VICAL: Global Calculator to Estimate Vegetation Indices for Agricultural Areas with Landsat and Sentinel-2 Data

Abstract

The vegetation indices (VIs) estimated from remotely sensed data are simple and based on effective algorithms for quantitative and qualitative evaluations of the dynamics of biophysical crop variables such as vegetation cover, leaf area, vigor and development, and many others. Over the last decade, many VIs have been proposed and validated to enhance the vegetation signal by reducing the noise from effects produced either by the soil or by vegetation such as brightness, shadows, color, etc. VIs are commonly calculated from satellite images such as ones from Landsat and Sentinel-2 because of their medium resolution and free availability. However, despite the VIs being fairly simple algorithms, it can take hours to calculate them for an established agricultural area, mainly due to the pre-processing of the images (including atmospheric corrections, the detection of clouds and shadows), size and download time of the images, and the capacity of the computer equipment used. Time increases as the number of images increases. In this sense, the free to use Google Earth Engine (GEE) platform was here used to develop an application called VICAL to calculate 23 VIs map (VIs commonly used in agricultural applications) and time series of any agricultural area in the world with images (cloud-free) from Landsat and Sentinel-2 data. It was found that VICAL can calculate these 23 VIs accurately, and shows the potential of the GEE cloud-based tools using multispectral dataset to assess many spectral VIs. This tool is very beneficial for researchers with poor access to satellite data or in institutions with a lack of computational infrastructure to handle the large volumes of satellite datasets, since it is not necessary for the user writing a single line of code. The VICAL is open-access image analysis platform that can be modified to carry out more complex analysis or adapt it to a specific VI application.

1. Introduction

Multi-spectral remotely sensed imagery is the main data source for land mapping, performing bands operations, and creating a composite image used for interpretation and analysis. The different combinations between these digital bands are called vegetation indices (VI) which are a numerical value qualifying the intensity of a phenomenon which is too complex to be decomposed into known parameters [1]. In agriculture, VIs have been used to indirectly estimate biophysical crop properties such as the crop coefficient, leaf area index, cover fraction, the vigor, and the dynamics of other biophysical crop variables. These VIs have been used in many agricultural applications, for example, to estimate the fraction of vegetation cover, leaf area index (LAI) [2], crop coefficients [3,4] monitoring of phenological stages [5], chlorophyll content, fraction of absorbed photosynthetically active radiation (fAPAR) [6], and biomass [7,8], among other.

The normalized difference vegetation index (NDVI) is one of the most used VIs for agricultural applications. However, in the last decade numerous spectral VIs have been proposed to characterise vegetation canopies and many of them have been applied in agriculture. There is no unified mathematical expression that defines all VIs due to the complexity of different light spectra combinations, instrumentation, platforms, and resolutions used. In this way, there are more than 100 VIs derived from multispectral digital images [9].

VIs can be obtained from satellite images of high (WorldView-2 and -3), medium (Landsat and Sentinel) and low (MODIS) spatial resolution, or with aerial platforms and, more recently, unmanned aerial vehicles (UAV). Although satellite data such as MODIS have been used extensively, their quality is far from satisfactory for many applications [10]. On the other hand, high-resolution sensors mounted on UAVs are often not suitable for regional-scale applications, and users have to acquire and manage the images themselves [11]. In this sense, medium-resolution satellite data such as data obtained from Landsat and Sentinel have been used extensively for global monitoring since they are freely available.

Although VIs are simple mathematical expressions, the extraction of information from Landsat and Sentinel images for a specific surface is time-consuming because the images must be downloaded and pre-processed. In addition, this process is associated with high computational costs and requires a large storage capacity [12,13]. These computational times and costs increase as the size of the images increases. Therefore, many modern applications are limited to relatively small areas due to limitations of storage and computing resources [12]. However, with technological advances and the emergence of free-to-use platforms such as the Google Earth Engine (GEE), the processing of a large number of images to map the intensity of the vegetation has been facilitated [14]. GEE includes the entire Landsat archive, as well as complete archives of data from Sentinel-1 and Sentinel-2; besides, GEE also offers the possibility of merging data from different satellites such as Landsat and Sentinel. In particular, the calculation of several VIs in GEE with different images allows vegetation studies to be conducted efficiently and quickly [13].

Many software (commercial and open-source) available for the computation of VIs and time series from satellite data, require spectral images as input data. This indicates that in a separate process the images must be downloaded and pre-processed; which is time consuming and requires computer space for data storage. On the other side, the use of GEE prevents these cumbersome process making more feasible and efficient the process of obtaining and analyzing spectral images. In this sense, The goal of this research work was the development of an analytical tool (VICAL, https://inifapcenidraspa.users.earthengine.app/view/vical (accessed on 16 June 2022)) within the GEE environment to assess 23 VIs (commonly used in agricultural applications among others analysis) using Landsat and Sentinel-2 data. VICAL can be used globally for monitoring any agricultural farm at regional or local scale using VIs or for the calibration of biophysical variables related to crop’s development.

The VICAL tool has three main functions: (i) calculation of 23 VIs with images (cloud-free) from Landsat (4, 5, 7, 8 and 9) and Sentinel-2 data from any user-defined area; (ii) VI time series plot for each polygon drawn by the user with Landsat and Sentinel-2 or both satellites, and iii) Regression maps (linear, quadratic, potential or exponential function) using VIs values. In addition, the GEE environment allows users to easily modify or incorporate other routines into VICAL to carry out a more complex analysis or adapt it to a certain application; this can be achieved by accessing the code available at: https://code.earthengine.google.com/ac86e7b52b29121ede7e9110570e1725 (accessed on 16 June 2022) (see Supplementary Material).

2. Materials and Methods

2.1. Satellite Images: Landsat and Sentinel

The Sentinel-2 dataset accessible from the European Space Agency and Landsat dataset from NASA (National Aeronautics and Space Administration) have been implemented in different applications for land use and land cover mapping in the agricultural context [15], especially in the development of crop management strategies that allow better resource management. The popularity behind the use of these images stems from their medium spatial resolution (30–100 m for Landsat images and 10–60 m for Sentinel-2 images) and freely available nature with a periodicity of less than or equal to 16 days. For theses reasons, VICAL calculates VIs using Landsat-4, 5, 7, 8 and 9 and Sentinel-2 images. The main characteristics of the Landsat and Sentinel-2 sensors are shown in

Table 1. Landsat and Sentinel-2 sensor specifications (adapted from [16,17]).

Characteristic		Landsat 4–5/TM	Landsat 7/ETM+	Landsat 8/OLI	Landsat 9/OLI-2	Sentinel-2A/MSI	Sentinel-2B/MSI
Launch date		16 July 1982 (Landsat-4)/1 March 1984 (Landsat-5)	15 April 1999	11 February 2013	27 September 2021	23 June 2015	7 March 2017
Repeat coverage		16 days	16 days	16 days	16 days	10 days
Spatial resolution		30 m/90 m (TIRS)	30 m/60 m (TIRS)	30 m (OLI)/100 m (TIRS)	30 m (OLI)/100 m (TIRS)	10 m/20 m/60 m
Swath/field of view			183 km/15°	180 km/15°	180 km/15°	290 km/20.6°
Spectral bands (central wavelength)	Ultra blue			443 nm	443 nm	443 nm (60 m)
	Blue (B)	485 nm	485 nm	482 nm	482 nm	490 nm (10 m)
	Green (G)	560 nm	560 nm	561 nm	561 nm	560 nm (10 m)
	Red (R)	660 nm	660 nm	655 nm	655 nm	665 nm (10 m)
	Red edge		-	-	-	705 nm (20 m), 740 nm (20 m), 783 nm (20 m), 865 nm (20 m)
	NIR	830 nm	835 nm	865 nm	865 nm	842 nm (10 m)
	SWIR1	1650 nm	1650 nm	1609 nm	1609 nm	1610 nm (20 m)
	SWIR2	2215 nm	2215 nm	2201 nm	2201 nm	2190 nm (20 m)
	Cirrus		-	1373 nm	1373 nm	1375 nm (60 m)
	Water vapor		-	-	-	945 nm (60 m)
	Thermal	11.45 μm	11.5 μm	10.9 μm, 12 μm	10.9 μm, 12 μm	–

NIR: Near infrared; SWIR₁: Shortwave infrared 1; SWIR₂: Shortwave infrared 2; ETM: Enhanced thematic mapper; OLI: Operational land imager; TIRS: Thermal infrared sensor; MSI: Multispectral instrument.

, whereas the comparison and location of the different spectral bands of these sensors are shown in Figure 1.

The free and open Landsat data distribution policy started in 2008 and it has completely revolutionized the way that Landsat data is utilized and has stimulated many agricultural applications based on Landsat time series [12]. On the other hand, the spatial resolution and number and positioning of spectral reflectance bands of Sentinel-2 excel at cropland and crop type classification, as well as in the monitoring of crops phenology, namely by enabling the measurement of growth (biomass) and health (stress symptoms) separately [18].

A single Landsat satellite overpasses the same location every 16 days, which means that it can potentially collect between 22 and 23 images per year for a given location (not considering overlapping areas). Two Landsat satellites (for example, missions 7 and 8) can provide a maximum of 45 to 46 images per year for the same location [12]. The number of images increases as the satellite datasets are combined. Indeed, Landsat-8 and either of the Sentinel-2 sensors together have global mean and median average revisit intervals of about 4.6 and 4.5 days, respectively; the two Sentinel-2 sensors together have global mean and median average revisit intervals of 3.8 and 3.7 days, respectively; and, for all three sensors, the global mean and global median average revisit interval is about 2.9 days [19]. Also, adding Landsat 9 OLI-2 to these sensors reduces the global mean revisit interval.

The bulk of the GEE catalog is made up of Earth-observing sensing imagery, including the entire Landsat archive as well as complete archives of data from Sentinel-2. This represents an advantage for the calculation of indices of vegetation of any agricultural surface in the world and for other applications.

2.2. Vegetation Indices (VIs)

The VIs calculated from satellite images allow the quantitative and functional relationship with different parameters or variables of the vegetation to be determined, where each pixel represents a unique soil-vegetation system. The most widely used VIs in agricultural applications in the literature is NDVI. However, in the last decades several spectral VIs have been developed that have been used to estimate the biophysical properties of vegetation. In this sense, for the VICAL design, more than 20 VIs used frequently in different agricultural applications were selected [1,9]. 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 mathematical expressions of the selected VIs are shown in

Table 2. Vegetation indices commonly used in agricultural applications and considered in the VICAL design.

#	Index	Abbreviation	Formula	Reference	Agricultural Application
1	Atmospherically resistant vegetation index	ARVI *	$\frac{\mathrm{NIR}-\mathrm{rb}}{\mathrm{NIR}+\mathrm{rb}}$ $\mathrm{rb}=\mathrm{R}-\mathsf{\gamma }\left(\mathrm{B}-\mathrm{R}\right)$ γ = 1.0	[21]	LAI, weed mapping [22,23]
2	Adjusted transformed soil-adjusted vegetation index	ATSAVI *	$\frac{\left[\mathrm{a}\left(\mathrm{NIR}-\mathrm{aR}-\mathrm{b}\right)\right]}{\left[\left(R+\mathrm{aNIR}-\mathrm{ab}+\mathrm{X}\left(1+{\mathrm{a}}^2\right)\right)\right]}$ a = 1; b = 0; X = 0.08	[6]	Biomass, canopy height, chlorophyll content, LAI [24,25,26]
3	Difference vegetation index	DVI	NIR-R	[27]	Forecasting (predicting) crop yield, vegetation coverage [28,29]
4	Enhanced vegetation index	EVI *	$2.5\left(\frac{\mathrm{NIR}-\mathrm{R}}{\mathrm{NIR}+{\mathrm{C}}_1\mathrm{R}-{\mathrm{C}}_2\mathrm{B}+\mathrm{L}}\right)$ C1 = 6.0, C2 = 7.5; L = 1.0	[30]	Water consumption, biomass, LAI, phenology monitoring [5,31,32]
5	Enhanced vegetation index	EVI2 *	$2.5 \left(\frac{\mathrm{NIR}-\mathrm{R}}{\mathrm{NIR}+{\mathrm{C}}_1\mathrm{R}+1}\right)$ C1 = 2.4	[33]	Crop coefficient, land surface phenology [34,35]
6	Green normalized difference vegetation index	GNDVI	$\frac{\mathrm{NIR}-\mathrm{G}}{\mathrm{NIR}+\mathrm{G}}$	[36]	Chlorophyll content, LAI, vegetation coverage, yield forecasting [37,38,39]
7	Modified soil adjusted vegetation index	MSAVI2	$\frac{\left(2\mathrm{NIR}+1\right)-\sqrt{{\left(\mathrm{2NIR}+1\right)}^2-8\left(\mathrm{NIR}-\mathrm{R}\right)}}{2}$	[40]	Biomass, nitrogen prediction, LAI [41,42]
8	Moisture stress index	MSI	$\frac{\mathrm{SWI}{\mathrm{R}}_1}{\mathrm{NIR}}$	[43]	Soil moisture, soil salinity [44,45]
9	Modified triangular vegetation index	MTVI	$1.2\left[1.2\left(\mathrm{NIR}-\mathrm{G}\right)-2.5\left(\mathrm{R}-\mathrm{G}\right)\right]$	[2]	Monitoring phenology, LAI, vegetation water content [46,47,48]
10	Modified triangular vegetation index-2	MTVI2	$\frac{1.5\left[1.2\left(\mathrm{NIR}-\mathrm{G}\right)-2.5\left(\mathrm{R}-\mathrm{G}\right)\right]}{\sqrt{{\left(2\mathrm{NIR}+1\right)}^2-\left(6\mathrm{NIR}-5\sqrt{\mathrm{R}}\right)-0.5}}$	[2]	Chlorophyll content, LAI [49,50,51]
11	Normalized difference tillage index (NDTI)	NDTI	$\frac{\mathrm{SWI}{\mathrm{R}}_1-\mathrm{SWI}{\mathrm{R}}_2}{\mathrm{SWI}{\mathrm{R}}_1+\mathrm{SWI}{\mathrm{R}}_2}$	[52]	Crop residue, soil tillage [53,54,55]
12	Normalized difference vegetation index	NDVI	$\frac{\mathrm{NIR}-R}{\mathrm{NIR}+\mathrm{R}}$	[56]	Crop coefficient, irrigation, monitoring phenology, vegetation coverage, vegetation water content, yield forecasting [5,35,37,38,57,58]
13	Normalized difference water index	NDWI	$\frac{\mathrm{NIR}-\mathrm{SWI}{\mathrm{R}}_1}{\mathrm{NIR}+\mathrm{SWI}{\mathrm{R}}_1}$	[59]	Biomass, vegetation water content [60,61]
14	Optimized soil adjusted vegetation index	OSAVI *	$1.16\left(\frac{\mathrm{NIR}-\mathrm{R}}{\mathrm{NIR}+\mathrm{R}+\mathrm{X}}\right)$ X = 0.16	[62]	LAI, water stress, [47,49,63]
15	Renormalized difference vegetation index	RDVI	$\frac{\mathrm{NIR}-\mathrm{R}}{\sqrt{\mathrm{NIR}+\mathrm{R}}}$	[64]	Biomass, canopy height, LAI, water stress [26,47,63]
16	Redness index	RI	$\frac{\mathrm{R}-\mathrm{G}}{\mathrm{R}+\mathrm{G}}$	[65]	Phenology monitoring, plant injury detection [66,67]
17	Ratio vegetation index	RVI	$\frac{\mathrm{R}}{\mathrm{NIR}}$	[68]	Biomass, LAI, vegetation coverage [29,32]
18	Soil adjusted vegetation index	SAVI *	$\frac{\mathrm{NIR}-\mathrm{R}}{\mathrm{NIR}+\mathrm{R}+\mathrm{L}}\left(1+\mathrm{L}\right)$ L = 0.5	[69]	crop coefficient, evapotranspiration, vegetation coverage [8,70]
19	Triangular vegetation index	TVI	$0.5\left[120\left(\mathrm{NIR}-\mathrm{G}\right)-200\left(\mathrm{R}-\mathrm{G}\right)\right]$	[71]	Chlorophyll content, LAI [46,51]
20	Transformed soil adjusted vegetation index	TSAVI *	$\frac{\left[\mathrm{a}\left(\mathrm{NIR}-\mathrm{aR}-\mathrm{b}\right)\right]}{\left[(\mathrm{R}+\mathrm{aNIR}-\mathrm{ab}\right]}$ a = 1; b = 0;	[72]	Soil moisture, chlorophyll content, LAI, yield forecasting [25,73,74]
21	Visible atmospherically resistant index	VARI	$\frac{\mathrm{G}-\mathrm{R}}{\mathrm{G}+\mathrm{R}-\mathrm{B}}$	[75]	Biomass, phenology monitoring, LAI, vegetation coverage [76,77,78]
22	Vegetation index number or simple ratio	VIN	$\frac{\mathrm{NIR}}{\mathrm{R}}$	[68]	Biomass, chlorophyll content, LAI [79,80]
23	Wide dynamic range vegetation index	WDRVI *	$\frac{\propto \mathrm{NIR}-\mathrm{R}}{\propto \mathrm{NIR}+\mathrm{R}}$ α = 0.2	[81]	Crop coefficient, phenology monitoring, yield forecasting [35,82,83]

* Some coefficients of the vegetation index can be configured by the user within VICAL.

.

2.3. Tool Development in the Google Earth Engine (GEE) Platform

The GEE platform provides access to: petabytes of publicly available remote sensing imagery and other ready-to-use products; high-speed parallel processing and machine learning algorithms using Google’s computational infrastructure; and a library of application programming interfaces (APIs) with development environments that support popular coding languages, such as JavaScript and Python [84].

The VICAL tool was developed on the GEE platform (https://earthengine.google.com/ (accessed on 16 June 2022)) and it was encoded in JavaScript from the Earth Engine Code Editor (https://code.earthengine.google.com/ (accessed on 16 June 2022)). The design principles for the “VICAL” were that it should provide, for any area (defined by the user) where there is a Landsat-4, 5, 7, 8 and 9 or Sentinel-2 image, an estimate of different VIs applied in agriculture, in addition, to plotting the VI time series for each polygon drawn. The general methodology of VICAL to calculate the VIs on the images as well as the time series is summarized in Figure 2. The VICAL tool does not require any additional software installation, however, some programming knowledge are required to modify or incorporate code into VICAL to carry out a more complex analysis or adapt it to a certain application.

Here, VICAL used the atmospherically corrected land surface reflectance images from Landsat (missions 4, 5, 7, 8 and 9, with images from 1982 to present) and Sentinel-2.

Table 3. Image collection of Landsat and Sentinel-2 within the Google Earth Engine (GEE).

Sensor	Dataset Availability	Collection ID
Landsat-4 TM	22 August 1982–24 June 1993	LANDSAT/LT04/C02/T1_L2
Landsat-5 TM	16 March 1993–05 May 2012	LANDSAT/LT05/C02/T1_L2
Landsat-7 ETM+	28 May 1999–present	LANDSAT/LE07/C02/T1_L2
Landsat-8 OLI	11 April 2013–present	LANDSAT/LC08/C02/T1_L2
Landsat-9 OLI-2	31 October 2021–present	LANDSAT/LC09/C02/T1_L2
Sentinel-2 (MSI)	28 March 2017–present	COPERNICUS/S2_SR_HARMONIZED

shows the properties of these image collections in the GEE. Thus, there are four calculation options in VICAL with these image collections: (i) Landsat (7, 8 and 9), (ii) Sentinel-2, (iii) Landsat (7, 8 and 9) and Sentinel-2 and (iv) Landsat (4 and 5). Options (i) and (iii) provide greater opportunities for cloudless surface observations since data from different sensors and/or satellites are combined.

For option (i), although the Landsat-7 ETM+ and Landsat-8 OLI images are from the same satellite set, they record information in bands with different wavelengths. Therefore, the procedure recommended by [85] was used to carry out the continuity (time series) of the VIs with these two sensors impartially. In this way, ETM+ data were spectrally adjusted to OLI (and OLI-2) spectral bands using the parameters of

Table 4. Surface reflectance sensor transformation functions (ETM+ to OLI) derived by ordinary least squares (OLS) regression [85].

Band Name	Slope	Intercept
Blue	0.8474	0.0003
Green	0.8483	0.0088
Red	0.9047	0.0061
NIR	0.8462	0.0412
SWIR1	0.8937	0.0254
SWIR2	0.9071	0.0172

, to generate a single harmonized dataset.

In the case of option (iii), the Harmonized Landsat Sentinel-2 (HLS) product from NASA was used [17], which provides a Level-2 Nadir BRDF (bidirectional reflectance distribution function)-adjusted surface reflectance at a 30-m spatial resolution. HLS combines observations of the land surface from the Landsat-8 OLI and Sentinel-2 MSI in a single data set. In this way, MSI data are spectrally adjusted to OLI and OLI-2 spectral bands using the parameters of

Table 5. Bandpass adjustment coefficients of linear regression for surface reflectance (OLI = slope × MSI + intercept) and the mean residual [17].

Band Name	Slope	Intercept	Residual
Ultra Blue	0.996	−0.00023	0.0004
Blue	0.977	−0.00411	0.0018
Green	1.005	−0.00093	0.0011
Red	0.982	0.00094	0.0015
NIR	1.001	−0.00029	0.0003
SWIR1	1.001	−0.00015	0.0001
SWIR2	0.996	−0.00097	0.0009

and ETM+ data were spectrally adjusted using parameter of Table 4, to generate a single harmonized dataset. The HLS dataset has the potential to support a wide variety of applications requiring high temporal and spatial resolution optical data, such as crop monitoring [17].

Before calculating the VIs, a filtering of the image collection performed out using three criteria: (i) a date range (start and end of the desired time frame) that was defined by the user; (ii) the location, through polygons (parcel) of any agricultural area that can be drawn on the map using GEE’s drawing tools; and (iii) a maximum threshold for clouds in the images by default established at 30%. The presence of clouds and their shadows in the images complicate the calculation of VIs, and therefore, cloud removal models were also implemented as indicated below.

The cloud cover filters from the CFMask algorithm [86] were used for Landsat images, which create a bitmask to determine cloud, cloud confidence, cloud shadow, snow/ice, and saturated pixels for each image. CFmask algorithm provides the best overall accuracy among many algorithms on Landsat scenes; it is also derived from a priori knowledge of physical phenomena and is operable without geographic restriction [87]. Since 2013, a dramatic increase in the use of CFMask has been seen in the detection of changes using Landsat time series [12] and has been used in GEE applications such as GEESEBAL [88]. For Sentinel-2 images, the cloud removal model s2cloudless (GEE library COPERNICUS/S2_CLOUD_PROBABILITY) was applied and additional scripts were used to mask shadows and snow/ice coverage. S2cloudless uses the machine learning approach to set the cloud occurrence probabilities in each pixel of Sentinel-2 scenes [89].

The previous steps resulted in a set of images in a range of dates defined within the drawn polygons and where the cloud pixels were removed. Therefore, the calculation of the VIs was carried out on these images using the formulas in Table 2. The values of the VIs can be presented as a map for a specific date or in a graph of a time series limited by the date interval (defined by the user). The average and the standard deviation of the VI values for the polygon (parcel) were calculated in the time series graph.

In addition to the VIs, a weighting factor (WF) of the index and regression models map (lineal, quadratic, potential and exponential function model) can be optionally calculated for a specific date (same date as the VI map). WF is the ratio between the value of the index in a pixel and the average of the index in the polygon (parcel). WF is calculated using Equation (1). The WF has been used in other agricultural studies [90] and, an agricultural parcel is a normalized indicator of the productive potential of each pixel in an image.

$$\mathrm{WF}=\left(\frac{\mathrm{V}{\mathrm{I}}_{\mathrm{pixel}}}{\mathrm{V}{\mathrm{I}}_{\mathrm{avg}}}\right)$$

(1)

where VI_pixel and VI_avg are the VI value of an individual pixel and the average value of the VI for the polygon (parcel), respectively.

While, regressions models allow to explain the behavior of a dependent variable according the fluctuation of the independent variable(s). In VICAL, to obtain the regression map, the user must provide the regression coefficients (a, b or c) as indicated in Equations (2)–(5) (

Table 6. Regression models maps considered in VICAL.

Function Type	Formula	Equation Number
lineal	$Y=a\ast \mathrm{VI}+b$	(2)
quadratic	$Y=a+b\ast \mathrm{VI}+c\ast \mathrm{V}{\mathrm{I}}^2$	(3)
potential	$Y=a\ast \mathrm{V}{\mathrm{I}}^b$	(4)
exponential	$Y=a\ast e^{b\ast \mathrm{VI}}$	(5)

).

Where, Y is the response variable; the values a, b and c are fitting coefficients, whose values are commonly determined by least squares regression; e is the Euler’s number; VI are the values of the vegetation indices obtained with remote sensing data.

Linear, quadratic, potential and exponential regression models have been used in different agricultural applications using remote sensing to explain the behavior of biophysical variables related to VIs. i.e., linear models to estimate crop coefficients [4,91,92], chlorophyll content in the leaf [39]; biomass [42] or exponential model to estimate LAI [93].

2.4. VICAL Performance Analyses

To evaluate the performance of the VICAL, individual images were downloaded for agricultural parcels from two irrigation districts: one for the irrigation district 075 located in the northern state of Sinaloa in north western Mexico and another for the irrigation district 017 located in the “Region Lagunera”, north central Mexico. Both irrigated areas are very important productive agricultural areas for the country (Figure 3). For the state of Sinaloa a total of two Landsat satellite images (7 and 8) were downloaded (https://glovis.usgs.gov/ (accessed on 22 November 2021)), which were corrected radiometrically and atmospherically to improve both position and radiometric quality, according to the methodology proposed by [94] for Landsat-7, and [95] for Landsat-8. For the “Region Lagunera”, one Sentinel-2 image Level-2A product was downloaded (

Table 7. Details of study areas and satellite images for the performance evaluation of VICAL.

Location	GEE ID	Image Collection	Number of Parcel (Polygons)	Image Acquisition Date
Northern Sinaloa, Mexico	projects/calcium-verbena-328905/assets/Bate	Landsat-7	1182	27 May 2018
		Landsat-8		19 May 2018
Region Lagunera, Mexico	projects/calcium-verbena-328905/assets/DR017Parce	Sentinel-2	1741	18 April 2019

). On these images, the 23 VIs shown in Table 2 were “manually” calculated using different types of software, but most of the tasks were implemented in the QGIS software [96]. Subsequently, the average values of each VI were obtained for each polygon (agricultural parcel or plot).

While, in VICAL, the GEE ID of the polygons (Table 7) of each irrigation district was written and the “Use vector file from GEE” option was activated. The 23 VIs (Table 2) for the selected dates and collection of images were calculated. The images of the VIs were exported to the QGIS software, obtaining the mean values of the VI for each polygon.

The average values of the VIs of each polygon obtained by the individual processing of the images were compared with those obtained with VICAL, and the VICAL performance was carried out with two statistical parameters: mean error (ME, Equation (6)) and coefficient of determination (R², Equation (7)).

$$\mathrm{ME}=\frac{{{\displaystyle \sum }}_i^n(\mathrm{V}{\mathrm{I}}_{\mathrm{o},i}-\mathrm{V}{\mathrm{I}}_{\mathrm{e},i})}{n}$$

(6)

$${\mathrm{R}}^2={\left[\frac{{{\displaystyle \sum }}_{i=1}^n\left(\mathrm{V}{\mathrm{I}}_{\mathrm{o},i}-\overline{\mathrm{V}}{\mathrm{I}}_{\mathrm{o}}\right)\left(\mathrm{V}{\mathrm{I}}_{\mathrm{e},i}-{\overline{\mathrm{VI}}}_{\mathrm{e}}\right)}{\sqrt{{{\displaystyle \sum }}_{i=1}^n{\left(\mathrm{V}{\mathrm{I}}_{\mathrm{o},i}-{\overline{\mathrm{VI}}}_{\mathrm{o}}\right)}^2}·\sqrt{{{\displaystyle \sum }}_{i=1}^n{\left(\mathrm{V}{\mathrm{I}}_{\mathrm{e},i}-{\overline{\mathrm{VI}}}_{\mathrm{e}}\right)}^2}}\right]}^2$$

(7)

where VI_o is the VI value obtained by individual image processing, VI_e is the VI value obtained with VICAL, i is the analyzed polygon, and n is the number of total analyzed polygons.

3. Results

3.1. Tool Development

Figure 4 shows the standard Windows interface, with a main menu, toolbar, and pop menus. As the application runs, the main window of “VICAL” displays a map where the user must draw the polygon that needs to be analyzed or use a vector file previously uploaded to GEE. In addition, it is necessary to indicate: (1) the date interval to obtain the VI time series, (2) the desired image collection, and (3) the VIs. The user can configure some coefficients of the VIs.

The GEE platform facilitated the computation of spectral VIs from multi-seasonal Landsat and Sentinel-2 data [97] and the computational time to obtain the VIs was reduced to a few minutes. However, some of the disadvantages of the GEE, and therefore VICAL, include the total number of simultaneous requests per user (40) [14].

3.2. Vegetation Index (VI) Map and Time Series

When VIs are calculated using VICAL, five layers are displayed on the map: (i) RGB combination, (ii) the selected VI, (iii) weighting factor (optional) computed by Equation (1), and (iv)regression map (optional), (v)user-drawn polygons. The image of the VI shown on the map can be downloaded alongside the values of the time series. Figure 5, shows these layers and the composition of different VIs calculated in VICAL for some agricultural parcel in northern Sinaloa, Mexico. Although VIs can easily be obtained in the GEE, VICAL includes a graphical user interface that offers the possibility of calculating 23 VIs without the user writing a single line of code.

In addition, VICAL can produce graphs of the VI time series for each polygon (parcel); these graphs can be generated using Landsat and Sentinel-2 data at the same time or separately. In particular, the dense time series (80% of the global surface will have a potential revisit period of cloud-free observations of eight days or fewer with the L7, L8, S-2A + S-2B) is adequate for detecting sharp surface changes, such as in vegetation or crop harvests [17]. Various softwares allow the generation of VI time series for certain applications. For example, TIMESAT (implemented in MATLAB software) processes satellite data and generates a time series to investigate problems related to global change and vegetation monitoring [98], QPhenoMetrics (implemented in QGIS software) produces a plot with the time series and corresponding phenology metrics based on NDVI and EVI values [99], or CropPhenology (R package) extracts crop phenology from VI time series (NDVI) [100]. Although these softwares are very useful, some are based on commercial softwares. In addition, the input data are the satellite images to be analyzed. With VICAL on the other hand, satellite images do not need to be downloaded to obtain the series of time of a polygon defined for a specific date range. Furthermore, the GEE environment allows users to easily incorporate other routines into VICAL to carry out more complex analyses or adapt it to a certain application.

The developed GEE calculator allows the easy calculation and visualization of VIs associated with spatial and temporal variations of several biophysical crop variables in any location in the world with minimal data processing or data management.

One of the problems that we have observed in VICAL is that the algorithms used to mask the clouds, especially in Sentinel-2 images, do not always work correctly and this may cause atypical points to appear in the graphs. An example of this is shown in Figure 6, where it can be seen that in the time series plot with Sentinel-2 images (Figure 6b) there are outliers produced by not completely removing all cloudy pixels.

This could be fixed by using a time series outlier filtering approach to remove outliers (mainly residual clouds) from time series, and while such filters are promising, one can notice that real surface changes can be mistaken for outliers [17]. Another option would be to use a more robust cloud detection method for Sentinel-2. For example, the MACCS-ATCOR Joint Algorithm (MAJA) [101] uses the time series of images for cloud detection and has been shown to provide a high level of precision for Sentinel cloud analysis although processing times could be longer.

3.3. Performance Analyses

According to the performance analysis, Figure 7, Figure 8 and Figure 9 show the R² and mean error (ME) values for the 23 VIs contemplated in VICAL using Landsat-8, Landsat-7, and Sentinel-2 images, respectively. These figures show that VICAL, supported by the GEE, calculates the VIs with precision, since in most cases, R² values were greater than 0.99. When the VIs values obtained from individual image processing (outside the GEE platform) are compared with those obtained with the VICAL calculator, R² values higher than 0.99 are obtained. In the case of the ME parameter, the highest values are found in the VIs calculated with the Landsat-7 ETM+ image; this is because the ETM + data were spectrally adjusted to the OLI spectral bands in VICAL, while the downloaded individual image was only radiometrically corrected and the ETM+ to OLI adjustment was not performed.

3.4. Future Perspectives

One of the future improvements to be implemented in VICAL is the reconstruction of satellite time series with a dynamic smoother method, including fitting asymmetric Gaussian or double logistic functions, or smoothing the data using a modified Savitzky-Golay filter or other methods such as [102] or [103]. This will help to reduce or eliminate outliers in the creation of time series of vegetation indices. Another improvement could be to allow the user to directly import vector GIS files so that the input parcels do not have to be digitized in the developed calculator. This is useful when the target agricultural area has a large number of plots (as shown for example in Figure 3). Up to this point, to use a vector file instead of digitizing the plots can only be achieved by modifying the VICAL code or uploading the file previously to GEE and then using its ID in VICAL.

4. Conclusions

The developed GEE calculator (VICAL) allows the easy calculation and visualization with accuracy of 23 VIs associated with spatial and temporal variations of several biophysical crop variables in any location in the world with minimal data processing or data management. VICAL does not require any additional software installation and allows users to modify or incorporate code into VICAL to carry out a more complex analysis or to adapt it to a certain application.

We believe that the VICAL tool saves time and avoids the repetitive and trivial procedures associated with “manual” VIs computations (downloading images, processing, etc.), which demand different types of softwares and that may lead to human errors. Besides, it is particularly beneficial for researchers with poor satellite data or in institutions with a lack of computational infrastructure to handle large volume of satellite data and high-performance data processing. We recommend that the user should define, prior to the use of the tool, the particularity of the crop they are looking at based on Table 2 to narrow down the suitable VIs for the aims of their work. VICAL is a useful application for researchers using VIs for the calibration of various biophysical parameters of vegetation, and for agricultural field managers worldwide.