ABSTRACT. We present the first dedicated study into the phenomenon of ice sails. These are clean ice structures that protrude from the surface of a small number of debris-covered glaciers and can grow to heights of over 25 m. We draw together what is known about them from the academic/exploration literature and then analyse imagery. We show here that ice sails can develop by one of two mechanisms, both of which require clean ice to become surrounded by debris-covered ice, where the debris layer is shallow enough for the ice beneath it to melt faster than the clean ice. Once formed, ice sails can persist for decades, in an apparently steady state, before debris layer thickening eventually causes a reversal in the relative melt rates and the ice sails decay to merge back with the surrounding glacier surface. We support our image-based analysis with a surface energy-balance model and show that it compares well with available observations from Baltoro Glacier in the Karakoram. A sensitivity analysis of the model is performed and confirms the results from our empirical study that ice sails require a relatively high evaporative heat flux and/or a relatively low sensible heat flux in order to exist.

Abstract. We describe and validate a Monte Carlo model to track photons over the full range of solar wavelengths as they travel into optically thick Antarctic blue ice. The model considers both reflection and transmission of radiation at the surface of blue ice, scattering by air bubbles within it, and spectral absorption due to the ice. The ice surface is treated as planar whilst bubbles are considered to be spherical scattering centres using the Henyey–Greenstein approximation. Using bubble radii and number concentrations that are representative of Antarctic blue ice, we calculate spectral albedos and spectrally integrated downwelling and upwelling radiative fluxes as functions of depth and find that, relative to the incident irradiance, there is a marked subsurface enhancement in the downwelling flux and accordingly also in the mean irradiance. This is due to the interaction between the refractive air–ice interface and the scattering interior and is particularly notable at blue and UV wavelengths which correspond to the minimum of the absorption spectrum of ice. In contrast the absorption path length at IR wavelengths is short and consequently the attenuation is more complex than can be described by a simple Lambert–Beer style exponential decay law – instead we present a triple-exponential fit to the net irradiance against depth. We find that there is a moderate dependence on the solar zenith angle and surface conditions such as altitude and cloud optical depth. Representative broadband albedos for blue ice are calculated in the range from 0.585 to 0.621. For macroscopic absorbing inclusions we observe both geometry- and size-dependent self-shadowing that reduces the fractional irradiance incident on an inclusion's surface. Despite this, the inclusions act as local photon sinks and are subject to fluxes that are several times the magnitude of the single-scattering contribution. Such enhancement may have consequences for the energy budget in regions of the cryosphere where particulates are present near the surface. These results also have particular relevance to measurements of the internal radiation field: account must be taken of both self-shadowing and the optical effect of introducing the detector. Turning to the particular example of englacial meteorites, our modelling predicts iron meteorites to reside at much reduced depths than previously suggested in the literature (< 10 cm vs. ∼ 40 cm) and further shows a size dependency that may explain the observed bias in their Antarctic size distribution.

Abstract. We describe and validate a Monte Carlo model to track photons over the full range of solar wavelengths as they travel into optically thick bubbled ice. The model considers surface effects, scattering by bubbles and spectral absorption due to the ice. Using representative Antarctic ice bubble radii and number concentrations we calculate spectral albedos and spectrally-integrated downwelling and upwelling radiative fluxes as a function of depth and find there is a marked subsurface enhancement in both the downwelling and upwelling fluxes relative to the incidence irradiance. This is due to the interaction between the refractive air-ice interface and the highly scattering interior and is particularly notable at blue and UV wavelengths which correspond to the minimum of the absorption spectrum of ice. A subsurface peak is also observed in the available radiative flux at depths of ~ 1 cm, and consequently the attenuation is more complex than can be described by a simple Lambert-Beer style exponential decay law. We find a moderate dependence on the solar zenith angle and surface conditions such as altitude and cloud optical depth. For macroscopic absorbing inclusions we observe geometry- and size- dependent self-shadowing that reduces the fractional irradiance incident on the inclusion's surface. Despite this the inclusions are subject to fluxes that are several times the magnitude of the single scattering contribution and act as local photon sinks. Such enhancement may have consequences for the energy budget in regions of the cryosphere where particulates are present near the surface. These results also have particular relevance to measurements of the internal radiation field: account must be taken of both self-shadowing and the optical effect of introducing the detector.

S1 Solar zenith angle dependence Here we investigate the influence of the incident solar zenith angle. For simplicity, the results presented in the main text have relied on the assumption that the incoming solar flux arrives from a diffuse hemispherical sky, with no direct component.

S1 Solar zenith angle dependence Here we investigate the influence of the incident solar zenith angle (SZA). For simplicity, the results presented in the main text have relied on the assumption that the incoming solar flux arrives from a diffuse hemispherical sky, with no direct component. However the angular dependence of Fresnel reflection coefficients at the ice-air interface may cause the solar flux within the ice to be sensitive to the solar zenith angle, irrespective of the absolute shortwave irradiance. To test this the model is rerun with a set of specific solar zenith angles covering the expected range experienced at the Frontier Mountain range (from 49° to 89° at 10° intervals) with the mean bubble parameter set in all cases. In Fig. S1a the impact of this change can be seen in the reduction of solar flux with increasing SZA, particularly at the highest angle of incidence. Also shown are the results for a diffuse sky which lies close to the 69° result. The reduction in the downwelling fluxes is principally due to the high incidence angle rather than an increased scattering path c.f. the vertical depth. This is expected as after 1 (1 −) ⁄ scattering events, the radiation field can be considered isotropic and retains no information of the initial beam direction. In