The influence of snow grain size and impurities on the vertical profiles of actinic flux and associated NO x emissions on the Antarctic and Greenland ice sheets

Abstract. We use observations of the absorption properties of black carbon and non-black carbon impurities in near-surface snow collected near the research stations at South Pole and Dome C, Antarctica, and Summit, Greenland, combined with a snowpack actinic flux parameterization to estimate the vertical profile and e-folding depth of ultraviolet/near-visible (UV/near-vis) actinic flux in the snowpack at each location. We have developed a simple and broadly applicable parameterization to calculate depth and wavelength dependent snowpack actinic flux that can be easily integrated into large-scale (e.g., 3-D) models of the atmosphere. The calculated e-folding depths of actinic flux at 305 nm, the peak wavelength of nitrate photolysis in the snowpack, are 8–12 cm near the stations and 15–31 cm away (>11 km) from the stations. We find that the e-folding depth is strongly dependent on impurity content and wavelength in the UV/near-vis region, which explains the relatively shallow e-folding depths near stations where local activities lead to higher snow impurity levels. We calculate the lifetime of NO x in the snowpack interstitial air produced by photolysis of snowpack nitrate against wind pumping (τ wind pumping ) from the snowpack, and compare this to the calculated lifetime of NO x against chemical conversion to HNO 3 (τ chemical ) to determine whether the NO x produced at a given depth can escape from the snowpack to the overlying atmosphere. Comparison of τ wind pumping and τ chemical suggests efficient escape of photoproduced NO x in the snowpack to the overlying atmosphere throughout most of the photochemically active zone. Calculated vertical actinic flux profiles and observed snowpack nitrate concentrations are used to estimate the potential flux of NO x from the snowpack. Calculated NO x fluxes of 4.4 × 10 8 –3.8 × 10 9 molecules cm −2 s −1 in remote polar locations and 3.2–8.2 × 10 8 molecules cm −2 s −1 near polar stations for January at Dome C and South Pole and June at Summit suggest that NO x flux measurements near stations may be underestimating the amount of NO x emitted from the clean polar snowpack.


M. C. Zatko et al.: Snow properties and associated NO x emissions
. Photochemical reactions in the snowpack have significant implications for the oxidizing capacity of the boundary layer over snow-covered regions Grannas et al., 2007 and references within;Thomas et al., 2012) and for the preservation of trace species such as H 2 O 2 and NO − 3 in ice cores (Lamarque et al., 2011;Mulvaney et al., 1998).
The formation and deposition of atmospheric nitrate (particulate NO − 3 and HNO 3 (g)) is typically thought to be a permanent sink for gaseous NO x (NO x = NO and NO 2 ) in the troposphere because gas-phase nitric acid (HNO 3 (g)) is not readily photolyzed at wavelengths (λ) >325 nm (Johnston and Graham, 1973). However, nitrate deposited to the snowpack can be re-released to the atmosphere both by photolysis (as NO x ) (Davis et al., 2008;Honrath et al., 1999Honrath et al., , 2002 and evaporation (as HNO 3 ) (Mulvaney et al., 1998) at depths below the snow surface followed by re-deposition to the surface snowpack (Rothlisberger et al., 2000). This is supported by observations of surface snow nitrate concentrations roughly an order of magnitude larger than nitrate concentrations at 10 cm depth in continental Antarctica snowpack Frey et al., 2009;Mayewski and Legrand, 1990;Rothlisberger et al., 2000) and by observations of an upward flux of NO x out of the snowpack in polar regions on the order of 1.3-6.7 × 10 8 molec cm −2 s −1 (Beine et al., 2002;Davis et al., 2004;Honrath et al., 1999;Jones et al., 2001;Oncley et al., 2004). The results of earlier isotopic (δ 15 N) studies disagree on whether evaporation or photodenitrification is the dominant process of nitrate removal from the snowpack (Blunier et al., 2005;Savarino et al., 2007), but results from Frey et al. (2009) and Erbland et al. (2012) suggest that photodenitrification is the dominant contributor to post-depositional processing of NO − 3 in East Antarctica (Dome C). The dominance of photodenitrification is consistent with observations of downward fluxes of HNO 3 to the snowpack . Although both NO x and HONO are produced from NO − 3 photolysis, observations of the upward flux of NO x above the snow surface at Summit, Greenland, were roughly an order of magnitude larger than the measured flux of HONO . Factors such as snow accumulation rate, snow acidity, and the gradient of temperature within the snow may influence the redistribution of snowpack nitrate (Rothlisberger et al., 2000).
Several process-based modeling studies have calculated the flux of NO x from the high-latitude snowpacks at Neumayer, Antarctica (Wolff et al., 2002), Ny-Ålesund, Svalbard (France et al., 2010), Summit, Greenland , Dome C, Antarctica (France et al., 2011), and Barrow, Alaska . Estimates of depth-integrated snowpack actinic flux are required to model the flux of NO x from the snowpack, where actinic flux is defined as the irradiance impingent through a given point in all (4π) directions.
Using surface irradiances from the British Antarctic Survey radiative transfer model (Gardiner and Martin, 1997) and a snowpack radiative transfer model (Grenfell, 1991), Wolff et al. (2002) calculated an e-folding depth of actinic flux in snowpack (z e ) of 3.7 cm at λ = 320 nm, where z e is defined as the depth in the snowpack where the actinic flux is 1/e of the surface value (Warren et al., 2006). This e-folding depth is now thought to be too shallow, and measured and calculated z e from later studies range from 6-9 cm at Ny-Ålesund, 10-20 cm at Dome C, and to 9-14 cm at Barrow (France et al., 2010(France et al., , 2011. Snowpack z e values are dependent upon snow physical and optical properties (e.g., grain size, bulk density, refractive index) as well as the type and concentration of impurities in the snow (e.g., black carbon). Snow albedo is also dependent upon snow physical and optical properties, which is highlighted in a recent study by Carmagnola et al. (2012). Pure ice is a moderate absorber of near-infrared and a strong absorber of infrared radiation, but an extremely weak absorber of ultraviolet (UV) radiation, the latter of which is relevant for photochemistry. At UV and near-UV wavelengths, snow grains are much more efficient scatterers than absorbers; however, multiple scattering of radiation in the snowpack increases the probability of absorption by ice grains and impurities in the snow. Because ice is so weakly absorbing at these wavelengths, the absorption in natural snow is dominated by impurities, even in the cleanest snow. Dust, brown carbon, and humic-like substances (HULIS) also absorb radiation and have a much stronger wavelength dependence across the ultraviolet/near-visible (UV/near-vis) compared to black carbon (BC) (France et al., 2011Hoffer et al., 2006). However, while the optical properties of HULIS have been estimated in several studies Hoffer et al., 2006;Kirchsetter et al., 2004;Roden et al., 2006;Voisin et al., 2012), the range of optical properties for HULIS is large. Also, the amount of HULIS in the Arctic and Antarctic snowpack has only been quantified in one recent study .
Since snow impurities dominate absorption in the UV/near-vis λ range, here we use optical measurements of particulate material collected on filters through which snow meltwater has been passed. We incorporate these impurity measurements into a simple parameterization to calculate depth-dependent actinic flux profiles in deep snowpack for λ between 289-850 nm in order to estimate the flux of NO x from the snowpack via NO − 3 photolysis. The parameterization is derived (in Sect. 2.3 below) from a well-tested discrete-ordinate-method radiative transfer model for optically thick snow and ice (Grenfell, 1991), and can easily be incorporated into large-scale models such as global climate models and global chemical transport models. To estimate photolysis in the snow, we calculate the depth profile of actinic flux using the parameterization and our observations of the absorption properties of snow. We use the actinic flux parameterization to evaluate the sensitivity of the e-folding depth to ice grain size (effective grain radius), wavelength, solar zenith angle, and snowpack BC and non-black carbon (nonBC) concentrations at λ = 305 nm. Results from the parameterization suggest that actinic flux is significant at depths greater than 1.5 m in the snow. We evaluate the assumption made in previous studies (France et al., 2010(France et al., , 2011Wolff et al., 2002) that all NO x produced in the snowpack will be ventilated to the overlying atmosphere by comparing the calculated depth-dependent lifetime of NO x in the snowpack interstitial air against physical and chemical sinks. The calculated actinic flux profile is integrated over snow depth and wavelength to compute the total flux of NO x from the snowpack, F NO x . Our calculated F NO x is compared to observations from inland sites in Antarctica and Greenland.

BC and nonBC absorption from filter samples
The amount of absorption from BC and nonBC material in the snowpack must be known to calculate the actinic flux profile using our parameterization. In this study, the amount of BC and nonBC absorption is estimated from optical measurements of impurities from snow collected on filters. Snow samples were collected for impurities in January 2004 at sites < 0.5 to 11 km from Dome C Station in Antarctica, and in June 2007 at sites 20-40 km from Summit Station in Greenland (see Table 1). The snow samples were processed in the field. Each sample was melted and filtered through a 0.4 µm Nuclepore filter to extract the particulate material in the meltwater. A maximum of 10 % of the particulate matter in the snow sample is lost during filtering. The filters were transported back to the University of Washington where the optical properties of the filters were measured using the ISSW spectrophotometer as described in Grenfell et al. (2011). The ISSW spectrophotometer uses an integrating sphere and integrating sandwich technique to determine the absorption spectrum in units of optical depth, T (λ) (dimensionless, e.g., cm 2 cm −2 ), from λ =300-750 nm of particu- Idealized absorption profiles (expressed in absorption optical depth, T (λ)) of BC (black) and nonBC (red) material from Grenfell et al. (2011) andHoffer et al. (2006). Also shown are absorption profiles of snow samples collected in remote Dome C (blue), remote Summit (green), and near-station Dome C (cyan). late material on filters while removing losses from scattering by the filter and the collected aerosols (Grenfell et al., 2011).
The spectral absorption measured by the spectrophotometer for each filter is conventionally characterized by an Angström exponent (Å tot ) associated with the absorption of total (BC + nonBC) impurities on each filter between two visible wavelengths (λ 1 and λ 2 ) according to the formulå where the total optical depth, T tot (λ), describes the absorption of all the impurities on each filter at a given λ. A larger Angström exponent indicates a greater absorption at shorter wavelengths ( Fig. 1), resulting in a more brownish color for the sample.
MeasuredÅ tot from λ = 450-600 nm is used together with the assumed values ofÅ BC = 1 andÅ nonBC = 5 (Doherty et al., 2010, and references within) to determine the fraction of absorption from λ = 450-600 nm due to BC impurities (f BC 450−600 ) from the relation where λ o = 525 nm. Since the absorption of radiation by BC is relatively constant with wavelength, f BC 450−600 is used to determine the fraction of absorption due to BC in the λ = 650-700 nm range (f BC 650−700 ), where BC is the dominant absorber of radiation (Grenfell et al., 2011). The maximum possible loading of BC on each filter (L maxBC , g cm −2 ) for a given T tot is calculated by assuming that all the absorption from λ = 650-700 nm is due to BC (f BC 650−700 = 1) and calibrating the attenuation of transmitted light through the sample filter from λ = 650-700 nm against a calibration curve created with commercially produced BC as described in Grenfell et al. (2011).
The best estimate of the BC loading on each filter, L BC (g cm −2 ), is determined by The best estimate of BC concentration on a filter, C BC (gC g −1 ), is calculated by multiplying L BC by the exposed area of the filter, A (cm 2 ), and dividing by the mass of meltwater filtered, M (g), as shown in Eq. (4): The maximum concentration of BC on a filter, assuming BC is responsible for the total absorption in the 650-700 nm λ interval (C maxBC ), is calculated as shown in Eq. (5): The total measured absorption optical depth (T tot ) of each filter can be represented as the sum of the optical depth associated with BC material (T BC ) and the optical depth associated with nonBC material (T nonBC ) on each filter.
T tot is measured directly by the spectrophotometer. T BC is calculated by multiplying L BC by the mean average mass absorption efficiency of BC (β BC ∼48 000 m 2 g −1 BC at λ = 675 nm), which is determined from Mie scattering calculations (R. Brandt, personal communication, 2010). We calculate T nonBC at various wavelengths using Eq. (7): Here, we assumeÅ BC = 1 andÅ nonBC = 5 in the wavelength range λ = 298-412 nm to calculate the optical properties of BC and nonBC (including T BC and T nonBC ) over that λ range. We use the optical properties of BC and nonBC to calculate the actinic flux profile in the snow at South Pole, Summit, and Dome C. We discuss the sensitivity of assumingÅ nonBC = 5 in Sect. 3.6.

Inherent optical properties of BC, nonBC, and snow
In addition to the concentration of light-absorbing impurities or the amount of absorption due to impurities in the snowpack, the inherent optical properties (IOPs) of the snowpack must also be known or estimated in order to calculate snowpack actinic flux. Inherent optical properties (IOPs), such as extinction coefficients (Kext) and co-albedos of single scattering (c ), describe the absorption, scattering, and extinction properties of a material (e.g., ice grains, BC, HULIS). Kext (cm −1 ) describes the amount of radiation removed from a beam of radiation traveling through a volume with a given cross-sectional area and length. c (dimensionless, e.g., cm cm −1 ) describes the amount of absorption compared to extinction (scattering + absorption) in a medium. IOPs vary with λ for most materials. The effective IOPs for a given λ needed for a snowpack containing contaminants can be written where Kext tot is the total extinction coefficient in the impurity-laden snowpack and Kext i represent the individual extinction coefficients for ice and impurities. Here, i indicates the components of the snowpack: ice and impurities (BC and nonBC). c eff is the effective co-albedo of single scattering (1 single scattering albedo) of the impurity-laden snowpack, and c i represents the individual co-albedos of single scattering for ice and impurities in the snow. The extinction coefficients and co-albedos of single scattering for snow, BC, and nonBC used in Eqs. (8) and (9) are given below. The extinction coefficient for snow (Kext snow ) can be expressed as (Wiscombe and Warren, 1980) where Q ext is the extinction efficiency for snow grains (dimensionless, 2.01 at 305 nm), ρ snow is snow density (g cm −3 ), ρ ice is the density of ice (0.917 g cm −3 ), and r e is the radiation equivalent mean grain radius (cm) (Hansen and Travis, 1974). r e is inversely proportional to specific surface area (SSA), where SSA = 3/(r e · ρ ice ).  The extinction coefficient for BC (Kext BC ) in the snow can be calculated using the following equation: where c BC is the single scattering co-albedo for BC (0.61 at 305 nm (R. Brandt, personal communication, 2010)). The wavelength dependence of the IOPs for both snow grains and soot particles are determined from Mie theory. The extinction coefficient of nonBC material (Kext nonBC ) is calculated using where c nonBC is the co-albedo of single scattering for nonBC material. The contribution of scattering by BC and nonBC is insignificant because Kext tot is dominated by snow grain scattering (see denominator of Eq. (9)). Also, the co-albedos of single scattering cancel in the numerator of Eq. (9), leaving only the terms associated with the absorption of BC, nonBC, and snow grains. Therefore any value of c nonBC (between 0 and 1) can be used in the parameterization (here, we use c nonBC = 1). In Eq. (12), if additional absorbers are to be included, the attenuation coefficient can be easily developed from a direct extension of Eqs. (8) and (9) and appropriate modifications to equations of the form of Eq. (11).

Snowpack actinic flux parameterization
Once the IOPs are calculated for snow grains and impurities and combined to determine the effective IOPs of the snowpack at various λ, the effective IOPs are used to calculate vertical profiles of the actinic flux. The snowpack radiative transfer model used here is a 4-stream plane parallel radiative transfer model that uses the discrete ordinates method (DOM) with a δ-M transformation as described in Grenfell (1991). The 4-stream approximation provides better than 1 % numerical accuracy in albedo and absorptivity relative to exact high-order models for optical properties representative of snow (Wiscombe, 1977), and produces results identical to those from the DISORT model (Stamnes et al., 1988). We use this snowpack radiative transfer model (Grenfell, 1991) to develop a parameterization to calculate the depth-dependent actinic flux profile in snowpacks. The motivation to develop this parameterization is based on the need to include snowpack chemical processes in large-scale models of the atmosphere in order to estimate the impact of these processes on regional-scale nitrogen and oxidant budgets. This parameterization is based on the δ-Eddington formulation (Wiscombe and Warren, 1980) modified by a correction factor from the 4-stream DOM model (Grenfell, 1991), and accounts for the spatio-temporal variations in the properties of the snowpack and ambient lighting conditions. New values of the optical properties of ice (Warren and Brandt, 2008) have been incorporated, which indicate much greater UV transmission in the snowpack than in previous work (Wolff et al., 2002). We vary r e with depth in the modeled snowpack following observed vertical r e profiles in snow pits near Dome C station (Gallet et al., 2011), but the vertical r e profiles and snow density in this parameterization can easily be altered in order to calculate actinic flux profiles in a wide range of snow types. These equations retain the general capability to vary the properties of the snow to represent actinic flux accurately over a wide range of snow conditions present in Antarctica and Greenland, provided that the snow cover is deeper than three times z e (3z e ). By this depth, 95% of radiation in snow has been attenuated. This parameterization is straightforward to implement into large-scale models of the atmosphere using calculated or assumed values of C BC , f nonBC , r e and ρ snow . For collimated incident radiation at the surface (z = 0), where I o (λ, z = 0) direct is the snowpack actinic flux from direct beam radiation at the surface, F inc (λ) direct (photons cm −2 s −1 nm −1 ) is the direct downwelling irradiance at the surface which has been integrated over wavelength, µ o is the cosine of the solar zenith angle (θ), and Corr(µ o ) is a correction factor for θ (see Table 2). The magnitude of the correction factor is less than 6.4 % for all θ less than 85 • . For θ > 85 • , the correction factors are greater than 6.4 % because these θ are not well represented by the δ-Eddington approximation. However, solar radiation levels are very low at these θ, so the large correction factors have little influence on the parameterization. Because the snowpack is such a strong volume scatterer in the UV (single scattering albedo > 0.9999), the direct beam downwelling irradiance, if present, becomes negligible within 2 cm of the upper surface of a thick snowpack. Thus it is convenient to define a reference depth (z ref ) of 2 cm below which the radiation field is purely diffuse.
For z ≥z ref , I o (λ, z) direct for collimated incident radiation follows an exponential decay law that depends on the physical properties of the snowpack and the concentration of www.atmos-chem-phys.net/13/3547/2013/ Atmos. Chem. Phys., 13, 3547-3567, 2013 impurities such as BC and nonBC as follows: where G is a factor designed to treat the non-exponential decay of radiation in the top 2 cm. G is calculated in Eq. (15): and the attenuation coefficient for diffuse radiation, ϒ, For the diffuse component of the actinic flux, I o (λ, z) diffuse follows an exponential decay law beginning from the snow surface (z = 0): where F inc (λ) diffuse (photons cm −2 s −1 nm −1 ) is the diffuse downwelling irradiance at the surface, which has been integrated over wavelength. Because of strong Rayleigh scattering in the UV, there is a significant diffuse component to the incident radiation even for cloud free cases. When both the direct and diffuse components of the downwelling irradiance are present, the combined (direct + diffuse) actinic flux, I o (λ, z) (photons cm −2 s −1 nm −1 ) at a given depth (z) and wavelength (λ) is calculated as where f dif is the fraction of diffuse incident radiation compared to total (direct + diffuse) radiation and F inc (λ) tot (photons cm −2 s −1 nm −1 ) is the sum of the direct (F inc (λ) direct ) and diffuse (F inc (λ) diffuse ) downwelling irradiance at the surface. Equation (18) can be integrated over depth and wavelength to calculate the total actinic flux (II o ( λ j , z i )) (photons cm s −1 ) contributing to photochemical reactions (see Appendix A). We use the Fast-J radiative transfer program (Wild et al., 2000) in the GEOS-Chem global chemical transport model (www.geos-chem.org) (Bey et al., 2001) to calculate the diffuse and direct downwelling solar radiation at the surface at different locations in Greenland and Antarctica in seven wavelength bins between λ = 289 nm and λ = 850 nm. We specify a UV surface albedo of 0.996 in GEOS-Chem based on discrete ordinate method results (Grenfell, 1991). The above parameterization (Eq. 18) is used to examine how each variable (e.g., BC, nonBC, r e , θ) influences the actinic flux (λ = 305 nm) profile in the snowpack.

Calculating the depth dependent lifetime of NO x in snowpack
The majority of NO x associated with nitrate photolysis is produced above 3z e , since most of the radiation in snow has been attenuated above that depth. Due to our calculated 3z e > 1.5 m in some locations (Sect. 3.3), we examine whether the NO x produced via NO − 3 photolysis at depth will escape into the overlying atmosphere via wind pumping before being re-oxidized to HNO 3 within the snowpack interstitial air. Although the diffusion of NO x from the snowpack interstitial air to the overlying atmosphere will also play a role in its transport, we exclude diffusion within the snowpack interstitial air from our analysis for reasons discussed in Sect. 3.5. We define the wind pumping lifetime (τ wind pumping ) as the lifetime of NO x in the snowpack interstitial air against transport to the overlying atmosphere via wind pumping. The chemical lifetime (τ chemical ) represents the lifetime of NO x in the snowpack interstitial air against conversion to HNO 3 , BrONO 2 , and IONO 2 in the snowpack via the following reactions: The characteristic escape time of NO x (and other gaseous compounds in the snowpack) for wind pumping is calculated according to Waddington et al. (1996): where, λ s is sastrugi wavelength (cm), h is sastrugi height (cm), U is horizontal wind speed at the surface (cm s −1 ) (see Table 3), is porosity (0.673), ρ air is air density (g cm −3 ) calculated from the ideal gas law and the hypsometric equation using average summer air temperatures and the altitude of each station, µ is air viscosity (1.6 × 10 −4 g cm −1 s −2 ), K is snow permeability (8 × 10 −6 cm 2 ), and C is a constant of proportionality (∼3) (Waddington et al., 1996). The lifetime of NO x in snowpack interstitial air against conversion to HNO 3 , BrONO 2 , and IONO 2 is calculated according to Seinfeld and Pandis (1998): where X = OH, BrO, or IO, and k X is the corresponding rate constant (cm 3 molec −1 s −1 ) for Reactions (R1)-(R3) from Sander et al. (2006). The effective lifetime of NO x against chemical conversion is calculated as   (2002); Six and Warren, unpublished data; Warren et al. (1998) Wind speed (U, cm s −1 ) * * 280 (150-500) 430 (200-600) 470 (420-520) Albert and Hawley (2002); Aristidi et al. (2005); Orvig (1970) Permeability (K, cm 2 ) 8 × 10 −6 (8 × 10 −5 -8 × 10 −7 ) Waddington et al. (1996) Viscosity (µ, g cm −1 s −2 ) 1.6 × 10 −4 (1 × 10 −3 -1 × 10 −6 ) Waddington et al. (1996) Snow density (ρ, g cm −3 ) 0.36 (0.1-0.9) Albert and Shultz (2002); Gallet et al. (2011);Grenfell et al. (1994) Tortuosity (ξ , cm cm −1 ) 1.33 (0.5-4) Pinzer et al. (2010) * Sastrugi aspect ratio (height/width) of 0.1 using h from unpublished results from Six and Warren (2006) to calculate λ at Dome C. * * Wind speeds at South Pole from Orvig (1970) are 10 m wind speeds. 10 m wind speeds should be used in Eq. (19) to calculate τ wind pumping when available. Formation of HNO 3 (g) is considered a sink for snowpack NO x because the lifetime of HNO 3 (g) against photolysis (10-30 days in the tropics and longer in polar regions (Jacob et al., 1996;Tie et al., 2001)) is much longer than its lifetime against deposition to the surface in polar regions (3.5-10 h) (Slusher et al., 2002;Wang et al., 2007). Hydrolysis of BrONO 2 and IONO 2 on the surface of snow crystals to form HNO 3 and HOBr/HOI is also considered a sink for snowpack NO x . However, BrONO 2 and IONO 2 can also photolyze to Br + NO 3 and I + NO 3 , respectively (or less commonly, BrO + NO 2 and IO + NO 2 , respectively).
The lifetime of BrONO 2 with respect to photolysis is calculated as where II o ( λ j , z i ) is the total actinic flux in the λ = 289-500 nm bin at a specified depth in the snowpack, φ BrONO 2 is the quantum yield for the photolysis of BrONO 2 (0.15 for λ > 300 nm) (Sander et al., 2006), and σ BrONO 2 is the absorption cross section for BrONO 2 (Sander et al., 2006). To calculate depth-dependent τ BrONO 2 photolysis in the snowpack, we use our calculated values of II o ( λ j , z i ) at λ = 289-500 nm (wavelengths relevant to BrONO 2 photolysis) (Burkholder et al., 1995) from Eq. (18) using µ o = 60°and r e = 100 µm at local solar noon in January at Dome C and South Pole and in June at Summit. To estimate F inc at λ < 500 nm in the λ = 412-850 nm range (con-sistent with Fast-J), we multiply the amount of direct radiation in the λ = 412-850 nm wavelength bin by the fraction [(500-412 nm)/(850-412 nm)]. This simplification is appropriate given that the solar flux is relatively constant throughout the λ = 412-850 nm range. The mean σ BrONO 2 in each wavelength bin is calculated by taking the average σ BrONO 2 within each bin from Burkholder et al. (1995). The photolysis rates are summed over the bins to create a depth-dependent BrONO 2 photolysis rate from λ = 289-500 nm.
The lifetime of BrONO 2 with respect to hydrolysis is calculated as where Here, k BrONO 2 +H 2 O(s) is the first-order rate constant for uptake of BrONO 2 on the ice crystal surface (molec cm −3 s −1 ), r e is the snow grain radius (0.01 cm), D g is the gasphase molecular diffusion coefficient of BrONO 2 in air (0.2 cm 2 s −1 ), γ is the reaction probability (0.2) (Sander et al., 2006), υ is the mean molecular speed of BrONO 2 in the gas phase (3 × 10 4 cm s −1 ), and SA is the corresponding snow grain surface area per unit volume of air (177 cm 2 cm −3 ) calculated in Eq. (25):   Thomas et al. (2011), which include the effect of transport in the snow interstitial air. The vertical chemical profiles from Thomas et al. (2011) at Summit indicate firn air NO x concentrations on the order of 10 −9 mol mol −1 , which is in good agreement with measured firn air NO x concentrations at Dome C (Frey et al., 2013). We examine the sensitivity of the lifetime of NO x with respect to chemical sinks using a range of summertime concentrations for each species at each location (see Table 4 for concentration ranges).

NO x flux calculations
Nitrate photolysis in the snowpack is represented as (Warneck and Wurzinger, 1988) The total potential flux of NO x out of the snowpack from the photolysis of nitrate, F NO x (molec cm −2 s −1 ), is calculated via In Eq. (26), σ − NO 3 is the absorption cross section for nitrate photolysis (cm 2 ), φ NO x is the quantum yield for nitrate photolysis (unitless), II o ( λ j , z i ) is the depth-integrated total actinic flux from z = 0 to 3z e in a given wavelength bin (photons cm s −1 ), and [NO − 3 ] is the average nitrate concentration over the integration depth (molec cm −3 ). Please see the Appendix A for calculation of II o ( λ j , z i ).
F NO x is calculated for local solar noon conditions in January at Dome C and South Pole and in June at Summit using II o ( λ j , z i ) calculated from Eq. (18) in the λ = 298-345 nm range and mean σ − NO 3 and φ NO x from Sander et al. (2006). The wavelength range from 298-345 nm encompasses four λ bins from the Fast-J program: 298-307, 307-312, 312-320, and 320-345 nm. We use the mean absorption cross sections in each λ bin. We use the average daily mean January temperatures at Dome C (243 K) (Frey et al., 2009) and South Pole (244 K) (Orvig, 1970) and June temperatures at Summit (257 K) (Steffen and Box, 2001) to calculate the temperature dependent quantum yield for NO x (φ NO x ) from Chu and Anastasio (2003). The monthly mean overhead ozone column abundance in GEOS-Chem for January is 293 DU at South Pole and 306 DU at Dome C, and for June is 349 DU at Summit.
We choose a range of nitrate concentrations appropriate for polar snowpacks based upon observations in the top 1 m of snowpack at each location (Dibb et al., , 2010Frey et al., 2009). The upper 2 cm of snowpack in polar regions have considerably higher nitrate concentrations compared to depths below 2 cm in the snowpack and experience a sharp decay in concentration from the surface to 2 cm (Frey et al., 2009;Rothlisberger et al., 2000). Below 2 cm, [NO − 3 ] decreases more gradually until concentrations oscillate (representing seasonality) around a relatively constant value. In this study, we calculate the flux of NO x from the snowpack (F NO x ) using a two layer approach (z = 0 − z ref and z = z ref − 3z e ) and assume a constant snowpack [NO − 3 ] below 2 cm.
It is thought that only nitrate in the surface layer of ice crystals is photolyzable, (Boxe et al., 2005;Boxe and Saiz-Lopez, 2008;Chu and Anastasio, 2003;Dubowski et al., 2001) while nitrate in the ice lattice does not contribute. Since the fraction of total nitrate in the surface layer is unknown, we assume that all nitrate in the snow is available for photolysis and that all NO x produced in the surface layer is transferred to the adjacent interstitial air. This combined with the fact that we assume that all NO x produced in the snowpack from the photolysis of nitrate escapes to the overlying atmosphere suggests that our calculations provide an upper limit for the flux of NO x from the snow. Table 1 describes the location and depth, the best estimate of the concentration of BC on the filter (C BC ), theÅngström exponent (Å) measured in the 450-600 nm λ range, and the estimated fraction of absorption in the λ = 650-700 nm and λ = 298-345 nm ranges due to nonBC impurities (f nonBC 650−700 , f nonBC 298−345 ) for snow samples averaged by location. Appendix B contains similar information about each individual snow sample.

BC and nonBC impurity concentrations from the filtering of snow samples
In the snow samples collected near (< 0.5 km) and away (11 km) from the Dome C station, the average C BC is 2.1 ± 1.3 ng g −1 and 0.6 ± 0.2 ng g −1 , respectively. In the snow samples collected 20-40 km from the Summit station, the average C BC is 1.4 ± 0.3 ng g −1 . C BC in snowpack near the station at Dome C is 1.5-3.5 times greater than C BC in snowpacks away from the stations at Dome C and Summit, highlighting the influence of station activity on impurity levels in the local snowpack. Hagler et al. (2008) present similar results for Summit, Greenland. C BC in Greenland snow is over two times higher than C BC in snow 11 km away from Dome C station. This combined with the low accumulation rate at Dome C (3 g cm −2 yr −1 ) (Rothlisberger et al., 2000) compared to Summit (25 g cm −2 yr −1 ) (Dibb and Fahnestock, 2004) highlights the higher concentration of pollutants in the Northern Hemisphere compared to the Southern Hemisphere.
Atmos. Chem. Phys., 13, 3547-3567, 2013 www.atmos-chem-phys.net/13/3547/2013/  Thomas et al. (2011) [NO] 111 ( MeasuredÅngström exponents for the particulate material on the filters fall between the values ofÅ = 1, considered representative of pure BC, andÅ = 5 for HULIS (Doherty et al., 2010), and are smaller thanÅ∼3.8 for dust (Zender et al., 2003). This suggests a mixture of nonBC and BC impurities in both the snowpacks near and remote from the station. The similarity in theÅngström exponents at remote locations near Summit and Dome C suggests that the ratio of C BC to C nonBC and the type of nonBC material is similar in Greenland and Antarctica, even with the factor of 2 difference in C BC at Summit and Dome C.
In all snow samples, nonBC material is responsible for 20-29 % of the absorption at λ =650-700 nm and 86-89 % of absorption at λ = 298-345 nm (photochemically relevant region). The increase in nonBC absorption in the UV results from assuming anÅngstrom exponent of nonBC material of 5. At λ = 650-700 nm, BC is the dominant absorber in the snow, but at λ = 298-345 nm nonBC material dominates absorption. The fraction of nonBC absorption (f nonBC ) increases and the concentration of BC (C BC ) decreases with increasing distance from the station. The mean change in the fraction of absorption by BC or nonBC from λ = 298-345 nm between snow near and 11 km away from Dome C station is 3.4%, while the corresponding change in BC concentration is 71.4%. While we cannot quantify the concentration of nonBC (C nonBC ), we can infer that the station is a source of both BC and nonBC because the change in the f nonBC is smaller than the change in C BC . This suggests that both BC and nonBC concentrations are decreasing away from the station (since f nonBC changes less drastically than C BC ), but that C BC is decreasing at a faster rate compared to C nonBC . Figure 2 compares the vertical actinic flux profile in the snowpack calculated according to Eq. (18) to the profile calculated using the full snowpack radiative transfer model (Grenfell, 1991) for a deep (depth > 3 m) snowpack. For this comparison, we use typical remote Antarctic conditions at λ = 305 nm: r e = 100 µm, ρ snow = 0.36 g cm −3 , and C BC = 0.3 ng g −1 . We assume C nonBC = 0 ng g −1 for simplic-  (Grenfell, 1991) for a representative deep (depth > 3 m) snowpack. For this comparison, the incident radiation field is entirely diffuse, λ = 305 nm, θ = 60°, r e = 100 µm, C BC = 0.3 ng g −1 , and C nonBC = 0 ng g −1 . For an isotropic radiation field, the ratio of actinic flux to surface downwelling radiation is equal to 4. This ratio is somewhat less than 4 for the present cases depending on the solar zenith angle and amount of cloud cover.

Sensitivity of snowpack actinic flux to variations in atmospheric conditions and snowpack radiative properties
ity and assume a constant reference density with depth of 0.36 g cm −3 . The parameterization shows good agreement (within 2 % in the top 150 cm and within 8 % from 150-500 cm) with the full snowpack radiative transfer model for the above scenario and additional scenarios using various combinations of snowpack and radiative properties (not shown). Figure 3 illustrates the dependence of snowpack actinic flux on wavelength (λ), impurity concentration (C BC and f nonBC ), snow grain effective radius (r e ) (Hansen and Travis, 1974), and solar zenith angle (θ). Snow density (ρ snow ) was also varied around a typical range, but the results are not shown in Fig. 3 because changes in ρ snow do not influence the actinic flux profile significantly. For all of the normalized actinic flux profiles in Fig. 3, 89 % of the absorption at λ = 305 nm is due to nonBC material. Figure 3a shows In (c), the black line is the depth profile of actinic flux using vertical r e profile ranging from 86 µm at the snow surface to 460 µm at a depth of 500 cm. In (d), a zoomed in view of the top 10 cm is provided. In (a-d),Å = 2.90, f nonBC 305 = 89 %, and λ, C BC , r e , and θ were varied around a reference case of θ = 60°, r e = 100 µm, λ = 305 nm, C BC = 0.6 ng g −1 .
that z e decreases with decreasing λ. The λ dependence is primarily due to the fact that nonBC material is assumed to absorb radiation more effectively at shorter wavelengths (e.g., A ∼5). If only BC is present, the λ dependence is negligible (not shown). Figure 3b shows the strong dependence of z e on BC and nonBC with the e-folding depth decreasing with increasing BC and nonBC absorption. As C BC is increased, the concentration of nonBC is also increasing because of our assumption that f nonBC ≈89 % at λ = 305 nm. The range of C BC in Fig. 3b (0.3-3 ng g −1 ) represents the observed range of C BC in Antarctica (Warren and Clarke, 1990;Warren et al., 2006). The snowpack actinic flux profile when C BC = 0 is included for reference. Figure 3c shows the strong dependence of z e on radiationequivalent ice grain radius (r e ) with z e values decreasing with decreasing r e (r e is assumed constant with depth). The decrease of z e with decreasing r e is due to the increased scat-tering that occurs as the number of grains per unit volume increases (see Eq. 10). The black curve in Fig. 3c is the snowpack actinic flux profile calculated when r e is varied from 86 µm at z = 0 to 460 µm at z = 500 cm based on r e measurements made near Dome C station by Gallet et al. (2011) that are linearly extrapolated below 50 cm. The average vertical r e profile measured near Dome C station by Gallet et al. (2011) is applied to all snowpacks simulated in this study in absence of detailed vertical r e profiles at South Pole and Summit, but we note that the vertical r e profiles between these locations may vary. Sensitivity studies reveal that BC and nonBC impurities in the snow influence z e more significantly than differences in r e profiles, as long as the snowpacks are not experiencing melt. Figure 3d shows the influence of the solar zenith angle (θ) on z e for the case of collimated incident radiation. In the top 2 cm (inset of Fig. 3d), where direct radiation is scattered and converted to diffuse radiation, θ influences both the amount Atmos. Chem. Phys., 13, 3547-3567, 2013 www.atmos-chem-phys.net/13/3547/2013/ Table 5. Calculated e-folding depths of actinic flux (z e ) in snow near the station and remote from the station in the designated clean-air sector for January at Dome C and South Pole and June at Summit for λ = 305 nm and λ = 400 nm. The range of e-folding depths represents the range between fully direct (smaller z e ) and fully diffuse (larger z e ) incident radiation conditions. Values of C BC , f nonBC 305 , and f nonBC 400 used to calculate z e at each location are shown. of radiation as well as the slope of the actinic flux profile in the snowpack. At θ< 50°, the actinic flux increases with depth in the first 2 cm. This is because scattering by an individual snow particle is strongly in the forward direction, increasing the penetration of the photons; more scattering events are needed to deflect the photons that have entered the snowpack at small solar zenith angles back to the atmosphere (Bohren and Barkstrom, 1972). Below 2 cm, where the radiation is entirely diffuse, the slopes of the actinic flux profiles are the same for all values of θ. The depth profile for purely diffuse incident radiation is exponential and corresponds closely to the profile for θ = 54°under clear sky conditions.
The results shown in Fig. 3 suggest that for a given λ, and a plausible range of values for the variables considered (Table 3), impurity concentration (C BC and C nonBC ) and radiation-equivalent mean ice grain radius (r e ) affect the actinic flux profile in snowpack most significantly. Due to the difficulty in measuring C nonBC and its optical properties, the concentration and optical properties of nonBC material, such as HULIS, represent the largest uncertainty in calculations of snowpack actinic flux since nonBC material is responsible for over 85 % of absorption in the UV wavelengths relevant for photochemistry. Table 5 lists the z e values for λ = 305 nm and λ = 400 nm for snow near the station at Dome C and South Pole and away from the station at Dome C, South Pole, and Summit calculated using Eq. (18) along with the observed C BC , f nonBC 305, and f nonBC 400 at each location. We also include observed C BC in South Pole snowpack; C BC = 3 ng g −1 was measured just downwind of the station and C BC = 0.3 ng g −1 was measured in the clean air sector (close to and upwind of the Atmospheric Research Observatory) (Warren and Clarke, 1990). We assume f nonBC 305 and f nonBC 400 are similar at all wavelengths between South Pole and Dome C because both stations are located high on the Antarctic plateau, which allows us to quantify the influence of nonBC material on UV/near-vis absorption at South Pole. In all cases, z e is shallower at λ = 305 nm than at λ = 400 nm due to the wavelength dependence of the inherent optical properties of nonBC material (see Fig. 1). In snowpacks with low impurity concentrations (remote, polar snowpacks), z e is even deeper because as r e increases with depth, scattering decreases, thus decreasing the probability of radiation absorption by impurities. z e values are a factor of 1.8-3.5 larger at remote locations (> 11 km) compared to locations near the stations (< 0.5 km) because C BC and the absorption of nonBC material is 3.5-10 times greater in near-station snowpacks compared to remote snowpacks. The increase in absorption of nonBC material can be inferred because our observations suggest that theÅngström exponents are roughly similar between near-station and remote snowpacks. Our calculated z e values compare well (within 30 %) with observed values, as detailed in Appendix C. Figure 4 shows the chemical lifetime of NO x (τ chemical ) in the snowpack against conversion to HNO 3 (τ NO 2 +OH ) and BrONO 2 (τ NO 2 +BrO ) for Summit. We assume that the formation of BrONO 2 represents a sink for NO x because the calculated lifetime of BrONO 2 against hydrolysis onto snow grains (0.0006 s) is much shorter than the lifetime against photolysis (3-5 min) due to the large surface area of snow grains in the snowpack (Michalowski et al., 2000). Thus, we consider Reactions (R1)-(R3) to be sinks for NO x in the snowpack. The vertical profiles of BrO, OH, NO, and NO 2 concentrations are determined using concentration profiles of OH, BrO, NO, and NO 2 from Thomas et al. (2011). At Summit, the chemical lifetime of NO x is mainly controlled by reactions with BrO when observed surface concentrations are scaled at depth to the actinic flux. The chemical profiles of OH, BrO, and NO increase from the surface, reach a maximum in concentration at 5-10 cm depth, then decay exponentially, following the decay of actinic flux in the snowpack. Efficient transport to the www.atmos-chem-phys.net/13/3547/2013/ Atmos. Chem. Phys., 13, 3547-3567, 2013 Table 6. Calculated and observed NO x fluxes (F NO x ) near Dome C, Summit, and South Pole.

The depth-dependent lifetime of NO x in the snowpack
Polar NO x fluxes (molec cm −2 s −1 ) *

Calculations (this work) Observations
Location Remote Station Station Reference Dome C 4.4 × 10 8 -1.7 × 10 9 3.2 × 10 8 -1.2 × 10 9 6.9 × 10 8  (days) of NO x in the snowpack against chemical conversion to HNO 3 (τ NO 2 +OH , pink curve), BrONO 2 (τ NO 2 +BrO , green curve), and the combination of the two reactions (τ chemical , blue curve) for near station snow at Summit. The lifetime curves are calculated using concentration profiles of BrO, OH, NO, and NO 2 from Thomas et al. (2011). atmosphere above 5-10 cm depth combined with decreasing actinic flux with depth in the snowpack results in maximum OH, BrO, and NO concentrations at depths of 5-10 cm in the snowpack . Model results from Thomas et al. (2011) show that NO 2 remains relatively constant with depth in the snowpack, likely because NO 2 has a longer lifetime than OH, BrO, and NO and its production rate and photolysis rate both decrease with depth. Figure 5 shows the vertical profiles of τ chemical and τ wind pumping in remote snowpacks of Summit calculated using average summertime values of snow density, snow permeability, sastrugi wavelength, sastrugi height, wind speed, and boundary layer [OH], [BrO], [NO], and [NO 2 ] at Summit (Table 3). In Fig. 5, τ wind pumping is shorter (more efficient) than τ chemical at all depths, meaning that NO x efficiently escapes from the snowpack throughout most of the photochemically active zone. The full range of expected values for each variable (snow density, snow permeability, sastrugi wavelength, sastrugi height, wind speed, [OH], [BrO], [NO], [NO 2 ]) in Eq. (19) (τ wind pumping ) and Eq. (21) (τ chemical ) are used in sensitivity studies. NO x efficiently escapes from the snowpack throughout most of the photochemically active zone when base-case conditions are considered and any value of snow density is assumed. τ chemical is shorter than τ wind pumping , meaning that NO x in the photochemically active zone is more likely to convert to HNO 3 rather than escape to the atmosphere, for a permeability of 1 × 10 −10 or less, a viscosity of 9 × 10 −5 or greater, and a sastrugi aspect ratio (height/wavelength) greater than 0.16. If τ chemical becomes shorter than τ wind pumping at a depth closer to the snow surface than 3z e , the actinic flux should be integrated to a shallower depth than 3z e when calculating the flux of NO x from the snowpack, F NO x , because a significant portion of NO x produced through photodenitrification would convert to HNO 3 before escaping to the atmosphere.
We have assumed [IO] = 0 in this study because IO that is produced in coastal regions due to biological activity quickly oxidizes and may deposit to coastal snow surfaces before being transported inland. However, if we assume IO concentrations are equal to the base-case BrO concentrations used in this study, our results are not changed. We find that the conversion of NO 2 to BrONO 2 and IONO 2 are equally dominant when concentrations of IO and BrO are equivalent due to similar reaction rate constants. The chemical concentrations of BrO, IO, and OH in the snowpack are highly uncertain, but are thought to be on the order of 10 −12 mol mol −1 in the snowpack . However, Frieß et al. (2010) observed IO concentrations at Neumayer on the order of 10 −9 mol mol −1 while surface atmosphere observations were on the order of 10 −12 mol mol −1 . If we use snowpack BrO and IO concentrations on the order of 10 −9 mol mol −1 , we find that NO x is not efficiently ventilated to the atmosphere (τ chemical is shorter than τ wind pumping at all depths). In this scenario, a significant portion of the NO x produced through photodenitrification would convert to HNO 3 before escaping to the atmosphere at all depths.
Given the uncertainty in snowpack NO x profiles, we have not explicitly considered diffusion as a means to transport NO x from the snowpack interstitial air to the overlying Atmos. Chem. Phys., 13, 3547-3567 (Table 3) and Summit chemical profiles calculated in Thomas et al. (2011) (Fig. 4). The e-folding depth in near-station snow at Summit is not calculated in this study because C BC and nonBC absorption are unknown. Three times the e-folding depth of actinic flux at λ = 305 nm (3z e ) for remote Summit snow is shown for reference (horizontal, black solid line), although 3z e in near station snow is likely more shallow due to enhanced impurity concentrations from local station activities.
atmosphere, though diffusion is likely important in reality. The chemical profiles calculated in the Thomas et al. (2011) study suggest that the concentration of NO 2 , NO, BrO, and OH are higher in the snow compared to the atmosphere until a depth of 20-30 cm. The profiles suggest that NO x produced by photodenitrification would diffuse towards the atmosphere from the snow surface to a depth of 20-30 cm, which is roughly 1-2 e-folding depths depending on snowpack impurity concentration. The inclusion of diffusion in our analysis would likely further shorten the lifetime of NO x against escape to the atmosphere. However, even without diffusion, wind pumping of NO x from the snowpack to the atmosphere is still dominant compared to NO x decay to HNO 3 when base-case conditions are assumed for variables used to calculate the wind pumping and chemical lifetime. Table 6 shows the results of our calculated flux of NO x from the snowpack to the overlying atmosphere, F NO x , using observed nitrate concentrations as described in Sect. 2.5. To calculate the F NO x , we assume that the NO x lifetime against wind pumping is always shorter than the chemical lifetime of NO x in the snow at all polar locations considered, and therefore that all NO x produced by nitrate photolysis from the snow surface to 3z e escapes from the snow to the atmosphere. The range of F NO x represents calculations using the full range of observed nitrate concentrations Frey et al., 2009;Rothlisberger et al., 2000). These results are an upper limit for the flux of NO x from the snow because we have assumed that all nitrate in the snow is available for photolysis, and that all of the NO x produced escapes from the snowpack to the overlying atmosphere. Our calculations are compared to observations in the vicinity (< 5 km) of each station. The NO x fluxes calculated in this study are in good agreement with observed NO x fluxes estimated near the station at South Pole (Oncly et al., 2004) and observed near the station Dome C (Frey et al., 2013). Oncley et al. (2004) estimated NO x fluxes using observed NO fluxes together with calculated photochemical equilibrium values for NO 2 . The vertical r e profile (Gallet et al., 2011) is the same for all snowpacks considered in the study, and therefore the concentration of impurities and NO − 3 in the snow influence our calculated flux of NO x from the snowpack most significantly.

Results of NO x flux calculations
The NO x fluxes from snowpacks greater than 11 km from the station are 1.4-2.3 times larger than the NO x fluxes from snowpacks near the stations at South Pole and Dome C because near-station snowpacks have higher concentrations of impurities, resulting in shallower e-folding depths. Shallower z e values near stations confine photodenitrification to a shallower layer, resulting in less NO x produced (and transported to the atmosphere) compared to remote snowpacks. Here we assume that the snowpack  at South Pole, Dome C, and Summit is the same for each station regardless of distance from the station. The range of F NO x at each location represents the difference between minimum and maximum observed snowpack . The contributions from the top 2 cm of snowpack to the total F NO x varies between stations (24-68 %), but are generally greater in snowpacks near the stations because of shallower e-folding depths of actinic flux. We expect the photodenitrification occurring in the top 2 cm of snow to significantly influence F NO x because I o (λ,z) and [NO − Observations of the absorption properties of black carbon and non-black carbon material (e.g., brown carbon, dust, organics) in snow collected near Dome C, Antarctica, and Summit, Greenland, show that near-station activities enhance the concentration of absorbing impurities by a factor of at least 2-3, and that the concentrations of absorbing impurities are a factor of 2.5-5 higher at remote locations in Greenland compared to remote locations in East Antarctica. TheÅngström exponents associated with the absorption of particulate matter in snow range from 2.3-3 and indicate a combination of black carbon and non-black carbon material in all snow sampled, the latter of which provides the dominant contribution to absorption of UV radiation in the snowpack. The absorption by both BC and nonBC material is increased in nearstation snowpacks compared to remote snowpacks. While we cannot quantify the concentration of nonBC (C nonBC ), we can infer that the station is a source of both BC and nonBC because the change in the f nonBC is smaller than the change in C BC at increasing distance from the stations . We find that both BC and nonBC concentrations are decreasing away from the station, but that C BC is decreasing at a faster rate compared to C nonBC . Our observations of absorption due to BC and nonBC in snowpack at Dome C, Summit, and South Pole are incorporated into a snowpack actinic flux parameterization.
The parameterization is used to calculate depth-dependent actinic flux profiles in snowpack and is based upon a 4stream, plane parallel snowpack radiative transfer model with a δ-M approximation (Grenfell, 1991). This parameterization is broadly applicable and allows straightforward inclusion of snowpack properties and impurity types and concentrations. It can be easily implemented into large-scale models and represents spatio-temporal variations in solar zenith angle, wavelength, radiation equivalent ice grain radius, snow density, and impurity concentration. The parameterization was used to calculate actinic flux profiles in snowpack for specific case studies near the stations at Dome C and South Pole and remote from Dome C, South Pole, and Summit. In the UV/near-vis region (the region relevant for photochemistry), the e-folding depth of actinic flux (z e ) is strongly dependent on impurity concentrations (BC and nonBC) and radiation equivalent mean ice grain radius (r e ). z e decreases with increasing impurity concentration and increases with increasing r e . Our calculated z e values range from 8-62 cm between wavelengths of λ = 305-400 nm; z e decreases with decreasing wavelength due to the wavelength dependence of nonBC absorption. Our calculated z e values agree well with previous studies (see Appendix C).
Our results from the parameterization suggest that UV/near-vis radiation is significant at depths greater than 1.5 m in the snowpack, which implies that photodenitrification can occur and produce NO x at those depths. We calculate the depth dependent lifetime of NO x in the snow-pack against ventilation to the overlying atmosphere by wind pumping (τ wind pumping ) and chemical sinks by reaction of NO 2 with OH and BrO (τ chemical ). Comparison of the vertical profiles of τ wind pumping and τ chemical at Summit reveals that NO x is efficiently ventilated to the overlying atmosphere at all depths in the snowpack. This result is sensitive to the assumed concentrations of BrO, snow permeability, viscosity, wind speed, and sastrugi Our calculated F NO x near Dome C, South Pole, and Summit range from 3.2 × 10 8 -3.8 × 10 9 molec cm −2 s −1 and represent an upper limit on the flux of NO x from the snow from snowpack nitrate photolysis. Calculated NO x fluxes in snowpack near stations are a factor of 1.4-2.4 smaller than > 11 km away from the stations due to the impact of absorbing impurity concentrations from local contamination on the e-folding depth of the actinic flux in snowpack. Observations of NO x fluxes near stations may be underestimating the amount of NO x emitted from the snowpack in remote locations by a similar factor of 1.4-2.4.

Appendix A NO x flux calculation
The flux of NO x from the snowpack (F NO x ) is calculated for two distinct layers in the snowpack: from the surface (z = 0) to z ref (2 cm) and from z ref to three times the e-folding depth (3z e ) of actinic flux in snow. These layers are separate because the decay of radiation with depth is in general nonexponential from 0-2 cm and exponential below 2 cm depth. Also, there are significant differences in the vertical profile of snowpack  in the two layers (see Sect. 2.5). The total downwelling irradiance at the snowpack surface is calculated for multiple wavelength bins by the Fast-J radiative transfer program (Wild et al., 2000) with the surface albedo specified to be consistent with our snowpack calculations (0.996). Summations over each λ bin are carried out after depth integrations to ensure that the λ dependence of the e-folding depths are properly included.
In the λ bin (λ j +1 − λ j = λ j ), I o ( λ j , z) is first calculated at each centimeter in the snowpack from the surface (z = 0 cm) to a depth of 3 times the e-folding depth of actinic flux in snow (3z e ). Once I o ( λ j , z) has been calculated at each centimeter, the total (integrated) actinic flux, II o ( λ j , z i ), is calculated in a 2 cm interval from z = 0 to z ref and 1 cm intervals from z = z ref to 3z e (z i+1 −z i = z i ). Intervals of 1-2 cm are used because IOPs (c eff and Kext tot ) vary with depth due to the dependence of grain radius on depth. In each depth interval and wavelength bin, an average ϒ value ϒ ij = cω 1 2 eff λ j , z i · Kext tot λ j , z i is used, which uses average values of Kext tot and c eff over λ j and each z i . From z 1 = 0 to z 2 = z ref , I o ( λ j, z) is numerically integrated over each λ bin ( λ j ) in the depth Atmos. Chem. Phys., 13, 3547-3567, 2013 www.atmos-chem-phys.net/13/3547/2013/ interval ( z 1 = z 2 − z 1 ) using the trapezoid rule.
When evaluated, Eq. (A2) becomes Values of II o λ j , z i calculated in each depth interval ( z i ) in the z = z ref to 3z e layer are summed in each λ bin ( λ j ).
The total flux of NO x from the snowpack from the layer z = 0 to 3z e in each λ bin, F NO x ( λ j , 0 cm to 3z e ), is calculated in Eq. (A5): F NO x λ j , 0 cm to 3z e =φ λ j ·σ λ j · NO − 3 z 1 ·II o λ j , 0 cm to 2 cm + NO − 3 z 2 to 3z e · II o λ j , 2 cm to 3z e , where φ λ j is the average quantum yield and σ λ j is the average absorption cross section in the wavelength bin, λ j . NO − 3 z 1 is the average snowpack nitrate concentration in the layer from z = 0 to z ref and NO − 3 z 2 to 3z e is the average snowpack nitrate concentration in the layer from z = z ref to 3z e .
The total flux of NO x (F NO x ) from the surface snowpack associated with all λ relevant for photodenitrification (λ = 298-345 nm) is calculated by summing the total depthintegrated flux of NO x from the snowpack in each λ bin. Here, 4 λ bins are used consistent with the Fast-J radiative transfer algorithm (Wild et al., 2000) to calculate F NO x (N λ = 4).
F NO x λ j , 0 cm to 3z e (A6) Appendix C Sensitivity of z e and F NO x to nonBC absorption nonBC material dominates absorption in the photochemically active wavelength region. In this study we have used a value ofÅ nonBC = 5 over the λ range 289-850 nm, which results in an exponential dependence of the absorption of nonBC to λ (Doherty et al., 2010, and references within).
To examine the sensitivity of z e and F NO x to the λ dependence of the absorption of nonBC, we linearly extrapolate Eq. (7) over the UV wavelengths relevant to photochemistry (λ = 289-345 nm). We continue to assumeÅ nonBC = 5 (exponential dependence) at λ longer than 345 nm. We find that linear extrapolation of E7 leads to smaller values for the optical depth of nonBC, T nonBC , indicating less absorption of UV radiation due to nonBC material in the snowpack compared to when we assume thatÅ nonBC = 5 in the UV. However, the nonBC absorption is still dominant over BC absorption in Table D1. e-folding depths measured in snowpacks at Dome C from France et al. (2011) (adapted from Fig. 1).
the UV (f nonBC 298−345 = 77-84 %). When assuming the linear dependence of the absorption of nonBC on λ in the UV, less absorption of UV radiation by nonBC material increases the e-folding depth at λ = 305 nm by 3-5 cm at all locations except remote South Pole, where the e-folding depth is increased by 10 cm. F NO x is increased by a factor of 1.1-1.2 depending on location.

Comparison of parameterization to observations and results from other snowpack radiative transfer models
We have compared the measured e-folding depths near the station at Dome C reported in France et al. (2011) to efolding depths calculated using our actinic flux parameterization. Table D1 (below) shows the e-folding depths measured in France et al. (2011), which have an uncertainty of ± 20%. We have assumed diffuse sky conditions and used the detailed Dome C snow grain radius and density stratigraphy from Gallet et al. (2011). We have used the average density profile measured by Gallet et al. (2011) near Dome C station for all comparisons, because variations in density are considerably smaller than variations in grain size. We calculate the e-folding depth for various snow BC concentrations using three different r e profiles from Gallet et al. (2011); the mean profile reported and two "extreme" profiles based upon Fig. 4 in Gallet et al. (2011) (see Table D2). During comparison, we vary BC concentrations from 1-5 ng g −1 because it is unclear how much BC was in the snow near Dome C station during the measurement period. We specifically cal-culate the e-folding depth using C BC = 3.3 ng g −1 because it was the average concentration measured near Dome C station by Warren et al. (2006). For all comparisons, we assume that nonBC material is responsible for 87 % of the absorption at λ = 305 and 70 % at λ = 400 nm, which is the f nonBC calculated from our snow samples collected near Dome C station. Using these assumptions, there is good agreement between the measured e-folding depths at Dome C by France et al. (2011) and the e-folding depths calculated using our parameterization for C BC = 3.3-5 ng g −1 . Table D3 compares the normalized actinic flux profile calculated using our parameterization and the normalized actinic flux profiles at Summit, Greenland, calculated with a Monte Carlo radiative transfer model described in Peterson et al. (2002) for a homogenous snowpack with ρ snow = 340 kg m −3 and snow grain thickness (diameter) = 0.25 mm. Table D4 compares the normalized actinic flux profiles for a stratified snowpack with ρ snow ranging from 260-390 kg m −3 and snow grain thickness (diameter) ranging from 0.15-0.3 mm. Because the Monte Carlo model does not include snowpack impurities, we have set the impurities in our parameterization to zero. There is good agreement (within 20 %) between the Monte Carlo model and our parameterization for both homogenous and heterogeneous snowpacks. Table D5 compares the nitrate photolysis rates calculated by Qiu et al. (2002) to our calculated nitrate photolysis rates. Qiu et al. (2002) calculates nitrate photolysis rates based upon chemical actiniometry at 305 nm for two-hour periods near noon in mid-June at Summit. For comparison, we multiply actinic flux at Summit in mid-June from GEOS-Chem by quantum yields and absorption cross sections from Qiu et Atmos. Chem. Phys., 13, 3547-3567, 2013 www.atmos-chem-phys.net/13/3547/2013/ Table D3. Comparison of snowpack actinic flux profile for Summit, Greenland, using our parameterization and a Monte Carlo radiative transfer model  for homogeneous snowpack with ρ snow = 340 kg m −3 , snow grain diameter = 0.25 mm, C BC = 0 ng g −1 , and diffuse sky conditions.  Table D4. Comparison of snowpack actinic flux profile for Summit, Greenland, using our parameterization and a Monte Carlo radiative transfer model  for stratified snowpack with ρ snow ranging from 260-390 kg m −3 , snow grain diameter ranging from 0.15-0.30 mm, C BC = 0 ng g −1 , and diffuse sky conditions.  Table D4. Noon time, mid-June Summit, Greenland, nitrate photolysis rates calculated in Qiu et al. (2002) compared to nitrate photolysis rates calculated using our parameterization.
in the snow, and Charlie Zender for information about the optical properties of dust.