SUPPLEMENTARY INFORMATION

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1 SUPPLEMENTARY INFORMATION DOI: /NGEO1745 Isotopic ratios of nitrite as source and age tracers for oceanic nitrite Carolyn Buchwald 1 and Karen L. Casciotti 2 1 Massachusetts Institute of Technology/ Woods Hole Oceanographic Institution Joint Program in Chemical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts. 2 Department of Environmental Earth System Science, Stanford University, Stanford, California. NATURE GEOSCIENCE 1

2 1. Sampling locations and ancillary data cast , 30 Fig. S1. Map of the locations sampled for primary nitrite maximum isotope measurements in the Arabian Sea during September-October Table S1. Ancillary data for primary nitrite maximum samples from the Arabian Sea. Sample Cast Lat. N Lon. E Depth (m) - ] [NO - 2 ] [NO 3 µmol L -1 µmol L -1 δ 18 O NO2 vs. VSMOW δ 15 N NO2 vs. N 2 δ 18 O NO3 vs. VSMOW δ 15 N NO ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± vs. N 2 2

3 Table S2. Isotope term descriptions and values Term Description Value (range tested) 15 ε k,ao Kinetic N isotope effect for ammonia oxidation 22 1 (0 to 22) 15 ε k,aa Kinetic N isotope effect for ammonium assimilation 20 2 (0 to 20) 15 ε k,nr Kinetic N isotope effect for nitrate reduction 5 3 (0 to 10) 15 ε k,no Kinetic N isotope effect for nitrite oxidation -15 4, 5 (-20 to -10) 15 ε k,na Kinetic N isotope effect for nitrite assimilation 1 2 (-4 to 6) 15 ε R Kinetic N isotope effect for OM remineralization 3 (-2 to 8) 18 ε k,o2 Kinetic O isotope effect for O 2 incorporation combined with 18 ε k,h2o,1 18 ε k,h2o,1 Kinetic O isotope effect for H 2 O incorporation 20 6 (15 to 25) 18 ε k,nr Kinetic O isotope effect for nitrate reduction 5 3 (0 to 10) 18 ε k,no Kinetic O isotope effect for nitrite oxidation -3 5 (-8 to 2) 18 ε k,na Kinetic O isotope effect for nitrite assimilation 1 2 (-4 to 6) 18 ε b,nr Branching O isotope effect for nitrate reduction 25 7 (20 to 30) 18 ε eq Equilibrium isotope effect for O atom exchange ; temperature dependent (this study) δ 15 N OM δ 15 N value of organic matter 8 8, 9 (3 to 13) δ 15 N NO3 δ 15 N value of ambient nitrate Measured δ 15 N NO2 δ 15 N value of ambient nitrite Measured δ 15 N NO2,source Flux-weighted δ 15 N average of nitrite sources Calculated, equation S7 δ 15 N NO2,AO δ 15 N value of ammonia oxidation source Calculated, equation S8 δ 15 N NH4 δ 15 N value of ambient ammonium Calculated, equation S9 δ 15 N NO2,NR δ 15 N value of nitrate reduction source Calculated, equation S10 δ 18 O O2 δ 18 O value of ambient dissolved oxygen 24.2 δ 18 O H2O δ 18 O value of water 0 δ 18 O NO3 δ 18 O value of ambient nitrate Measured 3

4 δ 18 O NO2 δ 18 O value of ambient nitrite Measured δ 18 O NO2,source Flux-weighted δ 18 O average of nitrite sources Calculated, equation S11 δ 18 O NO2,AO δ 18 O value of ammonia oxidation source Calculated, equation S12 δ 18 O NO2,NR δ 18 O value of nitrate reduction source Calculated, equation S13 δ 18 O NO2,eq Fully equilibrated δ 18 O NO2 value Calculated, see text below x AO Fraction of O atoms exchanged during AO , 10 ( ) 2. Steady state model 2.1 Full derivation of steady state model equations At steady state, the production of nitrite from ammonia oxidation (F AO ) and nitrate reduction (F NR ) balances the consumption of nitrite from nitrite oxidation (F NO ) and nitrite assimilation (F NA ). When summed together, the total input fluxes (F AO + F NR ) or output fluxes (F NO + F NA ) equal the biological flux (F B ), which is characteristic for each site: (S1) F AO + F NR + F NO + F NA = F B The biological flux can also be partitioned into fractions arising from ammonia oxidation (f AO ) and nitrate reduction (f NR ) or nitrite oxidation (f NO ) and nitrite assimilation (f NA ) (equations S2- S6). (S2) (S3) (S4) (S5) (S6) f AO + f NR = f NO + f NA =1 f AO = F AO /F B f NR = F NR /F B f NO = F NO /F B f NA = F NA /F B These flux fractions are then used to calculate the δ 15 N and δ 18 O values of biological nitrite sources (equations S7-S13) and sinks (equations S14-S17). 4

5 (S7) δ 15 N NO2,source = δ 15 N NO2,AO f AO + δ 15 N NO2,NR f NR (S8) δ 15 N NO2,AO = δ 15 N NH4 15 ε k,ao (S9) δ 15 N NH4 = δ 15 N OM 15 ε R + F AO /F R 15 ε k,ao + F AA /F R 15 ε k,aa (S10) δ 15 N NO2,NR = δ 15 N NO3 15 ε k,nr (S11) δ 18 O NO2,source = δ 18 O NO2,AO f AO + δ 18 O NO2,NR f NR (S12) δ 18 O NO2,AO = ½ [δ 18 O O2 + δ 18 O H2O ( 18 ε k,o ε k,h2o,1 )](1-x AO ) + (δ 18 O H2O + 18 ε eq )(x AO ) (S13) δ 18 O NO2,NR = δ 18 O NO3 18 ε k,nr + 18 ε b,nr (S14) δ 15 N NO2,NO = δ 15 N NO2 15 ε k,no (S15) δ 15 N NO2,NA = δ 15 N NO2 15 ε k,na (S16) δ 18 O NO2,NO = δ 18 O NO2 18 ε k,no (S17) δ 18 O NO2,NA = δ 18 O NO2 18 ε k,na The full steady state δ 15 N balance equation is given by S18: (S18) " 15 N NO2,AO # f AO +" 15 N NO2,NR # f NR = (" 15 N NO2 $ 15 % k,no )# f NO + (" 15 N NO2 $ 15 % k,na )# f NA The right hand side of equation S18 describes the sinks, with isotopic terms defined in Table S2. Equation S18 can be rearranged to obtain equation 3 in the main text. The oxygen isotope balance has a similar formulation (equation S19), except it includes additional terms to describe the fluxes associated with abiotic oxygen atom exchange (F eq ). (S19) " 18 O NO2,AO # f AO +" 18 O NO2,NR # f NR +" 18 O NO2,eq # F eq /F B = (" 18 O NO2 $ 18 % k,no )# f NO + (" 18 O NO2 $ 18 % k,na )# f NA +" 18 O NO2 # F eq /F B Both sides of equation S19 include the abiotic equilibration flux, which adds nitrite with δ 18 O NO2,eq and removes nitrite with δ 18 O NO2. Equation S19 can be rearranged to obtain equation 4 in the main text. It is useful to consider the steady state δ 18 O NO2 value when F eq = 0 and nitrite is 5

6 only affected by biological processes. We define this as the biological endmember, δ 18 O NO2,b. At the other extreme, when F eq >>F B, δ 18 O NO2 = δ 18 O NO2,eq. Equation S18 can be rearranged to solve for f AO (equation S20) by combining it with equation S2, and equation S19 can be rearranged to solve for F B (equation S21) by combining it with equations S3-S6. (S20) (S21) [( f AO = "15 N NO2 # 15 $ k,no )% f NO + (" 15 N NO2 # 15 $ k,na )% f NA #" 15 N NO2,NR ] " 15 N NO2,AO #" 15 N NO2,NR F B = ( ) F eq " (# 18 O NO2 $# 18 O NO2,eq ) [# 18 O NO2,AO " f AO +# 18 O NO2,NR " f NR $ (# 18 O NO2 $ 18 % k,no )" f NO $ (# 18 O NO2 $ 18 % k,na )" f NA ] At each site F eq can be calculated from k*[no - 2 ] using the T and ph to calculate the equilibration rate constant, k (described in the text and in more detail below, equation S29). δ 18 O NO2,eq at each site can be derived from δ 18 O H2O + 18 ε eq, using T to derive 18 ε eq (described in the text and in more detail below, equation S30). Each f is solved iteratively using the method described in the main text to produce a range of F B values that is consistent with the measured δ 15 N NO2 and δ 18 O NO2 values. 2.2 Uncertainties in δ 15 N NO2,AO In order to calculate δ 15 N NO2,AO values we used equations S8 and S9. For simplicity, we assumed that F AO /F R is much less than F AA /F R and fix the ratios at 0.1 and 0.9, respectively. At high concentrations of ammonium, 15 ε k,ao and 15 ε k,aa are quite similar (22 and 20, respectively) and δ 15 N NO2,AO is relatively insensitive to F AO /F R. For example, if F AO /F R and F AA /F R are reversed (0.9 and 0.1, respectively), the estimated δ 15 N NO2,AO values change by 1.6, 6

7 which is within the range of uncertainty in δ 15 N OM. However, when ammonium is limiting, the isotope effect for assimilation is expected to decrease significantly 2, 11. Changes in the ammonia oxidation isotope effect are less certain, but have been argued to be smaller, maintaining 15 ε k,aa near 20 even at low ammonium concentrations due to the large equilibrium isotope effect between ammonium and ammonia 12. In this case, the δ 15 N NO2,AO value produced by ammonia oxidation would be significantly lower (-13 ) than under ammonium replete conditions (+3.2 ), assuming it is still 10% of total ammonium consumption. The contribution of ammonia oxidation to nitrite production inferred from the model would need to be correspondingly lower to account for measured δ 15 N NO2 values between -3.7 and 2.4. A higher fraction of nitrite produced from nitrate reduction would, in turn, drive a higher δ 18 O NO2,b value. We tested the ammonium limitation case for the Arabian Sea samples and found that the calculated δ 18 O NO2,b values fell between 16 and 30. Since these δ 18 O NO2,b values fall above δ 18 O NO2,eq we would also expect our measured values to fall above δ 18 O NO2,eq (equilibration can only bring δ 18 O NO2 to equilibrium, not past it). However, all but one of the measured δ 18 O NO2 values (Table S1) were below δ 18 O NO2,eq, which is not consistent with large contributions from nitrate reduction. The only way to explain our δ 15 N NO2 and δ 18 O NO2 data with dissimilar 15 ε k,aa and 15 ε k,ao values at low ammonium concentrations is to have ammonia oxidation far exceed ammonium assimilation as a sink for ammonium, which seems unlikely in the euphotic zone. We conclude, therefore, that in this system 15 ε k,aa and 15 ε k,ao are similar, although we cannot distinguish between similar high values and similar low values. 7

8 3. Non-steady state model 3.1 Model description If steady state does not apply to the nitrite pool, the sources and sinks need not balance. The δ 15 N NO2 and δ 18 O NO2 values are still set by the δ 15 N and δ 18 O values of the sources, sinks and their relative fluxes, but here we need to consider the fractional consumption relative to production. Abiotic equilibration will still affect δ 18 O NO2, bringing it towards the fully equilibrated value (δ 18 O NO2,eq ) at a predictable rate. Here we model the evolution of δ 18 O NO2 in a stepwise manner with nitrite production occurring first, followed by nitrite consumption, and finally abiotic equilibration. To determine the δ 15 N NO2 and δ 18 O NO2 contributions of the input fluxes, we make the simplifying assumptions that both the ammonium and nitrate pools are held at constant concentrations and δ 15 N (and δ 18 O for nitrate) values. In this case, the δ 15 N and δ 18 O values of the sources are the same as in the steady state model described above, and the overall biological input flux has δ 15 N and δ 18 O values dictated by the weighted sum of the ammonia oxidation and nitrate reduction terms: (S22) δ 15 N NO2,source = f AO δ 15 N NO2,AO + f NR δ 15 N NO2,NR (S23) δ 18 O NO2,source = f AO δ 18 O NO2,AO + f NR δ 18 O NO2,NR Once the δ 15 N NO2,source and δ 18 O NO2,source values are calculated using equations S22 and S23 we allow the δ 15 N NO2 value to change due to Rayleigh fractionation during nitrite consumption, where a fraction (1 f) of the nitrite produced is consumed by nitrite oxidation (NO) and nitrite assimilation (NA), with their associate isotope effects ( 15 ε k,no ; 18 ε k,no ; 15 ε k,na ; 18 ε k,na ) 2, 4, 5. The N isotope effects for nitrite oxidation ( 15 ε k,no ) and nitrite assimilation ( 15 ε k,na ) (Table S2) are weighted by their relative contributions to the total nitrite consumption flux (f NO 8

9 and f NA, respectively) to describe the overall expressed N isotope effect for nitrite consumption (equation S24). Since f must be between 0 and 1, this puts constraints on the possible sources and sinks in order to match the measured δ 15 N NO2 values. (S24) " 15 N NO2 = ( f AO # " 15 N NO2,AO + f NR # " 15 N NO2,NR ) $ ( f NO # 15 % k.no + f NA # 15 % k.na )ln( f ) After calculating the f values, the biological endmember δ 18 O NO2 (δ 18 O NO2,b ), representing the δ 18 O NO2 value that would be observe in the absence of equilibrium, can be calculated from the δ 18 O values and isotope effects for each process (equation S25). (S25)! 18 O NO2,b = ( f AO!! 18 O NO2,AO + f NR!! 18 O NO2,NR ) " ( f NO! 18! k,no + f NA! 18! k,na )ln( f ) The non-steady state δ 18 O NO2,b is slightly different from the steady state value because the sources and sinks are not balanced. The application of equation S25 is similar to equation S24, except here δ 18 O NO2,b is the unknown instead of f. The predicted δ 18 O NO2,b value provides an additional constraint on the relative importance of source and sink processes since the measured δ 18 O NO2 value should fall between δ 18 O NO2,b and δ 18 O NO2,eq. Over time, abiotic equilibration between nitrite and water will overwrite the biotic δ 18 O NO2 signatures, leading to δ 18 O NO2 values closer to equilibrium the longer nitrite persists. The exchange of oxygen atoms between nitrite and water can be represented as a first order reaction, shown in equation S26. (S26) " 18 O NO2 = (" 18 O NO2.b #" 18 O NO2.eq )$ e #kt +" 18 O NO2.eq δ 18 O NO2 is the measured value of the sample, δ 18 O NO2,b is the signature of the biological endmember discussed above, and δ 18 O NO2,eq is the δ 18 O NO2 value expected at equilibrium for a given temperature and δ 18 O H2O. k is the rate constant for equilibration (in units of day -1 ), which is dependent on the ambient ph and temperature of seawater at the sampling location and 9

10 independent of nitrite concentration. k is related to F eq by the relationship F eq = k*[no - 2 ]. The closer individual δ 18 O NO2 values fall to their respective δ 18 O NO2,b values, the younger the nitrite is inferred to be. The closer they fall to their individual δ 18 O NO2,eq values, the older the nitrite is inferred to be. The calculation also takes into consideration the distance between δ 18 O NO2,b and δ 18 O NO2,eq for each sample so that the same measured δ 18 O NO2 value for two samples may represent different ages. 3.2 Results To calculate the average age of the nitrite in a sample from its measured δ 18 O NO2 and δ 15 N NO2 values, we need to know δ 18 O NO2,b (equation S25), δ 18 O NO2,eq (from T and δ 18 O H2O ), and the equilibration rate constant, k (from T and ph, equation S29). ph was estimated from a previously determined linear relationship between ph and dissolved oxygen concentration. δ 18 O NO2,eq was determined for each sample from 18 ε eq based on the T data and δ 18 O H2O estimated from salinity 13. The biological endmember, δ 18 O NO2,b, was predicted for each sample based on its δ 15 N NO2 value, as described above (equations S24-S25). Based on the measured δ 15 N NO2 and δ 18 O NO2 values, we assumed that for most samples the source of nitrite was ammonia oxidation (f AO =1) because the δ 18 O NO2 values were lower than the equilibrated value (Figure S2), whereas nitrate reduction would have given δ 18 O NO2 values higher than δ 18 O NO2,eq. The dominant sink was assumed to be nitrite oxidation (f NO = 1) because the range of measured δ 15 N NO2 values were all lower than the prospective sources. This requires consumption of nitrite with an inverse kinetic isotope effect, characteristic of nitrite oxidation 4,5. Nitrite assimilation has a small positive isotope effect 2, so consumption by this process alone could not explain the measured δ 15 N NO2 values, although the δ 15 N NO2 value would not be very 10

11 sensitive to nitrite assimilation fluxes. Because of the lack of mass balance constraints in the non-steady state model, the nitrite assimilation flux is very difficult to constrain. Using these assumptions, the average age of nitrite in the PNM was estimated to range from 13 to 144 days (Table S3) O-NO 2 ( vs. VSMOW) equilibration equilibration nitrite oxidation 50% AO 50% NR 4 18 O NO2, measured 18 O NO2,b 2 0 nitrite oxidation 100% AO 18 O NO2,source 18 O NO2,eq N-NO 2 ( vs. AIR) Figure S2. Interpretation of δ 15 N NO2 and δ 18 O NO2 values from the Arabian Sea PNM using the non-steady state model. Measured values (red triangles) reflect the balance of sources (ammonia oxidation, AO or nitrate reduction, NR, blue squares), consumption (nitrite oxidation, solid arrows), and oxygen isotope equilibration (vertical arrows). The blue circles represent the biological end member values (δ 15 N NO2 and δ 18 O NO2,b ) expected prior to equilibration. The dashed lines represent the range of δ 18 O NO2,eq values for the samples based on their in situ temperatures and salinities. Error bars indicated standard deviation of duplicate measurements of δ 18 O NO2 and δ 15 N NO2 and the propagated error for calculated δ 18 O NO2,b values. 11

12 There was one sample (Cast 20, 34 meters depth; Table S1) that had a δ 18 O NO2 value higher than δ 18 O NO2,eq, indicating that ammonia oxidation was not the only source of nitrite. We can constrain the δ 18 O NO2,b value for this sample based on the δ 15 N and δ 18 O source values, the nitrite oxidation fractionation factors, and the concentration of nitrite. Assuming nitrite oxidation is the primary sink (given the low δ 15 N NO2 value), we know the slope of the consumption trend in δ 18 O NO2 vs. δ 15 N NO2 space (solid lines, Figure S2). The starting point for the consumption line (blue squares, Figure S2) depends on the source contributions from ammonia oxidation and nitrate reduction. If we allow 50% to be produced from nitrate reduction and 50% from ammonia oxidation, the nitrite would have an average age of 44 days. When allowing only 30% from nitrate reduction, δ 18 O NO2,b falls below δ 18 O NO2,eq after nitrite oxidation has taken place. If nitrate reduction were assumed to comprise 60% of the nitrite source, the average age of the nitrite would be 65 days, also within the range of ages in our other samples. The nitrite production from nitrate reduction is therefore most likely between 40-60% for this sample, and assuming 50% from nitrate reduction places the nitrite age within the range of other samples (Table S3). This sample was taken from a different cast than the others making it plausible that a different set of processes could have been active, although it was collected from a similar depth (34 meters) and nitrite concentration (0.83 µmol L -1 ) as some of the other samples (Table S1). 12

13 Table S3. Results of the Non-steady state primary nitrite maximum model Sample Non-steady state Non-steady state Non-steady state Non-steady state Non-steady f AO f NR f NO f NA state age (days) Discussion Sensitivity The non-steady state disequilibrium model relies on knowing the δ 18 O NO2 value that would be set by biological sources and sinks in the absence of abiotic equilibration, a value we refer to as the biological endmember (δ 18 O NO2,b ). This parameter depends on the sources and sinks of nitrite in the PNM, the substrates involved, and isotope effects associated with the reactions. Due to the number and complexity of these parameters, it is the most uncertain parameter in equation S26. We acknowledge that there is still much uncertainty in many of the isotope effects and isotope signatures involved. In order to determine the sensitivity of our model to these uncertainties we have propagated a ±5 uncertainty in all the chosen isotope effects and values in Table S3, and have found that to cause a 3 to 4 uncertainty in the δ 18 O NO2,b value. Comparison to steady state model 13

14 Overall, the non-steady state model gives similar results as the steady state. The main difference from the two models is that the steady state model allows equilibration to occur at the same time as the biological production and consumption while the non-steady state model assumes that equilibration occurs after the biological processes occur. In the ocean, it is much more likely that the equilibration will be occurring while nitrite is produced and consumed, which supports using the steady state model. In the non-steady state model, many additional simplifications and assumptions were needed because of the lack of a mass balance constraint that is provided by the steady state model. In the non-steady state, we assumed that f AO = 1 for all but one of the samples, in which we assumed that f AO = 0.5 (described above). These values are similar to the parameter values needed to solve for the maximum age steady state result, where δ 18 O NO2,b is farthest from equilibrium. The average age obtained in the non-steady state model turns out to be similar to the maximum age calculated at steady state. The non-steady state model is also insensitive to the amount of nitrite assimilation, which has a small isotope effect. Since we have few other constraints on the fractions of nitrite consumption we assume all of the consumption of nitrite to be from nitrite oxidation. This yields the most conservative results for the biological fluxes. For example, if we include nitrite assimilation, the flux-weighted average isotope effect for nitrite consumption would be smaller, requiring more overall nitrite consumption. In the steady state model, we have stronger constraints on the overall nitrite consumption flux and its isotopic composition, and a definitive flux from nitrite assimilation is needed to offset the rather large inverse isotope effect for nitrite oxidation. In reality, we do expect some nitrite assimilation to occur, so we believe the assumptions used in the steady state model to be more realistic. 14

15 Finally, the steady state model yields a residence time for nitrite and total biological flux, which then can be used with the fractional contribution of each process to calculate the magnitude of each of the four fluxes (S3-S6). It is less clear how to apply the average age measured using the non-steady state model, to determine the rate of biological processes 4. Abiotic equilibration rate experiments The rate of abiotic equilibration was determined at six different temperatures and at 13 ph values between As described in the text, the change in δ 18 O NO2 over time in each condition was determined (in duplicate) and fit to an exponential equation with the form y = y 0 + A* exp(-k*x). The k value fit at a given temperature was then plotted vs. ph to determine the slope (Figure S3a) and intercept (Figure S3b) of the regression at each temperature. (S27) slope = " "1.4123# e " $ ln( T / ) ' 2 & ) % ( (S28) intercept = " e # $ ln(t / ) ' 2 & ) % ( These relationships can be combined to produce a single relationship between ph, T, and k (S20) to allow calculation of k for individual samples with known ph and T values. Salinity was found not to have a significant impact on k for salinities of $ (S29) k = &" "1.4123# e " & % $ ln( T / ) ' 2 & ) % ( ' )# ph # e" ) ( $ ln(t / ) ' 2 & ) % ( 15

16 ! " 6 Slope of ph versus K Intercept from ph versus K Temperature (K) Temperature (K) Fig. S3. The relationship of temperature and the slope (a) or intercept (b) of the linear regression between ph and k from experiments 1 and 3. Error bars indicate the error in the linear regression of ph vs. k. 16

17 4. Equilibrium isotope effect In addition to affecting the rate of abiotic equilibration between nitrite and water, temperature sets the isotope effect for this exchange reaction. Figure S4 shows the 18 ε eq estimates from two kinds of equilibration experiments. The first type of experiment was the long-term equilibration rate experiments described above. The δ 18 O value of the water used (δ 18 O H2O ) was subtracted from the ending δ 18 O NO2 value of these experiments when the δ 18 O NO2 values of two nitrite materials (one with δ 18 O NO2 starting above equilibrium and one with δ 18 O NO2 starting below equilibrium) were the same within analytical error (exp1 and exp3 in Figure S4). The second set of experiments included short-term experiments conducted at low ph with four separate temperatures. Again, two different nitrite materials were used to unambiguously determine the δ 18 O NO2,eq value. The observed relationship between 18 ε eq and T was: (S30) 18 ε eq = 0.12 T Fig S4. The relationship between equilibrium isotope effect ( 18 ε eq ) and temperature. Error bars 18!eq ( ) indicate the propagated error of standard deviation of measurements of δ 18 O NO2 and rapid eq exp 1 rapid eq exp 2 exp 1 exp 3 δ 18 O H2O used to calculate 18 ε eq Temperature (K)

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