Spatial variation of englacial radar attenuation: Modeling approach and application to the Vostok flowline

Constraining the spatial variation of englacial radar attenuation is critical for accurate inference of the spatial variation of the englacial and basal properties of ice sheets from radar returned power. Here we evaluate attenuation models that account for spatial variations in ice temperature and chemistry and test them along the flowline that passes through the Vostok ice core site, Antarctica. The simplest model, often used but rarely valid, assumes a uniform attenuation rate everywhere along the flowline, so that total attenuation is proportional to ice thickness. The next simplest model uses spatially varying temperatures predicted by an ice-flow model and assumes uniform chemistry. Additional models account for spatially varying chemistry using englacial stratigraphy. We find that the roundtrip attenuation to the bed can easily differ by 10 dB or more between the uniform attenuation-rate model and models that account for variable ice temperature. Such differences are sufficient to confound the delineation of dry and wet beds. Also including spatial variations in chemistry produces smaller differences (<10 dB), but the magnitude of these differences depends on the relative importance of dry and wet deposition of impurities in the past. Accounting for dry-deposited impurities requires ice-flow modeling and results in larger differences from all other models, which assume uniform chemistry or wet deposition only. These results indicate that modeling the spatial variation of attenuation requires a spatially varying temperature model in order to infer bed conditions from bed returned power accurately, and that both ice core data and radar stratigraphy are also strongly desirable.