Zhuang Jiang

Becky Alexander

Joel Savarino

Joseph Erbland

Lei Geng
email: genglei@ustc.edu.cn

Impacts of the photo-driven post-depositional processing on snow nitrate and its isotopes at Summit, Greenland: a model-based study

 Snow nitrate is redistributed in the photic zone by post-depositional processing  As much as 21 % snow nitrate is lost after deposition  The observed seasonality of snow δ 15 N(NO 3 -) is explained by the post-depositional processing

Introduction

Nitrate (NO 3 -

) is one of the most abundant inorganic ions preserved in ice cores.

Nitrate is the final product of atmospheric NO x (= NO + NO 2 ), and ice-core nitrate has been sought to provide information on past atmospheric NO x abundance [START_REF] Wolff | Nitrate in Polar Ice[END_REF]. One of the major subjects of ice-core nitrate studies involves the oxygen mass-independent isotope fractionation signal (Δ 17 O = δ 18 O -0.52  δ 17 O) of nitrate, which is a proxy to reconstruct past atmospheric oxidation capacity (Alexander & Mickley, 2015;[START_REF] Alexander | Impact of preindustrial biomass-burning emissions on the oxidation pathways of tropospheric sulfur and nitrogen[END_REF][START_REF] Geng | Isotopic evidence of multiple controls on atmospheric oxidants over climate transitions[END_REF]. There are many factors, e.g., atmospheric chemistry and transport, deposition and post-depositional processing of nitrate, affecting ice core nitrate and its isotopes (Geng et al., 2014;[START_REF] Geng | Effects of postdepositional processing on nitrogen isotopes of nitrate in the Greenland Ice Sheet Project 2 ice core[END_REF][START_REF] Morin | Tracing the origin and fate of NOx in the Arctic atmosphere using stable isotopes in nitrate[END_REF][START_REF] Wolff | The interpretation of spikes and trends in concentration of nitrate in polar ice cores, based on evidence from snow and atmospheric measurements[END_REF].

Deposition of atmospheric nitrate to snow is not irreversible. After deposition, nitrate can undergo post-depositional processing which causes changes in its concentration and isotopes [START_REF] Blunier | Isotopic view on nitrate loss in Antarctic surface snow[END_REF][START_REF] Erbland | Air-snow transfer of nitrate on the East Antarctic Plateau-Part 1: Isotopic evidence for a photolytically driven dynamic equilibrium in summer[END_REF][START_REF] Frey | Photolysis imprint in the nitrate stable isotope signal in snow and atmosphere of East Antarctica and implications for reactive nitrogen cycling[END_REF]. The post-depositional processing includes physical release of HNO 3 (i.e., desorption and evaporation) from snow and ultraviolet photolysis of snow nitrate.

Both processes result in loss of snow nitrate and isotope fractionations of nitrogen and oxygen. However, laboratory experiments and model calculations indicate a minor influence of the physical processes and it is photolysis that dominates the post-depositional processing [START_REF] Erbland | Air-snow transfer of nitrate on the East Antarctic Plateau-Part 1: Isotopic evidence for a photolytically driven dynamic equilibrium in summer[END_REF][START_REF] Frey | Photolysis imprint in the nitrate stable isotope signal in snow and atmosphere of East Antarctica and implications for reactive nitrogen cycling[END_REF][START_REF] Shi | Isotope fractionation of nitrate during volatilization in snow: a field investigation in Antarctica[END_REF].

Snow nitrate photolysis occurs when exposed to sunlight at wavelengths less than 345 nm [START_REF] Chu | Quantum yields of hydroxyl radical and nitrogen dioxide from the photolysis of nitrate on ice[END_REF]. The dominant photolysis products are NO 2 , which can be effectively transported to the overlying atmosphere via diffusion or wind pumping [START_REF] Zatko | The influence of snow grain size and impurities on the vertical profiles of actinic flux and associated NOx emissions on the Antarctic and Greenland ice sheets[END_REF] and impacts local atmosphere oxidation environment [START_REF] Thomas | Modeling chemistry in and above snow at Summit, Greenland-Part 2: Impact of snowpack chemistry on the oxidation capacity of the boundary layer[END_REF]. The released NO 2 can reform HNO 3 in the overlaying atmosphere, which will be then redeposited or exported from the site of photolysis.

The above-mentioned processes form a cycle of nitrate between the air-snow interface, resulting in redistribution of nitrate in snow layers.

The isotopic composition of nitrate changes significantly during photolysis. The isotope fractionation factors (ε p ) associated with snow nitrate photolysis is -47.9 ‰ for δ 15 N and -34 ‰ and δ 18 O under the conditions at Dome C, Antarctica (Berhanu et al., 2014;[START_REF] Frey | Photolysis imprint in the nitrate stable isotope signal in snow and atmosphere of East Antarctica and implications for reactive nitrogen cycling[END_REF]. These large negative values indicate that snow nitrate photolysis would induce large isotope fractionation which leave the nitrate remaining in the snowpack enriched in heavier isotopes (i.e., 15 N and 18 O). In comparison, Δ 17 O(NO 3 -) in snow will not be disturbed by photolysis directly. However, part of the photolysis product can undergo recombination reactions to reform nitrate before escaping from snow (i.e., the cage effect) [START_REF] Mccabe | Oxygen isotopic fractionation in the photochemistry of nitrate in water and ice[END_REF][START_REF] Meusinger | Laboratory study of nitrate photolysis in Antarctic snow. I. Observed quantum yield, domain of photolysis, and secondary chemistry[END_REF]. This process results in exchanges of oxygen atom with snow water, leading to decreases in snow Δ 17 O(NO 3 -) and δ 18 O(NO 3 -). These isotope effects in snow nitrate photolysis have been documented in multiple snowpack studies across east Antarctica, with increasing δ 15 N and decreasing Δ 17 O(NO 3 -)/δ 18 O(NO 3 -) with depth [START_REF] Erbland | Air-snow transfer of nitrate on the East Antarctic Plateau-Part 1: Isotopic evidence for a photolytically driven dynamic equilibrium in summer[END_REF][START_REF] Frey | Photolysis imprint in the nitrate stable isotope signal in snow and atmosphere of East Antarctica and implications for reactive nitrogen cycling[END_REF].

The degree of the photo-driven post-depositional processing is influenced by several factors including actinic flux, snow light-absorbing impurities (e.g., black carbon, organic acid and mineral dust) and snow accumulation rate [START_REF] Zatko | The influence of snow grain size and impurities on the vertical profiles of actinic flux and associated NOx emissions on the Antarctic and Greenland ice sheets[END_REF]. Snowpit observations from coastal to inland Antarctica reveal that the degree of the post-depositional processing and the induced isotope effects vary dramatically with snow accumulation rate [START_REF] Erbland | Air-snow transfer of nitrate on the East Antarctic Plateau-Part 1: Isotopic evidence for a photolytically driven dynamic equilibrium in summer[END_REF][START_REF] Shi | Investigation of post-depositional processing of nitrate in East Antarctic snow: isotopic constraints on photolytic loss, re-oxidation, and source inputs[END_REF]. Snow accumulation rate determines the residence time of nitrate in the snow photic zone where photolysis occurs and is defined as 3 times the e-folding depth of actinic flux in snow, and thus at sites with high snow accumulation rate the degree of post-depositional processing will be limited.

Distinct seasonality in the concentration and isotopes of snowpack nitrate were observed at Summit Greenland (Geng et al., 2014;[START_REF] Hastings | Seasonal variations in N and O isotopes of nitrate in snow at Summit, Greenland: Implications for the study of nitrate in snow and ice cores[END_REF]. The seasonality of δ 15 N was attributed to the variations in NO x sources [START_REF] Hastings | Seasonal variations in N and O isotopes of nitrate in snow at Summit, Greenland: Implications for the study of nitrate in snow and ice cores[END_REF] and a later study by [START_REF] Fibiger | The preservation of atmospheric nitrate in snow at Summit, Greenland[END_REF] further suggested at this site nitrate is largely preserved and its isotopic composition is representative of atmospheric nitrate. The effect of post-depositional processing was thought to be minimum at Summit [START_REF] Hastings | Seasonal variations in N and O isotopes of nitrate in snow at Summit, Greenland: Implications for the study of nitrate in snow and ice cores[END_REF][START_REF] Fibiger | The preservation of atmospheric nitrate in snow at Summit, Greenland[END_REF], largely due to the high snow accumulation rate (65 cm of accumulated snow per year) [START_REF] Dibb | Snow accumulation, surface height change, and firn densification at Summit, Greenland: Insights from 2 years of in situ observation[END_REF]. Nevertheless, there is evidence that post-depositional processing is active at this site. For example, [START_REF] Burkhart | Seasonal accumulation timing and preservation of nitrate in firn at Summit, Greenland[END_REF] and [START_REF] Dibb | Seasonal variations in the soluble ion content of snow at Summit. Greenland: Constraints from three years of daily surface snow samples[END_REF] have estimated < 7 % to 25 % loss of nitrate after deposition based on concentration measurements. Regardless of the various degrees of post-depositional processing of snow nitrate at Summit suggested by different studies, the large isotope fractionation factors associated with snow nitrate photolysis may induce significant isotope effects even for relatively small degree of post-depositional processing.

In this study, in order to investigate the impacts of snow nitrate photolysis on the preservation of nitrate and its isotopes at Summit, Greenland, we used a snow photochemical column model (TRANSITS, Transfer of Atmospheric Nitrate Stable Isotopes To the Snow, [START_REF] Erbland | Air-snow transfer of nitrate on the East Antarctic Plateau-Part 2: An isotopic model for the interpretation of deep ice-core records[END_REF] to simulate the recycling of nitrate at the air-snow interface, and compared the modeled seasonal variations in snowpack nitrate concentrations and isotopes with observations. The results should add insights into the preservation of nitrate at high snow accumulation sites and shied lights on the interpretation of ice-core nitrate and its isotopes.

Model description

TRANSITS is a multi-layer, 1-D model that simulates the recycling of nitrate at the air-snow interface, as well as the preservation of nitrate and its isotopes. In brief, the model divides a year into 52-time steps (i.e., weekly temporal resolution) and at each time step the snowpack is divided into 1 mm layers where photolysis of nitrate and the associated NO 2 production are calculated according to the depth-dependent actinic flux and nitrate concentration. NO 2 is then transported to the overlying atmosphere where it is re-oxidized to nitrate. At the next time step, a portion of the reformed nitrate together with primary nitrate originating from long-range transport deposit to snow surface. When snowfall occurs, the snowpack moves down a certain depth and the newly deposited snow on the top is immediately re-divided into 1 mm layers. A snow layer is archived once it is buried below the photic zone.

At each step, the model also calculates the isotope effects associated with the recycling of nitrate at the air-snow interface. In the model, nitrogen isotope fractionation mainly occurs during the photolysis of snow nitrate with a wavelength sensitive fractionation constant ε p , and another fractionation occurs during the deposition of nitrate with a fractionation constant ε d . The effect on oxygen isotopes is only calculated for Δ 17 O, which is caused by 1) exchange of oxygen atoms with water during snow nitrate photolysis (i.e., the cage effect), and 2) the local atmospheric NO-NO 2 cycling and the subsequent conversion of NO 2 to HNO 3 .

To run the model, actinic flux and its e-folding depth in snowpack, snow accumulation rate, as well as other atmospheric properties including the boundary layer height, surface ozone and HO x concentrations are needed. Additional model inputs are the flux of primary nitrate from long-range transport (F pri , the ultimate source of nitrate to the ice sheet) and its isotopic composition (i.e., δ 15 N and Δ 17 O).

In this study, we run the model from the year 2004 to 2007 constrained by observations of local conditions at Summit. The modeled snow nitrate concentration and isotope profiles were then compared with the observations (Geng et al., 2014).

Model parameterization and initiation are described in the following section.

Model inputs

Atmospheric characterization

The overlying atmosphere at Summit was assumed to be a well-mixed one-dimensional box with constant boundary layer height of 156 m [START_REF] Cohen | Boundary-layer dynamics and its influence on atmospheric chemistry at Summit, Greenland[END_REF], where primary nitrate and snow-sourced nitrate are mixed. Weekly air temperature, surface pressure, surface ozone concentration and total column ozone (TCO) at Summit were obtained from the NOAA ozonesonde dataset (https://www.esrl. noaa.gov/gmd/ozwv/ozsondes/sum.html). Local OH, peroxyl radicals (RO 2 , HO 2 ) and BrO concentrations used to calculate the cycling of NO and NO 2 and the subsequent reformation of HNO 3 were parameterized as described in SI.

Radiative transfer and nitrate photolysis rate in snow

The actinic flux in snow was obtained by using the Troposphere Ultraviolet and Visible (TUV) radiation model [START_REF] Madronich | Changes in biologically active ultraviolet radiation reaching the Earth's surface[END_REF] and the Two-stream Analytical Radiative TransfEr in Snow (TARTES) model [START_REF] Libois | Influence of grain shape on light penetration in snow[END_REF]. Downward actinic flux spectrum at snow surface from 280 to 350 nm in 1 nm increments was calculated using the TUV model constrained by the observed TCO.

The radiative transfer inside the snowpack was then computed using the TARTES model. Given Summit snow physical and chemical properties, we calculated an e-folding depth of 12.3 cm which is comparable to other studies (SI).

The photolysis rate constant of snow NO 3 -was calculated by:  

Where I is the actinic flux as a function of wavelength and depth in snowpack, Φ and σ is the quantum yield and absorption cross section of nitrate photolysis, respectively. To calculate J(z), we used the absorption cross sections of 14 NO 3 -and 15 NO 3 -calculated by the ZPE shift method from [START_REF] Berhanu | Laboratory study of nitrate photolysis in Antarctic snow. II. Isotopic effects and wavelength dependence[END_REF] and the depth and wavelength dependent I calculated using the TARTES model. A quantum yield of 0.002 was estimated based on observed j 0 (NO 3 -) in surface snow (SI).

Flux of primary nitrate (F pri ) and the export fraction

Primary nitrate from long range transport was assumed to be the only external nitrate source for Summit. Given the mean snow accumulation rate (250 kg m -2 a -1 ), and the mean snowpack nitrate concentration (117 ng g -1 ) at Summit, a minimum F pri of 6.610 -6 kgN m 2 a -1 was estimated and used in the model. This value is at the same order of magnitude as calculated by [START_REF] Zatko | The impact of snow nitrate photolysis on boundary layer chemistry and the recycling and redistribution of reactive nitrogen across Antarctica and Greenland in a global chemical transport model[END_REF] using the GEOS-Chem model (~ 210 -6 kgN m 2 a -1 ). In order to investigate the effect of the photo-driven post-depositional processing on snowpack nitrate profiles, we assumed that F pri was equally distributed in 52 weeks in a year, and with constant δ 15 N and Δ 17 O values of 0‰ and 30‰, respectively. The δ 15 N and Δ 17 O values are close to their observed annual average in Summit snow (Geng et al., 2014).

Another parameter influencing the preservation of nitrate is the export fraction, f exp , which represents the fraction of the snow sourced NO x and nitrate transported away from the site of photolysis via wind. According to Summit conditions, we estimated a f exp of 0.15 (SI) following the method used by [START_REF] Erbland | Air-snow transfer of nitrate on the East Antarctic Plateau-Part 2: An isotopic model for the interpretation of deep ice-core records[END_REF].

Calculation of the isotope effects

The nitrogen isotope fractionation constant ( 15 ε p ) during photolysis was calculated from the ratio of 14 NO 3 -and 15 NO 3 -photolysis rates ( 15 ε p = J 15 / J 14 -1), while for the fractionation constant associated with nitrate deposition, we adopted a ε d of 10 ‰ following [START_REF] Erbland | Air-snow transfer of nitrate on the East Antarctic Plateau-Part 1: Isotopic evidence for a photolytically driven dynamic equilibrium in summer[END_REF]. As the photolysis rate constant is wavelength sensitive, the calculated 15 ε p varies seasonally (Figure 3a). For oxygen isotopes, the Δ 17 O of the reformed nitrate in the air was assumed to be 2/3 of Δ 17 O(NO 2 ), and Δ 17 O(NO 2 ) was estimated according to the O 3 and BrO oxidation of NO to NO 2 versus HO 2 and RO 2 oxidation in the NO-NO 2 cycling. The Δ 17 O value of bulk O 3 was (22.9 ± 1.9) ‰ [START_REF] Vicars | Measurement of the 17 O-excess (Δ 17 O) of tropospheric ozone using a nitrite-coated filter[END_REF], that of BrO was 34.3 ‰, and other oxidants were 0‰. We assumed a cage effect of 15 % following [START_REF] Erbland | Air-snow transfer of nitrate on the East Antarctic Plateau-Part 2: An isotopic model for the interpretation of deep ice-core records[END_REF].

Model initiation

The model was initiated by deposition of primary nitrate mixed with snow-sourced nitrate formed through NO 2 emitted from the snowpack. The flux and isotope composition of the primary nitrate were set as described in the previous section. A real snowpack with a depth of 2.1 m and known nitrate concentration and isotope profiles (Geng et al., 2014) was used for the snowpack at time (t) = 0. We run

Results and discussion

3.1 The simulated snowpack nitrate depth profiles at Summit, Greenland -concentration was (115 ± 55) ng g -1 , similar to the observed value of (117 ± 62) ng g -1 . The modeled concentration profile displays high variability which is likely caused by variations in weekly snow accumulation.

Nevertheless, clear summer peaks and winter valleys similar to the observations are seen in the modeled profile. Since the input of primary nitrate remained the same throughout a year, the summer high nitrate concentration in the model was caused by the relative low snow accumulation rate in late spring and early summer (Figure S1)

and then the redistribution of snow nitrate caused by the post-depositional processing.

In ), although with some discrepancies, the modeled seasonal pattern reproduced the observations reasonably well. The discrepancies could be due to that the model didn't consider δ 15 N variations of F pri , and the interannual variability in snow accumulation. In addition, the model didn't consider the seasonal differences in local NO x chemistry and the associated isotope effect [START_REF] Jarvis | Influence of local photochemistry on isotopes of nitrate in Greenland snow[END_REF]. The modeled δ 15 N(NO 3 -) ranged from -9.5 ‰ to 11.9 ‰ in a year with a spring peak. In comparison, the observed δ 15 N(NO 3 -) varies from -12.6 ‰ to 10.1 ‰ over a year, and also with a spring peak [START_REF] Hastings | Seasonal variations in N and O isotopes of nitrate in snow at Summit, Greenland: Implications for the study of nitrate in snow and ice cores[END_REF]Geng et al. 2014). In our model, since δ 15 N(NO 3 -) of

  the model from July 2004 to July 2007. Snow accumulates weekly (i.e., 52-time steps in year) on the top of the pre-existing snowpack. The weekly snow accumulation rate used in the model is shown in FigureS1, which were obtained by averaging the observed snow accumulation of the same week (week 1 th to week 52 th ) of a year over the 5 years' of observations at Summit from 2003 to 2007 (data are available at ftp://ftp.summitcamp. org/pub/data/GEOSummit/Bales_UCM/ BambooForest/BambooForestAccumulationLog.xls). This averaged weekly snow accumulation rate was repeated for 3 years in the model. Average instead of real accumulation data were used to avoid negative values in some weeks due to wind blowing which causes net loss instead of gain of snow. After three years' simulation, the snow nitrate concentration and isotope profiles above the pre-existing snowpack were taken to compare with observations at Summit previously reported byGeng et al. (2014).

Figure 1 .

 1 Figure 1. Comparison between the observed and modeled snowpack nitrate profiles. We used same snow accumulation rate for each year in the model. The measured minimum Δ 17 O(NO 3 -) is used as indicator of June-July when local photochemistry is most active.

Figure 1

 1 Figure1shows the observed and modeled weekly snowpack nitrate concentration

FFigure 2 .

 2 Figure 2. Weekly distribution of photolysis flux (FP) and deposition flux (FD) and their nitrate isotopic compositions.

  particular, without photolysis, the concentration peak should appear in late spring/early summer when snow accumulation rate was low. But throughout summer, nitrate deposited earlier was recycled back to the surface continuously, shifting the peak to appear later in summer. The recycling relies on strong summer solar radiation which activates both snow chemistry and atmospheric chemistry. The result highlights the importance of local chemistry in the seasonal distribution of snow nitrate concentrations.

	though the model didn't consider local winter chemistry either. In addition, cage
	effect during the photolysis would further reduce Δ 17 O(NO 3	-) in snow, but this effect is
	negligible as discussed in section 3.3.
	For δ 15 N(NO 3	-
	The strong photolysis in summer also explains why the modeled Δ 17 O(NO 3	-)
	deviated by about -3 ‰ from primary nitrate (Δ 17 O(NO 3	-) = 30 ‰). In summer,
	nitrate reformed in the overlying atmosphere is mainly through OH oxidation of NO 2 .
	In the model, nitrate formed through this process possessed Δ 17 O of (19.7 ± 0.3) ‰ on
	average. This value is close to the model results (18.9‰) by Kunasek et al. (2008) who
	used a box model assuming local NO x chemistry is the only nitrate source and produced
	summer Δ 17 O(NO 3	-) (2-7) ‰ lower than the observations. In our model, the
	Δ 17 O(NO 3	-) of F pri was 30 ‰, and F pri mixed with the reformed nitrate resulting in 3 ‰
	lower Δ 17 O(NO 3	-) in summer than in other seasons (Figure 2c). In comparison, the
	observed seasonal Δ 17 O(NO 3	-) change is about 9 ‰, suggesting that the observed
	seasonality of Δ 17 O(NO 3	-) at Summit is probably mainly caused by the seasonal
	differences in Δ 17 O(NO 3	-) of F pri which was not taking into account in our model,

Acknowledgements:

L.G. acknowledges financial support from the National Natural Science Foundation of China (Awards: 41822605 and 41871051) and the Fundamental Research Funds for Central Universities. This work was partially supported by the French national programme LEFE/INSU, the ANR grants ANR-15-IDEX-02 (project IDEX Université Grenoble Alpes) and ANR-16-CE01-0011-01 (EAIIST project) of the French Agence Nationale de la Recherche (J.S. and J.E.). The French Polar institute (Institut Polaire Français -program SUNITEDC 1011) is thanked for field and funding support (JS, JE). B. A. acknowledges support from NSF (award PLR 1542723). Z. J. thanks John Robinson for his assistance in starting the TRNASITS model.

To discern the processes leading to the seasonal isotope patterns, we investigated the weekly nitrate deposition flux (FD) and its isotopes, as well as the weekly flux of snow-sourced nitrate (FP) and its isotopes in the model. Figure 2 displays the magnitude and isotope composition of nitrate in FP and FD. During mid-summer when actinic flux reached its maximum, FP also reached a maximum (and is zero in winter).

FD was a mixture of F pri and FP, so it also reached a maximum in summer due to the contribution of FP. This in part explains the modeled summer peak of nitrate concentration.

The δ 15 N of FP was severely depleted compared to F pri . δ 15 N of FP gradually increased from the onset of photolysis, and reached the highest in mid-summer and decreased after that (Figure 2b). This is mainly caused by the wavelength-dependent ε p which varied from -57 ‰ to -87 ‰ at Summit (Figure 3a) and reached its highest value in mid-summer. The δ 15 N(NO 3 -) of FD again was a combined effect of FP and F pri . ) was observed [START_REF] Erbland | Air-snow transfer of nitrate on the East Antarctic Plateau-Part 1: Isotopic evidence for a photolytically driven dynamic equilibrium in summer[END_REF][START_REF] Morin | Tracing the origin and fate of NOx in the Arctic atmosphere using stable isotopes in nitrate[END_REF][START_REF] Walters | Assessing the Seasonal Dynamics of Nitrate and Sulfate Aerosols at the South Pole Utilizing Stable Isotopes[END_REF]. This is due to the contribution of snow-sourced nitrate that is depleted in δ 15 N relative to atmospheric nitrate. The isotope effect in δ 15 N during the deposition of nitrate was also calculated but turned out to be negligible (SI).

After deposition, the post-depositional processing enriches δ 15 N(NO 3 -) in snow through photolysis until that snow layer is buried under the photic zone. Here we defined the enrichment in snow δ 15 N(NO 3 -) caused by the photolysis as PIE (the photolysis-induced isotope effect), which was the highest in the 18 th week of the year, corresponding to the highest remaining fraction (Figure 3a). with F pri (Δ 17 O = 30 ‰), leading to a summer minimum Δ 17 O of FD that was 2.9 ‰ lower than that of F pri . An additional ~ 0.1 ‰ difference was induced upon archival from the cage effect. The lost fraction (f loss ) of snow nitrate upon archival was plotted in Figure 3a, calculated as the difference in nitrate concentration of an archived layer to the concentration when it was at the surface. As shown in Figure 3a, throughout a year, the f loss varied from 1.8 % to 21.3 %, similar to the < 7 % to 25 % loss estimated by [START_REF] Burkhart | Seasonal accumulation timing and preservation of nitrate in firn at Summit, Greenland[END_REF] and [START_REF] Dibb | Seasonal variations in the soluble ion content of snow at Summit. Greenland: Constraints from three years of daily surface snow samples[END_REF]. In particular, [START_REF] Dibb | Seasonal variations in the soluble ion content of snow at Summit. Greenland: Constraints from three years of daily surface snow samples[END_REF] calculated the average NO 3 -concentrations in fresh and buried snow layers, and found a mean of ~ 9 % loss which is in good agreement with our calculated mean f loss of (10.6 ± 6.7) %. Note f loss calculated here was referred to a specific archived layer relative to when it was at the surface, and part of the loss was actually recycled to layers above that specific layer. Therefore, the net loss integrated over a certain period should be less than the loss of a specific layer.

Loss of snow nitrate due to photolysis at Summit

Here we calculated the annual net loss f loss as follows:

Where F a represents the modeled archived flux of nitrate (6.5210 -6 kgN m 2 a -1 ), and thef loss_annual was calculated as 1.7 %. This is consistent with the annual mean

Conclusions

In this study we applied the TRANSITS model to investigate the impact of the photo-driven post-depositional processing on the preservation of nitrate and its isotopes at Summit Greenland. The results suggest that the photo-driven post-depositional processing is very active at Summit, causing significant redistribution of snow nitrate accompanied by isotope effects in the photic zone. Overall, our results reinforce the effects of post-depositional processing on ice-core nitrate concentrations and isotopes even at high snow accumulation rate sites, and such effects have to be quantified and corrected in order to use ice-core nitrate records to retrieve past information on NO x emissions and abundance and atmospheric oxidation capacity.