In the context of a ship-based survey campaign from December 2012 to February 2013 in the Peruvian upwelling region, the Meteor cruise 91 (M91, carried out within the scope of BMBF project SOPRAN, Surface Ocean PRocesses in the ANthropocene, http://sopran.pangaea.de/, last access: 28 May 2019) in December 2012 was dedicated to studying biogeochemistry and emissions of various climate-relevant atmospheric trace gases. It yielded several observational parameters that serve this study's purpose to explore the magnitude, causes, and impacts of near-surface N2O concentration gradients. The data set is complemented by near-surface hydrographic time series from a campaign using several ocean gliders during the subsequent Meteor cruises M92 and M93, carried out as part of the German collaborative research center SFB754, https://www.sfb754.de/ (last access: 28 May 2019) . For cruise reports see , , and . On most of the ship stations during the December 2012 cruise, simultaneous profiles of conductivity–temperature–depth–oxygen (CTD-O2, ) and discrete samples of N2O were collected (Fig. ). These data were used to estimate the near-surface vertical N2O gradient, the stratification between 10 and 5 m, the thickness of the top layer (see Sect. ), and the depth of the OMZ upper boundary – here defined by a 20 µmol kg-1 oxygen threshold. The latter served to approximately locate the periphery to anoxic conditions, with a sharp oxygen gradient and with expected strong local N2O production, henceforth referred to as the “oxygen interface”. Four vertically high resolution N2O profiles of the top 10 m were measured from a drifting Zodiac positioned at least 1 km away from the research vessel (Fig. ). The Zodiac sampling aimed at identifying near-surface N2O gradients not affected by ship-induced turbulence. The top 1 m was sampled by a submersible centrifugal pump with radial intake, providing water at a rate of about 0.5 Lmin-1. For the water column from 1 to 10 m a manually triggered 5 L Niskin bottle was used, accompanied by a MicroCat to record pressure, temperature, and salinity.

During December 2012, N2O concentrations at 5.5 m were measured continuously from the ship's moon pool and are used in this study to complement the Zodiac high-resolution N2O profiles. In order to estimate N2O 5.5 m concentrations on the station, only values obtained near the station were considered when the vessel was steaming, to avoid disturbances of the water column by the ship's maneuvering and dynamic positioning. The water temperature at the thermosalinograph intake at the ship's hull (at 3 m depth) together with the vertical displacement of the intake was used to create an along-track time series of estimated near-surface stratification, in order to explore the link between strong near-surface stratification events and N2O gradients. Further, a campaign with seven gliders in January and February 2013 provided undisturbed near-surface hydrographic data with high temporal coverage for four local areas (Fig. ). For these areas which are characterized by different wind conditions and different distances to land, 1 h resolution time series of stratification in the top 12 m could be composed. These time series served to estimate the occurrence and characteristics of multi-day near-surface stratification, and to force a simple one-dimensional gas-transfer model of the top 12 m of the water column, aimed at producing time series of N2O distribution and outgassing for different stratifications and wind conditions.

We will argue here that multi-day persistence of near-surface stratification is able to explain the formation of strong near-surface gas gradients, and furthermore that it is unlikely to achieve strong gas gradients through near-surface stratification on shorter timescales. The basic linkage of near-surface stratification and vertical gradients of any property in the near-surface ocean has been established (particularly plainly stated by ) and is attributed to turbulence suppression in the temporally stratified layer, i.e., to surface trapping. However, studies dealing with consequences of near-surface stratification generally focus on short timescales, usually on the diurnal warm layer cycle . mention the possibility of preexisting stratification at sunrise (i.e., incomplete erosion of stratification during the night and longer timescales of near-surface stratification are implied), and observe subsequent amplification of surface warming, but they do not explore further consequences. Our database and results allow the view to be extended to the multi-day timescale. In this respect our results show, firstly, that multi-day near-surface stratification in the Peruvian upwelling region is not rare, lasts up to several nights in a row, and that remaining stratification at sunrise is strong of order N2=10-4 s-2 and more (Fig. ). Conditions which support the endurance of stratification through the night and thus multi-day timescales are basically the same as those that promote near-surface stratification on shorter timescales, that is, low wind energy input and low heat loss (Fig. ). Secondly, observations show that the absolute near-surface N2O gradient is positively related to the strength of near-surface stratification (Figs. , b), such that the observation that multi-day stratification is abundant and strong results in the expectation of associated abundant and strong N2O gradients. Thirdly, the duration of near-surface stratification can also be directly related to the strength of near-surface N2O gradients. This is indicated by three lines of observations and analyses. (i) During the cruise in December 2012, clusters of multi-day stratification coincided with clusters of the strongest N2O gradients (Fig. ). (ii) When estimating necessary trapping times to produce observed N2O gradients (Fig. c), the strongest quarter of gradients can only be caused by multi-day trapping. (iii) When on the other hand estimating N2O gradients caused by observed trapping conditions (process model with observed TLD time series; Fig. ), strong gradients become more and more likely with more frequent occurrences of multi-day stratification events.

Until here, the line of evidence supports the hypothesis that multi-day near-surface stratification can explain strong near-surface N2O gradients. To go beyond this, Figs. c and  and also the results of suggest that substantial gas gradients are not only made possible by but even need trapping times beyond the typical up to 12 h of the diurnal warm layer cycle. “Substantial” is unfortunately vague here, because the strength of gradients cannot be directly compared between the figures. Figure  indicates that region I which is dominated by the diurnal cycle is good for a typical R of 10 %, while region IV, which is dominated by multi-day near-surface stratification, exhibits R of 50 % to 100 %. The transition between diurnal and multi-day stratification cycles may be seen in regions II and III with R about 30 %. This is in line with , who find a maximum R of 30 % in their investigation of gas gradients caused by the diurnal warm layer cycle. For the gradients of Fig. c, information on concentrations above 5 m depth is lacking, so R cannot be calculated. However, we can still roughly estimate R by using the concentration at 5 m for cbulk, and using the concentration at 10 m for cns, as is done in Fig. . This results in a threshold for R of 30 % to 50 %, above which gradients can only be achieved by multi-day near-surface trapping. Overall, these three independent estimates indicate that near-surface stratification at diurnal timescale can only account for gradients worth R=30 % or less.

Can we understand better why the trapping time seems to play such an important role for gradients? Other factors such as TLD and wind speed are involved in the effectiveness of the surface trapping mechanism, but it seems they only occur in combinations which lead to necessary trapping times on multi-day scales in order to cause substantial N2O gradients. To gain some insight, we examine the formation of downward N2O gradients in a very simplified setting and work out the time and TLD dependence of relative emission bias R (as a measure for gradient strength). An initially homogeneous water column of concentration c0, which becomes stratified at the depth TLD at time t0=0, is assumed. The stratification immediately causes a complete shutdown of N2O supply from below, such that only gas exchange with the atmosphere acts and diminishes the concentration cTL in the TL. In the following we will call this simplified process model the “shutdown model”. The difference to the 1-D gas-transfer model of Sect.  is the lack of vertical movement of the TLD, which would permit N2O supply from below through entrainment. Using a bulk parameterization, the outgassing flux density will be Φ=kw⋅(cTL-ceq), and the change in top-layer concentration with time dcTLdt=-ΦTLD=-kwTLD⋅(cTL-ceq). The solution is cTL=ceq+(c0-ceq)⋅exp⁡-kwTLD⋅t, such that 6R=c0-ceqcTL-ceq-1=exp⁡kwTLD⋅t-1.

The decisive timescale here is TLDkw and the necessary trapping time to reach a certain R is 7Ttrap=TLDkw⋅log⁡(R+1).

For kw we choose the transfer velocity of , which after scaling to the N2O Schmidt number is a function of wind speed u10 only: kw=29⋅u102+13⋅u10⋅ScN2O600-0.5. To estimate trapping times Ttrap as a function of R and TLD, we use TLD from glider observations, and corresponding u10 from nearby ship time series, which were already employed to investigate the conditions for multi-day stratification (Fig. ). Displaying R as a function of Ttrap and TLD (Fig. a) shows that TLD has an effect, but R proves to be more sensitive to changes in Ttrap than in TLD, within the observed range of values. This can be explained by the relation of TLD and kw (or u10): weaker wind which tends to accompany thinner TL leads to a reduction in gas exchange so that gradient formation is only weakly intensified with decreasing TLD. However, for very thin TL with TLD ≤0.5 m, trapping on a diurnal timescale might produce R>30 %. Unfortunately, this is outside of our observational evidence.

So far we evaluated the strength of gas gradients in terms of relative flux overestimation R. If we want to evaluate the absolute impact of gas gradients on gas flux estimates, the transfer velocity and the actual gas concentration have to be accounted for as well. Keeping the shutdown model that was introduced just above, and defining the absolute flux bias ΔΦ as the difference between the flux estimate based on concentration c0 and the flux estimate based on concentration cTL, we get ΔΦ=kw⋅(c0-ceq)-kw⋅(cTL-ceq)8=kw⋅(c0-cTL), and using the definition of R (Eq. ) to eliminate cTL, 9ΔΦ=kw⋅R⋅(cTL-ceq)=kw⋅RR+1⋅(c0-ceq).

As there is no data for c0 to accompany the relation between kw and TLD, ΔΦ itself cannot be calculated, but we will examine the term 10ΔΦc0-ceq=kw⋅RR+1=B, which can be interpreted as a specific absolute flux bias per unit supersaturation. Comparing B for different conditions means assuming that c0 is independent of the conditions, while TLD and cTL react to wind speed and trapping time. Figure b shows that B is practically independent of TLD. This means that the enhancing effect on B of a stronger gas gradient, which comes with a thinner TL, is fully compensated for by the diminishing effect on B of the lower total gas transfer due to the lower wind speed which enabled the thinner TL in the first place.

Thus we may conclude from this subsection that (i) the trapping time is decisive for the formation of gas gradients of high impact on gas exchange estimates (Fig. ), and building on this, (ii) multi-day near-surface stratification can explain the observed gas gradients (Figs.  and ), while (iii) substantial flux bias is not to be expected from near-surface stratification at diurnal or shorter timescales (Figs. , , and  ).

Further using the shutdown model of Sect. , the timescale TLDkw as a function of wind speed u10 (Fig. a) suggests that there exists an optimum wind range for gas gradient formation. Gas gradients that cause a particular relative gas exchange bias R are reached after a trapping time that is proportional to the timescale TLDkw (see Eq. ) and can thus be achieved in the shortest time for moderate wind speeds between about 3 and 6 m s-1. That means that the strongest near-surface gradients are most likely to be observed in this wind speed range. For wind below 3 m s-1, gas exchange weakens while TLD remains about constant (see Fig. ). For wind above 6 m s-1, a more than proportional TLD increase outweighs the effect of increased gas exchange.

In order to examine the absolute gas exchange bias, Fig. b shows the wind speed dependence of specific flux bias B, as introduced in Sect. . B depends on trapping time, but the functional shape of B(u10) proves to be independent of Ttrap (at least up to Ttrap=48 h), such that different Ttrap mainly causes a factor in B or a constant offset in log10B. We arbitrarily chose Ttrap=12 h to produce Fig. b. Again, the moderate wind range of 3 to 6 m s-1 stands out. This time, for wind below 3 m s-1, low R and low air–sea gas exchange both mutually act to diminish flux bias. For wind above 6 m s-1, B is admittedly high, but practically the gas gradient is no longer a measurement issue, as TLD becomes greater than 5 to 10 m (see Fig. ), and routine near-surface measurements now happen within the TL.

The previous insights lead us to propose an explanation for the observed distribution of near-surface N2O gradients in the Peruvian upwelling region, particularly the qualitative zonation seen in Fig. a. There are several parameters in the upwelling region which are related to the distance to the coastline (Fig. ). Wind speed slows down toward the coast and sets favorable conditions for enhanced near-surface stratification and reduced top-layer thickness near the coast. The favorable wind speed range for gas gradient formation of 3 to 6 m s-1 (Sect. ) is covered more and more frequently toward the coast. The oxygen interface is shoaling toward the coast, due to upwelling and more intense biological production, and subsequently more intense oxygen consumption at depth . It reaches extremely shallow depths of about 10 m depth near coast, which, however, is not unusual . The oxygen interface is connected to peripheral hotspot production of N2O and therefore we expect to find a shoaling N2O source when approaching the coast. Even if N2O production by nitrification is probably inhibited by light , we consider the local conditions favorable to sustain a shallow N2O source near the coast: denitrification and nighttime nitrification can intensely produce N2O in a near-surface oxygen interface that exists below the TLD for multi-day periods. During daytime we observed very high chlorophyll content such that light absorption at 5 to 10 m depth may have been strong enough to even allow for shallow daytime nitrification. Figure  shows that the depth of the shallowest local N2O maximum and the depth of the oxygen interface coincide, although with large variability superposed. This leads us to generally link the N2O maximum to the oxygen interface and peripheral hotspot N2O production, a conclusion also made by after investigating the metabolic activity of N2O-producing microorganisms. This linkage is why we fit the shoaling of the oxygen interface and the shoaling of the N2O maximum by the same line. Altogether the previous considerations lead to the following scheme of processes affecting the pattern of N2O concentration: (i) accumulation of N2O is favored below the TLD, because N2O is produced below the TLD and at the same time surface trapping slows down N2O loss toward the TL; (ii) N2O diminishes toward the surface, because in the TL it is reduced by gas exchange; (iii) N2O below the oxygen interface diminishes toward the deep due to an increasing influence of active N2O loss processes toward the anoxic part of the OMZ. The resulting principal shape of the N2O profile is characterized by a local N2O maximum below the TLD at about the oxygen interface depth, and it shoals toward the coast because TLD and oxygen interface both shoal. Further the N2O maximum becomes more intense due to enhanced N2O production and more effective surface trapping toward the coast. A compilation of more and past N2O measurements off Peru confirms this first-order scheme.

Accepting this principal spatial structure, the horizontal zonation of observed N2O gradients (Fig. a) is immediately plausible as a consequence of scanning the tilted N2O field at a constant sampling depth. The two critical points are the land distance where the top-layer depth becomes shallower than the sampling depth, and the land distance where even the oxygen interface becomes shallower than the sampling depth (Fig. ). These critical points limit and define three zones: the offshore zone with no observed gradient when sampling above the top-layer depth because N2O should be homogeneous within the TL, the near-coastal zone with downward gradient when sampling between top-layer depth and oxygen interface or N2O maximum, and the coastal zone with upward gradient when sampling below the oxygen interface or N2O maximum. Arguments in the literature are for a lower oxygen threshold of maximum N2O production than the 20 µmol kg-1 we use, e.g., < 10 µmol kg-1 . In any case, both 10 and 20 µmol kg-1 oxygen isosurfaces are mostly positioned very close to the sharp oxycline – often beyond the practical uncertainty of which depth exactly the sampled water is from – and with standard CTD instrumentation and Winkler calibration, oxygen concentrations far above 5 µmol kg-1 are preferable due to reduced uncertainty. So 20 µmol kg-1 is a practical choice to mark the approximate position of the oxygen interface.

The fraction of profiles in the coastal zone which show upward gradients at 5 to 10 m depth seems particularly interesting, because they are very high in N2O at 5 m and thus could be very important for the total N2O emission of an upwelling region. However, the behavior of N2O above 5 m is unknown. An N2O reduction toward the surface from a shallow subsurface maximum is likely, because the occurrences of upward gradient profiles were under low wind conditions with very stable near-surface stratification, so that long-duration surface trapping can be expected. The encountered wind speed of generally below 3 m s-1 would though suggest that very long trapping times are necessary to produce strong downward gradients. In analogy to the process understanding of the downward gradient profiles farther offshore, the upward gradient profiles might be seen as an expression of local N2O production at the shallow oxygen interface. In this case a very strong and very shallow production is suggested to occur in a high productivity environment less than 5 m from the surface. However, while some upward gradient profiles indeed show a coincidence of highest measured N2O concentration at the depth of the oxygen interface, others are higher still above the oxygen interface, at oxygen levels larger than 100 µmol kg-1. found that maximum N2O concentrations near the coast were indeed uncorrelated to the oxygen level. They discuss this to be an expression of strong time variability of oxygen conditions, i.e., the patchiness in the N2O distribution was suggested to be due to different oxygen histories, including some events of high N2O production at near-anoxic level with resulting high N2O concentrations which are still captured after mixing with water of higher oxygen level. This explanation would still leave surface trapping plus (transient) peripheral hotspot production as dominant processes in the near coast zone. However, it cannot be ruled out that other processes are involved as well.

The impact of near-surface stratification on gas exchange seemed low so far, according to the rare studies. A study on oxygen gradients and fluxes in the open ocean during the GasEx98 project found weak gas gradients (average systematic oxygen flux overestimation of 4 % across the top 4 m, with peak maxima of 30 % in calm conditions). A study on oxygen and CO2 near-surface gradients in different open-ocean regions  found large variability of upward and downward near-surface gas gradients in the top 8 m, which, however, was unsystematic with the mean gradient not significantly different from zero (their Fig. 2). However, the present study with its different conditions (upwelling region instead of open ocean, tendency toward multi-day surface trapping, a gas which is basically biologically inactive in the near-surface layer) suggests a higher impact on gas exchange. We find stronger gas flux overestimations R of median 12 %, mean 37 %, a 95 % interval of [-40 % 180 %] and a maximum of 770 % across the depth range from 10 to 5 m from ship-based profiles, and the N2O gradients are systematically downward with the exception of the coastal zone (Fig. a). As the observed near-surface N2O gradients are both strong and systematic, we expect a non-negligible bias on N2O emission estimates for the entire Peruvian upwelling region. Assuming that the conclusions of the previous subsections are valid and that measurements are representative, and building on model results, we will estimate the total emission bias in the following, if relying on bulk flux parameterizations and sampling at 10 to 5 m depth.

For this purpose, N2O fluxes at the stations were calculated using the Nightingale bulk flux formulation, from 10 m measurements, 5 m measurements, and “true” bulk concentrations, using collocated shipborne wind speeds (see Sect. ). The “true” bulk concentrations are the main issue here, and, apart from the measured values of the 4 high-resolution profiles, have to be estimated. For this purpose we take advantage of common features of profiles in the three zones (Figs. a, ) and assume that near-surface gradients in each zone obey common distributions, which we estimate from the model results (Fig. ) and the high-resolution profiles (Fig. ). For the offshore zone we assume no multi-day stratification, as found in region I and in high-resolution profile B, and choose a normal distribution for R with mean zero and standard deviation 0.1, i.e., N(0, 10 %). For the near-coastal zone we use regions II to IV and high-resolution profiles A, C, and D, which are all from the zone of downward gradients, and choose N(40 %, 20 %) as R for 10 m concentrations and N(30 %, 20 %) as R for 5 m concentrations. The coastal zone is particularly uncertain, as we have no observations for the behavior of the upward-gradient profiles near the surface. Therefore, three alternative assumptions are compared. (i) The upward-gradient profiles could continue with a downward gradient above 5 m, and we choose R=60 %, which is the maximum R directly observed. (ii) The upward-gradient profiles could show constant concentration from 5 m up to the surface. And (iii) the upward-gradient profiles could continue with still upward gradient up to the surface. According to the assumptions above, expected distributions of bulk concentrations are then calculated for the three zones, and the total bias of emission estimates is calculated for the two cases of either using 10 m concentrations or 5 m concentrations instead of bulk concentrations (Table 1). Area weights are 0.5, 0.45, and 0.05 for offshore, near-coastal, and coastal zone, respectively, because of their land distance ranges of 120 to 60, 60 to 6, and 6 to 0 nm. The result is quite robust to the alternatives in the coastal zone, and to the choice of 10 or 5 m concentrations: total emission bias R is 20 % to 25 % overestimation for the region encompassing all three zones. If confining the bias estimation to the near-coastal and coastal zones where gradients are found within the top 10 m, we can give a more general number for expected bias through near-surface gradients, as 20 % to 35 % overestimation. We see that the offshore zone has a low impact on bias due to the absence of an N2O gradient on average and low N2O supersaturations causing low emissions. The coastal zone has a low impact due to its small area and low wind speed, causing low emissions. The near-coastal zone with systematic downward gradients and moderate wind dominates the total bias like it dominates the total emissions.

Note that this total bias is rather a conservative estimate, as we ignored extreme values of model runs and ship-based profiles, which suggest that downward gradients equivalent to R > 100 % may exist. Further we took into account the possibility that profiles from the coastal zone with upward gradients might even continue with increasing concentration up to the surface.

Our database is representative only for December 2012 to February 2013, and also the N2O field and emissions are not yet well constrained for other seasons and years. While the N2O emissions in other seasons could principally be surveyed, predictions of a future trend remain largely uncertain. The latter is mainly due to partly competing effects of expected increased wind speed and expected increased stratification and leads to uncertain predictions of the future development of the nitrogen cycle in coastal upwelling regimes , and the N2O formation, which depends sensitively on complex boundary conditions. However, we may speculate about the seasonal and future bias associated with the Δc sampling issue. We know that the wind speed during the entire year is higher than in December to February , and it is expected to increase in the future . Referring to our discussed results, the bias is most effective in the wind speed range between 3 and 6 m s-1 (Fig. ) and is practically absent beyond 6 m s-1, as the TLD will most probably lie below the sampling depth (Fig. ). When taking into account the observed wind distribution (Fig. ), and assuming a shift of the distribution to higher wind speeds, the wind range between 3 and 6 m s-1 will be less and less abundant, and the probability of finding strong biases in the region will be reduced. So we expect less impact of the Δc sampling issue for the seasons outside December to February, and also less impact in a future scenario characterized by increased winds.