Vegetation Isoline Equations with Higher Order Interaction Terms to Improve Accuracy in Retrieval of Vegetation Biophysical Parameters

This paper introduces derivations of vegetation isoline equation mainly in red and near-infrared reflectance space to improve its accuracy for the purpose of parameter retrieval such as leaf area index and fraction of vegetation cover within a target pixel. The former isoline equations were all derived by truncating the terms of photons which went through the interactions between canopy and soil layers more than once. The improvement is achieved by accounting the terms of higher order interactions which were neglected in the former derivations. As a result, the final form of the isoline equation becomes quadratic due to the inclusions of the second order interaction term. The numerical results indicates clearly that the accuracy, defined as difference of the derived isolines from the true isolines which includes all the interaction terms, was improved significantly from the former isoline equations by adding only one more interaction term (the second order interaction) only in the near-infrared band. It is concluded that higher accuracy can be achieved by adding one more term during the derivation while retaining the final form relatively simple.