## 2 What VIs Measure  
Although many different VIs have been formulated, most of them are related to the Simple Ratio (SR) [7]:  
\[\mathrm{SR}=\mathrm{\rho NIP/\rho Red} \tag{1}\]  
The most-used VI is the NDVI [1,3]:  
\[\mathrm{NDVI}=(\mathrm{\rho NIR}\ \mathrm{-\ \rho Red})/(\mathrm{\rho NIR}+ \mathrm{\rho Red}) \tag{2}\]  
where \(\mathrm{\rho NIR}\) and \(\mathrm{\rho Red}\) are reflectance values of Red and Near Infrared light received at the sensors. The NDVI was first formulated by [PERSON] _et al._[8] and applied to a wide range of practical remote sensing applications in a series of studies by [PERSON] and colleagues in the 1970s and 1980s, e.g. [9]. The SR and NDVI are built on the observation that chlorophylls a and b in green leaves strongly absorb light in the Red, with maximum absorption at about 690 nm, while the cell walls strongly scatter (reflect and transmit) light in the NIR region (about 850 nm) [10]. This results in a strong absorption contrast across a narrow wavelength band of 650 - 850 nm, captured by the NDVI and other VIs. NDVI and related VIs are functional variants of the SR. NDVI normalizes values between -1 to +1; dense vegetation has a high NDVI, while soil values are low but positive, and water is negative due to its strong absorption of NIR. [PERSON] [10] tested various combinations of the red, NIR, and green bands to predict biomass, water content, and chlorophyll content of grass plots. The NDVI was strongly correlated with chlorophyll content and crop characteristics that were directly related to chlorophyll content, such as green biomass and leaf water content. [PERSON] and [PERSON] [11] conducted a theoretical analysis showing that the SR and by extension other VIs are uniquely related to the amount of incident light reflected and therefore absorbed by a canopy, assuming a low and constant value for soil absorption. [PERSON] _et al._[12] showed that NDVI was near-linearly related to the chlorophyll content of single soybean leaves and curvilinearly related to the chlorophyll content of soybean canopies (because surface leaves intercept more light than leaves deeper in the canopy). [PERSON] [13] used a canopy radiative transfer model to show that NDVI is near-linearly related to area-averaged net carbon assimilation and plant transpiration, even at different values of \(\mathrm{f_{c}}\) and LAI over an area of interest. [PERSON] [14] analyzed the performance of VIs in estimating canopy conductance and transpiration at different scales of measurement over the Konza Prairie in the Great Plains, U.S. Data from ground flux towers were scaled by aerial and satellite imagery to progressively larger landscape units. As in the small-scale studies cited above, they found that NDVI was near-linearly related to canopy carbon assimilation and transpiration and that NDVI values were nearly scale-invariant in going from ground to aerial to satellite measurements. Thus, even in a mixed scene (providing there is no surface water and soil effects are minimal) a VI provides a true measure of area-averaged photosynthetic capacity based on light absorption by chlorophyll, and therefore of processes such as photosynthesis and plant transpiration that are determined by stomatal conduction [13,14]. (Photosynthesis and transpiration are mechanistically linked because carbon dioxide and water molecules enter and exit through stomata on the leaves and stems). Similar findings have been reported for other VIs. For example, the Enhanced Vegetation Index (EVI) [3] is calculated as:  
\[\mathrm{EVI}=2.5\ \mathrm{x}\ (\mathrm{\rho NIR}\ \mathrm{-}\ \mathrm{\rho Red})/(1+ \mathrm{\rho NIR}+(6\ \mathrm{x}\ \mathrm{\rho Red}\ \mathrm{-}\ 7.5\ \mathrm{x}\ \mathrm{\rho Blue}) \tag{3}\]  
where the coefficient \"1\" accounts for canopy background scattering and the blue and red coefficients, 6 and 7.5, minimize residual aerosol variations.