The KOSMOS system comprised eight mesocosms consisting of polyurethane bags 2 m in diameter extending to ∼ 18.7 m depth, with the last 2 m being a funnel-shaped sediment trap. After 2 d of thorough flushing and soaking of the bags, which had been pulled under the surface and were open to water exchange through a 3 mm mesh on both ends, the bags were secured above the water line, and the sediment traps were attached, enclosing about 54 m3 of a natural plankton assemblage. Sampling commenced on 26 February, i.e. day 1. Sampling days typically started in the morning between 06:30–07:00 PET (Peru time) by removing the material that had accumulated in the sediment traps with a pump, followed by CTD (conductivity, temperature, and depth) casts. The CTD (Sea & Sun Technology 90M memory probe) was additionally equipped with an optical oxygen sensor and a calibrated AMT (Analysenmesstechnik GmbH, Germany) amperometric hydrogen sulfide (H2S) sensor for details on the operation, the other sensors, and calibrations/corrections, see. CTD casts were followed by sampling with an integrating water sampler (IWS; Hydro-Bios). Because strong thermal stratification resulted in two distinct water masses at the surface (high oxygen and pH) and at the bottom (low oxygen and pH) of the mesocosms (Fig. a, b and c), two separate depth-integrated water samples were taken. According to changes in stratification, the depths were adjusted over time (days 1–2 – 0–5 and 5–17 m, surface and bottom, respectively; days 3–28 – 0–10 and 10–17 m, surface and bottom, respectively; days 30–50 – 0–12.5 and 12.5–17 m, surface and bottom, respectively).

Furthermore, to stabilise and maintain bottom water characteristics (as in the surrounding Pacific), a NaCl brine solution was homogeneously injected below 10 m on day 13 and below 12.5 m on day 33, increasing salinity, and, hence, stratification, by about 0.7 and 0.5 psu (practical salinity unit), respectively (see , for details).

While all seawater bulk parameters, such as particulate and dissolved organic matter or dissolved inorganic nutrients, were measured on the two depth-integrated samples (see Sect.  below for details), samples for N loss process incubations (see Sect.  below for details) were taken with a Niskin sampler from 15.25 m depth and treated as gas sensitive, i.e. filled into two 100 mL glass-stoppered DURAN bottles with at least one bottle volume of overflow, closed without headspace, and kept cold and in the dark (∼2–4 h) until processing. A direct comparison of oxygen concentrations in these samples by means of Winkler titrations, following the recommendations of , and with CTD–oxygen–optode measurements, revealed an offset by +13 µmol L-1 in the CTD data, although response time hysteresis had been corrected for τ=1 s, as described in . Hence, oxygen concentrations at depth, as shown here from CTD casts, are likely to have been significantly lower. The most likely explanation for this offset is that the response time of the sensor was actually slower, i.e. of the order of 2–2.5 s.

To simulate upwelling with two distinct OMZ signatures, in terms of N deficit, deep water was collected from 90 m at 12.044333∘ S, 77.377583∘ W, and 30 m at 12.028323∘ S, 77.223603∘ W, on days 5 and 10, respectively. However, both waters had quite a strong N deficit (N∗) in comparison to a typical N / P of 16/1 required for phytoplankton growth , and will be referred to as “low N / P” and “very low N / P” treatments in the following (compare Table ). The deep waters were collected into 100 m3 bags, without headspace, at the respective depths and sealed once brought back to the surface. Deep water was added by first removing about 20 m3 from each mesocosm and replacing it with the respective deep water that was injected into the bottom layer, between 14 and 17 m, on day 11, and the surface layer, between 1 and 9 m, on day 12. To minimise changes to deep water gas concentrations during injection, water was pumped from 2 m depth out of the deep water bags. For further details on collection and addition, see .

The two main N loss processes in oxygen-deficient waters off the Peruvian coast, i.e. denitrification and anammox (Fig. ), were assayed with incubations of water from 15.25 m depth, using labelled 15NH4Cl (≥ 98 atom %) or Na15NO2 (98 atom %), i.e. by an addition of 3 µmol L-1 each. During incubations with the former, anammox will be traced by the production of 29N2 (15N14N) and 30N2 (15N15N) if coupled to nitrification (although unlikely as it is an oxic process; compare Fig. ). During incubations with 15NO2-, anammox would again produce 29N2, while denitrification would produce both 29N2 and 30N2 (Fig. ). Here, a further complication for rate calculations would be coupled nitrate ammonification, i.e. dissimilatory nitrate or nitrite reduction to ammonium (DNRA), also leading to 30N2 production via anammox (compare Fig.  and ). Incubations were in 12 mL glass double wadded exetainers (Labco Ltd.) in duplicates for each of the four time points, i.e. 0, ∼ 2, ∼ 7 and ∼ 20 h after label addition (in order to avoid potential bottle effects), in the dark, and inverted at a fairly constant 17±0.2 ∘C, close to respective in situ conditions (similar to the protocols described in , , and ). All sample handling, such as filling of the exetainers with 8 mL of labelled sample water using an Eppendorf Multipette E3, was carried out in a glove box that had been evacuated three times with a vacuum pump, followed by flushing with N2 4.5 gas (this was also done to the open exetainers). To reduce large background 28N2 levels and facilitate the detection of the small isotopic signal of labelled N2 being produced during incubations, the exetainers were capped and sparged with Helium 5.0 at 3 psi for 6 min on a manifold that could hold all 16 exetainers of a single mesocosm. Based on previous calculations and measurements, such a set-up will replace about 20 times the volume of each exetainer (unpublished data). This is lower than the 24 times reported to ensure that the reduction in O2 concentration is by less than 20 % compared to in situ conditions . A similar reduction would also be observed for most other gases , except those buffered by conjugate acid–base pairs, such as H2S or CO2, for which the reduction would have been even less. Incubations were stopped at each time point by the injection of 50 µL of a ZnCl2 solution (50 % w/v), followed by thorough mixing.

Exetainer vials were stored upside down at room temperature in the dark. Prior to analysis, the headspace and water were equilibrated at room temperature by placing the exetainers on a platform mixer at 100 rpm (revolutions per minute) overnight. For measurements, 100 µL of headspace from each exetainer was injected, using an autosampler , into a PLOT (porous layer open tubular) gas chromatography (GC) column, at 2 mL min-1, housed in a TRACE GC oven and interfaced with a Thermo Scientific DELTA V Plus mass spectrometer via a GC Combustion III unit, followed by a liquid nitrogen trap. The latter minimises interference by CO (a constituent in air) and NO (a secondary product during ionisation of water and/or oxygen, followed by the production of reactive oxygen species and recombination with nitrogen) due to imperfect GC column peak separation. The mass spectrometer was calibrated for N2 concentrations by injections of known amounts of air.

Rate calculations were straightforward, as in most 15NH4+ incubations no enrichment over time in 29N2 was detected, indicating the absence of anammox. Hence, denitrification in the 15NO2- incubations (and because 30N2 was quite noisy) was calculated from the increase in 29N2 and the known ratio of labelled to unlabelled NO2- (in the rare cases where anammox was detected in the 15NH4+ incubations, denitrification was corrected for by subtraction). Rates were calculated from the linear regression slopes (see Fig. S1 in the Supplement) of the increase in the overall amount of N removed (as measured by areas 28A and 29A and associated δ15N), which was determined by the following conversions (modified from ): 1Nremovalt1-3µmolN2L-1=15r28A+29AcfMSVhVafN2aircf15Nt1-3-15r28A+29AcfMSVhVafN2aircf15Nt01000Vi, with 215r=15R1+15R, and 315R=δ15N100015Rair+1, where 15R and 15Rair denote the ratios of 15N/14N in a sample gas or air, respectively (the latter was determined from measured 28N2 and 29N2 by , i.e. 0.00367647, and recommended by ). δ15N is the resulting isotopic composition (‰), Vh, Vi, and Va are the volumes of headspace, sample incubated, and analysed (millilitres), respectively. cfMS is the determined calibration factor for each measurement run to convert mass spectrometer peak area (28A+29A) into abundance (µmol), fN2air is the fraction of N2 found in equilibrium in the 4 mL of headspace (Vh) in relation to the total amount, including the 8 mL of sample water (Vi), in an Exetainer, and t1–3 or t0 refer to the respective incubation sampling times. The conversion factor fN2air was calculated from N2 solubility for a lab temperature of 21 ∘C and a salinity of 35. To extrapolate from measured removal of 15N to total N a conversion factor, cf15N was calculated, taking into account the availability of labelled and overall substrate(s) together with the likelihood of 29N2 production, i.e. 2FN(1-FN), for denitrification incubations (binomial), and FN, for anammox, with FN denoting the ratio of labelled to total [NO2-] or [NH4+], respectively.

It is noted that there have been studies which found discrepancies between denitrification calculated using 29N2 as above, and 30N2, due to non-binomial distributions . This has been attributed to so-called intracellular NO3- / NO2- shunting, which leads to an error in the calculations of labelled to unlabelled substrate, based on known additions and measured seawater concentrations. With respect to noisy 30N2 data, we cannot check if that was an issue here; yet, it would lead to an underestimation of denitrification rates in both cases. Given the good agreement between our rate measurements and a full nitrogen budget (see Sect.  for details), it, however, appears that potential NO3- / NO2- shunting did not affect our rate measurements significantly.

In more than half of the denitrification incubations, measured N loss over a period of about 20 h was higher than the combined concentrations of in situ NO3- and NO2-. This indicates that the 3 µmol L-1 addition of Na15NO2 alleviated substrate limitation, and rates in the incubations were higher than theoretically sustainable at in situ conditions. Furthermore, acknowledging that rate measurements at different substrate concentrations in comparison to in situ conditions are always potential rates, we estimated in situ rates from a Michaelis–Menten kinetic by first calculating the maximum rate, Vmax, as follows: 4Vmax=Ratemeas.[S]in situ+15NO2-+K1/2[S]in situ+15NO2-, which was followed by the realised rates at in situ substrate concentrations: 5Ratein situ=[S]in situVmax[S]in situ+K1/2, with [S]in situ referring to in situ substrate concentrations of NO2- and NO3-, [15NO2-] referring to the 3 µmol L-1 label addition, and K1/2 referring to the reaction half-saturation constant. As we have not performed any substrate vs. rate essays ourselves, and since there is only little information on the kinetics of water column denitrification, we adopted a conservative approach and chose the highest published K1/2 of 5 µmol L-1 , over the 2.9 and 2.5 µmol L-1 of and , respectively.

Total N loss by denitrification and anammox was calculated only for the first 38 d of the experiment. The reason was to keep the estimates by rate measurements comparable to estimates from a full N budget of the mesocosms, as, after day 40, massive perturbations in the latter became obvious. This was caused by birds aggregating on the roofs of the mesocosms and depositing nitrogen-rich faeces (orni-eutrophication). The onset of this perturbation was estimated by the sudden increase in total particulate phosphorus deposition rates in the sediment traps, most likely from excrement, as phosphate concentrations during this time were relatively constant (Fig. S2; for details see ). Total N loss was then estimated by summing up hourly in situ rate estimates (Eq. 5) for each mesocosm (in case anammox was also detected, the measured rate was added to that of denitrification), factoring in the varying measurement intervals and, thus, filling in days without measurements. This hourly N2 loss was then multiplied by 24 h d1- × 2 (conversion between N2 to N) and divided by three (average contribution of bottom layer water to overall mesocosm volume), converting it to total N loss over the first 38 d of the experiment.

Dissolved inorganic nutrient concentrations in seawater, i.e. NO3-, NO2-, and NH4+ (together referred to as DIN) and PO43- and Si(OH)4 were measured colourimetrically on a segmented flow analyser (QuAAtro, SEAL Analytical) on site (for details, see ).

Dissolved organic nitrogen (DON) was calculated from a mass balance by subtracting measured DIN from total dissolved nitrogen (TDN) concentrations. The latter was also determined by segmented flow analysis after an oxidising step with Oxisolv (Merck) for 30 min in an autoclave.

Particulate organic nitrogen and carbon (PON and POC, respectively) concentrations in the water column were determined by filtering known amounts of seawater over precombusted glass fibre filters (GF/Fs) that were stored frozen until analysis on an elemental analyser (EA; EuroVector EA 3000; for details, see ).

The removal of nitrogen from the water column via sedimentation (Nsed) was determined on material collected every other day from the sediment traps which was quantitatively precipitated, freeze-dried, weighed, and then an aliquot was measured on an elemental analyser (EuroVector EA 3000; for details, see and again).

In order to assess what drives denitrification rates, stepwise multiple linear regressions (MLRs) with interaction terms were carried out. Prior to the regressions, outliers in estimated in situ denitrification rates (see Sect.  and Table  for details) were identified in a box-and-whisker plot and removed, i.e. five values with rates higher than 10 nmol L-1 h-1. In order to avoid overfitting and find a balance between model complexity and explanatory power, we followed a backward elimination process, starting with the full seven potential measured predictors, i.e. PON, PONsed, DON, NO3-, NO2-, O2, and H2S, all measured in the bottom layer of the mesocosms (with the exception of sedimenting PONsed). Note that we have opted to not include POC, which is highly co-correlated with PON, and DOC, which was not measured in the bottom layer (but probably would have a similar issue). In a next step, MLRs with all possible combinations of six potential predictors out of the overall seven and their resulting R2 were calculated, which was followed by further MLRs, subsequently reducing the number of predictors each time by one (a total of 119 MLRs were fitted). Calculations were performed using the functions “boxplot”, “stepwisefit”, and “plotEffects” in MATLAB.

Thermal stratification of the Pacific Ocean and the mesocosm waters during the initial phase of the experiment meant strict separation of well-oxygenated surface (∼ 0–10 m) from oxygen-depleted bottom waters (Fig. c). And while in the surrounding Pacific bottom waters oxygen remained depleted throughout, corresponding oxygen levels in the mesocosms started to increase (Figs.  and e). This was caused by the cooling of the surface waters due to upwelling in the surrounding Pacific and the resultant mixing of surface and bottom waters in the mesocosms. Such artificial behaviour was mitigated by increasing bottom layer salinity and, therefore, stratification on days 13 and 33, which brought oxygen concentrations at depth down to typical Pacific levels again (Fig. e).

All mesocosms started with significant amounts of dissolved inorganic nitrogen present as NO3- and NO2-, which, however, were quickly depleted within the first 2 weeks (Fig. c, d). The deep water addition significantly increased NO2- concentrations in the low N / P treatments, although it made only a minor contribution to the overall nitrogen budget (see the following sections for details).

Initial particulate and dissolved organic nitrogen concentrations (PON and DON) at depth were similar in all mesocosms (between 6 and 10 µmol L-1), and while there was no clear temporal trend for PON, DON saw a steady decline by about 30 % until day 40 (Fig. a, b).

H2S concentrations at depth were in the micromolar range in all mesocosms and the surrounding Pacific and mostly oscillated between 3 and 10 µmol L-1 (Fig. f), equivalent to 0.1–0.3 ppm. In contrast, concentrations in surface waters were mostly in the high to low nanomolar range (data not shown).

Measured denitrification rates in the 24 h incubations were similar in all mesocosms, ranging between less than 1 to up to ∼ 80 nmol L-1 h-1 (Table S1). More importantly, however, towards the end, measured rates exceeded those theoretically sustainable by substrate availability, i.e. combined in situ NO3- and NO2- concentrations. In comparison, measured denitrification rates in samples from the surrounding Pacific were comparable, although more variable, between consecutive measurement days.

Estimates for in situ denitrification (Eq. 5) were similar to measured rates at the beginning of the experiment when substrate availability was higher than or close to the half-saturation constant for denitrification. Towards the end, at high to low nanomolar substrate concentrations, in situ estimates were significantly lower (compare Tables  and S1).

Anammox was only detected on day 12 in mesocosms 7 and 8 at rates significantly smaller than those typical for denitrification (Table ). In contrast, anammox was occasionally detected in the surrounding Pacific Ocean, i.e. on days 8, 12, and 46.

When comparing potential nitrogen loss, calculated as the sum of in situ estimates of denitrification and anammox over the first 38 d prior to the onset of orni-eutrophication (see Sect.  and Table  for details), with estimates of total nitrogen losses in each mesocosm from a nitrogen budget approach (compare Table  and Fig.  and see the next section for details), they were similar, with a mean of 2.69±1.18 and 3.64±2.12 µmol L-1, respectively. It is acknowledged, however, that there was no statistically significant correlation between the two approaches.

Summing up all organic and inorganic nitrogen species (excluding dissolved gases) in the water column, i.e. PON, DON, NO3-, NO2-, NH4+, Nsed (nitrogen exported through the sediment traps), and NDW (overall deep water addition changes to the various nitrogen pools), revealed a first phase in all mesocosms for which the budget did not seem to be closed, as evidenced by a constant decline in total N during the first 2 weeks (Fig. ). This was followed by a steady increase in total N until day 40, which was still below starting levels in all mesocosms. This net loss reflects, as we will argue below, the combined nitrogen loss processes, such as denitrification and anammox, exceeding nitrogen fixation, which was less than 0.1 µmol L-1 over the entire water column in this period (Leila Kittu, personal communication, 2020). Finally, the last 10 d were characterised by a rapid increase in total N, mostly driven by rising surface PON concentrations, following continuous biomass production fuelled by external orni-eutrophication, i.e. the introduction of nitrogen-rich bird faeces to the mesocosms (see , for details).

In terms of R2, there was a turning point in the number of potential main variables to explain in situ denitrification rates in stepwise multiple linear regressions (MLRs) with interactions. Above four to five independent variables, R2 only increased slightly, while below it decreased relatively quickly (Fig. a). Both models with the highest R2, for four and five main variables, identified NO2-, NO3-, and PON as those with the highest positive main effect sizes, with the remaining variables having relatively low effect sizes (Fig. b, d; Table ). Finally, O2 had a small negative main effect size in both models.

The resulting linear regression of in situ (compare Table ) versus predicted denitrification rates slightly deviated from an ideal 1:1 relationship and had a small, yet positive, y axis intercept, meaning that lower denitrification rates would be over, while higher ones underestimated (Fig. c).

Denitrification rates measured in the incubations of water from the mesocosms and the surrounding Pacific of up to ∼ 80 nmol N2 L-1 h-1 (although mostly well below, at a median of 12.4) were within the range of reported rates in Peruvian ODZ and OMZ waters . This was despite significantly higher oxygen concentrations here than typical for suboxic ODZs, i.e. less than ∼ 6 µmol L-1 , although denitrification can be relatively insensitive to oxygen concentrations of up to at least 30–40 µmol L-1 , which is higher than levels in our study for most of the time (see Fig.  but also Sect. ).

Most interestingly, measured denitrification rates in incubations of mesocosm waters during the second half of the experiment exceeded those theoretically sustainable at in situ substrate availability (compare Sect.  and Table ). Nitrification, supplying additional nitrite for denitrification, can operate at low micromolar (and even nanomolar) levels such as those found in our study . However, a significant contribution to measured denitrification rates is unlikely as there and elsewhere nitrification rates were usually at least an order of magnitude lower than our measured denitrification rates. Hence, the reason for higher measured rates is most likely found in the fact that both NO3- and NO2- concentrations had dropped below 0.1 or even 0.01 µmol L-1 during this stage, indicating that the denitrifying community was actually substrate limited. Such an observation was also made by in a temperate fjord system. In comparison, denitrification rates in the surrounding Pacific waters had a higher day-to-day variability, and substrate limitation only occurred once. This is to be expected in a much more variable system characterised by frequent upwelling events of oxygen-depleted waters (Fig. ) with relatively higher NO3- and NO2- concentrations (Fig. c, d).

Calculated Michaelis–Menten kinetic scaled estimates for in situ denitrification in the mesocosms and the surrounding Pacific were lower than measured rates during the incubations. This was particularly the case during the second half of the experiment, which reinforces the notion of substrate limitation.

The primary drivers of in situ denitrification rates appeared to be the availability of NO2- and NO3-, followed by particulate organic matter (nitrogen), as indicated by multiple linear regression and effect size analysis (Fig. ). This suggests that heterotrophic rather than chemolithotrophic denitrification was dominant (compare Sect. ), as all three are substrates for the former process and eventually limit rates. The reason for NO2- rather than NO3- concentrations explaining the rates of denitrification in one of the MLRs could be found in the following. As denitrification from NO3- to N2 involves multiple and independent steps and organisms, the correlation between the N2 production rate and a substrate concentration should become better the closer one comes to the end of this chain (Fig. ). For example, there should be a perfect correlation between N2O concentrations and N2 production rate, and NO3- concentrations and their turnover to NO2- are meaningless if the intermediate steps to nitric and nitrous oxide are blocked or constitute a bottleneck. This would also contribute to the finding that denitrification rate measurements based on 15NO3- can be lower than those based on 15NO2- .

Overall nitrogen loss, calculated from in situ denitrification rates over the first 38 d of the experiment prior to the onset of orni-eutrophication, was comparable to an alternative estimate that was based on a full nitrogen budget in each mesocosm (Fig. ; Table ). The means of both methods, i.e. 2.69 ± 1.18 and 3.64 ± 2.12, were insignificantly different, although there was no statistically significant correlation when all mesocosms were compared. However, given that the nitrogen budget calculations involved a mass balance of seven entities with individual measurement uncertainties, this probably does not come as a surprise. There were also no statistically significant differences between the two deep water addition treatments, which was most likely due to relatively small differences in dissolved inorganic nitrogen in both waters in relation to the overall nitrogen pool in the mesocosms and a similar N deficit in both deep water batches (Table ). However, N loss estimated from in situ denitrification rates in the low N / P mesocosms was significantly lower than the budget estimate. It is noted, however, that in situ denitrification rates are a conservative estimate that potentially underestimate the true loss. For instance, adopting a lower half-saturation rate constant of 2 µmol L-1 (Eqs.  and ) would remove any statistically significant difference between the two approaches. Furthermore, NO3- and NO2- standing stocks most likely underestimate availability and, hence, in situ denitrification rates calculated here because of hidden turnover.

Finally, modelling exercises suggest that nitrogen loss in the water column is linked with mature El Niño/La Niña periods, with up to 70 % reduced rates during the former, most likely linked to increased water column oxygen concentrations at reduced upwelling and/or enhanced stratification , and increasing mesoscale turbulence and associated offshore nutrient export by eddies . This suggests that the rates observed here could actually be significantly higher in the more frequent La Niña periods.

Anammox and denitrification were first reported in the eastern tropical South Pacific (ETSP) in 2006 , and the ETSP remains the most frequently sampled and most thoroughly characterised open ocean OMZ region. Anammox was the dominant N loss process in several studies, where denitrification was either not or only sporadically detected. Subsequent studies in the ETSP detected both processes, and anammox was a substantial and mostly dominant part of the total N loss. There was an average of 78 % anammox along a Chilean coastal transect , 82 %–90 % at two high-resolution stations , and 49 ± 20 % over four high-resolution stations .

Anammox requires a source of NH4+ and NO2-, which must either be produced in situ by the remineralisation of organic matter in the absence of oxygen (as, for instance, by denitrification) or must be transported into the system from elsewhere, e.g. from adjacent sediments . When both processes are supported by organic matter remineralisation, then there is theoretical and experimental evidence that the ratio of denitrification to anammox should be connected to the elemental composition of organic matter being decomposed, at least on larger spatial and temporal scales. The reasoning behind this connection is that complete anaerobic organic matter decomposition by denitrification produces NH4+ and N2 in quantities mostly dependent on the carbon to nitrogen ratio (C / N) of the organic matter being decomposed. Hence, this ratio dictates the denitrification (only utilising NO3- and/or NO2-) to anammox (utilising both NO2- and NH4+) ratio in a steady state . However, DNRA could also supply NH4+ for anammox. Although there have been reports of DNRA in the ETSP , it is usually negligible in the water column and rather restricted to shallow coastal systems dominated by sediments . In the absence of DNRA, complete anaerobic decomposition of average phytoplankton-derived organic matter, i.e. C106H175O42N16P , would require a ∼ 28 % contribution of anammox to overall N loss via these two processes .

The reason for an anammox dominance in several studies mentioned above, despite above outlined stoichiometric constraints, could be partial denitrification of NO3- to NO2- without the following steps leading to N2 production, supplying both NO2- and NH4+ for anammox . Furthermore, the ratio of NO2- to NH4+ produced by organic matter decomposition of a certain C / N ratio could also be influenced by anaerobic chemolithotrophic nitrite oxidation (compare Fig. ), looping NO2- back to NO3- for further partial denitrification and associated NH4+ production .

In summary, anammox, in the absence of denitrification, is difficult to explain (although partial denitrification is not easily detected), while denitrification in the absences of anammox is rarely observed in the ETSP but presents no stoichiometric conflicts.