Four‐stream isosector approximation for canopy radiative transfer

Abstract

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.