agriwater

Introduction

The Simple Algorithm for Evapotranspiration Retrieving (SAFER) is based on the modeling of 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:

$$H = R_N - LE - G $$

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

Loading package "agriwater" and dependencies

library(agriwater)
library(raster)
library(sp)
library(rgdal)

Sentinel-2

Data base preparation using a single agrometeorological station

In the workspace must be the following files:

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

Data base preparation using a grid of agrometeorological data

In the workspace must be 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:

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:

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:

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:

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:

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:

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

In the workspace must be the following files:

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

Data base preparation using a grid of agrometeorological data

In the workspace must be 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:

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:

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:

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:

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:

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:

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

In the workspace must be the following files:

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

Data base preparation using a grid of agrometeorological data

In the workspace must be 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:

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:

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:

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:

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:

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:

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

In the workspace must be the following files:

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

Data base preparation using a grid of agrometeorological data

In the workspace must be 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:

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:

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:

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:

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:

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:

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.



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agriwater documentation built on Feb. 2, 2021, 9:07 a.m.