# Evaluation of the Landsat-8 Albedo Product across the Circumpolar Domain
## 2 Materials and Methods
### Operational Blue-Sky Albedo  
Bi-hemispherical reflectance (white-sky albedo) and directional hemispherical reflectance (black-sky albedo) represent opposite extremes in illumination conditions and thus are not the best indicator of albedo under ambient illumination conditions at a specific date and time. For forcing calculations and other modeling applications, instantaneous blue-sky albedo under specific illumination conditions is needed. There are several mechanisms for deriving blue-sky albedo. The isotropic blue-sky albedo is calculated as a weighted sum using the fractions of direct and diffuse illumination calculated for the observed optical depth. These measurements of direct and diffuse illumination can be measured directly by radiometers at validation towers and field sites such that:  
\[\text{BLUE}_{\text{iso}}=\overline{\overline{R}}\ p+\overline{R}\ (1-p)\]  
where BLUE\({}_{\text{iso}}\) is the isotropic blue-sky albedo, \(\overline{R}\) is the directional hemispherical reflectance or black-sky albedo and \(\overline{\overline{R}}\) is the bi-hemispherical reflectance under isotropic illumination conditions or white-sky albedo and \(p\) is the ratio of the surface downward diffuse shortwave radiation to the surface downward total shortwave radiation [36]. The isotropic blue-sky albedo calculation assumes the distribution of sky radiance is of minor importance as the generation of albedo quantities involves the integration over the full hemisphere. Additionally, it assumes that interaction between the incoming radiances and the ground (scattering and absorption) can be approximated within the definition of the diffuse proportion of the atmospheric conditions. However, under bright and complex surface conditions where multiple scattering events are more common (such as snow), these assumptions can lead to larger discrepancies between the actual albedo observed on the ground and modelled albedo measured by satellites [37]. Additional compounding factors that can lead to large errors in the calculation of blue-sky albedo are high solar zenith angles (which affect the quality of MODIS BRDFs) and atmospheric conditions with high concentrations of aerosols [36; 37; 38; 39]. In the development of an operational circumpolar albedo algorithm, the impact of solar zenith angles and multiple scattering characteristics of snow and ice are particularly important components in the calculation of blue-sky albedo at high latitudes and in the transition period between the snow and snow free season. To address the impact of multiple scattering on the blue-sky albedo calculation, [PERSON] et al. [37] developed a model to calculate a full expression blue-sky albedo from MODIS based upon extensive modeling of atmospheric and illumination conditions within the MODTRAN radiative transfer model. The model considers multiple scattering events and has been particularly valuable at capturing blue-sky albedo under snow covered conditions improving MODIS albedo validation biases by 0.004-0.013 absolute units (root mean-squared error) or 0.1-2.0% relative error [37]. For the implementation of a blue-sky albedo algorithm, atmospheric aerosol optical depth (AOD), a quantitative assessment of the amount of aerosol present in the atmosphere (measured by the extinction of a ray of light as it passes through the atmosphere), is required at the global scale. AOD for the operational blue-sky Landsat albedo derivation is iteratively retrieved from Terra and Aqua Aerosol Cloud Water Vapor Products (MOD08v06 and MYD08v06) at daily, eight-day and monthly time steps [40]. The mean AOD over land and ocean is reported for 1 \(\times\) 1 degree cells globally. AOD values and the target location are extracted first for MODIS Terra (morning overpass to pair with the Landsat acquisition time), then Aqua (afternoon overpass) on the day of interest. If no valid measurements were recorded on a daily timestep, the eight-day interval product and monthly products are queried.