Remote Sensor Images and Vegetation Indices to Optimize Rice Yield Analysis for Specific Growth Stages Within Extensive Data

Abstract

The crop yield in commercial fields is a very important parameter for farmers. The use of Precision Agriculture tools has been shown to improve rice crop yields. One of these tools is remote sensing on satellite platforms. Sentinel-2 provides free data on reflectance at different wavelengths. Focusing on commercial farms, correlations between the yield and satellite reflectance were studied over several years and locations for ‘JSendra’ rice crops. Four years of yield maps for 706 ha composed the database. Mid tillering-MT, panicle initiation-PI and grain filling-GF reflectance values and Vegetation Indices (VIs) were used. At MT, correlations with the yield were variable (0.23–0.70). At PI, correlations with the yield increased in NIR (0.39–0.85), but the other regions and VIs experienced a decrease. Visible bands and B05 Red Edge were significantly correlated with each other; similarly, B08 NIR was highly correlated with B06, B07, and B8A; SWIR bands were correlated with each other but not with the yield. At GF, the previous pattern was similar. Substantial limitations in estimating yield variability directly from reflectance or VIs were discussed. Two periods were established. The first is designing strategies to increase NIR and decrease red reflectance from MT to PI. The second is avoiding the relationship between crop greenness and NIR from PI to harvest. NIR was a better variable than VIs, but the single use of this band is challenging. Future recommendations focus on the visible–NIR collinearities to interpret differences between years or locations.

1. Introduction

The world’s cultivated area depends on crop yields, as increased yields would reduce the area of land used for agriculture. This leads to considerable efforts to produce according to efficiency criteria, more with less [1]. Rice is the staple food in several countries and is essential for food security [2].

Breeding programs are vital to increase yields, but their techniques are usually time-consuming [3]. In this sense, efficient crop management through Precision Agriculture (PA) tools can be an alternative to improve average yields [4]. Precision Agriculture is based on the recognition of spatial and temporal variability in crop production. It uses information technology (IT) in agricultural management with the aim of increasing productivity. Crop management is carried out considering a yield goal per cultivar; field decisions during the season when an adverse condition occurs, e.g., weather constraints, failures in management, or pest incidence, are based on a large amount of data from different sources. Therefore, several authors studied rice yield variability to build a pre-harvest forecast model, joining the different crop inputs [5,6,7,8,9]. The ORYZA2000 model developed by the International Rice Research Institute (IRRI) is a suitable example [10], but its applicability depends on the availability of an enormous database [11].

The use of PA requires different approaches to quickly evaluate field situations [12]. As a solution, in recent years, remote sensing (RS) in satellite platforms has emerged as a helpful technology in improving yield forecasts [13]. Images acquired by the Sentinel-2 satellite have introduced a new era in RS applications due to free data access, high temporal (5 days) and spatial resolution (10 m), and accuracy in measured reflectance [14]. Other existing technologies can be of higher spatial resolution, i.e., drone systems and equipped cameras on the farm machinery [15]; furthermore, private satellite platforms, such as the Planet Dove constellation, exhibit a better temporal resolution [16]. However, the open access to Sentinel-2 derived from the European Union (EU) public service demands novelty studies to deeply understand the data profitability for agronomic decisions at the farm scale [17]. Both industry and public institutions can benefit from analyzing the relations between crop productivity and data from public investments in new technologies, a key challenge in the EU’s future [18].

Currently, in the application of Sentinel-2 data, the analysis at the within-field level based on commercial fields across different years and areas to obtain an interpretable framework is a critical necessity [19,20]. The analytic methods to estimate yield variability are changeable. According to de la Torre et al. [21], empirical, process-based crop models, and semi-empirical models are the three main categories. On the one hand, empirical models are simple and site-specific; the equations are dependent on the database used in the study. On the other hand, process-based and semi-empirical models can be mechanistic and have high accuracy; however, several parameters about crop management and growing are required [22]. These mechanistic methods can lead to limitations similar to those of the classical models described above due to the needed complementary sensor systems and the problematic implementation in a changing agricultural system at the commercial level [23]. New efforts in the empirical approaches using Machine Learning (ML) techniques could obtain a transferable solution at the within-field level [24,25,26] and provide a fast yield forecast. However, interpretability is still challenging when the results are applied to a different database [27]. In addition, linear regression analysis can be performed to interpret ML outputs. The literature has widely studied linear regression, which is usually considered a pre-analysis for developing RS-based models [28]. Especially, the linear correlations between surface reflectance and important biophysical parameters in assessing crop status, such as the Leaf Area Index (LAI), Leaf Chlorophyll Content (LCC), or biomass, are used to explain the implementation of predictive models for such parameters [29].

Regarding this, leaf reflectance is directly correlated with the mentioned biophysical parameters [30], but regarding yield assessments, correlations can turn indirect, and the expected implications that reflectance and derived products show on yield can be highly variable [31,32]. Farmers aim to obtain fast control of all yield input parameters; for that reason, crop systems are often designed based on linear correlations to modify crop management rapidly [33,34]. The difficulty relies on identifying the limit of linear correlations; for instance, nitrogen rates are increased linearly up to a saturation point, and a weed incidence assessment is performed considering a partial linear correlation with yields in pest and disease management or weather effects [35,36,37,38].

Despite having the Sentinel-2 constellation fully completed at the operational level since 2017, few studies have simulated the real applicability of rice, comparing various years and regions at the within-field level [32]. The implementation of models to estimate yield variability in the rice industry when satellite imagery is used is commonly based on the spectral band’s combination in Vegetation Indices (VIs), aiming for a normalized value to interpret the measurement efficiently [39]. Several indices were designed based on linear correlations among bands, canopy properties, and the negative collinearity in comparing visible (blue, green, red) and near-infrared (NIR) [40]. In different satellite platforms of lower spatial (MODIS) and temporal resolution (Landsat missions), the use of VIs has been the solution to ensure easy data interpretability in cereal crops [41], but the results were highly variable to confirm the actual yield variability accurately [42]. The yield physiology may be uncorrelated with LAI, LCC, and biomass, owing to the carbohydrate partitioning in the grain-filling process [43]. Specifically, the correlation between reflectance and yield may vary with rice growth stages, summarized as intensive vegetative growth to produce fertile tillers, the process of panicle differentiation and flowering, and the accumulation of biomass in the grains, consuming the previous vegetative structures [44]. Therefore, the expected knowledge of RS can be altered to interpret each growth stage, modifying some usually assumed correlations; for example, an excessive crop greenness can result from low grain filling, resulting in higher NDVI but lower yields [45].

Recent studies have used the satellite bands from Sentinel-2, without combination in an index, to obtain linear regression models in wheat, corn, soybean, and rice [46,47,48]. The results were promising for better transferability because when only VIs are used, one spectral band can be overwhelmed by the other, losing information in the actual reflectance at each spectral region. Thenkabail et al. [49] reported that the red band reaches a saturation value level before the NIR band. The increasing resolution and accuracy for future spatial missions add special significance to analyzing individual reflectance values. The Sentinel-2 mission provides new bands at a 20 m resolution in the Red edge region (wavelengths between visible and NIR) and the Short Wave Infrared (SWIR) region. Spectral signatures of crop canopies can improve the applicability of the VIs, enhancing their interpretability. Similarly, ML algorithms require the analysis of basic correlations between each spectral band and crop yields at the within-field level. Thus, a fusion among spectral properties, VIs, and yield at commercial farms to study interpretable correlations between all variables lacks extensive database works in the rice industry.

The study of Franch et al. [48] in rice showed an interesting correlation between Sentinel-2 data and yields; such work was performed on a small dataset (<70 ha) and a single year and location. The results supported the industry’s utilization of RS commercial platforms (mainly Sentinel-2); however, more studies are needed to validate correlations in different years and locations. Skakun et al. [47] reported, in corn and soybean, a critical range of correlations, i.e., 0.67, between the yield and spectral bands in a two-year study in commercial farms. Similarly, Maestrini and Basso [50] found low correlations in corn, soybean, wheat, and cotton, showing an important threshold value of 0.50 in the Spearman correlation coefficient. Thus, as also reported by Kayad et al. [51], when several years are considered, stable correlations could be hard to find and interpret across the time-series.

It is supposed that surface reflectance and VI exhibit correlations with crop status and yield; thus, the research gap is placed in simulating operability for agronomic decisions. Are the correlations between Sentinel-2 data and yield significantly the same across years, locations, and growth stages? Do Sentinel-2 data always present the expected behavior for each spectral band and VI? Detailed analysis of the collinearities between spectral bands across growth stages, combined with the classical VI performance, may be crucial to provide a framework for data interpretability.

As a consequence, the central hypothesis of the present work is the existence of significant correlations between all Sentinel-2 spectral bands or VIs and yield variability for each growth stage within the field and for a broader data set representative of commercial fields spanning different years and locations. Four years of yield maps acquired by a combine harvester in 404 commercial fields (a total area of 706 ha) distributed in two Spanish locations (Valencia and Seville) were studied. We aim to study such correlations and the collinearity between bands and VIs, seeking the satellite data applicability to improve crop management. The results of the hypothesis would provide a source of information to ensure a more efficient implementation of Sentinel-2 in Spanish rice cultivation. Therefore, this work transfers the interpretability of the data rather than an empirical yield forecast.

2. Materials and Methods

2.1. Study Area

The study was conducted in two rice regions at sea level in Valencia and Seville (Spain). Rice is cultivated in the Albufera wetland in Valencia, a protected natural park near the city of Valencia, and in the Guadalquivir marshes, located south of Seville city, next to another critical wetland, the Doñana National Park. In both regions, the rivers and the lakes provide the necessary ecosystem for the crop (surface water via canals). Approximately 15,000 ha of rice are cultivated in Valencia, while the potential area without drought in Seville is 35,000 ha. Fields are generally small (less than 2 ha) in Valencia and more significant in Seville (5–10 ha on average). The selected fields were carefully managed by the growers, where weed management is a mixture of herbicide spraying and manual weed removal, avoiding large spots of extreme weed growth. The area of the fields in location 1 (Valencia) was considerably low, less than 1 ha in a high number of fields; in location 2 (Seville), the field area increased but was still significantly lower than the average values in other countries, like the U.S. Consequently, fields were leveled more frequently and soil properties in the field were usually the same. Papadakis’ agroclimatic classification system defines the climate in both areas as sub-tropical Mediterranean with hot and dry summers [52].

In both regions, the fields were sown under flooded conditions (broadcast sowing) in May, and the sowing date coincided with most farms. The water depth during sowing and the emergence stage is less than 5 cm. After emergence, the water depth is increased to a mean value of 8–10 cm. Fields are dried approximately two to three times during the vegetative stage for terrestrial treatments (herbicide spraying and top-dressing fertilization). For the rest of the season, the fields are flooded and only dry for the harvest in September and October. Common varieties, grower practices, and phenological stages are accurately described by Osca [53], Gómez de Barreda [54], and San Bautista et al. [55]. Rice varieties are short-, medium-, and long-grain; but the medium grain ‘JSendra’ variety (cross between Californian ‘M202’ and Spanish ‘Senia’ in 2005 by Instituto Valenciano de Investigaciones Agrarias, IVIA) represents approximately half of the Valencian rice area and an important percentage in Seville (between 10% and 20%). This cultivar exhibits a high average yield (≈8000 kg·ha⁻¹) and good culinary qualities, the season duration is ≈140 days. In Valencia, the other cultivars are less important (each cultivar represents an area less than 10%) because of their low yields (traditional varieties, e.g., ‘Bomba’ variety) or new cultivars from other Spanish regions or countries with problems in climatic, soil, and market adaptation. In Seville, the long-grain variety ‘Puntal’ is the most cultivated, but this cultivar is only grown in that region, being ‘JSendra’ the second variety in crop area. ‘JSendra’ is well adapted in both regions, and farmers are able to obtain its potential yield.

The study fields were selected, covering the entire wetland rice area in Valencia and the east part of the Seville region, where a representative number of ‘JSendra’ fields are grown, as shown in Figure 1. Thus, all the selected fields were commercial farms of the ‘JSendra’ variety to compare both regions, avoiding the variety influence. All fields followed the standard grower practices described by Osca [53]. The area, number of fields, and primary sowing date by year are shown in

Table 1. Area, number of fields, and main sowing date by location and year.

	Year	Area (ha)	Number of Fields	Main Sowing Date
Location 1	1 (Valencia)
	1 (2020)	139.97	89	25 May 2020
	2 (2021)	92.70	68	25 May 2021
	3 (2022)	160.27	131	9 June 2022 *
	4 (2023)	120.10	94	15 May 2023
Location 2	2 (Seville)
	1 (2019)	27.90	4	17 May 2019
	2 (2020)	60.52	8	10 June 2020 *
	3 (2021)	51.41	6	21 May 2021
	4 (2022)	53.52	4	26 May 2022
Total		706.39	404

* Sowing was delayed due to heavy rains in April and May.

. The number of fields throughout the years depended on the crop area, cultivar rotation, and the availability of combine harvesters with yield monitors.

2.2. Yield Data

Yield data were acquired by yield monitors equipped with commercial combine harvesters. Five combines were selected. The software used was provided by Topcon (Topcon, Tokyo, Japan) [56] and Trimble (Trimble Navigation Limited, Westminster, CO, USA) [57] companies. Each software estimates the volumetric grain flow with two optical sensors equipped on the combine, before the hopper. The result is a yield map in kg·ha⁻¹, using a spatial resolution of 7.6 m (cutting width). The possible variability due to the machine operator, software, and conditions of each field was corrected with the postprocessing protocol proposed by Fita et al. [58]. Thus, a uniform grid of 10 × 10 m polygons was obtained, wherein for each polygon, a yield value was recorded, considered as the reference yield value in kg·ha⁻¹. A negative buffer of 10 m was used to remove polygons near the edges of the fields (wrong satellite measurement, following the Fita et al. [58] protocol). Figure 2 shows an example of the original yield map (raw data) and the postprocessed map.

2.3. Satellite Data

Satellite images acquired by the Multi-Spectral Instrument (MSI) on board the Sentinel-2A/B constellation of tile 30SYJ for location 1 and 30STG for location 2 were used, following the Franch et al. [48] protocol. The product level was 2A, which provides surface reflectance. Images were downloaded using the Google Earth Engine (GEE) code editor. All the available spectral bands at a 10 m and 20 m spatial resolution were studied; the main characteristics of each band are shown in

Table 2. The study’s main characteristics are the Sentinel-2 spectral bands (name, wavelength, and spatial resolution).

Spectral Band Name	Wavelength (nm)	Spatial Resolution (m)
B02—Blue	458–523	10
B03—Green	543–578	10
B04—Red	650–680	10
B05—Vegetation Red Edge 1	698–713	20
B06—Vegetation Red Edge 2	733–748	20
B07—Vegetation Red Edge 3	773–793	20
B08—NIR	785–899	10
B8A—NIR narrow	855–875	20
B11—SWIR 1	1565–1655	20
B12—SWIR 2	2100–2280	20

.

Satellite data were merged with the postprocessed yield maps using the spatial resolution of 10 m. Thus, a 10 m reference pixel was composed of a single yield value and the reflectance of each spectral band, being the reflectance of the spectral bands at 20 m repeated every four pixels. The negative buffer at each field boundary was increased to 20 m to avoid the edge effect. Only cloud-free images from sowing to harvest were considered, with visual verification of each image. All selected images were free of clouds. The availability of cloud-free images based on Days After Sowing (DAS) for each year is indicated in

Table 3. Number of cloud-free images based on Days After Sowing (DAS) and the growth stage for each location and year, where the green color indicates a cloud-free date.

DAS	0	5	10	15	20	25	30	35	40	45	50	55	60	65	70	75	80	85	90	95	100	105	110	115	120	125	130	All
Stage	Vegetative											Reproductive							Ripening
Location 1
Year 1																												8
Year 2																												9
Year 3																												13
Year 4																												11
Location 2
Year 1																												16
Year 2																												20
Year 3																												15
Year 4																												13

.

In addition to the surface reflectance in the spectral bands, these were combined into the Vegetation Indices (VIs) normalized and most commonly used in the literature. VIs were selected based on the normalization function; thus, distinguishing from the reflectance values, a normalized VI is interpreted with relative values between −1 and 1. Non-normalized functions can hamper interpretability, and in previous studies [48,55], we examined other VIs and discussed their interpretability. In

Table 4. Vegetation Indices used in the study; each parameter in the equation (Eq.) represents the surface reflectance for each spectral band in Sentinel-2 nomenclature.

Vegetation Index	Equation	Equation Number	Reference
Normalized Difference Vegetation Index (NDVI)	${\displaystyle \frac{\mathrm{B}08-\mathrm{B}04}{\mathrm{B}08+\mathrm{B}04}}$	(1)	[59]
Land Surface Water Index (LSWI)	${\displaystyle \frac{\mathrm{B}08-\mathrm{B}11}{\mathrm{B}08+\mathrm{B}11}}$	(2)	[60]
Green NDVI (GNDVI)	${\displaystyle \frac{\mathrm{B}08-\mathrm{B}03}{\mathrm{B}08+\mathrm{B}03}}$	(3)	[61]
Normalized Difference Red Edge 1 (NDRE1)	${\displaystyle \frac{\mathrm{B}06-\mathrm{B}05}{\mathrm{B}06+\mathrm{B}05}}$	(4)	[62]
Normalized Difference Red Edge 2 (NDRE2)	${\displaystyle \frac{\mathrm{B}07-\mathrm{B}05}{\mathrm{B}07+\mathrm{B}05}}$	(5)	[62]
Normalized Crop Management Index (NCMI)	${\displaystyle \frac{\mathrm{B}08-(\mathrm{B}03+\mathrm{B}04)}{\mathrm{B}08+\mathrm{B}03+\mathrm{B}04}}$	(6)	[55]

, the name and equations of each VI are shown.

2.4. Methods

The data were analyzed using different approaches, organized into three sections.

Section 1: Study of the within-field variability of yield and area comparison. In the first section, the within-field yield variability provided by the combine was analyzed using the pixel yield anomaly by field and field area. The pixel yield anomaly by field represents the yield losses or increases inside each field in kg·ha⁻¹. Thus, the difference between each 10 m pixel yield of the postprocessed yield map and the mean yield at each field was calculated. The mathematical function is described in Equation (7). To assess the variability importance at each field, the yield field anomaly was compared with each area by location and year. This section aims to characterize the within-field variability. The mean yield for each field is the parameter farmers use to evaluate the campaign results; the deviation values from the field mean are a suitable reference to identify the fields that require more PA practices.

$${\mathrm{P}\mathrm{i}\mathrm{x}\mathrm{e}\mathrm{l} \mathrm{y}\mathrm{i}\mathrm{e}\mathrm{l}\mathrm{d} \mathrm{a}\mathrm{n}\mathrm{o}\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{y}}_{\mathrm{i},\mathrm{j}}={\mathrm{P}\mathrm{i}\mathrm{x}\mathrm{e}\mathrm{l} \mathrm{y}\mathrm{i}\mathrm{e}\mathrm{l}\mathrm{d}}_{\mathrm{i},\mathrm{j}}-{\mathrm{M}\mathrm{e}\mathrm{a}\mathrm{n} \mathrm{y}\mathrm{i}\mathrm{e}\mathrm{l}\mathrm{d}}_{\mathrm{j}}$$

(7)

where ${\mathrm{P}\mathrm{i}\mathrm{x}\mathrm{e}\mathrm{l} \mathrm{y}\mathrm{i}\mathrm{e}\mathrm{l}\mathrm{d} \mathrm{a}\mathrm{n}\mathrm{o}\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{y}}_{\mathrm{i},\mathrm{j}}$ is the yield anomaly for each pixel i at each field j; ${\mathrm{P}\mathrm{i}\mathrm{x}\mathrm{e}\mathrm{l} \mathrm{y}\mathrm{i}\mathrm{e}\mathrm{l}\mathrm{d}}_{\mathrm{i},\mathrm{j}}$ is the yield acquired by the combine for each pixel i at each field j; and ${\mathrm{M}\mathrm{e}\mathrm{a}\mathrm{n} \mathrm{y}\mathrm{i}\mathrm{e}\mathrm{l}\mathrm{d}}_{\mathrm{j}}$ is the mean yield acquired by the combine at each field j.

Section 2: Study of linear correlations among the yield, all bands, and VIs in the three main growth stages. At each main growth stage (Vegetative, Reproductive, and Ripening), a critical moment was defined as a rice growth substage inside each main stage when crop management can improve yields. Yield components were used as a reference to select the three moments [63]:

• 1st yield component, vegetative stage: number of tillers, one date per location and year corresponding to Mid Tillering (MT).
• 2nd yield component, reproductive stage: grain number per panicle, one date per location and year corresponding to Panicle Initiation (PI).
• 3rd yield component, ripening stage: grain weight, one date per location and year corresponding to half of Grain Filling (GF).

The scheme in Figure 3 summarizes the conceptualization.

Rice farms were monitored year by year at each location, and following our previous research [45,48,55,58], a DAS reference was used to determine the growth stages and the related yield components. Twenty-four dates were studied (three per year and location). Selected dates for MT were 35 DAS in all locations and years except location 1 in year 4 when the date was 40 DAS (no available image at 35 DAS). For PI, the images at 55 DAS were available in all locations and years. In GF, 110 DAS was considered in location 1 in years 1, 2, and 3 and location 2 in year 2, while the dates at 105 DAS were used in year 4 in location 1 and years 1, 3, and 4 in location 2 (no available images at 110 DAS).

The Pearson correlation coefficient (R), the ratio between the covariance of two variables and the product of their standard deviations, was used to determine linear correlations among yield, all Sentinel-2 bands, and VIs at each year and location (years and locations were not mixed in a single matrix). The analysis included two layers; on the first layer (first row in the correlation matrix), the yield was correlated with each spectral band or VIs as described in Equation (8). On a second layer (subsequent rows), a collinearity study between spectral bands, between spectral bands and VIs, and between VIs was performed, following the structure of Equation (9).

$${\mathrm{y}}_{\mathrm{y}\mathrm{i}\mathrm{e}\mathrm{l}\mathrm{d}}={{\mathrm{a}}_0+\mathrm{a}}_1·{\mathrm{x}}_{\mathrm{S}\mathrm{R} \mathrm{o}\mathrm{r} \mathrm{V}\mathrm{I},\mathrm{i},\mathrm{j}}$$

(8)

where ${\mathrm{y}}_{\mathrm{y}\mathrm{i}\mathrm{e}\mathrm{l}\mathrm{d}}$ is the yield acquired by the combine; ${\mathrm{a}}_0$, ${\mathrm{a}}_1$ are the regression coefficients; and ${\mathrm{x}}_{\mathrm{S}\mathrm{R} \mathrm{o}\mathrm{r} \mathrm{V}\mathrm{I},\mathrm{i},\mathrm{j}}$ is the surface reflectance (SR) or Vegetation Index (VI) value for a given image i at each spectral band or VI j.

$${\mathrm{y}}_{\mathrm{S}\mathrm{R} \mathrm{o}\mathrm{r} \mathrm{V}\mathrm{I},\mathrm{i},\mathrm{j}}={{\mathrm{a}}_0+\mathrm{a}}_1·{\mathrm{x}}_{\mathrm{S}\mathrm{R} \mathrm{o}\mathrm{r} \mathrm{V}\mathrm{I},\mathrm{i},\mathrm{j}}$$

(9)

where ${\mathrm{y}}_{\mathrm{S}\mathrm{R} \mathrm{o}\mathrm{r} \mathrm{V}\mathrm{I},\mathrm{i},\mathrm{j}}$ is the surface reflectance (SR) or Vegetation Index (VI) value for a given image i at each spectral band or VI j; ${\mathrm{a}}_0$, ${\mathrm{a}}_1$ are the regression coefficients; and ${\mathrm{x}}_{\mathrm{S}\mathrm{R} \mathrm{o}\mathrm{r} \mathrm{V}\mathrm{I},\mathrm{i},\mathrm{j}}$ is also the surface reflectance (SR) or Vegetation Index (VI) value for a given image i at each spectral band or VI j.

Section 3: Study of alternatives to linear correlations between yield and bands or VIs in the three main phenological stages. The Spearman rank correlation coefficient was determined as an alternative to linear correlations [64]. In addition to linear correlations, this coefficient allows us to find monotonic nonlinear correlations. Thus, the third section aimed to test the existence of correlations other than or better than the linear correlations obtained for the Pearson R. The analysis was carried out in bands and VIs with no strong collinear correlations after the results of Section 2.

In Figure 4, a workflow emphasizes the inputs and outputs for each section.

2.5. Software

Yield maps and satellite images were processed using QGIS 3.10.14 software [65]. The statistical analysis was carried out in Statgraphics Centurion 19 software [66].

3. Results

3.1. Within-Field Variability of Yields and Area Comparison

The pixel yield anomaly by field, location, and year is shown in Figure 5 (more detailed graphs by individual years are shown in Supplementary Materials Figure S1). Across all years and locations, regardless of the area and number of fields, the within-field yield variability was similar (no correlation was found). The mean positive value of the pixel yield anomaly at location 1 was 136 kg·ha⁻¹, while at location 2, it was 168 kg·ha⁻¹. Regarding the negative pixel yield anomaly, in location 1, the mean value was 143 kg·ha⁻¹ and 175 kg·ha⁻¹ in location 2. The ranges of variation between locations 1 and 2 were wide enough to generate sufficient variability to study linear and nonlinear correlations. The location effect did not show significant differences in the yield anomalies, so the larger mean field area and lower number of fields in location 2 did not influence the yield lower variability. In location 1, the number of fields with anomalies higher than +500 kg·ha⁻¹ was 23, representing 8% of the fields; for anomalies higher than +250 kg·ha⁻¹, it was 116 (38% of fields); for negative anomalies, fields with anomalies exceeding −500 kg·ha⁻¹ were 12% and 49% for −250 kg·ha⁻¹. In location 2, the low number of fields was not enough to compare anomalies at the field scale; nevertheless, accounting for several pixels, 76% of pixels were inside the interval (+250, −250 kg·ha⁻¹); in location 1, the percentage was 84%.

3.2. Linear Correlations Among the Yield, All Bands, and VIs in the Three Main Growth Stages

3.2.1. Linear Correlations Between Yield and All Bands

The results of linear correlations at MT are shown in

Table 5. Mean values correlation coefficients between yield and spectral band (B02, B03, B04, and B08 at 10 m; and B05, B06, B07, B8A, B11, and B12 at 20 m) reflectance for years and locations at MT. Individual results per location and year are shown in Supplementary Materials Table S1.

	B02		B03		B04		B08		B05		B06		B07		B8A	B11	B12
Yield	−0.33		−0.34		−0.36		0.43		−0.31		0.37		0.44		0.43	0.35	0.26
B02			0.94		0.92		−0.35		0.86		−0.24		−0.37		−0.32	−0.34	−0.24
B03					0.93		−0.30		0.94		−0.17		−0.32		−0.27	−0.29	−0.20
B04							−0.48		0.88		−0.38		−0.50		−0.45	−0.48	−0.39
B08									−0.23		0.97		0.99		0.99	0.92	0.82
B05											−0.09		−0.26		−0.21	−0.23	−0.14
B06													0.98		0.98	0.93	0.85
B07															0.99	0.93	0.83
B8A																0.93	0.83
B11																	0.95

, with the mean R. Regarding the yield correlation, mean values of R varied between 0.26 and 0.44 in B06, B07, B08, B08A, B11, and B12 and for B02, B03, B04, and B05, between −0.36 and −0.31. When locations and years were compared, the coefficients of correlation were variable, ranging from 0.25 to −0.62 in B04 and from 0.23 to 0.70 in B08, and this variability was similar in the other spectral bands (Table S1). Correlations with the yield were mainly negative in B02, B03, B04, and B05 across locations and years, while correlations were mostly positive in B06, B07, B08, B8A, B11, and B12. There were notable exceptions in some locations and years; the most remarkable was location 2 in year 3, when the correlations in the visible bands were not negative. However, this inconsistency between years was observed in both locations, i.e., year 2 in location 1 showed very low correlations, similar to those of years 3 and 4 in location 2. The collinearity study was useful to determine high correlations between some spectral bands. These results were, in this case, consistent for the mean values and each individual location and year, showing a clear pattern. The bands with a negative yield correlation (B02, B03, B04, and B05) were closely correlated with each other, reaching R-values of 0.91 on average (Table 5) and 0.74 when all locations and years were considered (Table S1). Spectral bands positively correlated with the yield (B08, B06, B07, B8A, B11, and B12) were closely correlated with each other with values close to 1 in the Red edge and NIR spectral bands (B08, B06, B07, and B8A) and values around 0.80 and 0.90 in the SWIR spectral bands (B11 and B12). Finally, weak correlations were found between the group of negative correlations with yield and the group of positive correlations with yield.

The results of linear correlations at PI are shown in

Table 6. Mean values of correlation coefficients between the yield and spectral band (B02, B03, B04, and B08 at 10 m; and B05, B06, B07, B8A, B11 and B12 at 20 m) reflectance for years and locations at PI. Individual results per location and year are shown in Supplementary Materials Table S2.

	B02		B03		B04		B08		B05		B06		B07		B8A		B11		B12
Yield	−0.12		−0.08		−0.16		0.58		−0.07		0.45		0.58		0.58		0.41		0.28
B02			0.75		0.76		−0.17		0.64		0.06		−0.15		−0.15		0.21		0.36
B03					0.77		−0.11		0.81		0.24		−0.08		−0.09		0.37		0.52
B04							−0.30		0.70		−0.06		−0.28		−0.27		0.16		0.37
B08									−0.08		0.85		0.98		0.98		0.70		0.49
B05											0.28		−0.07		−0.08		0.41		0.57
B06													0.87		0.86		0.85		0.67
B07															0.99		0.71		0.49
B8A																	0.72		0.50
B11																			0.91

with the mean R for all locations and years. The correlations between yield and spectral bands were lower (−0.16 to −0.07) in the group of negative correlations (B02, B03, B04, and B05) but higher (0.28 to 0.58) in the other bands. Differences were observed between the SWIR bands (B11 and B12) and the rest of the spectral bands, with the lowest R values (0.28 and 0.41). Conversely, with B07, B08, and B8A, R = 0.58 values were obtained in three spectral bands. Differences in R values between years were found in both locations similarly, being remarkable location 2 in year 3, when the correlations were positive and significant in all bands (Table S2), following a different pattern to the other years and to the previous growth stage. The results in the collinearity study were similar to MT, but the new correlation performance between the yield and bands was also found in the band-to-band collinearity. Thus, the coefficients of correlation among the B02, B03, B04, and B05 group were significant but lower than at MT; the correlations among B08, B07, and B8A approached 1, while with B06, they were lower but still of high value; and, finally, the collinearity between the SWIR bands and the other spectral regions started to decrease.

The results of linear correlations at GF are shown in

Table 7. Mean values of correlation coefficients between the yield and spectral band (B02, B03, B04, and B08 at 10 m; and B05, B06, B07, B8A, B11, and B12 at 20 m) reflectance for years and locations at GF. Individual results per location and year are shown in Supplementary Materials Table S3.

	B02		B03		B04		B08		B05		B06		B07		B8A		B11		B12
Yield	0.01		0.09		0.01		0.39		0.10		0.37		0.41		0.39		0.13		0.06
B02			0.71		0.75		−0.19		0.67		0.15		−0.19		−0.18		0.37		0.44
B03					0.80		−0.03		0.89		0.46		−0.03		−0.03		0.49		0.51
B04							−0.27		0.81		0.12		−0.29		−0.25		0.46		0.57
B08									−0.03		0.66		0.92		0.92		0.26		0.06
B05											0.47		−0.04		−0.02		0.53		0.55
B06													0.72		0.68		0.41		0.24
B07															0.94		0.20		0.00
B8A																	0.29		0.07
B11																			0.86

with the mean R for all locations and years. The correlations between the yield and B02, B03, B04, and B05 were again very low, closer to zero on average. Some years in both locations registered positive correlations of similar values to the negative correlations. Similarly, an identical result was found in B11 and B12. The correlations in B08, B06, B07, and B8A continued to be positive but with a lower value than at PI, a maximum mean of 0.41, with significant differences between years (ranging from 0.08 to 0.74). As in previous stages, differences in R values were found between years but not between locations, with both locations showing similar variability in the correlation between the yield and reflectance (Table S3). The collinearity study remarked on the pattern initiated at PI, with a weak correlation between SWIR and the rest of the bands. The results of the remaining collinear correlations were similar to the previous stage, consistent between locations and years.

3.2.2. Linear Correlations Between Yield and VIs

The study of linear correlation at MT between the yield and VIs is shown in

Table 8. Mean values of correlation coefficients between the yield and VIs for years and locations at MT. Individual results per location and year are shown in Supplementary Materials Table S4.

	NDVI		LSWI		GNDVI		NDRE1		NDRE2		NCMI
Yield	0.42		0.19		0.47		0.47		0.48		0.46
NDVI			0.11		0.98		0.97		0.96		0.99
LSWI					0.19		0.12		0.14		0.17
GNDVI							0.97		0.97		1.00
NDRE1									1.00		0.98
NDRE2											0.98

with the mean R for all locations and years. The correlation coefficients in the yield were similar to the maximum values obtained with the spectral bands (0.48), except for LSWI, which was lower. Most indices showed a high R in their correlations, except for the LSWI. The differences between years and locations were identical to the results of the spectral bands, in the analysis of yield variability and collinearity (Table S4).

At PI, the results are shown in

Table 9. Mean values of correlation coefficients between the yield and VIs for years and locations at PI. Individual results per location and year are shown in Supplementary Materials Table S5.

	NDVI		LSWI		GNDVI		NDRE1		NDRE2		NCMI
Yield	0.33		0.35		0.34		0.35		0.37		0.35
NDVI			0.77		0.91		0.86		0.85		0.97
LSWI					0.81		0.75		0.80		0.82
GNDVI							0.86		0.89		0.98
NDRE1									0.98		0.88
NDRE2											0.90

. In this case, correlations with the yield were lower and very similar in all indices (0.33–0.37). Compared with previous results in the spectral bands, R values were lower than B07, B08, and B8A but higher than B02, B03, B04, and B05. Thus, the VI performance for the yield estimation differed from the surface reflectance, mainly for visible bands. Furthermore, the decrease in the correlation experimented in the VIs at PI was inconsistent with the increase in B07, B08, and B8A. Regarding temporal variability, there were differences between years with a similar pattern to the spectral bands results. Considering collinearity, all VIs were correlated with each other, and this result was consistent between locations and years.

Finally,

Table 10. Mean values of correlation coefficients between the yield and VIs for years and locations at GF. Individual results per location and year are shown in Supplementary Materials Table S6.

	NDVI		LSWI		GNDVI		NDRE1		NDRE2		NCMI
Yield	0.13		0.27		0.12		0.10		0.12		0.13
NDVI			0.75		0.87		0.88		0.88		0.96
LSWI					0.68		0.70		0.71		0.75
GNDVI							0.86		0.89		0.97
NDRE1									0.98		0.90
NDRE2											0.92

shows the results at GF. The correlations with yield followed a similar pattern to the previous stage, with correlations decreasing to a maximum value of 0.27 in LSWI. VIs did not improve spectral band results; the correlations were lower than those of NIR region bands, showing more similarities to those of the visible region bands. Again, differences between years were notable and similar to spectral bands in the correlation with yields, showing non-uniform behavior with a similar pattern in both locations. Collinearity between indices was high (0.86–0.97) and significant in NDVI, GNDVI, NDRE1, and NDRE2, but between LSWI and the rest, it was lower (0.68–0.75).

3.3. Alternatives to Linear Correlations Between Yield and Bands and VIs: Spearman Rank Analysis

The results of Spearman’s rank analysis are shown in

Table 11. Results of the Spearman rank analysis between the yield and the bands B04, B08, and B11, and the index NDVI in the three main stages. Each value is the mean for all locations and years.

	B04	B08	B11	NDVI
MT	−0.38	0.40	0.35	0.43
PI	−0.16	0.54	0.41	0.33
GF	0.02	0.36	0.13	0.11

. The collinearities from the previous section were considered to show only a representative band of each spectral region and VI. The remaining bands and VIs yielded similar correlation values. Thus, the three main stages are merged in the table, focusing on the yield correlation. These correlations were similar to Pearson’s coefficients, with no improvement. The collinearities also showed the same pattern. The highest correlation was obtained at PI, with a value of 0.54 on the B08 spectral band; this band exhibited the best range of correlations (from 0.36 to 0.54). The other spectral bands showed fewer correlation values, ranging from 0.02 to −0.38 in B04 and 0.13 to 0.35 in B11. The NDVI performed better than B04 and B11, with values ranging from 0.11 to 0.43.

4. Discussion

In Section 1, the actual within-field yield anomaly provided the potential yield lost or gained compared to the average field. Few studies on rice cultivation analyze the actual within-field variability. Sarasso et al. [67] reported a maximum standard deviation of 1013 kg·ha⁻¹ in Italy. Also, Bellis et al. [68] found a similar deviation in Arkansas (U.S.). Despite the different metrics, this value would have a higher absolute variability than our study. The differences could be explained in terms of the experimental design; the first-mentioned study carried out different PA experimental practices, whereas, in our study, all fields followed the standard grower practices with no PA practices. Older studies, such as the one by Roel and Plant [69], showed differences between the maximum and minimum pixel of around 5000 kg·ha⁻¹ in California (U.S.); in that case, fields of larger areas (38 and 52 ha) were studied. In Russia, in a 3.60 ha field, Dobermann [70] measured differences of about 8000 kg·ha⁻¹ between the maximum and minimum yield, attributed to extreme weed growth. The variability found in our work was low.

The yield variability when the data were considered as a single matrix (mixing the 10 m pixels of all fields by location and year) made studying the correlation with Sentinel-2 reflectance and VIs possible. For instance, mean-field yields at location 1 differed by an average of 4609 kg·ha⁻¹, comparing the best with the worst field for each year; at location 2, the difference was 1940 kg·ha⁻¹. These differences between fields would be notable since the cultivar was the same, and there were no water supply restrictions. Regarding the productivity increase, the differences would show an interesting yield gap in both locations, indicating the existence of crop management with excellent yields in some fields. The applicability of Sentinel-2 data should aim to find this variability during the growing season.

Locations and years were analyzed as separate matrices, with a similar study conducted by Maestrini and Basso [50] on corn, wheat, soybean, and cotton, who reported a significant influence of weather variables when years and locations are mixed. Several studies focused on modeling weather effects on rice yield, finding complex interactions between them and crop yields [71,72,73]; in our research, we considered year-by-year and location-by-location to avoid these interactions. As a result, we can believe that the variability would be due to other yield input parameters. Therefore, the fields in each location were nearby, featuring highly similar annual weather trends. Thus, the main differences appeared between years and locations. Future work should be addressed to examine the inconsistencies in the R values. We could not find a clear pattern for integrating weather variables into our analysis. This assumption was derived from the database structure, i.e., crop management differed in each field, resulting in multiple strategies to avoid weather constraints. For example, the delayed sowing in 2022 at location 1 provoked essential changes in the timing of drying downs for herbicide spraying and top-dressing fertilization; some farmers carried out shorter drying downs to mitigate the detrimental effect of high temperatures. Consequently, the high temperatures may have impacted the fields differently. The correlation value in a year and location comparison could be due to weather adversities, as different authors have recently developed models integrating satellite data with meteorology [74,75]. Models incorporating weather variables are designed to provide the potential yield loss, but crop management can be crucial to modify the expected behavior [76,77]. Few studies have analyzed the physiological response to different crop-management strategies in extensive data at the within-field level [78,79]; regarding this, we found difficulties in explaining the differences between locations and years.

The correlations between Sentinel-2 and yields were also variable depending on the spectral region and growth stage. Firstly, the R values were similar to those obtained by the literature in similar studies with drone imagery and ML techniques; in this regard, Bellis et al. [68] also reported low yield correlations. Correlations were of high values when an external source of variability was studied, e.g., different nitrogen rates [80,81]. Secondly, in Sentinel-2 studies, high correlations can also be found when external variability is included in the experimental design [82]. From this consideration, few studies on rice at the within-field level examine the general estimation of yield variability with Sentinel-2 in a large dataset. Consequently, a comparison with similar studies in the experimental design is addressed to field-level studies; de la Torre et al. [21] reviewed the state-of-the-art reporting with satellite imagery, low coefficients of determination, and considerable errors. In addition, nonlinear and ML approaches showed similar final transferability to the linear analysis.

In other cereal and soybean crops, we can find studies at a within-field level in commercial fields with a similar experimental design. Maestrini and Basso [50] compared airborne and satellite imagery using yield maps from previous years; the correlations with yields using the images were weak and similar to those reported in our study. The historical yield map was a better source of information for anticipating variability when repeated over the years. However, they found a representative number of fields with errors in the estimation when such variability was not repeated, making the images a suitable alternative. The results of those authors could be related to the present work. Thus, the weak correlation in a large dataset of commercial fields should be an expected result. As noted in the study, the correlation between yield and the red reflectance was weak but consistently negative over locations and years. Similarly, Skakun et al. [47] reported higher importance of NIR reflectance in estimating the yield in various studies [46,83]. However, the correlation values were also insufficient; other authors have shown the year dependence [51] and random patterns as significant limitations in providing an applicable framework [84]. Consequently, the industry’s applicability is focused on identifying similar management zones based on VIs rather than absolute yield values [85]. We can find recent studies in the EU with the use of Sentinel-2 [86]. Thus, despite the difficulties in finding high-accuracy models, PA practices consider such limitations and base its applicability on the positive or negative sense of correlations with yields, as well as the theoretical basis that reflectance shows with some biophysical parameters (LAI, LCC, or biomass) [87,88,89]. Visible bands strongly correlate with the chlorophyll content, decreasing its reflectance values when the pigment content is increased [39]. The correlation between a high chlorophyll content and a high yield can be found in several studies about rice genetics [90,91,92], showing an indirect correlation between the reflectance and yield. Knowing this interaction, we can discuss the different results across the growth stages.

According to the literature, rice plants experiment with a high vegetative growth rate at MT, and a low visible reflectance would indicate a high rate (i.e., chlorophyll content is increasing) [93], but the correlations with yield were weak. Interestingly, we could assume that since tillering to harvest, more variables were affecting the yield besides the chlorophyll content. The importance of visible bands in the other growth stages was less noticeable, suggesting that the crop greenness had a low implication on the yield at PI and GF. The different senses of correlations for the spectral bands B06, B07, B08, and B8A can also be discussed based on the leaf optical properties. The NIR reflectance has no direct correlation with the pigment content; all the radiation is reflected or transmitted by the cell structures of the leaves, increasing with the amount of canopy [94]. The highest amount of canopy indicates high values of vegetative biomass, and this biomass can quickly provide more fertile tillers, the number of grains, and weight if the carbohydrate partitioning is correctly maintained [95].

The relation between NIR reflectance and the canopy amount reported by the literature would explain a positive correlation with the yield variability [45]. The highest correlation was obtained at PI when the vegetative growth ended, and the amount of canopy reached saturation. This correlation was lower at GF; this inconsistency could be associated with higher variability in the sub-growth stage sub-growth panicle presence. That means, at PI, the plants are very uniform in the vegetative canopy; however, at GF, the panicles are visible, and the canopy loses its uniformity, coexisting vegetative with reproductive structures. Moreover, from flowering to harvest, the subgrowth stages within the field can be more variable than in the vegetative period. At this point, the NIR radiation reflected by a canopy with panicles would be different from that without panicles, with differences in the panicle ripening. The panicles cover the leaves, and there is no clear evidence in the literature of how this can modify the reflectance.

The last significant region in the results was the SWIR; those spectral bands are correlated with the water content, decreasing the reflectance with a water content increase [96]. A high-water content would indicate a non-stressed plant; thus, when those bands or the LSWI are used, the goal is to find a negative correlation with the yield in the spectral bands and a positive correlation in the index [97]. However, the correlation in the spectral bands was positive at MT, with remarkable collinearity with the NIR region and closer to zero in the other growth stages. LSWI exhibited the worst correlation among all the indices. Given those results, SWIR would not be a suitable region to study rice yield variability. The water sheet maintained on the fields could alter all the optical properties; thus, a low number of plants at MT would allow the satellite to measure the field water better, showing low reflectance values. For example, the values would be higher when the canopy is superior and covers the soil surface. The inundated conditions could explain the low correlation between NDVI and LSWI [98]. B08 and B11 were positively correlated, losing the opposite sense of correlation that NDVI exhibits between B08 and B04.

To summarize the collinearity results, visible bands and B05 were highly correlated at the three stages; similarly, the NIR B08 band and B06, B07, and B8A were also highly correlated. Those results showed the dependence between spectral regions (visible, NIR, and SWIR), with the Red edge highly correlated with visible bands or NIR. The improvement given by the Red edge would be negligible, according to our study. This result is controversial with the new studies focused on exploiting the Red edge region, but, as far as our concern, those studies are more focused on other chemical and biological properties rather than the yield [99,100]. When the VIs were used, we observed an essential collinearity between them, and the correlation with the yield was similar or even lower than the bands. The VIs should be interpreted together with their band components, seeking the collinearities with the bands when this collinearity is the basis for interpreting the index [101]. In using the NDVI, the lack of correlation between NIR and the red band would represent a distinct interpretability to the most common use since the fundament is the correlation between a high NIR and low red reflectance value [102]. At PI and GF, the individual use of VIs would hamper the knowing of a low correlation between visible bands and the yield. The NIR region could better inform us about the yield variability, according to the variability of NIR around the Valencia and Seville land rice crop area (Figure S2). The recommendation should be to perform different interpretations for B04 (red reflectance) and B08 (NIR reflectance) variability. The strong influence of chlorophyll in the visible bands, reported in the literature [39], may have caused the low R. The NIR region, influenced by the cell structure, rather than the chlorophyll [30], also showed a different behavior in our results. Therefore, future work is presented to study why the cell structure might better predict yield than chlorophyll content [103].

The new VIs observed a slight improvement in comparison with the NDVI that it would obtain the exact estimation of yield variability using any of the other indices, except LSWI. The vast number of publications about the NDVI and its increasing use by the rice industry prompted us to consider this index as the best-normalized alternative for analyzing yield variability at the commercial level. Based on the correlations for each year and location, the best moment to use a normalized VI would be MT; however, for the use of a band, the best moment would be PI; in any case, at MT, the use of indices did not significantly improve the use of bands. The use of VIs should be adequate if the biophysical basis is previously confirmed. Thus, at MT, the increase in crop greenness and cell structures in a similar way would also result in similar correlations with the yield for spectral bands and VIs [104,105]. However, at PI and GF, the interpretability of VIs would be confusing, and it would not be the best option for studying yield variability.

This study has been focused on detailed research of direct correlations between the yield and spectral bands or VIs. Pearson’s and Spearman’s tests are simple methods that limit the current scope for yield estimations; however, the novel database of commercial yield maps requires first exploring simple statistical outputs. The present work can be useful in continuing the research to develop advanced yield forecasting models. Moreover, PA practices can be directly modified, especially when using VI or spectral bands at different growth stages. The work is considered a first step to ensure data interpretability, providing key information for various research gaps, such as yield estimations, PA practices, and rice physiology.

5. Conclusions

Correlations between the yield and spectral bands were low. When locations and years were compared, it was observed that the limiting factor was the year, as the differences in R values between yield and all spectral bands showed a weak correlation between one year and another but not between different locations. The results of Spearman’s analysis were similar to those of Pearson’s coefficients, with no improvement. The low and non-uniform correlations have complicated the design of an interpretable framework for agronomic decisions using RS data. The influence of growth stages in modifying the spectral response on the canopy and the yield physiology could represent significant limitations to directly identifying yield variability with only RS data. The expected behavior at each spectral region was changeable, affecting correlation values and the theoretical assumptions. The NIR (B08) spectral band was the most reliable for the estimating yield, consistently showing the highest R values at PI. This band is also available at a 10 m spatial resolution, making it particularly valuable for a detailed analysis. Visible spectral bands were inadequate to assess the NIR reflectance influence, and the correlations between both regions were disrupted.

The final recommendation is to consider two periods for using RS data. The first, with only vegetative structures (from MT to PI), is designing strategies to increase NIR reflectance and decrease red reflectance. The second, from PI to harvest, is avoiding the relations between crop greenness and NIR reflectance, i.e., high NIR values would not be observed on low visible reflectance areas, and excessive crop greenness would not result in higher yields. Due to the differences between years, future studies are needed to analyze the mentioned pattern. NIR reflectance was a better variable than VIs, but the single use of this spectral band could be improved using complementary variables.