Vegetation isoline equations with first- and second-order interaction terms for modeling a canopy-soil system of layers in the red and near-infrared reflectance space

摘要

A previously proposed vegetation isoline equation suffers from errors if the soil background of a canopy layer is bright. These errors arise from the truncation of the second- and higher-order terms that represent photon interactions between the canopy and the soil. An isoline equation that includes a second- order interaction term is introduced. The equation was initially derived by explicitly including a second- order interaction term in both the red and near-infrared (NIR) reflectance spectra (symmetric approximation). We also examined an alternative model in which the interaction term was included only in the NIR band (asymmetric approximation). In this model, the derived isolines tend to shift upward (overcorrection effects). Numerical experiments revealed that the errors in the isoline obtained by the asymmetric approximation were reduced in magnitude to nearly one-fifth of the errors in the previously proposed method. Its accuracy was higher than that of the symmetric approximation, despite the fact that the asymmetric approximation included fewer terms than the symmetric approximation. The improved model accuracy resulted from the overcorrection effects, which compensated for the truncation error. With the simplicity and improved accuracy, the current isoline equations provide a good alternative to the previous approach. (C) The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License.