Corresponding author: M. D. King, Department of Earth Sciences, Royal Holloway University of London, Egham, TW20 0EX, UK. (firstname.lastname@example.org)
 The contribution of snow photochemistry to snow and atmospheric oxidative capacity is controlled, in part, by snow albedo and e-folding depths in snow. Albedo ande-folding depths (and thus snow photochemistry) are a function of black carbon concentration in snow. The paper presented here demonstrates the complicated response of albedo, e-folding depth (wavelengths 300–600 nm) and depth-integrated production rates of NO2and OH radicals to increasing black carbon concentration in well-characterized snowpacks of the Barrow OASIS campaign, Alaska. All snowpacks were reworked layered windpacks and were found to have similar responses to changes in black carbon concentration. The radiative-transfer calculations demonstrate two light absorption regimes: ice-dominated and black carbon dominated. The ice-dominated and black carbon dominated behavior of albedo,e-folding depth and depth-integrated production rates with increasing black carbon concentrations are presented. For black carbon concentrations greater than 20 ng g−1 (wavelength range of 300–600 nm), e-folding depth and depth-integrated production rate have an inverse power law relationship with black carbon concentration. Doubling the black carbon concentration decreases thee-folding depth to ∼70% of the initial value and for solar zenith angles greater than 60°, doubling the black carbon concentration decreases depth-integrated production rates of NO2 and OH to ∼70% and ∼65% of their original values respectively.
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where Id is the irradiance in snow at a depth d relative to a reference irradiance Id′ at depth d′. Depth, d, is deeper than d′. Note d′ is a few cm below the surface of the snowpack where all irradiance is isotropic [e.g., King and Simpson, 2001].
 Previous radiative-transfer calculations of light propagation in snowpack undertaken by the authors and others have always required the addition of black carbon to the snow to match the modeled snowpack reflectivity ande-folding depth with field measurements ofe-folding depth and reflectivity of snowpacks [e.g.,Beine et al., 2006; Fisher et al., 2005; France et al., 2010; King et al., 2005, Lee-Taylor and Madronich, 2002]. Increases in the concentration of black carbon may decrease the albedo, e-folding depth and flux of chemicals from the snowpack and vice versa. Previous studies have considered the effect of black carbon on snowpack albedo [e.g.,Aoki et al., 2000; Chylek et al., 1983, 1987; Flanner et al., 2007; Warren and Wiscombe, 1980b, 1985] but to the authors' knowledge the response of e-folding depth and depth-integrated production rate of chemicals from snowpack has not been quantified solely as a function of black carbon concentration in snowpack. The detailed field and modeling study of the Barrow snowpacks during the OASIS campaign [France et al., 2012] provided enough data to allow e-folding depth, albedo and depth-integrated production rates to be calculated as a function of black carbon.
 Albedo, e-folding depth and depth-integrated production rates of OH and NO2 radicals for four Barrow snowpacks [France et al., 2012] are calculated from irradiances within snowpack as a function of black carbon content, solar zenith angle and sky conditions (i.e., clear or completely cloudy skies). It is necessary to describe (a) the snowpits selected for this study (b) the radiative-transfer calculations of irradiance in the snow and (c) the calculations of albedo,e-folding depth and depth-integrated production rates from irradiances in the snow.
 Generally the snowpack stratigraphy constituted a basal depth hoar with intermediate layers of faceted crystals and windpacked top layers frequently coated with a thin layer of diamond dust [Domine et al., 2011]. The four snowpacks were ‘soft’, ‘hard’, ‘snow on sea-ice’ and ‘inland’ and the snowpack considered here is the hard snowpack. The hard snowpack (also considered inFrance et al. ) was located at 71.31896°N, 156.6723°W and consisted of rounded grains with a density of 0.38 g cm−3 and a temperature of −15°C. Scattering values, σscatt, of 2.0, 2.0, 1.8, 1.8, 2.0, 2.2 and 3.0 were found at wavelengths of 300, 350, 400, 450, 500, 550 and 600 nm respectively. The snowpack is characteristic of the snowpack around the atmospheric chemistry experiments near the BARC building.
2.2. Radiative-Transfer Calculations
 Irradiances in the snowpack were calculated using the radiative-transfer code in the model TUV-snow [Lee-Taylor and Madronich, 2002]. TUV-snow is a coupled atmosphere-snow radiative-transfer model with an eight-stream discrete-ordinates scheme [Stamnes et al., 1988]. Downwelling and spherical irradiances of short-wave radiation (λ = 280–700 nm, Δλ= 1 nm) were calculated from the top of the atmosphere through sixty-five unequal layers, varying from 0.001, 0.01, 1 or 2 km, to 30 unequal snow layers varying from either 0.1, 0.5, 1, 5 or 10 cm (5 thinner layers (1 mm) are at the snow surface) all within a 1 m snowpack. The atmosphere was modeled with and without thick clouds to calculate irradiances (and thus photolysis rate coefficients) for photochemical reactions in snow for clear sky conditions and to calculate albedo ande-folding depths for diffuse sky conditions respectively. To obtain diffuse sky conditions a 100 m thick cloud layer is placed 1 km above the ground with an optical depth of 16, an asymmetry factor of 0.86 and single scattering albedo of 0.9999. For the work presented here the albedo of the snowpack was calculated as a ratio of upwelling and downwelling irradiance at the snow surface. The e-folding depth,ε, was calculated by fitting equation (1), to the downwelling irradiances, Id, at depths, d, of 10, 20, 30 and 40 cm in the snowpack with a reference depth, d′, of 10 cm. The depths of 10, 20, 30 and 40 cm are within the asymptotic zone [Simpson et al., 2002; Warren, 1982] where any direct radiation entering the snowpack is effectively diffused due to multiple scattering within the upper few cm of the snowpack.
 The albedo of a snowpack is a function of solar zenith angle [Warren, 1982, 1984; Warren and Clarke, 1986; Warren and Wiscombe, 1985]. The albedo measured under diffuse-only solar illumination (i.e., no direct radiation or solely isotropic radiation) is not dependent on solar zenith angle. The albedos are reported for diffuse solar radiation to demonstrate the effect of increasing black carbon on snowpack albedo and not the effect of solar zenith angle on snowpack albedo. The calculation of thee-folding depth is independent of the absolute values of irradiance incident on the snow surface and independent of the solar zenith angle as thee-folding depth is only measured in the asymptotic zone of the snowpack (i.e., below the top few cm) where all solar direct radiation has been converted to diffuse radiation by multiple scattering in the top few cm of snow [France and King, 2012; King and Simpson, 2001; Lee-Taylor and Madronich, 2002]. Depth-integrated production rates for the photolysis of H2O2 and NO3−(reactions (2) and (4)) were calculated for clear skies at four solar zenith angles: 60°, 69°, 75°, 86°. The Earth-Sun distance was based on the date of measurement of 11th March 2009, the ozone column was 428 Dobson units with no atmospheric aerosol (the presence or absence of atmospheric aerosol will not effect the calculation ofe-folding depth or diffuse albedo). Exploratory calculations showed that the inclusion of an atmospheric aerosol profile described byElterman  reduces the photolysis coefficient for the photolysis of NO2 by ∼10% at 5 cm depth in the snowpack. Previous work by the authors [Fisher et al., 2005; France et al., 2007, 2010, 2011a, 2012; King et al., 2005] have neglected atmospheric aerosol column and the work presented here is consistent with that work. The value of under-snow albedo is not important in the work described here as the snowpack thickness is large enough (typical >3–5e-folding depths) to ensure it is optically semi-infinite as demonstrated inFrance et al.  and previously by Warren and Wiscombe [1980a]. The asymmetry factor, g, used for snow was 0.89 [Lee-Taylor and Madronich, 2002]. Aoki et al. investigated the difference for single scattering parameters (asymmetry parameter, g) for snow grains between Mie theory and Henyey-Greenstein theory and note that for BRDF calculations at greater than 1.4μm there is a difference in asymmetry parameters determined by the different methods. However, for albedo and at wavelengths less than 1.4 μm the Mie theory gives the same results as the Henyey-Greenstein theory.
 The optical properties of the snowpack may be characterized by wavelength dependent scattering and absorption cross-sections [Lee-Taylor and Madronich, 2002]. The absorption cross-section,σabs, is the sum of light absorption owing to water-ice,σabsice, and absorption owing to all light-absorbing species in the snowpack,σabs+; for the study presented here, all absorption by light-absorbing species in the snowpack is due to black carbon. The absorption cross-section of ice was taken fromWarren and Brandt  and is plotted in Figure 1. The ice absorption cross-section is not well known in the wavelength region of 200–400 nm.Warren and Brandt  noted the imaginary part of the refractive index of ice is effectively no different from zero (below 2 × 10−11) in this wavelength region and therefore the value of the ice absorption cross-section used in this work is a linearly interpolated value between values for wavelengths of 200–400 nm.
 The absorption cross-section of black carbon particles was calculated after the work ofWarren and Wiscombe [1985, 1980b] and using the Mie code of Bohren and Huffman . The absorption cross-section used for the black carbon particle is reproduced inFigure 1. Briefly the black carbon particles were assumed to be spheres of radius 0.1 μm, with a density of 1 g cm−3and a complex refractive index of 1.8–0.5i. The uncertainty in these properties will be discussed later. The calculated absorption cross-section for black carbon agrees well with the measured black carbon absorption cross-section fromBond and Bergstrom , as shown in France et al. . Albedo and e-folding depths were calculated at seven discrete wavelengths: 300, 350, 400, 450, 500, 550 and 600 nm while photolysis rate coefficients were calculated every nanometer over 290–600 nm. The albedo,e-folding depth and photolysis rate coefficients for reactions (2) and (4) were calculated with concentrations of black carbon in snow of 1, 2, 4, 8, 16, 32, 64, 128, 256, 512 and 1024 ng g−1. The range encompasses the present-day black carbon concentrations of the Barrow snowpack but also with higher and lower concentrations to assess how increasing/decreasing black carbon concentration will affect thee-folding depth, albedo and photolysis rate coefficients. The concentrations of black carbon bracket the values found experimentally [Doherty et al., 2010]. To demonstrate the accuracy of the radiative-transfer method described above, the albedo ande-folding depth were calculated for a Barrow snowpack described inFrance et al. . Figure 2 demonstrates a measured nadir reflectivity and e-folding depth, and a sample model fit to the measurements using scattering cross-sections and absorption cross-sections inFrance et al. . Reproducing snow reflectivity and e-folding depth simultaneously is a rigorous test of the method as there are less parameters (more constrained) than fitting simply albedo [e.g.,Jacobson, 2004].
2.3. Depth-Integrated Production Rate Calculations
 Detailed descriptions for the calculation of photolysis rate coefficients, J, and depth-integrated production rates are found inFrance et al. . Briefly, photolysis rate coefficients, J, for reactions (2) and (4) were calculated using,
where σis the absorption cross-section for NO3− or H2O2 taken from Chu and Anastasio [2003, 2005] respectively, Φ is quantum yield (0.71 for H2O2 and 0.34 × 10−3 for NO3−) with values adjusted for temperature (T = −10°C) taken from Chu and Anastasio [2003, 2005]respectively; I is the spherical (or point) irradiance, sometimes termed ‘actinic flux’, calculated using TUV-snow [Lee-Taylor and Madronich, 2002] within the snowpack. Warren and Wiscombe [1980a]note that the diffuse albedo for snowpacks approximates the direct albedo at a solar zenith angle of ∼60°. Thus, to a first approximation, the photolysis rate coefficient calculated at a solar zenith angle of 60° may be taken as representative of diffuse-only sky conditions. Depth-integrated production rates, F, of NO2 and OH radicals were calculated using equation (6)
where z is the depth into the snowpack and [x] is the concentration of NO3− or H2O2; 3.9 μmol L−1 [Jacobi et al., 2012] and 0.4 μmol L−1 [Beine et al., 2011] respectively. A depth-integrated production rate of NO2 may be considered equal to a potential molecular flux of photolytically produced NO2 from the snowpack to the atmosphere in the absence of secondary reactions, photolysis or any impediment by the crystal matrix. Hydroxyl radicals are very reactive and have a very short lifetime thus they are not considered to advect from the snowpack.
Equation (6)assumes a depth-independent concentration of hydrogen peroxide or nitrate.France et al. demonstrated the concentration-depth dependence of a chromophore tends to decrease over an order of magnitude with depth compared to light irradiance which decreases over many orders of magnitude over the same snow depth.France et al. also demonstrated the depth-integrated production rate of hydroxyl radical from the South Polar snowpit varied by 3–5% when considering depth-dependent chromophore concentrations or constant depth chromophore concentrations.
3.1. Effect of Black Carbon Concentration on e-folding Depth
Figure 3 plots e-folding depth versus black carbon concentration. The variation ofe-folding depth with black carbon has two regimes dependent on black carbon concentration: In the first regime, the concentration of black carbon is less than 20 ng g−1 and light absorption is dominated by ice. The wavelength dependence of e-folding depths (for wavelengths 450–600 nm) is due to the absorption cross-section of ice,σice, increasing quickly with wavelength over the range 450–600 nm, as shown in Figure 1. In the second regime, black carbon concentration is greater than 20 ng g−1, and the absorption of solar radiation in the snowpack is dominated by black carbon (Figure 3). The variation of the absorption cross-section of black carbon,σabs+, with wavelength is small relative to ice and decreases from 300 nm to 1000 nm, i.e., opposite behavior to the absorption cross-section of ice with wavelength (Figure 1).
 For concentrations of black carbon greater than 10–20 ng g−1 (depending on wavelength), the variation of e-folding depth with respect to black carbon concentration obeys a simple power law (as shown inFigure 3).
The curves in Figure 3 are fitted to equation (7) for each wavelength. The values of αE and βE are displayed in Table 1 along with the range of black carbon concentration over which the power law is valid. The exponent, βE, in equation (7) is approximately −0.5 thus a doubling of the black carbon concentration (above 10–20 ng g−1) will reduce the light penetration depth to ∼70% of its initial value. All values have an uncertainty of 1 standard deviation from fitting the power law.
Table 1. Power Law Coefficients For Relating e-Folding Depth,ε, to Black Carbon Concentration for Black Carbon Concentrations Greater Than 20 ng g−1
3.2. Effect of Black Carbon Concentration on Albedo
Figure 4plots decreasing albedo with increasing black carbon concentration under diffuse sky conditions. Large decreases of the albedo for increasing black carbon are noted but the albedo response for each wavelength is different. As the black carbon concentration increases the wavelength dependence of the albedo reverses as the absorption of light within the snowpack is influenced more by black carbon and less by water-ice as described insection 3.1. The relationship in equation (7) is not valid for albedo. The decrease or increase in albedo for doubling or halving the concentration of black carbon around 32 ng g−1 is approximately 2–3%.
3.3. The Effect of Black Carbon Concentration on Snowpack Photochemistry
Figures 5 and 6 plot the variation of F(NO2) and F(OH), respectively, as a function of black carbon concentration. The dependence of F(NO2) and F(OH) on the concentration of black carbon matches the behavior shown in Figure 3 for the e-folding depth, with ice dominated absorption below 20 ng g−1 and black carbon dominated absorption above 20 ng g−1. The variation of F(NO2) and F(OH) with black carbon is fitted to the power law in equation (8) and the values of αF and βF are in Table 2.
Note the value of βF for all snowpack with black carbon concentrations greater than 16 ng g−1 and a solar zenith angle of greater than 60° is approximately −0.5 for F(NO2) and approximately −0.6 for F(OH). Thus, a doubling of snowpack black carbon concentration will reduce F(NO2) and F(OH) to ∼70% and ∼65% of initial values respectively.
Table 2. Power Law Coefficients for Relating F(NO2) and F(OH) to Black Carbon Concentration for Black Carbon Concentrations Greater Than 20 ng g−1 and Solar Zenith Angles Greater Than 60°
 The decrease in depth-integrated production rates of OH radicals and NO2 molecules with increasing black carbon concentrations were calculated at four different solar zenith angles and clear skies (Figures 5 and 6). The black carbon concentrations used in the calculations were between 1 and 1024 ng g−1, a range that encompasses the present-day black carbon concentrations of the Barrow snowpack but also with higher and lower concentrations to assess how increasing/decreasing black carbon concentration will affect snowpack photochemistry. The large black carbon concentrations used in this study are probably unrealistically large. Depth-integrated photolytic production rates reported byFrance et al.  are the actual values calculated for the OASIS 2009 campaign as absorption by both HULIS and black carbon is considered. Chemical measurements of black carbon and HULIS were made by Voisin et al. . The study presented here considers only black carbon absorption (the most efficient absorber per gram of carbon among aerosol carbonaceous constituents [Hoffer et al., 2006]) to assess how varying black carbon concentrations will affect the photochemical production rates of snowpacks. Note the three other snowpacks studied by France et al.  gave similar results as those shown in Figures 3–6 and are included for completeness in the auxiliary material.
 The discussion will focus on five aspects of the work: the identity of the light-absorbing snowpack impurities, the absorption spectrum of black carbon and the effect of black carbon concentration on snowpacke-folding depth, albedo and snowpack photochemistry.
4.1. Identity of the Light-Absorbing Impurity
 The main sources of organic carbon to the atmosphere and to snowpack are anthropogenic activities and biomass burning [e.g., Hegg et al., 2009; Goldberg, 1985; McConnell et al., 2007], the optical parameters of organic carbon from biomass burning aerosols have been reported by Kirchstetter et al. . Brown carbon, which includes HULIS (Humic Like Substances), is highly abundant yet a weaker absorber of visible light than black carbon which has the highest absorption cross-section among carbonaceous constituents of aerosols and therefore contributes significantly to atmospheric absorption by aerosols [e.g.,Hoffer et al., 2006]. France et al. demonstrated that black carbon alone could not account for all the absorption seen in the Barrow snowpacks and an additional absorption by HULIS and other chromophores was necessary to explain variation of the cross-section of light-absorbing impurities in snowpack,σabs+, with wavelength. It is important to note the effect of increased absorption due to impurities within the snowpack upon snowpack photochemistry, e-folding depth and albedo, especially black carbon as it is produced mainly by anthropogenic activity and therefore black carbon emissions are likely to be regulated or change in future. A reader of this work may adjust the results inFigures 3 and 4for another light-absorbing impurity (or change the properties of the black carbon particle) without repeating the radiative-transfer calculations. The concentration of black carbon may be converted to a specific absorption by snowpack light absorbing impurities (i.e.,σabs+ in France et al. ) by multiplying values on the ordinate of Figures 3 and 4with the absorption cross-section of black carbon (at the correct wavelength) inFigure 1. Dividing the specific absorption (σabs+) by the cross-section of the new absorber at the correct wavelength will allow the albedo ande-folding depth inFigures 3 and 4 to be reported as a function of concentrations of the new absorber. An example (replacing black carbon with HULIS) is included in the auxiliary material as a useful example.
4.2. Black Carbon Absorption Spectrum
 A proxy for black carbon in snow was adopted from the literature [e.g., Bohren, 1986; Roessler and Faxvog, 1980; Warren and Wiscombe, 1980b, 1985]. The major sources of uncertainty of the black carbon absorption cross-section are the values of the index of refraction, size and location of the soot particle relative to the snow crystal/grain. A black carbon particle internal to the snow grain increases the absorption cross-section of the composite particle by a factor of 1.4 relative to the black carbon particle external to the snow grain [Bohren, 1986]. In this work the black carbon was deposited external to the snowpack i.e., the black carbon was rimed onto the snow during snowfall or collected on the snowpack by atmospheric deposition or wind pumping. Chylek et al. added black carbon throughout the snow grain and using a very similar radiative-transfer model toWarren and Wiscombe [1980a] calculated snow albedo. It is not clear if black carbon should be modeled internal or external to the snow grain and the study described here has taken the majority view. The imaginary index of refraction, and therefore the absorption spectrum, of black carbon span a factor of 5 [e.g., Roessler and Faxvog, 1980; Bohren, 1986]. France et al.  demonstrate the black carbon absorption spectra in Figure 1 is consistent with experimental measurements [Bond and Bergstrom, 2006]. The third uncertainty is the shape of the black carbon, a spherical black carbon particle was used [e.g., France et al., 2011a; Warren and Wiscombe, 1980b, 1985]. A needle or disk shape increases the absorption cross-section by a factor of 1.48 and 2.1 relative to the sphere [Bohren, 1986]. Comprehensive arguments by Bohren  and Warren and Wiscombe [1980a, 1980b, 1985] justify the choice of black carbon properties used in this study. Fieldwork investigating black carbon in snow [i.e., Hegg et al., 2009; Clarke and Noone, 1985; Doherty et al., 2010; Ming et al., 2009] show that the concentration values of black carbon chosen in this work are reasonable. Jacobson , Qian et al. , Wang et al. , Warren , and Warren and Wiscombe [1980a, 1980b, 1985, Figure 1] have all investigated the effect of black carbon on albedo. The study presented here is different because it takes into account real snowpacks characterized both by e-folding depth and albedo, and reports the effects of black carbon concentration one-folding depth, albedo and photochemical fluxes. Atmospheric deposition of black carbon to snowpack would (a) give a distribution of black carbon particle sizes from different sources and (b) give a distribution of different complex index of refractions from different sources. The work presented here has not considered such distributions and the reader could use the data plotted inFigures 3 and 4 to recalculate the effect on e-folding depth, albedo and depth-integrated production rates.
4.3. Effect of Black Carbon Concentration on Snowpack Penetration Depth
 To the authors' knowledge, there has been no systematic quantitative study on the effect of increasing black carbon concentrations on e-folding depths in snowpacks.Table 3 contains a survey of the previous e-folding depth measurements, their scattering and absorption cross-section as modeled by TUV-snow and the predictede-folding depth using these cross-sections. Values ofe-folding depth are reported for a wavelength of 400 nm. The values of thee-folding depth presented here are within the range of values previously reported for coastal Antarctica [Beine et al., 2006]. The Barrow snowpacks were very similar to the coastal hard windpack, as reported by Beine et al. . Figure 2 shows the e-folding depth measured for the hard windpack in Barrow and the predictede-folding depth using the model. The agreement between modeled and measurede-folding depths gives confidence to the method described in the work presented here. In the study presented here it was assumed the black carbon was uniformly mixed within the snowpack but the effect of layered snow containing different concentrations of black carbon in different layers is possible. Preliminary field and modeling work on layered windpacks does not demonstrate any need to consider different black carbon concentrations in different wind packed layers [France et al., 2011a]. The snowpack studied had been re-worked by wind events and therefore the concentrations of particles are assumed to be well-mixed in the top layers of the snowpack, thus, a constant black carbon concentration with depth is assumed. Owing to the close proximity of our study sites to human activity in Barrow, Alaska the regional black carbon concentrations given byDoherty et al.  may not be representative of the black carbon concentration in snow found around Barrow; ∼70 ng g−1 of black carbon was found in the snowpack [France et al., 2012]. It may be better to consider the black carbon concentrations in Barrow akin to that of Eastern Russia; mean CequivBC values of (65 ± 44) ng g−1 [Doherty et al., 2010].
Table 3. Comparison of Measured and Predicted e-Folding Depths in Snow With Optical Constants Obtained From Radiative-Transfer Calculations
4.4. Effect of Black Carbon Concentration on Albedo
 The amount of black carbon in snow controls the albedo and just a small concentration of black carbon, i.e., 5 × 10−8 g g−1, increases the imaginary part of the refractive index by more than a factor of 10 [Chylek et al., 1983]. There have been many modeling studies into the effect of black carbon concentration on albedo [e.g., Jacobson, 2004; Qian et al., 2009; Wang et al., 2011; Warren, 1984; Warren and Wiscombe, 1980a, 1980b, 1985] that have mainly dealt with hypothetical snowpacks and the study presented here, in contrast, uses measurements on a specific snowpack that were part of a wider field campaign and plots albedo versus black carbon concentration for a specific wavelength.
4.5. The Effect of Black Carbon Concentration on Snowpack Photochemistry and Future Outlook
Lee-Taylor and Madronich  produced a very useful plot to calculate ∫ J(NO3−)dz/J(NO2 ↓), i.e., the depth-integrated photolysis rate constant of nitrate photolysis relative to surface downwelling photolysis coefficient for gaseous nitrogen dioxide (which is frequently measured for field campaigns) as a function of snow albedo,e-folding depth orσabs+. It is not possible to use Lee-Taylor and Madronich [2002, Figure 5] to generate the figures (Figures 3 and 4) presented in this work as albedo and e-folding depth are also a function of black carbon. The work ofLee-Taylor and Madronich [2002, Figure 5] is an excellent resource for field workers who may have measurements of albedo, e-folding depth and J(NO2 ↓) and want to estimate ∫ J(NO3−)dz whereas the work presented here demonstrates how the albedo, e-folding depth and depth-integration photolysis coefficients of reactions (2) and (4) respond to increasing or decreasing black carbon concentrations for snowpacks characterized in Barrow, Alaska in Spring.
 Inspection of Table 2 demonstrates that for solar zenith angles greater than 60° and black carbon concentrations greater than 20 ng g−1, the depth-integrated production rate of NO2production from snow approximately follows the inverse square-root of the concentration of black carbon (i.e., ). The depth-integrated production rate of OH radicals is similar but the power is closer to 0.6 (i.e., ). Such a simple approximate relationship can be used to estimate depth-integrated production rate response to increasing or decreasing black carbon scenarios for black carbon concentrations greater than 20 ng g−1i.e., doubling the black carbon in snow would reduce the depth-integrated production rates of NO2 and OH radicals to ∼70% and ∼65% of their initial values.
 Future trends of black carbon concentrations within snow are difficult to predict as the main controls are anthropogenic processes. Black carbon concentrations in snow have varied significantly during the past 215 years, gradually rising toward the mid 1800s until industrialization caused a sharp increase in black carbon concentrations [McConnell et al., 2007]. For around 50 years, after 1900, the seasonal variability of black carbon concentrations lessened as winter concentrations matched the normally higher summer concentrations but in the late 20th Century black carbon concentrations once again became seasonal [McConnell et al., 2007]. Ice cores from Greenland show that by 2000, black carbon concentrations in snow/ice equaled the pre-industrial concentration of 1–2 ng g−1 in clean snowpack regions [Doherty et al., 2010]. Doherty et al.  reported no increase in the black carbon concentrations of Arctic snow since 1984. Flanner et al. suggest that black carbon in midlatitude snow may be contributing indirectly to melt Arctic sea-ice by enhancing warm-air advection into the Arctic.Rosen et al.  show that aerosol at Barrow, Alaska has a large increase in black carbon during winter to spring, almost as large as found in urban areas. Sharma et al.  and Garrett et al. indicate the large black carbon concentrations seen in Barrow in winter and spring are due to long-range transport of pollutants. Black carbon removal is most efficient at warmer temperatures and higher humidities, thus a future warmer and wetter Arctic could be cleaner [Garrett et al., 2011].
 A decrease in black carbon concentrations in the snow will increase depth-integrated production rates of OH radicals and NO2 molecules and increase the oxidative capacity of snowpack and the atmospheric boundary layer above [e.g., Jones et al., 2001]. A “warmer” snowpack will tend to have a larger grain size and thus smaller values of σscatt leading to snowpacks with large e-folding depth, seeTable 3 [Fisher et al., 2005] and Warren for a detailed explanation. Thus “warmer” snowpacks may produce larger depth-integrated production rates of OH radicals and NO2 [Fisher et al., 2005] and as black carbon in snow causes warmer snowpacks, a future warmer climate could have two effects on snow photochemistry: First, snow photochemistry may become important (larger molecular fluxes from snowpack) in a warming world owing to more photochemistry occurring in the warm snowpack and second, a warming climate may cause a loss of snowpack thus snow photochemistry will become less important due to less snow cover. Thus a scenario may be envisaged where snow photochemistry may have a large effect on the oxidative potential of the overlying atmosphere but for a shorter duration.
 Increasing black carbon concentrations in snow reduces albedo, e-folding depths and depth-integrated production rates of photochemically derived species in a complicated way. For black carbon concentrations typically measured in the snow,e-folding depth, albedo and depth-integrated production rates of OH and NO2can switch from ice-dominated absorption to black carbon dominated absorption. Thee-folding depths and depth-integrated production rates (of NO2 and OH radicals) follow a power law relationship for black carbon concentrations greater than 20 ng g−1 and solar zenith angles greater than 60°.
 Black carbon amounts in snow are very closely linked to human activity and therefore the reduction or increase of depth-integrated production rates of OH and NO2 are linked to the increase or reduction of black carbon in the snow.
 M.D.K. and J.L.F. thank NERC (NE/F010788/1 and NE/F004796/1) and NERC FSF (555.0608). H.J.R. thanks RHUL for a Thomas Holloway studentship. M.D.K. also gratefully acknowledges receipt of an RSF award from RHUL. We thank an anonymous reviewer for the suggested calculations involving HULIS in the auxiliary material.