Air–sea exchanges in the South Atlantic and South-western

Indian Oceans

Sebastian Krieger∗

Instituto Oceanográfico, Universidade de São Paulo

Pça. do Oceanográfico 191, São Paulo – SP, 05508–120, Brazil∗

sebastian.krieger@usp.br

June 26, 2013

Contents

1 Introduction 4

1.1 Bulk heat, momentum and moisture fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Data and methodology 6

2.1 Sea surface temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Atmospheric state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3 Air–sea flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.4 Climate indices and correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3 Results and discussion 8

3.1 Sea surface temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.2 Bulk flux calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.3 Heat fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.4 Climate indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4 Conclusions 20

1

List of Figures

2.1 Time series of the NINO3.4 and Antarctic Oscillation climate indices . . . . . . . . . . . . . . . 7

3.1 Global zonal average of sea surface temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.2 Global area weighted sea surface temperature, climatological anomaly and trend . . . . . . . . . . 9

3.3 Area weighted sea surface temperature, climatological anomaly and trend in the South Atlantic and

South-western Indian Oceans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.4 Average sea surface temperature map in the South Atlantic and South-western Indian Oceans . . . 10

3.5 Sea surface temperature climatology maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.6 Bulk coefficients for drag, and evaporation and sensible heat transfer as a function of wind speed . 11

3.7 Average calculated global zonal and meridional momentum flux, and latent and sensible heat flux

maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.8 Global map of average atmospheric stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.9 Histogram of the atmospheric stability globally and in the South Atlantic and South-western Indian

Oceans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.10 Net heat flux climatology maps in the South Atlantic and South-western Indian Oceans. . . . . . . 13

3.11 Zonal momentum flux climatology maps in the South Atlantic and South-western Indian Oceans . 14

3.12 Latent and sensible heat flux climatology maps in the South Atlantic and South-western Indian

Oceans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.13 Zonal–temporal diagrams of the net heat flux and climatological anomaly in the South Atlantic and

South-western Indian Oceans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.14 Correlation of the net air–sea heat flux with NINO3.4 climate index in the Pacific Ocean . . . . . 17

3.15 Correlation of the latent heat flux with Antarctic Oscillation climate index in the South Atlantic

Ocean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.16 Correlation maps of net air–sea flux, latent heat flux and sensible heat flux with Antarctic Oscillation

and NINO3.4 indices in the South Atlantic and South-western Indian Oceans . . . . . . . . . . . 19

2

Acronyms

AAO Antarctic Oscillation.

AMO Atlantic Multidecadal Oscillation.

CESM Community Earth System Model.

CNYF Corrected Normal Year Forcing.

CORE Coordinated Ocean Research Experiments.

EOF empirical orthogonal function.

ITCZ Intertropical Convergence Zone.

MEI Multivariate ENSO Index.

MOC meridional overturning circulation.

NAM Northern Annual Mode.

NINO3.4 El Niño 3.4 sea surface temperature index.

PNA Pacific – North America.

SAM Southern Annular Mode.

SLP sea level pressure.

SOI Southern Oscillation Index.

SPI South Pacific Index.

SST sea surface temperature.

3

1

Introduction

Air-sea interaction plays an important role in the re-

gulation of the Earth’s climate. Even though Earth’s cli-

mate is forced, to the lowest order, by the sun radiation

and the geometry of the planet, much of the geophysical

dynamic processes occur because of the transfer of prop-

erties at the interface between the atmosphere and the

ocean. The large-scale wind-driven ocean circulation is

one example of such a process. Liu et al. (1979) point

out that while momentum is transferred by pressure gra-

dients, molecular diffusion is the only process in which

heat and mass can be transferred at the interface.

The ocean is forced by freshwater, heat and momen-

tum fluxes. The air-sea heat fluxes are estimated by

summing their different components,

Qas = QS +QL +QE +QH +QP , (1.1)

where QS is the short-wave solar radiation, QL is the

long-wave radiation, QH is the sensible heat flux, QE is

the latent heat flux, and QP is the precipitation heat flux.

The flux components are defined to be positive down,

i.e. fluxes passing into the ocean are positive. The heat

flux has radiative and turbulent components. Sensible

and latent heat fluxes are turbulent. Wind stress is also

a turbulent flux and is usually aligned with the ocean

surface current ~UO.

Precipitation (rain and snow) creates a negative heat

flux QP , since usually precipitating water is colder than

sea surface temperature (SST) and, as a consequence, the

ocean looses heat. Estimation of marine precipitation

is very limited due to the lack of continuous in situ

measurements and difficulties in partitioning into rain

and snow. Therefore, the present study does not consider

precipitation heat flux.

In the Atlantic Ocean, the Agulhas leakage transports

warm and salty Indian Ocean waters. It is a region

that attracts interest because of its complex and strong

meso-scale activity. There is a constant formation of

oceanic eddy structures, the Agulhas rings, as part of

the retroflection of the Agulhas current back into the

Indian Ocean. Recent studies indicate an increase in the

Agulhas leakage, which would enhance an ‘invasion’ of

Indian Ocean Water into the Atlantic Ocean and there-

fore affect the meridional overturning circulation (MOC)

(Biastoch et al. 2009; Haarsma et al. 2011).

The main objective of the present study is to under-

stand major challenges and uncertainties in estimating

turbulent heat and momentum fluxes from atmospheric

state climatologies. Furthermore, we also analyse the

variability of different heat fluxes and compare them to

climate indices. The focus is in the region of the South

Atlantic and South-western Indian Oceans.

1.1 Bulk heat, momentum and

moisture fluxes

The turbulent air-sea fluxes (momentum, sensible heat

and latent heat) can be estimated from the following bulk

formulae, respectively,

~τ = ρa CD |∆~U | ∆~U , (1.2a)

QH = ρa cp CH |∆~U | ∆θ , (1.2b)

QE = ρa Λv CE |∆~U | ∆q , (1.2c)

where ρa is the near surface air density,

cp ≈ 1000.5 J·kg−1 is the specific heat of air and

Λv ≈ 2.5 · 106 J·kg−1 is the latent heat of vaporization.

∆~U = ~U(zu)− ~UO is the difference between the wind

measured at height zu and the ocean surface current.

∆θ = θ(zθ) − SST is the difference between the

potential air temperature at height zθ and the sea surface

temperature SST. Since the air at the sea surface is

assumed to be saturated, ∆q = q(zq) − qsat(SST ) is

4

the difference between the specific humidity at height zqand the saturated specific humidity over seawater given

by,

qsat(q1, q2, SST ) =q1

ρaexp

( q2

SST

), (1.3)

where q1 = 0.98 · 640 380 kg·m3 and q2 = −5107.4 K.

It is important to note that the factor 0.98 applies only

over seawater.

The drag coefficient CD, and the transfer coefficients

for evaporation CE and sensible heat CH are functions

of height z, atmospheric stability ζ and ‘effective’ wind

speed ∆~U . At neutral stability ζ = 0 and reference

height z = 10 m, the coefficients are given by

CD =a1

|∆~U |+ a2 + a3|∆~U | , (1.4a)

CE =34.6

1000

√CD , (1.4b)

CH =

{18.01000

√CD, if ζ > 0 (stable)

32.71000

√CD, if ζ ≤ 0 (unstable).

(1.4c)

where a1 = 2.7× 10−3, a2 = 1.42× 10−4 and

a3 = 7.64× 10−5 are empirically estimated coeffi-

cients of a multiple regression analysis.

By applying the bulk formulae, one can estimate the

turbulent fluxes using near surface atmospheric state

(wind, temperature and humidity). The iterative proce-

dure to compute the bulk fluxes using this formulation is

described in Large and Yeager (2004) and Large (2006).

5

2

Data and methodology

In the present study we use three different climato-

logical data sets and two climate indices. We use a SST

dataset, an atmospheric state (wind, temperature, hu-

midity, sea level pressure) ‘normal year’ dataset, and a

global air–sea flux dataset.

2.1 Sea surface temperature

We use the Community Earth System Model (CESM)

SST and sea ice concentration dataset for uncoupled

simulations interpolated in the T62 global grid. The

dataset contains monthly maps of SST between January

1840 and March 2012 and is a merged blended product

(Hurrell et al. 2008).

2.2 Atmospheric state

To test and analyse the sensitivity of the iterative esti-

mation for the turbulent fluxes, we use the Corrected

Normal Year Forcing (CNYF) (Large and Yeager 2004).

It consists of a single annual cycle of the atmospheric

state data (wind, temperature, humidity, sea level pres-

sure) needed to solve equations (1.2). The data is repre-

sentative of climatological conditions over decades and

includes weather events, such as storms.

2.3 Air–sea flux

To analyse the annual and inter-annual variability of

the heat fluxes, we use the monthly maps of latent

heat (QH ), sensible heat (QE), downward long-wave

radiation (LW ↓), upward long-wave radiation (LW ↑)

and net short-wave radiation (QS) fluxes from the Co-

ordinated Ocean Research Experiments (CORE) Global

Air–Sea Flux Dataset version 2 (Large and Yeager 2009).

Only the period between 1984 and 2004 is used, because

in this dataset, radiation prior to 1984 and precipitation

before 1979 are given only as climatological mean an-

nual cycles.

2.4 Climate indices and correla-

tions

Climate indices are a simple diagnostic quantity used

to characterize an aspect (mode) of the climate system

such as a circulation pattern. They may be used as a

time series to show inter-annual to multi-decadal vari-

ability. Examples of such indices are El Niño 3.4 sea

surface temperature index (NINO3.4), Southern Oscilla-

tion Index (SOI), Antarctic Oscillation (AAO), Northern

Annual Mode (NAM), Atlantic Multidecadal Oscilla-

tion (AMO), Pacific – North America (PNA), Multivari-

ate ENSO Index (MEI), South Pacific Index (SPI). The

NINO3.4 and AAO time series between 1984 and 2004

are shown in figure 2.1.

The Niño index is calculated as the 5-month running

average of SST climatological anomaly over one of the

Niño regions (Trenberth 1997). In the case of NINO3.4,

the region is bounded by 120◦W–170◦W and 5◦S– 5◦N.

Niño indexes have a high negative correlation with SOI.

The AAO is the dominant mode of atmospheric

variability in the southern hemisphere. The index is

calculated as the difference between the normalized

monthly zonal mean sea level pressure (SLP) at 40◦S

and 65◦S (Gong and Wang 1999) describes. The AAO

is revealed as the leading empirical orthogonal func-

tion (EOF) in many atmospheric fields, such as surface

pressure, surface temperature, and zonal wind, for ex-

ample (Thompson and Wallace 2000). The AAO is also

6

Figure 2.1: Time series of the NINO3.4 and Antarctic Oscillation (AAO) climate indices between 1984 and 2004.

referred to as the Southern Annular Mode (SAM).

To calculate the correlation between between the

fluxes and climate indices, for longitude x and latitude

y, let Y (x, y, t) and I(t) be the climatological anoma-

lies of a flux and the climate index, respectively. The

standard deviation of both the fluxes and climate indices

are σY (x, y) and σI . Furthermore, let X(t) = IσI

. For

every grid point, the slope of a linear regression of Y

on X give CY X(x, y) and the correlation coefficient is

thus,

rY X =CY X

σY

. (2.1)

The correlation maps of the different fluxes with the cli-

mate indices, give the fraction of the variance of the flux

that may be represented by the chosen climate indices

and its spatial distribution.

7

3

Results and discussion

This section presents some of the analysis that has

been made with the data sets used in this study. We start

presenting the general distribution of SST first globally

and then in the Southern Atlantic and South-western

Indian Oceans. Afterwards we use the bulk flux formulae

to estimate turbulent fluxes and atmospheric stability.

Then we present the average heat flux patterns in our

region of interest and finally correlate them with the

climate indices.

3.1 Sea surface temperature

Since SST is perhaps the most important parameter in air–

sea interaction studies, we start our analysis describing

some of the observed variability in the region of interest,

namely the South Atlantic and South-western Indian

Oceans. Both the latent (QE) and sensible heat (QH )

fluxes are function of wind speed and SST, as described

by equations (1.2b), (1.2c) and (1.3). The SST is directly

associated with the incident solar radiation and has a

strong dependence with latitude, as illustrates the global

zonal average of SST from the CESM dataset shown in

figure 3.1.

The global area-weighted average SST time series,

and its climatological anomaly, are illustrated in fig-

ure 3.2 and used to analyse the average temporal vari-

ability. The time series shows 4 distinctive periods, from

1870 to 1910 temperatures seem to be stable and even

show a very slight decreasing trend. From 1910 to 1947,

temperatures rise, then fall and show no apparent trend

until 1975. Afterwards global average SST starts rising

again. The linear trend for the whole global average

SST climatological anomaly time series is 0.026 ◦C per

decade. Besides the trends, the time series also shows

inter-annual variability. The global area-weighted aver-

age SST is (19.29 ± 0.66) ◦C.

Figure 3.1: Global zonal average of sea surface tempera-

ture (SST) distribution with latitude (solid line) enclosed by

twice its standard deviation (dashed line).

In the South Atlantic and South-western Indian

Oceans, the average SST between January 1870 and

March 2012 is (16.5 ± 2.2) ◦C and its average distribu-

tion is illustrated in figure 3.4. The SST has an overall

zonal distribution, however, it shows a decrease in tem-

perature close to the African coast. This colder water is

probably upwelling water brought by Ekman pumping.

The average time series of SST in this region, and

its climatological anomaly, are illustrated in figure 3.3.

Compared to the global average, this time series has

higher variance. This might be due to the compensating

effect of seasonality when calculating global averages.

There are also distinctive periods in this time series and

8

Figure 3.2: (Top) Global area weighted average sea surface temperature (SST). The grey solid line is the monthly average and

the black solid line is the filtered average using a 12-month boxcar window. (Bottom) Global area weighted climatological SST

anomaly (black) and linear trend (grey) of 0.026 ◦C per decade. The time series span the period between January 1870 and

March 2012.

Figure 3.3: (Top) Area weighted average sea surface temperature (SST) in the South Atlantic and South-western Indian Oceans.

The grey solid line is the monthly average and the black solid line is the filtered average using a 12-month boxcar window.

(Bottom) Area weighted climatological SST anomaly (black) and linear trend (grey) of 0.022 ◦C per decade. The time series

span the period between January 1870 and March 2012.

9

Figure 3.4: Average sea surface temperature (SST) map in

the South Atlantic and South-western Indian Oceans between

January 1870 and March 2012.

inter-annual variability. From 1870 to 1930, approxi-

mately, the time series shows no trend. From 1930 to

1942 there is an increase in average SST, when it de-

creases again. After 1950, the SST starts to increase and

its trend seems to become higher from 1990 onwards.

The linear trend in SST climatological anomaly in that

region and for the whole dataset is 0.022 ◦C per decade.

A remarkable feature of the SST climatology of the

Southern Atlantic and South-western Indian Oceans, as

illustrated in figure 3.5, is the enhanced upwelling of

cold water during austral winter near the African coast in

the Atlantic Ocean. Near the coast of Angola, SST falls

from about 27 ◦C in April to about 15 ◦C in September.

This might be due to an increase in the wind regime and

should also affect the momentum flux, and the latent and

sensible heat fluxes.

3.2 Bulk flux calculations

The variation of CD, CE and CH , both for stable (CHs)

and unstable (CHu) conditions, as a function of wind

speed according to equation (1.4) is illustrated in fig-

ure 3.6. The drag, evaporation and unstable sensible

heat coefficients have similar values between approx-

imately 4 m·s−1 and 12 m·s−1 wind speed. Outside

this region, the drag coefficient is always the highest.

The evaporation transfer coefficient is higher than both

sensible heat coefficients. Stable sensible heat transfer

coefficient is the lowest.

Using the bulk formulae we apply the atmospheric

Figure 3.5: Sea surface temperature (SST) climatology maps

calculated for the period between January 1870 and March

2012.

state variables provided by the CNYF dataset to estimate

the turbulent fluxes. The flux calculations are forced

with CESM SST dataset during 1984. The average re-

sults for the turbulent fluxes are illustrated in figure 3.7.

Compared to the CORE Global Air–Sea Flux dataset cli-

matologies illustrated in figures 3.12, these results have

same order of magnitude and similar spatial distribution.

The zonal momentum flux (figure 3.7a) is stronger, and

has positive sign, over the westerly winds, as expected.

In the tropics, the τx has opposite direction and has low-

est values in the center of the great gyres. The meridional

10

Figure 3.6: Bulk drag coefficient CD , and transfer coefficients for evaporation CE and sensible heat CH as a function of

‘effective’ wind velocity ∆U at neutral stability ζ = 0 and reference height z = 10 m, using equations (1.4).

(a) (b)

(c) (d)

Figure 3.7: Average global zonal (a) and meridional (b) momentum flux and latent (c) and sensible (d) heat flux maps calculated

using atmospheric state variables using the Corrected Normal Year Forcing (CNYF) data sets.

11

Figure 3.8: Global map of the average atmospheric stability ζ

using the Corrected Normal Year Forcing (CNYF2) data set.

momentum flux (figure 3.7b) is one order of magnitude

smaller than the zonal momentum. The highest magni-

tude is found at the eastern boundary of the Atlantic and

Pacific Oceans, in the tropical Indian Ocean and over

the Antarctic circumpolar current eastwards from Africa

up to New Zealand. The latent heat flux (figure 3.7c)

has a zonal distribution with negative flux in the tropics,

besides the eastern equatorial Pacific, and positive flux

in higher latitudes. The sensible heat flux (figure 3.7d)

has an overall homogeneous distribution and is one order

of magnitude lower than the latent heat flux.

Constant testing of the bulk flux calculation algorithm

has shown that the turbulent flux estimations are very

sensitive to the atmospheric stability ζ. The average

distribution of ζ is illustrated in figure 3.8. In this case,

since ζ < 0 almost everywhere, it suggests that the

ocean is mostly unstable. The atmosphere appears to

be more unstable over the Intertropical Convergence

Zone (ITCZ). Figure 3.9 shows the histogram for both

the global average stability and the stability over the

South Atlantic and South-western Indian Oceans. Both

distributions are very similar. Globally, the average at-

mospheric stability is ζ =-0.43 with standard deviation

σζ =1.4. In the South Atlantic and South-western In-

dian Oceans, the average stability is ζ =-0.27 and has

standard deviation σζ =0.94.

3.3 Heat fluxes

The different heat components of the CORE Global Air–

Sea Flux Flux Dataset were added to give a total air–sea

heat flux, according to equation (1.1). Figure 3.10 shows

the climatology maps for the South Atlantic and South-

Figure 3.9: Histogram of the atmospheric stability ζ glob-

ally (top) and in the South Atlantic and South-western Indian

Oceans (bottom) calculated using atmospheric state variables

using the Corrected Normal Year Forcing (CNYF) data set.

western Indian Oceans. The net air–sea flux has a strong

seasonality. The highest net fluxes are observed dur-

ing austral summer (December, January and February),

whereas the lowest net fluxes are observed during austral

winter (May, June and July). Near the Agulhas current

retroflection region, at the southern tip of the African

12

Figure 3.10: Net heat flux (Qas) climatology maps in the

South Atlantic and South-western Indian Oceans using the

CORE.2 Global Air–Sea Flux Dataset calculated for the period

between 1984 and 2004.

continent, near the Cape of Good Hope, the net heat flux

is always lower than its surroundings. In this region,

since the net flux climatology is always negative, the

ocean looses heat to the atmosphere. On the other hand,

near the Brazil–Malvinas confluence region, it appears

that the absolute net heat flux is enhanced, regardless of

the direction of the flux in its surroundings.

The zonal (τx) and meridional (τy) momentum flux

climatology maps are illustrated in figure 3.11. τx seems

to have an uniform zonal distribution with different in-

tensities during the year. On the other hand, τy shows a

small displacement of the flux gradients, probably due

to the migration of the ITCZ. τy is about one order of

magnitude smaller than τx.

Figure 3.12 illustrates the latent (QE) and sensi-

ble (QH ) heat flux climatologies. Latent heat flux is

about 4 to 5 times higher than sensible heat flux. QE

shows a zonal distribution similar to that of SST (3.5).

QH has also zonal distribution with distinctive latitude

bands and strong seasonality. The tropical Atlantic

Ocean appears to be dominated by fronts, which could

indicate wave-like phenomena. However, analysis of

zonal-temporal diagrams of QH (not shown) did not

indicate propagation of the signal. These front-like pat-

terns seem to be stationary. There is year long variability

of QH over the Antarctic circumpolar current. As with

Qas, near the Cape of Good Hope, QH is always nega-

tive.

The temporal variability of the heat flux can be anal-

ysed through zonal–temporal diagrams. Figure 3.13

shows the zonal–temporal diagram of Qas and its clima-

tological anomaly at 22.5◦S latitude. Qas shows a clear

seasonal pattern and no apparent propagation. Close

to the African coast, at about 5◦E, is a region that dur-

ing austral summer where the net heat flux is constantly

over 200 W·m2, which might be due to the coastal up-

welling. The net heat flux climatological anomalies vary

from about -50 W·m2 to 50 W·m2. There are no appar-

ent trends in the climatological anomalies, although the

anomalies appear to be higher at the beginning of the

time series.

3.4 Climate indices

Sensible fluxes can be correlated to the NINO3.4 and

AAO climate indices according to equation (2.1). Fig-

ures 3.14 and 3.15 illustrate the calculation of the cor-

relation coefficient of the climatological anomaly of a

flux component and a normalized climatological index.

In the first case (figure 3.14) shows a high negative cor-

relation (r = −0.74) of the net heat flux climatological

anomaly Q̃as with the normalized NINO3.4 climate in-

dex in the Pacific Ocean at 120.5◦W 2.5◦S. In the second

case (figure 3.15), we try to correlate the sensible head

flux climatological anomaly Q̃as with normalized AAO

in the Atlantic Ocean at 20.5◦E 42.5◦S, and observe no

correlation. By taking a closer inspection of the indi-

vidual time series, it seems that QH might lead AAO

and correlate with it with a lag of a couple of months.

13

(a) (b)

Figure 3.11: Zonal momentum flux τx (a) and meridional momentum flux τy (b) climatology maps in the South Atlantic and

South-western Indian Oceans using the CORE.2 Global Air–Sea Flux Dataset calculated for the period between 1984 and 2004.

14

(a) (b)

Figure 3.12: Latent heat flux QE (a) and sensible heat flux QH (b) climatology maps in the South Atlantic and South-western

Indian Oceans using the CORE.2 Global Air–Sea Flux Dataset calculated for the period between 1984 and 2004.

15

Figure 3.13: Zonal–temporal diagrams of the net heat flux Qas (left) and its climatological anomaly (right) in the South

Atlantic and South-western Indian Oceans at 22.5◦S latitude from 1984 to 2004.

16

Figure 3.14: Correlation of the net air–sea heat flux Qas with NINO3.4 climate index in the Pacific Ocean at 120.5◦W 2.5◦S.

(Top) Time series of the net air-sea climatological anomaly Q̃as (solid line) and of the normalized NINO3.4 index (dashed line).

(Bottom) The linear regression between Q̃as and NINO3.4. In this case, the correlation between both variables is r =-0.74.

Figure 3.15: Correlation of the latent heat heat flux QH with Antarctic Oscillation (AAO) climate index in the Atlantic Ocean

at 20.5◦E 42.5◦S. (Top) Time series of the latent heat climatological anomaly Q̃H (solid line) and of the normalized AAO index

(dashed line). (Bottom) The linear regression between Q̃H and AAO. In this case, the correlation between both variables is

r =-0.01.

17

However the analysis of cross correlation with lag was

not performed.

Applying the same methodology to different time se-

ries in each location, it is possible to construct correla-

tion maps as illustrated in figure 3.16. In this case we

correlate the net air–sea flux Qas, the latent heat flux QE

and the sensible heat flux QE with both the NINO3.4

and AAO climate indices. In all cases correlation is less

than 50%. In general, the spatial distribution of the cor-

relation of all heat flux components with a climate index

is similar. NINO3.4 correlates best with the fluxes over

the Antarctic circumpolar current, while AAO correlates

best in the tropics.

18

(a) (b)

(c) (d)

(e) (f)

Figure 3.16: Correlation maps of net air–sea flux Qas (top), latent heat flux QE (middle) and sensible heat flux QH (bottom)

with Antarctic Oscillation (AAO) index (left) and NINO3.4 index (right) in the South Atlantic and South-western Indian Oceans

between 1984 and 2004.

19

4

Conclusions

The present study tries to present a short overview on

the main distribution of the momentum and heat flux

components in the South Atlantic and South-western

Indian Oceans. Using different data sets and the bulk

formulation, we tried to estimate the turbulent fluxes.

However, these estimates are as good as the quality of the

forcing data sets, since small changes in the parameters

can lead to big errors in the estimates. It is important to

remember that air–sea fluxes occur in a thin layer right

at the interface between the atmosphere and the ocean,

and therefore measuring flux parameters on board of a

floating device is not always possible nor an easy task.

Assuming that the Earth system is in dynamical bal-

ance, then the integrated long term heat and water fluxes

should be near zero. However, there is great uncertainty

in the estimation of these fluxes and many corrections

to the models have to be included to satisfy this con-

straint (Large 2006).

The parametrization of the model depends on the avail-

ability of data. For global heat, momentum and fresh-

water flux estimates, we need global long-term measure-

ments, including the Southern Ocean and ice covered

regions. There is not only the problem of lack of in situ

measurements, the quality and accuracy of the available

data is as important. Another issue is regarding time

scales. Although seasonal in nature, heat and momen-

tum fluxes vary significantly on shorter time scales, such

as diurnal changes, for example.

The bulk formulae are functions of properties that are

away from this skin layer between ocean and atmosphere

and the transition into molecular scales is not straightfor-

ward. Fairall et al. (1996), for example, incorporate into

their flux estimation algorithm cool-skin and warm-layer

effects on bulk sea temperature measurements. These

authors conclude that these corrections cannot be used

in calculations of the neutral transfer coefficients.

The correlations of flux parameters and climate in-

dices in the South Atlantic and South-western Indian

Oceans are relatively small. An extension to this ap-

proach could be to include a time lag, which could

suggest causality and possibly allow for predictability.

From the correlation coefficients given by equation (2.1)

it would then be possible to estimate Y (x, y, t) =CY X(x, y) ∗X(t− l).

For future studies it would be interesting to try to anal-

yse the variability on shorter time scales and asses the ef-

fect of vertical and horizontal heat advection, as already

attempted by early studies (?), for example. Achieve this

on a global scale is a great challenge.

Acknowledgements

The current report has been made as an assignment for

the IOC5911 – Tópicos Especiais em Oceanografia,

whose topic was ‘Air–sea interaction and climate

change’. The lectures were taught by Dr. William B.

Large and organized by Prof. Dr. Ilana Wainer at the

Oceanographic Institute of the University of São Paulo.

20

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