03-Indice.Rmd

# Vegetation Indices {#Iveg} 
The VIs allow the quantitative and functional relationship with different parameters or variables of the vegetation. There are 23 VIs considered in VICAL, these VIs are commonly used in agricultural applications [@Bannari2009],[@Xue2017].

The names of these VIs, their mathematical expression as well as their abbreviation are shown in the following list: 
**1: ARVI**: Atmospherically resistant vegetation index*
$$
ARVI = \frac{p(NIR-rb)}{NIR+rb};     
$$
$$
rb = {R-γ(B-R)}; \thinspace \thinspace  Default \thinspace value: \thinspace γ=1.0 
$$

**2: ATSAVI**: Adjusted transformed soil-adjusted vegetation index*
$$
ATSAVI = \frac{a(NIR-aR-b)}{(R+aNIR-ab+X(1+a^2))};
$$
$$
\thinspace \thinspace  Default \thinspace value: \thinspace a= 1 ;\thinspace b=0; \thinspace X= 0.08      
$$
**3: DVI: ** Difference vegetation index
$$
DVI = {(NIR-R)} ;   
$$
**4: EVI***: Enhanced vegetation index
$$
EVI = \frac{2.5*(NIR-R)}{NIR+C_1 R-C_2 B+L};     
$$
$$
\thinspace \thinspace  Default \thinspace value: \thinspace C_1= 6.0 ;\thinspace C_2=7.5; \thinspace L= 1.0      
$$
**5: EVI2***: Enhanced vegetation index
$$
EVI2 = \frac{2.5*(NIR-R)}{NIR+C_1 R+1}; \thinspace \thinspace  Default \thinspace value: \thinspace C_1= 2.4      
$$
**6: GNDVI**: Green normalized difference vegetation index
$$
GNDVI = \frac{NIR-G}{NIR+G};     
$$
**7: MSAVI2**: Modified soil adjusted vegetation index
$$
MSAVI2 = \frac{(2NIR+1)-\sqrt((2NIR+1)^2-8(NIR-R))}{2};     
$$
**8: MSI**: Moisture stress index
$$
MSI = \frac{SWIR_1}{NIR};     
$$
**9: MTVI**: Modified triangular vegetation index
$$
MTVI ={1.2[1.2*(NIR-G)-2.5*(R-G)]};     
$$

**10: MTVI2**: Modified triangular vegetation index-2
$$
MTVI2 = \frac{1.2[1.2*(NIR-G)-2.5*(R-G)]}{\sqrt((2NIR+1)^2-(6NIR-5\sqrt(R))-0.5)};     
$$
**11: NDTI**: Normalized difference tillage index (NDTI)
$$
NDTI = \frac{SWIR_1-SWIR_2}{SWIR_1+SWIR_2};     
$$
**12: NDVI**: Normalized difference vegetation index
$$
NDVI = \frac{NIR-R}{NIR+R};     
$$
**13: NDWI**: Normalized difference water index
$$
NDWI = \frac{NIR-SWIR_1}{NIR+SWIR_1};     
$$
**14: OSAVI**: Optimized soil adjusted vegetation index*
$$
OSAVI = \frac{1.16*(NIR-R)}{NIR+R+X}; \thinspace \thinspace  Default \thinspace value: \thinspace X= 0.16     
$$
**15: RDVI**: Renormalized difference vegetation index
$$
RDVI = \frac{NIR-R}{\sqrt(NIR+R)};     
$$
**16: RI**: Redness index
$$
RI = \frac{p(NIR-G)}{NIR+G};     
$$
**17: RVI**:  Ratio vegetation index
$$
RVI = \frac{R}{NIR};     
$$
**18: SAVI***: Soil adjusted vegetation index
$$
SAVI = \frac{(NIR-R)}{NIR+R+L} (1+ L);    \thinspace \thinspace  Default \thinspace value: \thinspace L= 0.5  
$$
**19: TVI**: Triangular vegetation index
$$
TVI = 0.5*{[120(NIR-G)-200(R-G)]};     
$$
**20: TSAVI***: Transformed soil adjusted vegetation index
$$
TSAVI = \frac{a(NIR-aR-b)}{R+aNIR-ab};  \thinspace \thinspace  Default \thinspace value: \thinspace a= 1,   \thinspace b=0.    
$$
**21: VARI**: Visible atmospherically resistant index
$$
VARI = \frac{G-R}{G+R-B};     
$$
**22: VIN**: Vegetation index number or simple ratio
$$
VIN = \frac{NIR}{R};     
$$
**23: WDRVI***:  Wide dynamic range vegetation index
$$
WDRVI = \frac{∝NIR-R}{∝NIR+R)}; \thinspace \thinspace  Default \thinspace value: \thinspace ∝= 0.2   
$$

VICAL allows the user to configure some VIs coefficient such as in **ARVI, ATSAVI, EVI, EVI2, OSAVI, SAVI, ATSAVI**, and **WDRVI**, that is, all those VIs that need, in addition to the spectrum bands, some adjustment variable.

The name of the bands with their abbreviations that were used in the VIs equations is shown in Table \@ref(tab:inOMBRE).
```{r inOMBRE, echo=FALSE, message=FALSE, warning=FALSE,}
Abreviatura<-c("B",	"G",	"R",	"RE",	"NIR",	"SWIR1",	"SWIR2")
Nombre <-c("Azul/Blue",	"Verde/Green",	"Rojo/Red",	"Borde Rojo/Red edge",	"Infrarrojo Cercano /Near infrared",	"Infrarrojo de onda corta 1/Shortwave infrared 1 ",	"Infrarrojo de onda corta 2/Shortwave infrared 2")

inOMBRE<-data.frame(Abreviatura,Nombre)

knitr::kable(inOMBRE, booktabs = TRUE, 
  caption = 'Abbreviation of the spectral bands used in the VI equations'
) 
```


_If you want to add another VI you can write to us at jimenez.sergio@inifap.gob.mx_