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Abstract. Accurate modeling of cryospheric surface albedo is essential for ourunderstanding of climate change as snow and ice surfaces regulate the globalradiative budget and sea-level through their albedo and massbalance. Although significant progress has been made using physicalprinciples to represent the dynamic albedo of snow, models of glacier icealbedo tend to be heavily parameterized and not explicitly connected withphysical properties that govern albedo, such as the number and size of airbubbles, specific surface area (SSA), presence of abiotic and biotic lightabsorbing constituents (LACs), and characteristics of any overlyingsnow. Here, we introduce SNICAR-ADv4, an extension of the multi-layertwo-stream delta-Eddington radiative transfer model with theadding–doubling solver that has been previously applied to represent snowand sea-ice spectral albedo. SNICAR-ADv4 treats spectrally resolved Fresnelreflectance and transmittance between overlying snow and higher-densityglacier ice, scattering by air bubbles of varying sizes, and numerous typesof LACs. SNICAR-ADv4 simulates a wide range of clean snow and ice broadbandalbedo (BBA), ranging from 0.88 for (30 µm) fine-grain snow to 0.03for bare and bubble-free ice under direct light. Our results indicate thatrepresenting ice with a density of 650 kg m−3 as snow with norefractive Fresnel layer, as done previously, generally overestimates theBBA by an average of 0.058. However, because mostnaturally occurring ice surfaces are roughened “white ice”, we recommendmodeling a thin snow layer over bare ice simulations. We find optimalagreement with measurements by representing cryospheric media with densitiesless than 650 kg m−3 as snow and larger-density media as bubbly icewith a Fresnel layer. SNICAR-ADv4 also simulates the non-linear albedoimpacts from LACs with changing ice SSA, with peak impact per unit mass ofLACs near SSAs of 0.1–0.01 m2 kg−1. For bare, bubble-free ice, LACsactually increase the albedo. SNICAR-ADv4 represents smooth transitionsbetween snow, firn, and ice surfaces and accurately reproduces measuredspectral albedos of a variety of glacier surfaces. This work paves the wayfor adapting SNICAR-ADv4 to be used in land ice model components of Earthsystem models.