Vegetation isoline equations for analysis of hyper-spectral data with higher order interaction terms

This study introduces a series of vegetation isoline equations derived by accounting higher-order interaction terms between canopy layer and soil surface. Our focus is to investigate accuracies of the derived isoline equations in the context of applications for hyperspectral data analysis. The objective is to derive vegetation isoline equations that relate reflectances between two wavelengths with higher order interaction terms under an assumption of partial vegetation cover (fraction of vegetation cover is less than unity). Accuracies of the derived isoline equations were evaluated numerically based on a radiative transfer model. The results show that the accuracy in the isoline equations are improved from the original form (the first-order approximation case) by including the higher-order interaction terms. However, a special caution is needed for the choice of the wavelengths and the form of the equations (which depends on the order of interaction terms considered during the derivation), since the accuracies of the isoline equations depends largely on those choices.