(�

2

s) Memo: World-wide survey of buoyan y generation requirements. 1

Memo

From: Dana Swift

To: Doug Webb

Date: January 27, 2000

Subje t: World-wide survey of buoyan y generation requirements.

Hi Doug,

As des ribed in the email that I sent you Thursday, here is the pro edure that I used for determining what

a \typi al pro�le" (TP) is and what a \typi al highly strati�ed pro�le" (THSP) is:

1. I have a ess (via CDRom) to all of the observed pro�les from the NODC ar hives for the entire world

along with previously written software for manipulating these data. I extra ted all of the data from

these regions and applied some basi QC to ea h station so that I examined only well-formed pro�les.

2. I evaluated the right-hand-side of the expression

ÆV (p)

V

=

�(p)

�(0)

� 1� p� � [T (0)� T (p)℄ (1)

where

ÆV (p)

V

is the spe i� -buoyan y (ie., the fra tional volume hange), p = 2000 dbars is the target

pressure,

:

= 2:52 � 10

�6

dbar

�1

is the oat ompressibility (whi h is the median ompressibility of 49

UW APEXs), �

:

= 6:9 � 10

�5 Æ

C

�1

is the oat's volume thermal expansion oeÆ ient, and �(p) & T (p)

are the in situ density & temperature pro�les. To the extent that and � are independent of the

a tual oat volume, using the spe i� -buoyan y rather than the buoyan y eliminates the need to know

the oat volume itself.

3. I omputed a umulative frequen y distribution (CFD) of the spe i� -buoyan y data. The CFD allowed

me to quantitatively determine what a \typi al pro�le" (TP) and a \typi al highly strati�ed pro�le"

(THSP) means.

4. The two pro�les that I pi ked ame from the 50

th

per entile and the 95

th

per entile of the CFD.

Con lusion: We need a oat that is apable of in reasing its buoyan y by 1.0!1.1%! Yeow, that's a long

way from where we are now (whi h is less than 0.7%) and even this doesn't give omfortable summertime

margins. I really don't see how this an reasonably be done without in reasing the diameter of the piston.

The South Pa i� NOPP Region.

The ARGO ommittee has spe i�ed that the deployment region for S. Pa i� NOPP will be 10 ! 20 S,

80! 140W. Allowing for oat dispersion, I arbitrarily de�ned the S. Pa i� NOPP region to be 30 S! 10 N,

80! 160 W. There are 1071 stations in this region that satisfy basi QC spe s. Fig. 1 shows the CFD based

on these stations. A oat must in rease its buoyan y by 0.63% to traverse a TP and 0.85% to traverse a

THSP. Overhead and a minimal safety-margin requires another 0.15{0.2%.

Con lusion: For 2000 de ibar pro�les, a minimum 1% displa ement apa ity is needed for the S. Pa i�

NOPP region.

Here is a TP from the 50

th

per entile of the CFD:

RCSfile : wr �Buoyan ySurvey:tex; v Revision : 2:1

(�

2

s) Memo: World-wide survey of buoyan y generation requirements. 2

$ lat lon date time

$ -16.40 -135.18 01/11/65 18.000

$ p s t rho

0.0 36.193 27.400 1.023490

24.0 36.182 27.270 1.023626

48.1 36.382 26.820 1.024025

72.1 36.434 25.720 1.024515

96.2 36.419 25.190 1.024771

143.3 36.396 24.600 1.025137

190.5 36.144 22.900 1.025655

237.7 35.818 20.810 1.026202

285.9 35.346 17.630 1.026883

333.1 34.945 14.650 1.027482

381.4 34.708 12.340 1.028001

429.7 34.521 9.730 1.028563

476.0 34.486 8.100 1.029018

524.4 34.463 7.090 1.029376

572.7 34.448 6.460 1.029677

667.5 34.479 5.830 1.030222

764.3 34.504 5.380 1.030745

956.0 34.520 4.530 1.031745

1148.0 34.545 3.850 1.032728

1435.2 34.582 2.950 1.034179

1722.9 34.615 2.410 1.035579

2110.5 34.650 2.030 1.037406

2600.6 34.670 1.790 1.039651

3091.8 34.681 1.680 1.041856

Here is a THSP from the 95

th

per entile of the CFD:

$ lat lon date time

$ 1.47 -87.90 02/17/69 6.900

$ p s t rho

0.0 32.957 26.540 1.021327

10.0 32.951 26.540 1.021365

20.0 32.934 26.400 1.021439

30.0 34.548 19.820 1.024597

40.0 34.946 17.010 1.025648

49.0 34.974 16.340 1.025867

74.1 34.978 15.130 1.026256

98.2 34.997 14.800 1.026450

147.4 35.011 14.610 1.026720

197.6 34.990 14.240 1.027007

299.1 34.877 12.500 1.027733

399.7 34.723 9.930 1.028550

600.0 34.620 7.490 1.029780

801.6 34.574 5.770 1.030915

1002.4 34.575 4.580 1.031993

1204.5 34.594 3.740 1.033038

1208.5 34.595 3.710 1.033061

1513.0 34.621 3.040 1.034551

RCSfile : wr �Buoyan ySurvey:tex; v Revision : 2:1

(�

2

s) Memo: World-wide survey of buoyan y generation requirements. 3

1815.8 34.643 2.550 1.036003

2017.7 34.654 2.320 1.036953

2220.7 34.667 2.100 1.037905

2322.3 34.666 2.090 1.038362

2424.9 34.666 2.060 1.038825

2627.3 34.665 2.070 1.039725

N. Atlanti NOPP Region.

The ARGO ommittee has spe i�ed that the deployment region for N. Atlanti NOPP will be 5 ! 15 N

a ross the whole Atlanti . Allowing for oat dispersion, I arbitrarily de�ned the N. Atlanti NOPP region

to be 0 ! 25 N. There are 3781 stations in this region that satisfy basi QC spe s. Fig. 1 shows the CFD

based on these stations. A oat must in rease its buoyan y by 0.65% to traverse a TP and 0.85% to traverse

a THSP.

Con lusion: For 2000 de ibar pro�les, a minimum 1% displa ement apa ity is needed for the N. Atlanti

NOPP region.

Here is a TP from the 50

th

per entile of the CFD:

$ lat lon date time

$ 13.43 -51.30 12/03/81 8.000

$ p s t rho

0.0 36.204 27.460 1.023479

12.0 36.226 27.470 1.023543

23.0 36.236 27.480 1.023595

37.0 36.236 27.480 1.023655

54.1 36.395 27.590 1.023812

78.1 37.082 26.010 1.024939

101.2 37.217 23.950 1.025773

150.4 36.804 20.000 1.026794

202.7 36.198 16.360 1.027479

252.9 35.674 13.430 1.027953

299.2 35.567 12.380 1.028292

394.8 35.244 10.270 1.028873

500.6 34.989 8.490 1.029459

595.3 34.832 7.320 1.029952

832.2 34.715 5.510 1.031202

1003.9 34.813 5.190 1.032103

1218.1 34.954 5.010 1.033208

1500.4 35.033 4.360 1.034636

2033.7 35.002 3.430 1.037141

Here is a THSP from the 95

th

per entile of the CFD:

$ lat lon date time

$ 5.10 -29.95 06/05/73 19.000

$ p s t rho

0.0 34.577 28.280 1.021987

9.0 34.926 28.600 1.022182

RCSfile : wr �Buoyan ySurvey:tex; v Revision : 2:1

(�

2

s) Memo: World-wide survey of buoyan y generation requirements. 4

17.0 35.049 28.600 1.022309

25.0 35.332 28.540 1.022576

42.0 35.918 28.160 1.023215

67.0 35.918 23.050 1.024907

89.1 35.805 18.110 1.026253

136.3 35.340 13.560 1.027150

183.6 35.286 12.640 1.027507

230.8 35.166 11.850 1.027781

324.3 34.946 10.430 1.028296

415.9 34.883 9.160 1.028882

504.5 34.731 7.620 1.029415

589.1 34.627 6.800 1.029842

691.9 34.611 6.020 1.030410

1002.6 34.731 4.800 1.032087

1216.8 34.857 4.630 1.033180

1491.9 34.972 4.280 1.034562

1929.7 34.985 3.640 1.036631

2885.3 34.997 2.720 1.041027

RCSfile : wr �Buoyan ySurvey:tex; v Revision : 2:1

(�

2

s) Memo: World-wide survey of buoyan y generation requirements. 5

938888349.7110452

Float Compressibility:γ=2.52 x 10-6 (decibar)-1

60˚S

40˚S

20˚S

0˚

20˚N

40˚N60˚N

60˚S

40˚S

20˚S

0˚

20˚N

40˚N60˚N

0102030405060708090

100

Cum

ulat

ive

Freq

uenc

y (%

)

0.000 0.002 0.004 0.006 0.008 0.010Specific Buoyancy at 2000 decibars (δm/M)

S. Pacific NOPP Region

20˚S

0˚

20˚N

40˚N

60˚N

20˚S

0˚

20˚N

40˚N

60˚N

0102030405060708090

100

Cum

ulat

ive

Freq

uenc

y (%

)

0.000 0.002 0.004 0.006 0.008 0.010Specific Buoyancy at 2000 decibars (δm/M)

N. Atlantic NOPP Region

0102030405060708090

100

Cum

ulat

ive

Freq

uenc

y (%

)

0.000 0.002 0.004 0.006 0.008 0.010Specific Buoyancy at 2000 decibars (δm/M)

Figure 1: Cumulative frequen y distribution for spe i� -buoyan y requirements at 2000 de ibars in the

N. Atlanti and S. Pa i� NOPP Regions. The ompressibility of the oat was taken to be median of 49

UW APEX drifters: = 2:52 � 10

�6

(dbar)

�1

.

RCSfile : wr �Buoyan ySurvey:tex; v Revision : 2:1

(�

2

s) Memo: World-wide survey of buoyan y generation requirements. 6

The Sargasso Region.

Just for grins, I applied the method to the Sargasso with a target pressure of 1000 de ibars. I predi t

that our APEXs in the Atlanti should make it to the surfa e OK. Interestingly, the CFD predi ts the

\hurri ane avoidan e feature" of APEX 010 | learly, we should have done this survey a long time ago. On

a related note, this analysis applied to the JES explains why the APEXs are performing marginally even at

800 de ibars.

938891814.2092852

Sargasso Region

0

10

20

30

40

50

60

70

80

90

100

Cum

ulat

ive

Freq

uenc

y (%

)

0.000 0.002 0.004 0.006 0.008 0.010Specific Buoyancy at 1000 decibars (δm/M)

80˚W 60˚W 40˚W 20˚W 0˚10˚S

0˚

10˚N

20˚N

30˚N

40˚N

50˚N

80˚W 60˚W 40˚W 20˚W 0˚10˚S

0˚

10˚N

20˚N

30˚N

40˚N

50˚N

Figure 2: Cumulative frequen y distribution for spe i� -buoyan y requirements at 1000 de ibars in the

Sargasso Region.

Sensitivity to in reased oat ompressibility.

Dan (in his alter ego as Doug) sent me an email Thursday whi h in luded the following request:

> Could you do it for 3 ompressibilities?

> 2.62, 3.2, 3.7

I did this ex ept that I used 2:52 (Mdbar)

�1

rather than 2:62 (Mdbar)

�1

(Do you like those units |Mdbar?).

I have re ords of an ensemble of 49 APEXs with measured ompressibilities in the range (2:45 ! 2:64) (Mdbar)

�1

with the median value being 2:52 (Mdbar)

�1

. Figures 3 & 4 illustrates that in reased ompressibility an

hypotheti ally buy for free (ie., no energy expenditure) the overhead & saftey margin needed.

A world-wide survey of buoyan y-generation requirements.

When Dan was here last month, I mentioned to him that I thought a world-wide survey of buoyan y-

generation requirements should be done. I did that this morning.

RCSfile : wr �Buoyan ySurvey:tex; v Revision : 2:1

(�

2

s) Memo: World-wide survey of buoyan y generation requirements. 7

938888385.7110452

Float Compressibility:γ=3.2 x 10-6 (decibar)-1

60˚S

40˚S

20˚S

0˚

20˚N

40˚N60˚N

60˚S

40˚S

20˚S

0˚

20˚N

40˚N60˚N

0102030405060708090

100

Cum

ulat

ive

Freq

uenc

y (%

)

0.000 0.002 0.004 0.006 0.008 0.010Specific Buoyancy at 2000 decibars (δm/M)

S. Pacific NOPP Region

20˚S

0˚

20˚N

40˚N

60˚N

20˚S

0˚

20˚N

40˚N

60˚N

0102030405060708090

100

Cum

ulat

ive

Freq

uenc

y (%

)

0.000 0.002 0.004 0.006 0.008 0.010Specific Buoyancy at 2000 decibars (δm/M)

N. Atlantic NOPP Region

0102030405060708090

100

Cum

ulat

ive

Freq

uenc

y (%

)

0.000 0.002 0.004 0.006 0.008 0.010Specific Buoyancy at 2000 decibars (δm/M)

Figure 3: Cumulative frequen y distribution for spe i� -buoyan y requirements at 2000 de ibars in the

N. Atlanti and S. Pa i� NOPP Regions. The ompressibility of the oat was taken to be = 3:2 �

10

�6

(dbar)

�1

.

RCSfile : wr �Buoyan ySurvey:tex; v Revision : 2:1

(�

2

s) Memo: World-wide survey of buoyan y generation requirements. 8

938888407.7110452

Float Compressibility:γ=3.7 x 10-6 (decibar)-1

60˚S

40˚S

20˚S

0˚

20˚N

40˚N60˚N

60˚S

40˚S

20˚S

0˚

20˚N

40˚N60˚N

0102030405060708090

100

Cum

ulat

ive

Freq

uenc

y (%

)

0.000 0.002 0.004 0.006 0.008 0.010Specific Buoyancy at 2000 decibars (δm/M)

S. Pacific NOPP Region

20˚S

0˚

20˚N

40˚N

60˚N

20˚S

0˚

20˚N

40˚N

60˚N

0102030405060708090

100

Cum

ulat

ive

Freq

uenc

y (%

)

0.000 0.002 0.004 0.006 0.008 0.010Specific Buoyancy at 2000 decibars (δm/M)

N. Atlantic NOPP Region

0102030405060708090

100

Cum

ulat

ive

Freq

uenc

y (%

)

0.000 0.002 0.004 0.006 0.008 0.010Specific Buoyancy at 2000 decibars (δm/M)

Figure 4: Cumulative frequen y distribution for spe i� -buoyan y requirements at 2000 de ibars in the

N. Atlanti and S. Pa i� NOPP Regions. The ompressibility of the oat was taken to be = 3:7 �

10

�6

(dbar)

�1

.

RCSfile : wr �Buoyan ySurvey:tex; v Revision : 2:1

(�

2

s) Memo: World-wide survey of buoyan y generation requirements. 9

Con lusion: As expe ted, Figures 5, 6, & 7 show that the buoyan y generation requirements are the most

demanding in the equatorial regions. However, these plots also show that CSIRO's little orner of the world

isn't so terribly spe ial | their requirements are only marginally more extreme than equatorial regions in

general.

Unfortunately, the olor semanti s in these plots will be lost when printed on a B&W printer. I hope you

an print them on your olor printer.

Regards,

�

2

s

RCSfile : wr �Buoyan ySurvey:tex; v Revision : 2:1

(�

2

s) Memo: World-wide survey of buoyan y generation requirements. 10

939925733.7110452

60˚S

40˚S

20˚S

0˚

20˚N

40˚N

60˚N

60˚S

40˚S

20˚S

0˚

20˚N

40˚N

60˚N

60˚S

40˚S

20˚S

0˚

20˚N

40˚N

60˚N

60˚S

40˚S

20˚S

0˚

20˚N

40˚N

60˚N

60˚S

40˚S

20˚S

0˚

20˚N

40˚N

60˚N

60˚S

40˚S

20˚S

0˚

20˚N

40˚N

60˚N

0102030405060708090

100

Cum

ulat

ive

Freq

uenc

y (%

)

0.000 0.002 0.004 0.006 0.008 0.010Specific Buoyancy at 2000 decibars (δm/M)

Equatorial Atlantic

0102030405060708090

100

Cum

ulat

ive

Freq

uenc

y (%

)

0.000 0.002 0.004 0.006 0.008 0.010Specific Buoyancy at 2000 decibars (δm/M)

Subtropical S. Atlantic

0102030405060708090

100

Cum

ulat

ive

Freq

uenc

y (%

)

0.000 0.002 0.004 0.006 0.008 0.010Specific Buoyancy at 2000 decibars (δm/M)

Subpolar S. Atlantic

0102030405060708090

100

Cum

ulat

ive

Freq

uenc

y (%

)

0.000 0.002 0.004 0.006 0.008 0.010Specific Buoyancy at 2000 decibars (δm/M)

Subtropical N. Atlantic

0102030405060708090

100

Cum

ulat

ive

Freq

uenc

y (%

)

0.000 0.002 0.004 0.006 0.008 0.010Specific Buoyancy at 2000 decibars (δm/M)

Subpolar N. Atlantic

0102030405060708090

100

Cum

ulat

ive

Freq

uenc

y (%

)

0.000 0.002 0.004 0.006 0.008 0.010Specific Buoyancy at 2000 decibars (δm/M)

Figure 5: Cumulative frequen y distribution for spe i� -buoyan y requirements at 2000 de ibars in the

Atlanti O ean. The ompressibility of the oat was taken to be = 2:52 � 10

�6

(dbar)

�1

.

RCSfile : wr �Buoyan ySurvey:tex; v Revision : 2:1

(�

2

s) Memo: World-wide survey of buoyan y generation requirements. 11

939925718.7110452

60˚S

40˚S

20˚S

0˚

20˚N

40˚N60˚N

60˚S

40˚S

20˚S

0˚

20˚N

40˚N60˚N

60˚S

40˚S

20˚S

0˚

20˚N

40˚N60˚N

60˚S

40˚S

20˚S

0˚

20˚N

40˚N60˚N

60˚S

40˚S

20˚S

0˚

20˚N

40˚N60˚N

60˚S

40˚S

20˚S

0˚

20˚N

40˚N60˚N

0102030405060708090

100

Cum

ulat

ive

Freq

uenc

y (%

)

0.000 0.002 0.004 0.006 0.008 0.010Specific Buoyancy at 2000 decibars (δm/M)

Equatorial Pacific

0102030405060708090

100

Cum

ulat

ive

Freq

uenc

y (%

)

0.000 0.002 0.004 0.006 0.008 0.010Specific Buoyancy at 2000 decibars (δm/M)

Subtropical S. Pacific

0102030405060708090

100

Cum

ulat

ive

Freq

uenc

y (%

)

0.000 0.002 0.004 0.006 0.008 0.010Specific Buoyancy at 2000 decibars (δm/M)

Subpolar S. Pacific

0102030405060708090

100

Cum

ulat

ive

Freq

uenc

y (%

)

0.000 0.002 0.004 0.006 0.008 0.010Specific Buoyancy at 2000 decibars (δm/M)

Subtropical N. Pacific

0102030405060708090

100

Cum

ulat

ive

Freq

uenc

y (%

)

0.000 0.002 0.004 0.006 0.008 0.010Specific Buoyancy at 2000 decibars (δm/M)

Subpolar N. Pacific

0102030405060708090

100

Cum

ulat

ive

Freq

uenc

y (%

)

0.000 0.002 0.004 0.006 0.008 0.010Specific Buoyancy at 2000 decibars (δm/M)

Figure 6: Cumulative frequen y distribution for spe i� -buoyan y requirements at 2000 de ibars in the

Pa i� O ean. The ompressibility of the oat was taken to be = 2:52 � 10

�6

(dbar)

�1

.

RCSfile : wr �Buoyan ySurvey:tex; v Revision : 2:1

(�

2

s) Memo: World-wide survey of buoyan y generation requirements. 12

938886630.7110452

60˚S

40˚S

20˚S

0˚

20˚N

40˚N

60˚S

40˚S

20˚S

0˚

20˚N

40˚N

0102030405060708090

100

Cum

ulat

ive

Freq

uenc

y (%

)

0.000 0.002 0.004 0.006 0.008 0.010Specific Buoyancy at 2000 decibars (δm/M)

Indian Ocean

0102030405060708090

100

Cum

ulat

ive

Freq

uenc

y (%

)

0.000 0.002 0.004 0.006 0.008 0.010Specific Buoyancy at 2000 decibars (δm/M)

Figure 7: Cumulative frequen y distribution for spe i� -buoyan y requirements at 2000 de ibars in the

Indian O ean. The ompressibility of the oat was taken to be = 2:52 � 10

�6

(dbar)

�1

.

RCSfile : wr �Buoyan ySurvey:tex; v Revision : 2:1