Derivation of vegetation isoline equations in red-NIR reflectance space

Derivation of Soil Line Influence on Two-Band Vegetation Indices and Vegetation Isolines

“…These results imply the possibility of estimating and correcting errors in the VIs induced by the general soil line assumption, which in turn implies more accurate retrievals of biophysical parameters such as green vegetation fraction based on the VIs. Since all the findings of this study have been derived analytically from the equations based on the physics of photon-vegetation interactions (i.e., vegetation isoline equations) [29], our results and their implications are deterministic under the conditions and assumptions of this study.…”

“…The other portion of reflectance (1 − β), which reaches to the soil without seeing the canopy layer, is then reflected back to the sensor or absorbed by the soil surface (no interaction with the canopy layer). Under these approximations, the reflectance of this system, ρ λ (θ, φ, θ 0 ), at the view angle of (θ, φ) with the sun angle of θ 0 at the wavelength of λ is then represented by the following equation [30],…”

“…The details of the derivation and explanation of the variables are provided in our previous work [30]. The denominator and numerator of γ are a weighted sum of the two-way transmittance and unity with β and (1 − β) as their weights.…”

“…Another advantage of using soil line parameters is that we can avoid parameter studies about variations of soil surface, since some aspects of soil influence can be reduced into the simple expression. In this context, an analytical form of a vegetation isoline (a set of reflectance spectra from a constant canopy with different soils [29,30]) was also assumed to be subject to systematic investigations.…”

Comparison of the Noise Robustness of FVC Retrieval Algorithms Based on Linear Mixture Models

“…Note that the parameter θ depends on the type of noise present. For example, an increase in the aerosol optical thickness increases the red reflectance but decreases the NIR reflectance [41], whereas the soil brightness beneath the vegetation canopy tends to shift the reflectance along the one-to-one line [42]. Although each effect influences the target spectrum in a different way, the robustness in the presence of noise can be compared by averaging the relative robustness over the parameter range θ.…”