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CM

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ödsmål, Kville sn»

Bohuslän

Hällristning

Fiskare frän bronsåldern

Rock carving Bronze age

fishermen

fv

MEDDELANDE från

HÂVSFISKELÂBORATORIET • LYSEKIL

BRQPJORDEN II

A

FORMULA SYSTEN FOR PRIMARY PRODUCTION

by

Bertil Öström

September 1973

(3)

i »

Whex computing large numbers of primary production data it is desirable to replace the older methods of reading tables and nomogram's with

formulas suitable for a computer. In this paper formulas are given which from temperature, salinity and pH values compute the total carbon dioxide content of the water. A formula using this carbon dioxide value and the number of geiger-müller-counts from the filter analysis then compute the final primary production value obtained by the C ^-tech

nique •

(4)

Symbols used In. the text

K,

IC,

K1f K2

a H20

H

Alk.

total

CO

2

0 s

Gl

as a prefix denote the negative 10-logarithm of the following variable

firat thermodynamic constant of carbon dioxide second :? " M

" n

first dissociation u " carbonic acid

second !t « "

u ”

molecular activity of water hydrogen ion activity

solubility of carbon dioxide in pure water

" !1 îs 11 M sea ?/ater dissociation constant of boric.acid alkalinity

total content of carbon dioxide primary production

salinity ehlorinlty

(5)

Hydrographical measurements performed by the Fishery Board of Sweden in investigating the Brofjorden and primary production measurements by The Marine Botanical Institute, University of Gothenburg, have taken place in close cooperation» A formula system has been developed in order to integrate the primary production data into the data proces

sing.

The formula system is used to calculate values of primary production using the carbon

-14

method*

The analyses are performed by the International Agency for deter

mination in Denmark, which gives the number of counts for the samples and values of the strength of the ampoules® The temperature and sali

nity values are obtained from the hydrographical measurements, and the pH values are measured from the production samples.

According to Sverdrup et. al, 1946 the first dissociation constant of carbonic acid is given by

PK' = PE1 - f x f/Cl

Where PK^ is given by Buell ( 1951 ) as

PK, « 1î052/Tabs + 215.21 x dog ïab0 - 0.12675 * Iabs - 545.560

1 n

and f is derived from the same source as f =

0.145

- 0.00025 x T K.j is then obtained by K.J = 10~ÎÂ1

The term is conventionally obtained as A =10 and Ag is given by Harvey (1966) as

A„ A s 1 - 0,000969 x 01

The proper relations for the temperature and chlorinity dépendance of the factors 0 and C were at this stage too laborious to work out, and they are here given in Intervals according to Buch (1945)

(6)

4 for

1 (°C) -2

%

h

10

13 20

25 30

0 x 104 o

394 C

?70 0

640 0

536 C

458 0

394 C

341 C

299 C

7 »22 X

»a

o

^{i 4*}

X Cl 6.51 X

¹

^er

⁴ X

Cl 5.37 X ^icT4

X

Cl 4.28

X

10“4

X 01 3 »54 X

^to

^“4 X G1

2.80 X

¹

^er

⁴ X

Cl 2.33 X ^10"4

X

Cl 1.96 X

^to

^“4

^X

Cl

The second dissociation constant for carbonic acid is with some modifi

cation taken from Buch (1951)

log K0 ~ ~2902.39/Taho + 6,4980 - 0,02379 x T&hei PKg « - log Kg - 0.510 x 3 Cl

Kg = 10”PK2

For the principal case, when computing primary production, in the open ocean, the boric acid dissociation constant must be established. The

following formula PK^ = 9.22 - 1,023 x \jüï - 0.0086 x 01+0.17-0,0093333 x Î is based on Buch's formula from 1932 for the chlorinity dépendance and is modified to account also for the temperature variation, a modifi

cation which is based on Buch's figures.

**Then K' is obtained from K,' * 1 o“PKB**

Then according to Harvey (1966) the titration alkalinity is 0,123 x 01 x 10 and the carbonate alkalinity is calculated as -3 carbonate alkalinity « titration alkalinity -

!C x 2.2 x Cl x 10'“5

AH + %

(7)

5 However,

for the actual case, the Brofjorden, the

so obtained alkalinity is

found

to

be considerably too

low

because of the

Baltic water influence

in the upper layer«

Another relation is therefore chosen which is deduced from

Buch

(1945;

and originally established by Hanna Wittig.

This is Aik = (1.26 + 0,056 z Cl)

x

10 ^

This relation is closely similar to Aik =

1,26 + 0.031 x S which is

used by the International Agency for 14C - determination in Denmark.

It must be clearly pointed out that this formula holds only for this specific area.

The

S

- Cl relation is given by Knudsen (1901) as S » 0.030 + 1.8050 x 01 For other areas, e.g. the Baltic, other relations for Aik must be

established.

All these expressions now give the total« carbon dioxide value for Brofjorden

Total COg

+

Cs Z aH

x Co X

z 12010

1 4

-

mg/1

For the general case of the open ocean Aik is replaced by titration alkalinity,

The primary production is then given by

'proa

counts x total 00^

x

10 ampstr. x duration

4-3

mg

G/nJ x h

Where counts is counts/minute from the Banish carbon isotope analyses and ampstr. is the strength of the 0 ' - ampoule

14

(8)

6

In

ALGOL the formula system looks like follows.

0 34 8 0349 0350 0351 0352 0353 0 354 0 355 0356 0357 0358 0359 0360 0 361 0 36 2 0 36 3 0364 0365 0 36 6 0 367 0368 0 369 0370 0 371 0372 0373 0374 0375 0376 0 3 77 03 78 0379 0330 0381 0 382 0 3 33 0 384 0385 5386 0 387 3 388 0389 0390 0391 0 392 0 393 3394 0395

PROD:

AHA :

GETft'E'ALfPHt ? > 113 Ï GETREÂUCOUNTS(Î) ,1) !

GETREAl(D

à

RKCOUNTSC j ) ,1> ?

'IF' ?N I X »THEN'* »BEGIN*

FACT : a 0,145- o', 000?5T } » COMMENT » FACT IS CALC FROM BUCH 1951 } PK1 : = 17fi52/TABS + 215 121 #LN CT AÖ8 ï/LN1Q - 0.12675TABS - 545,560 PKlPRIMïs PK1 - FACTCL»#(l/3)I K1 P R I M ! » 10#<-PK1PRIMi I

»COMMENT» SVERDRUP 1946 P

ag

F 200 WITH

* IF, r CNULL CMUU CNULL CMi ILL CNULL CNULL

1 GO *

= 849 j 77 0

= 440 i

= 636 I 4 58

= 394

**’AND* T<"1 »THEN» »BEGIN»**

CIS : S CNULL - ?,22**CL 'END»ELSE»IF» T »QQt^l CS!s CNULL -"6,51*01

'END’ELSE'IF* TGQ?2»5 C3:= CNULL - 513 7 » C L 'END 'ELSE* » IF» T»01*7,5

CS : = CNULL. - 4'. 28*CL

’END* »ELSE» » IF-»T>GQt‘l2.5 CS:= CNULL « 3,54*01

’END** ELSE * ? IFTGO*17,5 CS; = CNULL « 2 8 0 » C L

* END »EISE * I FT60*22,5 CS ! = CNULL - 2,3 3 « C L

»END» ELSE f I F » T » G Q « 2 7,5

CNULL î a 299 i CS: = CNULL - l’.96CL »END »ELSE* * GOTO* SEC î

* COMMENT * ACC Tn BUCH 1946 FENN IA 68 NO 5 PAGE 14 f AH : s to*«C-PH{ f5):

AH20:e 1-0 ,0OO969»CL

î

* COMMENT* HARVEY 1966 PA&E 169 » LOGK2is -?9ß2!39/TABS + 61.4980 « 0.02379*TABSI

PK2PRIM*. = -LOGK2 - 0

^,

510#CL ( 1 /3 ) 1 K2PR [ Ml a 10(-PK?PRIM>I

»COMMENT* BlCH 1951 HELSINKI HAVSFORSKNîNGST SKR|F TNÖ l5l PAGE? Î PKRPR I M : s 9 I 22 -0 11?3*CL** ( 1/3 5 - 0l0086CL 0,1? » 000933333T K 3 P R I H ; s îo«(-PKBPR I M ) I »COMMENT* REF RAPP. ET PROC.VERB. DES REUNIONS VOLUME LXXXV 1.932 PAGE 73 KURT BUCH MOD IF BY BSTRBM 1973 T I TRAlK : = 0,1?3»CL -3 ) ? »COMMENT» HARVEY 1966PP161 AND177J CARPALK : = T j TRA-iK - K8PR|M2.2CL10#*(-5) / C AH + KBPR j M

⁾

S

;

uull

;= ?4

i

FACT AMD PK1

»

REAL CONSTANTS

* AMD * T<2,5 'THEN'BEGIN

»AMD* T<7,5 »THEN* ’BEGIN*

* AND * T<12,5 »

then

* »

begin

*

*AND'T<17,5 »

then

* »

begin

*

» AND * T<22,5 'THEN* »BEGIN*

* AMD 1T<2? , 5 *

thfn

*»

begin

* 'THEN'BEGIN

‘COMMENT* HARVEY 1966 PAGE 166}

ALK : a(1,?6 + 01055789 » CL) *16-3 i

»COMMENT* ALTERNATiVE ALK S <1,26 ♦ ol030907 « S3 lE-3 ? CARB(|>:= ALK ( 1 +K2P.R ÎM/AH ♦CsAH/{KlPR(M»CNuLLAH?0))*12010/

£ j +2#K2PR I M/AH) ; »COMMENT* HARVEY .1966 PAGE 172 MOD ! F DURAT!s DURHO * DURM I N/60 }

CPRODf j ) ;= COUNTS ( I ) » CARS (I)«- lE3 / ( ÀMPSTR » DURAT) 3 DARKPROD{ f )‘a D

a

RKCOUNTS( I ) CARB( ! J # 1F3/(AMPSTRDURATJI

MF* D A R K P R C D ( I ) >0 ' AND » DARK PROD £ I KGPRODt f ) * THEN ? NFTPRoD £ S ) ! * CPROD £ I) - CARKPRODC I 3

*ELSE'NETPRRD( ! ’) :=~1 5

CORPROC15 U CPRODC I 3#1,1i

NETCOR £ I 3 ja NFTPRODf I ) «î , î )

(9)

?

Certain information in this paper is taken from

Buch, Kurt, 1932: "Der Borsäuregehalt des Meerwassers und seine Bedeu

tung bei der Berechnung des Kohlensäuresystems im leerwasser". Rapp, et Proc.-Verb. des Reunions

Vol» LXXXV. Cons, pem, Internat» pour L'exp, de la Mer,

ï!

Buch, K,, Harvey, H.W., Wattenberg, H. and Gripenberg, S., 1932: "liber das Kohlensäuresystem im Meerwasser”* Rapp, et Proc,- Verb» des Reunions Vol. LXXIX. Cons. Perm. Internat, pour Ii'exp. de la Mer»

Buch, Kurt, 1945: "Kolsyrejämvikten 1 Baltiska Havet”, Pennia 68, Mo 5.

Buch, Kurt, 1951: "Das Kohlensäure Gleichgewichtssystem im Meerwasser”

Havsforskningsinst. skrift Mo 151, Helsinki.

Harvey, H.W., 1966; "The chemistry and fertility of Sea Waters".

Cambridge Univ. Press.

Knudsen, Marin, 1901: "Hydrographical tables".

Lundén, Harald, 1908: "Affinitätsmessungen an schwachen Säuren und Basen". Thesis

Steemann Mielsen, S., 1958: "Experimental methods for Measuring Organic Production in the Sea". Rapp, et Proc,-Verb. Vol.144,

1958. Cons. Internat. Expier, de la Mer.

Sverdrup, H.Ü., Johnson, M. and Fleming, R., 1946: "The Oceans"

öström, Bertil, 1972; "Brofjorden I» Hydrographical measurement program and some basic data". Meddelande från Havsfiske

laboratoriet i Lysekil» lo» 144.

(10)

f fi/ (. i ,* r , . > ' , . ;!

i \’ v», * >■

- v

• •

■

> ■ /v mm : ^

v 1 ' C . ' '

. - kJ. • ■ - ■;

r-V

, ■ ,

.

: •>

■

-,

1

.

■

'

ödsmål, Kville sn»

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

ödsmål, Kville sn»

Hällristning

Fiskare frän bronsåldern

Rock carving Bronze age

fv

MEDDELANDE från

HÂVSFISKELÂBORATORIET • LYSEKIL

BRQPJORDEN II

FORMULA SYSTEN FOR PRIMARY PRODUCTION

by

Bertil Öström

September 1973

Whex computing large numbers of primary production data it is desirable to replace the older methods of reading tables and nomogram's with

nique •

K,

K1f K2

H

Alk.

CO

0

s

" n

u ”

-14

1 n

0.145

4

for

1 (°C) -2

13 20

25 30

0 x 104 o

394 C

?70 0

640 0

536 C

458 0

394 C

341 C

299 C

7 »22 X

o

X Cl 6.51 X

er

Cl 5.37 X icT4

Cl 4.28

10“4

X 01 3 »54 X

“4 X G1

2.80 X

er

Cl 2.33 X 10"4

Cl 1.96 X

“4

Cl

The second dissociation constant for carbonic acid is with some modifi­

cation taken from Buch (1951)

log K0 ~ ~2902.39/Taho + 6,4980 - 0,02379 x T&hei PKg « - log Kg - 0.510 x 3 Cl

Kg = 10”PK2

For the principal case, when computing primary production, in the open ocean, the boric acid dissociation constant must be established. The

following formula PK^ = 9.22 - 1,023 x \jüï - 0.0086 x 01+0.17-0,0093333 x Î is based on Buch's formula from 1932 for the chlorinity dépendance and is modified to account also for the temperature variation, a modifi­

cation which is based on Buch's figures.

Then K' is obtained from K,' * 1 o“PKB

Then according to Harvey (1966) the titration alkalinity is 0,123 x 01 x 10 and the carbonate alkalinity is calculated as -3 carbonate alkalinity « titration alkalinity -

!C x 2.2 x Cl x 10'“5

AH + %

5

However,

so obtained alkalinity is

to

low

Baltic water influence

Buch

x

1,26 + 0.031 x S which is

S

x Co X

1 4

^er

Cl 5.37 X ^icT4

^“4 X G1

^er

Cl 2.33 X ^10"4

^“4

The second dissociation constant for carbonic acid is with some modifi

following formula PK^ = 9.22 - 1,023 x \jüï - 0.0086 x 01+0.17-0,0093333 x Î is based on Buch's formula from 1932 for the chlorinity dépendance and is modified to account also for the temperature variation, a modifi

**Then K' is obtained from K,' * 1 o“PKB**

FACT : a 0,145- o', 000?5T } » COMMENT » FACT IS CALC FROM BUCH 1951 } PK1 : = 17fi52/TABS + 215 121 #LN CT AÖ8 ï/LN1Q - 0.12675TABS - 545,560 PKlPRIMïs PK1 - FACTCL»#(l/3)I K1 P R I M ! » 10#<-PK1PRIMi I

**’AND* T<"1 »THEN» »BEGIN»**

CIS : S CNULL - ?,22**CL 'END»ELSE»IF» T »QQt^l CS!s CNULL -"6,51*01

'END’ELSE'IF* TGQ?2»5 C3:= CNULL - 513 7 » C L 'END 'ELSE* » IF» T»01*7,5

’END** ELSE * ? IFTGO*17,5 CS; = CNULL « 2 8 0 » C L

* END »EISE * I FT60*22,5 CS ! = CNULL - 2,3 3 « C L

»END» ELSE f I F » T » G Q « 2 7,5

CNULL î a 299 i CS: = CNULL - l’.96CL »END »ELSE* * GOTO* SEC î

510#CL ( 1 /3 ) 1 K2PR [ Ml a 10(-PK?PRIM>I

* AMD * T<2,5 'THEN'BEGIN

* 'THEN'BEGIN

»COMMENT* ALTERNATiVE ALK S <1,26 ♦ ol030907 « S3 lE-3 ? CARB(|>:= ALK ( 1 +K2P.R ÎM/AH ♦CsAH/{KlPR(M»CNuLLAH?0))*12010/

RKCOUNTS( I ) CARB( ! J # 1F3/(AMPSTRDURATJI