Four-stream isosector approximation for canopy radiative transfer

This study develops an analytical four-stream isosector approximation for solar radiative transfer in a homogeneous canopy, based on the approximation of four spherical sectors of isotropic intensities (constant values for light intensities). Compared to results from a multilayer radiative transfer model, the four-stream isosector approximation substantially improves the accuracy in calculation of albedo, transmittance, and absorptance with respect to the corresponding two-stream approximation. For direct incident radiation, it has errors mostly under 5% for leaf area index less than 5, even when sun angles are very low, while the two-stream method has errors of about 10% or higher; more improvement is achieved in albedo and transmittance in the visible band, and transmittance and absorptance in the near-infrared (NIR) band. For diffuse incident radiation, both the two-stream and four-stream approximations always have a higher accuracy in the NIR band than in the visible band, but the improvement of the four-stream approximation is larger for the visible band than for the NIR band. In addition, they have a higher accuracy in describing canopy albedo, transmittance and absorption for direct incident radiation than for diffuse incident radiation. However, the improvement of the four-stream is higher for diffuse incident radiation than for direct incident radiation. The inclusion of soil albedo as the low boundary does not degrade the performance of the four-stream approximation. As an analytical model, the four-stream approximation can be easily applied as an efficient approach to improving the parameterization of land surface radiation in climate models.