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

Abstract

Abstract. 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.

Accelerated Snow Melt in the Russian Caucasus Mountains After the Saharan Dust Outbreak in March 2018

“…Prior to the estimation of the dust content, any pixel considered as cloud or snow-free was masked out, using the S2 snow mask from MAJA. Mixed pixels (NDSI smaller than 0.7-approximately corresponding to the threshold for 100% snow cover in Salomonson and Appel (2004)), steep pixels (slope greater than 40 • -where topographic effects require a detailed correction as explained in Picard et al, 2020) and noisy pixels on 12 March (standard deviation between reflectances in the visible Bands 2-4 greater than 0.03, that is, higher than the minimum errors in retrieved reflectance, Kokhanovsky et al (2019) were also discarded from the calculation (Figure 2b).…”

Effect of small-scale snow surface roughness on snow albedo and reflectance

“…Light attenuation within the snowpack is related to the density of the scattering elements per unit volume. In addition, layer structure, grain shape, anthropogenic and natural impurities (such as black carbon, dust and algae), and close-packing effects of snow grains affect scattering properties and thus the albedo of a snowpack (Warren and Wiscombe, 1980;Kokhanovsky and Zege, 2004;Aoki et al, 2011;Kokhanovsky, 2013;Libois et al, 2013;Libois et al, 2014;Komuro and Suzuki, 2015;Peltoniemi et al, 2015;Pirazzini et al, 2015;Räisänen et al, 2015;Cook et al, 2017;He et al, 2017, Kokhanovsky et al, 2018. Several models for the coupled mass and energy balances of snow on the ground have also been developed (Flanner and Zender, 2006;Essery, 2015).…”

Simulating optical top-of-atmosphere radiance satellite images over snow-covered rugged terrain

“…Sjoberg and Horn, 1983;Dozier and Frew, 1990;Dubayah and Rich, 1995;Richter, 1997;Sandmeier and Itten, 1997;Li et al, 1999;Xin et al, 2002;Mousivand et al, 2015) to sum the contributions of the different terms to the measured TOA radiance. Highly accurate 3-D ray-tracing models have also been implemented to render satellite scenes (Gastellu-Etchegorry et al, 2004;Poglio et al, 2006;Mayer et al, 2010), but their application is limited owing to the computational constraints of satellite image processing.…”