Three-dimensional effects in the remote sensing of surface albedo

Most of contemporary analysis of satellite data is based on the classical Chandrasekhar's formula for the mean radiance, which is valid only when the surface is infinite and uniform. Over an inhomogeneous surface, the measured radiance will also contain two variational terms describing the direct and diffuse atmospheric transmission of the solar radiation reflected from spatial variations of surface reflectance. Calculation of the diffuse transmission requires knowledge of the atmospheric point-spread function (PSF) or its Fourier transform (FT) optical transfer function (OTF), which is a solution of the 3D radiative transfer problem. Using a method of spherical harmonics, we have previously obtained a rigorous solution for a 2D problem, where surface albedo varies only in one of the coordinate axes. It allows us to precisely model radiance fields over arbitrarily nonhomogeneous Lambertian "striped" surfaces. The simplest surface of this type consists of a dark and a bright homogeneous half-planes. The radiance distribution for this surface model was well studied in the past at high sensor resolution in the nadir direction. In reality, land surface exhibits a broad range of spatial variations, and data available to the land remote sensing community have resolution from tens of meters to several kilometers, often at varying zenith view angles. A study of the 3D effects in these realistic conditions and assessments of the accuracy of atmospheric corrections based on a 1D radiative transfer theory are the main objectives of this work. The conclusions of this study can be summarized as follows. 3-D effects are the major source of albedo errors at high spatial resolution. The errors incurred may be as high as 0.04-0.06 in the near-IR and 0.01-0.04 in the visible range of the spectrum. At a medium resolution of 1 km, these errors are relatively small (0.005-0.02) and are comparable to other sources of errors, such as uncertainties in knowledge of aerosol scattering properties and of bidirectional reflectance in each pixel. However, most of the other errors have a random nature, while 3-D effects are systematic. They always increase the apparent reflectance of the dark targets and decrease the signal from the bright targets. As such, 3-D effects become important even at medium resolution, especially for off-nadir observations. Although our analysis was limited to l-D Lambertian surfaces, the results presented here are general enough to make quantitative conclusions in this still poorly studied but very important area.