Processing math: 100%

agriwater

Cesar de Oliveira Ferreira Silva, Antonio Heriberto de Castro Teixeira, Rodrigo Lilla Manzione

2023-06-08

Introduction

“The Simple Algorithm for Evapotranspiration Retrieving” (SAFER) aims to model the ETaET0 ratio. This ratio is calculated according to:

ETaET0=exp[a+b(T0α0NDVI)]

Where α0 is the surface albedo, T0 is the surface temperature and NDVI is the normalized difference vegetation index.

The surface albedo (α0, dimensionless) is obtained from the reflectivity for each band (αpb). For Landsat images was necessary to obtain the planetary albedo (αpb) applying this equation for each band:

αpb=Lbπd2Rcosϕ

Where Lb (W m2 sr1 μm1) 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 m2 μm1) is the mean solar irradiance at the top of the atmosphere for each band and ϕ the solar zenith angle.

The broadband αp is calculated as the total sum of the differenct reflectivities αpb values according to the weights for each band (wp):

αp=wpαpb

The data of αp (dimensionless) is atmospherically corrected to obtain the value of surface albedo (α0):

α0=c×αp+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 (ρnir) and red (ρred) and their sum.

Surface Temperature (T0,K) is derived from the Stefan-Boltzmann Equation according to equation below:

T0=4ϵAσTA+aLτWϵSσ

Where ϵA and ϵS are the atmospheric and surface emissivities, σ is the Stefan-Boltzmann constant, TA is the average air temperature, τW is the shortwave atmosphere transmissivity and aL is the regression coefficient.

Finally, actual evapotranspiration (ETa,mm day1) was obtained according to:

ETa=ET0(ETaET0)

For radiation balance assessment the following equation is used:

RN=H+LE+G

where G is the heat flux in the soil, RN is the net radiation, LE is the latent heat flux and H the sensible heat flux.

Net radiation (RN,W m2 sr1 μ m1) was obtained by the Slob’s equation:

RN=(1α0)RGαLτsw

Latent heat flux (LE,MJ day1) was obtained by:

LE=ETa×2.45

Heat flux in the soil (G,MJ day1) was estimated through its realtionship with the net radiation:

G=RN(3.98 exp(31.89α0))

Sensible heat flux (H,MJ day1) was obtained as a residue of the energy balance:

H=RNLEG

References

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

Loading package “agriwater” and dependencies

library(agriwater)
library(terra)

Sentinel-2

Data base preparation using a single agrometeorological station

The workspace must contain the following files:

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

Data base preparation using a grid of agrometeorological data

The workspace must contain the following files:

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

Modeling with a single agrometeorological station

Surface Albedo retrivieng at 10 m resolution

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.

Crop coefficient retrivieng at 10 m resolution

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 day1)
  • 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.

Atual evapotranspiration retrivieng at 10 m resolution

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 day1)
  • Ta is the average air temperature (Celsius degrees)
  • ET0 is the reference evapotranspiration (mm day1)
  • 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.

Radiation and energy balance at 10 m resolution

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 day1)
  • Ta is the average air temperature (Celsius degrees)
  • ET0 is the reference evapotranspiration (mm day1)
  • 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.

Modeling with a grid of agrometeorological data

Surface Albedo retrivieng at 10 m resolution

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.

Crop coefficient retrivieng at 10 m resolution

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.

Atual evapotranspiration retrivieng at 10 m resolution

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.

Radiation and energy balance at 10 m resolution

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.

Landsat-8 with thermal bands

Data base preparation using a single agrometeorological station

The workspace must contain the following files:

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

Data base preparation using a grid of agrometeorological data

The workspace must contain the following files:

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

Modeling with a single agrometeorological station

Reflectance at 30 m resolution

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.

Surface Albedo retrivieng at 30 m resolution

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.

Crop coefficient retrivieng at 30 m resolution

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 day1)
  • 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.

Atual evapotranspiration retrivieng at 30 m resolution

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 day1)
  • Ta is the average air temperature (Celsius degrees)
  • ET0 is the reference evapotranspiration (mm day1)
  • 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.

Radiation and energy balance at 30 m resolution

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 day1)
  • 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.

Modeling with a grid of agrometeorological data

Reflectance at 30 m resolution

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.

Surface Albedo retrivieng at 30 m resolution

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.

Crop coefficient retrivieng at 30 m resolution

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.

Atual evapotranspiration retrivieng at 30 m resolution

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

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.

Radiation and energy balance at 30 m resolution

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

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.

Landsat-8 without thermal bands

Data base preparation using a single agrometeorological station

The workspace must contain the following files:

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

Data base preparation using a grid of agrometeorological data

The workspace must contain the following files:

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

Modeling with a single agrometeorological station

Surface Albedo retrivieng at 30 m resolution

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.

Crop coefficient retrivieng at 30 m resolution

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 day1)
  • 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.

Atual evapotranspiration retrivieng at 30 m resolution

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 day1)
  • Ta is the average air temperature (Celsius degrees)
  • ET0 is the reference evapotranspiration (mm day1)
  • 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.

Radiation and energy balance at 30 m resolution

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 day1)
  • Ta is the average air temperature (Celsius degrees)
  • ET0 is the reference evapotranspiration (mm day1)
  • 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.

Modeling with a grid of agrometeorological data

Reflectance at 30 m resolution

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.

Surface Albedo retrivieng at 30 m resolution

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.

Crop coefficient retrivieng at 30 m resolution

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

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.

Atual evapotranspiration retrivieng at 30 m resolution

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

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.

Radiation and energy balance at 30 m resolution

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

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.

MODIS

Data base preparation using a single agrometeorological station

The workspace must contain the following files:

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

Data base preparation using a grid of agrometeorological data

The workspace must contain the following files:

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

Modeling with a single agrometeorological station

Surface Albedo retrivieng at 250 m resolution

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.

Crop coefficient retrivieng at 250 m resolution

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 day1)
  • 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.

Atual evapotranspiration retrivieng at 250 m resolution

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 day1)
  • Ta is the average air temperature (Celsius degrees)
  • ET0 is the reference evapotranspiration (mm day1)
  • 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.

Radiation and energy balance at 250 m resolution

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 day1)
  • Ta is the average air temperature (Celsius degrees)
  • ET0 is the reference evapotranspiration (mm day1)
  • 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.

Modeling with a grid of agrometeorological data

Surface Albedo retrivieng at 250 m resolution

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.

Crop coefficient retrivieng at 250 m resolution

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

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.

Atual evapotranspiration retrivieng at 250 m resolution

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

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.

Radiation and energy balance at 250 m resolution

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

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.