Predicting High-Dimensional Isotope Relationships from Diagnostic

Article Cite This: ACS Earth Space Chem. XXXX, XXX, XXX−XXX

http://pubs.acs.org/journal/aesccq

Predicting High-Dimensional Isotope Relationships from Diagnostic Fractionation Factors in Systems with Diffusional Mass Transfer Yuyang He* and Huiming Bao Department of Geology and Geophysics, Louisiana State University, E235 Howe Russell Kniffen, Baton Rouge, Louisiana 70803, United States

ACS Earth Space Chem. Downloaded from pubs.acs.org by UNIV OF SOUTH DAKOTA on 12/25/18. For personal use only.

S Supporting Information *

ABSTRACT: A dual or multiple stable isotope relationship, for example, a trajectory in a δ−δ (or δ′−δ′) space, can be used to deduce the relationship of underlying diagnostic isotope fractionation factors (α) and therefore reveal the mechanism of a reaction process. While temporal data sampled from a closed-system can be treated by a Rayleigh distillation model, spatial data should be treated by a reactiontransport model. Owing to an apparent similarity between the temporal and spatial trajectories, the research community has often ignored this distinction and applied a Rayleigh distillation model to cases where a reaction-transport model should be applied. To examine the potential error of this practice, here we compare the results of a Rayleigh distillation model to a diffusional reaction-transport model by simulating the trajectories in nitrate’s δ′18O−δ′15N space during a simple denitrification process. We found that an incorrect application of a Rayleigh distillation model can underestimate the degree of a diagnostic fractionation to 50% but results in an insignificant difference in the regression slope of a δ′−δ′ trajectory when α ≈ 1.0. The regression slope predicted by a Rayleigh distillation model can, however, be 0.03−0.3 greater than predicted by a reaction-transport model when NO3− is involved in complex nitrogen cycling. Our reaction-transport model rarely predicts a δ′18O−δ′15N regression slope > 1 for reasonable Earth surface conditions. We found that for those published cases of regression slopes > 1, many can be attributed to the grouping of multiple NO3− sources from independent origins. Our results highlight the importance of linking the underlying physical model to the plotted data points before interpreting their high-dimensional isotope relationships. KEYWORDS: reaction-transport, Rayleigh distillation, nitrate, denitrification, mixing, slope

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INTRODUCTION Two or more elements in an ion or molecule can have their stable isotope behavior bonded in a way that is characteristic of a specific chemical or physical process. These dual or multiple elemental isotope relationships have been used to identify biodegradation pathways, characterize source and sink, and uncover enzymatic reaction mechanisms of oxyanions and organic molecules. For instance, an approximately linear relationship with a regression slope of ∼1 exists in a δ18O−δ15N space for residual nitrate samples collected at different stages of laboratory denitrification experiments.1 Batch experiments show that residual ClO4− collected at different stages of biodegradation display a δ18O−δ37Cl regression slope of 2.5.2 Different biodegradation pathways of benzene, toluene, ethylbenzene, xylenes, 1,2-dichloroethane, and methyl tert-butyl ether have shown distinct δD−δ13C and/ or δD−δ13C−δ37Cl trajectories from batch experiments as well.3−7 These linear trajectories exist because the isotope fractionation factors (α’s) of multiple elements in an ion or molecule behave in a way that is bonded. If the isotope ratios are sampled from the residues in a closed-system at different times, a closed-system time-depend© XXXX American Chemical Society

ent Rayleigh distillation model can accurately quantify the process, and a diagnostic, constant α value can be obtained via R t /R 0 = f α− 1

(1)

in which Rt and R0 are isotope ratios of the residue at two separate times t and 0, f is the ratio of molar abundance of the major isotopologue at time t over time 0, which is very close to the fraction of the whole sample left at time t over time 0. Because we know well when a Rayleigh distillation model should apply, we know what we need to measure in an experiment and what such determined α means. The δ value, δ=

(

R sample R reference

)

(

− 1 , or the δ′ value, δ′ = ln

R sample R reference

), is used in

stable isotope community due to its superior measurement accuracy. The trajectory in a δ−δ or a δ′−δ′ space by plotting residues collected at different stages by a Rayleigh distillation model can be linked to a relationship between isotope Received: Revised: Accepted: Published: A

October 9, 2018 December 5, 2018 December 6, 2018 December 6, 2018 DOI: 10.1021/acsearthspacechem.8b00149 ACS Earth Space Chem. XXXX, XXX, XXX−XXX

Article

ACS Earth and Space Chemistry Δδ′ 18O

18

Some researchers have noticed that plotting spatially distributed samples in a δ−δ space would yield the same trajectory as if the spatial samples were snapshots of different temporal states in a Rayleigh distillation model. For instance, a relationship of Δδ18O/Δδ15N ≈ 1 has also been seen among NO3− samples collected at different depths in seawater columns.12,13 Similarly, a relationship of Δδ18O/Δδ37Cl ≈ 2.6 has been observed among samples collected from different sites in a groundwater system.9 Because there is no apparent trajectory difference between a Rayleigh distillation model and a reaction-transport model, most in the community are often plotted mixed spatial and/or temporal data in δ−δ spaces to deduce the underlying diagnostic α’s and their relationships. Conceptually, spatial data should not be treated with a Rayleigh distillation model. This transport issue has been raised in numerous publications and has been addressed to certain degrees in theoretical studies8,10,11,14,15 as well as in specific case studies.9 However, the impact of transport on the regression slope value of a trajectory in a δ−δ space has not been examined systematically. Diffusion and advection are two main transport modes. Physically, these two transport terms will both “dilute” the degree of isotope fractionation of a closed-system Rayleigh process. Diffusion is the key mass transfer process in still-water columns or in pore-water in marine sediments. Here, in this study, we explore the diffusional mass transfer effect on the high-dimensional α relationship analytically and numerically from the community scale to the geological scale (Figure 1A,B). Furthermore, laboratory experiments and natural processes are rarely a single-step process. Taking oxyanion reduction as an example, a reoxidation process often introduces a new flux of the same oxyanion and results in an increase or a slower decrease in its concentration. For instance, in a freshwater column, the observed nitrate δ18O−δ15N trajectories for samples collected at different depths commonly have a regression slope smaller than 1, a value expected if denitrification is the only reaction. The deviation from 1 has been interpreted as the result of different extents of nitrification and has been used to estimate relative N fixation fluxes.13,16−19 Considering the widespread practice of mixed plotting of spatial and/or temporal data in a δ18O−δ15N space, this deviation from the regression slope of 1 could stem from factors other than the addition of nitrification flux, which needs to be explored. One way to approach this problem is to model trajectories in a δ−δ space for a system using a set of parameters, such as reaction rates, initial NO3− concentrations, isotope compositions, and respective α’s. Such a “bottom-up” approach can help to reveal factors that affect the final trajectory in a δ−δ space. For nitrogen cycling, most of these parameters are now available, thanks to research done by many groups over the years.1,20−30 Simulation work has been performed in nitrate δ18O−δ15N space, notably the Lehmann model,31−33 GrangerWankel’s (GW) model,18 and Casciotti-Buchwald’s (CB) model,34 which used one-box, closed-system time-dependent model to reconstruct NO3− profiles in sediments or water columns. A reaction-transport model has also been applied to studying NO3− reduction in a sediment or water profile. Using an αap fitted by the Rayleigh distillation model, Lehmann et al. built a reaction-transport model to simulate δ18O and δ15N profiles of NO3− in marine sediments.31,35 Wankel et al.36 and Buchwald et al.17 built a simplified N cycling reaction-transport model with given α values to predict reaction complexity.

α−1

fractionation factor α’s ( Δδ′15N = 15α − 1 in the case of NO3−).8,9 It is important to note that the α obtained by Rayleigh distillation model may not be an intrinsic α. We reserve “intrinsic” only for kinetic isotope effect (KIE) or equilibrium α (αeq) of a defined process. Taking denitrification as an example, the intrinsic isotope fractionation for NO3− is the KIE or αeq for the N−O bond breaking and reforming processes at the molecular scale (Figure 1D). The intrinsic isotope

Figure 1. Schematic diagrams from intrinsic isotope fractionation on the enzymatic scale (D) to apparent isotope fractionations on the cellular (C), community (B), and geological (A) scales. Red balls represent oxygen atoms, blue balls represent nitrogen atoms, yellow blocks represent denitrification enzyme, and brown circles represent cell membranes.

fractionation may or may not be directly observed at the cellular scale since the expression of apparent α value (αap) is partially controlled by the substrate concentration, bioactivity, and transportation of NO3− through the cell membrane (Figure 1C). The competition between microbial individuals or groups will further influence the observed αap at the community scale (Figure 1B). Furthermore, when sampling at the geological scale, we are observing spatial isotope data that have experienced a series of reactions and transport (Figure 1A). Therefore, it has been a grand challenge to reduce an observed isotope effect at the geological scale down to the intrinsic effect at the molecular level and vice versa. Thanks to evolution, some biogeochemical processes can be wellcoordinated at the molecular and cellular levels, resulting in a relative constant αap value under different reaction conditions for a community in a defined process, and here we call such relatively conserved αap “diagnostic α”. A Rayleigh distillation model can be used to obtain a diagnostic α from a closed-system, time-dependent system. Nevertheless, if we link two samples and measure their concentration and isotope composition differences, we cannot assume a priori that these two data points are linked by a Rayleigh distillation model, and therefore a diagnostic α obtained from the two samples using eq 1 is not informative on the underlying processes that connect them, if any. It has been reported that, if a system does not fit strictly a Rayleigh distillation model, such as the case of a spatial concentration gradient in sediment pore water or groundwater systems, the degree of the diagnostic fractionation is usually underestimated.8−11 The reason for the underestimation is that a direct application of a Rayleigh distillation model to spatially distributed data ignores mass transfer via diffusion and/or advection that occurs in, for example, laboratory sediment columns, natural water bodies, or seafloor sediment porewater profiles. B

DOI: 10.1021/acsearthspacechem.8b00149 ACS Earth Space Chem. XXXX, XXX, XXX−XXX

Article

ACS Earth and Space Chemistry Table 1. Parameters Used in Modelsa parameters

descriptions

[NO3−]ini [NO2−]ini [NH4+]ini δ′15NNO3−ini

initial initial initial initial

δ′18ONO3−ini

initial nitrate 18O isotope composition

δ′ N

values

refs

10 μmol/L 0 μmol/L 10 μmol/L 0‰

nitrate concentration nitrite concentration ammonium concentration nitrate 15N isotope composition

0‰

initial ammonium N isotope composition

0‰

δ′18OH2O

water 18O isotope composition

0 to −20‰

δ′18OO2

O2 18O isotope composition

23‰

θ kNAR kNXR kNIR kAMO kAMX kexch 15 αNAR 18 αNAR 18 αNAR.BR 15 αNXR 18 αNXR.NO2

triple oxygen isotope component rate constant for denitrification (NAR) (day−1) rate constant for nitrification (NXR) (day−1) rate constant for nitrite reduction (NIR) (day−1) rate constant for aerobic ammonia oxidation (AMO) (day−1) rate constant for anammox (AMX) (day−1) rate constant for nitrite exchange with water (day−1) NAR 15N isotope fractionation factor NAR 18O isotope fractionation factor NAR branching 18O isotope fractionation factor NXR 15N isotope fractionation factor NXR 18O isotope fractionation factor for nitriteoxidation

0.52 10−3 = 0 to 2 × kNAR = 1 to 100 × kNAR = 0 to 100 × kNAR = 1 to 100 × kNAR = 0 to 1000 × kNAR 0.985 = 15αNAR 0.975 1.015 1.004

15

+ NH4 ini

17

αNXR.H2O

34

see S2. equations 1 1 29 20 21

18

NXR 18O isotope fractionation factor for wateroxidation

0.986

21

αNIR 18 αNIR 15 αAMO 18 αAMO.H2O

NIR 15N isotope fractionation factor NIR 18O isotope fractionation factor AMO 15N isotope fractionation factor for ammoniaoxidation AMO 18O isotope fractionation factor for wateroxidation

0.995 = 15αNIR 0.936 0.986

29 29 24 22

αAMO.O2

AMO 18O isotope fractionation factor for O2 oxidation

0.986

22

αAMX

AMX 15N isotope fractionation factor nitrite−water equilibrium 18O isotope fractionation factor

1.035 0.9865

25 23

KIEexch.f DNO3−

nitrite-water exchange 18O forward kinetic isotope effect diffusion coefficient for nitrate (m2 day−1)

1 0.1728

38

DNO2−

diffusion coefficient for nitrite (m2 day−1)

= 1 to 5× DNO3−

DNH4+

diffusion coefficient for ammonium (m2 day−1)

= DNO3−

15

18 15

αNO2−−H2O(eq) 18

All processes are assumed to be mass dependent with 17θ = 0.52 (δ′17Oini = δ′18Oini × 17θ and 17α = 18α17θ). Initial isotope compositions of NO2− are not applicable, since [NO2−]ini are set as 0 μmol/L. However, the initial isotope compositions and concentrations of NO2− are adjustable in our given script (S4. Model details and Script in R language). Diagnostic fractionation factors for 15N and 18O isotopes are adopted from the “standard” GW model, 18kNAR is adopted from CB model.34 We set δ′18ONO3−ini = 0‰. Therefore, δ′18OH2O actually represents the initial δ′18O difference between water and NO3− (Δδ′18ONO3−− H2O). a

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NITROGEN CYCLING MODEL Our N cycling model is adopted and revised from the GW model.18 In brief, NO3− is reduced to NO2− by denitrification (NAR). NO2− is consumed by nitrification (NXR), during which NO2− is oxidized to NO3−. NO2− can be further reduced (NIR) to other nitrogen pools. NH4+ is consumed to produce NO2− by aerobic ammonia oxidation (AMO) while being oxidized by anammox (AMX) to other nitrogen pools (Figure S1). Our model differs from previous models in three aspects: (1) We focus on the fractionation relationship between δ18O and δ15N with consideration of both reaction and diffusional mass transfer in a reaction-transport model, which should in principle be applied to samples collected from different depths of a water/sediment pore water column, or a surface/ground stream with a single point source. (2) The GW model assumed constant reaction rates.18 The CB model considered reaction rate as first-order kinetics with unchanged17,34 or decayed13

Nevertheless, the difference between the Rayleigh distillation model and reaction-transport model are not analyzed systematically. In this study, given a set of diagnostic α’s, k’s, initial concentrations, and isotope compositions, we built a closedsystem, time-dependent Rayleigh distillation model and a onedimensional, diffusion, steady-state, single-source reactiontransport model to predict the changes of concentrations for 14 N, 15N, 16O, 17O, and 18O of NO3−, NO2−, and NH4+ through time (Rayleigh distillation model) or depth (reaction-transport model). We first highlight the principal differences between the trajectories in a δ′−δ′ space generated by a Rayleigh distillation model and a reaction-transport model, mainly through a set of analytical solutions. Next, we explore and compare NO3− trajectories in δ′−δ′ spaces predicted by a Rayleigh distillation model versus by a reaction-transport model using a revised nitrogen cycling model. C


Article

ACS Earth and Space Chemistry rate constants (k). Wankel’s model36 treats denitrification as a first-order reaction but nitrification as a constant in rate for simplification. Lehmann’s model considered the reaction as Michaelis−Menten kinetics.31−33,35 Biochemical reactions, the changes of substrates, are generally described by Michaelis− Menten kinetics: V × [S ] d [S ] = max dt KM + [S ]

(2)

where Vmax denotes the maximum rate that can be reached at saturating substrate concentration. KM is the Michaelis constant, which is the substrate concentration at which the reaction rate is half of Vmax.37 At low concentration, where [S] V d[ S ] ≪ KM, dt ≈ Kmax × [S ], biochemical reactions can be M

simplified to first-order kinetics. Therefore, our model assumed that all the reactions are first-order kinetics, and our k’s do not change over time, which is adopted by the CB model.17,34 (3) Our models include 17O, which can be used to predict the triple oxygen isotope effect. All processes are assumed to be mass-dependent with 17θ = 0.52 (17θ ≡ ln17α/ln18α in the case of triple oxygen, see S2. Notations in the Supporting Information). Here, we will only discuss the influence of diffusional mass transfer on the observed regression slope in a δ′17O−δ′18O space for the NAR process. Since all the 17θs are assigned to be 0.52, the trajectories in a δ′17O−δ′18O space are identical between a Rayleigh distillation model and a reactiontransport model and under different dynamics. Thus, the δ′17O−δ′18O trajectory will not be discussed further in this paper. The models will be useful for future applications. Our model script in R language is posted in S4. Model details and script in R. The δ′ notation is used in our own modeling study here to simplify mathematical treatment (see S2. Notations). We keep using a δ notation that was applied in previous studies. The δ′−δ′ trajectories in this paper refer only to those of the NO3− data points. Because δ′ ≈ δ, our modeled trajectory can be compared with those of GW and CB models where the δ notation is used (Table 1).

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Figure 2. Predicted denitrification trajectories in δ′17O−δ′18O (A,C) and δ′18O−δ′15N (B,D) spaces for nitrate by a reaction-transport model (top) and a Rayleigh distillation model (bottom) (kNXR/kNAR = 0), respectively, with the given diagnostic 18α = 15α = 0.985, 17α = 0.992, and 17θ = 0.52. We set DNO2−/DNO3− = 1 for the reactiontransport model.

where r denotes the rare isotope, c denotes the common isotope, and k denotes the reaction constant. For a Rayleigh distillation model, the change of residual concentration through time in isotope form is i

C(t ) = iC 0 exp(−kt )

where C(t) is the concentration at time t, C0 is the initial concentration, and i denotes different isotopes. For a reaction-transport model, let us explore a point-source of ion or molecule of interest with an input concentration of C0. Setting the depth of the input at 0 and considering diffusion, advection, and reaction, we can describe the system by a mass conservation equation:39

DENITRIFICATION

The trajectory in a δ′−δ′ space describes the relationship between the changes of two isotope compositions (e.g., δ′18O and δ′15N, or δ′17O and δ′18O) with time (Rayleigh distillation model) or space at the isotope steady-state (reaction-transport model). Figure 2 illustrates NO3− trajectories in a δ′−δ′ space predicted by a Rayleigh distillation model and a reactiontransport model for the scenario of NAR only (kNXR/kNAR = 0). As we can see, the reaction-transport model and the Rayleigh distillation model resulted in almost the same slope (S) in a δ′17O−δ′18O space (Figure 2A,C) or numerically identical ones in a δ′18O−δ′15N space (Figure 2B,D). Here, we examine how the resulting trajectories in δ′−δ′ spaces produced by a reaction-transport model and a Rayleigh distillation model differ in a single-source system with a given pair of diagnostic α’s. Assuming a reaction rate (R) is the first-order kinetics of concentration (C, i.e., R = −k × C), the diagnostic α is defined as

∂ ∂ΦC ∂ ij ∂C y jjDΦ zzz − = (ωΦC) + Φ ∑ R i ∂t ∂z k ∂z { ∂z

(5)

where D is the diffusion coefficient, z is depth, Φ is sediment porosity, ω is the sedimentation rate, and ΣRi is the sum of the individual reaction rate for the production and consumption of a given constituent or isotope. In a sediment column in which a sedimentation rate is negligible in the given time scale or in a still water column, the advection term (∂(ωΦC)/∂z) in eq 5 can be omitted. Assuming D and Φ remain constant in the whole system during the observation period, and the system has sufficient time to reach an isotope steady-state (∂C/∂t = 0),40 eq 5 can be simplified to the consumption term and the diffusion term, expressed as D

r

k αin ≡ c k

(4)

∂ 2C − kC = 0 ∂z 2

(6)

At a moment to of observation, when the system reaches steady-state, with the boundary condition C(0, to) = C0,

(3) D


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ACS Earth and Space Chemistry

Figure 3. Predicted trajectory slope differences between a reaction-transport model and a Rayleigh distillation model (ΔS, y-axis) vs slopes predicted by a reaction transport model SRTM, (x-axis). SRTM is in range of 0 to 1 (left), and 1 to 5 (right). Gradient scale indicates the intrinsic α of species A. We set DNO2−/DNO3− = 1 for the reaction-transport model.

triple isotope relationship where θ ≈ 0.5 as is the case for 17θ of oxygen and 33θ of sulfur, the slope obtained by a reactiontransport model can have a maximum deviation of ∼0.004 from that obtained from a Rayleigh distillation model. When SRTM > 1, the maximum ΔS decreases with increasing SRTM value. The ΔS can be −0.282 when αA = 0.95 and SRTM = 5. Therefore, this difference is small for most natural processes. In the case of denitrification, assuming the intrinsic 15αNAR = 18 αNAR. For a Rayleigh distillation process, the trajectory in

C(∞,to) = 0, the concentration at different depths of this column can be solved and expressed in a isotope form as ij C(z , to) = iC 0 expjjjj − j k

i

yz k zz × z zz i z D { i

(7)

The diffusional isotope fractionation of aqueous oxyanions is ignored in our model; thus, we have rD = cD. Solving the diagnostic α by eq 7 and eq 3, we obtain R (z , to)/R (0, to) = f

α −1

δ′18O−δ′15N space has the slope SRDM =

(8)

SRTM =

αB − 1 αA − 1

δ′18O−δ′15N space has slope SRTM =

α NAR − 1

= 1. For a

18

α NAR − 1

15

α NAR − 1

that also

equals 1, because 18α NAR = 15α NAR . Thus, if denitrification is the only process in a reaction-transport system with diffusional mass transfer, the observed slope of trajectory in a δ′18O−δ′15N space should still be 1 for denitrification. Therefore, an observed slope deviation of a nitrate δ′18O−δ′15N trajectory from 1 must be caused by other processes. Now, let us examine one of the likely causes, complex nitrogen cycling.

(9)

αB − 1 αA − 1

α NAR − 1

15

diffusional reaction-transport model, the trajectory in

for a single-source reaction-transport model at steady-state. This equation is similar in form to eq 1 from a Rayleigh distillation model, with an “α” being replaced by a “ α ” in the reaction-transport model. The slopes of trajectories in δ′−δ′ spaces for a Rayleigh distillation model (SRDM) and a single-source reactiontransport model (SRTM) are SRDM =

18

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(10)

N CYCLING For a system when NO3− is involved in a complex nitrogen cycling with NAR, NXR, and NIR, the predicted δ′18O−δ′15N trajectories for nitrate by a reaction-transport model or a Rayleigh distillation model under different kNXR/kNAR ratios and δ′18H2O are shown in Figure 4. Here we plot only the trajectory with Δδ′15N < 20‰, largely the observed range of Δδ′15N in the field12,13 (Our predicted trajectories under different dynamics in a wider range of Δδ′15N < 40‰ can be found in S1. Model Results). The predicted trajectories for complex N cycling processes are not linear. Thus, the slope we refer to here is the linear regression slope of the predicted (δ′18O, δ′15N) points. The regression slopes of the Rayleigh distillation model trajectories are always greater than that of the reaction-transport model trajectories, regardless of the regression slope of the Rayleigh distillation model trajectory being greater or less than 1 (Figure 4 and Figures S3−S7). When Δδ′15N < 20‰, the deviation of a reaction-transport model regression slope from a Rayleigh distillation model regression slope ranges from 0.03 to 0.3. For instance, larger fluxes of NXR (kNXR/kNAR = 2) with initial Δδ′18ONO3−−H2O =

In a δ′17O−δ′18O space, given a 17θ value of 0.52, we will get a SRDM of 0.522 (Figure 1C) and a SRTM of 0.521 (Figure 1A). In a δ′18O−δ′15N space for nitrate, SRDM = SRTM = 1 if we assign 18α = 15α (Figure 1 B,D). Our analysis indicates that for a defined reaction, the two trajectories in δ′−δ′ spaces from a Rayleigh distillation model and from a one-dimensional diffusional, steady-state, single-source reaction-transport model are numerically similar because the diagnostic α’s for both isotope systems (e.g., δ′18O−δ′15N or δ′17O−δ′18O) in most natural isotope systems are close to 1.0. We tested the deviation of SRDM from SRTM (ΔS = SRDM − SRTM) given the intrinsic αA value in the range of 0.95 to 1.00, and the SRTM value from 0.1 to 1 (Figure 3, left) and from 1 to 5 (Figure 3, right), respectively. If the αA value is close to 1.0, we found the deviation is small in the entire range of SRDM (SRDM ≈ SRTM, Figure 3, dark gray). This is because α − 1 ≈ ln α and α0.5 − 1 ≈ 0.5 × ln α, when α does not deviate far from unity or the degree of fractionation is small. Larger isotope fractionation produces larger ΔS. When 0 < SRTM < 1, we found that the maximum deviation ΔS of 0.004 occurs when αA = 0.95 and SRTM = 0.5. For a mass-dependent E



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Article

IMPLICATIONS

Our analysis demonstrates that an incorrect use of a Rayleigh distillation model to spatial or mixed spatial and temporal data would not give us the right diagnostic α values. In fact, we would always underestimate the degree of diagnostic fractionation in such a case. However, the regression slope of a trajectory in a δ′18O−δ′15N space for spatial data, which should be treated by a single-source reaction-transport model, would be almost identical to the trajectory predicted by a Rayleigh distillation model when only a simple process such as denitrification is considered. This “coincidence” certainly vanishes when the system has multiple NO3− sources. In other words, if the plotted data points consist of NO3− of independent origins, the regression slope of the trajectory can be any value. We must understand the underlying physical processes of a set of data before we decide to plot them in a δ−δ space. Otherwise, diagnostic isotope fractionation parameters cannot be deduced. NO3− collected from different depths of water or sediment columns,12,13,19,43,44 different sites at a study area,45−59 or a mixture of temporal and spatial data60−62 have been plotted, often indiscriminately, in a δ−δ space to explore nitrate-related reaction kinetics and dynamics. The observed δ18O−δ15N regression slope varies from 1,44,52,54,58,59 and to none (no significant correlation).49,55−57,60,61 Some of these cases, in which samples were collected from different depths of water or sediment columns,12,13,19,43,44 can be simplified to a diffusional reaction-transport model with a single NO3− source. The rest of them, especially those with mixed temporal and spatial data, cannot be easily described by a simple reaction-transport model or Rayleigh distillation model. One outstanding result of our modeling exercise is that the regression slope of δ′18O−δ′15N trajectories predicted by the reaction-transport model is rarely greater than 1 when the nitrite−water oxygen isotope exchange is faster than NXR in N cycling (kexch/kNAR > 10, Figure S5). This is a result that is different from previous studies18 and warrants further investigation. Here we assumed kexch/kNAR = 10, kNXR/kNAR = 0−2, kNIR/kNAR = 0.1−2, and δ′18OH2O = 0 ∼ −20‰ with kAMO/kNAR = 0 and explored the δ′18O−δ′15N trajectories predicted by a reaction-transport model using a Monte Carlo method (Figure 5). Our given conditions cover most of the natural settings on Earth surface. We found that the regression slope of the δ′18O−δ′15N trajectories can only be slightly greater than 1 ( 1.6 and kNIR/ kNAR < 0.5 (black dots in Figure 5). The current observed range of Δδ′18ONO 3−−H 2O in freshwater systems is 9− 30‰,52,55,61 which should exclude the possibility of a δ′18O−δ′15N trajectory with a regression slope greater than 1. In a seawater system where δ′18OH2O is close to 0‰ and a NO3− source with δ′18ONO3− < 4‰, the regression slope of the observed trajectory can be greater than 1 when the NXR flux is large (a rare case in anoxic environment). This result is comparable with the previous studies.17,18,34 With this model prediction in mind, let us examine the reported regression slope > 1 cases in the literature. The NO3− profiles from Monterey Bay, California, at different seasons display some regression slopes that are greater than 1, for which the original authors interpreted it as possibly the result

Figure 4. Predicted δ′18O−δ′15N trajectories for nitrate with kNXR/ kNAR = 0.1 (A) and kNXR/kNAR = 2 (B), by a reaction-transport model (solid lines) and a Rayleigh distillation model (dash lines). The δ′18OH2O was set at 0‰ (blue) or −20‰ (pink). We set kexch/kNAR = 10, kNIR/kNAR = 1, kAMO/kNAR = 0, [NO2−]ini = 0 μmol/L for both models, and DNO2−/DNO3− = 1 for the reaction-transport model. The black line is the reference line with a slope of 1.

0‰ produces a regression slope of 1.375 in a Rayleigh distillation model (blue dash lines, Figure 4B), whereas the regression slope of a reaction-transport model is approximately equal to 1 (1.012, blue solid lines, Figure 4B). Although definitive data are lacking, the k for nitrite−water oxygen isotope exchange is likely much faster than the k’s for either NAR or NXR in both freshwater and seawater systems.12,18,23,34,41 Assuming kexch/kNAR = 10,12,23,34 NO2− can quickly reach oxygen isotope equilibrium with water. NXR produces NO3− by introducing one oxygen from water to NO2−.21 Thus, eventually, the δ′18ONO3− will reach isotope steady-state, which is buffered by the δ′18OH2O value. The isotope steady-state is displayed by a flattening-out NO3− trajectory with a constant δ′18O but an increasing δ′15N with time. The regression slope is defined by the initial and the steady-state isotope compositions, as well as the rate of the system approaching isotope steady-state. The regression slope of a δ′18O−δ′15N trajectory can be negative if the initial Δδ′18ONO3−−H2O is large, since the isotope steady-state has a much lower δ′18O than the source δ′18ONO3−ini. For instance, in a reaction-transport system where atmospheric NO3− (δ′15N ≈ 0‰ and δ′18O ≈ 70‰42) is the only NO3− source, and δ′18OH2O = 0‰, the regression slope of δ′18O−δ′15N trajectory will be −0.987 given that kNXR/kNAR = 2, kexch/kNAR = 10, kNIR/ kNAR = 1, and kAMO/kNAR = 0. The diffusion coefficient difference between NO2− and NO3−, if any, has little influence on the δ′18O−δ′15N trajectory (Figure S1). Therefore, it can be omitted in the discussion of diffusional mass transfer. The trajectories predicted by a reaction-transport model and a Rayleigh distillation model respond to changing parameters similarly and are comparable to the results in the GW model (see S1. Model Results). The δ′18O−δ′15N trajectory of NO3− is mainly controlled by the initial Δδ′18ONO3−−H2O and the net NO3− consumption flux.18 The greater the initial Δδ′18ONO3−−H2O is, the smaller the regression slope will be. The greater the net NO 3 − consumption flux is, the closer the trajectory is to the 1:1 ratio. Larger net NO3− consumption fluxes could be the results of smaller kNXR/kNAR ratios (Figure S5) or larger kNIR/kNXR ratios (Figure S6). F


Article


kNAR > 1.6 and kNIR/kNAR < 0.5). In fact, we pointed out that many of the reported cases of regression slopes >1 are the results of plotting together multiple NO3− sources of different space and/or time. To deduce diagnostic parameters of mechanistic implication, we must understand a priori the physical processes underlying data points of interest.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsearthspacechem.8b00149. (S1) Model results: δ′18O−δ′15N trajectories for nitrate with different parameters; (S2) notations of isotope parameters; (S3) equations that have been used to calculate rate constants; (S4) model details and script in R language (PDF)

Figure 5. Predicted nitrate isotope compositions in profiles as discrete points simulated by a Monte Carlo method in a δ′18O−δ′15N space in a reaction-transport model. kNXR/kNAR = 0−2, kNIR/kNAR = 0.1−2, δ′18OH2O = 0 ∼ −20‰, kexch/kNAR = 10, kAMO/kNAR = 0, [NO2−]ini = 0 μmol/L, and DNO2−/DNO3− = 1. The black dots are generated under the conditions of δ′18OH2O < 4‰, kNXR/kNAR > 1.6 and kNIR/kNAR < 0.5. The black lines are reference lines with slope of 1 (solid) and 1.2 (dashed), respectively.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

of mixing of upwelling NO3− from oxygen-deficient waters with NO3− assimilated by phytoplankton in the euphotic zone.44 NO3− samples collected from water columns at different sites and seasons in the Yellow Sea have the Δδ18O/Δδ15N = 1 to 3.58,59 NO3− samples from different sites of Changjiang (the Yangtze River) align on a δ18O−δ15N regression slope of 1.5 (stream52) and 1.29 (estuary54). We noticed that in all these cases the sample sets contain samples from different sites. Thus, the >1 regression slope can readily be explained by the mixing of different NO3− sources that differ more in the δ18O than in the δ15N, just like the Monterey case.44 Even when a set of NO3− samples collected from different depths, sites, and/or seasons displays a good linear relationship of regression slope less than 1 in a δ18O−δ15N space,43,45−48,50,51 it does not necessarily mean that they were produced by different extents of NXR, if the physical processes linking the samples are not constrained a priori.

Yuyang He: 0000-0003-3220-1432 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Karline SOETAERT, Yining ZHANG and You ZHOU for valuable discussion on the algorithms of our model. The project benefited from comments from Xiaobin CAO and Shanggui GONG. Financial support is partially provided by the strategic priority research program (B) of CAS (XDB18010104) and China NSFC Grant 41490635 to H.B.

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REFERENCES

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CONCLUSIONS Assuming reactions are of first-order kinetics and giving a set of diagnostic fractionation factors, we compared a Rayleigh distillation model with a reaction-transport model in their predictions of the trajectories in a δ′18O−δ′15N space of nitrate involved in different complexities of N cycling processes. When a Rayleigh distillation model is incorrectly applied to spatial data to which a reaction-transport model should have been applied, the degree of the diagnostic isotope fractionation is always underestimated. However, the derived trajectories in a δ′18O−δ′15N space are almost unaffected in a system with just denitrification processes (NAR). When NO3− is involved in more complex N cycling processes than just a NAR, the regression slope of a temporal data trajectory in a δ′18O−δ′15N space predicted by a Rayleigh distillation model is slightly, but measurably greater than that of the respective spatial data trajectories predicted by a reaction-transport model. Our reaction-transport model shows that a regression slope value >1 in a δ′18O−δ′15N space is unlikely in single-sourced N cycling processes in nature, except for the rare condition when the initial δ′18O difference between water and NO3− is smaller than 4‰ and the reoxidation flux is exceptionally large (kNXR/ G


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