# Evaluation of the Landsat-8 Albedo Product across the Circumpolar Domain
## 2 Materials and Methods  
The Landsat albedo algorithms couple finer resolution surface reflectance Landsat products with coincident same-day coarser resolution MODerate Resolution Imaging Spectroradiometer (MODIS) derived Bidirectional Reflectance Distribution Function (BRDF) characteristics using a method developed by [PERSON] et al. [28], [PERSON] et al. [31] and [PERSON] et al. [30] as described below. Landsat-8 surface reflectance is generated from the Landsat Surface Reflectance Code (LaSRC), which makes use of the unique coastal aerosol band to perform aerosol inversion tests as well as using auxiliary climate data from MODIS in a unique radiative transfer model [32]. The MODIS BRDF parameters are derived from the Moderate Resolution Imaging Spectroradiometer (MODIS) MCD43A1 Version 6 Bidirectional Reflectance Distribution Function and Albedo (BRDF/Albedo) Model Parameters dataset, produced daily using both Terra and Aqua MODIS data at 500-meter (m) resolution [33; 34]. The generation of a hemispherical albedo requires a BRDF model of each land surface field of view to capture surface anisotropy. The BRDF describes the behavior of a scattering surface and is defined as the ratio of the reflected radiance in a particular direction to the incident irradiance from a specified direction in a solid angle [35]. To accurately describe the BRDF of a surface, the anisotropic character of the surface must be observed through sufficient and well distributed angular reflectance measurements. The near nadir acquisition geometry of the Landsat sensors is not capable of generating such a BRDF and therefore the BRDF models from the coarser resolution MODIS are utilized. To generate finer resolution albedo products, Landsat surface reflectance measures are then adjusted by MODIS- BRDF parameters using an Albedo-to-Nadir Reflectance (AN) ratio for each spectral band. To generate this ratio, an automatic classification algorithm is first run on the six Landsat bands coincident with MODIS (bands 2-7 for Landsat-8). The classification map and MODIS derived BRDF parameters are stacked to identify suitable \"pure patches\" within the classification layer. A pure patch is considered as such when it spatially matches more than 85% of its coincident MODIS pixel. For the identified pure patches, the AN ratio is generated using MCD43 BRDF-based estimates of reflectances and albedos at the at the illumination and near-nadir view geometry of the Landsat and MODIS albedo at two extreme illumination conditions--wholly direct radiation (black-sky or directional hemispherical) and wholly diffuse radiation (white-sky or bi-hemisphericalreflectance). The average MODIS AN ratio for each class within the classification layer is derived and the ratio is applied to the Landsat surface reflectance within each class to generate the Landsat albedo. In homogenous, pure pixels at MODIS resolution, the AN ratio of albedo and reflectance is assumed to be similar at Landsat and MODIS spatial resolutions at Landsat viewing geometries. The black-sky and white-sky albedo can then be calculated for each pixel in the Landsat scene as:  
\[ \begin{array}{l}\overline{R}_{\lambda,l}\ (\theta_{s})=\overline{a}_{\lambda,\,l}\ (\Omega_{l})*R_{\lambda,\,l}\ (\Omega_{l})=\overline{a}_{\lambda,\,m}\ (\Omega_{l})*R_{\lambda,\,l}\ (\Omega_{l})\\ \overline{R}_{\lambda,l}\ =\overline{a}_{\lambda,\,l}\ (\Omega_{l})*R_{\lambda,\,l}\ (\Omega_{l})= \overline{a}_{\lambda,\,m}\ (\Omega_{l})*R_{\lambda,\,l}\ (\Omega_{l})\end{array}