A Python Framework for Crop Yield Estimation Using Sentinel-2 Satellite Data

Abstract

Remote sensing technologies are essential for monitoring crop development and improving agricultural management. This study investigates the automation of Sentinel-2 satellite data processing to enhance wheat growth monitoring and provide actionable insights for smallholder farmers. The objectives include (i) analyzing vegetation indices across phenological stages to refine crop growth monitoring and (ii) developing a cost-effective user-friendly web application for automated Sentinel-2 data processing. The methodology introduces the “Area Under the Curve” (AUC) of vegetation indices as an independent variable for yield forecasting. Among the indices examined (NDVI, EVI, GNDVI, LAI, and a newly developed RE-PAP), GNDVI and LAI emerged as the most reliable predictors of wheat yield. The findings highlight the importance of the Tillering to the Grain Filling stage in predictive modeling. The developed web application, integrating Python with Google Earth Engine, enables real-time automated crop monitoring, optimizing resource allocation, and supporting precision agriculture. While the approach demonstrates strong predictive capabilities, further research is needed to improve its generalizability. Expanding the dataset across diverse regions and incorporating machine learning and Natural Language Processing (NLP) could enhance automation, usability, and predictive accuracy.

1. Introduction

Satellite data have become an indispensable tool in crop yield monitoring, offering a range of spatial, temporal, and spectral resolutions that enhance the precision and accuracy of agriculture-related assessments. The integration of high-resolution satellite imagery, such as that from Sentinel-2, with artificial intelligence (AI) techniques has significantly advanced crop yield estimation. AI models, including machine learning and deep learning, utilize vegetation indices derived from Sentinel-2 data to predict yields for various crops with high accuracy, although there is a need for standardized methodologies to ensure consistent results across studies [1]. Similarly, the use of satellite-derived gross primary production (GPP) data, combined with dimension reduction techniques and deep learning models, has shown promise in forecasting corn yield and price changes, particularly in regions like Malawi, where predictive capabilities were notably enhanced [2]. The comparison of hyperspectral narrowbands from PRISMA and multispectral broadbands from Sentinel-2 has revealed that these data sources can complement each other in predicting crop biomass and yield, with PRISMA’s narrowbands offering slightly better performance in some cases [3]. Moreover, the fusion of Sentinel-1 and Sentinel-2 data with environmental factors has been effective in constructing dense NDVI time series, crucial for continuous crop monitoring despite challenges like cloudy weather conditions [4]. The combination of PlanetScope and Sentinel-2 imagery with environmental data has also improved wheat yield estimation, demonstrating the benefits of integrating multiple data sources for enhanced accuracy [5]. However, challenges remain, such as the need for more robust methods to ensure the reliability of satellite-derived crop information and the integration of additional biophysical variables to fully explain yield variability [6,7]. Overall, the synergy between satellite data and advanced analytical techniques holds great potential for improving agricultural management and food security, though further research is needed to address existing limitations and optimize methodologies [8,9]. Furthermore, the integration of advanced machine learning techniques with satellite data not only enhances yield predictions, but also facilitates the real-time monitoring of crop health and stress factors. For instance, recent studies have demonstrated that combining Sentinel-1’s radar backscatter data with optical imagery from Sentinel-2 can significantly improve the estimation of crop biomass under varying weather conditions, providing a more resilient approach to agricultural assessments [10]. Additionally, incorporating environmental variables such as soil moisture and temperature into these models has been used to capture the complexities of yield variability caused by climatic fluctuations, ultimately leading to more accurate forecasting methods [11]. As researchers continue to refine these methodologies, there is an opportunity to develop comprehensive frameworks that leverage both remote sensing technologies and on-the-ground data collection, creating a holistic view of agricultural productivity that is essential for addressing food security challenges globally.

Vegetation indices (VIs) play a crucial role in crop monitoring and yield prediction, leveraging remote sensing technologies to provide valuable insights into crop health and productivity. Various studies have demonstrated the effectiveness of different VIs in monitoring diverse crops such as potatoes, wheat, cotton, sugarcane, and corn [12,13,14,15,16,17,18]. For instance, the Normalized Difference Vegetation Index (NDVI) is frequently used across multiple studies for its ability to predict yield and monitor crop growth stages effectively. In potato cultivation, the NDVI, along with the red-edge chlorophyll index and optimized soil-adjusted vegetation index, is particularly useful during the tuber initiation stage for yield prediction and growth monitoring [15]. Similarly, in wheat, NDVI combined with machine learning models like Random Forests has shown promise in predicting yield with high accuracy, especially when used at key growth stages such as jointing and Flowering [19]. For cotton, the integration of VIs with texture features derived from UAV-based RGB images has enhanced yield prediction accuracy, highlighting the potential of combining different data types for improved monitoring [17]. In sugarcane, RGB-based VIs such as GLI and MGRVI, when used with machine learning models, have provided accurate growth predictions, demonstrating the utility of low-cost UAV platforms in crop management [18]. The use of Sentinel-2 data and VIs like GNDVI has been effective in assessing the within-field variability of corn yield, with machine learning techniques further enhancing prediction accuracy [20]. Despite the advantages, challenges remain, such as the need for selecting appropriate VIs and growth stages for specific crops, and the difficulty in differentiating crops with similar spectral signatures [21]. Overall, the integration of VIs with advanced remote sensing technologies and machine learning models offers a robust framework for dynamic crop monitoring and yield estimation, aiding precision agriculture practices across various crop types [15,17,18,19,20,21].

Crop growth models like WOFOST (World Food Studies) [22] are pivotal in simulating crop development and predicting yields, which are essential for precision agriculture and food security. The WOFOST model, a process-based model, simulates the mechanistic processes of crop growth and yield production, and has been enhanced through various integrations and adaptations to improve its accuracy and applicability across different crops and environmental conditions. For instance, the integration of remote sensing data, such as UAV-derived vegetation indices, with the WOFOST model using the ensemble Kalman filter algorithm has significantly improved the accuracy of maize yield predictions, achieving a relative error of less than 5% when assimilating historical meteorological data [23]. Similarly, the coupling of WOFOST with other models, such as the WHEATGROW [24] and FROSTOL [25] models, has enhanced its ability to simulate winter wheat growth under low-temperature stress, improving simulation accuracy by 8.03% in frost years [26]. Sensitivity analyses using methods like EFAST [27] have further refined the model’s parameters, enhancing its adaptability and accuracy in specific regions, such as the Yellow River Irrigation Area in China [28]. Additionally, the integration of deep learning techniques with WOFOST has shown promise in improving yield prediction accuracy at various growth stages, particularly during the reproductive phase of crops like corn [29]. The assimilation of high-resolution remote sensing data, such as Sentinel-2, into WOFOST has also been explored, demonstrating improved yield estimation accuracy at finer spatial resolutions [30,31]. Moreover, the development of the WOFOST-N model, which incorporates nitrogen dynamics, has expanded the model’s applicability to fruit trees, such as the Korla Fragrant pear, by accurately simulating growth and nitrogen use efficiency [32]. Despite these advancements, challenges remain, such as accurately simulating agricultural stresses like lodging, which can affect yield estimates [31]. Overall, the continuous development and integration of WOFOST with other models and technologies underscore its critical role in advancing crop yield prediction and supporting agricultural decision making [33,34,35]. While these models offer high accuracy, they often require detailed field data, extensive parameter calibration, and computational resources, limiting their accessibility for smallholder farmers.

Developing a web application for the automated processing of Sentinel-2 data to facilitate systematic crop monitoring and to provide support to smallholder farmers necessitates the integration of advanced technologies and methodologies, as outlined in the referenced studies. The integration of machine learning and artificial intelligence can significantly enhance the ability of smallholder farmers to manage crops by providing expert advice and automatic disease detection, achieving high accuracy in identifying plant diseases and recommending fertilizers [36].

The use of Sentinel-2 data facilitates the precise mapping of cropping systems over multiple years, which is essential for understanding the spatial and temporal distribution of crops in smallholder regions [37]. This workflow, implemented on Google Earth Engine, effectively classifies complex cropping patterns and provides valuable insights into crop type changes. A cloud-based GIS system leveraging Sentinel-2 data to visualize crop type maps and calculate vegetation indices, offering a scalable solution for agricultural monitoring, has been developed [38]. The ADDPro pipeline further enhances efficiency by automating satellite data downloading and processing on AWS, delivering near-real-time vegetation health information while reducing data transfer costs through efficient compression techniques [39]. Open-source remote sensing tools present a cost-effective decision support system for precision agriculture, particularly benefiting resource-constrained settings [40]. Automated workflows for processing high-resolution satellite images have proven invaluable for tracking crop development and storing critical spectro-temporal data for smallholder agriculture [41].

The “Sentinel-2 for Agriculture” project advances global agricultural monitoring by developing open-source systems to generate relevant agricultural products, thereby enhancing market transparency and improving food production data [42]. Additionally, integrating multiscale and multitemporal systems, and combining satellite and UAV data, enables improved plant management and fosters better environmental health [43]. Finally, creating a real-time cropland mask using Sentinel-2 data is crucial for timely agricultural monitoring across diverse agro-ecological contexts, ensuring responsive and effective decision making [44].

Collectively, these studies highlight the potential of a web application powered by Sentinel-2 data and advanced processing techniques to deliver actionable insights to smallholder farmers and experts involved in the field, improving crop monitoring and promoting sustainable agricultural practices.

This study proposes an alternative methodology that automates Sentinel-2 data processing for crop monitoring through a cost-effective user-friendly web application. Unlike traditional crop growth models, this approach focuses on real-time vegetation index analysis and predictive insights tailored to smallholder farmers. By leveraging open-source tools such as Python and Google Earth Engine in order to eliminate the need for proprietary software and complex data preprocessing, it makes advanced crop monitoring more accessible and scalable.

The aim of this research was to investigate the potential for automating the processing of Sentinel-2 satellite data to enhance crop growth monitoring and provide valuable agricultural insights for smallholder farmers. The specific objectives and final outputs of the study include the following:

• Analyzing vegetation indices across different phenological stages to generate more detailed and actionable crop growth monitoring insights.
• Developing a cost-effective user-centric web application for automated Sentinel-2 data processing designed to support agronomists, farmers, and other agricultural professionals by enabling systematic crop growth monitoring.

2. Materials and Methods

2.1. Operational Crop Fields Under Investigation

The operational crop fields under investigation are situated on the outskirts of the town of Ptolemaida, approximately 100 km west of Thessaloniki, within the Western Macedonia regional unit of Greece, Figure 1.

The present research focuses on nine operational wheat crop fields, Figure 2, five (5) of these fields (marked in red) were sown with durum wheat (Triticum durum) and are located to the north and south of the town of Ptolemaida, while the remaining four (4) fields (marked in yellow) were sown with soft wheat (Triticum aestivum) and are situated to the west and south of Ptolemaida.

Since this research was conducted in operational fields rather than controlled experimental conditions, key information such as crop installation dates and farmer interventions was obtained through farmer interview and ancillary data sources. However, the interviewed farmer did not maintain a detailed farm calendar. Additional data, including publicly available soil maps and meteorological records, were used to complement the information. The available information is summarized as follows:

• Crop installation: The installation of crops across different fields took place over a period of 3 to 9 days.
• Wheat cultivars:

  ○

  Durum wheat: Svevo

  ○

  Soft wheat: Giorgione

• Farmer interventions: Agronomic practices related to fertilization, weed control, and disease management were consistent across all fields under investigation. Specifically, this includes the following:
• Fertilization:

  ○

  Base fertilization: A winter application of fertilizer (N = 20, P = 23, K = 0) at a rate of 25 kg per stremma (1000 m²) in December.

  ○

  Spring fertilization: Two separate applications (N = 40, P = 0, K = 0) in early March and early April, with 15 kg per stremma (1000 m²) per application.

• Weed control: Application of Avoxa Maxx 12/2.88 OD (Syngenta) herbicide between 15 April and 20 April.
• Fungal disease prevention: Application of Amistar Gold 12.5/12.5 SC (Syngenta) fungicide in early May.

Weather data, including temperature and precipitation during the growing season, were obtained from a nearby meteorological station located approximately 5 km from the study fields. The station, Ardassa (Coordinates: Latitude: 40.50 N, Longtitude: 21.60 E, Elevation: 625 m, CRS: WGS84; EPSG: 4326), is operated by the National Observatory of Athens/Institute of Environmental Research and Sustainable Development and the data are public available (https://www.meteo.gr/, accessed on 24 February 2025).

Table 1. Monthly weather conditions during the growing season.

Month	Mean Maximum Temperature (°C)	Mean Minimum Temperature (°C)	Mean Temperature (°C)	Total Precipitation (mm)
December 2023	11.7	−0.9	3.6	72.8
January 2024	8.8	−0.8	3.6	36.0
February 2024	13.8	2.4	7.6	25.4
March 2024	15.8	3.5	9.3	45.2
April 2024	21.7	6.7	14.3	38.6
May 2024	22.4	10.9	16.4	27.4
June 2024	32.4	16.1	24.4	12.4

presents the monthly average temperatures (mean, maximum, and minimum) and total precipitation recorded during the study period.

Since specific soil data were not available from the farmer for each field, soil characteristics were derived from a publicly available soil map (https://iris.gov.gr/SoilServices/, accessed on 24 February 2025).

Table 2. Soil characteristics for each field under investigation.

Field ID	Soil Texture			Soil Type	Parent Material	Hydromorphy
	Depth 0–25 cm	Depth 25–75 cm	Depth 75–150 cm
Soft Wheat
FID 1 and FID 2	Moderately Fine	Medium to Moderately Fine	Moderately Fine to Fine	Luvisols	Alluvial Terraces	Well-Drained Soils
FID 3 and FID 4	Fine	Moderately Fine to Fine	Moderately Fine to Fine	Vertisols	Alluvial Deposits	Well-Drained Soils
Durum Wheat
FID 1, FID 2, FID 3, and FID 4	Fine	Moderately Fine to Fine	Moderately Fine to Fine	Vertisols	Alluvial Deposits	Well-Drained Soils
FID 6	Moderately Fine	Coarse	Moderately Fine to Fine	Cambisols	Alluvial Terraces	Well-Drained Soils

summarizes the soil properties for the investigated fields.

2.2. Satellite Data

The publicly accessible Sentinel-2 MSI (Multispectral Imager) Surface Reflectance (SR), previously denoted as Bottom of Atmosphere (BOA) reflectance, datasets were selected for this investigation owing to their superior spatial resolution, regular temporal coverage, and convenient accessibility. The atmospheric bands, which encompass Coastal Aerosol, Water Vapor, and SWIR-Cirrus, were omitted from the analysis and are consequently not represented in

Table 3. Sentinel-2 MSI bands.

Sentinel-2 Bands	Spectral Region	Central Wavelength (μm)	Resolution (m)
Band 2	Blue	0.490	10
Band 3	Green	0.560	10
Band 4	Red	0.665	10
Band 5	Red Edge 1	0.705	20
Band 6	Red Edge 2	0.740	20
Band 7	Red Edge 3	0.783	20
Band 8	NIR	0.842	10
Band 8A	Vegetation Red Edge	0.865	20
Band 11	SWIR 1	1.610	20
Band 12	SWIR 2	2.190	20

. All datasets were procured at no financial cost from the Copernicus Dataspace (formerly known as the Copernicus Open Access Hub) [45].

The acquisition dates of the images used in this study are presented in

Table 4. Wheat phenological stages and the corresponding imagery acquisition date.

Phenological Stage	Days per Stage	BBCH Scale	Imagery Acquisition Date
Emergence	7–14 days	BBCH 10–19	13 January 2024
Tillering	25–40 days	BBCH 20–29	26 January 2024
			15 February 2024
			17 February 2024
			22 February 2024
Stem Elongation	20–30 days	BBCH 30–39	3 March 2024
			21 March 2024
Booting	20–30 days	BBCH 40–49	28 March 2024
Heading	7–14 days	BBCH 51–59	15 April 2024
Flowering	5–10 days	BBCH 61–69	7 May 2024
Grain Filling	10–20 days	BBCH 71–77	22 May 2024
			27 May 2024
Maturity and Harvest	10–20 days	BBCH 83–99	9 June 2024
Post Harvest			24 June 2024

, along with the corresponding phenological stages. The phenological stages are defined based on the BBCH (Biologische Bundesanstalt, Bundessortenamt und Chemische Industrie) scale. This scale categorizes the plant’s developmental cycle into 10 distinct principal stages [46].

2.3. Yield Data

Since this research was conducted on operational crop fields, actual yield data for each wheat field were provided by the farmer. The data were collected using yield mapping equipment, specifically, the FarmTRX™ system mounted on combine machinery. The data were presented in vector point format (ESRI shapefile) and underwent pre-processing to remove any inaccurate or erroneous value entries, including extreme high and low yield values.

The growing season for this dataset extends from December 2023 to June 2024. Descriptive statistics for each wheat field are summarized in

Table 5. Descriptive statistics of the measured yield production per operational field and crop.

Field ID	Mean (Kg/stremma *)	Standard Deviation	Minimum (Kg/stremma *)	Maximum (Kg/stremma *)	Range (Kg/stremma *)
Soft Wheat
FID 1	373.54	127.00	100.28	737.88	637.60
FID 2	598.44	94.25	351.06	841.57	490.51
FID 3	635.82	86.61	350.37	898.26	547.89
FID 4	605.32	115.08	150.12	649.91	499.79
Durum Wheat
FID 1	425.59	105.98	150.12	649.91	499.79
FID 2	290.09	73.16	119.88	534.89	415.01
FID 3	258.73	82.42	61.04	542.13	481.09
FID 4	367.79	86.24	200.47	645.8	445.33
FID 6	339.34	63.99	200.6	561.36	360.76

* 1 stremma = 1000 m².

, while the spatial distribution, and interpolated yield value derived from the Inverse Distance Weighted method (IDW), of yield in each wheat crop field is illustrated in Figure 3.

2.4. Software

This study exclusively employed noncommercial and open-source software and programming frameworks. ESA SNAP software (version 10.0.0) [47] was utilized for Sentinel-2 MSI data preprocessing, while Quantum GIS (version 3.34.5) [48] facilitated the manipulation of vector data, including yield data.

To enhance workflow efficiency and automation, Python (version 3.11.1) [49] was employed within a Jupyter Notebook (version 7.0.6) environment [50] for data analysis, including regression analysis.

The development of the web application utilized Google Earth Engine (GEE) [51] for data access and analysis, implemented using the Streamlit (version 1.24.0) [52] open-source application framework.

2.5. Methods

2.5.1. Satellite Data Pre-Processing

To ensure a consistent spatial resolution of 10 m across all bands, spatial resampling of the satellite data was performed using the S2 Resampling Processor tool in the open-source ESA SNAP software. Subsequently, cloud masking was applied to each image using the ‘Land/Sea Mask’ tool by selecting the ‘Use Vector as Mask’ option and incorporating the ‘Opaque_clouds’ and ‘Cirrus_clouds’ masks provided by ESA. Finally, a subset of each dataset was created for the study area, ensuring that the area of interest, including the fields, remained free of cloud cover.

2.5.2. Satellite Data Processing

All vegetation indices (NDVI, GNDVI, EVI, LAI, RE-PAP) used in this study were calculated in the ESA SNAP software using the ‘Band Maths’ tool. Following the computation and extraction of the new data via the ‘Bands Extractor’ processor, the results were imported into QGIS. In QGIS, the mean index values for each date were extracted at the field level for each field using the Zonal Statistics tool.

2.5.3. Yield Estimation

Yield estimation was conducted using regression analysis to assess the relationship between the ‘Area Under the Curve’ (AUC) of vegetation index plots (mean index value) and the corresponding mean yield values across all fields. The AUC was calculated over the entire growing season as well as within a specific time period (3 March 2024 to 27 May 2024), corresponding to key phenological stages from Tillering to Stem Elongation and continuing through Grain Filling. The AUC, ${\int }_{t_1}^{t_2}f\left(t\right)\cdot dt$, was computed using the trapezoidal rule, implemented in Python. The analysis was conducted independently for durum and soft wheat crop fields.

For this study, five (5) distinct vegetation indices were examined, as summarized in

Table 6. Sentinel-2 vegetation indices under investigation.

Index	Formula
NDVI	${\displaystyle \frac{NIR-RED}{NIR+RED}}$	(1)
GNDVI	${\displaystyle \frac{NIR-GREEN}{NIR+GREEN}}$	(2)
EVI	$2.5{\displaystyle \frac{NIR-RED}{\left(NIR+6RED-7.5BLUE\right)+1}}$	(3)
LAI	$3.618\ast EVI-0.118$	(4)
RE-PAP	${\displaystyle \frac{Vegetation RE3\left(B7\right)-Vegetation RE1\left(B5\right)}{Vegetation RE2\left(B6\right)}}\ast {\displaystyle \frac{NIR \left(B8\right)}{RED\left(B4\right)}}$	(5)

. These include the Normalized Difference Vegetation Index (NDVI) [53], Green Normalized Difference Vegetation Index (GNDVI) [54], Enhanced Vegetation Index (EVI) [55], and the Leaf Area Index (LAI) [56], which was derived from EVI [57]. Additionally, a novel vegetation index, RE-PAP, was developed utilizing the Red Edge (RE) bands of Sentinel-2. This new index is based on findings from the literature that highlight the value of the RE region in improving the performance of vegetation indices (VIs) [58]. The RE region is particularly effective in capturing variations in chlorophyll content. Healthy plants, which have higher chlorophyll levels, exhibit a red-edge shift toward longer wavelengths. Conversely, unhealthy plants with lower chlorophyll content display a red-edge shift toward shorter wavelengths [59]. The formulation of this index is grounded in the following rationale. The subtraction term (RE3 − RE1) effectively captures the physiological state of vegetation by isolating red-edge shifts, which serve as key indicators of chlorophyll content. The division by RE2 (B6) accounts for variations in light penetration and scattering influenced by the canopy structure, thereby functioning as a reference band to normalize reflectance variations and ensure that the index output accurately reflects structural and physiological changes in vegetation. Finally, the multiplication by the ratio (NIR/RED) enhances the sensitivity of the index to vegetation vigor by leveraging the pronounced contrast between the high near-infrared (NIR) reflectance and low red reflectance observed in healthy plants.

2.5.4. Web Application Development

The web application was implemented using the Python programming language (version 3.11.1) along with Python libraries (geemap, folium, fastkml, shapely, jsonlib, os-sys, pandas, numpy, plotly, Python-IO, tempfile, zipfile, osgeo) in combination with Google Earth Engine. To further enhance user interaction and accessibility, the Streamlit framework (version 1.24.0) was exploited. The graphical user interface (GUI) was designed to be user-friendly and accessible to users with limited expertise in remote sensing. The interface adopts a two-panel layout: the left panel allows users to select and configure task parameters, while the right panel displays the results of these tasks in an interactive map format, complemented by relevant informational notifications, Figure 4. This design emphasizes usability and fosters efficient intuitive interaction with the application.

Table 7. Configuration and parameterization of tasks within the application.

Configure Task Parameters	Type
Search available Sentinel 2 imagery
Start date/end date	Date picker
Cloud cover	Slider
Shadow Threshold	Slider—optional
Apply cloud mask	Check box—optional
Dates upload	Upload txt file with desired dates for acquisition—optional
Upload Region of Interest (ROI)	Upload GeoJSON or KML file
Calculate vegetation index
Select the available images	List box
Select index to calculate	Drop—down list
Display image	Button—optional
Generate histogram	Button—optional
Export images	Button—optional
Index statistics per parcel
Upload parcels	Upload GeoJSON or KML file
Calculate mean index value for each parcel	Button
Download values to CSV	Button—optional
Plot results	Button—optional
Dates subset for AUC calculation
Subset start date/end date	Drop—down list/optional
Plot subset results	Button—optional
Yield prediction
Yield prediction	Button
Download yield prediction results to CSV	Button—optional
Update parcel information (on the app)	Button—optional
Download updated parcels to GeoJSON or KML	Button—optional
Shadow/Cloud mask check
Show shadow mask layer	Check box—optional
Plot histogram (Original/Masked)	Button—optional
Download metadata to TXT	Button—optional

provides a summary of the parameterization of the available tasks as presented in the left panel of the graphical user interface (GUI).

Appendix A presents a comprehensive summary of the application components, including the corresponding Streamlit functions, in the form of Streamlit pseudo-code.

3. Results

3.1. Yield Estimation

In this study, we investigated the relationship between the Area Under the Curve (AUC) of mean values of Vis (NDVI; GNDVI; EVI; LAI; and RE-PAP) during the growing season as well as within a specific time period (3 March 2024 to 27 May 2024), corresponding to key phenological stages from Tillering to Stem Elongation and continuing through Grain Filling, and the measured yield at the field scale. AUC values were computed using the trapezoidal rule, complemented by regression analysis conducted within a Python environment. The predicted yield (Ypred) is expressed in Kg/stremma, where stremma is an area measurement unit corresponding to 1000 square meters, which is officially used in Greece.

The results are presented in the following tables:

Table 8. Regression analysis results: durum wheat.

Vegetation Index	Time Period	Reg. Equation	R2	MAPE (%)	RMSE
EVI	Growing season	Ypred = 59.852 × AUC	0.97	16.8	59.36
EVI	Subset of growing season (from Tillering to Stem Elongation through Grain Filling)	Ypred = 85.849 × AUC	0.98	15.7	54.26
GNDVI	Growing season	Ypred = 127.889 × AUC	0.98	13.4	50.85
GNDVI	Subset of growing season (from Tillering to Stem Elongation through Grain Filling)	Ypred = 243.181 × AUC	0.99	11.9	41.35
LAI	Growing season	Ypred = 17.876 × AUC	0.97	16.9	60.03
LAI	Subset of growing season (from Tillering to Stem Elongation through Grain Filling)	Ypred = 24.962 × AUC	0.97	15.7	54.61
NDVI	Growing season	Ypred = 60.643 × AUC	0.98	14.5	53.28
NDVI	Subset of growing season (from Tillering to Stem Elongation through Grain Filling)	Ypred = 91.409 × AUC	0.98	13.5	47.46
RE-PAP	Growing season	Ypred = 10.105 × AUC	0.97	15.1	59.78
RE-PAP	Subset of growing season (from Tillering to Stem Elongation through Grain Filling)	Ypred = 12.798 × AUC	0.97	13.4	59.34

for durum wheat and

Table 9. Regression analysis results: soft wheat.

Vegetation Index	Time Period	Reg. Equation	R2	MAPE (%)	RMSE
EVI	Growing season	Ypred = 105.827 × AUC	0.98	14.3	79.91
EVI	Subset of growing season (from Tillering to Stem Elongation through Grain Filling)	Ypred = 160.186 × AUC	0.99	10.8	61.54
GNDVI	Growing season	Ypred = 116.035 × AUC	0.97	18.8	102.22
GNDVI	Subset of growing season (from Tillering to Stem Elongation through Grain Filling)	Ypred = 169.039 × AUC	0.98	14.7	81.17
LAI	Growing season	Ypred = 31.814 × AUC	0.98	13.9	77.83
LAI	Subset of growing season (from Tillering to Stem Elongation through Grain Filling)	Ypred = 46.913 × AUC	0.99	10.3	59.13
NDVI	Growing season	Ypred = 98.754 × AUC	0.98	14.3	79.24
NDVI	Subset of growing season (from Tillering to Stem Elongation through Grain Filling)	Ypred = 154.527 × AUC	0.99	10.9	62.16
RE-PAP	Growing season	Ypred = 17.233 × AUC	0.98	11.1	78.51
RE-PAP	Subset of growing season (from Tillering to Stem Elongation through Grain Filling)	Ypred = 21.972 × AUC	0.98	11.8	86.21

for soft wheat. The regression plots are illustrated in the subsequent figures, Figure 5 and Figure 6, corresponding to durum wheat and soft wheat, respectively.

The regression analysis conducted for both durum and soft wheat yields demonstrates exceptionally high Coefficient of Determination (R²) values, indicative of a strong linear relationship between yield and the AUC of vegetation indices. However, these high R² values may partly reflect overfitting, which can be attributed to several factors. Firstly, the relatively small dataset examined in this study may limit the generalizability of the results and amplify the appearance of a strong fit. Secondly, the characteristics of the data itself, including the variability and distribution of the AUC values, most likely contribute to the observed trends. Lastly, the use of a zero-intercept model was deliberately chosen due to its physical relevance as a scenario where AUC = 0 logically corresponds to yield = 0. This approach ensures that the regression equation is rooted in agronomic reality.

By modeling yield as a function of AUC rather than directly using vegetation index values, this study aims to establish a predictive framework grounded in an independent variable with clear temporal and physiological significance. While the results highlight the potential of the models, further validation with larger datasets and additional variables is necessary to confirm their predictive reliability and broader applicability.

For durum wheat, the Root Mean Square Error (RMSE) ranges from 40 to 60 kg per stremma (1 stremma = 1000 m²), with the best performance observed for the GNDVI during the subset of the growing season (Tillering to Stem Elongation through Grain Filling), achieving a Mean Absolute Percentage Error (MAPE) of 11.9% and an RMSE of 41.35. The second-best performance was recorded for the NDVI during the subset period, followed by the GNDVI for the entire growing season. These findings emphasize the strong predictive capacity of GNDVI, particularly when focused on critical phenological stages, and the reliability of NDVI during the same subset period for yield estimation.

In the case of soft wheat, the Root Mean Square Error (RMSE) spans from 59 to 102 kg per stremma (kg per 1000 m²). The most accurate predictions were achieved using the LAI during the subset of the growing season (Tillering to Stem Elongation through Grain Filling), which yielded a Mean Absolute Percentage Error (MAPE) of 10.3% and an RMSE of 59.13. The EVI during the same subset period ranked as the second-best predictor, reflecting its close relationship with LAI, as the latter is derived from EVI. Following this, the NDVI for the subset period also demonstrated strong predictive performance. These results highlight the robustness of LAI and related indices when focused on critical growth stages for soft wheat yield estimation.

Across both wheat types, models based on the subset of the growing season consistently outperform those utilizing the full growing season in terms of predictive accuracy. This underscores the significance of focusing on critical phenological stages, where crop growth and yield formation are most responsive to environmental and management factors. Furthermore, the models for durum wheat demonstrate relatively lower prediction errors, indicating a more consistent and robust relationship between AUC values and yield. These findings highlight the potential for subset period models to enhance yield prediction accuracy while emphasizing the distinct physiological and agronomic characteristics influencing each wheat type.

By examining the best-performing index, GNDVI (durum wheat), in relation to phenological stages, as illustrated in Figure 7, it becomes evident that fields with larger yields, such as Field 1 (425.59 kg/stremma) and Field 4 (367.79 kg/stremma), when compared to lower-yielding fields such as Field 2 (290 kg/stremma) and Field 3 (258.73 kg/stremma), exhibit greater GNDVI values during the Stem Elongation to Booting stages. This finding suggests that these phenological stages are particularly critical for yield prediction. Moreover, Field 1 shows notably higher GNDVI values during the Booting and Heading stages than Field 4, which may highlight the additional, albeit less pronounced, importance of these stages in supporting yield potential. Field 6, with a yield of 339.34 kg/stremma, performs slightly better than Fields 2 and 3. This advantage persists despite Field 6 having lower GNDVI values during the Stem Elongation to Booting stages. The increased GNDVI values observed in Field 6 from the end of Booting to Flowering likely contribute to its performance, as Fields 2 and 3 display a slight decline in GNDVI during the same period, particularly at the Heading stage. This trend underscores the potential impact of later phenological stages on yield outcomes when earlier growth stages are less optimal.

The evaluation of the best-performing index, LAI (soft wheat), in relation to phenological stages, as depicted in Figure 8, reveals that fields with higher yields, such as Field 3 (636 kg/stremma), Field 4 (605 kg/stremma), and Field 2 (598 kg/stremma), tend to maintain elevated LAI values during the critical period spanning from Stem Elongation to Flowering. In contrast, the lower-yielding Field 1 (374 kg/stremma) shows comparatively reduced LAI values during these stages, highlighting their central role in influencing productivity. Additionally, variations in yield among the top-performing fields appear to be influenced by the LAI dynamics from Booting to Grain Filling, indicating that maintaining robust LAI values during these growth phases is crucial for maximizing yield potential.

3.2. Functional Overview and User Interaction Design for Web Application Development

The web application features a carefully designed graphical user interface (GUI) that prioritizes accessibility and efficient navigation. The interface is systematically divided into two primary sections: the left panel facilitates task selection and configuration, while the right panel presents the outcomes of executed tasks through an interactive map, complemented by contextual informational notifications. This structured layout is intentionally developed to enhance usability and support effective user interaction, ensuring a coherent and productive experience.

The application comprises four (4) primary functionalities:

• Search Sentilel-2 images: As shown in Figure 9, users can search for satellite imagery (Sentinel-2 L2A, Surface Reflectance) based on specific parameters, including area of interest (AOI; this can be uploaded in either GeoJSON or KML format), cloud cover percentage, and date ranges. Additionally, users have the option to upload their dates of interest in a text format, with dates separated by commas. Moreover, users can optionally apply a cloud mask and a shadow threshold to remove cloud-covered areas and pixels affected by cloud shadows.

2.

Vegetation index calculator: This feature enables users to select and compute various spectral indices from the chosen Sentinel-2 images, Figure 10. The resulting vegetation index maps are displayed interactively and can be exported. Additionally, users can generate and visualize histograms of the computed indices.

3.

VIs statistics calculator: This feature allows users to upload their fields and calculate statistics for previously computed vegetation indices for their areas of interest, Figure 11 and Figure 12. Users can also specify a time period to subset the VI statistics and generate corresponding plots.

4.

Yield prediction: This feature leverages the selected vegetation index to predict crop yield for the entire growing season or a specified subset of the season, Figure 13. Additionally, it offers the option to update the fields with the generated yield predictions, Figure 14.

4. Discussion

4.1. Yield Estimation

Since the 1970s, the employment of satellite remote sensing has been crucial in the assessment of key agricultural crops by scrutinizing agro-climatic conditions, crop health, and yield predictions, with certain systems also evaluating food security to deliver early warnings of possible food deficits. The integration of free access to medium to high-resolution satellite data with cloud-computing platforms like Amazon, Google Earth Engine, and Microsoft AI for Earth has significantly enhanced crop monitoring capabilities by overcoming previous constraints related to data processing and information extraction [6].

Pre-harvest yield estimation insights provide farmers and experts involved in farming with essential information to guide critical decisions, such as determining the ideal quantity of fertilizers to apply [60]. The predictive efficacy of various vegetation indices (VIs) in relation to wheat yield exhibits considerable variability across research investigations, with each index presenting distinct benefits contingent upon the specific context and methodological approach utilized. The Normalized Difference Vegetation Index (NDVI) is frequently used due to its simplicity and suitability for predicting winter wheat yield, particularly when combined with meteorological data [61]. Other indices such as the Modified Soil-Adjusted Vegetation Index (MSAVI) and the Green Normalized Difference Vegetation Index (GNDVI) have illustrated improved correlation coefficients with real yield metrics, especially during critical growth periods including Flowering [62]. The Enhanced Vegetation Index (EVI) has been competently used together with machine learning methodologies, including Random Forest (RF), to estimate winter wheat yields, demonstrating a strong relation with yield estimation (an R² of 0.81 and an RMSE of 1250 kg/ha) and providing substantial insights for winter wheat yield forecasting, especially when data from various growth intervals are factored in [63].

For durum wheat, GNDVI outperformed all other tested indices, consistent with findings from previous studies [64]. Furthermore, GNDVI also demonstrated superior predictive capabilities over NDVI, which ranked as the second most effective predictor [65]. For soft wheat, LAI, derived from EVI, demonstrates superior performance over all other examined indices. However, its predictive capability shows only a marginal difference when compared to NDVI, as corroborated by findings in previous studies [66].

4.2. Web Application Development

The developed web application represents a significant advancement in wheat growth monitoring by utilizing Sentinel-2 satellite data to deliver actionable agricultural insights. This advancement holds significant implications for smallholder agricultural producers, agronomists, and professionals in the agricultural sector who encounter both financial limitations and technical challenges. By integrating open-source frameworks and leveraging freely available Sentinel-2 data, the application offers an accessible and cost-effective solution that addresses the economic barriers often associated with traditional crop monitoring systems. This affordability is complemented by the automation of data processing workflows, which provide real-time insights into wheat growth across phenological stages. These capabilities empower users to make informed decisions regarding resource allocation, such as optimizing fertilizer application and irrigation schedules, thereby enhancing productivity and promoting sustainable agricultural practices.

The application’s scalability and flexibility further extend its utility across diverse agricultural contexts. Users can customize their analyses by selecting vegetation indices, adjusting parameters, and focusing on specific growth stages, enabling the tool to accommodate both small-scale and large-scale farming operations. The intuitive graphical user interface facilitates accessibility for individuals possessing diverse degrees of technical proficiency, thereby effectively connecting sophisticated geospatial technologies with their pragmatic applications in the field. Through these features, the web application fosters a more inclusive approach to precision agriculture, providing a robust framework for systematic crop monitoring.

4.3. Future Work

Future research should include repeated analyses in subsequent cultivation periods to further validate the findings of this study, as well as an expansion of the study to incorporate a larger number of fields for the cross-validation of results. Additionally, evaluating the model’s applicability across different geographical regions with varying soil properties and climatic conditions is essential to assess its sensitivity to these factors. Another important direction for future research is extending the analysis to include other crops, such as maize and sunflowers, to evaluate the model’s adaptability and predictive capabilities.

Since the application is designed to assist small-scale farmers and agronomists with limited knowledge of geospatial technology, future work could focus on further automation. This includes estimating phenological stages based on sowing dates provided by farmers combined with historical climate data—such as regional climatic zones—to determine the necessary imagery for each stage. These advancements will enhance the application’s ability to deliver more precise and actionable insights to farmers. Additionally, integrating Natural Language Processing (NLP) [67] into the web application will further enhance usability. By leveraging NLP, the system will minimize the time and effort required for farmers to interact with the application, allowing for intuitive communication with minimal input—such as sowing dates—while improving accessibility and ease of use. Moreover, the application possesses significant potential for future advancements beyond its existing functionalities, especially in the realm of incorporating artificial intelligence (AI) to augment the analysis of geospatial data. The use of innovative machine intelligence frameworks, featuring both machine learning and deep learning approaches, offers a remarkable opportunity to enrich the functionality of systems in exploring massive datasets, uncovering essential correlations and crafting accurate prediction models. For example, incorporating AI-driven methods for disease detection, pest management, and multi-crop monitoring would further enhance its utility and relevance. Such technological advancements would facilitate the application’s capacity to tackle a wider array of challenges inherent in precision agriculture, thereby augmenting global initiatives directed towards the enhancement of food security and the promotion of environmental sustainability.

4.4. Limitations

A significant limitation of this study is the availability of data for every phenological stage. Adverse meteorological conditions in a given region may hinder the acquisition of satellite imagery during one or more phenological stages. This issue can be partially mitigated by utilizing alternative satellite imagery sources (e.g., Landsat), which offer different revisit times. However, the limitation persists, as unfavorable weather conditions may still prevent the capture of high-quality data over the study area.

Another limitation concerns the spatial resolution of freely available satellite data. In the case of very small fields, the presence of mixed pixels—where a single pixel encompasses multiple land cover types—may reduce model accuracy.

Lastly, a critical limitation is the presence of weeds, as they can significantly alter vegetation index values, leading to results that do not accurately reflect true crop growth. Consequently, this may result in false predictions, as the AUC values will be artificially inflated.

5. Conclusions

In this study, the monitoring of wheat crops, including both durum and soft wheat, was conducted throughout the growing season to investigate the relationship between yield and the independent variable “Area Under the Curve” (AUC) of vegetation indices. This research demonstrates the effectiveness of specific vegetation indices (VIs) in estimating wheat yield, with GNDVI emerging as the most reliable predictor for durum wheat and LAI for soft wheat. Phenological stages are widely recognized for their pivotal role in determining crop productivity, and the integration of AUC offers a robust method for correlating yield with dynamic changes observed across these stages. The findings of this study highlight the significance of specific phenological stages for yield prediction. The results indicate that the time period spanning from Tillering to Stem Elongation and extending through Grain Filling plays a pivotal role in wheat crop yield monitoring. This observation aligns with the existing literature reinforcing the critical importance of these growth stages in determining crop productivity. The results of this investigation emphasize the resilience of the suggested methodology; however, additional inquiry is essential to enhance its relevance. The expansion of the dataset to incorporate a larger array of wheat cultivation areas, additional growth periods, and diverse geographic regions will substantially enhance the external validity and rigor of the results. Such efforts will provide deeper insights into the spatial and temporal dynamics of wheat crop yield prediction, paving the way for more comprehensive monitoring and management strategies in varied agricultural contexts. While the proposed framework shows strong predictive capabilities, certain limitations exist, including the impact of adverse weather conditions on data availability, spatial resolution constraints, and potential interference from weeds. Additionally, the web application exemplifies a robust and user-centered methodology for agricultural monitoring, providing real-time actionable intelligence while maintaining cost-efficiency and accessibility. Its capacity to facilitate data-informed decision making accentuates its significance in endorsing sustainable practices and enhancing agricultural productivity. The integration of artificial intelligence for geospatial data analysis signifies a promising pathway for augmenting the application’s functionalities, thereby laying the groundwork for more comprehensive and intelligent solutions within the realm of precision agriculture.