# A New Pabs Model for Quantitatively Diagnosing Phosphorus Nutritional Status in Corn Plants
## 3 Methodology
### Sobol Sensitivity Analysis
\begin{table}
\begin{tabular}{c c c} \hline
**Vegetation Index** & **Formula** & **Ref.** \\ \hline Normalized Difference Vegetation Index 1 (NDVI1) & \((\text{NIR}-\text{R})/(\text{NIR}+\text{R})\) & [25] \\ Normalized Difference Vegetation Index 2 (NDVI2) & \((\text{NIR}-\text{G})/(\text{NIR}+\text{G})\) & [26] \\ Normalized Difference Vegetation Index 3 (NDVI3) & \((\text{NIR}-\text{B})/(\text{NIR}+\text{B})\) & [25] \\ Renormalized Difference Vegetation Index 1 (RDVI1) & \((\text{NIR}-\text{B})/SQRT(\text{NIR}+\text{B})\) & [27] \\ Renormalized Difference Vegetation Index 2 (RDVI2) & \((\text{NIR}-\text{G})/SQRT(\text{NIR}+\text{G})\) & [27] \\ Renormalized Difference Vegetation Index 3 (RDVI3) & \((\text{NIR}-\text{R})/SQRT(\text{NIR}+\text{R})\) & [27] \\ Wide Dynamic Range Vegetation Index 1 (WDRV11) & \((0.12\text{ NIR}-\text{R})/(0.12\text{NIR}+\text{R})\) & [28] \\ Wide Dynamic Range Vegetation Index 2 (WDRV12) & \((0.12\text{ NIR}-\text{G})/(0.12\text{NIR}+\text{G})\) & [28] \\ Wide Dynamic Range Vegetation Index 3 (WDRV13) & \((0.12\text{ NIR}-\text{B})/(0.12\text{NIR}+\text{B})\) & [28] \\ Soil Adjusted Vegetation Index (SAVI) & \(1.5(\text{NIR}-\text{R})/(\text{NIR}+\text{R}+0.5)\) & [29] \\ Optimization of soil-adjusted VI (OSAVI) & \((1+0.16)(\text{NIR}-\text{R})/(\text{NIR}+\text{R}+0.16)\) & [30] \\ Green Soil Adjusted Vegetation Index (GSAVI) & \(1.5(\text{NIR}-\text{G})/(\text{NIR}+\text{G}+0.5)\) & [29] \\ Blue Soil Adjusted Vegetation Index (BSAVI) & \(1.5(\text{NIR}-\text{B})/(\text{NIR}+\text{B}+0.5)\) & [29] \\ Modified Simple Ratio (MSR) & \((\text{NIR}/\text{R}-1)/SQRT(\text{NIR}/\text{R}+1)\) & [31] \\ Green Optimal Soil Adjusted Vegetation Index (G0 SAVI) & \((1+0.16)(\text{NIR}-\text{G})/(\text{NIR}+\text{G}+0.16)\) & [30] \\ Blue Optimal Soil Adjusted Vegetation Index (BOSAVI) & \(0.5[2\text{-NIR}+1-SQRT[(2\text{-NIR}+1)2-8(\text{NIR}-\text{R})]]\) & [32] \\ Modified Green Soil Adjusted Vegetation Index (MGSAVI1) & \(0.5[2\text{-NIR}+1-SQRT[(2\text{-NIR}+1)2-8(\text{NIR}-\text{G})]]\) & [32] \\ Modified Blue Soil Adjusted Vegetation Index (MBSAVI) & \(0.5[2\text{-NIR}+1-SQRT[(2\text{-NIR}+1)2-8(\text{NIR}-\text{B})]]\) & [32] \\ Three-band vegetation indices & \(0.5[2\text{-NIR}+1-SQRT[(2\text{-NIR}+1)2-8(\text{NIR}-\text{B})]]\) & [32] \\ Simple Ratio Vegetation Index (SR) & \(\text{R}/\text{G}\times\text{NIR}\) & [33] \\ Modified Normalized Difference Vegetation Index 1 (mNDVI1) & \((\text{NIR}-\text{R}+2.\text{G})/(\text{NIR}+\text{R}-2.\text{G})\) & [34] \\ Modified Normalized Difference Vegetation Index 2 (mNDVI2) & \((\text{NIR}-\text{R}+2.\text{B})/(\text{NIR}+\text{R}-2.\text{B})\) & [34] \\ New Modified Simple Ratio (mSR) & \((\text{NIR}-\text{B})/(\text{R}-\text{B})\) & [35] \\ Visible Atmospherically Resistant Index (VARI) & \((\text{G}-\text{R})/(\text{G}+\text{R}-\text{B})\) & [36] \\ Structure Imsensitive Pigment Index (SIPI) & \((\text{NIR}-\text{B})/(\text{NIR}-\text{R})\) & [37] \\ Structure Imsensitive Pigment Index 1 (SIPI1) & \((\text{NIR}-\text{B})/(\text{NIR}-\text{G})\) & [37] \\ Normalized Different Index (NDI) & \((\text{NIR}-\text{R})/(\text{NIR}-\text{G})\) & [33] \\ Plant Senescence Reflectance Index (PSRI) & \((\text{R}-\text{B})/\text{NIR}\) & [35] \\ Modified nonlinear VI (MNVI) & \(1.5(\text{NIR}2-\text{G})/(\text{NIR}2+\text{R}+0.5)\) & [38] \\ Plant Senescence Reflectance Index 1 (PSRI1) & \((\text{R}-\text{G})/(\text{NIR}2-\text{G})\) & [35] \\ Triangular Vegetation Index (TVI) & \(0.5\,[120\,(\text{NIR}-\text{G})-200\,(\text{R}-\text{G})]\) & [39] \\ Modified Triangular Vegetation Index 1 (MTVI1) & \(1.2\,[1.2\,(\text{NIR}-\text{G})-2.5\,(\text{R}-\text{G})]\) & [40] \\ Modified Triangular Vegetation Index 2 (MTVI2) & \(1.5\,[1.2\,(\text{NIR}-\text{G})-2.5\,(\text{R}-\text{G})]/SQRT \(\{2\text{-NIR}+1\})\)\(2-\) & [40] \\ Modified Triangular Vegetation Index 3 (MTVI3) & \((\text{6}-\text{NIR}-\text{5}\)SQRT(\(\text{R}-\text{0}\).5)\) & [41] \\ Enhanced Vegetation Index (EVI) & \(2.5(\text{NIR}-\text{R})/(\text{1}+\text{NIR}+\text{6}-7.5\text{B})\) & [42] \\ Triangular Chlorophyll Index (TCI) & \(1.2(\text{NIR}-\text{G})-5(\text{R}-\text{G})(\text{NIR}/\text{R})^{0.5}\) & [43] \\ Modified Chlorophyll Absorption in Reflectance Index 1 (MCARI) & \([(\text{NIR}-\text{R})-0.2(\text{R}-\text{G})]\times(\text{NIR}/\text{R})\) & [40] \\ Modified Chlorophyll Absorption in Reflectance Index 1 & \(1.2\,[2.5\,(\text{NIR}-\text{R})-1.3\,(\text{NIR}-\text{G})]\) & [40] \\ Modified Chlorophyll Absorption in Reflectance Index 2 & \((\text{MCARI}2)\) & [40] \\ Transformed Chlorophyll Absorption in Reflectance Index & \((\text{R}-\text{NIR}-\text{R})/(\text{1}+\text{NIR}+\text{6}-7.5\text{B})\) & [40] \\ (TCARI) & \(3\,[(\text{NIR}-\text{R})-0.2\,(\text{NIR}-\text{G})(\text{NIR}/\text{R})]\) & [40] \\ TCARI/OSAVI & TCARI/OSAVI & [41] \\ MCARI/MTVI2 & MCARI/MTVI & [42] \\ TCARI/MSAVI & TCAI/OSAVI & [43] \\ \hline \end{tabular}
\end{table}