First spectral measurements of light attenuation in Greenland Ice Sheet bare ice suggest shallower subsurface radiative heating and ICESat-2 penetration depth in the ablation zone

Light transmission into bare glacial ice affects surface energy balance, bio-photochemical cycling, and light detection and ranging (LiDAR) laser elevation measurements but has not previously been reported for the Greenland Ice Sheet. We present in-ice solar irradiance measured over the spectral range 350 900 nm and 12 77 cm depth collected at a site in the 15 western Greenland ablation zone. The acquired spectral irradiance measurements are used to calculate flux attenuation coefficients using an exponential decay Bouguer law model and are compared to values calculated from two-stream radiative transfer theory. Relative to asymptotic two-stream theory, our empirical attenuation coefficients are up to one order of magnitude larger in the range 350 530 nm, suggesting light absorbing particles embedded in ice enhance visible light absorption at our field site. The empirical coefficients accurately describe light attenuation in the ice interior but underestimate 20 ligh a en a ion nea he ice face. Con e en l , Bo g e la o e e ima e an mi ed fl b p o 50% depending on wavelength. Refraction is unlikely to explain the discrepancy. Instead, vertical variation in the ice microstructure and the concentration of light absorbing particles appears to enhance near-surface attenuation at our field site. The magnitude of this near-surface attenuation implies that optical penetration depth is lower by up to 19 cm (28%) at wavelengths relevant to visiblewavelength lidar altimetry of ice surface elevation (e.g. 532 nm for the Ice, Cloud, and Land Elevation Satellite-2) than is 25 suggested by e-folding depths inferred from two stream theory for optically pure glacier ice. This enhanced near-surface attenuation implies shallower light transmission and therefore lower subsurface light availability for subsurface radiative heating and bio-photochemical cycling. We recommend radiative transfer models applied to bare ice in the Greenland Ice Sheet ablation zone account for vertical variation in light attenuation due to the vertical distribution of light absorbing particles and ice microstructure, and we provide new values of flux attenuation, absorption, and scattering coefficients to support model 30 validation and parameterization. https://doi.org/10.5194/tc-2020-53 Preprint. Discussion started: 17 March 2020 c © Author(s) 2020. CC BY 4.0 License.


Introduction
Understanding the transmission, absorption, and scattering of light in ice is important for snow and ice energy balance modelling (Brandt and Warren, 1993), lidar remote sensing of snow surface elevation and grain size (Deems et al., 2013;Yang et al., 2017), primary productivity beneath sea ice Grenfell, 1979), bio-photochemical cycling in ice and 35 snow (France et al., 2011), and heo e ical p edic ion of Sno ball Ea h paleoclima e (Dadic et al., 2013;Warren et al., 2002). Each of these applications requires knowledge of the vertical distribution of light attenuation in ice, which for a medium (such as glacier ice) that both absorbs and scatters light is specified by the spectral flux attenuation coefficient: (1) where [m -1 ] is the spectral flux absorption coefficient, [m -1 ] is the spectral flux scattering coefficient, and all are functions of wavelength, . This study reports on of bare glacier ice in the Greenland Ice Sheet ablation zone, a critical 40 parameter needed to calculate subsurface absorption and backscattering of transmitted radiation that to our knowledge has received no direct field study.
Measurements of in snowpack and sea ice indicate three main sources of variation with relevance to geophysical applications. First, the magnitude of is primarily controlled by ice microstructure via its control on , which for the 45 range of air bubble and ice grain sizes observed in natural snow and ice is nearly independent of wavelength (Perovich, 1996).
Spectrally, is low in the near-ultraviolet and blue-green spectral region (~250 600 nm) where is extremely low (<10end of the solar spectrum (Warren and Brandt, 2008). Vertically, is at a maximum at the incident boundary (the snow or ice surface) where a significant portion of upwelling radiation (i.e. transmitted flux reflected upwards) escapes the ice volume 50 before re-reflection downward. Within this near-surface optical boundary layer (Bohren and Barkstrom, 1974), attenuation rates rapidly decrease with depth to an asymptotic value as multiple scattering establishes an isotropic (diffuse) radiation field (Briegleb and Light, 2007;Warren, 1982). For fine-grained dry snow, a few cm depth is typically sufficient to reach the diff e a mp o ic egime where is constant (Brandt and Warren, 1993). For sea ice the depth required is typically larger and can exceed >20 cm depending on near-surface ice microstructure and the vertical location of the refractive boundary if 55 present (Grenfell, 1991;Grenfell and Maykut, 1977). Attenuation coefficients are also influenced by the horizontal distribution of ice type and surface cover  but this source of variation is not examined here.
In addition to experimental values obtained from measurements of light transmission in ice or snow, is obtained analytically from optical theory (Bohren, 1987;Warren et al., 2006). Light attenuation in pure ice is specified analytically by 60 the complex index of refraction i , where is the real refractive index (~1.31 in the visible), is the imaginary index, is wavelength, and , 4 is the absorption coefficient of pure ice (Warren et al., 2006;Warren and Brandt, 2008). Light attenuation in glacier ice differs from pure ice owing to compositional and structural factors https://doi.org/10.5194/tc-2020-53 Preprint. Discussion started: 17 March 2020 c Author(s) 2020. CC BY 4.0 License.
that control scattering and absorption, such as the size, geometry, and vertical distribution of embedded light absorbing particles (LAPs) and light scattering air bubbles and ice grains of size > wavelength (Askebjer et al., 1997;Picard et al., 2016;65 Price and Bergström, 1997;Warren et al., 2006). Analytical methods typically assume ice and snowpack can be approximated as homogeneous plane-parallel slabs of spherical ice grains and/or air bubbles, for which Mie theory is used to calculate singlescattering properties and two-stream radiative transfer theory is used to calculate multiple scattering and bulk absorption in the ice volume. Such models have been used to calculate subsurface meltwater production caused by penetration of solar radiation in ice both in Greenland (van den Broeke et al., 2008;Kuipers Munneke et al., 2009) and Antarctica (Brandt and Warren, 70 1993;Hoffman et al., 2014;Liston et al., 1999aListon et al., , 1999bListon and Winther, 2005). However, theoretical values for used as input to such models are rarely validated experimentally, and to our knowledge no such experimental values exist for glacier ice.
In addition to ice surface energy balance, understanding light attenuation in ice is important for interpreting interactions 75 between visible-wavelength light sources and ice surfaces, for example laser altimetry measurements of ice surface elevation (Deems et al., 2013;Gardner et al., 2015;Greeley et al., 2017). The reciprocal of is the attenuation length, or the average distance travelled by a photon before attenuation by absorption or scattering (Ackermann et al., 2006). In the context of altimetry, the attenuation length is sometimes referred to as the penetration depth, or the average depth to which the electromagnetic signal penetrates before it is backscattered to the atmosphere (Ridley and Partington, 1988;Rignot et al., 2001;80 Zebker and Weber Hoen, 2000). The laser altimeter onboard Ice, Cloud, and Land Elevation Satellite-1 (ICESat-1) transmitted 1064 nm laser pulses to measure the distance (range) between the satellite and ice sheet surfaces (Schutz et al., 2005). Photons with wavelength 1064 nm penetrate snowpack no more than a few centimetres (Brandt and Warren, 1993;Järvinen and Leppäranta, 2013). This length scale is smaller than typical laser altimetry surface elevation errors due to ice and snow surface roughness and geolocation uncertainty (Deems et al., 2013). In contrast, the laser altimeter onboard ICESat-2 transmits 532 85 nm laser pulses (Markus et al., 2017). Ice is ~10 more transparent at 532 nm than at 1064 nm (Warren and Brandt, 2008), and photons at 532 nm may penetrate many tens of centimetres into glacier ice. These subsurface scattered photons may introduce a range bias in ICESat-2 surface elevation retrievals over glacier ice, similar to radar penetration into snow (Brunt et al., 2016;Gardner et al., 2015;Greeley et al., 2017). To our knowledge no in situ observations of 532 nm optical penetration depth for bare glacier ice exist, thereby precluding field validation of penetration depth obtained from theoretical radiative 90 transfer models.
The purpose of this investigation is to provide experimental values for obtained from measurements of solar flux attenuation in bare ice in the Greenland Ice Sheet ablation zone, and to compare them with theoretical values for obtained from the two-stream analytical solution (c.f. Eq. 26 Bohren, 1987;Schuster, 1905). We benchmark our field estimates against 95 the two-stream solution because of its wide use in surface energy balance models applied to snow and ice. In Sect. 2 we describe the field measurements and the optical theory used to interpret the solar flux attenuation. In Sect. 3 we report values https://doi.org/10.5194/tc-2020-53 Preprint. Discussion started: 17 March 2020 c Author(s) 2020. CC BY 4.0 License. for and obtained from our measurements, compare them with values obtained from two-stream theory, and propose a simple empirical model that accounts for enhanced near-surface attenuation. In Sect. 4 we discuss how our values differ from prior experimental values acquired in sea ice and snowpack and from theoretical values, and the implication of these 100 differences for modelling radiative transfer in bare glacier ice. To demonstrate the broader implications of our study, we suggest how our findings can be used to understand interactions between visible-light laser altimetry (e.g. ICESat-2) and bare glacial ice surfaces, and how they can be used to improve models for subsurface heating of ablating glacier ice.

Transmittance measurements 105
Ice transmittance was measured on 20 July 2018 in the Kangerlussuaq sector of the western Greenland Ice Sheet. The study site (67.15 o N, 50.02 o W) is located ~1 km from the ice sheet margin at 840 m a.s.l. Subsurface (in-ice) spectral irradiance was measured at 0.35 nm spectral resolution in the wavelength range 300 900 nm with an Ocean Optics® JAZ spectrometer calibrated for absolute irradiance. Light was guided from the ice interior to the spectrometer with a 3 mm diameter Kevlarsheathed fibre optic cable fitted inside a 2 m long insulated white PVC tube ( Figure 1). The fibre was affixed at one end to a 110 Spectralon remote cosine receptor (RCR) diffuser via a 90 o collimating lens adapter. The RCR barrel was wrapped in white PTFE tape and set 2 mm out from the PVC tube exterior to act as a contact horizon between its diffusing element and the ice.
The system was operated from a battery-powered computer running the Ocean Optics Ocean View software. The computer and spectrometer were placed on a tripod platform oriented 180 o away from the sun and 2.5 m horizontal distance from the measurement location. 115 To access the interior of the ice, holes were drilled horizontally into a 2-m high sidewall of a natural ice feature with a battery powered hand drill fitted with a 3 cm diameter Kovacs auger bit. Each hole was drilled 2 m deep into the ice. Starting at the lowest hole near the bottom of the sidewall, the auger was advanced into the sidewall approximately 20 cm, levelled horizontally with a digital spirit level, and the sequence repeated to 2 m horizontal depth. The PVC tube-fibre optic assembly 120 was then inserted into the hole, RCR facing upward, and a 2 m long ruler was shimmed under the bottom of the PVC tube to ensure the RCR barrel preserved contact with the overlying ice thus minimizing stray light contamination into the RCR field of view. Ice shavings were packed around the drill hole to prevent light reflection into the hole. Spectral irradiance was recorded at 1 Hz frequency using a 20-scan average and 44 Hz integration time for 30 seconds yielding 30 irradiance profiles, after which the tube was removed, the next hole was drilled, and the sequence was repeated working from the bottom toward the 125 ice surface.
Background upwelling and downwelling spectral irradiance were measured continuously at 2 m height above the ice surface approximately 3 m away from the in-ice measurements using a dual-channel Ocean Optics JAZ spectrometer calibrated for https://doi.org/10.5194/tc-2020-53 Preprint. Discussion started: 17 March 2020 c Author(s) 2020. CC BY 4.0 License. absolute irradiance. These data were recorded at 1 min frequency using a 20-scan average and 92 Hz integration time. Light 130 was guided to the spectrometer via two 3 m fibre optic cables attached to two RCRs mounted in upward-looking and downward-looking orientation on a 2 m long horizontally levelled boom attached to a vertical mast drilled into the ice. The measurements were completed between 13:45 and 14:35 local time (UTC -3), at solar zenith angles of ~48 51 o . Solar noon at this time and location is ~13:26.

Experimental determination of asymptotic flux attenuation coefficients 135
Spectral asymptotic flux attenuation coefficients are estimated by fitting a Bouguer-law exponential decay model as per Grenfell and Maykut (1977) to the in-ice irradiance depth profiles: where λ is the asymptotic flux attenuation coefficient for wavelength λ, I z is in-ice spectral irradiance at depth z, I z is background downwelling spectral irradiance, z is the ice surface, and z, λ I z, λ /I z , λ is spectral transmittance.
The raw 0.35 nm spectra were interpolated to 1 nm using bilinear interpolation and smoothed with a centred moving mean 140 filter with window size 3 nm. Estimates of λ for each 1 nm band were estimated as the slope of the ordinary least-squares linear solution to ln z, λ vs. z z ).
The optical depth z, λ is a dimensionless path length that scales the physical thickness of a layer by its attenuation rate: The attenuation length λ is the inverse of λ , and is referred to elsewhere as the photon mean free path (Ackermann et 145 al., 2006). It is equivalent to the path length in ice required to attenuate irradiance to 37% (1/ ) of its incident intensity, i.e. the path length at which 1/ and 1: Note that attenuation is expressed in terms of λ in Sect. 3.4 and 4.3 to describe its physical in-situ length-scale. Solid iceequivalent values of λ , λ , and λ are provided in Appendix 1.

Theoretical determination of asymptotic flux attenuation coefficients 150
Theoretical values of λ are calculated using the solution given by the two-stream radiative transfer approximation (Schuster, 1905): where is ice sample density (kg m -3 ), is pure ice density (917 kg m -3 ), is the extinction efficiency, is the effective scattering particle radius (m), is the average cosine of the scattering angle, and is the single-scattering albedo. Eq. (5) describes light attenuation by multiple scattering and absorption in a homogeneous plane-parallel slab of 155 absorbing spheres. Its derivation is available in Bohren (1987).
To estimate , Eq. (5) is iteratively solved for the value of that minimizes the difference between measured and calculated at 600 nm. This method assumes all absorption at 600 nm is due to ice (Warren et al., 2006). If absorption was influenced by LAPs would be over-estimated. Values for , , and are obtained from Mie scattering 160 algorithms provided as MATLAB code by Mätzler (2002), is from Warren and Brandt (2008), and is obtained from an ice core extracted at the measurement location with depth-weighted measured ice density 835 kg m -3 . The optimal value is 2.8 mm and this value is used in all subsequent calculations. Warren et al. (2006) developed a method to estimate , from measurements of flux attenuation in snow in Antarctica. 165

Flux absorption coefficients
The method relies on three assumptions: 1) the value of , at 600 nm is known accurately, 2) the value of at 600 nm is not affected by LAPs in the measured snow or ice, and 3) varies so little as to be effectively independent of wavelength in the spectral range considered (here the near-UV and visible). Warren et al. (2006) verified the validity of these assumptions for the spectral range 350 600 nm and obtained the following relation (Eq. 15 of that paper) between flux attenuation and flux absorption: 170 (6) where 600 nm is the reference wavelength. Eq. (6) was used by Warren et al. (2006) to estimate for pure ice (i.e. , ) from 350 600 nm.
Eq. (6) requires that absorption at the reference wavelength (600 nm) is not affected by LAPs but the relation can be used to estimate at any other wavelength, including those where absorption is affected by LAPs. At those wavelengths, Eq. (6) 175 will predict values for higher than those for pure ice if LAPs are present in the measured snow or ice volume, due to the influence of LAPs on . Consequently, although not developed for this purpose, Eq. (6) provides a means to infer the influence of LAPs on measured flux attenuation by comparison with values of , provided by Warren et al. (2006), which are compiled in Brandt and Warren (2008). A similar approach was used to infer LAP absorption in snowpack (Tuzet et al., 2019). Here, we exploit this to interpret differences between our theoretical and experimental values of on the basis of 180 differences between , (Warren et al., 2006) and the values that we obtain for glacier ice from Eq. (6).

Near surface effects
The λ values calculated using Eq.
(2) are applicable at distances far enough from the incident boundary (here the ice surface) that the radiation field is diffuse and λ is constant with depth. Near the ice surface the radiation field is converted via multiple scattering from direct to diffuse flux, and attenuation is enhanced by transmission of upward reflected light out of 185 the ice volume before re-reflection downward (Briegleb and Light, 2007). Attenuation may also be enhanced by specular reflection at the ice surface, depending on its roughness (Dadic et al., 2013;Mullen and Warren, 1988). To parameterize these near-surface effects, we introduce a modified form of Eq. (2): where χ is the fraction of incident spectral irradiance attenuated in the near-surface boundary layer (inclusive of the surface) and all other terms are as previously defined. The χ parameter is analogous to the parameter introduced by Grenfell and 190 Maykut (1977) to partition the bulk (spectrally-integrated) net absorbed solar flux between the upper 10 cm of sea ice, which he e med he S face Sca e ing La e (SSL), and he ice in e io , in hich adia ion i e ponen iall a en a ed at a constant rate. The parameter has been widely adopted in energy balance models of glaciers and sea ice where radiation penetration is important (Bintanja and Van Den Broeke, 1995;Hoffman et al., 2014;Holland et al., 2012). For example, the sea ice component of the Community Earth System Model (CESM) uses 30% (Briegleb and Light, 2007). The important 195 distinction is that is a spectrally integrated value applicable to energy balance modelling whereas χ is applicable for comparison with measurements of downward spectral irradiance within ice.

Spectral transmittance measurements
Four spectra of in-ice irradiance were collected at 12 cm, 36 cm, 58 cm, and 77 cm depth below the ice surface ( Figure 2a). 200 These spectra are normalized by the coincident-in-time surface spectra to calculate spectral transmittance, (Figure 2c). At all depths, is maximum at 430 nm and maintains relatively stable and high values up to about 500 nm in the visible, beyond which decreases into the red end of the visible spectrum where absorption by ice is higher. Maximum values vary from 78% at 12 cm to 41% at 77 cm. For λ 500 nm rapidly decreases both with wavelength and with depth. Beyond about 800 nm nearly all incident light is attenuated below 36 cm, with <2% at 36 cm and <0.6% at 58 and 77 cm depth. In contrast, 205 at 12 cm decreases from 18% at 800 nm to 5% at 900 nm, suggesting substantial subsurface flux absorption in the 12 36 cm depth region (Figure 2c).

Field estimates of flux attenuation coefficients and albedo
Example log-linear fits to Eq.

215
Albedo spectra correspond closely to patterns in transmittance and spectra ( Figure 3c). The near-UV and blue wavelengths that efficiently transmit into ice mostly re-emerge as reflected light, owing to the extremely low values of ice absorption coefficient in the wavelength range 350 500 nm where albedo is maximum (Warren et al., 2006). The maximum measured albedo value (0.83) occurs at 447 nm, suggesting a slight red shift relative to the location of the minimum value (0.96 m -1 ) at 396 nm, however albedo varies little in the region of minimum and is 0.82 at 396 nm. Beyond about 500 nm, albedo 220 decreases rapidly, and most transmitted light is absorbed, as indicated by the larger values and the extremely low transmittance at depths below 36 cm.

Theoretical flux attenuation coefficients
Theoretical values predicted by the two-stream solution are nearly one order of magnitude lower than field estimates of for λ 500 nm (blue circles vs orange line, Figure 4a). This discrepancy can be inferred to relate to the presence of LAPs 225 embedded in the ice matrix that increase the effective absorption of the ice volume. For example, differences between the fieldestimate of and , (Figure 4b) mirror those between the field-estimate and theoretical estimate of ( Figure 4a).
Namely, is nearly one order of magnitude larger than , in the range 350 500 nm, where even very small concentrations of LAPs in the measured ice volume would dominate absorption (Warren et al., 2006). In contrast, the twostream solution and theory converge at λ 530 nm where absorption is dominated by grain-size effects. 230 To gain further insight into the mechanisms that drive differences between field estimates and two-stream theory, we compare  Warren et al., 2006). This holds true when considering structural differences between snow and ice that control scattering (i.e. snow grains vs air bubbles) since https://doi.org/10.5194/tc-2020-53 Preprint. Discussion started: 17 March 2020 c Author(s) 2020. CC BY 4.0 License. ≫ in either case. In contrast, field estimates for glacier ice clearly diverge from theoretical estimates with a wavelengthdependent offset in the spectral range 350 530 nm where LAPs dominate absorption (blue circles vs. orange line, Figure 4a).
Finally, it is evident that scattering by fine-grained snow greatly enhances flux attenuation. This comparison provides a useful 245 contrast between the flux attenuation properties of snow vs glacier ice that is discussed in Sect. 4.

Transmitted irradiance and near-surface attenuation
Nea he ice face i adiance i no a en a ed e ponen iall and Bo g e la doe no hold, a confi med b heintercepts of the straight lines in Fig. 3b at values <100%. This suggests values are higher in the 0 12 cm near-surface region where irradiance measurements were not obtained. Consequently, transmitted irradiance is overestimated by 5 50% if 250 Bo g e la is applied to the incident surface irradiance using values from the 12 77 cm region, with median overestimation 16% (Figure 5a). The value of χ (Eq. (7) that minimizes the root-mean-squared-difference between measured and predicted transmitted irradiance, weighted equally at all depths and all , is 15%. Transmitted irradiance spectra predicted using Eq. (7) with χ 15% are shown in Figure 5c.

255
Expressed in terms of attenuation rate, effective values for the 0 12 cm region estimated from a finite-difference solution to Eq. (2) are ~1.5 higher than those in the 12 77 cm region for λ 570 nm, and are up to 3.7 higher between 400 570 nm ( Figure 6). This suggests attenuation enhancement by LAPs is higher in the 0 12 cm region than in the 12 77 cm region, consistent with the expectation that impurity concentration is higher near the ice surface. Stated in terms of attenuation length, varies from 117 cm at 356 nm to 14 cm at 700 nm. These values are calculated by combining the effective values for the 260 0 12 cm region with the values for the 12 77 cm region and therefore correspond to effective penetration depths. Effective penetration depths are smaller than attenuation lengths inferred from values for the 12 77 cm region (i.e. from Eq. 4), owing to the higher attenuation in the 0 12 cm region. The effective penetration depth at 532 nm is 49 cm, or 15 cm lower than the 64 cm attenuation length implied by our empirical values in the 12 77 cm region, and 19 cm lower than the 68 cm attenuation length implied by theoretical values for optically pure glacier ice. 265 The enhanced near-surface attenuation found here is consistent with observations of enhanced attenuation in the granular and porous surface layer on sea ice (Grenfell and Maykut, 1977). The field measurements were collected following several days of light but persistent rainfall and cloud cover, conditions that inhibit development of granular near-surface ice (e.g. ea he ing c ) (Müller and Keeler, 1969). Qualitatively, the ice surface was semi-granular to a depth of ~4 cm, below 270 which the ice transitioned to solid bubbly ice (Figure 7). For example, the upper four centimetres of ice core could not be recovered owing to its granular structure. The recovered core was split into three segments corresponding to depths of 4 45 cm, 45 74 cm, and 74 122 cm below the ice surface. The density of these segments was 801 kg m -3 , 884 kg m -3 , and 888 kg https://doi.org/10.5194/tc-2020-53 Preprint. Discussion started: 17 March 2020 c Author(s) 2020. CC BY 4.0 License. m -3 , respectively. An ice screw was used to recover an ice sample from the upper 8 cm. The density of this ice was 699 kg m -3 , confirming the presence of low-density granular near-surface ice. 275 For smooth ice surfaces, attenuation may be enhanced by refraction at the ice-air interface (Mullen and Warren, 1988). If present, a refractive boundary would enhance near-surface attenuation via external specular reflection, and possibly via enhanced near-surface absorption of the internally reflected downward flux. Following Briegleb and Light (2007), we calculate the external diffuse specular reflectivity for a flat ice surface to be 0.063, meaning specular reflection could enhance attenuation 280 by up to 6.3%. This value is smaller than the 10 25% surface attenuation implied by the y-intercepts in Figure 3c, suggesting specular reflection alone cannot explain the discrepancy. Instead, we suggest that enhanced scattering by the granular nearsurface ice microstructure, together with absorptive impurities, enhanced near-surface light attenuation at our field site.

Uncertainty analysis
We repeated the entire analysis reported in Sect. 3 using 801 kg m and 884 kg m , values that bracket the 285 range of ice density measured in the ice interior. The optimal values were 2.5 mm and 3.2 mm, respectively. However, the single-scattering properties varied so little (max difference 0.2% for 800 nm) that all reported results were identical. The ice-equivalent values given in Appendix 1 are referenced to the depth-weighted ice density measured in the 4 74 cm region (835 kg m -3 ). The reader is advised that ice density varied from 801 884 kg m -3 between 4 122 cm depth; however, this analysis reports on measurements collected between 12 77 cm depth, for which ice density varied from 801 842 kg m -3 . 290 Two separate observers made ten independent measurements of the vertical distance between the in-ice irradiance collections.
The mean error ( one standard deviation) was 0.9 1.2 cm. During the period 19 22 July one of these observers measured the height of an ablation stake using the same ruler that was used to measure the vertical distance between the in-ice irradiance collections. Two measurements were taken each time, for 41 total replicates. The mean error ( one standard deviation) was 295 0.2 1.2 cm. This suggests 1.2 cm is a reasonable approximation for vertical measurement uncertainty, and is represented as horizontal uncertainty bars on the in-ice transmittance values in Figure 3b and as shaded uncertainty bounds on the nearsurface attenuation rates in Figure 6.

Comparison with attenuation spectra for sea ice and snowpack 300
We report first spectral measurements of near-UV and visible light transmission in bare ablating glacier ice. These measurements are used to estimate asymptotic flux attenuation coefficients for the spectral range 350 700 nm. Prior studies quantified for sea ice (c.f. Frey et al., 2011;Grenfell and Maykut, 1977;Light et al., 2008;Pegau and Zaneveld, (Fisher et al., 2005;Gerland et al., 2000;Järvinen and Leppäranta, 2013;King and Simpson, 2001;Meirold-Mautner and Lehning, 2004;Picard et al., 2016;Tuzet et al., 2019;Warren et al., 2006), and for compressed glacial ice at 800 305 2350 m depth in the Antarctic Ice Sheet for which optical scattering is not representative of near-surface ablating glacier ice (Ackermann et al., 2006;Askebjer et al., 1995Askebjer et al., , 1997. Light attenuation in glacier ice differs from sea ice and snowpack in several important ways. Figure 8 compares the spectra for glacier ice measured here to seven previously published spectra for snowpack and sea ice. Light attenuation in sea ice 310 is controlled by its unique vertical composition, including brine inclusions, air pockets, solid salts, sea ice algae, dissolved organic matter, and radiative interactions between the ice and underlying ocean (Perovich, 1996). Relative to prior measurements in sea ice Grenfell and Maykut, 1977), our results suggest light attenuation by glacial ice is lower at blue-green wavelengths and higher at orange-red wavelengths, likely reflecting differences in the absorption spectra of light absorbing material found in sea ice relative to that found in glacier ice (Figure 8). Relative to prior measurements made 315 in snow near Summit, Greenland (Meirold-Mautner and Lehning, 2004), our results suggest attenuation by glacial ice has a similar spectral shape but lower attenuation at all wavelengths, likely due to enhanced scattering from the fine-grained structure of polar snow. Snow near Dome-C in Antarctica has lower attenuation at blue-green wavelengths than snow near Summit, Greenland, but is nearly identical at longer wavelengths, suggesting visible-light attenuation at Summit is enhanced by higher LAP concentration. Attenuation within the surface scattering layer (SSL) of sea ice is higher still, and attenuation at 5 cm 320 depth in snow near Summit is highest of all, likely due to direct scattering of light out of the near-surface optical boundary layer. The comparison demonstrates the tremendous variation in values caused by differences in ice structure and composition, and the importance of site-specific studies such as ours for characterization of ice optical properties.

Relevance to surface energy balance modelling and subsurface meltwater production
Our field estimates of are up to one order of magnitude larger in the spectral range 350 530 nm than those obtained from 325 two-stream theory for optically clean ice. This is important because visible light transmission provides an energy source for subsurface heating and internal melting of glacier ice in the ablation zones of glaciers and ice sheets (Cooper et al., 2018;Hoffman et al., 2014;Liston and Winther, 2005;Schuster, 2001). Prior estimates of subsurface meltwater production in bare ice used two-stream theory forced by values of for pure ice to calculate and the absorbed solar flux as a function of depth below the ice surface in both Greenland and Antarctica (van den Broeke et al., 2008;Hoffman et al., 2014;Kuipers 330 Munneke et al., 2009;Liston and Winther, 2005). Comparison with the spectral absorption coefficient of pure ice (Figure 4c) suggests the discrepancy we find is likely due to LAPs present in the measured ice volume, which appear to disproportionately enhance energy absorption near the ice surface.
Examples of LAPs found in near-surface glacier ice include dust, black carbon, and microorganisms such as cyanobacteria 335 and algae, each of which absorb light at wavelengths < ~600 nm (Bøggild et al., 2010;Ryan et al., 2018;Stibal et al., 2017; https://doi.org/10.5194/tc-2020-53 Preprint. Discussion started: 17 March 2020 c Author(s) 2020. CC BY 4.0 License. Takeuchi, 2002;Warren et al., 2006;Yallop et al., 2012). To our knowledge, the influence of LAPs on subsurface meltwater production has not been quantified and is beyond our scope here, but our results point to the potential for subsurface energy absorption enhancement by LAPs in ablating glacier ice. This is consistent with inferences made for surface melt rates caused by distributed LAPs on bare ice surfaces in Greenland (Bøggild et al., 1996;Goelles et al., 2015;Goelles and Bøggild, 2017), 340 and for subsurface energy absorption in snowpack (Tuzet et al., 2019). Moreover, if present in higher concentration near the ice surface, LAPs would reduce light availability for subsurface heating at depth. This is supported by the enhanced attenuation rates found at wavelengths between 400 570 nm for the 0 12 cm region relative to those for the 12 77 cm interior ice region ( Figure 6b).

Relevance of enhanced near-surface attenuation to ICESat-2 345
Our results suggest penetration depth of visible wavelength light into solid glacier ice is lower by up to 19 cm at wavelengths relevant to visible-wavelength lidar altimetry of ice surface elevation (e.g. 532 nm for the Ice, Cloud, and Land Elevation Satellite-2). Our asymptotic values suggest e-folding penetration depth (the physical depth in units of ice thickness equivalent to one optical depth; equivalently, the physical depth required to attenuate incident irradiance to 1/ or ~37%) at 532 nm is 64 cm, in relatively close agreement with two-stream theory that predicts 68 cm. However, this path length is only 350 relevant at depths within the ice volume where the light field is diffuse and attenuation rates are asymptotic (Briegleb and Light, 2007). Near the ice surface attenuation rates are enhanced and rapidly decrease to their asymptotic value. The net effect at our field site is to reduce 532 nm penetration depth to ~49 cm. This enhanced near-surface attenuation is expected, but its magnitude has not previously been measured in near-surface glacier ice. The optimal value χ 15%, which parameterizes the magnitude of enhanced near-surface attenuation relative to the interior asymptotic attenuation rate, is one-half the canonical 355 30% value used in two-layer sea ice models (Briegleb and Light, 2007;Grenfell and Maykut, 1977). This lower value is consistent with our field observations of an anomalously thin (~4 cm) near-surface weathered ice layer (Figure 7), likely due to several days of persistent rain prior to our field measurements. This suggests penetration depths could be reduced further over heavily weathered ice or impurity-laden ice (for which backscatter magnitude may also be reduced), conditions that are common in the Greenland Ice Sheet ablation zone (Cooper and Smith, 2019;Goelles and Bøggild, 2017;Ryan et al., 2018;360 Tedstone et al., 2017).
The following caveats are important for interpreting the relevance of this experiment to ICESat-2. This experiment quantified the in-ice attenuation of diffuse solar flux. The ICESat-2 instrument transmits and receives discrete laser pulses over finite timesteps at 0 o incidence and records the distribution of single-photon travel times returned through the intervening atmosphere 365 (Markus et al., 2017). The penetration depth values given here are therefore not estimates of ICESat-2 laser penetration depth in glacier ice but provide validation data for radiative transfer models specific to the ICESat-2 measurement problem.

Suggestions for further work
Our results suggest that existing methods for sea ice radiative transfer modelling are readily applicable to ablating glacier ice (Holland et al., 2012;Light et al., 2004). Observations of non-exponential attenuation in sea ice due to enhanced near-surface 370 scattering and vertical variations in ice microstructure motivated adoption of two-layer and then multi-layer models with vertically-varying inherent optical properties, providing a ready template for the enhanced near-surface attenuation we describe here (Briegleb and Light, 2007;Grenfell, 1991;Grenfell and Maykut, 1977;Light et al., 2003). The simple empirical model we demonstrate ( Figure 5) suggests the need for a two-layer approach to modelling light attenuation in glacier ice. Vertical variation in ice microstructure and/or scattering geometry can be approximated by treating and as free parameters 375 (Meirold-Mautner and Lehning, 2004), or by using a similarity approach that infers optimal scattering and absorption coefficient values from co-located observations of albedo and transmittance (Light et al., 2004). The values we report provide a possible first step toward using this approach to diagnose structural controls on albedo and radiative transfer in ablating glacier ice. Finally, the values we report provide new insight into the magnitude of this fundamental but uncertain optical property, and provide support for the lower bound pure ice estimate from Warren et al (2006) (Figure 9). 380

Conclusion
We report first in-situ spectral measurements of near-UV and visible light attenuation coefficients for near-surface bare glacial ice, collected in the Greenland Ice Sheet ablation zone during July 2018. In general, our empirical values are nearly one order of magnitude larger in the range 350 530 nm than predicted by asymptotic two-stream radiative transfer theory using canonical values for the complex index of refraction of pure ice (Warren and Brandt, 2008). This suggests light absorbing 385 particles enhance visible light absorption and reduce optical penetration depth at our field site. The simple Bouguer exponential decay model accurately describes light attenuation in the ice interior but underestimates light attenuation near the ice surface.
Consequently, light transmission is overestimated by 5 50% depending on wavelength. This enhanced near-surface attenuation is consistent with observations of enhanced scattering from the semi-granular near-surface ice layer on sea ice and appears to be further enhanced at our field site by light absorbing particles concentrated near the ice surface. The magnitude of this near-390 surface attenuation suggests that visible-light penetration depth at wavelengths relevant to ice surface laser altimetry (e.g. 532 nm for Ice, Cloud, and Land Elevation Satellite-2) is lower by 19 cm than would be inferred from two stream theory for optically pure glacier ice. This enhanced near-surface attenuation implies shallower light transmission and therefore lower light availability for bio-photochemical cycling and subsurface energy absorption in glacier ice.      increasing wavelength from the near-UV through the blue-green; (f) as in (d) the spectral pattern of error due to near-surface attenuation is preserved, but errors are much lower due to the parameter. Taken together, near-surface attenuation enhancement is on the order 5 50% but has less relative influence in the blue-green spectrum and more relative influence in the red-orange and near-UV and violet regions of the visible spectrum.

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https://doi.org/10.5194/tc-2020-53 Preprint. Discussion started: 17 March 2020 c Author(s) 2020. CC BY 4.0 License. values are ~1.6 higher at wavelengths larger than about 600 nm but are ~3.7 higher between 400 600 nm. The shaded bounds represent 1.2 cm vertical measurement uncertainty. The spectral dependence suggests 660 higher influence of absorptive impurities on attenuation enhancement near the ice surface than in the ice interior. In contrast, the relatively constant attenuation enhancement beyond about 600 nm suggests near-surface ice microstructure, for example the size, shape, and orientation of weathered ice grains or air bubbles, contributes to enhanced near-surface attenuation.