Spectral albedo measurements over snow-covered slopes: theory and slope effect corrections

Surface albedo is an essential variable to determine the Earth's surface energy budget, in particular for snow-covered areas where it is involved in one of the most powerful positive feedback loops of the climate system. In situ measurements of broadband and spectral albedo are therefore common. However they are subject to several artefacts. Here we investigate the sensitivity of spectral albedo measurements to surface slope, and we propose simple correction algorithms to retrieve the intrinsic albedo of a slope from measurements, as if it were flat. For this, we first derive the analytical equations relating albedo measured on a slope to intrinsic direct and diffuse albedo, the apportionment between diffuse and direct incoming radiation, and slope inclination and aspect. The theory accounts for two main slope effects. First, the slope affects the proportion of solar radiation intercepted by the surface relative to that intercepted by the upward-looking, horizontal, sensor. Second, the upward- and downward-looking sensors receive reduced radiation from the sky and the surface respectively and increased radiation from neighbouring terrain. Using this theory, we show that (i) slope has a significant effect on albedo (over 0.01) from as little as a ≈1∘ inclination, causing distortions of the albedo spectral shape; (ii) the first-order slope effect is sufficient to fully explain measured albedo up to ≈15∘, which we designate “small-slope approximation”; and (iii) for larger slopes, the theory depends on the neighbouring slope geometry and land cover, leading to much more complex equations. Next, we derive four correction methods from the small-slope approximation, to be used depending on whether (1) the slope inclination and orientation are known or not, (2) the snow surface is free of impurities or dirty, and (3) a single or a time series of albedo measurements is available. The methods applied to observations taken in the Alps on terrain with up to nearly 20∘ slopes prove the ability to recover intrinsic albedo with a typical accuracy of 0.03 or better. From this study, we derive two main recommendations for future field campaigns: first, sloping terrain requires more attention because it reduces the measurement accuracy of albedo even for almost invisible slopes (1–2∘). Second, while the correction of the slope effect is possible, it requires additional information such as the spectral diffuse and direction partitioning and if possible the actual slope inclination and aspect, especially when the absence of impurities can not be assumed.