Reply to Nicholson's comment on “Consistent calculation of aquatic

Biogeosciences, 9, 2921–2933, 2012www.biogeosciences.net/9/2921/2012/doi:10.5194/bg-9-2921-2012© Author(s) 2012. CC Attribution 3.0 License.

Biogeosciences

Reply to Nicholson’s comment on“Consistent calculation of aquatic gross production from oxygentriple isotope measurements” by Kaiser (2011)

J. Kaiser1 and O. Abe2

1School of Environmental Sciences, University of East Anglia, Norwich, UK2Graduate School of Environmental Studies, Nagoya University, Nagoya, Japan

Correspondence to:J. Kaiser ([email protected])

Received: 13 October 2011 – Published in Biogeosciences Discuss.: 26 October 2011Revised: 29 June 2012 – Accepted: 3 July 2012 – Published: 3 August 2012

Abstract. The comment by Nicholson (2011a) questionsthe “consistency” of the “definition” of the “biological end-member” used by Kaiser (2011a) in the calculation of oxygengross production. “Biological end-member” refers to the rel-ative oxygen isotope ratio difference between photosyntheticoxygen and Air-O2 (abbreviated17δP and18δP for 17O/ 16Oand18O/ 16O, respectively). The comment claims that thisleads to an overestimate of the discrepancy between previ-ous studies and that the resulting gross production rates are“30 % too high”.

Nicholson recognises the improved accuracy of Kaiser’sdirect calculation (“dual-delta”) method compared to pre-vious approximate approaches based on17O excess (17∆)and its simplicity compared to previous iterative calculationmethods. Although he correctly points out that differences inthe normalised gross production rate (g) are largely due todifferent input parameters used in Kaiser’s “base case” andprevious studies, he does not acknowledge Kaiser’s observa-tion that iterative and dual-delta calculation methods give ex-actly the sameg for the same input parameters (disregardingkinetic isotope fractionation during air-sea exchange). Thecomment is based on misunderstandings with respect to the“base case”17δP and18δP values. Since direct measurementsof 17δP and18δP do not exist or have been lost, Kaiser con-structed the “base case” in a way that was consistent andcompatible with literature data. Nicholson showed that an al-ternative reconstruction of17δP givesg values closer to pre-vious studies. However, unlike Nicholson, we refrain frominterpreting either reconstruction as a benchmark for the ac-curacy ofg.

A number of publications over the last 12 months havetried to establish which of these two reconstructions is moreaccurate. Nicholson draws on recently revised measurementsof the relative17O/ 16O difference between VSMOW andAir-O2 (17δVSMOW; Barkan and Luz, 2011), together withnew measurements of photosynthetic isotope fractionation,to support his comment. However, our own measurementsdisagree with these revised17δVSMOW values. If scaled fordifferences in18δVSMOW, they are actually in good agreementwith the original data (Barkan and Luz, 2005) and supportKaiser’s “base case”g values. The statement that Kaiser’sg values are “30 % too high” can therefore not be accepted,pending future work to reconcile different17δVSMOW mea-surements.

Nicholson also suggests that approximated calculationsof gross production should be performed with a triple iso-tope excess defined as17∆#

≡ ln(1+17δ)–λ ln(1+

18δ), withλ = θR = ln(1+

17εR) / ln(1+18εR). However, this only im-

proves the approximation for certain17δP and18δP values, forcertain net to gross production ratios (f ) and for certain ra-tios of gross production to gross Air-O2 invasion (g). In othercases, the approximated calculation based on17∆†

≡17 δ–

κ 18δ with κ = γR =17εR/18εR (Kaiser, 2011a) gives more

accurate results.

Published by Copernicus Publications on behalf of the European Geosciences Union.

2922 J. Kaiser and O. Abe: Reply to Nicholson’s comment

1 Introduction

Kaiser (2011a) introduced an improved method to calculateaquatic gross production from oxygen triple isotope mea-surements, dubbed the “dual-delta method”. This methoduses17δ and 18δ measurements of dissolved O2 relative toAir-O2 directly, rather than the17O excess (17∆) and usingan approximation (Luz and Barkan, 2000). The calculationuses the following equation:

g =

(1+17εE)

17δ−17δsat1+17δ

− γR(1+18εE)


+ s(17εE − γ 18R εE)

17δ−17δ

1+17δ− γR

18δP−18δ

1+18δ

(1)

Equation (1) is based on Eq. (48) in Kaiser (2011a), buttakes into account that previous measurements of the kineticisotope fractionation during O2 gas exchange refer to evasionfrom solution to gas phase (Kaiser, 2011b; Knox et al., 1992).The symbols have the following meaning:

g = P / (kcsat): ratio of gross oxygen production to grossAir-O2 invasion.

17δ, 18δ: relative17O/ 16O and18O/ 16O differences be-tween dissolved O2 and Air-O2.

17δsat, 18δsat: relative17O/ 16O and18O/ 16O differencesbetween dissolved O2 at air saturation and Air-O2.

17δP, 18δP: relative17O/ 16O and18O/ 16O differences be-tween photosynthetic O2 and Air-O2.

17εE, 18εE: kinetic 17O/ 16O and18O/ 16O fractionationsduring O2 evasion from sea to air.

γR =17 εR / 18εR: ratio of respiratory17O/ 16O fractiona-

tion and18O/ 16O fractionation.s = c/csat – 1: relative supersaturation of dissolved O2.Prokopenko et al. (2011) developed virtually the same

method, but did not include kinetic isotope fractionation dur-ing O2 gas transfer. This resulted in the simplified solution

g =


− γR18δ−18δsat

1+18δ17δP−17δ

1+17δ− γR

18δP−18δ

1+18δ

(2)

The comment by Nicholson (2011a) does not question thevalidity of the dual-delta method. Unlike the approximatedcalculation of Luz and Barkan (2000), it does not assumesteady state for O2 concentrations and can, therefore, be ex-pected to be more universally applicable. Only the assump-tion of isotopic steady state is needed. In contrast to the claimthat the dual-delta method requires17εR and18εR (Nichol-son, 2011b), the above equations clearly show that onlyγR isrequired, which is better constrained than17εR and18εR (Luzand Barkan, 2005).

The comment paper and the reviews it has received (Luz,2011; Prokopenko, 2011) demonstrate that the definition anduse of triple isotope excess values can be very confusing,even for experts in the field. The use of different17∆ defi-nitions with different coefficients causes delays and misun-derstandings during scientific communication, which can be

avoided with the dual-delta method. In this paper,17∆ valuesare reported in conjunction with the underlying17δ and18δ

values and the definition of17∆ is indicated by the indicesintroduced in Kaiser (2011a), to avoid any further confusion.

In Sect. 2, we discuss the merits of Nicholson’s commentin view of different reconstructions of the isotopic compo-sition of photosynthetic O2. In Sect. 3, we evaluate his sug-gested approximated solution to the calculation ofg fromoxygen triple isotope measurements.

2 Isotopic composition of photosynthetic O2 (δP)

In his comment, Nicholson (2011a) questions the “consis-tency” of the “definition” of the isotopic composition ofthe “biological end-member” (i.e., photosynthetic O2) inKaiser 2011a). Specifically, he remarks that the triple iso-tope excess (17∆) adopted for the base case is “too low”and, therefore, also17δP. He does not question the value of−22.835 ‰ assumed for18δP.

The “definition” of the base case17δP or 18δP values inSect. 5 of Kaiser (2011a) followed the approach of previ-ous studies that used the measured17O excess of O2 evolvedin flask studies of17∆†(0.521)= (249± 15) ppm (Luz andBarkan, 2000) and combined its numerical value with the in-ferred 18δP value and an entirely different17O excess def-inition, in this case17∆#(γR), where γR = 0.5179. Eventhough the reconstructed17δP value of−11.646 ‰ must beconsidered hypothetical, it is consistent with17δP valuesderived from actual literature data following two differentapproaches: one based on the measured isotopic composi-tion of VSMOW and oceanic waters with respect to Air-O2(Barkan and Luz, 2005; Luz and Barkan, 2010), combinedwith the measured photosynthetic isotope fractionation bythe cyanobacterium strainSynechocystissp. PCC 6803 (Hel-man et al., 2005); the other based on dark-light incubationsof the coralAcropora (with its symbiotic algae) in airtightflasks (Luz and Barkan, 2000). The first approach was alsoused to derive18δP = −22.835 ‰ .

Nicholson suggests that17∆#(θR) should be used to recon-struct17δP, whereθR = ln(1+

17εR)/ ln(1+18εR) = 0.5154

for 18εR = −20 ‰. This assumes concentration steady statein Luz and Barkan’s flask experiments and near-zerosteady-state18δ values (18δS0). The resulting17δP value of−11.588 ‰ (for18δP = −22.835 ‰ ) gives gross productionrates that are about 30 % higher than for Kaiser’s “base case”.

To dispel any confusion about how the isotopic compo-sition of photosynthetic O2 (including the triple isotope ex-cess) was calculated, we show the corresponding equationsand results in the following subsections and include data thatwere previously omitted or not yet published. The resulting17δP and18δP values are shown in Table 3. We also updateany values in Kaiser (2011a) and Nicholson (2011a) to re-flect recent publications by Luz and Barkan displaying them

Biogeosciences, 9, 2921–2933, 2012 www.biogeosciences.net/9/2921/2012/

J. Kaiser and O. Abe: Reply to Nicholson’s comment 2923

with more decimals than previously; however, this does notsignificantly change any results or conclusions.

2.1 Calculation ofδP based on the isotopic compositionof source water (δW) and the photosynthetic isotopefractionation (εP)

The relative isotope ratio difference of photosynthetic O2 toAir-O2 (δP) can be calculated via

δP = (1+ δW)(1+ εP) − 1 (3)

whereδW is the relative isotope ratio difference of sourcewater to Air-O2 and εP is the photosynthetic isotope frac-tionation. The corresponding triple isotope excess is

17∆†P =

17δP− κ18δP

=17δW +

17εP+17δW

17εP

− κ(18δW +18εP+

18δW18εP)

=17∆

†W + (γP− κ)18εP

−

[κ(1− γP)18δW − γP

17∆†W

]18εP (4)

whereγP =17 εP/18εP and

17∆#P = ln(1+

17 δP) − λ ln(1+18 δP)

= ln(1+17 δW) + ln(1+

17εP) − λ ln(1+18 δW)

− λ ln(1+17 δP)

=17 δ∆#

W + (θP− λ) ln(1+18εP) (5)

whereθP = ln(1+17εP)/ ln(1+18εP).

Note that the respiratory isotope fractionationεR does notenter into these equations.εR is only needed if the isotopiccomposition of O2 in steady state between photosynthesisand respiration (δS) was required.δS can be calculated usingEq. (31) in Kaiser (2011a). For comparison with Sect. 2.2,the correspondingδS0 values for a net to gross productionratio of f = 0 are also shown in Table 3; see also Eq. (6)below.

Kaiser (2011a) choseδW to correspond to the iso-topic composition of seawater.18δW was set equal to18δVSMOW = (−23.323± 0.02) ‰ (Barkan and Luz, 2005).17δW was calculated as17δW = (1+

17δVSMOW)e−5 ppm–1= (1− 11.936 ‰)e−5 ppm– 1= (−11.941± 0.01) ‰ (Luzand Barkan, 2010). Barkan and Luz (2011) reportedmore decimals and these values need to be corrected to18δW = −23.320 ‰ and17δW = −11.936 ‰ (Table 1, row 3;Table 3, row 5). Other measurements of17δVSMOW were dis-regarded because they were less precise (Table 1, rows 1 and2) or did not differ in terms of the17O excess (Table 1, row 4),which is critical for the magnitude ofg; see Sect. 2.4 belowfor the impact of new17δVSMOW measurements listed in Ta-ble 1, rows 5 and 6.

For εP, a cyanobacterium strain that lacked the gene forphotorespiration (Synechocystissp. PCC 6803) was consid-ered with 18εP = (0.5± 0.5) ‰ and θP = 0.5354± 0.0020(Helman et al., 2005; Kaiser, 2011a). The uncertainty of18εPwas chosen to reflect the range of photosynthetic isotopefractionation in other systems (Guy et al., 1993). This gave18δP = (−22.835± 0.5) ‰, 17δP = (−11.676± 0.26) ‰,17∆

†P(0.5179) = (150± 13) ppm; with the δW up-

date referred to above, 18δP= (−22.832± 0.5) ‰,17δP = (−11.671±0.26) ‰,17∆

†P(0.5179) = (153±6) ppm;

with the actual 18εP = (0.467± 0.17) ‰ (Table 2),18δP= (−22.864± 0.17) ‰, 17δP= (−11.689± 0.09) ‰,17∆

†P(0.5179) = (152± 6) ppm (Table 3, row 5a). The

propagated error in17∆ is smaller than for17δP becausethe uncertainties in17δP and 18δP are correlated in amass-dependent way.

Eisenstadt et al. (2010) reported on18εP and θP valuesfor four additional phytoplankton species:Nannochlorop-sis oculata(a eustigmatophyte),Phaeodactylum tricornu-tum (a diatom),Emiliania huxleyi(a coccolithophore) andChlamydomonas reinhardtii(a green alga). The18εP val-ues are significantly higher than forSynechocystissp. PCC6803 and range from (2.850± 0.05) ‰ for N. oculatato (7.04± 0.10) ‰ for C. reinhardtii (Table 2). TheθPvalues are lower than forSynechocystissp. PCC 6803and range from 0.5198± 0.0001 for C. reinhardtii to0.5253± 0.0004 forN. oculataandE. huxleyi. The resulting17∆

†P(0.5179) values range from (178± 4) ppm forN. ocu-

lata to (214± 5) ppm forE. huxleyi(Table 3, rows 5b–5e).These high18εP values contradict the notion that water un-dergoes little isotopic fractionation during photosynthetic O2production, based on measurements (Guy et al., 1993; Hel-man et al., 2005) and theoretical considerations (Tcherkezand Farquhar, 2007). They might be explained by cell-internal O2 consumption. However, discrepancies also ap-pear between the18εP value of 0.62 ‰ reported forP. tricor-nutumby Guy et al. (1993) and the value of (4.426± 0.01) ‰reported by Eisenstadt et al. (2010), although in both casesessentially the same experimental setup (helium-sparging ofcell cultures) was used. Eisenstadt et al.’s attribution of thisdifference to improved methods for the measurement of therelative isotope ratio difference between the evolved O2 andthe source water is not in line with the small difference inmeasurements of the “Dole effect” (i.e., the18O/ 16O dif-ference between Air-O2 and VSMOW) by the same researchgroup (Barkan and Luz, 2005), compared to independent es-timates of (23.8± 0.1) ‰ (Coplen et al., 2002; Kroopnickand Craig, 1972) and (24.36± 0.06) ‰ (Kaiser, 2008). De-spite these inconsistencies, we will consider the measure-ments of Eisenstadt et al. (2010) here to work outδP values;an approach that was also taken by Luz and Barkan (2011b).

www.biogeosciences.net/9/2921/2012/ Biogeosciences, 9, 2921–2933, 2012


Table 1.Historic and new measurements of the relative oxygen isotope ratio differences between Vienna Standard Mean Ocean Water (VS-MOW) and Air-O2 (17δVSMOW, 18δVSMOW, 17∆VSMOW). For clarity, all values are shown with the same number of decimals, irrespectiveof their uncertainty.

Row Reference 18δVSMOW/‰ 17δVSMOW/‰ 17∆†VSMOW(0.5179)/ppm 17∆#

VSMOW(0.5179)/ppm

1 Thiemens et al. (1995) −22.873± 0.04 −11.744± 0.08 102± 80a 170± 80a

2 Luz et al. (1999); based on Thiemens et al. (1995)−22.960b −11.778b 113b 182b

3 Barkan and Luz (2005) −23.320± 0.02 −11.931± 0.01 146± 4 218± 44 Kaiser (2008); based on Barkan and Luz (2005) −23.771± 0.06 −12.167± 0.04 144± 4 218± 45 Barkan and Luz (2011) −23.324± 0.02 −11.883± 0.01 196± 4 268± 46 This paper −23.647± 0.04 −12.102± 0.03 145± 6 218± 6

a Minimum error based on the uncertainty of the corresponding17δ value.b No error estimate was given.

Table 2. Photosynthetic oxygen isotope fractionation for different marine (rows 2 to 4) and freshwater (rows 1 and 5) species (Eisenstadt etal., 2010; Helman et al., 2005). The third decimal of18εP in rows 2 to 4 has been reconstructed from Luz and Barkan (2011b). The meanθP value has been calculated from a linear regression of the five species-dependent ln(1+

17εP) and ln(1+18εP) values. It is useful for errorpropagation purposes. The resultant y-axis intercept of (0.012± 0.013) ‰ is statistically indistinguishable from zero. For clarity,θP and17εPvalues are shown with the same number of decimals, irrespective of their uncertainty.

Row Species θP18εP/‰ 17εP/‰

1 Synechocystissp. strain PCC 6803 0.5354± 0.0020 0.467± 0.17 0.2502 Nannochloropsis oculata 0.5253± 0.0004 2.850± 0.05 1.4963 Phaeodactylum tricornutum 0.5234± 0.0004 4.426± 0.01 2.3144 Emiliania huxleyi 0.5253± 0.0004 5.814± 0.06 3.0505 Chlamydomonas reinhardtii 0.5198± 0.0001 7.04± 0.10 3.653

Mean 0.5203± 0.0027 4.119± 2.6 2.153

2.2 Calculation of δP based on flask cultures in steadystate between photosynthesis and respiration

Following Sect. 3.4 in Kaiser (2011a), the isotopic compo-sition of oxygen in concentration steady state (net to grossproduction ratiof = 0) is given by

δS0 =1+ δP

1+ εR− 1 =

δP− εR

1+ εR(6)

To deriveδP, Eq. (6) is rearranged to

δP = (1+ δS0)(1+ εR) − 1 (7)

In addition toδS0, this calculation also requiresεR.Luz and Barkan (2000) performed incubations of aNan-

nochloropsisspecies and the hermatypic coralAcroporain airtight flasks. These incubations are supposed to cor-respond to steady state. No values were reported forδS0,only 17∆

†S0(0.521) = (244± 20) ppm for Nannochloropsis

and (252± 5) ppm for Acropora; anecdotal evidence sug-gests thatδS0 was close to 0 (Barkan and Luz, 2011).

For Acropora, Luz and Barkan (2005) reported18εR = (−13.8± 0.5) ‰ andγR = 0.519± 0.001. Assuming18εP = (0.5± 0.5) ‰ and 18δW = −23.320 ‰, this gives18δP = (−22.832± 0.5) ‰ and 18δS0 = (−9.16± 0.71) ‰(Kaiser, 2011a, b). With

17δS0 =17 ∆

†S0(0.521) + 0.52118δS0 (8)

this gives 17δS0 = (−4.52± 0.37) ‰ and, using Eq. (7),17δP = (−11.649± 0.26) ‰ and 17∆

†P(0.5179) =

(175± 15) ppm (Table 3, row 3a). The photosyntheticisotope fractionation forAcropora is not known; if weassume the highest value reported for a marine species (E.huxleyi), the resulting17∆

†P(0.5179) value is (210± 15) ppm

(Table 3, row 3b).Kaiser (2011a) mentioned that no corresponding calcu-

lation could be performed forNannochloropsisbecause18εR and γR values have not been reported for thisspecies. In Sect. 4 of Nicholson (2011a), this calculationis performed nonetheless, assuming18εR = −20 ‰ andγR = 0.5179 (without uncertainties). Here, we repeatthis calculation, assuming more realistic uncertainty es-timates of 4 ‰ for 18εR and 0.0006 forγR. This gives18δP = (−22.832± 0.5) ‰, 17δP = (−11.606± 0.26) ‰ and17∆

†P(0.5179) = (218± 38) ppm for 8εP = (0.5± 0.5) ‰

(Table 3, row 4a). If18εP = (2.850± 0.05) ‰ (Eisenstadtet al., 2010) is used instead,17δP = (−10.399± 0.047) ‰and17∆

†P(0.5179) = (237± 39) ppm (Table 3, row 4b). Both

values clearly differ from17∆†P(0.5179) = (178± 4) ppm

derived forN. oculatabased onδW andεP (Sect. 2.1; Table 3,row 5b). The increased uncertainty estimates compared toAcroporaare due to the higher uncertainty in17∆

†S0(0.521)

of 20 ppm and the higher uncertainty in18εR of 4 ‰.



Tabl

e3.

Isot

opic

com

posi

tion

ofph

otos

ynth

etic

O 2(17

δ P,

18δ P

,17

∆P)

and

O 2at

stea

dyst

ate

betw

een

phot

osyn

thes

isan

dre

spira

tion

with

ane

tto

gros

spr

oduc

tion

ratio

off

=0

(17δ S

0,18

δ S0,

17∆

S0)

,cal

cula

ted

aspe

rSec

t.2.

For

clar

ity,a

llva

lues

are

show

nw

ithth

esa

me

num

bero

fdec

imal

s,irr

espe

ctiv

eof

thei

runc

erta

inty

.Dire

ctly

mea

sure

dva

lues

are

inbo

ld.

Ass

umed

valu

esar

ein

bold

italic

s,i.e

.,fo

r“K

aise

r(20

11a)

”(ro

w1)

,17

∆# P(0

.517

9)=

(249

±15

)ppm

;for

“Nic

hols

on(2

011a

)”(r

ow2)

,17∆

# S0(

0.51

54)=

(249

±15

)ppm

.Oth

erva

lues

wer

eca

lcul

ated

usin

gγ R=

0.51

79±

0.00

06,18

εR

=(−

20±

4)‰

,θR

=0.

5154

,exc

eptf

or“Acr

op

ora

(flas

k)”

whe

reγ

R=

0.51

9±0.

001,

18εR

=(−

13.8

±0.

5)‰

,θR

=0.

5173

.For

“Acr

op

ora

(flas

k)”

and

“Na

nn

och

loro

psi

s(flas

k)”,

17∆

† S0(

0.52

1)=

(252

±5)

ppm

and

(244±

20)p

pm,r

espe

ctiv

ely,

wer

eus

ed(L

uzan

dB

arka

n,20

00).

δ Pva

lues

inro

ws

1to

5mar

eba

sed

onth

eδ VS

MO

Wva

lues

inTa

ble

1,ro

w3

(Bar

kan

and

Luz,

2005

);ro

ws

6to

6mar

eba

sed

onTa

ble

1,ro

w5

(Bar

kan

and

Luz,

2011

);ro

ws

7to

7mar

eba

sed

onTa

ble

1,ro

w6

(thi

spa

per)

;all

acco

untf

orth

e5

ppm

low

er17O

/16

Ora

tioof

ocea

nw

ater

com

pare

dto

VS

MO

W(L

uzan

dB

arka

n,20

10)

and

the

phot

osyn

thet

icis

otop

efr

actio

natio

nsin

Tabl

e2.

Des

crip

tion

18δ P

17δ P

17∆

† P(0

.517

9)17

∆# P(0

.517

9)18

δ S0

17δ S

017

∆† S

0(0.

5179

)17

∆# S

0(0.

5179

)17

∆† S

0(0.

5154

)

Row

Uni

t‰

‰pp

mpp

m‰

‰pp

mpp

mpp

m

1K

aise

r(2

011a

),18εP

=(0

.50±

0.50

)‰−

22.8

32−

11.6

4418

0±15

249±

15−

2.88

9−

1.30

019

719

819

12

Nic

hols

on(2

011a

),18εP

=(0

.50±

0.50

)‰−

22.8

32−

11.5

8723

8±35

307±

35−

2.88

9−

1.24

225

525

624

9±15

3aA

cro

po

ra(fl

ask)

,18εP

=(0

.50±

0.50

)‰−

22.8

32−

11.6

4917

5±15

a24

4±15

a−

9.15

8−

4.51

922

4a23

5a−

a

3bA

cro

po

ra(fl

ask)

,18εP

=(5

.814

±0.

06)‰

−22

.832

−8.

927

210±

15b

251±

15b

−3.

895

−1.

777

240b

242b

−b

4aN

an

no

chlo

rop

sis(fl

ask)

,18εP

=(0

.50±

0.50

)‰−

22.8

32−

11.6

0621

8±38

287±

38−

2.88

9−

1.26

123

523

622

94b

Na

nn

och

loro

psi

s(flas

k),18

εP

=(2

.85±

0.05

)‰−

20.5

36−

10.3

9923

7±39

293±

40−

0.54

7−

0.04

124

224

224

1

5δ W

base

don

Bar

kan

and

Luz

(200

5),

εP

=0

−23

.320

−11

.936

141±

421

3±4

−3.

388

−1.

594

160

162

153

5aεP

(Syn

ech

ocy

stis,s

p.st

rain

PC

C68

03)

−22

.864

−11

.689

152±

622

1±5

−2.

923

−1.

345

169

170

163

5bεP

(Na

nn

och

loro

psi

so

cula

ta)−

20.5

36−

10.4

5817

8±4

234±

4−

0.54

7−

0.10

118

318

318

15c

εP

(Ph

ae

od

act

ylu

mtr

ico

rnu

tum)

−18

.997

−9.

649

189±

423

7±4

1.02

30.

716

186

186

189

5dεP

(Em

ilia

nia

hu

xley

i)−

17.6

42−

8.92

221

4±5

256±

52.

407

1.45

120

420

521

15e

εP

(Ch

lam

ydo

mo

na

sre

inh

ard

tii)−

16.4

44−

8.32

619

0±4

226±

43.

628

2.05

317

417

518

45m

mea

nof

row

s5a

to5e

−19

.297

−9.

809

185±

2223

4±13

0.71

80.

555

183±

1418

3±14

185±

18

6δ W

base

don

Bar

kan

and

Luz

(201

1),

εP

=0

−23

.324

−11

.888

192±

426

3±4

−3.

392

−1.

546

211

212

204

6aεP

(Syn

ech

ocy

stis,s

p.st

rain

PC

C68

03)

−22

.868

−11

.641

202±

627

2±5

−2.

927

−1.

297

219

221

213

6bεP

(Na

nn

och

loro

psi

so

cula

ta)−

20.5

40−

10.4

1022

8±4

284±

4−

0.55

2−

0.05

223

323

423

26c

εP

(Ph

ae

od

act

ylu

mtr

ico

rnu

tum)

−19

.001

−9.

601

239±

428

8±4

1.01

90.

765

237

237

239

6dεP

(Em

ilia

nia

hu

xley

i)−

17.6

46−

8.87

426

4±5

306±

52.

402

1.49

925

525

526

16e

εP

(Ch

lam

ydo

mo

na

sre

inh

ard

tii)−

16.4

48−

8.27

824

0±4

277±

43.

624

2.10

222

522

623

56m

mea

nof

row

s6a

to6e

−19

.301

−9.

761

235±

2228

5±13

0.71

40.

603

234±

1423

4±14

236±

18

7δ W

base

don

this

pape

r,ε P=

0−

23.6

47−

12.1

0714

0±6

213±

6−

3.72

2−

1.76

716

016

315

37a

εP

(Syn

ech

ocy

stis,s

p.st

rain

PC

C68

03)

−23

.192

−11

.860

151±

722

2±7

−3.

257

−1.

518

169

171

162

7bεP

(Na

nn

och

loro

psi

so

cula

ta)−

20.8

65−

10.6

2917

7±6

235±

6−

0.88

2−

0.27

418

318

418

17c

εP

(Ph

ae

od

act

ylu

mtr

ico

rnu

tum)

−19

.326

−9.

821

188±

623

8±6

0.68

80.

543

187

187

189

7dεP

(Em

ilia

nia

hu

xley

i)−

17.9

71−

9.09

421

3±6

256±

72.

071

1.27

820

520

521

17e

εP

(Ch

lam

ydo

mo

na

sre

inh

ard

tii)−

16.7

74−

8.49

818

9±6

227±

63.

292

1.88

017

517

618

47m

mea

nof

row

s7a

to7e

−19

.625

−9.

980

184±

2323

5±14

0.38

20.

382

184±

1518

4±15

185±

18

aT

heco

rres

pond

ing

valu

esfo

rλ

=κ

=0.

519

are1

7 ∆† P(0

.517

9)=

(200

±15

)ppm

,17 ∆

# P(0

.517

9)=

(269

±15

)ppm

,17 ∆

† S0(

0.51

79)=

234

ppm

,17 ∆

# S0(

0.51

79)=

245

ppm

and1

7 ∆# S

0(0.

5173

)=

229

ppm

.b

The

corr

espo

ndin

gva

lues

for

λ=

κ=

0.51

9ar

e17 ∆

† P(0

.517

9)=

(229

±15

)ppm

,17 ∆

# P(0

.517

9)=

(271

±15

)ppm

,17 ∆

† S0(

0.51

79)=

244

ppm

,17 ∆

# S0(

0.51

79)=

247

ppm

and1

7 ∆# S

0(0.

5173

)=

240

ppm

.



2.3 Hypothetical “base case” values for the isotopiccomposition of photosynthetic O2

Based on the discrepancy between the17O excess for pho-tosynthetic O2 produced bySynechocystisand Acropora,Kaiser (2011a) found it impossible to assign a best value for17δP. The inclusion ofNannochloropsiswith Nicholson’s as-sumptions does not help to resolve this.

Instead, Kaiser (2011a) constructed a hypothetical basecase in a way that was mathematically consistent withprevious studies (Hendricks et al., 2004; Juranek andQuay, 2010; Reuer et al., 2007). The base case adopteda triple isotope excess of17∆#

P(0.5179) = (249± 15) ppm(Table 3, row 1). This is the same numerical value forthe triple isotope excess used in previous studies, althoughλ values of 0.516 (Hendricks et al., 2004; Reuer et al.,2007) and 0.518 were used elsewhere (Juranek and Quay,2010). 17∆#

P(0.5179) = (249± 15) ppm results in17δP =

−11.646 ‰ (−11.644 ‰ with theδW update referred toin Sect. 2.1; Table 3, row 1), which is slightly higherthan the corresponding values of−11.671 ‰ for Syne-chocystisand−11.649 ‰ forAcropora. The resulting valueof 17∆

†P(0.5179) = (180± 15) ppm is compatible with the

17∆†P(0.5179) values for other species based on the18εP mea-

surements of Eisenstadt et al. (2010) (Table 3, rows 5b, 5c,5e) except forE. huxleyi(Table 3, row 5d).

Nicholson (2011a) questions the validity of this basecase and suggests thatλ should be chosen such that17∆#

S0(λBSS) =17 ∆#

P(λBSS) and that these values shouldequal (249± 15) ppm. This “tuned”λ value, denotedλBSS(for biological steady state) by Nicholson (2011a), is actu-ally identical to the triple isotope fractionation coefficient forrespiration (θR) and calculated as

λBSS= θR

=ln(1+

17εR)

ln(1+ 18εR)=

ln(1+ γR18εR)

ln(1+ 18εR)(9)

This leads to a set of calculation parameterswith 18δP = −22.832 ‰, 17δP = −11.587 ‰ and17∆

†P(0.5179) = (238± 35) ppm (Table 3, row 2). Within

error, this agrees with theNannochloropsisflask exper-iments if the assumptions ofγR = 0.5179± 0.0006 and18εR = (−20± 4) ‰ for these experiments are correct.It differs substantially from the corresponding values forthe Acropora flask experiments assuming18εP = 0.5 ‰(Table 3, row 3a) and the results for all species based onthe isotopic composition of seawater and the photosyntheticisotope fractionation (Table 3, rows 5a–c, 5e) except forE. huxleyi(Table 3, row 5d). It may be reconciled with theAcropora flask experiments if18εP = 5.814 ‰ is assumed(Table 3, row 3b).

In Sect. 4, Nicholson (2011a) comments that17∆#P(θR) =

231 ppm for the Nannochloropsisflask experiments isvery close to17∆#

P(θR) = 234 ppm for theAcropora flask

experiments. Notwithstanding that our own calculations giveidentical results of17∆#

P(θR) = 229 ppm for both cases (Ta-ble 3, row 4a and footnote to row 3a), this is not a fair com-parison becauseθR = 0.5173 forAcroporaandθR = 0.5154for Nannochloropsis. Clearly, the17δP values differ in bothcases (for the same18δP value) and calculations of gross pro-duction using the accurate dual-delta method would lead todifferent results. This illustrates the perils associated with us-ing 17∆ values in isolation.

2.4 New measurements of18δVSMOW and 17δVSMOW

Four days after publication of Kaiser (2011a) and threedays before publication of Nicholson (2011a), new mea-surements of18δVSMOW and 17δVSMOW were published(Barkan and Luz, 2011). The authors of this paper foundthat they could not reproduce their earlier results for17δVSMOW (Barkan and Luz, 2005). Their new results gave17δVSMOW = (−11.883± 0.012) ‰ (Table 1, row 5), whichis 0.048 ‰ or five standard deviations higher than theoriginal value of (−11.931± 0.01) ‰ (Barkan and Luz,2005). The new18δVSMOW value of (−23.324± 0.017) ‰was virtually unchanged compared to the original value of(−23.320± 0.02) ‰. In terms of17∆

†VSMOW(0.5179), this

amounts to a change from (146± 4) ppm to (196± 4) ppm.The authors do not give an explanation for this change, otherthan that “experimental system and measurement procedureswere somewhat improved” (Barkan and Luz, 2011).

The revised measurements allow recalculatingδP basedon δW andεP (Sect.2.1). 18δP remains virtually unchanged,but the corresponding17δP and 17∆

†P(0.5179) values in-

crease by about 50 ppm (Table 3). Within error, the re-vised 17∆

†P(0.5179) values agree with those estimated for

Nannochloropsis(flask), Acropora (flask; assuming18εP =

5.814 ‰) and Nicholson (2011a). They disagree with theAcropora(flask; assuming18εP = 0.5 ‰) and Kaiser (2011a)values.

Our own measurements of VSMOW relative to Air-O2 give 18δVSMOW = (−23.647± 0.04) ‰ and17δVSMOW =

(−12.102± 0.03) ‰ (Table 1, row 6). Taking into ac-count the17O/ 16O depletion of ocean water with respectto VSMOW, this gives 17δW = (−12.107± 0.03) ‰ and17∆

†W(0.5179) = (140± 6) ppm (Table 3, row 7). The uncer-

tainty of 17∆†W is lower than for17δW because the errors in

18δ and17δ are correlated in a mass-dependent way.Our 17∆

†W(0.5179) value is in good agreement with the

original measurements of Barkan and Luz (2005), but dis-agrees with their revised results (Barkan and Luz, 2011).Just as the results of Barkan and Luz, our data have beenobtained using CoF3 fluorination on a Finnigan MAT DeltaPlus isotope ratio mass spectrometer (University of Nagoya).However, our results have been corrected for a 0.8 % scalecontraction, based on gravimetrically calibrated mixturesof 99.7 % pure H18

2 O with tap water. The scale correction



affected17∆†W(0.5179) by a 2 ppm increase only. It actually

brings18δVSMOW into closer agreement with independent es-timates of (−23.771± 0.06) ‰ (Table 1, row 4), based onisotope measurements in CO2 (Kaiser and Rockmann, 2008).Barkan and Luz (2005, 2011) did not perform a scale correc-tion, even though their measured SLAP-VSMOW differenceof (−55.11± 0.05) ‰ (Barkan and Luz, 2005) differs fromthe internationally accepted value of−55.5 ‰ (Gonfiantini,1977, 1978). If the value of−55.5 ‰ were accurate, the cor-responding scale contraction would amount to 0.7 %. A scalecontraction of 0.7 to 0.8 % may be typical for this particulartype of mass spectrometer.

The varying results for the relative isotope ratio differ-ences between VSMOW and Air-O2 within a single labora-tory and between laboratories warrant further measurementsof this important parameter and perhaps inter-laboratorycomparisons.

For comparison purposes, we construct mean parametersets from the species-dependentδP values (Table 3, rows5m, 6m and 7m). For the photosynthetic isotope fraction-ation, we adopt the arithmetic average of the correspond-ing values based on Eisenstadt et al. (2010), i.e.,18εP =

(4.119± 2.6) ‰ and17εP = (2.153± 1.3) ‰ (Table 2). This18εP value is in good agreement with the global average18εPof 4 ‰ derived by Luz and Barkan (2011a). A similar ap-proach was taken by Luz and Barkan (2011b), but they ex-cludedC. reinhardtii from their meanδP values. It would notbe appropriate to take the arithmetic average ofθP reportedfor various organisms to derive17εP because17εP is essen-tially linearly related to17δP whereasθP is not.

The good agreement between our own measurements ofthe isotopic composition of VSMOW relative to Air-O2and those of Barkan and Luz (2005) is also reflected bythe closely matching species-dependent17∆P(0.5179) values(Table 3, rows 5a–5e and 7a–7e). In the next section, we willillustrate the systematic impact of differentδP values ong.

3 Dependence ofg on the isotopic composition ofphotosynthetic O2

3.1 Accurate calculation ofg using thedual-delta method

Since the interaction between the parameters17δP, 18δPand γR is not straightforward to predict based on Eq. (1),their impact ong is best illustrated through example cal-culations (Kaiser, 2011a). Results forg based on17δP and18δP derived in Sects.2.1–2.3, including the parameterssuggested by Nicholson (2011a) and Kaiser (2011a) arecompared with those using the meanδP values based onBarkan and Luz (2005; Table 3, row 5m; Fig. 1a and b)and based on Barkan and Luz (2011; Table 3, row 6m;Fig. 1c and d). The same scenarios as in Kaiser (2011a)were used, i.e.,g = 0.4 with −1.0 ≤ f ≤ +1.0 (Fig. 1a

and c) andf = 0.1 with 0.01≤ g ≤ 10 (Fig. 1b and d).Parameters related to gas exchange were left unchangedat 17δsat= 0.382 ‰, 18δsat= 0.707 ‰, 17εE = −1.463 ‰,18εE = −2.800 ‰ (Kaiser, 2011a, b).

As may be expected from the corresponding17∆P values,there is relative good agreement betweeng based on “Ta-ble 3, row 5m” (using VSMOW measurements reported byBarkan and Luz, 2005), “Table 3, row 7m” (using VSMOWmeasurements reported here), “Kaiser (2011a)”, “Acropora(flask, 18εP = 0.5 ‰)” and the species-specific parametersfor N. oculata, C. reinhardtiiandP. tricornutum(Fig. 1a andb). However,g based onSynechocystisparameters is≥ 24 %higher;g based on “Nicholson (2011a)”, “Nannochloropo-sis(flask, 2.85 ‰)” and “Luz and Barkan, 2011b” is≥ 27 %lower than “Table 3, row 5m”.g values based on “E. hux-leyi” and “Acropora(flask, 5.814 ‰)” and “Nannochloropo-sis (flask, 0.5 ‰)” are in between. Forf < 0.1 or g > 0.1,these relative deviations are higher (Fig. 1a and b) The rela-tive deviations ofg for theE. huxleyiparameters are≤–16 %from the base case forf = 0.1, which means theg valuesdeviate≤–32 % from theg values based onSynechocystisparameters, a significant species-related uncertainty.

For g based on “Table 3, row 6m” (using VSMOW mea-surements reported by Barkan and Luz, 2011), the species-specific parameters forN. oculata, C. reinhardtii andP. tri-cornutumagain agree well with the meanδP set (Fig. 1cand d). There is also relative good agreement with “Nichol-son (2011a)”, “Luz and Barkan (2011b)”, “Acropora(flask,5.814 ‰)” and “Nannochloroposis(flask, 2.85 ‰)”. How-ever, the relative deviations are≥ 35 % for “Kaiser (2011a)”,“Table 3, row 5m” and “Table 3, row 7m” and≤–12 % for“E. huxleyi”. Again, for f < 0.1 org > 0.1, these deviationstend to be even higher (Fig. 1c and d). The relative deviationsof g for theSynechocystisparameters are≥ +18 % from thebase case, which means theg values based onE. huxleyipa-rameters deviate≤–26 % from theg values based onSyne-chocystisparameters. The span between these two species isslightly smaller than for “Table 3, row 5m” because the dif-ferent base case parameters lead to different17δ and18δ sce-narios for the same two cohorts. Nevertheless, there is stilla significant uncertainty ing related to which species is as-sumed to have produced the O2 and, therefore, which set ofparameters17δP, 18δP andγR is adopted for the calculation.

To summarise, the experimental evidence can accommo-date both theδP parameters of Nicholson (2011a) as wellas those of Kaiser (2011a). Both the base cases used byKaiser (2011a) and by Nicholson (2011a) are hypothetical.On their own, they should therefore not be used to draw con-clusions on the quantitative accuracy of the resultingg val-ues. While we agree with Nicholson’s notion that differentparameters used in Kaiser (2011a) can explain the lowerg

values based on parameters used in previous studies (e.g.,Hendricks et al., 2004; Reuer et al., 2007; Juranek and Quay,2010), this should not be used to single out one parameter setas superior to the other. Kaiser (2011a) did not make such



-‐80%

-‐60%

-‐40%

-‐20%

0%

20%

40%

60%

80%

-‐1 -‐0.5 0 0.5 1

rel. dev.

f

-‐80%

-‐60%

-‐40%

-‐20%

0%

20%

40%

60%

80%

0.01 0.1 1 10

rel. dev.

g

Synechocys4s Acropora, 0.5‰

N. oculata Acropora, 5.814‰

C. reinhard4i Nannochl., 0.5‰

P. tricornutum Nannochl., 2.85‰

E. huxlyei Kaiser (2011a)

Table 3, row 5m Nicholson (2011a)

Table 3, row 7m Luz & B. (2011b)

c d -‐80%

-‐60%

-‐40%

-‐20%

0%

20%

40%

60%

80%

0.01 0.1 1 10

rel. dev.

g

-‐80%

-‐60%

-‐40%

-‐20%

0%

20%

40%

60%

80%

-‐1 -‐0.5 0 0.5 1

rel. dev.

f

a b

Fig. 1. Relative difference ofg for different sets of17δP, 18δP andγR (Table 3) tog based on row 5m (a, b; Barkan and Luz, 2005) and row6m (c, d; Barkan and Luz, 2011). (a, c) correspond tog =0.4 and−1.0 ≤ f ≤ 1.0; (b, d) to f = 0.1 and 0.01≤ g ≤ 10 (logarithmic axis).Red curves correspond to rows 5a–e (a, b) and 6a–e (c, d). “Kaiser (2011a)”, “Nicholson (2011a)”, “Acropora, 0.5 ‰”, “Acropora, 5.814 ‰”,“Nannochl., 0.5‰” and “Nannochl., 2.85 ‰” correspond to rows 1, 2, 3a, 3b, 4a and 4b. “Luz & B. (2011b)” uses17δP = −10.126 ‰ and18δP = −20.014 ‰ (Luz and Barkan, 2011b).



a claim and rather used the disagreement between differ-ent estimates of the isotopic composition of photosyntheticO2 to highlight the need for additional measurements of therequired parameters, especially17δP. The claim by Nichol-son (2011a) that theg values calculated using the base caseof Kaiser (2011a) were 30 % too high is not justified.

Nicholson (2011a) also commented that Kaiser (2011a)overestimates the discrepancy ofg based on differentcalculation methods/parameters, as seen in Fig. 3 ofKaiser (2011a) compared to Fig. 1 in Nicholson (2011a).However, this is largely due to how the results are presented(as relative deviations), and as we argue above, Kaiser’s“base case” just provides a reference for comparison, not abenchmark for other studies.

3.2 Approximate calculation ofg

Even though the development of the accurate dual-deltamethod makes use of approximations in the calculation ofg unnecessary, we will revisit the different approximationsused in the past to address Nicholson’s comment that17∆

should be defined as17∆#(θR) ≡ ln(1+17δ)−θR ln(1+

18δ).Luz and Barkan (2000) suggested the following approx-

imate calculation of oxygen gross production from oxygentriple isotope measurements

g =

17∆ −17∆sat

17∆P−17∆(10)

with the triple isotope excess defined as17∆†(0.521) ≡17 δ−

0.52118δ, i.e., using a linear definition.The same authors later revised this method and stated that

the triple isotope excess should be defined using the natu-ral logarithm (ln) as17∆#(γR) ≡ ln(1+

17 δ) –γR ln(1+18δ)

with γR = 0.5179 (Luz and Barkan, 2005), but that this def-inition shall not apply to17∆P. Instead, the photosyntheticend-member should be set equal to17∆#

P(θR), with θR =

0.5154 forγR = 0.5179 and18εR = −20 ‰ (Sect. 2.3). Asevidenced by its use in Luz and Barkan (2009), a coefficientof γR is also meant to apply to17∆#

sat.The use of different coefficients for the triple isotope ex-

cess is confusing, especially for the non-expert reader. More-over,θR can only be computed if18εR is also known. Eventhough the influence of the uncertainty in18εR is not as se-vere as when18δ were used for the calculation directly (Quayet al., 1993), this goes against the rationale behind the tripleoxygen isotope technique (i.e., the absence of the need toknow18εR). Finally, the suggested approximations are math-ematically inconsistent with Eqs. (1) and (2).

Instead, Kaiser (2011a) suggested that Eq. (10) is usedwith the triple isotope excess defined as17∆†(γR) ≡

17

δ − γR18δ. This definition is consistent with the asymptotic

behaviour of Eq. (2) for17δ, 18δ → 0. However, it wasshown that this approximated calculation can lead to system-atic biases from the accurate solution calculated using the

dual-delta method and the use of this approximation was notrecommended.

Nicholson (2011a) comments that the approximations ofKaiser (2011a) and, by implication, Luz and Barkan 2005)can be improved if a definition of the triple isotope excessas17∆#(θR) is adopted. The corresponding17∆#

P(θR) valueis named17∆BSS for “biological steady state” because it isidentical to the17∆#

S0(θR) value under concentration steadystate (f = 0). However, as shown in Sect. 3.4 and the un-corrected Fig. 1 of Kaiser (2011a), isotopic steady state canalso be achieved forf 6= 0 and in this case,17∆#

S(θR) 6=

17∆#P(θR). It is, therefore, not clear a priori whether the ap-

proximation suggested by Nicholson (2011a) performs bet-ter than the other approximations.

Just as in Sect.3.1, we, therefore, compare the differ-ent approximations to the accurate solution using a rangeof scenarios. The scenarios correspond to 0.01≤ g ≤ 10 and−1 ≤ f ≤ 1 (in steps of 0.2). The underlying parameters17δP, 18δP andγR correspond to “Kaiser (2011a)” (Table 3,row 1; Fig. 2); the meanδP based on the VSMOW measure-ments of Barkan and Luz (2011) (Table 3, row 6m; Fig. 3),which is similar to “Nicholson (2011a)”; and the parametersderived from theAcroporaflask experiments (18εP= 0.5 ‰;Table 3, row 3a; Fig. 4).

The approximate solutions are calculated using Eq. (10)with the triple isotope excess defined as (a)17∆†(γR) (Kaiser,2011a) (Figs. 2a, 3a, 4a); (b)17∆#(γR) in general, but17∆#

P(θR) for photosynthetic O2 (Luz and Barkan, 2005)(Figs. 2b, 3b, 4b); (c)17∆#(γR) (shown for completeness)(Figs. 2c, 3c, 4c) and (d)17∆#(θR) (Nicholson, 2011a)(Figs. 2d, 3d, 4d). In the following, we refer to these defi-nitions as methods (a) to (d).

None of the approximations deliver unbiased results forg > 1. Of course, such conditions rarely occur in the environ-ment (except for intense blooms or very low wind speeds).However, even forg < 1 significant biases can occur in allcases under certain conditions.

For all scenarios, method (c) performs worst. However,17∆#(γR) on its own has actually never been used togetherwith Eq. (10), as far as we know, so this has no consequencefor already published data.

For the base case adopted by Kaiser (2011a) (Table 3,row 1; Fig. 2), method (a) returns nearly unbiased results forf = 0 andg < 0.1. Forg < 1 and−0.4≤ f ≤ 0.2, the rel-ative deviation from the accurate solution does not exceed± 22 % (Fig. 2a).g values based on Nicholson’s method (d)are biased 10 % low forf = 0, but the relative deviation fromthe base case is at most−21 % for g ≤ 0.4 (Fig. 2d). Luzand Barkan’s method (b) is biased only 7 % low forf = 0(Fig. 2b), but otherwise the derivedg values have larger de-viations from the accurate solution than those for method (d),more similar to method (a).

For the scenario using the meanδP value based on the VS-MOW measurements of Barkan and Luz (2011) (Table 3, row



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0.01% 0.1% 1% 10%

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0.01% 0.1% 1% 10%

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1%0.8%0.6%0.4%0.2%0%!0.2%!0.4%!0.6%!0.8%!1%

!80%%

!60%%

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0.01% 0.1% 1% 10%

g"

1%0.8%0.6%0.4%0.2%0%!0.2%!0.4%!0.6%!0.8%!1%

a" b"

c" d"

Fig. 2. Relative deviation of the approximated solution forg (Eq. 10) from the accurate solution (Eq. 1) for the parameters in Table 3, row 1(Kaiser, 2011a).(a) linear definition of17∆ with κ = γR (Kaiser, 2011a):17∆

†P(0.5179)= 180 ppm,17∆

†sat(0.5179)= 16 ppm.

(b) ln-definition of17∆ with λ = γR except for17∆#P (Luz and Barkan, 2005):17∆#

P(0.5154)= 191 ppm,17∆#sat(0.5179)= 16 ppm.

(c) ln-definition of17∆ with λ = γR: 17∆#P(0.5179)= 249 ppm,17∆#

sat(0.5179)= 16 ppm.

(d) ln-definition of17∆ with λ = θR (Nicholson, 2011a):17∆#P(0.5154)= 191 ppm,17∆#

sat(0.5154)= 18 ppm.

6m; Fig. 3), methods (a), (b) and (d) give nearly unbiased re-sults for f = 0 and the entire range ofg values explored.Method (d) has the least bias forg < 1, whereas methods (a)and (b) perform similarly.

For the scenario based on theAcroporaflask experiments(18εP= 0.5 ‰; Table 3, row 3a; Fig. 4), method (a) givesthe least bias forf = 0. In this case, methods (b) and (d)are biased low by 19 % and 12 %, respectively. Interestingly,method (d) does not show any significant variation in thisbias forg < 0.1 and the entire range inf .

In summary, none of the calculation methods is free frombias under all conditions and scenarios. The value Nichol-son (2011a) attributed to method (d) may be due to the

particular hypothetical scenario he has chosen, which is verysimilar to that defined by “Table 3, row 6m” (Fig. 1c andd). However, if other17δP and18δP parameters were adoptedsuch as those of theAcroporaflask experiments (assuming18εP = 0.5 ‰), then significant deviations from the accuratesolution would occur.

4 Conclusions

It is important to make the distinction between different cal-culation methods (e.g., iterative versus dual-delta method;approximate based on17∆ versus accurate based on17δ



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1%0.8%0.6%0.4%0.2%0%!0.2%!0.4%!0.6%!0.8%!1%

a" b"

c" d"

Fig. 3. Relative deviation of the approximated solution forg (Eq. 10) from the accurate solution (Eq. 1) for the parameters in Table 3, row6m (δW based on Barkan and Luz, 2011).(a) linear definition of17∆ with κ = γR (Kaiser, 2011a):17∆

†P(0.5179)= 235 ppm,17∆

†sat(0.5179)= 16 ppm.


P(0.5154)= 236 ppm,17∆#sat(0.5179)= 16 ppm.


sat(0.5179)= 16 ppm.


sat(0.5154)= 18 ppm.

and 18δ pairs) and different calculation parameters. Withthe development of the dual-delta method (Kaiser, 2011a;Prokopenko et al., 2011), it is time to abandon approximatedsolutions based on the triple isotope excess (17∆). The endof the discussion about what the appropriate definition is for17∆, which is the right coefficient and whether it should bedefined in terms ofδ or ln(1+δ), will also help alleviate theconfusion that newcomers and students feel when they firstenter this field of research.

Even though the methodological bias due to the use ofEq. (10) may often be smaller than the uncertainty dueto wind speed-gas exchange parameterisations, there is no

reason for such bias to exist at all if the dual-delta method isadopted.

We agree with Nicholson (2011a) that different parametersare key to explaining the differences between Kaiser’s basecase and previous studies (e.g., Hendricks et al., 2004; Reueret al., 2007; Juranek and Quay, 2010). However, considerablesystematic uncertainty remains in the calculation ofg due tothe uncertainty in the isotopic composition of photosyntheticO2, 17δP and18δP. Part of this uncertainty is due to conflict-ing results for the17O/ 16O isotope ratio of seawater relativeto Air-O2 (Sect. 2.4). Moreover, the experiments by Eisen-stadt et al. (2010) and the results in Fig. 1 show that thereis considerable interspecies variability in the photosynthetic



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1%0.8%0.6%0.4%0.2%0%!0.2%!0.4%!0.6%!0.8%!1%

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c" d"

Fig. 4. Relative deviation of the approximated solution forg (Eq. 10) from the accurate solution (Eq. 1) for the parameters in Table 1, row3a (Acropora(flask),18εP = 0.5 ‰ ).(a) linear definition of17∆ with κ = γR (Kaiser, 2011a):17∆

†P(0.519)= 200 ppm,17∆

†sat(0.519)= 15 ppm.


P(0.5173)= 229 ppm,17∆#sat(0.519)= 15 ppm.


sat(0.5179)= 15 ppm.


sat(0.5173)= 17 ppm.

isotope fractionation and the inferred gross productiong, de-pending on what species is assumed to have produced theoxygen. Independent measurements and perhaps laboratorycomparison exercises should be performed to establish thereproducibility of 17O/ 16O isotope ratio measurements inwater. Further experiments with cultures under steady-stateconditions would help to verify the calculations based on theisotopic composition of water and the photosynthetic isotopefractionation.

The comment by Nicholson (2011a) on “Consistent calcu-lation of aquatic gross production from oxygen triple isotopemeasurements” by Kaiser (2011a) centred on the appropriatechoice of17δP and18δP. At the moment, however, it seems

to be more important to emphasise the differences that resultfrom different parameters and calculation methods. The de-mand for the “correct” choice is premature and besides themain topic of Kaiser’s original paper.

Acknowledgements.Jan Kaiser would like to thank the RoyalSociety for support through Wolfson Research Merit AwardWM052632. Osamu Abe was supported during a sabbatical yearat UEA by the JSPS “Institutional Program for Young ResearcherOverseas Visits”.

Edited by: J. Middelburg



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http://dx.doi.org/10.1007/s11120-009-9518-z

http://dx.doi.org/10.1104/pp.105.063768

http://dx.doi.org/10.1029/2009gb003492

http://dx.doi.org/10.1016/j.gca.2007.12.011

http://dx.doi.org/10.5194/bg-8-1793-2011

http://dx.doi.org/10.5194/bg-8-2561-2011

http://dx.doi.org/10.5194/bg-8-2561-2011

http://dx.doi.org/10.1016/j.gca.2010.08.016

http://dx.doi.org/10.1029/2010gb003883

http://dx.doi.org/10.1029/2011gl049138

http://dx.doi.org/10.5194/bg-8-2993-2011

http://dx.doi.org/10.1029/2011gl047652

http://dx.doi.org/10.1071/FP07168

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