Derivation and approximation of soil isoline equations in the red-near-infrared reflectance subspace

This study describes the derivation of an expression for the relationship between red and near-infrared reflectances, called soil isolines, as an orthogonal concept for the vegetation isoline. An analytical representation of soil isoline would be useful for estimating soil optical properties. Soil isolines often contain a singular point on a dark soil background. Singularities are difficult to model using simple polynomial forms. This difficulty was circumvented in this work by rotating the original axis and employing a vegetation index-like parasite parameter. This approach produced a soil isoline model that could yield any desired level of accuracy based on the use of an index-like parameter. A technique is further introduced for approximating the removal of the parasite parameter from the relationship by truncating the higher-order terms during the derivation steps. Numerical experiments by PROSAIL were conducted to investigate the influence of the truncation errors on the accuracy of the approximated soil isoline equation. The numerical results showed that truncating terms of order greater than two in both bands, yielded negligible truncation errors. These results suggest that the derived and approximated soil isoline equations may be useful in other applications, such as the analysis and retrieval of soil optical properties. (C) The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.