“The Simple Algorithm for Evapotranspiration Retrieving” (SAFER) aims to model the \(\frac{ET_a}{ET_0}\) ratio. This ratio is calculated according to:

\[\frac{ET_a}{ET_0} = exp \left[ a+b \left( \frac{T_0}{\alpha_0 NDVI} \right) \right]\]

Where \(\alpha_0\) is the surface albedo, \(T_0\) is the surface temperature and \(NDVI\) is the normalized difference vegetation index.

The surface albedo (\(\alpha_0\), dimensionless) is obtained from the reflectivity for each band (\(\alpha_{pb}\)). For Landsat images was necessary to obtain the planetary albedo (\(\alpha_{pb}\)) applying this equation for each band:

\[\alpha_{pb} = \frac{L_b \pi d^2}{R cos \phi}\]

Where \(L_b\) (\(W \ m^{-2} \ sr^{-1} \ \mu m^{-1}\)) is the spectral radiance for the wavelenghts of the band (\(b\) from 1 to 7), \(d\) (\(m\)) is the relative earth-sun distance, \(R\) (\(W \ m^{-2} \ \mu m^{-1}\)) is the mean solar irradiance at the top of the atmosphere for each band and \(\phi\) the solar zenith angle.

The broadband \(\alpha_p\) is calculated as the total sum of the differenct reflectivities \(\alpha_{pb}\) values according to the weights for each band (\(w_p\)):

\[\alpha_p = \sum w_p \alpha_{pb}\]

The data of \(\alpha_p\) (dimensionless) is atmospherically corrected to obtain the value of surface albedo (\(\alpha_0\)):

\[\alpha_0 = c \times \alpha_p + d\]

where \(c\) and \(d\) are regression coefficients which are specific for each satellite.

The normalized difference vegetation index (NDVI, dimensionless) is calculated through the ratio of the difference between the planetary reflectivities of the near infrared (\(\rho_{nir}\)) and red (\(\rho_{red}\)) and their sum.

Surface Temperature (\(T_0, K\)) is derived from the Stefan-Boltzmann Equation according to equation below:

\[ T_0 = \sqrt[4] \frac{ \epsilon_A \sigma T_A + a_L \tau_W }{ \epsilon_S \sigma } \]

Where \(\epsilon_A\) and \(\epsilon_S\) are the atmospheric and surface emissivities, \(\sigma\) is the Stefan-Boltzmann constant, \(T_A\) is the average air temperature, \(\tau_W\) is the shortwave atmosphere transmissivity and \(a_L\) is the regression coefficient.

Finally, actual evapotranspiration (\(ET_a, mm \ day^{-1}\)) was obtained according to:

\[ET_a = ET_0 \left( \frac{ET_a}{ET_0} \right)\]

For radiation balance assessment the following equation is used:

\[R_N = H + LE + G \]

where \(G\) is the heat flux in the soil, \(R_N\) is the net radiation, \(LE\) is the latent heat flux and \(H\) the sensible heat flux.

Net radiation (\(R_N, W \ m^{-2} \ sr^{-1} \ \mu \ m^{-1}\)) was obtained by the Slob’s equation:

\[R_N = (1 - \alpha_0) R_G - \alpha_L \tau_{sw}\]

Latent heat flux (\(LE, MJ \ day^{-1}\)) was obtained by:

\[LE = ET_a \times 2.45 \]

Heat flux in the soil (\(G, MJ \ day^{-1}\)) was estimated through its realtionship with the net radiation:

\[ G = R_N(3.98 \ exp(-31.89 \alpha_0))\]

Sensible heat flux (\(H, MJ \ day^{-1}\)) was obtained as a residue of the energy balance:

\[H = R_N - LE - G \]

Teixeira (2010) https://doi.org/10.3390/rs0251287

Teixeira et al. (2015) https://dx.doi.org/10.3390/rs71114597

Silva et al. (2018) https://doi.org/10.3390/horticulturae4040044

Silva et al. (2019) http://dx.doi.org/10.1016/j.envsoft.2019.104497

Teixeira et al. (2021) http://dx.doi.org/10.1016/j.rsase.2021.100514

```
library(agriwater)
library(terra)
```

The workspace must contain the following files:

“B2.tif” - Blue - with wavelength between 0.439 - 0.535 micrometers - 10 m of resolution

“B3.tif” - Green - with wavelength between 0.537 - 0.582 micrometers - 10 m of resolution

“B4.tif” - Red - with wavelength between 0.646 - 0.685 micrometers - 10 m of resolution

“B8.tif” - Near Infrared (NIR) - with wavelength between 0.767 - 0.908 micrometers - 10 m of resolution

“mask.shp” - Shapefile of study area to mask digital images

All must have the same projection in decimal degrees (geographical)

The workspace must contain the following files:

“B2.tif” - Blue - with wavelength between 0.439 - 0.535 micrometers - 10 m of resolution

“B3.tif” - Green - with wavelength between 0.537 - 0.582 micrometers - 10 m of resolution

“B4.tif” - Red - with wavelength between 0.646 - 0.685 micrometers - 10 m of resolution

“B8.tif” - Near Infrared (NIR) - with wavelength between 0.767 - 0.908 micrometers - 10 m of resolution

“ET0.tif” - Reference evapotranspiration (\(mm \ day^{-1}\)) spatially interpolated by the user’s preferred method.

“RG.tif” - Solar radiation incident (\(MJ \ day^{-1}\)) spatially interpolated by the user’s preferred method.

“Ta.tif” - Average air temperature (Celsius degrees) spatially interpolated by the user’s preferred method.

“mask.shp” - Shapefile of study area to mask digital images

All must have the same projection in decimal degrees (geographical)

With Sentinel-2 bands in the workspace, run:

`albedo_s2()`

A raster file named “Alb_24.tif” will be generated with the same projection as the raster input.

With Sentinel-2 bands in the workspace, run:

`kc_s2(doy, RG, Ta, a, b)`

Where:

- doy is the Day of Year (DOY)
- RG is the global solar radiation (\(MJ \ day^{-1}\))
- Ta is the average air temperature (Celsius degrees)
- a is one of the regression coefficients of SAFER algorithm
- b is one of the regression coefficients of SAFER algorithm

Raster files named “Alb_24.tif”, “NDVI.tif”, “LST.tif”, “Rn_MJ” and “kc.tif” will be generated with the same projection as the raster input.

With Sentinel-2 bands in the workspace, run:

`evapo_s2(doy, RG, Ta, ET0, a, b)`

Where:

- doy is the Day of Year (DOY)
- RG is the global solar radiation (\(MJ \ day^{-1}\))
- Ta is the average air temperature (Celsius degrees)
- ET0 is the reference evapotranspiration (\(mm \ day^{-1}\))
- a is one of the regression coefficients of SAFER algorithm
- b is one of the regression coefficients of SAFER algorithm

Raster files named “Alb_24.tif”, “NDVI.tif”, “LST.tif”, “Rn_MJ”, “kc.tif” and “evapo.tif” will be generated with the same projection as the raster input.

With Sentinel-2 bands in the workspace, run:

`radiation_s2(doy, RG, Ta, ET0, a, b)`

Where:

- doy is the Day of Year (DOY)
- RG is the global solar radiation (\(MJ \ day^{-1}\))
- Ta is the average air temperature (Celsius degrees)
- ET0 is the reference evapotranspiration (\(mm \ day^{-1}\))
- a is one of the regression coefficients of SAFER algorithm
- b is one of the regression coefficients of SAFER algorithm

Raster files named “Alb_24.tif”, “NDVI.tif”, “LST.tif”, “Rn_MJ”, “kc.tif” , “evapo.tif”, “LE_MJ.tif”, “H_MJ.tif” and “G_MJ.tif” will be generated with the same projection as the raster input.

With Sentinel-2 bands in the workspace, run:

`albedo_s2()`

A raster file named “Alb_24.tif” will be generated with the same projection as the raster input.

With Sentinel-2 bands and agrometeorological data in the workspace, run:

`kc_s2_grid(doy, a, b)`

Where:

- doy is the Day of Year (DOY)
- a is one of the regression coefficients of SAFER algorithm
- b is one of the regression coefficients of SAFER algorithm

Raster files named “Alb_24.tif”, “NDVI.tif”, “LST.tif”, “Rn_MJ” and “kc.tif” will be generated with the same projection as the raster input.

With Sentinel-2 bands and agrometeorological data in the workspace, run:

`evapo_s2_grid(doy, a, b)`

Where:

- doy is the Day of Year (DOY)
- a is one of the regression coefficients of SAFER algorithm
- b is one of the regression coefficients of SAFER algorithm

Raster files named “Alb_24.tif”, “NDVI.tif”, “LST.tif”, “Rn_MJ”, “kc.tif” and “evapo.tif” will be generated with the same projection as the raster input.

With Sentinel-2 bands and agrometeorological data in the workspace, run:

`radiation_s2_grid(doy, a, b)`

Where:

- doy is the Day of Year (DOY)
- a is one of the regression coefficients of SAFER algorithm
- b is one of the regression coefficients of SAFER algorithm

Raster files named “Alb_24.tif”, “NDVI.tif”, “LST.tif”, “Rn_MJ”, “kc.tif” , “evapo.tif”, “LE_MJ.tif”, “H_MJ.tif” and “G_MJ.tif” will be generated with the same projection as the raster input.

The workspace must contain the following files:

“B1.tif” - Ultra Blue (coastal/aerosol) - with wavelength between 0.435 - 0.451 micrometers - 30 m of resolution

“B2.tif” - Blue - with wavelength between 0.452 - 0.512 micrometers micrometers - 30 m of resolution

“B3.tif” - Green - with wavelength between 0.533 - 0.590 micrometers - 30 m of resolution

“B4.tif” - Red - with wavelength between 0.636 - 0.673 micrometers - 30 m of resolution

“B5.tif” - Near Infrared (NIR) - with wavelength between 0.851 - 0.879 micrometers - 30 m of resolution

“B6.tif” - Shortwave Infrared (SWIR) 1 - with wavelength between 1.566 - 1.651 micrometers - 30 m of resolution

“B7.tif” - Shortwave Infrared (SWIR) 2 - with wavelength between 2.107 - 2.294 micrometers - 30 m of resolution

“B10.tif” - Thermal Infrared (TIRS) 1 - with wavelength between 10.60 - 11.19 micrometers - 100 m of resolution

“B11.tif” - Thermal Infrared (TIRS) 2 - with wavelength between 11.50 - 12.51 micrometers - 100 m of resolution

“mask.shp” - Shapefile of study area to mask digital images

“.txt” - a text file of metadata provided with Landsat-8 images

All must have the same projection in decimal degrees (geographical)

The workspace must contain the following files:

“B1.tif” - Ultra Blue (coastal/aerosol) - with wavelength between 0.435 - 0.451 micrometers - 30 m of resolution

“B2.tif” - Blue - with wavelength between 0.452 - 0.512 micrometers - 30 m of resolution

“B3.tif” - Green - with wavelength between 0.533 - 0.590 micrometers - 30 m of resolution

“B4.tif” - Red - with wavelength between 0.636 - 0.673 micrometers - 30 m of resolution

“B5.tif” - Near Infrared (NIR) - with wavelength between 0.851 - 0.879 micrometers - 30 m of resolution

“B6.tif” - Shortwave Infrared (SWIR) 1 - with wavelength between 1.566 - 1.651 micrometers - 30 m of resolution

“B7.tif” - Shortwave Infrared (SWIR) 2 - with wavelength between 2.107 - 2.294 micrometers - 30 m of resolution

“B10.tif” - Thermal Infrared (TIRS) 1 - with wavelength between 10.60 - 11.19 micrometers - 100 m of resolution

“B11.tif” - Thermal Infrared (TIRS) 2 - with wavelength between 11.50 - 12.51 micrometers - 100 m of resolution

“mask.shp” - Shapefile of study area to mask digital images

“.txt” - a text file of metadata provided with Landsat-8 images

“ET0.tif” - Reference evapotranspiration (\(mm \ day^{-1}\)) spatially interpolated by the user’s preferred method.

“RG.tif” - Solar radiation incident (\(MJ \ day^{-1}\)) spatially interpolated by the user’s preferred method.

“Ta.tif” - Average air temperature (Celsius degrees) spatially interpolated by the user’s preferred method.

All must have the same projection in decimal degrees (geographical)

With Landsat-8 bands in the workspace, run:

`reflectance_l8()`

Raster files named from “B1_reflectance_landsat8” to “B7_reflectance_landsat8” will be generated with the same projection as the raster input.

With Landsat-8 bands in the workspace, run:

`albedo_l8()`

A raster file named “Alb_24.tif” will be generated with the same projection as the raster input.

With Landsat-8 bands in the workspace, run:

`kc_l8t(doy, RG, Ta, a, b)`

Where:

- doy is the Day of Year (DOY)
- RG is the global solar radiation (\(MJ \ day^{-1}\))
- Ta is the average air temperature (Celsius degrees)
- a is one of the regression coefficients of SAFER algorithm
- b is one of the regression coefficients of SAFER algorithm

Raster files named “Alb_24.tif”, “NDVI.tif”, “LST.tif”, “Rn_MJ” and “kc.tif” will be generated with the same projection as the raster input.

With Landsat-8 bands in the workspace, run:

`evapo_l8t(doy, RG, Ta, ET0, a, b)`

Where:

- doy is the Day of Year (DOY)
- RG is the global solar radiation (\(MJ \ day^{-1}\))
- Ta is the average air temperature (Celsius degrees)
- ET0 is the reference evapotranspiration (\(mm \ day^{-1}\))
- a is one of the regression coefficients of SAFER algorithm
- b is one of the regression coefficients of SAFER algorithm

Raster files named “Alb_24.tif”, “NDVI.tif”, “LST.tif”, “Rn_MJ”, “kc.tif” and “evapo.tif” will be generated with the same projection as the raster input.

With Landsat-8 bands in the workspace, run:

`radiation_l8t(doy, RG, Ta, ET0, a, b)`

Where:

- doy is the Day of Year (DOY)
- RG is the global solar radiation (\(MJ \ day^{-1}\))
- Ta is the average air temperature (Celsius degrees)
- a is one of the regression coefficients of SAFER algorithm
- b is one of the regression coefficients of SAFER algorithm

Raster files named “Alb_24.tif”, “NDVI.tif”, “LST.tif”, “Rn_MJ”, “kc.tif” , “evapo.tif”, “LE_MJ.tif”, “H_MJ.tif” and “G_MJ.tif” will be generated with the same projection as the raster input.

With Landsat-8 bands in the workspace, run:

`reflectance_l8()`

Raster files named from “B1_reflectance_landsat8” to “B7_reflectance_landsat8” will be generated with the same projection as the raster input.

With Landsat-8 bands in the workspace, run:

`albedo_l8()`

A raster file named “Alb_24.tif” will be generated with the same projection as the raster input.

With Sentinel-2 bands in the workspace and agrometeorological data, run:

`kc_l8t_grid(doy, a, b)`

Where:

- doy is the Day of Year (DOY)
- a is one of the regression coefficients of SAFER algorithm
- b is one of the regression coefficients of SAFER algorithm

Raster files named “Alb_24.tif”, “NDVI.tif”, “LST.tif”, “kc.tif” will be generated with the same projection as the raster input.

With Landsat-8 bands in the workspace and agrometeorological data, run:

`evapo_l8t_grid(doy, a, b)`

Where:

- doy is the Day of Year (DOY)
- a is one of the regression coefficients of SAFER algorithm
- b is one of the regression coefficients of SAFER algorithm

With Landsat-8 bands and agrometeorological data in the workspace, run:

`radiation_l8t_grid(doy, a, b)`

Where:

- doy is the Day of Year (DOY)
- a is one of the regression coefficients of SAFER algorithm
- b is one of the regression coefficients of SAFER algorithm

The workspace must contain the following files:

“B1.tif” - Ultra Blue (coastal/aerosol) - with wavelength between 0.435 - 0.451 micrometers - 30 m of resolution

“B2.tif” - Blue - with wavelength between 0.452 - 0.512 micrometers - 30 m of resolution

“B3.tif” - Green - with wavelength between 0.533 - 0.590 micrometers - 30 m of resolution

“B4.tif” - Red - with wavelength between 0.636 - 0.673 micrometers - 30 m of resolution

“B5.tif” - Near Infrared (NIR) - with wavelength between 0.851 - 0.879 micrometers - 30 m of resolution

“B6.tif” - Shortwave Infrared (SWIR) 1 - with wavelength between 1.566 - 1.651 micrometers - 30 m of resolution

“B7.tif” - Shortwave Infrared (SWIR) 2 - with wavelength between 2.107 - 2.294 micrometers - 30 m of resolution

“mask.shp” - Shapefile of study area to mask digital images

“.txt” - a text file of metadata provided with Landsat-8 images

All must have the same projection in decimal degrees (geographical)

The workspace must contain the following files:

“B2.tif” - Blue - with wavelength between 0.452 - 0.512 micrometers - 30 m of resolution

“B3.tif” - Green - with wavelength between 0.533 - 0.590 micrometers - 30 m of resolution

“B4.tif” - Red - with wavelength between 0.636 - 0.673 micrometers - 30 m of resolution

“mask.shp” - Shapefile of study area to mask digital images

“.txt” - a text file of metadata provided with Landsat-8 images

“ET0.tif” - Reference evapotranspiration (\(mm \ day^{-1}\)) spatially interpolated by the user’s preferred method.

“RG.tif” - Solar radiation incident (\(MJ \ day^{-1}\)) spatially interpolated by the user’s preferred method.

“Ta.tif” - Average air temperature (Celsius degrees) spatially interpolated by the user’s preferred method.

All must have the same projection in decimal degrees (geographical)

With Landsat-8 bands in the workspace, run:

`albedo_l8()`

A raster file named “Alb_24.tif” will be generated with the same projection as the raster input.

With Landsat-8 bands in the workspace, run:

`kc_l8(doy, RG, Ta, a, b)`

Where:

- doy is the Day of Year (DOY)
- RG is the global solar radiation (\(MJ \ day^{-1}\))
- Ta is the average air temperature (Celsius degrees)
- a is one of the regression coefficients of SAFER algorithm
- b is one of the regression coefficients of SAFER algorithm

With Landsat-8 bands in the workspace, run:

`evapo_l8(doy, RG, Ta, ET0, a, b)`

Where:

- doy is the Day of Year (DOY)
- RG is the global solar radiation (\(MJ \ day^{-1}\))
- Ta is the average air temperature (Celsius degrees)
- ET0 is the reference evapotranspiration (\(mm \ day^{-1}\))
- a is one of the regression coefficients of SAFER algorithm
- b is one of the regression coefficients of SAFER algorithm

With Landsat-8 bands in the workspace, run:

`radiation_l8(doy, RG, Ta, ET0, a, b)`

Where:

- doy is the Day of Year (DOY)
- RG is the global solar radiation (\(MJ \ day^{-1}\))
- Ta is the average air temperature (Celsius degrees)
- ET0 is the reference evapotranspiration (\(mm \ day^{-1}\))
- a is one of the regression coefficients of SAFER algorithm
- b is one of the regression coefficients of SAFER algorithm

With Landsat-8 bands in the workspace, run:

`reflectance_l8()`

Raster files named from “B1_reflectance_landsat8” to “B7_reflectance_landsat8” will be generated with the same projection as the raster input.

With Landsat-8 bands in the workspace, run:

`albedo_l8()`

A raster file named “Alb_24.tif” will be generated with the same projection as the raster input.

With Sentinel-2 bands in the workspace, run:

`kc_l8_grid(doy, a, b)`

Where:

- doy is the Day of Year (DOY)
- a is one of the regression coefficients of SAFER algorithm
- b is one of the regression coefficients of SAFER algorithm

With Landsat-8 bands in the workspace and agrometeorological data, run:

`evapo_l8_grid(doy, a, b)`

Where:

- doy is the Day of Year (DOY)
- a is one of the regression coefficients of SAFER algorithm
- b is one of the regression coefficients of SAFER algorithm

With Landsat-8 bands and agrometeorological data in the workspace, run:

`radiation_l8_grid(doy, RG, Ta, ET0, a, b)`

Where:

- doy is the Day of Year (DOY)
- a is one of the regression coefficients of SAFER algorithm
- b is one of the regression coefficients of SAFER algorithm

The workspace must contain the following files:

“B1.tif” - Red - with wavelength between 0.620 - 0.670 micrometers - 250 m of resolution

“B2.tif” - Near Infrared (NIR) - with wavelength between 0.841 - 0.876 micrometers - 250 m of resolution

“mask.shp” - Shapefile of study area to mask digital images

All must have the same projection in decimal degrees (geographical)

The workspace must contain the following files:

“B1.tif” - Red - with wavelength between 0.620 - 0.670 micrometers - 250 m of resolution

“B2.tif” - Near Infrared (NIR) - with wavelength between 0.841 - 0.876 micrometers - 250 m of resolution

“mask.shp” - Shapefile of study area to mask digital images

All must have the same projection in decimal degrees (geographical)

With MODIS bands in the workspace, run:

`albedo_modis()`

A raster file named “Alb_24.tif” will be generated with the same projection as the raster input.

With MODIS bands in the workspace, run:

`kc_modis(doy, RG, Ta, a, b)`

Where:

- doy is the Day of Year (DOY)
- RG is the global solar radiation (\(MJ \ day^{-1}\))
- Ta is the average air temperature (Celsius degrees)
- a is one of the regression coefficients of SAFER algorithm
- b is one of the regression coefficients of SAFER algorithm

With MODIS bands in the workspace, run:

`evapo_modis(doy, RG, Ta, ET0, a, b)`

Where:

- doy is the Day of Year (DOY)
- RG is the global solar radiation (\(MJ \ day^{-1}\))
- Ta is the average air temperature (Celsius degrees)
- ET0 is the reference evapotranspiration (\(mm \ day^{-1}\))
- a is one of the regression coefficients of SAFER algorithm
- b is one of the regression coefficients of SAFER algorithm

With MODIS bands in the workspace, run:

`radiation_modis(doy, RG, Ta, ET0, a, b)`

Where:

- doy is the Day of Year (DOY)
- RG is the global solar radiation (\(MJ \ day^{-1}\))
- Ta is the average air temperature (Celsius degrees)
- ET0 is the reference evapotranspiration (\(mm \ day^{-1}\))
- a is one of the regression coefficients of SAFER algorithm
- b is one of the regression coefficients of SAFER algorithm

With MODIS bands in the workspace, run:

`albedo_modis()`

A raster file named “Alb_24.tif” will be generated with the same projection as the raster input.

With MODIS bands in the workspace, run:

`kc_modis_grid(doy, a, b)`

Where:

- doy is the Day of Year (DOY)
- a is one of the regression coefficients of SAFER algorithm
- b is one of the regression coefficients of SAFER algorithm

With MODIS bands and agrometeorological data in the workspace, run:

`evapo_modis_grid(doy, a, b)`

Where:

- doy is the Day of Year (DOY)
- a is one of the regression coefficients of SAFER algorithm
- b is one of the regression coefficients of SAFER algorithm

With MODIS bands in the workspace, run:

`radiation_modis_grid(doy, a, b)`

Where:

- doy is the Day of Year (DOY)
- a is one of the regression coefficients of SAFER algorithm
- b is one of the regression coefficients of SAFER algorithm