Introduction

Snowpack hydroxyl radicals, OH, have been implicated in the production of gaseous fluxes from snowpack to the lower atmosphere (e.g. formaldehyde and acetaldehyde (Reference ShepsonShepson and others, 1996; Reference Hutterli, Röthlisberger and BalesHutterli and others, 1999; Reference Sumner and ShepsonSumner and Shepson, 1999; Reference Couch, Sumner, Dassau, Shepson and HonrathCouch and others, 2000; Reference DassauDassau and others, 2002; Reference GrannasGrannas and others, 2002; Reference HoudierHoudier and others, 2002; Reference Hutterli, McConnell, Bales and StewartHutterli and others, 2003, Reference Hutterli, McConnell, Chen, Bales, Davis and Lenschow2004; Reference Mabilia, Di Palo, Cassardo, Ciuchini, Pasini and PossanziniMabilia and others, 2007) and the fluxes of many other species such as halogens, alkenes, alkyl nitrates, peroxides and organic acids (Reference Couch, Sumner, Dassau, Shepson and HonrathCouch and others, 2000; Reference BoudriesBoudries and others, 2002; Reference DassauDassau and others, 2002; Reference Dibb and ArsenaultDibb and Arsenault, 2002; Reference GrannasGrannas and others, 2002; Reference GuimbaudGuimbaud and others, 2002; Reference FreyFrey and others, 2009)). Laboratory studies have demonstrated the formation of OH radicals within snowpack from the photolysis of nitrate (Reference Honrath, Guo, Peterson, Dziobak, Dibb and ArsenaultHonrath and others, 2000; Reference Dubowski, Colussi and HoffmannDubowski and others, 2001, Reference Dubowski, Colussi, Boxe and Hoffmann2002; Reference Chu and AnastasioChu and Anastasio, 2003; Reference Cotter, Jones, Wolff and BaugitteCotter and others, 2003; Reference Anastasio, Galbavy, Hutterli, Burkhart and FrielAnastasio and others, 2007; Reference Jacobi and HilkerJacobi and Hilker, 2007),

where h is Planck’s constant and υ is the frequency of the radiation, and from the photolysis of hydrogen peroxide (Reference Chu and AnastasioChu and Anastasio, 2005; Reference Jacobi, Annor and QuansahJacobi and others, 2006; Reference Anastasio, Galbavy, Hutterli, Burkhart and FrielAnastasio and others, 2007),

In the presence of oxygen, formation of OH radicals within snowpack will create a radical-initiated oxidizing medium, allowing oxidation of chemicals in the snowpack. Trace organics in snowpack, suggested as palaeoclimate indicators in ice cores (Reference Grannas, Hockaday, Hatcher, Thompson and Mosley-ThompsonGrannas and others, 2006), may be altered through photo-produced hydroxyl radical chemistry, and therefore may be unsuitable as palaeoindicators without a correction (Reference Anderson, Dibb, Griffin, Hagler and BerginAnderson and others, 2008).

Fluxes of gaseous NO₂ and HONO have been observed from snowpacks in Arctic and Antarctic environments (Reference BeineBeine and others, 1997, Reference Beine, Dahlback and Ørbaek1999, Reference Beine, Allegrini, Sparapani, Ianniello and Valentini2001, Reference Beine, Honrath, Dominé, Simpson and Fuentes2002a,Reference Beineb, Reference Beine2003, Reference Beine2006, Reference Beine, Colussi, Amoroso, Esposito, Montagnoli and Hoffmann2008; Reference JonesJones and others, 2001; Reference ZhouZhou and others, 2001; Reference HonrathHonrath and others, 2002; Reference Oncley, Buhr, Lenschow, Davis and SemmerOncley and others, 2004; Reference KleffmannKleffmann, 2007). Gaseous NO₂ is produced in snow through the photolysis of NO₃ ⁻ (Equation (1a); Reference Honrath, Guo, Peterson, Dziobak, Dibb and ArsenaultHonrath and others, 2000), in analogy to the liquid phase reaction (Reference Mack and BoltonMack and Bolton, 1999). An overall assessment of snowpack photochemistry is provided by Reference GrannasGrannas and others (2007).

In the work discussed here, the 1997 Ny-Ålesund (Svalbard) field measurements by Reference GerlandGerland and others (1999) are used to determine snowpack optical properties, and to calculate NO₂ fluxes from these snowpacks and OH production rates within the snowpacks. Reference GerlandGerland and others (1999) measured the broadband transmission of photosynthetically active radiation (PAR; 400–700 nm) through snow, and the snow surface spectral albedo at different sites near the Ny-Ålesund base in May and June 1997. The two snowpacks described by Reference GerlandGerland and others (1999) are hereafter described as ‘fresh’ and ‘melting’. Further details of these snowpacks are given in Table 1 and by Reference GerlandGerland and others (1999). We present calculations, with appropriate assumptions, of photolysis rate coefficients of nitrate and hydrogen peroxide photolysis within the snowpack, using the discrete-ordinate radiative transfer code (DISORT) model, TUV-snow (Reference Lee-Taylor and MadronichLee-Taylor and Madronich, 2002). A photolytic rate coefficient, J, for Equations (1a) and (2), respectively, is defined by the kinetic rate equations

and

where t is time. Photolytic rate coefficients may be calculated by integrating the product of the chromophore (i.e. nitrate or hydrogen peroxide) absorption cross section, σ(λ,T), the chromophore quantum yield, Φ(λ,T), and the spherical irradiance, F(λ), over the wavelength of the irradiance, λ, at a known temperature:

The reported values of light attenuation and albedo (Reference GerlandGerland and others, 1999) are used to optically characterize the snowpack for the TUV-snow model using a previously described method (e.g. Reference Fisher, King and Lee-TaylorFisher and others, 2005). The depth-resolved photolysis rate coefficients of nitrate and hydrogen peroxide are then used to calculate the formation rate of OH radicals within the snowpack, and the fluxes of NO₂ from the snowpack. The photolytic rate coefficients of Equations (1) and (2) depend upon the optical properties of the snowpack, described by a scattering and an absorption coefficient. Values for these coefficients may be constrained by observations of albedo, e-folding depth (characteristic distance over which the diffuse irradiance in the snowpack decays to 1/e or ∼37% of its initial value (Reference King and SimpsonKing and Simpson, 2001)) and snow density. Measurements of albedo, light transmission and density were recorded by Reference GerlandGerland and others (1999) for fresh and melting snowpacks. The validity of using the TUVsnow DISORT radiative-transfer coding (Reference Lee-Taylor and MadronichLee-Taylor and Madronich, 2002) to describe photochemistry in snow was borne out in experiments by Reference Phillips and SimpsonPhillips and Simpson (2005) that showed good agreement between photolysis of a chromophore within laboratory snow and predictions based on the TUV-snow model.

Methods

The TUV-snow model (Reference Lee-Taylor and MadronichLee-Taylor and Madronich, 2002) employs an eight-stream pseudo-spherical, discrete-ordinates, radiative-transfer scheme (Reference Stamnes, Tsay, Wiscombe and JayaweeraStamnes and others, 1988). It allows optical characterization of a snowpack from knowledge of albedo and light transmission into the snowpack, without the need for knowledge of snow grain size. The optical information is used to derive a wavelength-dependent absorption coefficient for, , and a wavelength-independent scattering coefficient, σ _scatt. A detailed description of the modelling process to find values for these coefficients is given by Reference Lee-Taylor and MadronichLee-Taylor and Madronich (2002).

The parameters used to derive the absorption cross section, , and scattering cross section, σ _scatt, for the two snowpacks assumes an under-snow ground albedo of 0.1, no atmospheric aerosol, and stratospheric ozone columns of 325 and 375 DU (Dobson units; daily values for 19 June 1997 (melting snow) and 19 May 1997 (fresh snow), respectively). Ozone column data were taken from the NASA Total Ozone Massing Spectrometer (TOMS) programme (Reference McPetersMcPeters and others, 1998). Earth–sun distances were calculated for the dates of the original snowpack measurements and are needed to calculate solar irradiance at the top of the atmosphere. The absorption cross section of ice was taken from Reference Warren and BrandtWarren and Brandt (2008). Values of e-folding depths are kept constant over the wavelength range 400–700 nm, as only PAR (cumulative radiation over wavelengths from 400 to 700 nm) attenuation is reported by Reference GerlandGerland and others (1999). Spectral albedo data between 350 and 1300 nm are reported by Reference GerlandGerland and others (1999). Values are derived for and σ _scatt cross sections for the two types of snowpack at 400 nm, and the values derived for and σ _scatt at 400 nm are used to calculate photolysis rate coefficients for Equations (1a) and (2). Reference King and SimpsonKing and Simpson (2001) show that e-folding depth varies by only ∼9% over the wavelength range 330–400 nm, suggesting that it is reasonable to use values of and σ _scatt assessed at 400 nm. The aqueous ultraviolet (UV) absorption cross section of hydrogen peroxide and nitrate anion decreases rapidly with increasing wavelength in the 320 nm region. The irradiance of incident solar radiation increases rapidly with increasing wavelength in this region. The product of these two functions results in a new function that peaks around 320 nm as shown by Reference Chu and AnastasioChu and Anastasio (2005, Reference Chu and Anastasio2008). Using values of and σ _scatt at 400 nm to calculate photolysis rate coefficients of nitrate and hydrogen peroxide is also consistent with previous work (Reference King and SimpsonKing and Simpson, 2001; Reference Lee-Taylor and MadronichLee-Taylor and Madronich, 2002; Reference Fisher, King and Lee-TaylorFisher and others, 2005; Reference BeineBeine and others, 2006; Reference France, King and Lee-TaylorFrance and others, 2007).

The TUV-snow model can predict photolysis rate coefficients at any number of depths within snowpacks with a minimum resolution of 1 mm, provided that , σ _scatt, the snowpack density, ρ, location, time, ozone column depth and sky conditions are known (Reference Lee-Taylor and MadronichLee-Taylor and Madronich, 2002). In this work, 30 unequally spaced separate snowpack layers, with more thin layers near the snow surface, within a 1 m deep and laterally semi-infinite snowpack slab were used. The layer spacing is the same as used by Reference Lee-Taylor and MadronichLee-Taylor and Madronich (2002). Photolysis rate constants, J, are calculated for each snow layer for Equations (1) and (2). Depth-integrated photolysis rate coefficients (also known as transfer velocities), υ, for the production of and OH (υ_OH) radical from the photolysis of NO₃ ⁻ and H₂O₂ in snow, respectively, are calculated as

where J _(1a) and J ₍₂₎ are the photolysis rate coefficients for Equations (1a) and (2), respectively, and z is the snowpack depth with z = 1 m the snowpack surface and z = 0 m the snowpack interface with the ground.

Reference GerlandGerland and others (1999) reported snow thicknesses for some of their melting-snow pits of 0.48 and 0.78 m where PAR transmission through the snowpack was measured. For modelling in this work, we use a 1 m thick snowpack to ensure an optically semi-infinite snowpack (Reference Lee-Taylor and MadronichLee-Taylor and Madronich, 2002). The minimum snowpack depth to ensure an optically semi-infinite snowpack was discussed by Reference GerlandGerland and others (1999) and suggested from a review of literature to be 50 cm for the snowpacks studied in this work. The issue of minimum depth for semi-infinite snowpack has also been investigated by Reference FranceFrance (2008) who found the molecular flux (and depth-integrated production rate) from Equation (2) was independent of snowpack depth provided the snowpack is thicker than three e-folding depths, i.e. ∼0.3 m for the melting snowpack (and 0.18 m for the fresh snowpack). Thus, whether the snowpack thickness is 0.3, 0.48. 0.78 or 1 m makes a negligible (<3%) difference to the flux of material from the snowpack. The irradiance of light in the snowpack decays exponentially with depth below the first few cm. For melting-snowpack thicknesses less than 0.3 m, the albedo of the ground underlying the snowpack will become significant in determining snow surface albedo. Melting snowpacks less than 0.3 m thick are not considered here, as the main aim is to show the importance of considering photochemistry at depth within the snowpack.

For calculating photolysis rate coefficients (Equation (5)), the absorption cross section for hydrogen peroxide was taken from Reference Chu and AnastasioChu and Anastasio (2005), and the nitrate absorption cross section from Reference Burley and JohnstonBurley and Johnston (1992), for consistency with our previous studies (Reference Simpson, King, Beine, Honrath and ZhouSimpson and other 2002; Reference Fisher, King and Lee-TaylorFisher and others 2005; Reference France, King and Lee-TaylorFrance and others 2007; Reference Beine, Colussi, Amoroso, Esposito, Montagnoli and HoffmannBeine and others 2008). The temperature-dependent quantum yields used to calculate nitrate and hydrogen peroxide photolysis rate coefficients are taken from Reference Chu and AnastasioChu and Anastasio (2003, Reference Chu and Anastasio2005, respectively). The snowpack modelling in this study uses snowpack temperatures from Reference GerlandGerland and others (1999) (Table 1).

The predicted molecular flux of NO₂, , from the snowpack to the atmosphere, owing to nitrate photolysis within the snowpacks, is

assuming that all the NO₂ formed from the photolytic reaction (Equation (1)) can escape the snowpack. Depth-integrated production rates of OH radicals are calculated for Equations (2) and (1), respectively:

It is assumed that in-snow concentrations of NO₃ ⁻ and H₂O₂ are independent of depth, and that Equation (1a) is the rate-limiting step in producing OH radicals from nitrate photolysis. Equations (8) and (10) are mathematically the same: Equation (1) produces one NO₂ molecule and one OH radical, but for clarity we have written out the equation for each chemical reaction. Note we term a molecular flux of NO₂ from the snowpack, whereas we term a depth-integrated production rate because the OH radicals are too reactive to leave the snowpack. The terms ‘flux’ and ‘depth-integrated production rate’ continue the nomenclature used for similar work (e.g. Reference France, King and Lee-TaylorFrance and others, 2007).

Nitrate concentrations in Svalbard snowpacks are taken from five studies and adjusted to a nitrate concentration per unit volume of snow (as opposed to liquid water). Reference BeineBeine and others (2003) reported nitrate concentrations of 0.47–3.8 nmol cm⁻³, with a typical value of 1.26 nmol cm⁻³. They noted that anion concentration in the snowpack was very varied horizontally and vertically, owing to wind events. Reference Heaton, Wynn and TyeHeaton and others (2004) reported nitrate values in snow of 0.9–1.8 nmol cm⁻³ (fresh) and 0.45–3.6 nmol cm⁻³ (older). Reference Semb, Brækkan and JorangerSemb and others (1984) found nitrate concentrations in surface snow of <0.45–1.8 nmol cm⁻³ and reasonably invariant concentration depth profiles. By crude visual interpolation of the values reported by Reference GrannasGrannas and others (2007), one can deduce nitrate anion concentrations in snow of 0.87–1.09 nmol cm⁻³. The nitrate data from the Arctic Monitoring and Assessment Program report (AMAP, 1998) could not be used in this study. Nitrate concentrations in snow for other archipelagos in the Arctic Ocean are ∼0.9 nmol cm⁻³ for Franz Josef Land (Reference NickusNickus, 2003) and 0.36–1.09 nmol cm⁻³ for Severnaya Zemlya (Reference OpelOpel and others, 2009). Reference NickusNickus (2003) and Reference OpelOpel and others (2009) noted that nitrate concentrations correspond well to the values found in Greenland, parts of the Canadian Arctic and Alaska and that concentration–depth profiles in Severnaya Zemlya are similar to those from Svalbard. For the studies reported here, a nitrate in snow concentration of 1 nmol cm⁻³ is used based on the above measurements.

The authors are unaware of any snow hydrogen peroxide concentration measurements for Svalbard, so the work presented here has had to rely on data presented for Summit, Greenland, and South Pole. Studies of hydrogen peroxide concentration in south polar snow report values of 1.35–6.75 nmol cm⁻³ (Reference Hutterli, McConnell, Chen, Bales, Davis and LenschowHutterli and others, 2004), 0.9–9.9 nmol cm⁻³ (Reference McConnell, Winterle, Bales, Thompson and StewartMcConnell and others 1997) and 0.9–9 nmol cm⁻³ (Reference McConnell, Bales, Stewart, Thompson, Albert and RamosMcConnell and others 1998). For Summit, concentrations are typically 0.27–7.92 nmol cm⁻³ (Reference Hutterli, McConnell, Bales and StewartHutterli and others, 2003), with annual means of 1.56–3.52 nmol cm⁻³ (Reference Anklin and BalesAnklin and Bales, 1997) and ∼2–16 nmol cm⁻³ variation in depth and surface snow (Reference Anastasio, Galbavy, Hutterli, Burkhart and FrielAnastasio and others 2007). Hydrogen peroxide values between sites are similar, in part reflecting the local source of H₂O₂ from deposition following gas-phase generation in the atmosphere, whereas nitrate is associated with precipitation and deposition. Surface snow concentrations of H₂O₂ in snow vary seasonally, with large values in spring and small values in winter. Seasonal variation of the concentration of H₂O₂ in surface snow results in a depth dependence of H₂O₂ concentrations. Here a value of 4 nmol cm⁻³ in snow (invariant with depth) is considered, and later in the discussion the small effect of a concentration–depth dependence on molecular fluxes out of the snowpack.

The molecular fluxes (or depth- integrated production rates), calculated by Equations (8–10), are linearly proportional to the snowpack concentration of nitrate and hydrogen peroxide. Thus, the reader can adjust the molecular fluxes reported in this paper for their values of the concentration of nitrate or hydrogen peroxide in the snowpack by simply dividing the molecular flux (or depth-integrated production rate) by the concentration of nitrate or hydrogen peroxide used here and multiplying by preferred values of concentration of nitrate or hydrogen peroxide in their snowpack.

Surface photolysis rate coefficients, J, transfer velocities (depth- integrated photolysis rate coefficients), υ, and molecular fluxes (depth-integrated production rates), F, were calculated for both NO₃ ⁻ and H₂O₂ photolysis for fresh and melting snowpacks.

Results

The values of scattering and absorption coefficients (Table 1) are within the range of other studies (e.g. (Reference Lee-Taylor and MadronichLee-Taylor and Madronich, 2002), 4.3–37 (Reference BeineBeine and others, 2006) and 0.7–1 (Reference Fisher, King and Lee-TaylorFisher and others, 2005); and σ _scatt = 1.1–30 (Reference Lee-Taylor and MadronichLee-Taylor and Madronich, 2002), 1–6 (Reference BeineBeine and others, 2006) and 1–5 (Reference Fisher, King and Lee-TaylorFisher and others, 2005)). The fresh Ny-Ålesund snowpack is optically most similar to Arctic spring wind-blown snowpack (Reference King and SimpsonKing and Simpson, 2001), and the melting Ny-Ålesund snowpack is optically transitional between coastal maritime Antarctic wind-blown (Reference BeineBeine and others, 2006) and Arctic summer melting snowpack (Reference Grenfell and MaykutGrenfell and Maykut, 1977).

Figures 1 and 2 show surface and depth-integrated photolysis rate coefficients, J, and transfer velocities, υ, for Equations (1a) and (2) versus solar zenith angles 0–90° for both snowpack types at Ny-Ålesund based on the assumptions discussed. In Figure 1, the surface photolysis rate coefficients are larger for the fresh snow than for the melting snow, but in Figure 2 the transfer velocities are larger for the melting snow than for the fresh snow. Using the surface photolysis rate coefficients (Fig. 1) instead of the depth-integrated photolysis rate coefficients (Fig. 2) can lead to errors in calculation of the fluxes of NO₂ from the snowpack. Considering only the surface photolysis rate coefficients to calculate NO₂ fluxes will lead to the false conclusion that the fresh Ny-Ålesund snowfall will produce a larger flux than the melting snowpack. The authors consider this issue a result that demonstrates the importance of modelling photolysis rate coefficients for a whole snow-pack rather than considering just the surface snow layer. A similar argument can be constructed for the depth-integrated production rates of OH radicals.

Fig. 1. Photolysis rate coefficients for NO₃ ⁻ and H₂O₂ at the snow surface, J _(1a) and J ₍₂₎, versus solar zenith angles 0–90° for both melting and fresh snowpack. J _(1a) is the coefficient for photolysis of nitrate, and J ₍₂₎ is the coefficient for photolysis of hydrogen peroxide. Values of J _(1a) and J ₍₂₎ are larger for fresh snow.

Fig. 2. Depth- integrated photolysis rate coefficients (i.e. transfer velocities), and , for a 1 m deep snowpack versus 0–90° solar zenith angles, for both melting and fresh snowpacks. Values of and are larger for melting snow, in contrast to Figure 1.

Depth-integrated production rates of OH radicals from the photolysis of NO₃ ⁻ and H₂O₂ are shown in Figure 3. Hydroxy radical production from H₂O₂ photolysis is over 100 times larger than from NO₃ ⁻ photolysis, as has been shown by Reference Chu and AnastasioChu and Anastasio (2005) for surface OH production and by Reference France, King and Lee-TaylorFrance and others (2007) for depth-integrated OH production rates at other snowpack sites. The results plotted in Figure 3 show that depth-integrated OH production rates are larger within the melting snowpack than within the fresh snowpack.

Fig. 3. Depth- integrated production rates, and , at 0–90° solar zenith angles for both melting and fresh snowpacks.

The molecular fluxes of gaseous NO₂ from melting and fresh snowpack at Ny-Ålesund for solar zenith angles of 30–90° and clear sky conditions are shown in Figure 4. For solar zenith angles of 60°, 70° and 80° the modelled fluxes of NO₂ from the fresh snowpack are 11.6, 5.6 and 1.7 nmol m⁻² h⁻¹, respectively, while for the melting snowpack they are 19.7, 9.1 and 2.9 nmol m⁻² h⁻¹, respectively.

Fig. 4. Flux of NO₂ produced in 1 m of fresh and melting snowpack from the photolysis rate of NO₃ ⁻ for 30–90° solar zenith angles with clear sky conditions.

Discussion

For the two snowpacks considered here, the predicted fluxes of NO₂ from the snowpack to the atmosphere are comparable with values of NO _x observed in other snowpack studies (Table 2). Maximum fluxes of NO _x above the snowpack have been measured to be ∼40 nmol m⁻² h⁻¹ at Alert, Canada (Reference Beine, Honrath, Dominé, Simpson and FuentesBeine and others, 2002a,Reference Beineb), 30 nmol m⁻² h⁻¹ at South Pole (Reference Oncley, Buhr, Lenschow, Davis and SemmerOncley and others, 2004) and 13 nmol m⁻² h⁻¹ at Neumayer, Antarctica (Reference Wolff, Hall, Mulvaney, Pasteur, Wagenbach and LegrandWolff and others, 2002). The maximum solar zenith angle was 68° for the South Pole campaign and approximately 60° for the Neuymayer and Alert studies.

The modelled fluxes of NO₂ leaving the snowpack using the TUV-snow model for the fresh and melting Ny-Ålesund snowpacks at a solar zenith angle of 60° are 11.6 and 19.7 nmol m⁻² h⁻¹ respectively. Thus, the magnitude of modelled NO _x fluxes above Ny-Ålesund snowpack is consistent with previous measurements at other sites. The actual molecular flux of NO₂ from the snowpack may be affected by secondary processes, such as photolysis of NO₂ before venting from the snowpack or snow microphysics preventing the release of NO₂ from the snowpack. Reference BoxeBoxe and others (2003, Reference Boxe2005, Reference Boxe, Colussi, Hoffmann, Perez, Murphy and Cohen2006) showed that emission rates of gaseous NO₂ from irradiated ice (containing nitrate anions) increase with increasing ice temperature. Gaseous emissions of NO₂ are partially controlled by mass transfer, and hence the morphology, of polycrystalline ice (Reference Boxe, Colussi, Hoffmann, Perez, Murphy and CohenBoxe and others, 2006). Laboratory experiments by Reference BoxeBoxe and others (2003, Reference Boxe2005) showed that photolysis of nitrate in polycrystalline ice produces large NO₂ emissions above an ice temperature of −8°C. Reference Boxe, Colussi, Hoffmann, Perez, Murphy and CohenBoxe and others (2006) could not reproduce the [NO₂]/[NO] ratio in field measurement studies, but Reference BoxeBoxe and others (2003, Reference Boxe2005, Reference Boxe, Colussi, Hoffmann, Perez, Murphy and Cohen2006) did demonstrate that there may be some loss of photogenerated NO₂ in snowpack. NO₂ loss in snowpack is minimal at higher ice temperatures. Both snowpacks considered here have temperatures greater than −8°C, and the comparative nature of this work means the loss of photogenerated NO₂ is not critical for the main result. The availability in the Arctic environment of NO _x from snowpack emissions has been shown to have a substantial impact upon the oxidative capacity of the lower troposphere, especially in the spring (Reference MorinMorin and others, 2008).

Previous work has shown that UV radiation penetrates deeper into warmer, wetter snows with larger grain sizes than into colder, drier, smaller-grained snowpacks, so wetter snowpacks have larger photolysis rate coefficients at depth (Reference Fisher, King and Lee-TaylorFisher and others, 2005). The melting snowpack described by Reference GerlandGerland and others (1999) and modelled in this work may be considered as a maritime snowpack using the classification from Reference Sturm, Holmgren and ListonSturm and others (1995) and is similar to the Scottish snowpack described by Reference Fisher, King and Lee-TaylorFisher and others (2005). The melting snowpack has a higher measured liquid water content than the fresh snowpack (Reference GerlandGerland and others, 1999), and as expected has a lower value of σ _scatt than the fresh snowpack, as liquid water effectively increases snow grain size (Reference WarrenWarren, 1982). The measured electrical conductivities of the fresh and melting snowpacks from Ny-Ålesund are similar within the top 10 cm of snowpack (Reference GerlandGerland and others, 1999). Photochemistry occurs mainly in the top 10 cm of the the snowpack, so it is speculated that ionic chemical concentrations in the two snowpacks are similar, supporting the assumption that the concentrations of nitrate and hydrogen peroxide have similar values in each snowpack. The assumption that the concentrations of nitrogen and hydrogen peroxide have similar values in each snowpack is not critical here, as our aim is to demonstrate the effect of considering photolysis at depth in the snowpack. The large difference in absorption between the two snowpacks is probably due to depositional accumulation of coloured, non-ionic chemicals (e.g. black carbon or humic material) as the snowpack ages. The older, melting snowpack, having had longer to accumulate such absorbers, will thus have a higher value of . The presence of absorbers in snowpack has been shown to cause a climatic feedback loop, leading to further melting of the snowpack due to lowering of the surface albedo, and thus increasing the absorption of solar radiation (Reference Qian, Gustafson, Leung and GhanQian and others, 2009). The TUV-snow model uses a monochromatic black carbon absorber to determine the absorption coefficient, which is a good first approximation to Svalbard soil with its high coal content (Reference FranceFrance, 2008).

An interesting result of this work is the comparison between surface photolysis rate coefficients and depth-integrated photolysis rate coefficients. The origin of the larger depth- integrated photolysis rate coefficients in the melting snow, and of the larger surface photolysis rate coefficients in the fresh snow, is shown in Figure 5. The large value of albedo and the shorter e-folding depth in the fresh snow give larger values of surface photolysis rate coefficients, but little penetration into the snowpack compared to the melting snowpack. The photolysis rate coefficient–depth profiles for the two snowpacks are equal at approximately 2 cm (nitrate) and 5 cm (hydrogen peroxide) depth in the snowpack. The value of the fresh-snowpack photolysis rate coefficient decreases faster with depth than the melting-snowpack photolytic rate constant. Integration of the photolysis rate coefficient over the depth for the snowpacks results in a larger flux of the melting snowpack than of the fresh snowpack. Therefore, snowpack photolytic emission fluxes should always be calculated using depth-integrated photolysis rate coefficients, not just surface photolysis rate coefficients.

Fig. 5. Photolysis rate coefficients versus depth within a 1 m deep snowpack for both melting and fresh Ny-Ålesund snow: (a) for photolysis of nitrate, and (b) for photolysis of hydrogen peroxide. The inserts are the same data at larger scale for the region where the photolysis rate constants of fresh and melting snowpack are equal.

Nitrate and hydrogen peroxide concentrations vary with season and depth within the snowpack. Here the concentration–depth profile of nitrate and hydrogen peroxide is considered constant. Reference France, King and Lee-TaylorFrance and others (2007) undertook a sensitivity study of the effect of three different concentration–depth profiles on the calculated molecular fluxes (and depth-integrated production rates) using the same model used here. They showed that for hydrogen peroxide photolysis the differences in calculated depth-integrated production rates of hydroxyl radical were negligible when comparing (1) a concentration–depth profile of hydrogen peroxide from a field study, (2) a constant surface concentration of hydrogen peroxide, invariant with depth, and (3) a constant concentration of hydrogen peroxide averaged over the equivalent of two e-folding depths, but invariant with depth. They repeated the calculation for nitrate photolysis using three comparable concentration–depth profiles and noted that agreement between the three calculations was within a factor of two, i.e. a much smaller uncertainty than the natural variation in concentrations of nitrate in surface snow at Ny-Ålesund, as reported by Reference BeineBeine and others (2003). The depth dependence of the nitrate or hydrogen peroxide has little effect on the flux (or depth-integrated production rate) because the concentration of hydrogen peroxide or nitrate may only decrease by a factor of four over the depth of a snow pit, whereas the spherical solar irradiance will decrease exponentially with depth (a few cm below the surface).

To test the sensitivity of depth- integrated production rates to the initial values of albedo and e-folding depth, the depth-integrated production rate of OH radicals in the melting snowpack was recalculated using 90% of the original albedo and 110% of the original e-folding values to generate a lower limit of and σ _scatt, and 110% of the original albedo and 90% of the original e-folding values to generate upper values of and σ _scatt. These newly derived values were used to calculate upper- and lower-limit depth-integrated rates for OH radical production from NO₃ ⁻ and H₂O₂ photolysis. The resulting uncertainty is insensitive to solar zenith angle, and equal to .Thus, fortuitously, a 10% error on both albedo and e-folding depth results in approximately a 10% error in depth-integrated production rates (fluxes).

Conclusions

Calculated depth-resolved photolysis rate coefficients of NO₃ ⁻ anions and H₂O_2, along with depth-integrated OH production rates and molecular fluxes of NO₂, for melting and fresh snowpacks at Ny-Ålesund show the importance of using a depth-resolved method to model photolysis rate coefficients in snowpack, rather than considering only the surface photolysis rate coefficients. The depth-integrated photolysis rate coefficients are greater for melting snow than for fresh snow. This study shows the importance of always considering the photochemistry of the total snowpack, not just of the snow surface.

Modelled fluxes from the two snowpacks, of NO₂ due to NO₃ ⁻ photolysis, at appropriate solar zenith angles are of the same order of magnitude as NO _x fluxes measured at other snowpack sites. Hydroxyl radical production from both snowpacks is dominated by H₂O₂ photolysis.