## 5 Conclusions  
This study addressed the fundamental question of linking multispectral vegetation indices to hyperspectral mixture models for agricultural applications. Using a compilation of 125 subsets from 15 airborne imaging spectroscopy flight lines spanning a diverse agricultural mosaic, we simulated 64,000,000 multispectral SuperDove reflectance spectra and used them to compute 6 commonly used vegetation indices. We then compared these indices against the photosynthetic vegetation fraction estimated from the inversion of a linear mixture model applied to the original 5 nm hyperspectral data (F\({}_{\rm v}\)). We quantified complementary aspects of the bivariate distributions using both parametric (\(\rho\)) and nonparametric (MI) metrics. DVI and NIRv were strongly colinear (\(\rho>0.99\); MI = 2.45) and approximately linearly related to \(\mathrm{F_{v}}\) (\(\rho>0.95\); MI \(>1.4\)), with minimal sensitivity to the substrate background reflectance (0 to 0.1 for unvegetated spectra) but substantial deviation from 1:1 (the DVI and NIRv values of 0.6 for \(\mathrm{F_{v}}\) values of 1.0). EVI and EVI2 also performed similarly to each other (\(\rho>0.99\); MI = 2.3) and were also approximately linear to \(\mathrm{F_{v}}\) (\(\rho=0.95\); MI \(>1.2\)), but with both a more prominent impact of background reflectance (0 to 0.2 for unvegetated spectra) and greatly reduced deviation from 1:1. Of the indices, NDVI and SR exhibited by far the weakest relationships to \(\mathrm{F_{v}}\) (\(\rho=0.84\) and 0.81; MI = 0.69). NDVI in particular showed severe saturation effects and sensitivity to soil background reflectance. Comparison of parametric (\(\rho\)) and nonparametric (MI) similarity statistics yielded a roughly log-linear relationship, with a notable exception supporting a nonlinear analytical relationship between NDVI and SR. Notably, because SuperDove data were simulated directly from AVIRIS-ng, results can be attributed to the spectral modeling step alone (and thus isolated from acquisition-specific idiosyncrasies such as the view and illumination angle). Taken together, this analysis suggests that for agricultural applications:  
1. EVI2 can likely serve as a proxy for EVI in situations where a blue band is not available, and both can serve as proxies for \(\mathrm{F_{v}}\) in situations where SWIR bands are not available. 2. DVI and NIRv yield very similar values (\(\rho>0.99\), 99% of \(\mid\)DVI-NIRv \(\mid<0.07\)). 3. DVI and NIRv show low sensitivity to substrate background reflectance, but systematically underestimate \(\mathrm{F_{v}}\). A linear bias correction reduces deviation from 1:1 but increases substrate background effects. 4. Bivariate distributions of \(\rho\) and the MI can usefully contextualize nonlinear VI relationships. 5. As metrics of subpixel vegetation abundance, NDVI and SR exhibit severe challenges in nonlinearity, heteroskedasticity, and sensitivity to substrate background reflectance. The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/rs15040971/s1](https://www.mdpi.com/article/10.3390/rs15040971/s1)]([https://www.mdpi.com/article/10.3390/rs15040971/s1](https://www.mdpi.com/article/10.3390/rs15040971/s1)), Figure S1: additional VI relationships; Figure S2: parametric versus nonparametric statistics; Table S1: AVIRIS-ng flightlines used for this analysis; Table S2: mutual information matrix; Table S3: correlation matrix; analytical exercise S1: An exploration of the relationship between the SR and NDVI. Conceptualization, D.S. and C.S. ; methodology, D.S. and C.S. ; formal analysis, D.S. and C.S. ; investigation, D.S. and C.S. ; resources, D.S. and C.S. ; data curation, D.S. and C.S. ; writing--original draft preparation, D.S. ; writing--review and editing, D.S. and C.S. ; visualization, D.S. and C.S. ; funding acquisition, D.S. and C.S. All authors have read and agreed to the published version of the manuscript. The data supporting this manuscript can be downloaded free of charge from the web portal listed in the main text.