Vegetation isoline equations for atmosphere-canopy-soil system of layer with second order interaction term

Abstract

Retrieval of biophysical parameters from satellite data (including hyperspectral data) often involves algebraic manipulation of band reflectance (e.g. spectral vegetation index) that is either empirically or theoretically justified to enhance signals from target of interest. Use of these algebraic manipulation for parameter retrieval bases on a fundamental assumption such that relationship among reflectances varies along with the amount of target object. Therefore, investigation of such relationships among reflectance of different wavelength would serve for better understanding of retrieval algorithm. The objective of this paper is to derive relationships among reflectances, known as vegetation isoline equation, for a system of layers that consists of atmosphere, vegetation, and soil layers. Vegetation isoline equation is a relationship between two reflectance of different wavelength, which has been a basis of several vegetation indices, and also used directly for retrieval of biophysical parameter such as fraction of green cover. The derivation was performed to increase its accuracy in approximation by including higher-order interaction terms of photons between the canopy and soil layers. To validate the derived expression regarding its accuracy, a series of numerical experiments were conducted using a set of radiative transfer model to simulate reflectance spectra at the top of atmosphere. It is concluded that approximation error of the newly derived expression becomes approximately one order smaller than the error of the previously derived isoline equation which includes only up to the first-order interaction term under various atmospheric conditions.