Nitrate photolysis is at the core of the model. At each time step, the photolyzed nitrate mass in a layer equals e-JΔt×m, where m is the initial nitrate mass in the layer and J is the photolysis rate constant of NO3- (Eq. 1). The UV actinic fluxes (I) required for the calculation of J have been computed in the 280–350 nm range using offline runs of the TUV-snow radiative transfer model (Lee-Taylor and Madronich, 2002). TUV-snow has been run for the DC location and snowpack for various dates (i.e., solar zenith angle, θ), assuming a clear aerosol-free sky and using the extraterrestrial irradiance from Chance and Kurucz (2010) and a constant Earth–Sun distance as that of 27 December 2010. Ozone profiles from 25 to 500 DU with a resolution of 25 DU have been used to run the radiative transfer model. Next, we denote k the “photic zone compression factor”, which represents variations in depth of the photic zone under the effect of changes in physical properties of the snowpack due to snow metamorphism or in chemical properties. In Eq. (1), the term “z” is therefore replaced by “z/k”. A typical Dome C snowpack is represented by a k value of 1. Lower k values mean that the UV radiation is extinguished more rapidly with depth. Last, we denote q the “actinic flux enhancement factor”, which accounts for variations in the actinic flux received at the snow surface and hence at depth. This parameter represents changes in the actinic flux emitted from the Sun or changes in the Earth–Sun distance due to variations in the Earth's orbit. In Eq. (1), the term “I” is therefore replaced by “q × I”. In the modern DC case, q is set to 1.

Another key control on J is the quantum yield (Φ), a parameter which is strongly governed by nitrate location in the snow ice matrix and which corresponds to nitrate availability to photolysis. Nitrate is assumed to deposit to the snow under the form of HNO3, but its adsorption and/or dissociation to NO3-+ H+ are not explicitly represented. Indeed, modeling nitrate location in the snow is well beyond the scope of the present study, and a recent molecular dynamic study demonstrated the fast ionization of HNO3 (picosecond timescale) at the ice interface (Riikonen et al., 2014). For the sake of simplicity, we assume that nitrate location in the snow ice matrix is constant. Therefore, Φ is set to a constant value.

Nitrate photolysis is assumed to only produce NO2. We acknowledge that other volatile nitrogen species such as NO or HONO may be produced. However, the photolysis of HONO in the atmosphere would rapidly produce NO, which would contribute to the NO / NO2 cycle, similar to the NO2 production.

In the model, 15εpho is explicitly calculated at each time step and in each snow layer using Eq. (3). Because the layering of the physical properties of snow is fixed, 15εpho is constant with time. In the UV spectral range (280–350 nm), we have earlier assumed that e-folding depth is constant with wavelength; therefore, even though ρ modulates the e-folding depth, 15εpho is independent of ρ as well as depth, in agreement with the laboratory study of Berhanu et al. (2014a) and the field study of Berhanu et al. (2014b). As a consequence, the modeled 15εpho is entirely determined by the spectral distribution of the UV radiation received at the surface of the snowpack. The Rayleigh fractionation model applied to nitrate photolysis allows for the δ15N in the photolyzed nitrate to be calculated, applying Eq. (2) with the use of 15εpho, and δ15N in the remaining nitrate by simple mass balance. Nitrate photolysis is assumed to be a mass-dependent process, so that the Δ17O in the initial, photolyzed and remaining nitrate is kept the same.

A constant fraction of the photolyzed nitrate (denoted fcage) is assumed to undergo cage recombination, so that the photo-fragment NO2 reacts back with OH to re-form HNO3. In the cage effect process, OH is assumed to undergo an isotopic exchange with the water molecules of the ice lattice, so that the recombined HNO3 contains an oxygen atom originating from H2O and featuring Δ17O(H2O) = 0  ‰ (McCabe et al., 2005).

The total photolytic flux (FP) represents the potential emission of NO2 from the snow to the atmosphere in accordance with the terminology used in France et al. (2011) and is the sum of the photolytic fluxes originating from each snow layer. A simple isotopic mass balance is applied to calculate the δ15N and Δ17O of the photolytic loss flux. The extraction of NO2 from the snowpack is assumed to preserve its chemical and isotopic integrity – i.e., it does not undergo any chemical reaction or any isotopic fractionation in the snowpack.

Atmospheric chemistry is not explicitly modeled but only conceptually represented. Δ17O(NO2) is calculated following the approach of Morin et al. (2011), i.e., assuming photochemical steady state (PSS) of NOx (when the photolytic lifetime of NOx is shorter than 10 min), an assumption which is valid for most of the sunlit season (τ(NO2) < 10 min from 27 September to 7 March; Frey et al., 2013, 2015). We therefore denote Δ17O(NO2, PSS), the Δ17O value harbored by NO2 after its local cycling, which is represented by (Morin et al., 2008, 2011) Δ17ONO2,PSS=α×Δ17OO3+NONO2, with α a variable which accounts for the perturbation of the Leighton cycle by various radicals such as peroxy radicals (RO2) and halogen oxides. For simplicity, we only consider BrO, HO2 and CH3O2 to be the species perturbing the Leighton cycle. The α variable is calculated at each time step as in Eq. (8) assuming Δ17O(HO2)=Δ17O(CH3O2)= 0 ‰ (Morin et al., 2011). Recent observations at DC seem to support the assumption Δ17O(CH3O2)= 0 ‰ because CH3O2 may entirely originate from the reaction R + O2 or photolysis of species (CH3CHO) featuring Δ17O = 0 ‰ (Kukui et al., 2014). The assumption Δ17O(HO2)= 0 ‰ is also supported by the same observations, although 5 % of HO2 originates from the reaction O3+ OH, which leads to Δ17O(HO2) > 0 ‰. For simplicity, we stick to the assumption Δ17O(HO2)= 0 ‰. α=kO3+NO⚫O3+kBrO+NO⚫BrOkO3+NO⚫O3+kHO2+NO⚫HO2+kCH3O2+NO⚫CH3O2+kBrO+NO⚫BrO, with temperature- and pressure-dependent kinetic rate constants from Atkinson et al. (2004, 2006, 2007) and the mixing ratios of O3, BrO, HO2 and CH3O2 at the surface. Savarino et al. (2008) found that O3 preferentially transfers one of its terminal O atom when oxidizing NO with a probability of 92 %, which translates into the following equation: Δ17OO3+NONO2×103=1.18×Δ17OO3bulk×103+6.6, with Δ17O(O3)bulk the isotopic anomaly of local bulk ozone. The O atom in BrO originates from the terminal oxygen atom of ozone through its reaction with bromine (Morin et al., 2007, and references therein). For simplicity, we assume that the O atom transferred during the NO oxidation by O3 and BrO is identical.

NO2 is directly converted to HNO3 with the preservation of the N atom. However, a local additional oxygen atom is incorporated. This is a reasonable assumption given the short chemical lifetime of NOx with respect to NO2+ OH (on the order of hours) in comparison with the approximately 1-week time step used in the model. The Δ17O of HNO3 is given by Eq. (10): Δ17OHNO3=23Δ17ONO2+13Δ17Oadd.O.

Similar to the local cycling of NO2, the local oxidation of this species is only conceptually represented. For simplicity, we assume that the formation of HNO3 only occurs through the pure daytime channel, i.e., the reaction of NO2 and OH :Δ17O(add. O) =Δ17O(OH).

In the framework of the OPALE campaign, Δ17O(OH) has been discussed in a submitted paper (Savarino et al., 2015). The results of this study show that Δ17O(OH) varies in a narrow range, between 1 and 3 ‰, around summer solstice 2011–2012. As a result, we set Δ17O(OH) = 3 ‰ throughout the entire sunlit season.

The snow accumulation thickness depends on the snow accumulation rate (A) as well as on snow density (ρ). Older layers are buried, preserving their nitrate mass and isotopic composition. Immediately after snow accumulation, the modeled snowpack is resampled at a 1 mm resolution (Δz=1 mm).

The export flux (FE) is modeled as a constant fraction of all incoming nitrate fluxes to the atmosphere FE =fexp × (FP + FS + FT), assuming that NOx conversion to HNO3 is instantaneous and that nitrate is homogeneous in the atmospheric box, at the chosen time step.

The deposited flux (FD) and its isotopic composition (Δ17O(FD) and δ15N(FD)) are obtained by solving Eqs. (4) to (6) (Fig. 2). For the sake of simplicity, the downward deposition flux is modeled assuming a pure physical deposition of HNO3 on the top layer of the snowpack. The deposition process is assumed to preserve Δ17O. This process is associated with a 15N / 14N fractionation constant (15εdep).

Nitrate diffusion in the snowpack leads to changes in nitrate mass fraction and isotope profiles in the snowpack, and it is represented by the use of a diffusivity coefficient denoted D and by a zero-flux boundary condition at the top and bottom of the snowpack (z= 1 m): ∂ω(z,t)∂t=D∂2ω(z,t)∂z2∂ω(top.,t)∂z=0∂ω(bot.,t)∂z=0 where ω(z, t) is the nitrate mass fraction in each layer and z and t are space and time, respectively. Given the assumption of a constant snow density and a uniform mesh grid, Eq. (11) also applies to the snow mass in the layer (m). Equation (11) is solved at a time step of 3.4 h (i.e., 50 times shorter than the main time step of the model), which must respect the following: (Δz)23.4h≪D. Space and time derivatives are approximated by the finite-difference method.

Most of the observed data originate from Erbland et al. (2013). Atmospheric nitrate concentration and isotopic measurements were measured 2 m above ground at Dome C during the years 2007–2008 (Frey et al., 2009) and 2009–2010 (Erbland et al., 2013). In this second study, nitrate mass fraction and isotopic composition have also been measured in the skin layer (the (4±2) mm of top snow) and for the 2009–2010 period. Nitrate mass fractions and isotopic profiles are available from three 50 cm snow pits sampled at Dome C during the austral summers 2007–2008 and 2009–2010 (Frey et al., 2009; Erbland et al., 2013). From these snow-pits data and from the DC mean snow density profile given by Libois et al. (2014), we calculate m50 cm(NO3-), δ15N50 cm(NO3-) and Δ17O50 cm(NO3-), the integrated nitrate mass and isotopic composition per unit horizontal surface area in the top 5 cm of the snowpack. NOx emission fluxes were measured at Dome C from 22 December 2009 to 28 January 2010 (Frey et al., 2013).

Forty-five 50 cm deep snow profiles were collected at DC from February 2010 to February 2014 and nitrate mass fractions were measured as in Erbland et al. (2013). These previously unpublished profiles were collected approximately every month by the DC overwintering team. From the fifty-one 50 cm snow pits collected at DC (45 unpublished and 6 published in Röthlisberger et al., 2000; Frey et al., 2009; France et al., 2011; Erbland et al., 2013), we also calculate m50 cm(NO3-) as well as δ15N50 cm(NO3-) and Δ17O50 cm(NO3-) for the snow pits where δ15N and Δ17O data are available.

In East Antarctica, nitrate isotopic and mass fraction measurements are available from twenty-one 50 cm depth snow pits, including the three DC snow pits presented above (Erbland et al., 2013). They were sampled along two transects which link D10 (a location in the immediate vicinity of the French Dumont d'Urville (DDU) station) to DC and DC to Vostok. The sample collection and analysis as well as the data reduction are described in Erbland et al. (2013). Reduced data include the asymptotic mass fraction (ω(as.)) and isotopic composition (δ15N(as.) and Δ17O(as.)), which represent nitrate below the zone of active nitrate mass loss in the top decimeters of snow, and 15εapp and 17Eapp apparent fractionation constants.

Table 3 gives a summary of the parameters and variables used for the TRANSITS DC realistic simulation. Below, we discuss their choice. Note that the adjustment parameters (Φ, fexp, fcage, D and 15εdep) were adjusted manually and not set by an error minimizing procedure.

The thickness of the atmospheric boundary layer is set to a constant value of 50 m, a value which sits between the median wintertime value (ca. 30 m) simulated by Swain and Gallée (2006) and the mean value simulated around 27 December 2012 (Gallée et al., 2015). The time series of the nitrate concentration in the atmospheric box was obtained by smoothing the atmospheric measurements performed at Dome C in 2009–2010 (Erbland et al., 2013).

Stratospheric denitrification is responsible for the input of an estimated nitrogen mass of (6.3 ± 2.6) × 107 kgN per year (Muscari and de Zafra, 2003), a value 3 times higher than the estimate of Wolff et al. (2008). Taking into account the area inside the Antarctic vortex where intense denitrification occurs ((15.4 ± 3.0) × 106 km2; Muscari and de Zafra, 2003), this gives a flux of FS = (4.1 ± 2.5) × 10-6 kgN m-2 a-1. The modeled stratospheric flux is set to occur constantly for a duration of 12 weeks (approximately 3 months) from 21 June to 13 September, the period when the mean air temperature at 50 mb allows the formation of PSCs of type I (T<-78 ∘C) (NOAA observations in 2008, available at http://www.cpc.ncep.noaa.gov/products/stratosphere/polar/polar.shtml). Transitions before and after the 12-week FS(t) plateau are assumed to be linear and to last 4 weeks (Fig. 4a). The δ15N(FS) value is set to 19 ‰ as estimated by Savarino et al. (2007) based on computations from chemical mechanisms, fractionation factors, and isotopic measurements. No direct measurement of Δ17O in stratospheric nitrate exists. Savarino et al. (2007) estimated that Δ17O is higher than 40 ‰, and we set Δ17O(FS) to 42 ‰.

There is no estimate of the nitrogen mass flux received on the Antarctic continent by long-range transport (FT). In the absence of such information and for simplicity, we assume that, annually, FS / FPI = 50 %. This means that the annual fluxes FT and FS are equal. We also assume a uniform distribution of FT throughout the year. We agree that this hypothesis is debatable given that air mass movement into the Antarctic Plateau may be hampered at times when the polar vortex is strongest. As for the flux, the δ15N and Δ17O of this nitrate source are not known. However, we assume that it features δ15N(FT) = 0 ‰ and Δ17O(FT) = 30 ‰, which represent averaged values for tropospheric nitrate in pristine areas in low/middle latitudes (Morin et al., 2009). Annual snow accumulation rates measured at Dome C vary considerably at the interannual timescale as a result of snow redistribution by the wind (Libois et al., 2014). For example, years with net ablation are as frequent as 15 %. The same process also affects the distribution of snow accumulation rates at a sub-annual timescale. For the sake of simplicity, the annual snow accumulation rate is set to a constant value of 28 kg m-2 a-1 (93 mm of snow per year for ρ= 300 kg m-3), which is representative of the Dome C site (Frezzotti et al., 2004; Libois et al., 2014). We also assumed a uniform distribution of snow accumulation within the computed year. Snow densities also vary considerably at the decimeter scale both horizontally and vertically (Libois et al., 2014). To simplify, the snow density has been set to 300 kg m-3, the average value found for the snow top layers at Dome C (France et al., 2011). This value is close to the average value (316 kg m-3) observed in a mean 25 cm depth DC profile (Libois et al., 2014). We note that our choice of snow density for the nitrate mass and isotopic calculations is consistent with that used for the optical calculations in the soft windpack layer at the surface, where most of the action occurs.

The adjustment parameter 15εdep (representing the 15N / 14N fractionation associated with HNO3 deposition) is set to a value of +10 ‰ in order to match the shift in δ15N between observed atmospheric and skin layer nitrate (Erbland et al., 2013). The diffusivity coefficient is set to 1.0 × 10-11 m2 s-1. The fraction of nitrate fluxes which is horizontally exported from the atmospheric box is adjusted to a constant value of fexp=20 %. The parameter Φ is adjusted to a constant value of 0.026 and the magnitude of the cage effect is adjusted using a constant parameter of fcage=0.15, which means that 15 % of the photolyzed nitrate undergoes cage recombination and isotopic exchange with water.

We used absorption cross sections of 14NO3- and 15NO3- in snow recommended by Berhanu et al. (2014a). The TUV-snow model used to model the actinic flux in the DC snowpack was run using constant k and q parameters set to 1. An additional input is the ozone column and we used the measurements at Dome C over the 2000–2009 period. The 2000–2005 data were derived from the measurements made by the Earth Probe Total Ozone Mapping Spectrometer (EP/TOMS) and processed by the NASA (data obtained at http://ozoneaq.gsfc.nasa.gov/). The 2007–2009 data were obtained from the Système d'Analyse par Observation Zénithale (SAOZ) observation network at the surface (data obtained at http://saoz.obs.uvsq.fr/index.html). Weekly averages have been calculated over the 2000–2009 period and converted to obtain the same resolution (25 DU) as that used for the offline runs of the TUV-snow model (Fig. 3).

The variable α has been calculated from Eq. (8) using weekly average mixing ratios of O3 measured at Dome C in 2007–2008 (Legrand et al., 2009). During the OPALE campaign, Frey et al. (2015) measured BrO mixing ratios of 2–3 pptv. We assume that [BrO] is constant throughout the year and equal to 2.5 pptv. Air temperatures and pressures at each time step were calculated from the 3 h observations from the Concordia Automatic Weather Station (AWS 8989) in 2009–2010 (University of Wisconsin–Madison, data available at ftp://amrc.ssec.wisc.edu/pub/aws/q3h/, accessed 4 July 2013). Mixing ratios of HO2 and CH3O2 were deduced from those of RO2 assuming RO2= HO2+ CH3O2 and [HO2] / [RO2] = 0.7 (Kukui et al., 2014). Mixing ratios of RO2 were estimated from their linear relationship with J(NO2): [RO2] / (molecule m-3)= 7.25 × 1015 × (J(NO2)/ s-1) (Fig. 3b in Kukui et al., 2014). The time series of J(NO2) was calculated with the TUV model for the appropriate solar zenith angle.

We note that Frey et al. (2015) have measured high [NO2] / [NO] ratios which are not consistent with other measurements available at Dome C. The authors suggest that either an unknown mechanism which converts NO into NO2 or interferences in the NOx measurements are responsible for the discrepancy observed. Given that the oxidant budget is not yet fully resolved at DC, we stick to our simple parameterization of the local resetting of the oxygen isotopic composition of NO2 (Eq. 7). We note here that we have made various simplifications in the description of the local cycling and oxidation of NO2. These assumptions include Δ17O(HO2)= 0 ‰, the simplified description of Δ17O(OH), the simplified NO to NO2 conversion reaction scheme (and the potential greater influence of O3) and, also, the neglected nighttime NO2 oxidation pathway at the beginning and end of the sunlit season (which, again, involves O3). For these reasons, we anticipate that the Δ17O values simulated by TRANSITS at DC will represent the lower bound of the observations, because O3-dominated oxidation will imply larger Δ17O values.

Sampled sites on the D10–DC–Vostok route are characterized by a wide range of annual snow accumulation rates which gradually drop from 558 kg m-2 a-1 close to the coast (D10) to 20 kg m-2 a-1 high on the plateau (around Vostok) (Erbland et al., 2013). In the simulation of nitrate in East Antarctic snowpacks and the investigation of TRANSITS's ability to reproduce such wide snow accumulation conditions, we consider 10 test sites, whose snow accumulation rates are [20, 25, 30, 40, 50, 75, 100, 200, 300, 600] kg m-2 a-1, respectively. For simplicity, we consider that A is the sole variable used to characterize different sites from the coast to the plateau in East Antarctica. All the other parameters and variables are kept the same as those for DC. TRANSITS is therefore run in the DC realistic configuration described above. This means that we do not consider changes in latitude, elevation or ozone column conditions which would impact the TUV-modeled actinic fluxes. Also, the physical, optical and chemical properties of the snowpacks are considered constant. No changes in atmospheric temperature (which would affect D) and local atmospheric chemistry are taken into account, and the horizontal export of nitrogen from locations on the plateau to those close to the coast is not modeled. Last, we hypothesize that the time series of atmospheric nitrate concentrations are the same as that measured at DC. This assumption is supported by the observation of Savarino et al. (2007), who show comparable atmospheric nitrate concentration time series at the coastal DDU station and at DC.

The parameters and variables used for the DC realistic simulation as well as those used for the simulations across East Antarctica are given in Table 3.

The 1 m snowpack is initialized with a constant nitrate profile of ω(NO3-)= 50 ngNO3- g-1, Δ17O(NO3-)= 30 ‰ and δ15N(NO3-)= 50 ‰. The atmosphere box is initialized with γ(NO3-)= 5 ngNO3- m-3 and Δ17O and δ15N values of 30 nd 5 ‰, respectively.

The model is run for a time sufficiently long to allow it to converge (e.g., 25 years for DC conditions). Raw data generated by the model are processed to obtain the time series of concentration and isotopic composition of atmospheric nitrate and in a top skin layer of 4 mm, the depth profiles of mass fraction, δ15N and Δ17O in snow nitrate, and the time series of the NO2 flux from the snow to the atmosphere.

From the simulated profiles of nitrate mass and isotopic composition in snow, we calculate the apparent fraction constants (15εapp and 17Eapp) as in Erbland et al. (2013). Also, the nitrate mass and isotopic composition in the top 5 cm are calculated. We note here that the model also computes the simulated mass fraction and isotopic composition in the archived nitrate, which can be compared to the observed asymptotic values.

Figure 4 gives the results at the air–snow interface for the DC-like realistic simulation: simulated nitrate concentrations, δ15N and Δ17O in both the atmospheric and skin layer compartments, and the simulated fluxes (FD, FE, FP) together with the observations at Dome C in 2007–2008 and 2009–2010. Table 4 gives a summary of averages and minimum/maximum of the simulated values in the atmosphere and skin layer.

In the atmospheric compartment, the average nitrate concentration is 32 ng m-3, which represents an average mass of 3.6 × 10-4 mgN m-2. Atmospheric concentrations start to rise by the beginning of August and peak at 110 ng m-3 at the end of November, returning to winter background values (5 ng m-3) in March. The simulated annual weighted δ15N value is +0.2 ‰. Simulated atmospheric δ15N values first show a 20 ‰ decrease in spring from the winter mean value of approximately +10 ‰, which concurs with the beginning of the increase in atmospheric concentrations (mid-August to mid-October) and then an increase at a rate of approximately 10 ‰ per month. The highest atmospheric δ15N value is approximately +20 ‰ and is simulated in early February. The simulated annual weighted Δ17O value is 23.7 ‰. The highest atmospheric Δ17O values are simulated in winter (39.3 ‰ in July–August). They rapidly decrease by 18 ‰ from mid-August to October, remain stable around 22 ‰ throughout the summer and slowly start to rise in February, reaching winter values in July.

In the skin layer compartment, the average simulated nitrate mass fraction is 3074 ng g-1, which represents an average mass of 0.8 mgN m-2. Skin layer mass fractions start to rise in June, when the stratospheric nitrate input occurs, and peak at 5706 ng g-1 at the end of December, gradually returning to winter background values (700 ng g-1) in June. We note that only the simulated results are described in Sect. 3.2. The reader may refer to Sect. 3.3 for a comparison of the simulated and observed data, in particular the discrepancy between simulated and observed nitrate mass fraction in the skin layer (Fig. 4g). The simulated annual weighted δ15N value is +34.9 ‰. Simulated δ15N values in the skin layer and atmosphere show similar variations: δ15N values in the skin layer are stable in winter (+20 ‰), decrease by 5 ‰ in spring, increase at a rate of approximately 20 ‰ per month in summer, and reach a maximum value of +60 ‰ in early February before decreasing at a rate of ca. 10 ‰ per month in winter. The simulated annual weighted Δ17O value is 25.5 ‰. Here, simulated atmospheric Δ17O values in the skin layer and atmosphere show similar variations: maximum Δ17O values in skin layer are simulated in winter (38.9 ‰ in July–August), rapidly decrease by 18 ‰ from mid-September to October, and remain stable around 21 ‰ throughout the summer and slowly start to rise in February, reaching winter values in July.

The comparison of those two compartments shows that the average nitrate mass in the skin layer compartment is 2300 times higher than that in the atmospheric compartment. Also, we observe that nitrate mass fractions in the skin layer start to rise 2 months earlier than atmospheric concentrations do and that the summer maxima is simulated 1 month later. Annual weighted δ15N and Δ17O values in the skin layer are shifted by +34.7 and +1.7 ‰, respectively, compared to the atmospheric value. Variations in δ15N in both compartments are in phase; however, the spring decrease in δ15N values is smaller in the skin layer than in the atmosphere and the increasing rate in summer is 2 times higher. Consequently, the difference between δ15N values in skin layer and atmospheric nitrate varies from +10 ‰ in winter to 38 ‰ in summer. Variations in Δ17O values in both compartments are almost in phase. The difference between Δ17O in skin layer and atmospheric nitrate is variable and negative in winter, increases in spring, reaching +8 ‰, and is stable and slightly negative (-1 ‰) in summer.

Figure 5 and Table 5 give the snowpack results for the DC-like realistic simulation: simulated nitrate mass fraction and isotopic composition in the top 5 cm of snow and in the archived flux as well as the simulated apparent fractionation constants. The simulated nitrate mass in the top 5 cm (Fig. 5a) shows an average value of (8.1 ± 1.6) mgN m-2 (mean ± 1σ). The simulated m50 cm(NO3-) varies in the range 6.2–11.0 mgN m-2, with its maximum reached by the end of September and its minimum reached by the end of January. The simulated isotopic composition of nitrate in the top 5 cm shows weighted averages of +100.5 and 23.3 ‰ for δ15N and Δ17O, respectively (Fig. 5c and f). The two time series also show cycles with variations respectively in anti-phase and in phase with variations in m50 cm(NO3-). δ15N50 cm(NO3-) and Δ17O50 cm(NO3-) respectively vary in the 77.4–127 and 20.0–27.4 ‰ ranges.

The simulated 15N / 14N apparent fractionation constant shows an annual average of (-49.5 ± 3.7) ‰, with weak annual variations (from -43.0 to -53.6 ‰) (Fig. 5d). The annually averaged 15εapp value is slightly higher than the annual weighted mean 15εpho value (-55.1 ‰). Compared to 15εapp, 17Eapp shows variations in greater relative amplitude (from 0.7 to 2.4 ‰) with an annual average of (1.4 ± 0.6) ‰.

Figure 6 shows the specific case of the simulated snow nitrate for the week around 24 December in the case of the DC realistic simulation. Simulated nitrate mass fractions decrease by more than 2 orders of magnitude in the top 15 cm and δ15N and Δ17O values increase and decrease with depth from 40 ‰ to a mean background value above 290 ‰ and from 21 ‰ to a mean background value below 18 ‰ at around 20–3 cm depth, respectively. The simulated profiles are smooth and a small secondary peak can be observed in the mass fraction profile at around 9 cm depth, a depth which corresponds to 1 year of snow accumulation.

Table 6 gives the simulated nitrate mass fluxes and their isotopic composition in the case of the DC realistic simulation. The FA / FPI ratio for the DC-like simulation is 1.8 %, which means that a small fraction of the primary input flux of nitrate is archived below 1 m. The remaining fraction (FE / FPI =1-FA/FPI=98.2 %) is exported outside the atmospheric box. The photolytic, deposition and export fluxes show a peak whose timing follows the sunlit season (Fig. 4a). The annual photolytic flux is 32.1 × 10-6 kgN m-2 a-1 and is compensated for by an annual deposition flux of 32.2 × 10-6 kgN m-2 a-1. Annually, the simulated FD and FP fluxes represent 4 times the primary input flux of nitrate (FD ≈ FP ≈ 4 × FPI). In the archived nitrate, the simulated mass fraction, δ15N and Δ17O values are constant throughout the season: 23.0 ng g-1, 318 ‰ and 17.8 ‰, respectively (Fig. 5, Table 6).

Figure 7 shows the results for the TRANSITS simulations across East Antarctica in which only the snow accumulation rate is varied. The simulated 15N / 14N apparent fractionation constants are low ((-46.1 ± 2.2) ‰, n=4) for East Antarctic Plateau sites (A≤50 kg m-2 a-1; Erbland et al., 2013) and close to zero ((-10.3 ± 9.0) ‰, n=3) for coastal sites (A≥200 kg m-2 a-1). Also, simulated plateau sites feature an average 17Eapp value, which is significantly positive ((+1.0 ± 0.3) ‰, Fig. 7b). The simulated archived flux (FA) and Δ17O(FA) both decrease with increasing 1/A (Fig. 7e and d). Simulated δ15N(FA) values monotonically increase with increasing 1/A.

Figure 8 presents the same results in a different way. Panel a is a “modified Rayleigh plot” where ln(δ15N(FA) + 1) is represented as a function of ln(FA) (which equals ln(ω(FA) × A)) instead of ln(ω(FA)). In this representation, we observe that the simulated data fall on a line whose slope is -0.064. Figure 8b shows that Δ17O(FA) and δ15N(FA) (Fig. 8b) are negatively correlated.

The nitrate mass loss is quantitatively represented in the TRANSITS model. Indeed, Fig. 6a shows that nitrate mass fractions decrease by a factor of 10 in the top 1 cm of the snowpack in agreement with observations. Also, the simulated archived nitrate mass fractions values are consistent with the observations (Fig. 5). This means that the nitrate mass fraction lost by photolysis (1-f) and calculated from the photolytic rate constant (J, Eq. 1) is quantitatively simulated by TRANSITS model runs.

Nitrate–δ15N isotopic profiles in snow also show that the 15N / 14N fractionation associated with nitrate photolysis is quantitatively represented within the uncertainties. Indeed, the DC realistic simulation reproduces well the depth profile of δ15N in snow nitrate as observed in Fig. 6b, with simulated δ15N values as high as 150 ‰ at 1 cm depth. First, the simulated 15N / 14N apparent fractionation constants are consistent with the observations at Dome C (Fig. 5d) and for plateau sites (A≤50 kg m-2 a-1, Fig. 7a). This means that the absorption cross sections used for 14NO3- and 15NO3- (Berhanu et al., 2014a) and the variables used in the TUV-snow model (O3 column) allow a quantitative description of the 15N / 14N fractionation constant associated with nitrate photolysis (15εpho, Eq. 3). Secondly, the δ15N values in the archived nitrate are well reproduced by the model: the simulated δ15N(FA) value (318 ‰) compares well with the observations (from 275 to 300 ‰, Fig. 5f). This is further evidence that the nitrate mass fraction lost by photolysis (1-f) is quantitatively simulated by TRANSITS model runs. Indeed, using a quantum yield of 2.1 × 10-3 at 246 K as in France et al. (2011) leads not only to an unrealistic FA / FPI ratio (71 %) and ω(FA) value (917 ng g-1) but also to a very small δ15N(FA) value (+20.3 ‰), which clearly reflects a weak recycling and an overestimate of primary nitrate trapped in snow. The adjusted photolytic quantum yield of Φ=0.026 allows for computation of a consistent variation range of δ15N in nitrate archived at depth. Given the choice of a modeled cage effect of fcage= 0.15, we obtain an apparent modeled quantum yield of 0.85 × 0.026 ≈ 0.022, a value smaller than the mean value for buried nitrate (0.05) but higher than the smallest value observed for this domain (0.003) (Meusinger et al., 2014).

Additionally, we observe from Fig. 6a that the simulated profiles are smooth and that a small secondary peak can be observed in the simulated mass fraction profile at around 9 cm depth. Such smooth profiles can only be simulated because nitrate diffusion was taken into account, and turning this process off leads to simulated mass fraction and isotope profiles in the snow showing unrealistic spiky seasonal variations similar to those simulated by Wolff et al. (2002) and France et al. (2011). The secondary peak observed in simulated nitrate mass fraction profiles (at 9 cm depth, which corresponds to 1 year of snow accumulation) represents nitrate residual from the previous year's skin layer. This is consistent with secondary peaks observed in some snow pits on the Antarctic Plateau, e.g., snow pits S1 (at 1 cm depth), S2 (at 7 and 17 cm depth) and S3 (around 1 cm depth) in the Supplement (Erbland et al., 2013). Since TRANSITS is able to reproduce such a feature, we conclude that a simplified description of nitrate diffusion (i.e., constant diffusion coefficient) is not detrimental.

The adjusted value used for D can be compared to the effective diffusivity of nitric acid in snow (denoted Deff) as calculated in Herbert et al. (2006) and by assuming that the snow layers are always undersaturated in nitrate. Such an approach is followed because HNO3 is a sticky gas. According to Herbert et al. (2006), the Deff is a function of the diffusivity of HNO3 in the interstitial air, which depends on temperature and pressure (Massmann, 1998). Using a specific surface area of snow of 38 m2 kg-1 (Gallet et al., 2011), a snow density of 300 kg m-3, the median temperature and pressure for DC summer 2012 (Kukui et al., 2014) and a partition coefficient in the uptake of HNO3 on ice (Crowley et al., 2010), we find Deff= 7.3 × 10-12 m2 s-1. Our adjusted value for D (1.0 × 10-11 m2 s-1) is close to the effective diffusivity of nitric acid in snow (denoted Deff) and more than 3 orders of magnitude higher than the diffusion coefficient of nitrate ion in a single monocrystal of ice calculated at the same temperature (2.6 × 10-15 m2 s-1; Thibert and Dominé, 1998), which means that the macroscopic mobility of nitrate in the snowpack is mostly the consequence of HNO3 mobility in the interstitial air. We note that our description of nitrate diffusion in the snowpack is basic and that the picture may well be more complicated with, for example, wind pumping effects and temperature gradients in snow.

The choice of a non-zero value for fcage allows for reproduction of the positive apparent 17O-excess fractionation constant (17Eapp) which is observed at DC (from (+1.2 ± 0.3) ‰ to (+2.3 ± 0.7) ‰ in summer, Fig. 5g) and on the Antarctic Plateau (Frey et al., 2009; Erbland et al., 2013). Indeed, Fig. 5g shows that the simulated 17Eapp values at DC are positive, while a TRANSITS model run with the cage effects switched off (i.e., fcage=0) leads to a simulated mean December/January 17Eapp value of almost zero: (+0.3 ± 0.2) ‰ (date not shown). The simulation across East Antarctica confirms the ability of the model to reproduce the sensitivity of Δ17O to the nitrate mass loss (Fig. 7b). Indeed, for sites with A≤50 kg m-2 a-1, the model calculates a mean 17Eapp value of (+1.0 ± 0.3) ‰ for the December/January period, while the observed average value is (+2.0 ± 1.2) ‰ (mean ± 1σ, n=10). The model therefore confirms the decreasing contribution of cage recombination effects to Δ17O(NO3-) as originally observed in the lab by McCabe et al. (2005).

Figure 6c shows that a non-zero value for fcage allows for generation of decreasing Δ17O profiles in snow in accordance with the observations in three snow pits from DC and with the simulated and observed positive 17Eapp values. While this subtle depth trend is reproduced by the model, we observe from the same figure that, quantitatively, the choice of a non-zero value for fcage is detrimental to the reproduction of the Δ17O values of nitrate in the top 5 cm of snow. Indeed, modeled Δ17O values in the 40–50 cm depth range are approximately 18 and 23.5 ‰ in the cases where the cage effects are switched on and off, respectively, in comparison with observed Δ17O values in the 27–30 ‰ range. We refer the reader to Sect. 3.3.8, where the ability of the model to quantitatively reproduce the observed Δ17O values is discussed.

The primary input flux of nitrate to the air–snow system (FPI) derived from Muscari and de Zafra (2003) (and from our assumption FT = FS) is realistic. Indeed, simulated and observed East Antarctica data almost fall on the same line of slope -0.065 in the modified Rayleigh plot (Fig. 8a). In this representation, changing FPI leads to the horizontal shift of the simulated data, thus confirming the realistic value of FPI = 8.2 × 10-6 kgN m-2 a-1. We note that our simulation in East Antarctica is very simple because it only takes into account changes in snow accumulation rates, which are large on the D10–DC–Vostok route. A more sophisticated simulation along this line is beyond the scope of the present study because it would require including a radiative transfer model such as TUV-snow (or TARTES; Libois et al., 2014) in TRANSITS in order to deal with latitudinal and elevation changes. Also, the simulation should take into account boxes from Vostok to D10 with the exchange of nitrate horizontally exported from the center of the continent towards the coast, basically changing our 1-D model into a 2-D model.

The maximum value of the photolytic flux (FP) simulated for DC is 3.27 × 10-12 kgN m-2 s-1 (Fig. 4a, Table 6), a value around 40 times higher than that obtained by France et al. (2011). This difference is not surprising since we are using a quantum yield 12 times higher than France et al. (2011). The different scaling may be explained by the differences in the complexities of the two models (TRANSITS includes recycling and a net export). The observed median NOx emission fluxes are 1.6 × 10-13 kgN m-2 s-1 and 3.7 × 10-13 kgN m-2 s-1 over the 22 December 2009 to 28 January 2010 period (Frey et al., 2013) and the 1 December 2011 to 12 January 2012 period (Frey et al., 2015), respectively. Our computed median NO2 fluxes over the same periods are 2.8 × 10-12 kgN m-2 s-1 and 3.3 × 10-12 kgN m-2 s-1, i.e., values respectively 18 and 9 times higher than in the observations by Frey et al. (2013, 2015).

The discrepancy between simulated and observed FP values may be explained by the fact that FP represents the potential flux of NO2 emitted from the snow to the atmosphere, i.e., an upper limit when comparing to the observed NO2 flux (measured between 0.01 and 1 m above the snowpack; Frey et al., 2013, 2015). TRANSITS does not take into account various potential processes affecting NOx emission from snow, such as gas-phase diffusion or chemical conversion prior to emission and forced ventilation from the snowpack (France et al., 2011; Frey et al., 2013; Meusinger et al., 2014). Future improvements to the model could include an explicit representation of the vertical transport of NO2 within and outside the snowpack with the following processes: NOx diffusion, wind pumping, chemical conversion and deposition prior to the net emission from the snow, the latter depending on oxidant levels in firn air (HOx, O3, and maybe halogens; Zatko et al., 2013). Another improvement could be the modeling of two nitrate domains (photolabile and buried nitrate; Meusinger et al., 2014).

We note that, if HONO production is greater than assumed at Dome C, following the recent laboratory study of Scharko et al. (2014), this will not change the main conclusions of this study. Indeed, the photolytically produced HONO will be photolyzed to form NO in the atmosphere and this NO would simply enter the NO / NO2 cycles, where oxygen isotopes are reset.

The parameterization of HNO3 deposition is simplistic since it solves the mass-balance equation (Eq. 4) in order to reproduce the nitrate concentration in the atmosphere. A sensitivity test of TRANSITS has been run using nitrate atmospheric concentrations 10 times higher than the ideal DC time series used for the DC realistic simulation. The higher nitrate concentration in the atmosphere had no significant impact on any of the nitrate reservoirs both in terms of mass and isotopic composition. Indeed, in the case of the DC realistic simulation, the atmospheric nitrate mass represents 1/2300 and 1/22 500 of nitrate mass in the skin layer and in the top 5 cm, respectively. Future improvements to the model could use a physical description of the deposition of HNO3 using, for example, a vertical deposition velocity.

Hereafter, the ratio FA / FPI is termed the “nitrate trapping efficiency” because it reflects the fraction of nitrate that is trapped below the photic zone. In the DC realistic simulation, the nitrate trapping efficiency is 1.8 % (Table 6), which means that only a small fraction of the primary nitrate is archived. Consequently, the net export of nitrate is significant (FE = 98.2 % of the nitrate of primary origin = 8.05 × 10-6 kgN m-2 a-1, Table 6) and reflects the chosen adjusted value of fexp (0.2). To the best of our knowledge, there is no observation that could independently corroborate this FE value because it would require the direct measurement of this flux. However, we point out that a non-zero fexp parameter is necessary to reproduce realistic δ15N values both in the atmosphere and skin layer. Indeed, when running the model with fexp=0, δ15N values in those compartments become highly negative (≤-120 ‰), which is clearly not realistic when compared to the observations (Fig. 4e and h) and what is seen in Frey et al. (2009). Also, in such conditions, the model does not converge within a reasonable time and simulated nitrate endlessly builds up in the photic zone.

The parameter fexp can, however, be related to physical variables. Indeed, it represents the competition between the export of NOy (NO2 or HNO3) and the deposition of (to make it simple) HNO3. Let us consider atmospheric NO2 and HNO3 at steady state. The deposition of NO2 is neglected because it is a factor of 8.0 ± 3.2 slower than that of HNO3 (Zhang et al., 2009). Also, oxidation by OH is considered to be the only channel of NO2 oxidation (an assumption valid in summer). Following the approach of Jacob (1999), a summertime value for fexp can be approached by considering the chemical lifetime of NO2 with respect to its oxidation by OH, the residence time of atmospheric NO2 against horizontal export and that of atmospheric HNO3 against deposition and horizontal export processes. Using kinetic rate constants from Atkinson et al. (2004), T,P, wind speeds and OH mixing ratios for mean summertime conditions at DC (Kukui et al., 2014), HNO3 dry deposition velocity from Huey et al. (2004), and vertical and horizontal characteristic dimensions of 100 m (average summertime boundary layer height, Gallée et al., 2015) and 400 km (Antarctic Plateau width), respectively, we obtain fexp=0.20, a value which equals the value used to adjust the model but which is rather fortuitous. Indeed, we acknowledge that this calculation suffers from a number of uncertainties; for example, using kinetic rate constants of NO2+ OH from Sander et al. (2006), we obtain fexp=0.36. Future improvements to the model could aim at a physical parameterization of the nitrate export.

Results from the East Antarctica simulations show that the observed linear δ15N(FA) versus 1/A relationship (Freyer et al., 1996; Erbland et al., 2013) is very well reproduced (Fig. 7c). This demonstrates that the residence time of nitrate in the snowpack zone of active photochemistry is treated in a realistic manner in the model. When snow accumulation rates get very low (A<20 kg m-2 a-1), simulated δ15N(FA) values do not seem to reach an asymptotic value as observed in the field where δ15N(as.) seems to reach a plateau not exceeding 360 ‰ (Fig. 7c). This observed feature could be the result of the different nitrate locations on snow grains, with buried nitrate (Meusinger et al., 2014), whose photolysis constitutes a lower limit in the photolysis loss process.

Nitrate recycling at the air–snow interface at DC is illustrated by the simulated macroscopic photolytic and deposition fluxes at the snowpack surface. Indeed, FP and FD almost equilibrate, and these annual fluxes are 4 times higher than the annual primary input of nitrate (FPI, Table 6).

Here, our main focus is on nitrate which is archived below the zone of active photochemistry, because only that is ultimately archived in ice cores. One key issue to determine is the “average number of recyclings” undergone by the archived nitrate (hereafter denoted ANR(FA)). To this end, a new tracer, denoted CYCL, has been introduced in the TRANSITS model. In a given box (snow layer or atmosphere), CYCL represents the average number of recyclings undergone by nitrate in the considered box. The CYCL variable follows a numerical treatment comparable to that of δ15N and Δ17O, i.e., a “recycling” (instead of an isotopic) mass balance, diffusion and the calculation of CYCL values in the macroscopic fluxes (FP, FD, FE, FA). The CYCL value for primary nitrate is set to 0, and CYCL variables in the boxes are incremented by 1 each time NO2 molecules cross the air–snow interface. ANR(FA) is calculated as a mass-weighted average of the CYCL values of the 52 snow layers which are archived below 1 m over the course of 1 year, in order to average out any seasonal variability.

Following the above approach for the Dome C simulation, we obtain ANR(FA) = 4.0 for the last layer before leaving the photic zone, which means that, on average, the archived nitrate at Dome C has undergone 4.0 recyclings (i.e., loss, local oxidation, deposition). We note that this number of recyclings represents an average value for the archive nitrate. Considering individual ions in the archived nitrate, the range of the number of recyclings must be wide since some ions may well have traveled through the entire snowpack zone of active photochemistry without being recycled, while some underwent many recyclings.

Figure 7g shows the ANR(FA) values calculated for the 10 simulated sites in East Antarctica. We observe that ANR(FA) is proportional to 1/A for A≥50 kg m-2 a-1, which means that the burial of nitrate (i.e., the residence time of nitrate in the photic zone) determines the ANR(FA) value. On the Antarctic Plateau, where snow accumulations rates are below this threshold value, ANR(FA) reaches a plateau on the order of four recyclings. Concurrently, we observe that FP remains constant at 32.8 × 10-6 kgN m-2 a-1 (data not shown) because increasing residence time of nitrate in the photic zone with decreasing snow accumulation rates leads to a nitrate mass fraction profile in snow which becomes more asymmetric, with most of the nitrate getting confined in a thinner layer at the top. As a result, FP levels off due to the negative feedback of the decreasing nitrate mass fractions at depth. Figure 7g clearly shows the following relationship between ANR(FA) and FP: ANR(FA) =FPFPI. This finding represents an independent confirmation of the definition given by Davis et al. (2008) on the basis of the macroscopic yearly primary and photolytic fluxes: the “nitrogen recycling factor”, NRF, which is the ratio of nitrogen emission and nitrogen deposition. While we are satisfied to end up with the Davis et al. (2008) expression for ANR(FA) using our independent model-based tracer experiment, it must be noted that we define ANR as the average number of recyclings undergone by the archived nitrate, while Davis et al. (2008) define it as the “nitrogen recycling factor within a photochemical season”.

Nitrate mass in the different compartments is reasonably well reproduced by the model. Indeed, the simulated average nitrate mass in the atmospheric compartment represents 1/22 500 of that in the top 5 cm of snow, and this is consistent with observations in 2009–2010 where this ratio is 1/8300 (Tables 4 and 5, considering a constant boundary layer height of 50 m). Also, the annual variations in nitrate mass fractions in the skin layer are well reproduced by the model: deviations from the winter background values occur during the sunlit season, reaching a maximum in December (Fig. 4g). However, we note that the period of high values above background is longer (September to April) for the simulation than in the observations (October/February). Lastly, simulated nitrate mass in the top 5 cm of snow has been shown to increase in winter and decrease during the sunlit season (Fig. 5a), similar to the observed data: the average winter m50 cm(NO3-) value ((3.6 ± 0.5) mgN m-2, May to November) is higher than the average summer value ((3.2 ± 1.2) mgN m-2, December to April). In winter, the input and output to the nitrate reservoir in the top 5 cm of snow are the deposition and archiving fluxes, respectively. During this season, the deposition flux is greater than the archiving flux, which leads to an increase in m50 cm(NO3-). When the sunlit season starts, the additional photolysis output flux starts, causing the sum FA + FP to exceed FD and thus m50 cm(NO3-) to decrease.

Additionally, the simulated average mass ratio between the skin layer and the top 5 cm of snow is 10 % (Tables 4 and 5), a value approximately 3 times higher than the 2009–2010 observed value (3 %, considering a snow density of 300 kg m-3 for the skin layer snow). This discrepancy is accompanied by a factor of 2.4 between simulated and observed annual average m50 cm(NO3-) values ((8.1 ± 1.6) mgN m-2 versus (3.4 ± 1.0) gN m-2, Fig. 5a) and by a factor of 7.9 between simulated and observed annual average mass fractions in the skin layer (3074 ng g-1 versus 390 ng g-1, Fig. 4g). Nitrate masses in the top 5 cm and in the skin layer are therefore higher in the DC simulation than in the observations, and nitrate in the skin layer is more concentrated in the simulation.

Fully resolving these discrepancies is beyond the scope of this paper. However, we first note that lower observed skin layer mass fractions could be linked to heterogeneities in sampling the skin layer (whose thickness is (4 ± 2) mm; Erbland et al., 2013), especially when considering that different overwintering volunteers were involved in this task. For instance, sampling 6 mm instead of 4 mm could lead to the sampling of a more diluted skin layer. However, we acknowledge that this sampling issue would have a limited impact on the observed skin layer mass fractions. Secondly, higher simulated annual m50 cm(NO3-) values could be the result of the time response of the modeled snowpack to past changes in primary input fluxes. Indeed, when run in the DC realistic simulation with a multiplication of FPI by a factor of 10 after 25 years of simulation, TRANSITS shows a time response of approximately 21 years. This means that the snowpack requires 21 years to reach stable m50 cm(NO3-) values again. As a consequence, the different m50 cm(NO3-) value observed today at Dome C could reflect changes in primary input flux conditions as far back as one or two decades in the past. A third explanation involves the absence of a snow erosion process during which wind blows away a significant fraction of the non-cohesive skin layer. This process would decrease nitrate mass fractions in the skin layer as observed in the field around 10 January 2010 (Erbland et al., 2013) and, in turn, decrease nitrate mass fractions in the snow layers below.

In Sect. 3.2.1, we have seen that the simulated δ15N profiles in snow are consistent with the observations. In particular, apparent 15N / 14N fractionation constants are well reproduced leading the simulation of realistic δ15N(FA) values. In this section, we compare the simulated and observed time series of δ15N in the atmospheric and skin layer nitrate.

Overall, the annual variations in δ15N values in skin layer and atmospheric nitrate are generally well reproduced by the model, although some discrepancies can be noted Fig. 4e and h). For example, the winter observed δ15N values and 10 ‰ shift between atmosphere and snow are well simulated, supporting the choice of the 15N / 14N fractionation constant associated with the deposition of nitric acid (+10 ‰), the positive sign of 15εdep being consistent with a dry deposition of HNO3. Also, the spring variations and timing of atmospheric δ15N are well reproduced. Indeed, the lowest δ15N values in the atmospheric nitrate occur in October (simulated: -25.3 ‰; observed: -17.0 ‰, Fig. 4e), when the stratospheric input has stopped and when the UV radiation becomes significant enough to encourage the production of isotopically depleted NOx from the snowpack. The return to positive atmospheric δ15N(NO3-) values in summer is faster at Dome C than has been observed at DDU, and this feature has been attributed to the longer exposure time of nitrate at the snow surface at Dome C (Savarino et al., 2007; Frey et al., 2009). TRANSITS confirms this suggestion when run with the higher snow accumulation rate which characterizes DDU (data not shown). At Dome C, shortly after the decrease, δ15N values rapidly start to rise again because the nitrate in snow becomes more enriched in 15N and the extracted NO2 has rising δ15N values as well. With large θ values at the end of the summer, the apparent ozone column crossed by the UV rays is more important and the photolytic fractionation constant (15εpho) becomes more negative (Fig. 5d). This leads to decreasing δ15N values extracted from the snowpack even if the enrichment does not stop there. Finally, wintertime values of δ15N are reached back by the end of April/beginning of May, when the nitrate photolysis stops.

The simulated annual variation in skin layer δ15N is also consistent with the observations. However, the spring decrease observed in 2009–2010 is more marked than the simulation one (25 and 5 ‰, respectively, Fig. 4h). One reason is that the simulated δ15N values in skin layer start to rise 1.5 months earlier than in the observations (Fig. 4h). Although simulated δ15N values start to rise earlier, we note that the summer increasing rate in skin layer δ15N values is similar in the simulations and in the observations (approximately +20 ‰ per month). One consequence of the 1.5-month delay between simulated and observed skin layer δ15N values is that the δ15N difference between skin layer and atmospheric nitrate at the end of the summer is greater in the simulation than it is for the observation (approximately +40 ‰ versus +20 ‰). Focusing on the beginning of the skin layer, δ15N records (Fig. 4h) show that the end of summer 2008–2009 was different than the next year, with differences up to 40 ‰ between the simulation and observation. In particular, the large observed variations which lead to skin layer δ15N values as high as +60 ‰ (Erbland et al., 2013) are not reproduced by the model. This could be the result of snow sampling effects (i.e., local spatial heterogeneity or different sampling of the operator in the field).

The simulated variations in Δ17O in the atmospheric and skin layer compartments are consistent with the observations – i.e., Δ17O decreases from high winter values to the lowest values in the middle of summer (Fig. 4f and i). The model also reproduces well the small negative difference between the atmospheric and skin layer annual weighted Δ17O values (simulated: -1.2 ‰; observed: -2.3 ‰). When considering the annual variability of the difference in Δ17O in the atmosphere and skin layer, the model reproduces well the important shift in early October (simulated: -8 ‰; observed: -7 ‰) as well as the small negative shift by the end of the summer (simulated: approximately -2 ‰; observed: approximately -2 ‰).

The above observations show that TRANSITS is able to qualitatively reproduce the Δ17O variations in nitrate for each compartment. Concurrent variability in Δ17O in atmospheric and skin layer nitrate indicates equilibrium at the air–snow interface. The simulated and observed differences between Δ17O in the atmosphere and skin layer are the result of their respective nitrate reservoirs and indicate that the isotopic equilibrium is dynamic. Further evidence for the different size reservoir is that the (oxygen and nitrogen) isotope time series in the skin layer are smoother than in the atmosphere (Fig. 4).

The photolytic and deposition fluxes in summer show that there is an intense nitrate recycling at the air–snow interface during this season (Fig. 4a), a feature which is confirmed by our calculation of the average number of recyclings undergone by the archived nitrate (ANR(FA) = 4.0). The local signature of NO2 cycling and oxidation harbored by Δ17O is therefore incorporated in skin layer nitrate. Given the good qualitative agreement between the simulated and observed Δ17O in skin layer nitrate throughout the year, we conclude that TRANSITS has a realistic representation of the local cycling and oxidation of NO2 in the atmosphere.

We also observe that TRANSITS reproduces well the Δ17O(FA) / δ15N(FA) anti-correlation and general trend in the case of the simulation across East Antarctica (Fig. 8c). This anti-correlation is partly the result of the cage recombination effects, but some of it is also due to the greater incorporation of the summertime isotopic signature of the local cycling and oxidation of the photolytically produced NO2. On the same figure, the observations show a large scattering of approximately 5 ‰ when compared to data simulated by TRANSITS. One reason for that is the inability of the model to reproduce variations in Δ17O in nitrate below 2 cm, which can be as high as 5 ‰ (Fig. 6c). Such variations may be linked to variability in ozone column, snow accumulation, local atmospheric chemistry, and primary inputs of nitrate from one year to another which are not accounted for by TRANSITS. McCabe et al. (2007) first observed such 2–3-year period cycles in a 6 m snow pit from the South Pole and attributed these cycles to variability in the stratospheric ozone column or to stratospheric nitrate import; the same periodicity in Δ17O is found in DC surface snow (Frey et al., 2009; Erbland et al., 2013). Future work should investigate the impact of the variations in the ozone column on the Δ17O in the archived nitrate.

Quantitatively speaking, Δ17O values in the atmosphere, the skin layer, the top 5 cm of snow and the archived nitrate are not well reproduced. Indeed, the simulated annual weighted Δ17O values in the atmosphere and skin layer are approximately 6 ‰ lower than in the observations (23.7 ‰ versus 29.4 ‰ and 25.5 ‰ versus 31.7 ‰, respectively). The same is observed for simulated Δ17O50 cm(NO3-) and Δ17O(FA) values (Fig. 5f and h). From Fig. 4f and i, we observe that wintertime Δ17O values in atmospheric and skin layer nitrate are reasonably well reproduced, while most of the discrepancies are observed in summer.