Inter-sensor relationship of two-band spectral vegetation index based on soil isoline equation: derivation and numerical validation

Differences in spectral response function among sensors have known to be a source of bias error in derived data products such as spectral vegetation indices (VIs). Numerous studies have been conducted to identify such bias errors by comparing VI data acquired simultaneously by two different sensors. Those attempts clearly indicted two facts: 1) When one tries to model a relationship of two VIs from different sensors by a polynomial function, the coefficients of polynomial depends heavily on region to be studied: 2) Although increase of the degree of polynomial improves the translation accuracies, this improvement is very limited. Those facts imply that a better functional form than a simple polynomial may exist to model the VI relationships, and also that the coefficients of such a relationship can be written as a function of variables other than vegetation biophysical parameters. This study tries to address those issues by deriving an inter-sensor VI relationship analytically. The derivation has been performed based on a relationship of two reflectances at different wavelengths (bands), called soil isoline equation. The derived VI relationship becomes a form of rational function with the coefficients that depend purely on the soil reflectance spectra. The derived relationship has been demonstrated numerically by a radiative transfer model of canopy, PROSAIL. It is concluded that a rational function is a good candidate to model inter-sensor VI relationship. This study also shows the mechanism of how the coefficients of such a relationship could vary with the soil reflectance underneath the canopy.