Parametric representation of soil isoline equation and its accuracy estimation in red-NIR reflectance space

Retrieval of biophysical parameters from remotely sensed reflectance spectra often involves algebraic manipulations, e.g. spectral vegetation index, to enhance pure signals from a target of one‘s interest. An underlying assumption of those processes is an existence of high correlation between an obtained value from the manipulations and amount of the target object. These correlations can be seen in scatter plots of reflectance spectra as isolines that represent a relationship between two reflectances of different wavelengths (bands) under constant values of physical parameters. Therefore, modeling the isolines would contribute to better understanding of retrieval algorithms and eventually to improve their accuracies. The objective of this study is to derive one such relationship observed under a constant spectrum of soil surfaces, known as soil isolines, in red-NIR reflectance space. This work introduces a parametric representation of the soil isolines (soil isoline equation) with the parameter obtained by rotating the red-NIR reflectance space by approximately a quarter of pi radian counter clockwise. The accuracy in the soil isoline equation depends on the order of polynomials used for the representations: It was investigated numerically by conducting experiments with radiative transfer models for vegetation canopy. The results showed that when the first-order approximation were employed for both bands, the accuracy of the parametric representations/approximations of the soil isolines is approximately 0.02 in terms of mean absolute difference from the simulated spectra (with no approximation). The accuracies improved dramatically when one retains the polynomial terms up to the second-order or higher for both bands.