Canopy spectra modeling based on spectral invariant theory and the adding method: The multilayer CANOP model

Canopy radiative transfer models (RTMs) are essential tools for characterizing the complex interactions between solar radiation and vegetation canopies. Vegetation canopies exhibit pronounced vertical heterogeneity in terms of their biophysical and optical properties at different growth stages, significantly influencing canopy reflectance. Existing multilayer canopy RTMs predominantly use the 4-stream theory and the adding method to calculate multiple scattering. In these models, the eigenvector decomposition method is used to solve the differential equations and derive the layer scattering matrices, which are then used to calculate multiple scattering. However, for a vertically heterogeneous canopy, deriving analytical solutions to the layer scattering matrices is difficult since each canopy layer exhibits distinct scattering characteristics. The aim of this study is to develop a new multilayer canopy RTM, CANOP, based on the spectral invariant theory and the adding method. The new model employed spectral invariants, instead of intractable layer scattering matrices, to link the scattering properties at the leaf and canopy levels and derive the adding operators for multilayer canopy. The spectral invariants enable a realistic and anisotropic representation of the top and bottom reflectances, as well as the upward and downward transmittances of multilayer canopy. The CANOP model was compared with the multilayer 4-stream and discrete anisotropic radiative transfer (DART) models, and the field-measured paddy rice vertical profile data. The CANOP model performs better than the 4-stream model in simulating multilayer canopy reflectance. It also shows good agreement with the measured layered paddy rice data, achieving high R2 (0.99), low RMSE (0.038) and bias (0.019) values. CANOP provides an accurate and efficient approach for multilayer canopy spectral modeling and can be used for multilayer canopy reflectance modeling and inversion of vegetation biophysical and biochemical parameters.