce Department data, consisting of
mean monthly sea level records fon Charleston, South Caroline; May-
port, Florida; and Fernandina, Florida. These records were corrected
for atmospheric pressure, after Patullo [.3] ; i.e. , one centimeter was
added to the recorded sea level for each millibar of pressure by which
the local pressure exceeded the average over all the oceans.

Mean monthly surface pressure maps for the period 1945 through
September 1955 were obtained from the United States Weather Bureau.
Since these charts were analyzed in five millibar increments, which
gave too gross an indication of the wind flow, the author interpolated
the pressure field in one millibar increments, for the investigated area,

The values for the annual surface velocity fluctuations of the Gulf
Stream used in this paper were those computed by Fuglister [_43 • They
represent the annual mean variation of surface velocities in the area.

The annual variation of non-advective heat transfer for the area, in
terms of sea level changes shown in plate 4, was determined by the
following procedure. The monthly values of incoming sun and sky radia-
tion received at the surface in the area [ICQ were computed * From these
were subtracted the monthly values of back radiation assuming a relative
humidity of 85 per cent \_ll] , the local mean sky-cover conditions, and

18

local sea surface temperature \_12t] . Also subtracted was the reflected
radiation assumed constant at 7 per cent of the incoming radiation [l3j .
To these monthly radiation values were added the mean monthly latent
and sensible heat losses 1 14 J „ These totals were then converted to sea
level changes by assuming that the effects of heating were manifested
uniformly throughout the upper 100 meters of the ocean. Average values
for the coefficient of thermal expansion and the specific heat at constant
pressure of sea water were used.

The values for the annual variation of advective anomalies shown
in plate 6 were derived simply by computing the differences between the
monthly values of sea level due to advection shown in plate 5. These
differences are proportional to the slope of the curve shown in plate 5 .

The ice information was derived from the 1949 through 1956 editions
of \ 8 ] . The 1956 edition was the latest giving summarized data avail-
able from the Danish Meteorology Institute.

19